Author: "Systèmes Désordonnés et Applications" - Searchworks@Jio Institute Digital Library Search Results

Your search keyword '"Systèmes Désordonnés et Applications"' showing total 96 results

Start Over Author "Systèmes Désordonnés et Applications"

96 results on '"Systèmes Désordonnés et Applications"'

1. Bootstrapping traceless symmetric $O(N)$ scalars

Author: Reehorst, Marten, Refinetti, Maria, Vichi, Alessandro, Institut des Hautes Etudes Scientifiques (IHES), IHES, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), and HEP, INSPIRE
Subjects: High Energy Physics - Theory, family, [PHYS.PHYS.PHYS-GEN-PH] Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], FOS: Physical sciences, General Physics and Astronomy, [PHYS.HLAT] Physics [physics]/High Energy Physics - Lattice [hep-lat], singlet: scalar, Condensed Matter - Strongly Correlated Electrons, effective field theory, High Energy Physics - Lattice, correlation function, bootstrap, Condensed Matter - Statistical Mechanics, lattice, kink, Statistical Mechanics (cond-mat.stat-mech), Strongly Correlated Electrons (cond-mat.str-el), [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th], [PHYS.HLAT]Physics [physics]/High Energy Physics - Lattice [hep-lat], High Energy Physics - Lattice (hep-lat), operator: dimension, critical phenomena, O(N), [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], High Energy Physics - Theory (hep-th), fixed point, [PHYS.HTHE] Physics [physics]/High Energy Physics - Theory [hep-th]
Abstract: We use numerical bootstrap techniques to study correlation functions of traceless symmetric tensors of $O(N)$ with two indexes $t_{ij}$. We obtain upper bounds on operator dimensions for all the relevant representations and several values of $N$. We discover several families of kinks, which do not correspond to any known model and we discuss possible candidates. We then specialize to the case $N=4$, which has been conjectured to describe a phase transition in the antiferromagnetic real projective model ARP$^{3}$. Lattice simulations provide strong evidence for the existence of a second order phase transition, while an effective field theory approach does not predict any fixed point. We identify a set of assumptions that constrain operator dimensions to a closed region overlapping with the lattice prediction. The region is still present after pushing the numerics in the single correlator case or when considering a mixed system involving $t$ and the lowest dimension scalar singlet., 49 pages, 27 figures Fixed minor typos. Added a subsection on "External operator as the lowest dimensional operator of its kind". Included bounds using this additional assumption in figures 8a and 8b
Published: 2023

2. Cosmology with cosmic web environments II. Redshift-space auto and cross power spectra

Author: Bonnaire, Tony, Kuruvilla, Joseph, Aghanim, Nabila, Decelle, Aurélien, HEP, INSPIRE, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Institut d'astrophysique spatiale (IAS), Institut national des sciences de l'Univers (INSU - CNRS)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-Centre National d’Études Spatiales [Paris] (CNES), Université Paris-Saclay, ANR-19-P3IA-0001,PRAIRIE,PaRis Artificial Intelligence Research InstitutE(2019), and European Project: 695561,ByoPiC
Subjects: Cosmology and Nongalactic Astrophysics (astro-ph.CO), Space and Planetary Science, FOS: Physical sciences, Astronomy and Astrophysics, [PHYS.ASTR]Physics [physics]/Astrophysics [astro-ph], [PHYS.ASTR] Physics [physics]/Astrophysics [astro-ph], Astrophysics - Cosmology and Nongalactic Astrophysics
Abstract: Degeneracies among parameters of the cosmological model are known to drastically limit the information contained in the matter distribution. In the first paper of this series, we shown that the cosmic web environments; namely the voids, walls, filaments and nodes; can be used as a leverage to improve the real-space constraints on a set of six cosmological parameters, including the summed neutrino mass. Following-upon these results, we propose to study the achievable constraints of environment-dependent power spectra in redshift space where the velocities add up information to the standard two-point statistics by breaking the isotropy of the matter density field. A Fisher analysis based on a set of thousands of Quijote simulations allows us to conclude that the combination of power spectra computed in the several cosmic web environments is able to break some degeneracies. Compared to the matter monopole and quadrupole information alone, the combination of environment-dependent spectra tightens down the constraints on key parameters like the matter density or the summed neutrino mass by up to a factor of $5.5$. Additionally, while the information contained in the matter statistic quickly saturates at mildly non-linear scales in redshift space, the combination of power spectra in the environments appears as a goldmine of information able to improve the constraints at all the studied scales from $0.1$ to $0.5$ $h$/Mpc and suggests that further improvements are reachable at even finer scales., 10 pages, 6 figures, 3 tables. Comments are welcome
Published: 2023

3. Creating bulk ultrastable glasses by random particle bonding

Author: Misaki Ozawa, Yasutaka Iwashita, Walter Kob, Francesco Zamponi, Laboratoire Interdisciplinaire de Physique [Saint Martin d’Hères] (LIPhy ), Centre National de la Recherche Scientifique (CNRS)-Université Grenoble Alpes (UGA), Kyoto Sangyo University, Laboratoire Charles Coulomb (L2C), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and European Project: 723955,GlassUniversality
Subjects: Multidisciplinary, Statistical Mechanics (cond-mat.stat-mech), Soft Condensed Matter (cond-mat.soft), FOS: Physical sciences, General Physics and Astronomy, Disordered Systems and Neural Networks (cond-mat.dis-nn), General Chemistry, Condensed Matter - Soft Condensed Matter, Condensed Matter - Disordered Systems and Neural Networks, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], Condensed Matter - Statistical Mechanics, General Biochemistry, Genetics and Molecular Biology
Abstract: A recent breakthrough in glass science has been the synthesis of ultrastable glasses via physical vapor deposition techniques. These samples display enhanced thermodynamic, kinetic and mechanical stability, with important implications for fundamental science and technological applications. However, the vapor deposition technique is limited to atomic, polymer and organic glass-formers and is only able to produce thin film samples. Here, we propose a novel approach to generate ultrastable glassy configurations in the bulk, via random particle bonding, and using computer simulations we show that this method does indeed allow for the production of ultrastable glasses. Our technique is in principle applicable to any molecular or soft matter system, such as colloidal particles with tunable bonding interactions, thus opening the way to the design of a large class of ultrastable glasses., 8 pages, 6 figures + supplementary information. Improved version thanks to referees' comments
Published: 2023

4. Machine-learning-assisted Monte Carlo fails at sampling computationally hard problems

Author: Simone Ciarella, Jeanne Trinquier, Martin Weigt, Francesco Zamponi, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Biologie Computationnelle et Quantitative = Laboratory of Computational and Quantitative Biology (LCQB), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de Biologie Paris Seine (IBPS), Institut National de la Santé et de la Recherche Médicale (INSERM)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), and European Project: 723955,GlassUniversality
Subjects: Human-Computer Interaction, Artificial Intelligence, FOS: Physical sciences, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Software
Abstract: Several strategies have been recently proposed in order to improve Monte Carlo sampling efficiency using machine learning tools. Here, we challenge these methods by considering a class of problems that are known to be exponentially hard to sample using conventional local Monte Carlo at low enough temperatures. In particular, we study the antiferromagnetic Potts model on a random graph, which reduces to the coloring of random graphs at zero temperature. We test several machine-learning-assisted Monte Carlo approaches, and we find that they all fail. Our work thus provides good benchmarks for future proposals for smart sampling algorithms.
Published: 2022

5. Microscopic observation of two-level systems in a metallic glass model

Author: Felix C. Mocanu, Ludovic Berthier, Simone Ciarella, Dmytro Khomenko, David R. Reichman, Camille Scalliet, Francesco Zamponi, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Systèmes Désordonnés et Applications, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Laboratoire Charles Coulomb (L2C), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Dipartimento di Fisica [Roma La Sapienza], Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome] (UNIROMA), Columbia University [New York], Department of Applied Mathematics and Theoretical Physics [Cambridge] (DAMTP), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), ANR-10-EQPX-0029,EQUIP@MESO,Equipement d'excellence de calcul intensif de Mesocentres coordonnés - Tremplin vers le calcul petaflopique et l'exascale(2010), and European Project: 723955,GlassUniversality
Subjects: [PHYS.PHYS.PHYS-COMP-PH]Physics [physics]/Physics [physics]/Computational Physics [physics.comp-ph], General Physics and Astronomy, FOS: Physical sciences, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], Disordered Systems and Neural Networks (cond-mat.dis-nn), [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], Physical and Theoretical Chemistry, Computational Physics (physics.comp-ph), Condensed Matter - Disordered Systems and Neural Networks, Physics - Computational Physics
Abstract: The low-temperature quasi-universal behavior of amorphous solids has been attributed to the existence of spatially-localized tunneling defects found in the low-energy regions of the potential energy landscape. Computational models of glasses can be studied to elucidate the microscopic nature of these defects. Recent simulation work has demonstrated the means of generating stable glassy configurations for models that mimic metallic glasses using the swap Monte Carlo algorithm. Building on these studies, we present an extensive exploration of the glassy metabasins of the potential energy landscape of a variant of the most widely used model of metallic glasses. We carefully identify tunneling defects and reveal their depletion with increased glass stability. The density of tunneling defects near the experimental glass transition temperature appears to be in good agreement with experimental measurements., 17 pages, 12 figures
Published: 2022

6. Glasses and aging: A Statistical Mechanics Perspective

Author: Arceri, Francesco, Landes, François, Berthier, Ludovic, Biroli, Giulio, Department of Physics, University of Oregon, Université Paris-Sud - Paris 11 - Faculté des Sciences (UP11 UFR Sciences), Université Paris-Sud - Paris 11 (UP11), Laboratoire de Recherche en Informatique (LRI), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), TAckling the Underspecified (TAU), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire Interdisciplinaire des Sciences du Numérique (LISN), Institut National de Recherche en Informatique et en Automatique (Inria)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire Charles Coulomb (L2C), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), University of Cambridge [UK] (CAM), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and We thank all the collaborators who worked with us on glass physics. This work was supported by a grant from the Simons Foundation (Grant No. 454933, L. B., Grant No. 454935, G. B.)
Subjects: Condensed Matter::Soft Condensed Matter, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], Condensed Matter::Disordered Systems and Neural Networks, [PHYS.COND.CM-SCM]Physics [physics]/Condensed Matter [cond-mat]/Soft Condensed Matter [cond-mat.soft]
Abstract: 50 pages, 24 figs. This is an updated version of a chapter initially written in 2009 for the Encyclopedia of Complexity and Systems Science (Springer); International audience; We review the field of the glass transition, glassy dynamics and aging from a statistical mechanics perspective. We give a brief introduction to the subject and explain the main phenomenology encountered in glassy systems, with a particular emphasis on spatially heterogeneous dynamics. We review the main theoretical approaches currently available to account for these glassy phenomena, including recent developments regarding mean-field theory of liquids and glasses, novel computational tools, and connections to the jamming transition. Finally, the physics of aging and off-equilibrium dynamics exhibited by glassy materials is discussed.
Published: 2022

7. The Asymptotics of the Clustering Transition for Random Constraint Satisfaction Problems

Author: Guilhem Semerjian, Louise Budzynski, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: FOS: Computer and information sciences, Phase transition, Spin glass, Discrete Mathematics (cs.DM), FOS: Physical sciences, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], 01 natural sciences, 010305 fluids & plasmas, Combinatorics, 0103 physical sciences, FOS: Mathematics, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], 010306 general physics, Cluster analysis, ComputingMilieux_MISCELLANEOUS, Mathematical Physics, Constraint satisfaction problem, Random graph, Physics, Probability (math.PR), Statistical and Nonlinear Physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 16. Peace & justice, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Mathematics - Probability, Computer Science - Discrete Mathematics
Abstract: Random Constraint Satisfaction Problems exhibit several phase transitions when their density of constraints is varied. One of these threshold phenomena, known as the clustering or dynamic transition, corresponds to a transition for an information theoretic problem called tree reconstruction. In this article we study this threshold for two CSPs, namely the bicoloring of $k$-uniform hypergraphs with a density $\alpha$ of constraints, and the $q$-coloring of random graphs with average degree $c$. We show that in the large $k,q$ limit the clustering transition occurs for $\alpha = \frac{2^{k-1}}{k} (\ln k + \ln \ln k + \gamma_{\rm d} + o(1))$, $c= q (\ln q + \ln \ln q + \gamma_{\rm d}+ o(1))$, where $\gamma_{\rm d}$ is the same constant for both models. We characterize $\gamma_{\rm d}$ via a functional equation, solve the latter numerically to estimate $\gamma_{\rm d} \approx 0.871$, and obtain an analytic lowerbound $\gamma_{\rm d} \ge 1 + \ln (2 (\sqrt{2}-1)) \approx 0.812$. Our analysis unveils a subtle interplay of the clustering transition with the rigidity (naive reconstruction) threshold that occurs on the same asymptotic scale at $\gamma_{\rm r}=1$., Comment: 35 pages, 8 figures
Published: 2020

8. Out of equilibrium Phase Diagram of the Quantum Random Energy Model

Author: Marco Schiró, Marco Tarzia, Giulio Biroli, Davide Facoetti, Pierpaolo Vivo, École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Jeunes Équipes de l'Institut de Physique du Collège de France (JEIPCdF), Collège de France (CdF (institution))-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique de la Matière Condensée (LPMC), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Schiro, Marco, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, and European Project: 723955,GlassUniversality
Subjects: [PHYS.COND.GAS]Physics [physics]/Condensed Matter [cond-mat]/Quantum Gases [cond-mat.quant-gas], FOS: Physical sciences, 02 engineering and technology, 01 natural sciences, [PHYS] Physics [physics], symbols.namesake, [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph], Spin glasses, Phase (matter), 0103 physical sciences, Many-body localization, Ergodic theory, Anderson localization, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], Statistical physics, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Quantum, Condensed Matter - Statistical Mechanics, Phase diagram, Physics, [PHYS]Physics [physics], Quantum Physics, Statistical Mechanics (cond-mat.stat-mech), Random energy model, Diagram, Hilbert space, Disordered Systems and Neural Networks (cond-mat.dis-nn), Eigenfunction, Condensed Matter - Disordered Systems and Neural Networks, 021001 nanoscience & nanotechnology, Disordered systems, Quantum Gases (cond-mat.quant-gas), symbols, 0210 nano-technology, Quantum Physics (quant-ph), Condensed Matter - Quantum Gases
Abstract: In this paper we study the out-of-equilibrium phase diagram of the quantum version of Derrida's Random Energy Model, which is the simplest model of mean-field spin glasses. We interpret its corresponding quantum dynamics in Fock space as a one-particle problem in very high dimension to which we apply different theoretical methods tailored for high-dimensional lattices: the Forward-Scattering Approximation, a mapping to the Rosenzweig-Porter model, and the cavity method. Our results indicate the existence of two transition lines and three distinct dynamical phases: a completely many-body localized phase at low energy, a fully ergodic phase at high energy, and a multifractal "bad metal" phase at intermediate energy. In the latter, eigenfunctions occupy a diverging volume, yet an exponentially vanishing fraction of the total Hilbert space. We discuss the limitations of our approximations and the relationship with previous studies., 21 pages, 13 figures
Published: 2021

9. Modeling sequence-space exploration and emergence of epistatic signals in protein evolution

Author: Bisardi, Matteo, Rodriguez-Rivas, Juan, Zamponi, Francesco, Weigt, Martin, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Biologie Computationnelle et Quantitative = Laboratory of Computational and Quantitative Biology (LCQB), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de Biologie Paris Seine (IBPS), Sorbonne Université (SU)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: epistasis, fitness landscapes, Populations and Evolution (q-bio.PE), FOS: Physical sciences, Biomolecules (q-bio.BM), Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Quantitative Biology - Quantitative Methods, Article submission, methods section protein evolution, Quantitative Biology - Biomolecules, sequence space, FOS: Biological sciences, [SDV.BBM]Life Sciences [q-bio]/Biochemistry, Molecular Biology, Quantitative Biology - Populations and Evolution, Quantitative Methods (q-bio.QM), data-driven models
Abstract: During their evolution, proteins explore sequence space via an interplay between random mutations and phenotypic selection. Here we build upon recent progress in reconstructing data-driven fitness landscapes for families of homologous proteins, to propose stochastic models of experimental protein evolution. These models predict quantitatively important features of experimentally evolved sequence libraries, like fitness distributions and position-specific mutational spectra. They also allow us to efficiently simulate sequence libraries for a vast array of combinations of experimental parameters like sequence divergence, selection strength and library size. We showcase the potential of the approach in re-analyzing two recent experiments to determine protein structure from signals of epistasis emerging in experimental sequence libraries. To be detectable, these signals require sufficiently large and sufficiently diverged libraries. Our modeling framework offers a quantitative explanation for the variable success of recently published experiments. Furthermore, we can forecast the outcome of time- and resource-intensive evolution experiments, opening thereby a way to computationally optimize experimental protocols., 16 pages, 14 figures
Published: 2021

10. Active matter in infinite dimensions: Fokker–Planck equation and dynamical mean-field theory at low density

Author: Frédéric van Wijland, Francesco Zamponi, Alessandro Manacorda, Thibaut Arnoulx de Pirey, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), CNRS UMR 7057 - Laboratoire Matières et Systèmes Complexes (MSC) (MSC), Centre National de la Recherche Scientifique (CNRS), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: Physics [G04] [Physical, chemical, mathematical & earth Sciences], FOS: Physical sciences, General Physics and Astronomy, Condensed Matter - Soft Condensed Matter, Space (mathematics), 01 natural sciences, 010305 fluids & plasmas, 0103 physical sciences, Point (geometry), Statistical physics, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], Physical and Theoretical Chemistry, 010306 general physics, Condensed Matter - Statistical Mechanics, ComputingMilieux_MISCELLANEOUS, Physics, Steady state, Statistical Mechanics (cond-mat.stat-mech), Pair distribution function, Disordered Systems and Neural Networks (cond-mat.dis-nn), Hard spheres, Condensed Matter - Disordered Systems and Neural Networks, Active matter, Physique [G04] [Physique, chimie, mathématiques & sciences de la terre], Soft Condensed Matter (cond-mat.soft), Fokker–Planck equation, Transient (oscillation)
Abstract: We investigate the behavior of self-propelled particles in infinite space dimensions by comparing two powerful approaches in many-body dynamics: the Fokker-Planck equation and dynamical mean-field theory. The dynamics of the particles at low densities and infinite persistence time is solved in the steady-state with both methods, thereby proving the consistency of the two approaches in a paradigmatic out-of-equilibrium system. We obtain the analytic expression for the pair distribution function and the effective self-propulsion to first order in the density, confirming the results obtained in a previous paper and extending them to the case of a non-monotonous interaction potential. Furthermore, we obtain the transient behavior of active hard spheres when relaxing from equilibrium to the nonequilibrium steady-state. Our results show how collective dynamics is affected by interactions to first order in the density, and point out future directions for further analytical and numerical solutions of this problem., 25 pages, 5 figures
Published: 2021

11. adabmDCA: adaptive Boltzmann machine learning for biological sequences

Author: Anna Paola Muntoni, Andrea Pagnani, Francesco Zamponi, Martin Weigt, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Biologie Computationnelle et Quantitative = Laboratory of Computational and Quantitative Biology (LCQB), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de Biologie Paris Seine (IBPS), Sorbonne Université (SU)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: QH301-705.5, Computer science, Computer applications to medicine. Medical informatics, R858-859.7, Boltzmann machine, FOS: Physical sciences, Quantitative Biology - Quantitative Methods, 01 natural sciences, Biochemistry, Boltzmann machine learning, Domain (software engineering), Machine Learning, 03 medical and health sciences, symbols.namesake, RNA modelling, Structural Biology, 0103 physical sciences, Statistical inference, Code (cryptography), Humans, Pruning (decision trees), Biology (General), [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Molecular Biology, Quantitative Methods (q-bio.QM), 030304 developmental biology, Lossless compression, 0303 health sciences, Applied Mathematics, Proteins, Protein modelling, Biomolecules (q-bio.BM), Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Computer Science Applications, Quantitative Biology - Biomolecules, FOS: Biological sciences, Boltzmann constant, symbols, RNA, Pairwise comparison, Algorithm, Software
Abstract: BackgroundBoltzmann machines are energy-based models that have been shown to provide an accurate statistical description of domains of evolutionary-related protein and RNA families. They are parametrized in terms of local biases accounting for residue conservation, and pairwise terms to model epistatic coevolution between residues. From the model parameters, it is possible to extract an accurate prediction of the three-dimensional contact map of the target domain. More recently, the accuracy of these models has been also assessed in terms of their ability in predicting mutational effects and generatingin silicofunctional sequences.ResultsOur adaptive implementation of Boltzmann machine learning, , can be generally applied to both protein and RNA families and accomplishes several learning set-ups, depending on the complexity of the input data and on the user requirements. The code is fully available athttps://github.com/anna-pa-m/adabmDCA. As an example, we have performed the learning of three Boltzmann machines modeling the Kunitz and Beta-lactamase2 protein domains and TPP-riboswitch RNA domain.ConclusionsThe models learned by are comparable to those obtained by state-of-the-art techniques for this task, in terms of the quality of the inferred contact map as well as of the synthetically generated sequences. In addition, the code implements both equilibrium and out-of-equilibrium learning, which allows for an accurate and lossless training when the equilibrium one is prohibitive in terms of computational time, and allows for pruning irrelevant parameters using an information-based criterion.
Published: 2021

12. Good speciation and endogenous business cycles in a constraint satisfaction macroeconomic model

Author: Dhruv Sharma, Marco Tarzia, Jean-Philippe Bouchaud, Francesco Zamponi, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: Statistics and Probability, Physics - Physics and Society, General Economics (econ.GN), media_common.quotation_subject, FOS: Physical sciences, Physics and Society (physics.soc-ph), 01 natural sciences, Microeconomics, FOS: Economics and business, Debt, 0502 economics and business, 0103 physical sciences, Business cycle, Economics, 050207 economics, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Constraint (mathematics), Budget constraint, Constraint satisfaction problem, ComputingMilieux_MISCELLANEOUS, Economics - General Economics, media_common, 05 social sciences, Statistical and Nonlinear Physics, Constraint satisfaction, Macroeconomic model, Bankruptcy, Statistics, Probability and Uncertainty
Abstract: We introduce a prototype agent-based model of the macroeconomy, with budgetary constraints at its core. The model is related to a class of constraint satisfaction problems (CSPs), which has been thoroughly investigated in computer science. The CSP paradigm allows us to propose an alternative price-setting mechanism: given agents' preferences and budgets, what set of prices satisfies the maximum number of agents? Such an approach permits the coupling of production and output within the economy to the allowed level of debt in a simplified framework. Within our model, we identify three different regimes upon varying the amount of debt that each agent can accumulate before defaulting. In presence of a very loose constraint on debt, endogenous crises leading to waves of synchronized bankruptcies are present. In the opposite regime of very tight debt constraining, the bankruptcy rate is extremely high and the economy remains structure-less. In an intermediate regime, the economy is stable with very low bankruptcy rate and no aggregate-level crises. This third regime displays a rich phenomenology:the system spontaneously and dynamically self-organizes in a set of cheap and expensive goods (i.e. some kind of "speciation"), with switches triggered by random fluctuations and feedback loops. Our analysis confirms the central role that debt levels play in the stability of the economy. More generally, our model shows that constraints at the individual scale can generate highly complex patterns at the aggregate level., Comment: 14 Pages, 11 Figures. Updated Journal Reference
Published: 2021

13. Low-frequency vibrational spectrum of mean-field disordered systems

Author: Pierfrancesco Urbani, Edan Lerner, Francesco Zamponi, Eran Bouchbinder, Corrado Rainone, Soft Condensed Matter (ITFA, IoP, FNWI), ITFA (IoP, FNWI), IoP (FNWI), Weizmann Institute of Science [Rehovot, Israël], Institute of Theoretical Physics [Amsterdam] (ITFA), University of Amsterdam [Amsterdam] (UvA), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Grant from the Simons Foundation (No. 454955), ANR-10-LABX-0039,PALM,Physics: Atoms, Light, Matter(2010), European Project: 723955,GlassUniversality, Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Physics, Spin glass, Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, Disordered Systems and Neural Networks (cond-mat.dis-nn), 02 engineering and technology, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Soft Condensed Matter, 021001 nanoscience & nanotechnology, Coupling (probability), 01 natural sciences, Omega, Mean field theory, Critical line, 0103 physical sciences, Soft Condensed Matter (cond-mat.soft), [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, 0210 nano-technology, Ground state, Pseudogap, Condensed Matter - Statistical Mechanics, Mathematical physics, Phase diagram
Abstract: We study a recently introduced and exactly solvable mean-field model for the density of vibrational states $\mathcal{D}(\omega)$ of a structurally disordered system. The model is formulated as a collection of disordered anharmonic oscillators, with random stiffness $\kappa$ drawn from a distribution $p(\kappa)$, subjected to a constant field $h$ and interacting bilinearly with a coupling of strength $J$. We investigate the vibrational properties of its ground state at zero temperature. When $p(\kappa)$ is gapped, the emergent $\mathcal{D}(\omega)$ is also gapped, for small $J$. Upon increasing $J$, the gap vanishes on a critical line in the $(h,J)$ phase diagram, whereupon replica symmetry is broken. At small $h$, the form of this pseudogap is quadratic, $\mathcal{D}(\omega)\sim\omega^2$, and its modes are delocalized, as expected from previously investigated mean-field spin glass models. However, we determine that for large enough $h$, a quartic pseudogap $\mathcal{D}(\omega)\sim\omega^4$, populated by localized modes, emerges, the two regimes being separated by a special point on the critical line. We thus uncover that mean-field disordered systems can generically display both a quadratic-delocalized and a quartic-localized spectrum at the glass transition., Comment: 18 pages, 3 figures
Published: 2021

14. Relationship between two-level systems and quasilocalized normal modes in glasses

Author: David R. Reichman, Francesco Zamponi, D. Khomenko, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Work (thermodynamics), Spatial correlation, Materials science, Physics and Astronomy (miscellaneous), Mode (statistics), Energy landscape, FOS: Physical sciences, 02 engineering and technology, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 021001 nanoscience & nanotechnology, 01 natural sciences, Nonlinear system, Normal mode, 0103 physical sciences, General Materials Science, Statistical physics, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, 0210 nano-technology, Quantum tunnelling, ComputingMilieux_MISCELLANEOUS
Abstract: Tunneling two-level systems (TLSs) dominate the physics of glasses at low temperatures. Yet TLSs are extremely rare, and it is thus difficult to directly observe them in silico. Developing simple structural predictors, which can provide markers for determining if a TLS is present in a given glass region, is crucial for a more efficient search. It has been speculated that vibrational quasilocalized modes (QLMs) are closely related to TLSs, and that one can extract information about TLSs from QLMs. In this work we address this possibility. In particular, we investigate the degree to which a linear or nonlinear vibrational mode analysis can predict the location of TLSs independently found by energy landscape exploration. We find that even though there is a notable spatial correlation between QLMs and TLSs, in general TLSs are strongly nonlinear, and their global properties cannot be predicted by a simple vibrational mode analysis.
Published: 2021

15. Efficient generative modeling of protein sequences using simple autoregressive models

Author: Jeanne Trinquier, Andrea Pagnani, Martin Weigt, Francesco Zamponi, Guido Uguzzoni, Biologie Computationnelle et Quantitative = Laboratory of Computational and Quantitative Biology (LCQB), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de Biologie Paris Seine (IBPS), Sorbonne Université (SU)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Department of Applied Science and Technology [Politecnico di Torino] (DISAT), Politecnico di Torino = Polytechnic of Turin (Polito), Italian Institute for Genomic Medicine, Istituto Nazionale di Fisica Nucleare, Sezione di Torino (INFN, Sezione di Torino), Istituto Nazionale di Fisica Nucleare (INFN), Systèmes Désordonnés et Applications, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris)
Subjects: Statistical methods, Computer science, General Physics and Astronomy, computer.software_genre, Quantitative Biology - Quantitative Methods, 0302 clinical medicine, Simple (abstract algebra), [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], Databases, Protein, Quantitative Methods (q-bio.QM), 0303 health sciences, Sequence, Multidisciplinary, Condensed Matter - Disordered Systems and Neural Networks, Autoregressive model, symbols, Sequence space (evolution), Science, Protein design, FOS: Physical sciences, Machine learning, General Biochemistry, Genetics and Molecular Biology, Article, Evolution, Molecular, symbols.namesake, 03 medical and health sciences, Entropy (information theory), Fraction (mathematics), Amino Acid Sequence, Condensed Matter - Statistical Mechanics, 030304 developmental biology, Structure (mathematical logic), Models, Statistical, Statistical Mechanics (cond-mat.stat-mech), business.industry, Deep learning, Computational Biology, Proteins, Epistasis, Genetic, Biomolecules (q-bio.BM), Disordered Systems and Neural Networks (cond-mat.dis-nn), General Chemistry, Quantitative Biology - Biomolecules, FOS: Biological sciences, Mutation, Boltzmann constant, Molecular evolution, Artificial intelligence, business, Sequence Alignment, computer, Biological physics, 030217 neurology & neurosurgery, Generative grammar
Abstract: Generative models emerge as promising candidates for novel sequence-data driven approaches to protein design, and for the extraction of structural and functional information about proteins deeply hidden in rapidly growing sequence databases. Here we propose simple autoregressive models as highly accurate but computationally efficient generative sequence models. We show that they perform similarly to existing approaches based on Boltzmann machines or deep generative models, but at a substantially lower computational cost (by a factor between $10^2$ and $10^3$). Furthermore, the simple structure of our models has distinctive mathematical advantages, which translate into an improved applicability in sequence generation and evaluation. Within these models, we can easily estimate both the probability of a given sequence, and, using the model's entropy, the size of the functional sequence space related to a specific protein family. In the example of response regulators, we find a huge number of ca. $10^{68}$ possible sequences, which nevertheless constitute only the astronomically small fraction $10^{-80}$ of all amino-acid sequences of the same length. These findings illustrate the potential and the difficulty in exploring sequence space via generative sequence models., 12 pages, 4 Figures + Supplementary Material
Published: 2021

16. V-, U-, L-or W-shaped economic recovery after Covid-19: Insights from an Agent Based Model

Author: Stanislao Gualdi, Jean-Philippe Bouchaud, Francesco Zamponi, Marco Tarzia, Dhruv Sharma, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU), Institut Universitaire de France (IUF), Ministère de l'Education nationale, de l’Enseignement supérieur et de la Recherche (M.E.N.E.S.R.), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: Inflation, Viral Diseases, Systems Analysis, Economics, Epidemiology, Macroeconomics, Social Sciences, Monetary Policy, Medical Conditions, Salaries, Medicine and Health Sciences, 050207 economics, Duration (project management), media_common, Data Management, Agent-based model, [PHYS]Physics [physics], 050208 finance, Multidisciplinary, 05 social sciences, Monetary policy, Models, Economic, Infectious Diseases, Inflation, Economic, Income, Medicine, Research Article, Employment, Computer and Information Sciences, media_common.quotation_subject, Science, Supply and demand, Microeconomics, 0502 economics and business, Humans, Phase Diagrams, Pandemics, Inflation Rates, Data Visualization, COVID-19, Covid 19, Shock (economics), Systems analysis, Unemployment, Public Finance, Labor Economics, Economic recovery, Money Supply and Banking, Finance
Abstract: International audience; We discuss the impact of a Covid-19-like shock on a simple model economy, described by the previously developed Mark-0 Agent-Based Model. We consider a mixed supply and demand shock, and show that depending on the shock parameters (amplitude and duration), our model economy can display V-shaped, U-shaped or W-shaped recoveries, and even an L-shaped output curve with permanent output loss. This is due to the economy getting trapped in a self-sustained "bad" state. We then discuss two policies that attempt to moderate the impact of the shock: giving easy credit to firms, and the so-called helicopter money, i.e. injecting new money into the households savings. We find that both policies are effective if strong enough. We highlight the potential danger of terminating these policies too early, although inflation is substantially increased by lax access to credit. Finally, we consider the impact of a second lockdown. While we only discuss a limited number of scenarios, our model is flexible and versatile enough to accommodate a wide variety of situations, thus serving as a useful exploratory tool for a qualitative, scenario-based understanding of post-Covid recovery. The corresponding code is available on-line.
Published: 2021

17. Dynamical instantons and activated processes in mean-field glass models

Author: Valentina Ros, Giulio Biroli, Chiara Cammarota, Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Instanton, Gaussian, QC1-999, General Physics and Astronomy, FOS: Physical sciences, 01 natural sciences, Langevin dynamics, 010305 fluids & plasmas, symbols.namesake, rough landscapes, 0103 physical sciences, Initial value problem, Statistical physics, 010306 general physics, Saddle, Condensed Matter - Statistical Mechanics, Physics, [PHYS]Physics [physics], Statistical Mechanics (cond-mat.stat-mech), activated dynamics, activated dynamics, rough landscapes, instantons, Langevin dynamics, Energy landscape, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Maxima and minima, Mean field theory, symbols, instantons
Abstract: We focus on the energy landscape of a simple mean-field model of glasses and analyze activated barrier-crossing by combining the Kac-Rice method for high-dimensional Gaussian landscapes with dynamical field theory. In particular, we consider Langevin dynamics at low temperature in the energy landscape of the pure spherical $p$-spin model. We select as initial condition for the dynamics one of the many unstable index-1 saddles in the vicinity of a reference local minimum. We show that the associated dynamical mean-field equations admit two solutions: one corresponds to falling back to the original reference minimum, and the other to reaching a new minimum past the barrier. By varying the saddle we scan and characterize the properties of such minima reachable by activated barrier-crossing. Finally, using time-reversal transformations, we construct the two-point function dynamical instanton of the corresponding activated process., Comment: v3, conclusions extended and minor revisions
Published: 2021

18. Mean-field model of interacting quasilocalized excitations in glasses

Author: Eran Bouchbinder, Corrado Rainone, Pierfrancesco Urbani, Edan Lerner, Francesco Zamponi, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), IoP (FNWI), Soft Condensed Matter (ITFA, IoP, FNWI), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Physics, QC1-999, Anharmonicity, Universality (philosophy), FOS: Physical sciences, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 01 natural sciences, Omega, 010305 fluids & plasmas, Mean squared displacement, Mean field theory, 0103 physical sciences, Density of states, Probability distribution, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, ComputingMilieux_MISCELLANEOUS, Mathematical physics, Dimensionless quantity
Abstract: Structural glasses feature quasilocalized excitations whose frequencies $\omega$ follow a universal density of states ${\cal D}(\omega)\!\sim\!\omega^4$. Yet, the underlying physics behind this universality is not fully understood. Here we study a mean-field model of quasilocalized excitations in glasses, viewed as groups of particles embedded inside an elastic medium and described collectively as anharmonic oscillators. The oscillators, whose harmonic stiffness is taken from a rather featureless probability distribution (of upper cutoff $\kappa_0$) in the absence of interactions, interact among themselves through random couplings (characterized by strength $J$) and with the surrounding elastic medium (an interaction characterized by a constant force $h$). We first show that the model gives rise to a gapless density of states ${\cal D}(\omega)\!=\!A_{\rm g}\,\omega^4$ for a broad range of model parameters, expressed in terms of the strength of stabilizing anharmonicity, which plays a decisive role in the model. Then -- using scaling theory and numerical simulations -- we provide a complete understanding of the non-universal prefactor $A_{\rm g}(h,J,\kappa_0)$, of the oscillators' interaction-induced mean square displacement and of an emerging characteristic frequency, all in terms of properly identified dimensionless quantities. In particular, we show that $A_{\rm g}(h,J,\kappa_0)$ is a nonmonotonic function of $J$ for a fixed $h$, varying predominantly exponentially with $-(\kappa_0 h^{2/3}\!/J^2)$ in the weak interactions (small $J$) regime -- reminiscent of recent observations in computer glasses -- and predominantly decaying as a power-law for larger $J$, in a regime where $h$ plays no role. We discuss the physical interpretation of the model and its possible relations to available observations in structural glasses, along with delineating some future research directions., Comment: Updated manuscript, scaling theory and extensive numerics added (9 pages, 6 figures)
Published: 2021

19. Large deviations of extreme eigenvalues of generalized sample covariance matrices

Author: Antoine Maillard, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: Open problem, FOS: Physical sciences, General Physics and Astronomy, Mathematics - Statistics Theory, Statistics Theory (math.ST), 01 natural sciences, 010104 statistics & probability, 0103 physical sciences, FOS: Mathematics, Rare events, Applied mathematics, 0101 mathematics, 010306 general physics, Condensed Matter - Statistical Mechanics, Eigenvalues and eigenvectors, Mathematics, Statistical Mechanics (cond-mat.stat-mech), Probability (math.PR), Analytical technique, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph], Principal component analysis, Large deviations theory, Random matrix, Mathematics - Probability, Importance sampling
Abstract: We present an analytical technique to compute the probability of rare events in which the largest eigenvalue of a random matrix is atypically large (i.e.\ the right tail of its large deviations). The results also transfer to the left tail of the large deviations of the smallest eigenvalue. The technique improves upon past methods by not requiring the explicit law of the eigenvalues, and we apply it to a large class of random matrices that were previously out of reach. In particular, we solve an open problem related to the performance of principal components analysis on highly correlated data, and open the way towards analyzing the high-dimensional landscapes of complex inference models. We probe our results using an importance sampling approach, effectively simulating events with probability as small as $10^{-100}$., 7 pages + 7 pages appendix. Updated version matching the published article
Published: 2021

20. Mean-field caging in a random Lorentz gas

Author: Harukuni Ikeda, Yi Hu, Grzegorz Szamel, Giulio Biroli, Patrick Charbonneau, Francesco Zamponi, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Duke University [Durham], The University of Tokyo (UTokyo), Colorado State University [Fort Collins] (CSU), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Path (topology), Lorentz transformation, FOS: Physical sciences, Condensed Matter - Soft Condensed Matter, 010402 general chemistry, 01 natural sciences, Condensed Matter::Disordered Systems and Neural Networks, Minimal model, symbols.namesake, 0103 physical sciences, Materials Chemistry, Limit (mathematics), Physical and Theoretical Chemistry, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], Condensed Matter - Statistical Mechanics, ComputingMilieux_MISCELLANEOUS, Mathematical physics, Physics, 010304 chemical physics, Statistical Mechanics (cond-mat.stat-mech), Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 0104 chemical sciences, Surfaces, Coatings and Films, Mean field theory, Percolation, symbols, Soft Condensed Matter (cond-mat.soft), Resolution (algebra)
Abstract: The random Lorentz gas (RLG) is a minimal model of both percolation and glassiness, which leads to a paradox in the infinite-dimensional, $d\rightarrow\infty$ limit: the localization transition is then expected to be continuous for the former and discontinuous for the latter. As a putative resolution, we have recently suggested that as $d$ increases the behavior of the RLG converges to the glassy description, and that percolation physics is recovered thanks to finite-$d$ perturbative and non-perturbative (instantonic) corrections [Biroli et al. arXiv:2003.11179]. Here, we expand on the $d\rightarrow\infty$ physics by considering a simpler static solution as well as the dynamical solution of the RLG. Comparing the $1/d$ correction of this solution with numerical results reveals that even perturbative corrections fall out of reach of existing theoretical descriptions. Comparing the dynamical solution with the mode-coupling theory (MCT) results further reveals that although key quantitative features of MCT are far off the mark, it does properly capture the discontinuous nature of the $d\rightarrow\infty$ RLG. These insights help chart a path toward a complete description of finite-dimensional glasses., Comment: 12 pages, 2 figures
Published: 2021
Full Text: View/download PDF

21. Dynamical mean-field theory for stochastic gradient descent in Gaussian mixture classification

Author: Francesca Mignacco, Florent Krzakala, Pierfrancesco Urbani, Lenka Zdeborová, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Mignacco, Francesca, Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Statistics and Probability, FOS: Computer and information sciences, Computer Science - Machine Learning, MathematicsofComputing_NUMERICALANALYSIS, FOS: Physical sciences, Machine Learning (stat.ML), Mathematics - Statistics Theory, Statistics Theory (math.ST), 01 natural sciences, 010305 fluids & plasmas, Machine Learning (cs.LG), [PHYS] Physics [physics], Statistics - Machine Learning, 0103 physical sciences, FOS: Mathematics, 010306 general physics, [PHYS]Physics [physics], Statistical and Nonlinear Physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 16. Peace & justice, [STAT] Statistics [stat], [STAT]Statistics [stat], machine learning, learning theory, systems, Statistics, Probability and Uncertainty
Abstract: We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for a single-layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides a prototype of a non-convex loss landscape with interpolating regimes and a large generalization gap. We define a particular stochastic process for which SGD can be extended to a continuous-time limit that we call stochastic gradient flow. In the full-batch limit, we recover the standard gradient flow. We apply dynamical mean-field theory from statistical physics to track the dynamics of the algorithm in the high-dimensional limit via a self-consistent stochastic process. We explore the performance of the algorithm as a function of the control parameters shedding light on how it navigates the loss landscape., 8 pages + appendix, 4 figures
Published: 2020

22. On the Number of Limit Cycles in Diluted Neural Networks

Author: Giorgio Parisi, Francesco Zamponi, Jacopo Rocchi, Sungmin Hwang, Giancarlo Ruocco, Enrico Lanza, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Random graph, Spin glass, Logarithm, Artificial neural network, Computer science, FOS: Physical sciences, Statistical and Nonlinear Physics, Monotonic function, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Belief propagation, 01 natural sciences, 010305 fluids & plasmas, 0103 physical sciences, Attractor, Limit (mathematics), Statistical physics, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Mathematical Physics, ComputingMilieux_MISCELLANEOUS
Abstract: We consider the storage properties of temporal patterns, i.e. cycles of finite lengths, in neural networks represented by (generally asymmetric) spin glasses defined on random graphs. Inspired by the observation that dynamics on sparse systems have more basins of attractions than the dynamics of densely connected ones, we consider the attractors of a greedy dynamics in sparse topologies, considered as proxy for the stored memories. We enumerate them using numerical simulation and extend the analysis to large systems sizes using belief propagation. We find that the logarithm of the number of such cycles is a non monotonic function of the mean connectivity and we discuss the similarities with biological neural networks describing the memory capacity of the hippocampus., Comment: 10 pages, 11 figures
Published: 2020

23. Modèles macroéconomiques à agents : une perspective de physique statistique

Author: Sharma, Dhruv, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Systèmes Désordonnés et Applications, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres, Francesco Zamponi, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris)
Subjects: Agent-based models, Complex systems, Disordered systems, [PHYS.PHYS]Physics [physics]/Physics [physics], Physique statistique, Modeles à agents, Macroeconomics, Statistical physics, Macroeconomie, Systèmes complexes, Systèmes désordonnées
Abstract: Agent-based models (ABMs) have emerged as a complementary paradigm for modeling macroeconomic phenomena. Compared to other, more established models such as DSGE (Dynamic Stochastic General Equilibrium) models, ABMs provide a flexible framework for understanding the complexity of the macroeconomy while at the same time taking into account the heterogeneous nature of economic actors, institutions and markets without making overly restrictive assumptions. ABMs take a “bottom-up” approach towards macroeconomic modeling by simulating the behavior of each individual agent in the economy and then aggregating to reveal emergent phenomena such as endogenous business cycles or flash crashes. The object of this thesis is to advance a methodology commonly used in statistical physics and apply it to the study of two macroeconomic agent-based models. In both models studied here, we first determine the “phase-diagram” of the model to identify the relevant macroscopic regimes to develop an intuitive understanding of the macro-dynamics using a small subset of parameters. The first ABM presented here builds upon the paradigm of constraint satisfaction problems (CSPs) and integrates it within the model’s behavioral rules via agents’ budgetary constraints. These constraints, similar to the well-studied perceptron CSP, reveal the existence of three regimes and underscore the importance of debt for macroeconomic stability: at lowlevels of debt, the economy remains structure-less with frequent bankruptcies while high debt leads to endogenous business cycles. Between these two extremes, an intermediate regime of relative stability is found with low levels of bankruptcies for all times. Within this ABM, agents’ preferences, serving as the source of disorder in the CSP, evolve continuously in time. We thus study a simple dynamical scheme for the perceptron and discover that a rugged landscape can indeed exist with dynamic, annealed disorder. Finally, we extend the Mark-0 ABM to simulate exogenous consumption and productivity shocks due to the Covid pandemic. Whereas standard approaches design a model to understand a particular outcome, this model can generate a variety of scenarios after a Covid-like shock. Furthermore, we also investigate the efficacy of several policies, including the much-debated “helicopter money” drop, in avoiding economic collapse. We thus highlight the importance of ABMs as multi-purpose “scenario generators”, for producing outcomes that are difficult to foresee due to the intrinsic complexity of macro-economic dynamics.; Les modèles à agents (Agent-Based Models ou ABMs) sont apparus comme un paradigme complémentaire pour la modélisation des phénomènes macro-économiques. Par rapport à d’autres modèles plus établis, tels que les modelés DSGE (Dynamic Stochastic General Equilibrium), les ABMs offrent un cadre flexible pour comprendre la complexité de la macroéconomie tout en prenant en compte la nature hétérogène des acteurs économiques, des institutions et des marchés, sans faire d’hypothèses trop restrictives. Ces modelés adoptent une approche “bottom-up” de la modélisation macro-économique en simulant le comportement de chaque agent individuel dans l’économie puis en s’agrégeant pour révéler des phénomènes émergents tels que les cycles économiques endogènes ou les crashs soudains. L’objet de cette thèse est de faire progresser une méthodologie communément utilisée en physique statistique et de l’appliquer à l’étude de deux modèles macro-économiques. Dans les deux modèles étudiés ici, nous déterminons d’abord le “diagramme de phase” du modèle pour identifier les régimes macroscopiques pertinents afin de développer une compréhension intuitive de la macro-dynamique en n’utilisant qu’un petit sous-ensemble de paramètres. Le premier modèle présenté ici s’appuie sur le paradigme des problèmes de satisfaction des contraintes (de l’anglais Constraint Satisfaction Problems, CSPs) et l’intègre dans le cadre des règles de comportement du modèle via les contraintes budgétaires des agents. Ces contraintes, similaires à celles du perceptron, un CSP bien-etudié, révèlent l’existence de trois régimes et soulignent l’importance de la dette pour la stabilité macro-économique : à un faible niveau d’endettement, l’économie reste sans structure et les faillites sont fréquentes, alors qu’à un niveau élevé la dette conduit à des cycles économiques endogènes. Entre ces deux extrêmes, l’on trouve un régime intermédiaire de stabilité relative avec de faibles niveaux des faillites tout le temps. Dans ce modèle, les préférences des agents, qui sont à l’origine du désordre dans le CSP, évoluent continuellement dans le temps. Nous étudions donc un schéma dynamique simple pour le perceptron et découvrons qu’un paysage rugueux peut en effet exister avec un désordre dynamique. Enfin, nous généralisons l’ABM Mark-0 pour simuler les chocs exogènes de consommation et de productivité dus à la pandémie de COVID. Alors que les approches standards élaborent un modèle pour comprendre un résultat particulier, ce modèle peut générer une variété de scénarios après un choc de type COVID. En outre, nous étudions également l’efficacité de plusieurs politiques, notamment la très controversée “monnaie hélicoptère”, pour éviter l’effondrement économique. Nous insistons donc sur l’importance des ABMs comme des “générateurs de scénarios” polyvalents, pour produire des résultats difficiles à prévoir en raison de la complexité intrinsèque de la dynamique macro-économique.
Published: 2020

24. Biased measures for random constraint satisfaction problems: larger interaction range and asymptotic expansion

Author: Guilhem Semerjian, Louise Budzynski, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: Statistics and Probability, FOS: Computer and information sciences, Discrete Mathematics (cs.DM), FOS: Physical sciences, 0102 computer and information sciences, [INFO.INFO-DM]Computer Science [cs]/Discrete Mathematics [cs.DM], 01 natural sciences, Measure (mathematics), Combinatorics, 0103 physical sciences, FOS: Mathematics, Limit (mathematics), [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], 010306 general physics, Constraint satisfaction problem, ComputingMilieux_MISCELLANEOUS, Physics, Random graph, Probability (math.PR), Statistical and Nonlinear Physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], 010201 computation theory & mathematics, Statistics, Probability and Uncertainty, Constant (mathematics), Asymptotic expansion, Mathematics - Probability, Interaction range, Computer Science - Discrete Mathematics
Abstract: We investigate the clustering transition undergone by an exemplary random constraint satisfaction problem, the bicoloring of $k$-uniform random hypergraphs, when its solutions are weighted non-uniformly, with a soft interaction between variables belonging to distinct hyperedges. We show that the threshold $\alpha_{\rm d}(k)$ for the transition can be further increased with respect to a restricted interaction within the hyperedges, and perform an asymptotic expansion of $\alpha_{\rm d}(k)$ in the large $k$ limit. We find that $\alpha_{\rm d}(k) = \frac{2^{k-1}}{k}(\ln k + \ln \ln k + \gamma_{\rm d} + o(1))$, where the constant $\gamma_{\rm d}$ is strictly larger than for the uniform measure over solutions., Comment: 33 pages, 11 figures, minor corrections
Published: 2020

25. Searching for the Gardner transition in glassy glycerol

Author: Pierfrancesco Urbani, Giulio Biroli, Samuel Albert, R. Tourbot, François Ladieu, Service de physique de l'état condensé (SPEC - UMR3680), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), The Simons Foundation (#454935), ANR-10-LABX-0039,PALM,Physics: Atoms, Light, Matter(2010), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris)
Subjects: Physics, Random field, Condensed matter physics, Transition temperature, FOS: Physical sciences, General Physics and Astronomy, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 01 natural sciences, Condensed Matter::Disordered Systems and Neural Networks, Amorphous solid, Magnetic field, Condensed Matter::Soft Condensed Matter, Dipole, Phase (matter), 0103 physical sciences, Orders of magnitude (data), [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], 010306 general physics, Glass transition
Abstract: We search for a Gardner transition in glassy glycerol, a standard molecular glass, measuring the third harmonics cubic susceptibility $\chi_3^{(3)}$ from slightly below the usual glass transition temperature down to $10K$. According to the mean field picture, if local motion within the glass were becoming highly correlated due to the emergence of a Gardner phase then $\chi_3^{(3)}$, which is analogous to the dynamical spin-glass susceptibility, should increase and diverge at the Gardner transition temperature $T_G$. We find instead that upon cooling $| \chi_3^{(3)} |$ decreases by several orders of magnitude and becomes roughly constant in the regime $100K-10K$. We rationalize our findings by assuming that the low temperature physics is described by localized excitations weakly interacting via a spin-glass dipolar pairwise interaction in a random magnetic field. Our quantitative estimations show that the spin-glass interaction is twenty to fifty times smaller than the local random field contribution, thus rationalizing the absence of the spin-glass Gardner phase. This hints at the fact that a Gardner phase may be suppressed in standard molecular glasses, but it also suggests ways to favor its existence in other amorphous solids and by changing the preparation protocol., Comment: 9 pages, 5 figures
Published: 2020

26. Barrières algorithmiques dans les problèmes aléatoires de satisfaction de contraintes

Author: Budzynski, Louise, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Systèmes Désordonnés et Applications, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres, Guilhem Semerjian, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris)
Subjects: Random, [PHYS.PHYS]Physics [physics]/Physics [physics], Constraint satisfaction problems, Algorithmic barriers, Barrières algorithmiques, Problèmes de satisfaction de contraintes, Aléatoire
Abstract: The typical complexity of Constraint Satisfaction Problems (CSP) can be studied using random ensembles of instances. One observes threshold phenomena when the density of constraints increases, in particular a clustering phase transition at which typical solutions shatter into disconnected components. In this PhD, we introduce a bias that breaks the uniformity among solutions of a given instance of CSP, and look at the evolution of the clustering threshold under this bias, focusing on the bicoloring of k-uniform random hypergraphs. For small values of k, we show that this bias can delay the clustering transition to higher densities of constraints, and that it has a positive impact on the performances of Simulated Annealing algorithm to find a solution for a given instance of the bicoloring problem. In the large k limit, we compute the asymptotic expansion of the clustering threshold for the uniform and the biased measure, and characterize the gain obtained with our implementation of the bias.; La complexité typique des Problèmes de Satisfaction de Contraintes (CSP) peut être étudiée à l'aide d'ensembles aléatoires de contraintes. On observe un phénomène de seuil quand la densité de contraintes augmente. En particulier à la transition de clustering, l'ensemble des solutions typiques se fracture en groupes de solutions séparés les uns des autres. Dans cette thèse nous introduisons un biais qui brise l'uniformité entre les solutions d'une instance de CSP, et nous étudions son effet sur la valeur du seuil de clustering. Nous étudions en particulier le problème de bicoloriage de k-hypergraphes. Pour de petites valeurs de k, nous montrons que ce biais peut augmenter la valeur du seuil clustering, et que cela a un effet positif sur les performances de l'algorithme de Simulated Annealing pour la recherche de solutions d'une instance du problème de bicoloriage. Dans la limite où k tend vers l'infini, nous calculons le développement asymptotique du seuil de clustering pour la mesure uniforme et pour une mesure biaisée. Nous évaluons le gain obtenu avec cette implémentation du biais.
Published: 2020

27. Glasses and aging: A Statistical Mechanics Perspective

Author: Arceri, Francesco, Landes, Fran��ois P., Berthier, Ludovic, Biroli, Giulio, Department of Physics, University of Oregon, Université Paris-Sud - Paris 11 - Faculté des Sciences (UP11 UFR Sciences), Université Paris-Sud - Paris 11 (UP11), TAckling the Underspecified (TAU), Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Laboratoire de Recherche en Informatique (LRI), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS)-CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Recherche en Informatique (LRI), CentraleSupélec-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Laboratoire Charles Coulomb (L2C), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, U.K, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), We thank all the collaborators who worked with us on glass physics. This work was supported by a grant from the Simons Foundation (Grant No. 454933, L. B., Grant No. 454935, G. B.), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Condensed Matter::Soft Condensed Matter, Statistical Mechanics (cond-mat.stat-mech), Soft Condensed Matter (cond-mat.soft), FOS: Physical sciences, Disordered Systems and Neural Networks (cond-mat.dis-nn), [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Soft Condensed Matter, Condensed Matter::Disordered Systems and Neural Networks, [PHYS.COND.CM-SCM]Physics [physics]/Condensed Matter [cond-mat]/Soft Condensed Matter [cond-mat.soft], Condensed Matter - Statistical Mechanics
Abstract: We review the field of the glass transition, glassy dynamics and aging from a statistical mechanics perspective. We give a brief introduction to the subject and explain the main phenomenology encountered in glassy systems, with a particular emphasis on spatially heterogeneous dynamics. We review the main theoretical approaches currently available to account for these glassy phenomena, including recent developments regarding mean-field theory of liquids and glasses, novel computational tools, and connections to the jamming transition. Finally, the physics of aging and off-equilibrium dynamics exhibited by glassy materials is discussed., 50 pages, 24 figs. This is an updated version of a chapter initially written in 2009 for the Encyclopedia of Complexity and Systems Science (Springer). arXiv admin note: text overlap with arXiv:1011.2578
Published: 2020

28. Random assignment problems on ${2d}$ manifolds

Author: Matteo d'Achille, Emanuele Caglioti, Gabriele Sicuro, Dario Benedetto, Sergio Caracciolo, Andrea Sportiello, Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome] (UNIROMA), Università degli Studi di Milano = University of Milan (UNIMI), Istituto Nazionale di Fisica Nucleare, Sezione di Milano (INFN), Istituto Nazionale di Fisica Nucleare (INFN), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Centre interdisciplinaire de recherche en biologie (CIRB), Labex MemoLife, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Collège de France (CdF (institution))-Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI Paris), Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Université de Versailles Saint-Quentin-en-Yvelines - UFR Sciences de la santé Simone Veil (UVSQ Santé), Université de Versailles Saint-Quentin-en-Yvelines (UVSQ), Laboratoire de Mathématiques d'Orsay (LMO), Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), King‘s College London, Université Paris 13 (UP13), Centre National de la Recherche Scientifique (CNRS), ANR-18-CE40-0033,DIMERS,Dimères : de la combinatoire à la mécanique quantique(2018), Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome], Università degli Studi di Milano [Milano] (UNIMI), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS Paris), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI Paris), Université Paris sciences et lettres (PSL)-Collège de France (CdF (institution))-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Collège de France (CdF (institution))-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Sportiello, Andrea, and Dimères : de la combinatoire à la mécanique quantique - - DIMERS2018 - ANR-18-CE40-0033 - AAPG2018 - VALID
Subjects: [MATH.MATH-PR] Mathematics [math]/Probability [math.PR], random optimization problems, FOS: Physical sciences, 01 natural sciences, Omega, Assignment, Combinatorics, [PHYS.COND.CM-SM] Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], finite-size corrections, Linearization, 0103 physical sciences, FOS: Mathematics, Disorder, matching, assignment, optimal transportation, disorde, 0101 mathematics, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Mathematical Physics, Mathematics, Operator (physics), Probability (math.PR), 010102 general mathematics, Spectrum (functional analysis), Order (ring theory), Statistical and Nonlinear Physics, Mathematical Physics (math-ph), Disordered Systems and Neural Networks (cond-mat.dis-nn), disorder, Condensed Matter - Disordered Systems and Neural Networks, Manifold, [MATH.MATH-PR]Mathematics [math]/Probability [math.PR], Constant (mathematics), Unit (ring theory), Mathematics - Probability
Abstract: We consider the assignment problem between two sets of $N$ random points on a smooth, two-dimensional manifold $\Omega$ of unit area. It is known that the average cost scales as $E_{\Omega}(N)\sim\frac{1}{2\pi}\ln N$ with a correction that is at most of order $\sqrt{\ln N\ln\ln N}$. In this paper, we show that, within the linearization approximation of the field-theoretical formulation of the problem, the first $\Omega$-dependent correction is on the constant term, and can be exactly computed from the spectrum of the Laplace--Beltrami operator on $\Omega$. We perform the explicit calculation of this constant for various families of surfaces, and compare our predictions with extensive numerics., Comment: 34 pages, 7 figures
Published: 2020

29. Role of fluctuations in the yielding transition of two-dimensional glasses

Author: Gilles Tarjus, Misaki Ozawa, Ludovic Berthier, Giulio Biroli, Laboratoire Charles Coulomb (L2C), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de Physique Théorique de la Matière Condensée (LPTMC), Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire des colloïdes, verres et nanomatériaux (LCVN), Université Montpellier 2 - Sciences et Techniques (UM2)-Centre National de la Recherche Scientifique (CNRS), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), and Centre National de la Recherche Scientifique (CNRS)-Université Pierre et Marie Curie - Paris 6 (UPMC)
Subjects: [PHYS]Physics [physics], Condensed Matter - Materials Science, Yield (engineering), Materials science, Condensed matter physics, Materials Science (cond-mat.mtrl-sci), FOS: Physical sciences, Non-equilibrium thermodynamics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 01 natural sciences, Condensed Matter::Disordered Systems and Neural Networks, 010305 fluids & plasmas, Discontinuous transition, Brittleness, Critical point (thermodynamics), 0103 physical sciences, Thermodynamic limit, [PHYS.COND.CM-MS]Physics [physics]/Condensed Matter [cond-mat]/Materials Science [cond-mat.mtrl-sci], [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], Zero temperature, 010306 general physics, ComputingMilieux_MISCELLANEOUS
Abstract: We numerically study yielding in two-dimensional glasses which are generated with a very wide range of stabilities by swap Monte-Carlo simulations and then slowly deformed at zero temperature. We provide strong numerical evidence that stable glasses yield via a nonequilibrium discontinuous transition in the thermodynamic limit. A critical point separates this brittle yielding from the ductile one observed in less stable glasses. We find that two-dimensional glasses yield similarly to their three-dimensional counterparts but display larger sample-to-sample disorder-induced fluctuations, stronger finite-size effects, and rougher spatial wandering of the observed shear bands. These findings strongly constrain effective theories of yielding., 11 pages, 10 figures
Published: 2020

30. Depletion of Two-Level Systems in Ultrastable Computer-Generated Glasses

Author: Francesco Zamponi, Camille Scalliet, D. Khomenko, Ludovic Berthier, David R. Reichman, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Columbia University [New York], Laboratoire Charles Coulomb (L2C), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Department of Applied Mathematics and Theoretical Physics [Cambridge] (DAMTP), Faculty of mathematics Centre for Mathematical Sciences [Cambridge] (CMS), University of Cambridge [UK] (CAM)-University of Cambridge [UK] (CAM), University of Cambridge [UK] (CAM), Department of Chemistry [New York], Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: Condensed Matter - Materials Science, Materials science, Statistical Mechanics (cond-mat.stat-mech), Condensed matter physics, Monte Carlo method, Materials Science (cond-mat.mtrl-sci), FOS: Physical sciences, General Physics and Astronomy, Energy landscape, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, 01 natural sciences, Amorphous solid, Delocalized electron, 0103 physical sciences, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Quantum tunnelling, Condensed Matter - Statistical Mechanics
Abstract: Amorphous solids exhibit quasi-universal low-temperature anomalies whose origin has been ascribed to localized tunneling defects. Using an advanced Monte Carlo procedure, we create {\it in silico} glasses spanning from hyperquenched to ultrastable glasses. Using a multidimensional path-finding protocol, we locate tunneling defects with energy splittings smaller than $k_{B}T_Q$, with $T_Q$ the temperature below which quantum effects are relevant ($T_Q \approx 1 \,$K in most experiments). We find that as the stability of a glass increases, its energy landscape as well as the manner in which it is probed tend to deplete the density of tunneling defects, as observed in recent experiments. We explore the real-space nature of tunneling defects, and find that they are mostly localized to a few atoms, but are occasionally dramatically delocalized., 6 pages, 4 figures + Supplementary Material
Published: 2020

31. Aligning biological sequences by exploiting residue conservation and coevolution

Author: Anna Paola Muntoni, Martin Weigt, Francesco Zamponi, Andrea Pagnani, Biologie Computationnelle et Quantitative = Laboratory of Computational and Quantitative Biology (LCQB), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de Biologie Paris Seine (IBPS), Sorbonne Université (SU)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Computer science, Sequence analysis, FOS: Physical sciences, Sequence alignment, Biomolecular structure, Computational biology, 01 natural sciences, Quantitative Biology - Quantitative Methods, 010305 fluids & plasmas, Evolution, Molecular, 03 medical and health sciences, chemistry.chemical_compound, Protein structure, 0103 physical sciences, Physics - Biological Physics, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Protein secondary structure, ComputingMilieux_MISCELLANEOUS, Quantitative Methods (q-bio.QM), Coevolution, Conserved Sequence, 030304 developmental biology, 0303 health sciences, Models, Genetic, RNA, Biomolecules (q-bio.BM), Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Structure and function, chemistry, Quantitative Biology - Biomolecules, Biological Physics (physics.bio-ph), FOS: Biological sciences, Simulated data, Computational problem, DNA
Abstract: Sequences of nucleotides (for DNA and RNA) or amino acids (for proteins) are central objects in biology. Among the most important computational problems is that of sequence alignment, i.e. arranging sequences from different organisms in such a way to identify similar regions, to detect evolutionary relationships between sequences, and to predict biomolecular structure and function. This is typically addressed through profile models, which capture position-specificities like conservation in sequences, but assume an independent evolution of different positions. Over the last years, it has been well established that coevolution of different amino-acid positions is essential for maintaining three-dimensional structure and function. Modeling approaches based on inverse statistical physics can catch the coevolution signal in sequence ensembles; and they are now widely used in predicting protein structure, protein-protein interactions, and mutational landscapes. Here, we present DCAlign, an efficient alignment algorithm based on an approximate message-passing strategy, which is able to overcome the limitations of profile models, to include coevolution among positions in a general way, and to be therefore universally applicable to protein- and RNA-sequence alignment without the need of using complementary structural information. The potential of DCAlign is carefully explored using well-controlled simulated data, as well as real protein and RNA sequences., 20 pages, 11 figures + Supplementary Information
Published: 2020

32. Interplay between percolation and glassiness in the random Lorentz gas

Author: Francesco Zamponi, Yi Hu, Harukuni Ikeda, Grzegorz Szamel, Eric I. Corwin, Patrick Charbonneau, Giulio Biroli, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: Physics, Toy model, Statistical Mechanics (cond-mat.stat-mech), Lorentz transformation, FOS: Physical sciences, Order (ring theory), 01 natural sciences, Condensed Matter::Disordered Systems and Neural Networks, 010305 fluids & plasmas, Minimal model, Condensed Matter::Soft Condensed Matter, symbols.namesake, Percolation, 0103 physical sciences, symbols, Particle, Statistical physics, Limit (mathematics), [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Glass transition, ComputingMilieux_MISCELLANEOUS, Condensed Matter - Statistical Mechanics
Abstract: The random Lorentz gas (RLG) is a minimal model of transport in heterogeneous media. It also models the dynamics of a tracer in a glassy system. These two perspectives, however, are fundamentally inconsistent. Arrest in the former is related to percolation, and hence continuous, while glass-like arrest is discontinuous. In order to clarify the interplay between percolation and glassiness in the RLG, we consider its exact solution in the infinite-dimensional $d\rightarrow\infty$ limit, as well as numerics in $d=2\ldots 20$. We find that the mean field solutions of the RLG and glasses fall in the same universality class, and that instantonic corrections related to rare cage escapes destroy the glass transition in finite dimensions. This advance suggests that the RLG can be used as a toy model to develop a first-principle description of hopping in structural glasses., 10 pages, 5 figures
Published: 2020

33. Numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids

Author: Alessandro Manacorda, Grégory Schehr, Francesco Zamponi, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Discretization, Iterative method, Physics [G04] [Physical, chemical, mathematical & earth Sciences], FOS: Physical sciences, General Physics and Astronomy, Condensed Matter - Soft Condensed Matter, 01 natural sciences, 010305 fluids & plasmas, 0103 physical sciences, Limit (mathematics), [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], Physical and Theoretical Chemistry, 010306 general physics, ComputingMilieux_MISCELLANEOUS, Condensed Matter - Statistical Mechanics, Physics, Statistical Mechanics (cond-mat.stat-mech), Disordered Systems and Neural Networks (cond-mat.dis-nn), Function (mathematics), Hard spheres, Condensed Matter - Disordered Systems and Neural Networks, Mean squared displacement, Classical mechanics, Physique [G04] [Physique, chimie, mathématiques & sciences de la terre], Kinetic theory of gases, Soft Condensed Matter (cond-mat.soft), SPHERES
Abstract: We present a numerical solution of the dynamical mean field theory of infinite-dimensional equilibrium liquids established in [Phys. Rev. Lett. 116, 015902 (2016)]. For soft sphere interactions, we obtain the numerical solution by an iterative algorithm and a straightforward discretization of time. We also discuss the case of hard spheres, for which we first derive analytically the dynamical mean field theory as a non-trivial limit of the soft sphere one. We present numerical results for the memory function and the mean square displacement. Our results reproduce and extend kinetic theory in the dilute or short-time limit, while they also describe dynamical arrest towards the glass phase in the dense strongly-interacting regime., 27 pages, 6 figures
Published: 2020

34. Jamming with Tunable Roughness

Author: Francesco Zamponi, Carolina Brito, Matthieu Wyart, Harukuni Ikeda, Graduate School of Arts and Sciences, The University of Tokyo, Universidade Federal do Rio Grande do Sul [Porto Alegre] (UFRGS), Instituto de Fisica [Porto Alegre], Institute for Theoretical Physics [Lausanne], Ecole Polytechnique Fédérale de Lausanne (EPFL), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: FOS: Physical sciences, General Physics and Astronomy, Jamming, Rugosidade de superfície, Surface finish, Condensed Matter - Soft Condensed Matter, 01 natural sciences, Interferencia, Rigidity (electromagnetism), Transition point, 0103 physical sciences, Surface roughness, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Contact number, Condensed Matter - Statistical Mechanics, Physics, density, Statistical Mechanics (cond-mat.stat-mech), Mathematical analysis, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Ellipsoid, rigidity, Rough surface, Soft Condensed Matter (cond-mat.soft), mechanics
Abstract: We introduce a new model to study the effect of surface roughness on the jamming transition. By performing numerical simulations, we show that for a smooth surface, the jamming transition density and the contact number at the transition point both increase upon increasing asphericity, as for ellipsoids and spherocylinders. Conversely, for a rough surface, both quantities decrease, in quantitative agreement with the behavior of frictional particles. Furthermore, in the limit corresponding to the Coulomb friction law, the model satisfies a generalized isostaticity criterion proposed in previous studies. We introduce a counting argument that justifies this criterion and interprets it geometrically. Finally, we propose a simple theory to predict the contact number at finite friction from the knowledge of the force distribution in the infinite friction limit., 6 pages, 6 figures
Published: 2020

35. Sparse generative modeling via parameter-reduction of Boltzmann machines: application to protein-sequence families

Author: Martin Weigt, Kai Shimagaki, Francesco Zamponi, Anna Paola Muntoni, Pierre Barrat-Charlaix, Biologie Computationnelle et Quantitative = Laboratory of Computational and Quantitative Biology (LCQB), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Institut de Biologie Paris Seine (IBPS), Sorbonne Université (SU)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS)-Institut National de la Santé et de la Recherche Médicale (INSERM)-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, Computer science, Structure (category theory), FOS: Physical sciences, Overfitting, 01 natural sciences, Machine Learning (cs.LG), 03 medical and health sciences, Protein sequencing, Critical point (set theory), 0103 physical sciences, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Condensed Matter - Statistical Mechanics, 030304 developmental biology, 0303 health sciences, Decimation, Statistical Mechanics (cond-mat.stat-mech), Noise (signal processing), Statistical model, Biomolecules (q-bio.BM), Quantitative Biology - Biomolecules, FOS: Biological sciences, Pairwise comparison, Algorithm
Abstract: Boltzmann machines (BM) are widely used as generative models. For example, pairwise Potts models (PM), which are instances of the BM class, provide accurate statistical models of families of evolutionarily related protein sequences. Their parameters are the local fields, which describe site-specific patterns of amino-acid conservation, and the two-site couplings, which mirror the coevolution between pairs of sites. This coevolution reflects structural and functional constraints acting on protein sequences during evolution. The most conservative choice to describe the coevolution signal is to include all possible two-site couplings into the PM. This choice, typical of what is known as Direct Coupling Analysis, has been successful for predicting residue contacts in the three-dimensional structure, mutational effects, and in generating new functional sequences. However, the resulting PM suffers from important over-fitting effects: many couplings are small, noisy and hardly interpretable; the PM is close to a critical point, meaning that it is highly sensitive to small parameter perturbations. In this work, we introduce a general parameter-reduction procedure for BMs, via a controlled iterative decimation of the less statistically significant couplings, identified by an information-based criterion that selects either weak or statistically unsupported couplings. For several protein families, our procedure allows one to remove more than $90\%$ of the PM couplings, while preserving the predictive and generative properties of the original dense PM, and the resulting model is far away from criticality, hence more robust to noise., Comment: 7 pages, 5 figures, plus Appendix
Published: 2020
Full Text: View/download PDF

36. Modelling the influence of data structure on learning in neural networks: the hidden manifold model

Author: Sebastian Goldt, Florent Krzakala, Lenka Zdeborová, Marc Mézard, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), This research was supported in part by the National Science Foundation under Grant No. NSF PHY-1748958, 'Chaire de recherche sur les modeles et sciences des donnees', Fondation CFM pour la Recherche-ENS, ANR-17-CE23-0023,PAIL,Diagramme de Phase et Algorithme pour l'inference et l'apprentissage(2017), European Project: 714608,SMILE, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL
Subjects: FOS: Computer and information sciences, Computer Science - Machine Learning, Computer science, QC1-999, FOS: Physical sciences, General Physics and Astronomy, Machine Learning (stat.ML), 01 natural sciences, Machine Learning (cs.LG), 010305 fluids & plasmas, law.invention, Statistics - Machine Learning, law, 0103 physical sciences, 010306 general physics, Condensed Matter - Statistical Mechanics, [PHYS]Physics [physics], Statistical Mechanics (cond-mat.stat-mech), Artificial neural network, business.industry, Physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Data structure, Settore FIS/07 - Fisica Applicata(Beni Culturali, Ambientali, Biol.e Medicin), Deep neural networks, Artificial intelligence, business, Manifold (fluid mechanics)
Abstract: Understanding the reasons for the success of deep neural networks trained using stochastic gradient-based methods is a key open problem for the nascent theory of deep learning. The types of data where these networks are most successful, such as images or sequences of speech, are characterized by intricate correlations. Yet, most theoretical work on neural networks does not explicitly model training data or assumes that elements of each data sample are drawn independently from some factorized probability distribution. These approaches are, thus, by construction blind to the correlation structure of real-world datasets and their impact on learning in neural networks. Here, we introduce a generative model for structured datasets that we call the hidden manifold model. The idea is to construct high-dimensional inputs that lie on a lower-dimensional manifold, with labels that depend only on their position within this manifold, akin to a single-layer decoder or generator in a generative adversarial network. We demonstrate that learning of the hidden manifold model is amenable to an analytical treatment by proving a “Gaussian equivalence property” (GEP), and we use the GEP to show how the dynamics of two-layer neural networks trained using one-pass stochastic gradient descent is captured by a set of integro-differential equations that track the performance of the network at all times. This approach permits us to analyze in detail how a neural network learns functions of increasing complexity during training, how its performance depends on its size, and how it is impacted by parameters such as the learning rate or the dimension of the hidden manifold.
Published: 2020

37. The role of regularization in classification of high-dimensional noisy Gaussian mixture

Author: Mignacco, Francesca, Krzakala, Florent, Lu, Yue, Zdeborová, Lenka, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Harvard University, PNRIA, ANR-17-CE23-0023,PAIL,Diagramme de Phase et Algorithme pour l'inference et l'apprentissage(2017), ANR-19-P3IA-0001,PRAIRIE,PaRis Artificial Intelligence Research InstitutE(2019), European Project: 714608,SMILE, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Harvard University [Cambridge], Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris)
Subjects: [PHYS]Physics [physics], FOS: Computer and information sciences, Computer Science - Machine Learning, FOS: Physical sciences, Mathematics - Statistics Theory, Machine Learning (stat.ML), Disordered Systems and Neural Networks (cond-mat.dis-nn), Statistics Theory (math.ST), Condensed Matter - Disordered Systems and Neural Networks, Machine Learning (cs.LG), Machine Learning, Statistics - Machine Learning, Statistics Theory, FOS: Mathematics, Disordered Systems and Neural Networks
Abstract: We consider a high-dimensional mixture of two Gaussians in the noisy regime where even an oracle knowing the centers of the clusters misclassifies a small but finite fraction of the points. We provide a rigorous analysis of the generalization error of regularized convex classifiers, including ridge, hinge and logistic regression, in the high-dimensional limit where the number $n$ of samples and their dimension $d$ go to infinity while their ratio is fixed to $\alpha= n/d$. We discuss surprising effects of the regularization that in some cases allows to reach the Bayes-optimal performances. We also illustrate the interpolation peak at low regularization, and analyze the role of the respective sizes of the two clusters., Comment: 8 pages + appendix, 6 figures
Published: 2020
Full Text: View/download PDF

38. Triple descent and the two kinds of overfitting: Where & why do they appear?

Author: D'Ascoli, Stéphane, Sagun, Levent, Biroli, Giulio, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Facebook AI Research [Paris] (FAIR), Facebook, ANR-19-P3IA-0001,PRAIRIE,PaRis Artificial Intelligence Research InstitutE(2019), Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: [INFO]Computer Science [cs]
Abstract: International audience; A recent line of research has highlighted the existence of a "double descent" phenomenon in deep learning, whereby increasing the number of training examples $N$ causes the generalization error of neural networks to peak when $N$ is of the same order as the number of parameters $P$. In earlier works, a similar phenomenon was shown to exist in simpler models such as linear regression, where the peak instead occurs when $N$ is equal to the input dimension $D$. Since both peaks coincide with the interpolation threshold, they are often conflated in the litterature. In this paper, we show that despite their apparent similarity, these two scenarios are inherently different. In fact, both peaks can co-exist when neural networks are applied to noisy regression tasks. The relative size of the peaks is then governed by the degree of nonlinearity of the activation function. Building on recent developments in the analysis of random feature models, we provide a theoretical ground for this sample-wise triple descent. As shown previously, the nonlinear peak at $N\!=\!P$ is a true divergence caused by the extreme sensitivity of the output function to both the noise corrupting the labels and the initialization of the random features (or the weights in neural networks). This peak survives in the absence of noise, but can be suppressed by regularization. In contrast, the linear peak at $N\!=\!D$ is solely due to overfitting the noise in the labels, and forms earlier during training. We show that this peak is implicitly regularized by the nonlinearity, which is why it only becomes salient at high noise and is weakly affected by explicit regularization. Throughout the paper, we compare analytical results obtained in the random feature model with the outcomes of numerical experiments involving deep neural networks.
Published: 2020

39. Dynamical mean-field theory and aging dynamics

Author: Chiara Cammarota, Ada Altieri, Giulio Biroli, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), King‘s College London, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)
Subjects: Statistics and Probability, Replica method, Degrees of freedom (physics and chemistry), Phase (waves), General Physics and Astronomy, FOS: Physical sciences, 01 natural sciences, 010305 fluids & plasmas, Dynamical mean field theory, 0103 physical sciences, Thermal, Statistical physics, Symmetry breaking, 010306 general physics, Mathematical Physics, Condensed Matter - Statistical Mechanics, Physics, [PHYS]Physics [physics], Aging dynamics, Disordered systems, Dynamical mean-field formalism, Basis (linear algebra), Statistical Mechanics (cond-mat.stat-mech), Replica, Dynamics (mechanics), Statistical and Nonlinear Physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Modeling and Simulation
Abstract: Dynamical Mean-Field Theory (DMFT) replaces the many-body dynamical problem with one for a single degree of freedom in a thermal bath whose features are determined self-consistently. By focusing on models with soft disordered $p$-spin interactions, we show how to incorporate the mean-field theory of aging within dynamical mean-field theory. We study cases with only one slow time-scale, corresponding statically to the one-step replica symmetry breaking (1RSB) phase, and cases with an infinite number of slow time-scales, corresponding statically to the full replica symmetry breaking (FRSB) phase. For the former, we show that the effective temperature of the slow degrees of freedom is fixed by requiring critical dynamical behavior on short time-scales, i.e. marginality. For the latter, we find that aging on an infinite number of slow time-scales is governed by a stochastic equation where the clock for dynamical evolution is fixed by the change of effective temperature, hence obtaining a dynamical derivation of the stochastic equation at the basis of the FRSB phase. Our results extend the realm of the mean-field theory of aging to all situations where DMFT holds., 28 pages, 3 figures
Published: 2020

40. An analytic theory of shallow networks dynamics for hinge loss classification

Author: Pellegrini, Franco, Biroli, Giulio, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), Systèmes Désordonnés et Applications, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), ANR-19-P3IA-0001,PRAIRIE,PaRis Artificial Intelligence Research InstitutE(2019), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris)
Subjects: [INFO]Computer Science [cs]
Abstract: 16 pages, 6 figures; International audience; Neural networks have been shown to perform incredibly well in classification tasks over structured high-dimensional datasets. However, the learning dynamics of such networks is still poorly understood. In this paper we study in detail the training dynamics of a simple type of neural network: a single hidden layer trained to perform a classification task. We show that in a suitable mean-field limit this case maps to a single-node learning problem with a time-dependent dataset determined self-consistently from the average nodes population. We specialize our theory to the prototypical case of a linearly separable dataset and a linear hinge loss, for which the dynamics can be explicitly solved. This allow us to address in a simple setting several phenomena appearing in modern networks such as slowing down of training dynamics, crossover between rich and lazy learning, and overfitting. Finally, we asses the limitations of mean-field theory by studying the case of large but finite number of nodes and of training samples.
Published: 2020

41. How to iron out rough landscapes and get optimal performances: Averaged gradient descent and its application to tensor PCA

Author: Giulio Biroli, Federico Ricci-Tersenghi, Chiara Cammarota, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), King‘s College London, Physics Department,Rome University 'LaSapienza' (Physics Department,Rome University 'LaSapienza'), Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome], ANR-19-P3IA-0001,PRAIRIE,PaRis Artificial Intelligence Research InstitutE(2019), Laboratoire de physique de l'ENS - ENS Paris (LPENS), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)
Subjects: FOS: Computer and information sciences, Statistics and Probability, tensor PCA, Computer Science - Machine Learning, FOS: Physical sciences, General Physics and Astronomy, Machine Learning (stat.ML), 02 engineering and technology, Space (mathematics), 01 natural sciences, Machine Learning (cs.LG), Statistics - Machine Learning, 0103 physical sciences, 0202 electrical engineering, electronic engineering, information engineering, averaged gradient descent, gradient descent, [INFO]Computer Science [cs], Point (geometry), Tensor, 010306 general physics, Condensed Matter - Statistical Mechanics, Mathematical Physics, Mathematics, Statistical Mechanics (cond-mat.stat-mech), Message passing, 020206 networking & telecommunications, Statistical and Nonlinear Physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Function (mathematics), Condensed Matter - Disordered Systems and Neural Networks, Noise, Data point, Modeling and Simulation, Gradient descent, Algorithm
Abstract: In many high-dimensional estimation problems the main task consists in minimizing a cost function, which is often strongly non-convex when scanned in the space of parameters to be estimated. A standard solution to flatten the corresponding rough landscape consists in summing the losses associated to different data points and obtain a smoother empirical risk. Here we propose a complementary method that works for a single data point. The main idea is that a large amount of the roughness is uncorrelated in different parts of the landscape. One can then substantially reduce the noise by evaluating an empirical average of the gradient obtained as a sum over many random independent positions in the space of parameters to be optimized. We present an algorithm, called Averaged Gradient Descent, based on this idea and we apply it to tensor PCA, which is a very hard estimation problem. We show that Averaged Gradient Descent over-performs physical algorithms such as gradient descent and approximate message passing and matches the best algorithmic thresholds known so far, obtained by tensor unfolding and methods based on sum-of-squares., 23 pages, 16 figures, including Supplementary Material
Published: 2020

42. Who is Afraid of Big Bad Minima? Analysis of Gradient-Flow in a Spiked Matrix-Tensor Model

Author: Mannelli, Stefano Sarao, Biroli, Giulio, Cammarota, Chiara, Krzakala, Florent, Zdeborová, Lenka, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP), King‘s College London, ANR-17-CE23-0023,PAIL,Diagramme de Phase et Algorithme pour l'inference et l'apprentissage(2017), European Project: 714608,SMILE, Laboratoire de physique de l'ENS - ENS Paris (LPENS), Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Cité (UPCité)-Département de Physique de l'ENS-PSL, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université de Paris (UP)-Sorbonne Université (SU)-École normale supérieure - Paris (ENS Paris)
Subjects: FOS: Computer and information sciences, [PHYS]Physics [physics], Computer Science - Machine Learning, Statistics - Machine Learning, FOS: Mathematics, FOS: Physical sciences, Mathematics - Statistics Theory, Machine Learning (stat.ML), Disordered Systems and Neural Networks (cond-mat.dis-nn), Statistics Theory (math.ST), Condensed Matter - Disordered Systems and Neural Networks, Machine Learning (cs.LG)
Abstract: Gradient-based algorithms are effective for many machine learning tasks, but despite ample recent effort and some progress, it often remains unclear why they work in practice in optimising high-dimensional non-convex functions and why they find good minima instead of being trapped in spurious ones. Here we present a quantitative theory explaining this behaviour in a spiked matrix-tensor model. Our framework is based on the Kac-Rice analysis of stationary points and a closed-form analysis of gradient-flow originating from statistical physics. We show that there is a well defined region of parameters where the gradient-flow algorithm finds a good global minimum despite the presence of exponentially many spurious local minima. We show that this is achieved by surfing on saddles that have strong negative direction towards the global minima, a phenomenon that is connected to a BBP-type threshold in the Hessian describing the critical points of the landscapes., Comment: 9 pages, 4 figures + appendix. Appears in Proceedings of the Advances in Neural Information Processing Systems 2019 (NeurIPS 2019)
Published: 2020

43. Self-planting: digging holes in rough landscapes

Author: Francesco Zamponi, Marco Tarzia, Dhruv Sharma, Jean-Philippe Bouchaud, Capital Fund Management (CFM), Capital Fund Management, Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), and Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Statistics and Probability, Conjecture, Optimization problem, Statistical Mechanics (cond-mat.stat-mech), FOS: Physical sciences, Statistical and Nonlinear Physics, Class (philosophy), Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, Perceptron, 01 natural sciences, 010305 fluids & plasmas, Exponential function, Iterated function, 0103 physical sciences, Statistics, Probability and Uncertainty, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], 010306 general physics, Gradient descent, Algorithm, Condensed Matter - Statistical Mechanics, ComputingMilieux_MISCELLANEOUS, Mathematics, Simple (philosophy)
Abstract: Motivated by a potential application in economics, we investigate a simple dynamical scheme to produce planted solutions in optimization problems with continuous variables. We consider the perceptron model as a prototypical model. Starting from random input patterns and perceptron weights, we find a locally optimal assignment of weights by gradient descent; we then remove misclassified patterns (if any), and replace them by new, randomly extracted patterns. This "remove and replace" procedure is iterated until perfect classification is achieved. We call this procedure "self-planting" because the "planted" state is not pre-assigned but results from a co-evolution of weights and patterns. We find an algorithmic phase transition separating a region in which self-planting is efficiently achieved from a region in which it takes exponential time in the system size. We conjecture that this transition might exist in a broad class of similar problems., 12 pages, 6 figures; introduction and discussion of model made clearer
Published: 2019

44. Comparing dynamics: deep neural networks versus glassy systems

Author: Marco Baity-Jesi, Mario Geiger, Gérard Ben Arous, Stefano Spigler, Yann LeCun, Matthieu Wyart, Chiara Cammarota, Levent Sagun, Giulio Biroli, Department of Physics and Astronomy [Philadelphia], University of Pennsylvania [Philadelphia], Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Ecole Polytechnique Fédérale de Lausanne (EPFL), Laboratoire de Physique Théorique et Modèles Statistiques (LPTMS), Centre National de la Recherche Scientifique (CNRS)-Université Paris-Sud - Paris 11 (UP11), Institut de Mathématiques (IMA), King‘s College London, Facebook AI Research [Paris] (FAIR), Facebook, Service de Physique Théorique (SPhT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Centre National de la Recherche Scientifique (CNRS), Laboratoire de Physique Statistique de l'ENS (LPS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), University of Pennsylvania, Université Paris-Sud - Paris 11 (UP11)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS-PSL)
Subjects: Statistics and Probability, FOS: Computer and information sciences, Computer Science - Machine Learning, Computer science, FOS: Physical sciences, Machine Learning (stat.ML), 01 natural sciences, Machine learning, glassy dynamics, loss landscape, 010305 fluids & plasmas, Machine Learning (cs.LG), [STAT.ML]Statistics [stat]/Machine Learning [stat.ML], Statistics - Machine Learning, 0103 physical sciences, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], 010306 general physics, ComputingMilieux_MISCELLANEOUS, business.industry, Statistical and Nonlinear Physics, Disordered Systems and Neural Networks (cond-mat.dis-nn), Condensed Matter - Disordered Systems and Neural Networks, states, Dynamics (music), Deep neural networks, Artificial intelligence, Statistics, Probability and Uncertainty, business
Abstract: We analyze numerically the training dynamics of deep neural networks (DNN) by using methods developed in statistical physics of glassy systems. The two main issues we address are (1) the complexity of the loss landscape and of the dynamics within it, and (2) to what extent DNNs share similarities with glassy systems. Our findings, obtained for different architectures and datasets, suggest that during the training process the dynamics slows down because of an increasingly large number of flat directions. At large times, when the loss is approaching zero, the system diffuses at the bottom of the landscape. Despite some similarities with the dynamics of mean-field glassy systems, in particular, the absence of barrier crossing, we find distinctive dynamical behaviors in the two cases, showing that the statistical properties of the corresponding loss and energy landscapes are different. In contrast, when the network is under-parametrized we observe a typical glassy behavior, thus suggesting the existence of different phases depending on whether the network is under-parametrized or over-parametrized., 10 pages, 5 figures. Version accepted at ICML 2018
Published: 2019

45. Nature of excitations and defects in structural glasses

Author: Camille Scalliet, Ludovic Berthier, Francesco Zamponi, Laboratoire Charles Coulomb (L2C), Université de Montpellier (UM)-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), Centre National de la Recherche Scientifique (CNRS)-Université de Montpellier (UM), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Scalliet, Camille [0000-0002-7969-891X], Berthier, Ludovic [0000-0003-2059-702X], and Apollo - University of Cambridge Repository
Subjects: Materials science, Science, FOS: Physical sciences, General Physics and Astronomy, Jamming, 639/766/530/2804, Condensed Matter - Soft Condensed Matter, Condensed Matter::Disordered Systems and Neural Networks, 01 natural sciences, General Biochemistry, Genetics and Molecular Biology, 010305 fluids & plasmas, Delocalized electron, Molecular glasses, 0103 physical sciences, cond-mat.dis-nn, [PHYS.COND.CM-SM]Physics [physics]/Condensed Matter [cond-mat]/Statistical Mechanics [cond-mat.stat-mech], lcsh:Science, cond-mat.stat-mech, 010306 general physics, Condensed Matter - Statistical Mechanics, ComputingMilieux_MISCELLANEOUS, cond-mat.soft, Condensed Matter - Materials Science, Range (particle radiation), Multidisciplinary, Statistical Mechanics (cond-mat.stat-mech), Condensed matter physics, Glasses, article, Materials Science (cond-mat.mtrl-sci), Energy landscape, Disordered Systems and Neural Networks (cond-mat.dis-nn), General Chemistry, Condensed Matter - Disordered Systems and Neural Networks, cond-mat.mtrl-sci, 639/301/923/218, Amorphous solid, Condensed Matter::Soft Condensed Matter, Quasiparticle, Soft Condensed Matter (cond-mat.soft), lcsh:Q, Statistical physics
Abstract: Funder: L'Oréal UNESCO For Women in Science Fellowship, The nature of defects in amorphous materials, analogous to vacancies and dislocations in crystals, remains elusive. Here, we explore their nature in a three-dimensional microscopic model glass-former that describes granular, colloidal, atomic and molecular glasses by changing the temperature and density. We find that all glasses evolve in a very rough energy landscape, with a hierarchy of barrier sizes corresponding to both localized and delocalized excitations. Collective excitations dominate in the jamming regime relevant for granular and colloidal glasses. By moving gradually to larger densities describing atomic and molecular glasses, the system crosses over to a regime dominated by localized defects and relatively simpler landscapes. We quantify the energy and temperature scales associated to these defects and their evolution with density. Our results pave the way to a systematic study of low-temperature physics in a broad range of physical conditions and glassy materials.
Published: 2019

46. A jamming transition from under- to over-parametrization affects generalization in deep learning

Author: Mario Geiger, Giulio Biroli, Levent Sagun, Stéphane d'Ascoli, Matthieu Wyart, Stefano Spigler, Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), Laboratoire de Physique Statistique de l'ENS (LPS), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)
Subjects: Statistics and Probability, overparametrization, Computer science, Generalization, General Physics and Astronomy, Jamming, 01 natural sciences, 010305 fluids & plasmas, 0103 physical sciences, Statistical physics, [PHYS.COND.CM-DS-NN]Physics [physics]/Condensed Matter [cond-mat]/Disordered Systems and Neural Networks [cond-mat.dis-nn], 010306 general physics, jamming, generalization, Mathematical Physics, ComputingMilieux_MISCELLANEOUS, Artificial neural network, business.industry, Transition (fiction), Deep learning, Statistical and Nonlinear Physics, neural networks, Modeling and Simulation, Artificial intelligence, business, Parametrization
Abstract: In this paper we first recall the recent result that in deep networks a phase transition, analogous to the jamming transition of granular media, delimits the over- and under-parametrized regimes where fitting can or cannot be achieved. The analysis leading to this result support that for proper initialization and architectures, in the whole over-parametrized regime poor minima of the loss are not encountered during training, because the number of constraints that hinders the dynamics is insufficient to allow for the emergence of stable minima. Next, we study systematically how this transition affects generalization properties of the network (i.e. its predictive power). As we increase the number of parameters of a given model, starting from an under-parametrized network, we observe for gradient descent that the generalization error displays three phases: (i) initial decay, (ii) increase until the transition point?where it displays a cusp?and (iii) slow decay toward an asymptote as the network width diverges. However if early stopping is used, the cusp signaling the jamming transition disappears. Thereby we identify the region where the classical phenomenon of over-fitting takes place as the vicinity of the jamming transition, and the region where the model keeps improving with increasing the number of parameters, thus organizing previous empirical observations made in modern neural networks.
Published: 2019

47. Phase Transitions, Optimal Errors and Optimality of Message-Passing in Generalized Linear Models

Author: Barbier, Jean, Krzakala, Florent, Macris, Nicolas, Miolane, Léo, Zdeborová, Lenka, Laboratoire de Physico-Chimie Théorique (LPCT), ESPCI ParisTech-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Université Paris Diderot - Paris 7 (UPD7)-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), Ecole Polytechnique Fédérale de Lausanne (EPFL), Dynamics of Geometric Networks (DYOGENE), Département d'informatique de l'École normale supérieure (DI-ENS), École normale supérieure - Paris (ENS Paris)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria), Institut de Physique Théorique - UMR CNRS 3681 (IPHT), Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Paris-Saclay-Centre National de la Recherche Scientifique (CNRS), Horizon 2020 Research and Innovation Programme Grant Agreement 714608-SMiLe., ANR-17-CE23-0023,PAIL,Diagramme de Phase et Algorithme pour l'inference et l'apprentissage(2017), European Project: 307087,EC:FP7:ERC,ERC-2012-StG_20111012,SPARCS(2012), Ecole Superieure de Physique et de Chimie Industrielles de la Ville de Paris (ESPCI Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), Inria de Paris, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Département d'informatique - ENS Paris (DI-ENS), Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche en Informatique et en Automatique (Inria)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Institut National de Recherche en Informatique et en Automatique (Inria)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS)-Inria de Paris
Subjects: [INFO.INFO-LG]Computer Science [cs]/Machine Learning [cs.LG], [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph], [MATH.MATH-IT]Mathematics [math]/Information Theory [math.IT], [INFO.INFO-AI]Computer Science [cs]/Artificial Intelligence [cs.AI]
Abstract: 35 pages, 3 figures
Published: 2019

48. Strong anisotropy of superfluid He-4 counterflow turbulence

Author: Anna Pomyalov, Ganapati Sahoo, Victor S. L'vov, Itamar Procaccia, Luca Biferale, D. Khomenko, Department of Mathematics and Statistics, Department of Physics, Department of Physics (INFN), Istituto Nazionale di Fisica Nucleare (INFN)-Università degli Studi di Roma Tor Vergata [Roma], Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), and Weizmann Institute of Science [Rehovot, Israël]
Subjects: LIQUID HELIUM-II, FOS: Physical sciences, 02 engineering and technology, 01 natural sciences, 114 Physical sciences, Superfluidity, 0103 physical sciences, HEAT CURRENT, SPECTRA, 010306 general physics, Anisotropy, 112 Statistics and probability, ComputingMilieux_MISCELLANEOUS, Physics, Condensed Matter::Quantum Gases, Range (particle radiation), Heat current, Condensed matter physics, Settore FIS/02, Plane (geometry), Turbulence, Condensed Matter::Other, MUTUAL FRICTION, Dissipation, 021001 nanoscience & nanotechnology, Coupling (probability), STATISTICS, Condensed Matter - Other Condensed Matter, [PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other], 0210 nano-technology, Other Condensed Matter (cond-mat.other)
Abstract: We report on a combined theoretical and numerical study of counterflow turbulence in superfluid $^{4}$He in a wide range of parameters. The energy spectra of the velocity fluctuations of both the normal-fluid and superfluid components are strongly anisotropic. The angular dependence of the correlation between velocity fluctuations of the two components plays the key role. A selective energy dissipation intensifies as scales decrease, with the streamwise velocity fluctuations becoming dominant. Most of the flow energy is concentrated in a wavevector plane which is orthogonal to the direction of the counterflow. The phenomenon becomes more prominent at higher temperatures as the coupling between the components depends on the temperature and the direction with respect to the counterflow velocity., 16 pages, 11 figures
Published: 2019

49. On the critical exponent α of the 5D random-field Ising model

Author: Nicolas Sourlas, Nikolaos G. Fytas, Victor Martin-Mayor, Marco Picco, Giorgio Parisi, Coventry University (UK), Coventry University, Center for Statistical Mechanics and Complexity, INFM Roma 'La Sapienza' and Dipartimento di Fisica, Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome], Laboratoire de Physique Théorique et Hautes Energies (LPTHE), Université Pierre et Marie Curie - Paris 6 (UPMC)-Université Paris Diderot - Paris 7 (UPD7)-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7), Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), and Universidad Complutense de Madrid = Complutense University of Madrid [Madrid] (UCM)
Subjects: Statistics and Probability, Physics, [PHYS]Physics [physics], Specific heat, Física, Statistical and Nonlinear Physics, Condensed Matter - Disordered Systems and Neural Networks, 01 natural sciences, 010305 fluids & plasmas, Alpha (programming language), Random field ising model, Dimensional reduction, [PHYS.COND.CM-GEN]Physics [physics]/Condensed Matter [cond-mat]/Other [cond-mat.other], 0103 physical sciences, Ising model, Statistical physics, Statistics, Probability and Uncertainty, 010306 general physics, Critical exponent, Condensed Matter - Statistical Mechanics
Abstract: We present a complementary estimation of the critical exponent $\alpha$ of the specific heat of the 5D random-field Ising model from zero-temperature numerical simulations. Our result $\alpha = 0.12(2)$ is consistent with the estimation coming from the modified hyperscaling relation and provides additional evidence in favor of the recently proposed restoration of dimensional reduction in the random-field Ising model at $D = 5$., Comment: 11 pages, 7 figures, final version with minor corrections
Published: 2019

50. Mean-field stability map of hard-sphere glasses

Author: Ada Altieri, Francesco Zamponi, Department of Physics [Roma La Sapienza], Università degli Studi di Roma 'La Sapienza' = Sapienza University [Rome], Laboratoire de Physique Théorique de l'ENS (LPTENS), Université Pierre et Marie Curie - Paris 6 (UPMC)-Fédération de recherche du Département de physique de l'Ecole Normale Supérieure - ENS Paris (FRDPENS), École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-École normale supérieure - Paris (ENS Paris), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Centre National de la Recherche Scientifique (CNRS), Systèmes Désordonnés et Applications, Laboratoire de physique de l'ENS - ENS Paris (LPENS (UMR_8023)), Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)-École normale supérieure - Paris (ENS Paris), and Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Centre National de la Recherche Scientifique (CNRS)-Sorbonne Université (SU)-Université Paris Diderot - Paris 7 (UPD7)
Subjects: Spinodal, Materials science, Statistical Mechanics (cond-mat.stat-mech), Condensed matter physics, FOS: Physical sciences, Jamming, Disordered Systems and Neural Networks (cond-mat.dis-nn), Hard spheres, Condensed Matter - Disordered Systems and Neural Networks, Condensed Matter - Soft Condensed Matter, 01 natural sciences, 010305 fluids & plasmas, Amorphous solid, Condensed Matter::Soft Condensed Matter, Mean field theory, 0103 physical sciences, Shear stress, Soft Condensed Matter (cond-mat.soft), [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat], 010306 general physics, Glass transition, Condensed Matter - Statistical Mechanics, ComputingMilieux_MISCELLANEOUS, Phase diagram
Abstract: The response of amorphous solids to an applied shear deformation is an important problem, both in fundamental and applied research. To tackle this problem, we focus on a system of hard spheres in infinite dimensions as a solvable model for colloidal systems and granular matter. The system is prepared above the dynamical glass transition density, and we discuss the phase diagram of the resulting glass under compression, decompression, and shear strain, expanding on previous results [P. Urbani and F. Zamponi, Phys.Rev.Lett. 118, 038001 (2017)]. We show that the solid region is bounded by a "shear jamming" line, at which the solid reaches close packing, and a "shear yielding" line, at which the solid undergoes a spinodal instability towards a liquid, flowing phase. Furthermore, we characterize the evolution of these lines upon varying the glass preparation density. This work aims to provide a general overview of yielding and jamming phenomena in hard-sphere systems by a systematic exploration of the phase diagram., 9 pages, 3 figures
Published: 2019

Catalog

Books, media, physical & digital resources

See catalog results

Searchworks

Select search scope, currently: Articles Catalog books, media & more in Jio Institute collections Articles journal articles & other e-resources

Search

Search Constraints

Refine your results

Search Limiters

Topic

Publication Year Range

Language

Journal

Database

Publisher

96 results on '"Systèmes Désordonnés et Applications"'

Search Results

Catalog

Select search scope, currently: Articles

Catalog

books, media & more in Jio Institute collections

Articles

journal articles & other e-resources