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We derive, within the replica formalism, a generalisation of the Crisanti-Sommers formula to describe the large deviation function (LDF) ${\cal L}(e)$ for the speed-$N$ atypical fluctuations of the intensive ground-state energy $e$ of a generic spherical spin-glass in the presence of a random external magnetic field of variance $\Gamma$. We then analyse our exact formula for the LDF in much detail for the Replica symmetric, single step Replica Symmetry Breaking (1-RSB) and Full Replica Symmetry Breaking (FRSB) situations. Our main qualitative conclusion is that the level of RSB governing the LDF may be different from that for the typical ground state. We find that while the deepest ground-states are always controlled by a LDF of replica symmetric form, beyond a finite threshold $e\geq e_{t}$ a replica-symmetry breaking starts to be operative. These findings resolve the puzzling discrepancy between our earlier replica calculations for the $p=2$ spherical spin-glass and the rigorous results by Dembo and Zeitouni which we are able to reproduce invoking an 1-RSB pattern. Finally at an even larger critical energy $e_{c}\geq e_{t}$, acting as a "wall", the LDF diverges logarithmically, which we interpret as a change in the large deviation speed from $N$ to a faster growth. In addition, we show that in the limit $\Gamma \to 0$ the LDF takes non-trivial scaling forms (i) ${\cal L}(e) \sim G((e-e_c)/\Gamma)$ in the vicinity of the wall (ii) ${\cal L}(e) \sim \Gamma^{\eta \nu} F((e-e_{\rm typ})/\Gamma^{\nu})$ in the vicinity of the typical energy, characterised by two new exponents $\eta\geq 1$ and $\nu$ characterising universality classes. Via matching the latter allows us to formulate several conjectures concerning the regime of {\it typical fluctuations}, identified as $e-e_{\rm typ} \sim N^{-1/\eta}$ and $\Gamma \sim N^{-1/(\eta \nu)}$., Comment: 58 pages, 14 figures

This article appears as chapter 21 of Prince (2023, Understanding Deep Learning); a complete draft of the textbook is available here: http://udlbook.com. This chapter considers potential harms arising from the design and use of AI systems. These include algorithmic bias, lack of explainability, data privacy violations, militarization, fraud, and environmental concerns. The aim is not to provide advice on being more ethical. Instead, the goal is to express ideas and start conversations in key areas that have received attention in philosophy, political science, and the broader social sciences., Comment: Copyright in this Work has been licensed exclusively to The MIT Press, https://mitpress.mit.edu, which will be releasing the final version to the public in 2023. All inquiries regarding rights should be addressed to The MIT Press, Rights and Permissions Department

In this work, we study the effects of a transverse magnetic field in a Kondo lattice model with two $f$ orbitals interacting with the conduction electrons. The $f$ electrons that are present on the same site interact through Hund's coupling, while on neighboring sites they interact through intersite exchange. We consider here that part of $f$ electrons are localized (orbital 1) while another part (orbital 2) are delocalized, as it is frequent in uranium systems. Then, only electrons in the localized orbital 1 interact through exchange interaction with the neighboring ones, while electrons in orbital 2 are coupled with conduction electrons through a Kondo interaction. We obtain a solution where ferromagnetism and Kondo effect coexist for small values of an applied transverse magnetic field for $T\rightarrow0$. Increasing the transverse field, two situations can be obtained when Kondo coupling vanishes: first, a metamagnetic transition occurs just before or at the same time of the fully polarized state, and second, a metamagnetic transition occurs when the spins are already pointing out along the magnetic field., Comment: 15 pages, 7 figures

Since the seminal work of Idelsohn, O\~nate and Del-Pin (2004), the Particle Finite Element Method (PFEM) has relied on a Delaunay triangulation and the Alpha--Shape (AS) algorithm in the remeshing process. This approach guarantees a good quality of the Lagrangian mesh, but introduces a list of shortcomings that demand geometrical treatments tailored to each problem. In order to improve the remeshing process in PFEM, this work proposes the use of a Level--Set (LS) function instead of the Alpha--Shape algorithm. Since the Level--Set considers the boundary of the fluid and its interior, and not only a geometric criterion as does the Alpha--Shape, the proposed strategy (PFEM--LS) shows more robustness than the classical approach (PFEM--AS) owing to three main improvements. First, the LS function allows for a better control over the elements that are created during the fluid/fluid contact, which helps to reduce mass creation. Second, it helps to preserve the smoothness of the free surface and to reduce mass loss. Third, it allows the meshing of solitary particles that are detached from the free surface, which improves the representation of drops in PFEM. The methodology is presented and validated using free surface flow problems in 2D., Comment: 28 pages, research article

Early observations of transient explosions can provide vital clues to their progenitor origins. In this paper we present the nearby Type Iax (02cx-like) supernova (SN), SN 2020udy that was discovered within hours ($\sim$7 hr) of estimated first light. An extensive dataset of ultra-violet, optical, and near-infrared observations was obtained, covering out to $\sim$150 d after explosion. SN 2020udy peaked at -17.86$\pm$0.43 mag in the r band and evolved similarly to other 'luminous' SNe Iax, such as SNe 2005hk and 2012Z. Its well-sampled early light curve allows strict limits on companion interaction to be placed. Main-sequence companion stars with masses of 2 and 6 M$_\odot$ are ruled out at all viewing angles, while a helium-star companion is allowed from a narrow range of angles (140-180$^\circ$ away from the companion). The spectra and light curves of SN2020udy are in good agreement with those of the 'N5def' deflagration model of a near Chandrasekhar-mass carbon-oxygen white dwarf. However, as has been seen in previous studies of similar luminosity events, SN 2020udy evolves slower than the model. Broad-band linear polarisation measurements taken at and after peak are consistent with no polarisation, in agreement with the predictions of the companion-star configuration from the early light curve measurements. The host galaxy environment is low metallicity and is consistent with a young stellar population. Overall, we find the most plausible explosion scenario to be the incomplete disruption of a CO white dwarf near the Chandrasekhar-mass limit, with a helium-star companion., Comment: 18 pages, 14 figures, submitted to MNRAS

This paper deals with stability of classical Runge-Kutta collocation methods. When such methods are embedded in linearly implicit methods as developed in [12] and used in [13] for the time integration of nonlinear evolution PDEs, the stability of these methods has to be adapted to this context. For this reason, we develop in this paper several notions of stability, that we analyze. We provide sufficient conditions that can be checked algorithmically to ensure that these stability notions are fulfilled by a given Runge-Kutta collocation method. We also introduce examples and counterexamples used in [13] to highlight the necessity of these stability conditions in this context.

We show that collective multiphonon states in atomic nuclei emerge at high excitation energies when quantum fluctuations in the collective space are included beyond the independent-particle approximation. The quadrupole response of a nucleus is studied using an extension of the nuclear time-dependent density-functional theory that mixes several many-body trajectories. While a single trajectory can account for the excitation of the first collective quantum, the second and the third quanta emerge due to the interference between trajectories. The collective spectrum, found as nearly harmonic, is in excellent agreement with the experimentally observed three quanta of the isoscalar giant quadrupole resonance in $^{40}$Ca. This study offers guidance for multiphonon searches in other self-bound systems and demonstrates the resistance to internal excitation of finite Fermi liquids., Comment: 7 pages, 4 figures

In this paper, we study conformal points among the class of $\mathcal{E}$-models. The latter are $\sigma$-models formulated in terms of a current Poisson algebra, whose Lie-theoretic definition allows for a purely algebraic description of their dynamics and their 1-loop RG-flow. We use these results to formulate a simple algebraic condition on the defining data of such a model which ensures its 1-loop conformal invariance and the decoupling of its observables into two chiral Poisson algebras, describing the classical left- and right-moving fields of the theory. In the case of so-called non-degenerate $\mathcal{E}$-models, these chiral sectors form two current algebras and the model takes the form of a WZW theory once realised as a $\sigma$-model. The case of degenerate $\mathcal{E}$-models, in which a subalgebra of the current algebra is gauged, is more involved: the conformal condition yields a wider class of theories, which includes gauged WZW models but also other examples, seemingly different, which however sometimes turn out to be related to gauged WZW models based on other Lie algebras. For this class, we build non-local chiral fields of parafermionic-type as well as higher-spin local ones, forming classical $\mathcal{W}$-algebras. In particular, we find an explicit and efficient algorithm to build these local chiral fields. These results (and their potential generalisations discussed at the end of the paper) open the way for the quantisation of a large class of conformal $\mathcal{E}$-models using the standard operator formalism of two-dimensional CFT., Comment: v3: References added, 68+10 pages

This paper considers the numerical integration of semilinear evolution PDEs using the high order linearly implicit methods developped in a previous paper in the ODE setting. These methods use a collocation Runge--Kutta method as a basis, and additional variables that are updated explicitly and make the implicit part of the collocation Runge--Kutta method only linearly implicit. In this paper, we introduce several notions of stability for the underlying Runge--Kutta methods as well as for the explicit step on the additional variables necessary to fit the context of evolution PDE. We prove a main theorem about the high order of convergence of these linearly implicit methods in this PDE setting, using the stability hypotheses introduced before. We use nonlinear Schr\''odinger equations and heat equations as main examples but our results extend beyond these two classes of evolution PDEs. We illustrate our main result numerically in dimensions 1 and 2, and we compare the efficiency of the linearly implicit methods with other methods from the litterature. We also illustrate numerically the necessity of the stability conditions of our main result.

Quantum computing technologies are making steady progress. This has opened new opportunities for tackling problems whose complexity prevents their description on classical computers. A prototypical example of these complex problems are interacting quantum many-body systems: on the one hand, these systems are known to become rapidly prohibitive to describe using classical computers when their size increases. On the other hand, these systems are precisely those which are used in the laboratory to build quantum computing platforms. This arguably makes them one of the most promising early use cases of quantum computing. In this review, we explain how quantum many-body systems are used to build quantum processors, and how, in turn, current and future quantum processors can be used to describe large many-body systems of fermions such as electrons and nucleons. The review includes an introduction to analog and digital quantum devices, the mapping of Fermi systems and their Hamiltonians onto qubit registers, as well as an overview of methods to access their static and dynamical properties. We also highlight some aspects related to entanglement, and touch on the description, influence and processing of decoherence in quantum devices.

We consider the problem of finding the initial vertex (Adam) in a Barab\'asi--Albert tree process $(\mathcal{T}(n) : n \geq 1)$ at large times. More precisely, given $ \varepsilon>0$, one wants to output a subset $ \mathcal{P}_{ \varepsilon}(n)$ of vertices of $ \mathcal{T}(n)$ so that the initial vertex belongs to $ \mathcal{P}_ \varepsilon(n)$ with probability at least $1- \varepsilon$ when $n$ is large. It has been shown by Bubeck, Devroye & Lugosi, refined later by Banerjee & Huang, that one needs to output at least $ \varepsilon^{-1 + o(1)}$ and at most $\varepsilon^{-2 + o(1)}$ vertices to succeed. We prove that the exponent in the lower bound is sharp and the key idea is that Adam is either a ``large degree" vertex or is a neighbor of a ``large degree" vertex (Eve)., Comment: 11 pages, comments are welcome !

Measurements of the growth rate of structures at $z < 0.1$ with peculiar velocity surveys have the potential of testing the validity of general relativity on cosmic scales. In this work, we present growth-rate measurements from realistic simulated sets of type-Ia supernovae (SNe Ia) from the Zwicky Transient Facility (ZTF). We describe our simulation methodology, the light-curve fitting and peculiar velocity estimation. Using the maximum likelihood method, we derive constraints on $f\sigma_8$ using only ZTF SN Ia peculiar velocities. We carefully tested the method and we quantified biases due to selection effects (photometric detection, spectroscopic follow-up for typing) on several independent realizations. We simulated the equivalent of 6 years of ZTF data, and considering an unbiased spectroscopically typed sample at $z < 0.06$, we obtained unbiased estimates of $f\sigma_8$ with an average uncertainty of 19% precision. We also investigated the information gain in applying bias correction methods. Our results validate our framework which can be used on real ZTF data., Comment: 20 pages, 13 figures

In preparation for the 2023 NSAC Long Range Plan (LRP), members of the Nuclear Science community gathered to discuss the current state of, and plans for further leveraging opportunities in, QIST in NP research at the Quantum Information Science for U.S. Nuclear Physics Long Range Planning workshop, held in Santa Fe, New Mexico on January 31 - February 1, 2023. The workshop included 45 in-person participants and 53 remote attendees. The outcome of the workshop identified strategic plans and requirements for the next 5-10 years to advance quantum sensing and quantum simulations within NP, and to develop a diverse quantum-ready workforce. The plans include resolutions endorsed by the participants to address the compelling scientific opportunities at the intersections of NP and QIST. These endorsements are aligned with similar affirmations by the LRP Computational Nuclear Physics and AI/ML Workshop, the Nuclear Structure, Reactions, and Astrophysics LRP Town Hall, and the Fundamental Symmetries, Neutrons, and Neutrinos LRP Town Hall communities., Comment: A white paper for the 2023 nuclear physics long-range planning activity, emerging from the workshop "Quantum Information Science for U.S. Nuclear Physics Long Range Planning'', held in Santa Fe, New Mexico on January 31 - February 1, 2023. 26 pages with 7 figures

We introduce LLaMA, a collection of foundation language models ranging from 7B to 65B parameters. We train our models on trillions of tokens, and show that it is possible to train state-of-the-art models using publicly available datasets exclusively, without resorting to proprietary and inaccessible datasets. In particular, LLaMA-13B outperforms GPT-3 (175B) on most benchmarks, and LLaMA-65B is competitive with the best models, Chinchilla-70B and PaLM-540B. We release all our models to the research community.

This paper studies thermal transport in nanoporous silicon with a significant specific surface area. First, the equilibrium molecular dynamics approach was used to obtain the dependence of thermal conductivity on a specific surface area. Then, a modified phonon transport kinetic theory-based approach was developed to analyze thermal conductivity. Two models were used to evaluate the phonon mean free path in the porous materials. The first model approximates the dependence of the mean free path only with the specific surface area, and the second one investigates the dependence of the mean free path variation with the porosity in the peculiar case of a highly porous matrix. Both models approximate molecular dynamics data well for the smaller porosity values, while the first model fails for large porosities. The second model matches well with molecular dynamics simulations for all considered ranges of the porosities. This work illustrates that the phonon mean free path dependence with the porosity/volume fraction of composite materials is essential for describing thermal transport in systems with significant surface-to-volume fractions.

In the context of high-dimensional Gaussian linear regression for ordered variables, we study the variable selection procedure via the minimization of the penalized least-squares criterion. We focus on model selection where the penalty function depends on an unknown multiplicative constant commonly calibrated for prediction. We propose a new proper calibration of this hyperparameter to simultaneously control predictive risk and false discovery rate. We obtain non-asymptotic bounds on the False Discovery Rate with respect to the hyperparameter and we provide an algorithm to calibrate it. This algorithm is based on quantities that can typically be observed in real data applications. The algorithm is validated in an extensive simulation study and is compared with several existing variable selection procedures. Finally, we study an extension of our approach to the case in which an ordering of the variables is not available., Comment: 34 pages, 4 figures, 1 algorithm, 4 tables

The 24-hour activity cycle (24HAC) is a new paradigm for studying activity behaviors in relation to health outcomes. This approach captures the interrelatedness of the daily time spent in physical activity (PA), sedentary behavior (SB), and sleep. We illustrate and compare the use of three popular approaches, namely isotemporal substitution model (ISM), compositional data analysis (CoDA), and latent profile analysis (LPA) for modeling outcome associations with the 24HAC. We apply these approaches to assess an association with a cognitive outcome, measured by CASI item response theory (IRT) score, in a cohort of 1034 older adults (mean [range] age = 77 [65-100]; 55.8% female; 90% White) who were part of the Adult Changes in Thought (ACT) Activity Monitoring (ACT-AM) sub-study. PA and SB were assessed with thigh-worn activPAL accelerometers for 7 days. We highlight differences in assumptions between the three approaches, discuss statistical challenges, and provide guidance on interpretation and selecting an appropriate approach. ISM is easiest to apply and interpret; however, the typical ISM model assumes a linear association. CoDA specifies a non-linear association through isometric logratio transformations that are more challenging to apply and interpret. LPA can classify individuals into groups with similar time-use patterns. Inference on associations of latent profiles with health outcomes need to account for the uncertainty of the LPA classifications which is often ignored. The selection of the most appropriate method should be guided by the scientific questions of interest and the applicability of each model's assumptions. The analytic results did not suggest that less time spent on SB and more in PA was associated with better cognitive function. Further research is needed into the health implications of the distinct 24HAC patterns identified in this cohort., Comment: 51 pages, 11 tables, 8 figures

This paper investigates thermal transport in a nanocomposite system "porous silicon matrix filled with ionic liquid". First, the thermal conductivity and heat capacity of two imidazolium and one ammonium ionic liquids were evaluated using the photoacoustic approach in piezoelectric configuration and differential scanning calorimetry, respectively. Then, the thermal transport properties of the composite system "ionic liquid confined inside porous silicon matrix" were investigated with the photoacoustic approach in gas-microphone configuration. It was found that a significant enhancement of the thermal conductivity of the composite when compared to the individual components, i.e. (i) more than two times for pristine porous silicon and (ii) more than eight times for ionic liquids. These results provide new paths for innovative solutions in the field of thermal management in highly efficient energy storage devices.

The ability to execute high-fidelity operations is crucial to scaling up quantum devices to large numbers of qubits. However, signal distortions originating from non-linear components in the control lines can limit the performance of single-qubit gates. In this work, we use a measurement based on error amplification to characterize and correct the small single-qubit rotation errors originating from the non-linear scaling of the qubit drive rate with the amplitude of the programmed pulse. With our hardware, and for a 15-ns pulse, the rotation angles deviate by up to several degrees from a linear model. Using purity benchmarking, we find that control errors reach $2\times 10^{-4}$, which accounts for half of the total gate error. Using cross-entropy benchmarking, we demonstrate arbitrary-angle single-qubit gates with coherence-limited errors of $2\times 10^{-4}$ and leakage below $6\times 10^{-5}$. While the exact magnitude of these errors is specific to our setup, the presented method is applicable to any source of non-linearity. Our work shows that the non-linearity of qubit drive line components imposes a limit on the fidelity of single-qubit gates, independent of improvements in coherence times, circuit design, or leakage mitigation when not corrected for.

Large language models (LLMs) have been shown to be able to perform new tasks based on a few demonstrations or natural language instructions. While these capabilities have led to widespread adoption, most LLMs are developed by resource-rich organizations and are frequently kept from the public. As a step towards democratizing this powerful technology, we present BLOOM, a 176B-parameter open-access language model designed and built thanks to a collaboration of hundreds of researchers. BLOOM is a decoder-only Transformer language model that was trained on the ROOTS corpus, a dataset comprising hundreds of sources in 46 natural and 13 programming languages (59 in total). We find that BLOOM achieves competitive performance on a wide variety of benchmarks, with stronger results after undergoing multitask prompted finetuning. To facilitate future research and applications using LLMs, we publicly release our models and code under the Responsible AI License.

This article introduces a new numerical method for the minimization under constraints of a discrete energy modeling multicomponents rotating Bose-Einstein condensates in the regime of strong confinement and with rotation. Moreover, we consider both segregation and coexistence regimes between the components. The method includes a discretization of a continuous energy in space dimension 2 and a gradient algorithm with adaptive time step and projection for the minimization. It is well known that, depending on the regime, the minimizers may display different structures, sometimes with vorticity (from singly quantized vortices, to vortex sheets and giant holes). In order to study numerically the structures of the minimizers, we introduce in this paper a numerical algorithm for the computation of the indices of the vortices, as well as an algorithm for the computation of the indices of vortex sheets. Several computations are carried out, to illustrate the efficiency of the method, to cover different physical cases, to validate recent theoretical results as well as to support conjectures. Moreover, we compare this method with an alternative method from the literature.

The formalization of existing mathematical proofs is a notoriously difficult process. Despite decades of research on automation and proof assistants, writing formal proofs remains arduous and only accessible to a few experts. While previous studies to automate formalization focused on powerful search algorithms, no attempts were made to take advantage of available informal proofs. In this work, we introduce Draft, Sketch, and Prove (DSP), a method that maps informal proofs to formal proof sketches, and uses the sketches to guide an automated prover by directing its search to easier sub-problems. We investigate two relevant setups where informal proofs are either written by humans or generated by a language model. Our experiments and ablation studies show that large language models are able to produce well-structured formal sketches that follow the same reasoning steps as the informal proofs. Guiding an automated prover with these sketches enhances its performance from 20.9% to 39.3% on a collection of mathematical competition problems.

We present a new method to perform variation after projection in many-body systems on quantum computers that does not require performing explicit projection. The technique employs the notion of ``oracle'', generally used in quantum search algorithms. We show how to construct the oracle and the projector associated with a symmetry operator. The procedure is illustrated for the parity, particle number, and total spin symmetries. The oracle is used to restore symmetry by indirect measurements using a single ancillary qubit. An Illustration of the technique is made to obtain the approximate ground state energy for the pairing model Hamiltonian.