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Finding players with similar profiles is an important problem in sports such as football. Scouting for new players requires a wealth of information about the available players so that similar profiles to that of a target player can be identified. However, information about the position of the players in the field is seldom used. For this reason, a novel approach based on spatial data analysis is introduced to produce a spatial similarity index that can help to identify similar players. The use of this new spatial similarity index is illustrated to identify similar players using spatial data from the Spanish competition "La Liga", season 2019-2020.

The quasi-projective dimension and quasi-injective dimension are recently introduced homological invariants that generalize the classical notions of projective dimension and injective dimension, respectively. For a local ring $R$ and finitely generated $R$-modules $M$ and $N$, we provide conditions involving quasi-homological dimensions where the equality $\sup \lbrace i\geq 0: \operatorname{Ext}_R^i(M,N)\not=0 \rbrace =\operatorname{depth} R-\operatorname{depth} M$, which we call Ischebeck's formula, holds. One of the results in this direction generalizes a well-known result of Ischebeck concerning modules of finite injective dimension, considering the quasi-injective dimension. On the other hand, we establish an inequality relating the quasi-projective dimension of a finitely generated module to its grade and introduce the concept of a quasi-perfect module as a natural generalization of a perfect module. We prove several results for this new concept similar to the classical results. Additionally, we provide a formula for the grade of finitely generated modules with finite quasi-injective dimension over a local ring, as well as grade inequalities for modules of finite quasi-projective dimension. In our study, Cohen-Macaulayness criteria are also obtained., Comment: 20 pages, comments and suggestions are welcome

This paper considers a broadcast multiple-input multiple-output (MIMO) network with multiple users and simultaneous wireless information and power transfer (SWIPT). In this scenario, it is assumed that some users are able to harvest power from radio frequency (RF) signals to recharge batteries through wireless power transfer from the transmitter, while others are served simultaneously with data transmission. The criterion driving the optimization and design of the system is based on the weighted sum rate for the users being served with data. At the same time, constraints stating minimum per-user harvested powers are included in the optimization problem. This paper derives the structure of the optimal transmit covariance matrices in the case where both types of users are present simultaneously in the network, particularizing the results to the cases where either only harvesting nodes or only information users are to be served. The tradeoff between the achieved weighted sum rate and the powers harvested by the user terminals is analyzed and evaluated using the rate-power (R-P) region. Finally, we propose a two-stage user grouping mechanism that decides which users should be scheduled to receive information and which users should be configured to harvest energy from the RF signals in each particular scheduling period, this being one of the main contributions of this paper., Comment: Paper accepted to be published at EURASIP Journal on Wireless Communications and Networking, https://jwcn-eurasipjournals.springeropen.com/articles/10.1186/s13638-019-1460-y

Federated Learning (FL) has emerged as a solution for distributed model training across decentralized, privacy-preserving devices, but the different energy capacities of participating devices (system heterogeneity) constrain real-world implementations. These energy limitations not only reduce model accuracy but also increase dropout rates, impacting on convergence in practical FL deployments. In this work, we propose LeanFed, an energy-aware FL framework designed to optimize client selection and training workloads on battery-constrained devices. LeanFed leverages adaptive data usage by dynamically adjusting the fraction of local data each device utilizes during training, thereby maximizing device participation across communication rounds while ensuring they do not run out of battery during the process. We rigorously evaluate LeanFed against traditional FedAvg on CIFAR-10 and CIFAR-100 datasets, simulating various levels of data heterogeneity and device participation rates. Results show that LeanFed consistently enhances model accuracy and stability, particularly in settings with high data heterogeneity and limited battery life, by mitigating client dropout and extending device availability. This approach demonstrates the potential of energy-efficient, privacy-preserving FL in real-world, large-scale applications, setting a foundation for robust and sustainable pervasive AI on resource-constrained networks.

Motivated by an equivalence of categories established by Kapranov and Schechtman, we introduce, for each non-negative integer d, the category of connected bialgebras modulo d+1. We show that these categories fit into an inverse system of categories whose inverse limit category is equivalent to the category of connected bialgebras. In addition, we extend the notion of approximation of connected bialgebras to those that are not necessarily generated in degree 1 and show that, for connected bialgebras in the category of Yetter-Drinfeld modules over a Hopf algebra, approximation is compatible with cocycle twisting.

The development of deep neural networks is witnessing fast growth in network size, which requires novel hardware computing platforms with large bandwidth and low energy consumption. Optical computing has been a potential candidate for next-generation computing systems. Specifically, wavelength-division multiplexing (WDM) has been widely adopted in optical neural network architecture to increase the computation bandwidth. Although existing WDM neural networks architectures have shown promise, they face challenges in the integration of light sources and further increase of the computing bandwidth. To overcome these issues, we introduce a mode-division multiplexing (MDM) strategy, offering a new degree of freedom in optical computing within the micro-ring resonator platform. We propose a MDM approach for small-scale networks and a multi-dimensional architecture for large-scale applications, supplementing WDM with MDM to enhance channel capacity for computations. In this work, we design and experimentally demonstrate key components for the MDM computing system, i.e., a multimode beam splitter, a thermo-optical tuner for the high-order mode, and a multimode waveguide bend. We further show a 2-by-2 matrix multiplexing system fabricated in a foundry that works for both MDM and MDM-WDM computing, which confirms that our approach successfully increases the input vector size for computing and ensures compatibility with existing WDM networks., Comment: 6 pages, 4 figures

Chirality in tellurium derives from a Peierls distortion driven by strong electron-phonon coupling, making this material a unique candidate for observing a light-induced topological phase transition. By using time- and angle-resolved photoelectron spectroscopy (trARPES), we reveal that upon near-infrared photoexcitation the Peierls gap is modulated by displacively excited coherent phonons with $\mathrm{A_{1g}}$ symmetry as well as chiral-symmetry-breaking $\mathrm{E'_{LO}}$ modes. By comparison with state-of-the-art TDDFT+U calculations, we reveal the microscopic origin of the in-phase oscillations of band edges, due to phonon-induced modulation of the effective Hubbard $U$ term., Comment: 6 pages, 3 figures

We study an extension to directed graphs of the parameter called the $b$-chromatic number of a graph in terms of acyclic vertex colorings: the dib-chromatic number. We give general bounds for this parameter. We also show some results about tournaments and regular digraphs., Comment: 10 pages, 1 figure

The study of twisted two-dimensional (2D) materials, where twisting layers create moir\'e superlattices, has opened new opportunities for investigating topological phases and strongly correlated physics. While systems such as twisted bilayer graphene (TBG) and twisted transition metal dichalcogenides (TMDs) have been extensively studied, the broader potential of a seemingly infinite set of other twistable 2D materials remains largely unexplored. In this paper, we define "theoretically twistable materials" as single- or multi-layer structures that allow for the construction of simple continuum models of their moir\'e structures. This excludes, for example, materials with a "spaghetti" of bands or those with numerous crossing points at the Fermi level, for which theoretical moir\'e modeling is unfeasible. We present a high-throughput algorithm that systematically searches for theoretically twistable semimetals and insulators based on the Topological 2D Materials Database. By analyzing key electronic properties, we identify thousands of new candidate materials that could host rich topological and strongly correlated phenomena when twisted. We propose representative twistable materials for realizing different types of moir\'e systems, including materials with different Bravais lattices, valleys, and strength of spin-orbital coupling. We provide examples of crystal growth for several of these materials and showcase twisted bilayer band structures along with simplified twisted continuum models. Our results significantly broaden the scope of moir\'e heterostructures and provide a valuable resource for future experimental and theoretical studies on novel moir\'e systems., Comment: 15+81 pages, 5+187 figures, 4+104 tables. The Topological 2D Materials Database is available at https://topologicalquantumchemistry.com/topo2d/index.html . See also the accompanying paper "Two-dimensional Topological Quantum Chemistry and Catalog of Topological Materials"

We develop algorithms for the optimization of convex objectives that have H\"older continuous $q$-th derivatives with respect to a $p$-norm by using a $q$-th order oracle, for $p, q \geq 1$. We can also optimize other structured functions. We do this by developing a non-Euclidean inexact accelerated proximal point method that makes use of an inexact uniformly convex regularizer. We also provide nearly matching lower bounds for any deterministic algorithm that interacts with the function via a local oracle.

The study of the structure and mechanical properties of complex fluid interfaces has gained increasing interest in recent decades as a result of its significant scientific relevance to the understanding of biological systems, drug development, and industrial applications. The in situ combination of molecular-level structural measurements with the assessment of dynamical (rheological) properties is particularly valuable, as comparing measurements conducted on separate samples under challenging-to-reproduce experimental conditions can be problematic. In this work, we present a new sample environment at the FIGARO instrument, the horizontal neutron reflectometer at the Institut Laue-Langevin, which includes an interfacial shear rheometer operating in the Double Wall-Ring (DWR) geometry, compatible with commercial rotational rheometers. This innovative setup enables simultaneous structural (neutron reflectometry) and dynamical (shear interfacial rheology) measurements on the same sample.

In this paper we investigate the Lie algebra structure of the first relative Hochschild cohomology and its relation with the relative notion of fundamental group. Let $A,B$ be finite-dimensional basic $k$-algebras over an algebraically closed field of characteristic zero, such that $Q_B$ is a subquiver of $Q_A$. We show that if the complement of $Q_A$ by the arrows of $Q_B$ is a simple directed graph, then the first relative Hochschild cohomology $\text{HH}^1(A|B)$ is a solvable Lie algebra. We also compute the Lie algebra structure of the first relative Hochschild cohomology for radical square zero algebras and for dual extension algebras of directed monomial algebras. Finally, we introduce the notion of fundamental group for a pair of an algebra $A$ and a subalgebra $B$ and we construct the relative version of the map from the dual fundamental group into the first Hochschild cohomology., Comment: 28 pages

Methods of Machine and Deep Learning are gradually being integrated into industrial operations, albeit at different speeds for different types of industries. The aerospace and aeronautical industries have recently developed a roadmap for concepts of design assurance and integration of neural network-related technologies in the aeronautical sector. This paper aims to contribute to this paradigm of AI-based certification in the context of supervised learning, by outlining a complete validation pipeline that integrates deep learning, optimization and statistical methods. This pipeline is composed by a directed graphical model of ten steps. Each of these steps is addressed by a merging key concepts from different contributing disciplines (from machine learning or optimization to statistics) and adapting them to an industrial scenario, as well as by developing computationally efficient algorithmic solutions. We illustrate the application of this pipeline in a realistic supervised problem arising in aerostructural design: predicting the likelikood of different stress-related failure modes during different airflight maneuvers based on a (large) set of features characterising the aircraft internal loads and geometric parameters., Comment: 38 pages, 17 figures

In cancer epidemiology, the \emph{relative survival framework} is used to quantify the hazard associated with cancer by comparing the all-cause mortality hazard in cancer patients to that of the general population. This framework assumes that an individual's hazard function is the sum of a known population hazard and an excess hazard associated with the cancer. Several estimands are derived from the excess hazard, including the \emph{net survival}, which are used to inform decisions and to assess the effectiveness of interventions on cancer management. In this paper, we introduce a Bayesian machine learning approach to estimating the excess hazard and identifying vulnerable subgroups, with a higher excess risk, using Bayesian additive regression trees (BART). We first develop a proportional hazards extension of the BART model to the relative survival setting, and then extend this model to non-proportional hazards. We develop tools for model interpretation and posterior summarization and then present an application using colon cancer data from England, highlighting the insights our proposed methodology offers when paired with state-of-the-art data linkage methods. This application demonstrates how these methods can be used to identify drivers of inequalities in cancer survival through variable importance quantification.

We consider the anyonic spin systems with a global symmetry, the so-called symmetry enriched topological (SET) phases. We introduce the phase characterizing the symmetry fractionalization of the anyons. Our assumptions on how the global symmetry acts prevents anyon permutation effects.

Isospin symmetry is a fundamental concept in nuclear physics. Even though isospin symmetry is partially broken, it holds approximately for most nuclear systems, which makes exceptions very interesting from the nuclear structure perspective. In this framework, it is expected that the spins and parities of the ground states of mirror nuclei should be the same, in particular for the simplest systems where a proton is exchanged with a neutron or vice versa. In this work, we present evidence that this assumption is broken in the mirror pair $^{71}$Br and $^{71}$Kr system. Our conclusions are based on a high-statistics $\beta$ decay study of $^{71}$Kr and on state-of-the-art shell model calculations. In our work, we also found evidence of a new state in $^{70}$Se, populated in the $\beta$-delayed proton emission process which can be interpreted as the long sought coexisting 0$^+$ state., Comment: 8 pages with references, 3 figures. Supplemental material 4 pages (1 table, 3 figures)

Embedding materials in optical cavities has emerged as an intriguing perspective for controlling quantum materials, but a key challenge lies in measuring properties of the embedded matter. Here, we propose a framework for probing strongly correlated cavity-embedded materials through direct measurements of cavity photons. We derive general relations between photon and matter observables inside the cavity, and show how these can be measured via the emitted photons. As an example, we demonstrate how the entanglement phase transition of an embedded H$_2$ molecule can be accessed by measuring the cavity photon occupation, and showcase how dynamical spin correlation functions can be accessed by measuring dynamical photon correlation functions. Our framework provides an all-optical method to measure static and dynamic properties of cavity-embedded materials., Comment: 5 pages, 3 figures + supplemental material (20 pages)

Time-dependent Wannier functions were initially proposed as a means for calculating the polarization current in crystals driven by external fields. In this work, we present a simple gauge where Wannier states are defined based on the maximally localized functions at the initial time, and are propagated using the time-dependent Bloch states obtained from established first-principles calculations, avoiding the costly Wannierization at ech time step. We show that this basis efficiently describes the time-dependent polarization of the laser driven system through the analysis of the motion of Wannier centers. We use this technique to analyze highly nonlinear and non-perturbative responses such as high harmonic generation in solids, using the hexagonal boron nitride as an illustrative example, and we show how it provides an intuitive picture for the physical mechanisms.

We present a generalization of the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to cavity quantum-electrodynamical (QED) matter systems. The method can be formulated in both the Coulomb and the dipole gauge. We verify its accuracy by benchmarking calculations on a set of small molecules against full configuration interaction and state-of-the-art QED coupled cluster (QED-CCSD) calculations. Our results show that (i) gauge invariance can be achieved within correlation-consistent Gaussian basis sets, (ii) the accuracy of QED-CCSD can be enhanced significantly by adding the standard perturbative triples correction without light-matter coupling, and (iii) there is a straightforward way to evaluate the differential expression for the photon occupation number that works in any gauge. The high accuracy and favorable computational scaling of our AFQMC approach will enable a broad range of applications. Besides polaritonic chemistry, the method opens a way to simulate extended QED matter systems., Comment: 10 pages, 7 figures

A beyond electric-dipole light-matter theory is needed to describe emerging X-ray and THz applications for characterization and control of quantum materials but inaccessible as nondipole lattice-aperiodic terms impede on the use of Bloch's theorem. To circumvent this, we derive a formalism that captures dominant nondipole effects in intense electromagnetic fields while conserving lattice translational symmetry. Our approach enables the first accurate nondipole first-principles microscopic simulation of nonperturbative harmonic generation in Si. We reveal nondipole-induced transverse currents generating perturbative even-ordered harmonics and display the onset of nondipole high harmonic generation near the laser damage threshold., Comment: 8 pages, 3 figures

Projected entangled pair states (PEPS) are very useful in the description of strongly correlated systems, partly because they allow encoding symmetries, either global or local (gauge), naturally. In recent years, PEPS with local symmetries have increasingly been used in the study of non-perturbative regimes of lattice gauge theories, most prominently as a way to construct variational ansatz states depending only on a small number of parameters and yet capturing the relevant physical properties. For the case of one-dimensional PEPS (Matrix Product States - MPS) a bidirectional connection was established between the internal structure of the tensor network, i.e. the mathematical properties of the constituent tensors, and the symmetry. In higher dimensions this has only been done for global symmetries, where in the local (gauge) case it is known only how to construct gauge-invariant states, but not what the symmetry implies on the internal structure of the PEPS. In the present work we complete this missing piece and study the internal structure of projected entangled pair states with a gauge symmetry. The PEPS we consider consist of matter and gauge field tensors placed on the vertices and edges, respectively, of arbitrary graphs., Comment: 11 pages, 4 figures

Understanding trajectories in multi-agent scenarios requires addressing various tasks, including predicting future movements, imputing missing observations, inferring the status of unseen agents, and classifying different global states. Traditional data-driven approaches often handle these tasks separately with specialized models. We introduce TranSPORTmer, a unified transformer-based framework capable of addressing all these tasks, showcasing its application to the intricate dynamics of multi-agent sports scenarios like soccer and basketball. Using Set Attention Blocks, TranSPORTmer effectively captures temporal dynamics and social interactions in an equivariant manner. The model's tasks are guided by an input mask that conceals missing or yet-to-be-predicted observations. Additionally, we introduce a CLS extra agent to classify states along soccer trajectories, including passes, possessions, uncontrolled states, and out-of-play intervals, contributing to an enhancement in modeling trajectories. Evaluations on soccer and basketball datasets show that TranSPORTmer outperforms state-of-the-art task-specific models in player forecasting, player forecasting-imputation, ball inference, and ball imputation. https://youtu.be/8VtSRm8oGoE, Comment: Accepted to ACCV 2024

This article presents a theoretical analysis of a one-dimensional heat transfer problem in two layers involving diffusion, advection, internal heat generation or loss linearly dependent on temperature in each layer, and heat generation due to external sources. Additionally, the thermal resistance at the interface between the materials is considered. The situation of interest is modeled mathematically, explicit analytical solutions are found using Fourier techniques, and a convergent finite difference scheme is formulated to simulate specific cases. The solution is consistent with previous results. A numerical example is included that shows coherence between the obtained results and the physics of the problem. The conclusions drawn in this work expand the theoretical understanding of two-layer heat transfer and may also contribute to improving the thermal design of multilayer engineering systems., Comment: 22 Pages, 7 Figures, 3 Tables

Density functional theory (DFT) offers a desirable balance between quantitative accuracy and computational efficiency in practical many-electron calculations. Its central component, the exchange-correlation energy functional, has been approximated with increasing levels of complexity ranging from strictly local approximations to nonlocal and orbital-dependent expressions with many tuned parameters. In this work, we formulate a general way of rewriting complex density functionals using deep neural networks in a way that allows for simplified computation of Kohn-Sham potentials as well as higher functional derivatives through automatic differentiation, enabling access to highly nonlinear response functions and forces. These goals are achieved by using a recently developed class of robust neural network models capable of modeling functionals, as opposed to functions, with explicitly enforced spatial symmetries. Functionals treated in this way are then called global density approximations and can be seamlessly integrated with existing DFT workflows. Tests are performed for a dataset featuring a large variety of molecular structures and popular meta-GGA density functionals, where we successfully eliminate orbital dependencies coming from the kinetic energy density, and discover a high degree of transferability to a variety of physical systems. The presented framework is general and could be extended to more complex orbital and energy dependent functionals as well as refined with specialized datasets., Comment: 5 pages, 3 figures (supplementary material 8 pages, 2 figures)

The gravitational physics landscape is evolving rapidly, driven by our ability to study strong-field regions, in particular black holes. Black Holes Inside and Out gathered world experts to discuss the status of the field and prospects ahead. We hope that the ideas and perspectives are a source of inspiration. Structure: Black Hole Evaporation - 50 Years by William Unruh The Stability Problem for Extremal Black Holes by Mihalis Dafermos The Entropy of Black Holes by Robert M. Wald The Non-linear Regime of Gravity by Luis Lehner Black Holes Galore in D > 4 by Roberto Emparan Same as Ever: Looking for (In)variants in the Black Holes Landscape by Carlos A. R. Herdeiro Black Holes, Cauchy Horizons, and Mass Inflation by Matt Visser The Backreaction Problem for Black Holes in Semiclassical Gravity by Adrian del Rio Black Holes Beyond General Relativity by Enrico Barausse and Jutta Kunz Black Holes as Laboratories: Searching for Ultralight Fields by Richard Brito Primordial Black Holes from Inflation by Misao Sasaki Tests of General Relativity with Future Detectors by Emanuele Berti Black Holes as Laboratories: Tests of General Relativity by Ruth Gregory and Samaya Nissanke Simulating Black Hole Imposters by Frans Pretorius Black Hole Spectroscopy: Status Report by Gregorio Carullo VLBI as a Precision Strong Gravity Instrument by Paul Tiede Testing the nature of compact objects and the black hole paradigm by Mariafelicia De Laurentis and Paolo Pani Some Thoughts about Black Holes in Asymptotic Safety by Alessia Platania Black Hole Evaporation in Loop Quantum Gravity by Abhay Ashtekar How the Black Hole Puzzles are Resolved in String Theory by Samir D. Mathur Quantum Black Holes: From Regularization to Information Paradoxes by Niayesh Afshordi and Stefano Liberati, Comment: 221 pages, 21 contributions

Quantum-enhanced sensors, which surpass the standard quantum limit (SQL) and approach the fundamental precision limits dictated by quantum mechanics, are finding applications across a wide range of scientific fields. This quantum advantage becomes particularly significant when a large number of particles are included in the sensing circuit. Achieving such enhancement requires introducing and preserving entanglement among many particles, posing significant experimental challenges. In this work, we integrate concepts from Floquet theory and quantum information to design an entangler capable of generating the desired entanglement between two paths of a quantum interferometer. We demonstrate that our path-entangled states enable sensing beyond the SQL, reaching the fundamental Heisenberg limit (HL) of quantum mechanics. Moreover, we show that a decoding parity measurement maintains the HL when specific conditions from Floquet theory are satisfied$\unicode{x2013}$particularly those related to the periodic driving parameters that preserve entanglement during evolution. We address the effects of a priori phase uncertainty and imperfect transmission, showing that our method remains robust under realistic conditions. Finally, we propose a superconducting-circuit implementation of our sensor in the microwave regime, highlighting its potential for practical applications in high-precision measurements.

Chirality, the breaking of improper rotational symmetry, is a fundamental concept spanning diverse scientific domains. In condensed matter physics, chiral phonons, originating from circular atomic motions that carry angular momentum, have sparked intense interest due to their coupling to magnetic degrees of freedom, enabling potential phonon-controlled spintronics. However, modes and their counter-rotating counterparts are typically degenerate at the Brillouin zone center. Selective excitation of a single-handed circulating phonon requires external stimuli that break the degeneracy. Whether energetically nondegenerate circularly polarized phonons can appear spontaneously without structural or external symmetry breaking remains an open question. Here, we demonstrate that nondegenerate elliptically polarized phonon pairs can be induced by coupling to magnons with same helicity in the van der Waals antiferromagnet $\mathrm{FePSe_3}$. We confirm the presence of magnon-phonon hybrids, also known as magnon polarons, which exhibit inherent elliptical polarization with opposite helicities and distinct energies. This nondegeneracy enables their coherent excitation with linearly polarized terahertz pulses, which also endows these rotating modes with chirality. By tuning the polarization of the terahertz drive and measuring phase-resolved polarimetry of the resulting coherent oscillations, we determine the ellipticity and map the trajectory of these hybrid quasiparticles. Our findings establish a general approach to search for intrinsically nondegenerate phonons with angular momentum at the center of the Brillouin zone and introduce a new methodology for characterizing their ellipticity, outlining a roadmap towards chiral-phonon-controlled spintronic functionalities., Comment: 14 pages, 4 figures

Bayesian methods promise enhanced device performance and accelerated data collection. We demonstrate an adaptive Bayesian measurement strategy for atom number estimation in a quantum technology experiment, utilising a symmetry-informed loss function. Compared to a standard unoptimised strategy, our method yields a five-fold reduction in the fractional variance of the atom number estimate. Equivalently, it achieves the target precision with a third of the data points previously required. We provide general expressions for the optimal estimator and error for any quantity amenable to symmetry-informed strategies, facilitating the application of these strategies in quantum computing, communication, metrology, and the wider quantum technology sector., Comment: 6 + 5 pages, 3 + 2 figures, 1 + 1 tables. Updated references and minor revisions

We present a randomized differential testing approach to test OpenMP implementations. In contrast to previous work that manually creates dozens of verification and validation tests, our approach is able to randomly generate thousands of tests, exposing OpenMP implementations to a wide range of program behaviors. We represent the space of possible random OpenMP tests using a grammar and implement our method as an extension of the Varity program generator. By generating 1,800 OpenMP tests, we find various performance anomalies and correctness issues when we apply it to three OpenMP implementations: GCC, Clang, and Intel. We also present several case studies that analyze the anomalies and give more details about the classes of tests that our approach creates.

We propose a systematic framework to construct a (d+1)-dimensional stabilizer model from an initial generic d-dimensional abelian symmetry. Our approach builds upon the iterative gauging procedure, developed by one of the authors in [J. Garre-Rubio, Nature Commun. 15, 7986 (2024)], in which an initial symmetric state is repeatedly gauged to obtain an emergent model in one dimension higher that supports the initial symmetry at its boundary. This method not only enables the construction of emergent states and corresponding commuting stabilizer Hamiltonians of which they are ground states, but it also provides a way to construct gapped boundary conditions for these models that amount to spontaneously breaking part of the boundary symmetry. In a detailed introductory example, we showcase our paradigm by constructing three-dimensional Clifford-deformed surface codes from iteratively gauging a global 0-form symmetry that lives in two dimensions. We then provide a proof of our main result, hereby drawing upon a slight extension of the gauging procedure of Williamson. We additionally provide two more examples in d=2 in which different type-I fracton orders emerge from gauging initial linear subsystem and Sierpinski fractal symmetries. En passant, we provide explicit tensor network representations of all of the involved gauging maps and the emergent states.

No-hair theorems are uniqueness results constraining the form of the metric of black holes in general relativity. These theorems are typically formulated under idealized assumptions, involving a mixture of local (regularity of the horizon) and global aspects (vacuum spacetime and asymptotic flatness). This limits their applicability to astrophysical scenarios of interest such as binary black holes and accreting systems, as well as their extension to horizonless objects. A previous result due to G\"urlebeck constrains the asymptotic multipolar structure of static spacetimes containing black holes surrounded by matter although not revealing the possible structure of the metric itself. In this work, we disentangle some of these assumptions in the static and axisymmetric case. Specifically: i) we show that only a one-parameter family of black-hole geometries is compatible with a given external gravitational field, ii) we also analyze the case in which the central object is close to forming an event horizon but is still horizonless and show that the deviations from the natural black-hole shape have to die off as one approaches the black hole limit under the physical principle that curvatures are bounded., Comment: 57 pages, 16 figures; v2: Some discussions are expanded and references added

The attainment of accurate numerical solutions of ill-conditioned linear algebraic problems involving totally positive matrices has been gathering considerable attention among researchers over the last years. In parallel, the interest of $q$-calculus has been steadily growing in the literature. In this work the $q$-analogue of the Abel polynomial basis is studied. The total positivity of the matrix of change of basis between monomial and $q$-Abel bases is characterized, providing its bidiagonal factorization. Moreover, well-known high relative accuracy results of Vandermonde matrices corresponding to increasing positive nodes are extended to the decreasing negative case. This further allows to solve with high relative accuracy several algebraic problems concerning collocation, Wronskian and Gramian matrices of $q$-Abel polynomials. Finally, a series of numerical tests support the presented theoretical results and illustrate the goodness of the method where standard approaches fail to deliver accurate solutions.

The extended ultraviolet (XUV) disks of nearby galaxies show ongoing massive star formation, but their parental molecular clouds remain mostly undetected despite searches in CO(1-0) and CO(2-1). The recent detection of 23 clouds in the higher excitation transition CO(3-2) within the XUV disk of M83 requires an explanation. We test the hypothesis: the clouds in XUV disks have a clump-envelope structure similar to those in Galactic star-forming clouds, having star-forming dense clumps (or concentrations of multiple clumps) at their centers, which predominantly contribute to the CO(3-2) emission, surrounded by less-dense envelopes, where CO molecules are photo-dissociated due to the low-metallicity environment there. We utilize new high-resolution ALMA CO(3-2) observations of a subset (11) of the 23 clouds in the XUV disk. We confirm the compactness of the CO(3-2)-emitting dense clumps (or their concentrations), finding clump diameters below the spatial resolution of 6-9~pc. This is similar to the size of the dense gas region in the Orion A molecular cloud, the local star-forming cloud with massive star formation. The dense star-forming clumps are common between normal and XUV disks. This may also indicate that once the cloud structure is set, the process of star formation is governed by the cloud internal physics rather than by external triggers. This simple model explains the current observations of the clouds with ongoing massive star formation, although it may require some adjustment, e.g., including an effect of cloud evolution, for a general scenario of star formation in molecular clouds., Comment: A&A accepted; 15 pages, 8 figures - after proof

Selective excitation of vibrational modes using strong laser pulses has emerged as a powerful material engineering paradigm. However, to realize deterministic control over material properties for device applications, it is desirable to have an analogous scheme without a drive, operating in thermal equilibrium. We here propose such an equilibrium analog of the light-driven paradigm, leveraging the strong coupling between lattice degrees of freedom and the quantum fluctuations of the electric field of a THz micro-cavity. We demonstrate this approach by showing, using \textit{ab initio} data, how electric field fluctuations can induce a sub-dominant ferromagnetic order, on top of the dominant zig-zag antiferromagnet order, in FePS$_3$ close to its N\'eel temperature., Comment: 5 pages, 3 figures

This paper investigates a critical aspect of wind energy research - the development of wind turbine wake and its significant impact on wind farm efficiency. The study focuses on the exploration and comparison of two mesh refinement strategies, h- and p-refinement, in their ability to accurately compute the development of wind turbine wake. The h-refinement method refines the mesh by reducing the size of the elements, while the p-refinement method increases the polynomial degree of the elements, potentially reducing the error exponentially for smooth flows. A comprehensive comparison of these methods is presented that evaluates their effectiveness, computational efficiency, and suitability for various scenarios in wind energy. The findings of this research could potentially guide future studies and applications in wind turbine wake modeling, thus contributing to the optimization of wind farms using high-order h/p methods. This study fills a gap in the literature by thoroughly investigating the application of these methods in the context of wind turbine wake development., Comment: 35 pages, 24 figures

Gravitational waves offer an unprecedented opportunity to look into the violent high-energy processes happening during the reheating phase of our Universe. We consider a Hubble-induced phase transition scenario as a source of a post-inflationary stochastic background of gravitational waves and analyse the main characteristics of its spectrum for the first time via numerical methods. The output of a large number of fully-fledged classical lattice simulations is condensed in a set of parametric formulas that describe key features of the gravitational wave spectrum, such as its peak amplitude and characteristic frequency, and avoid the need for further time-consuming simulations. The signal from such stochastic background is compared to the prospective sensitivity of future gravitational-wave detectors., Comment: 17 pages

We present a series of algorithms in tensor networks for anomaly detection in datasets, by using data compression in a Tensor Train representation. These algorithms consist of preserving the structure of normal data in compression and deleting the structure of anomalous data. The algorithms can be applied to any tensor network representation. We test the effectiveness of the methods with digits and Olivetti faces datasets and a cybersecurity dataset to determine cyber-attacks., Comment: 10 pages, 13 figures

Coherent manipulation of magnetism through the lattice provides unprecedented opportunities for controlling spintronic functionalities on the ultrafast timescale. Such nonthermal control conventionally involves nonlinear excitation of Raman-active phonons which are coupled to the magnetic order. Linear excitation, in contrast, holds potential for more efficient and selective modulation of magnetic properties. However, the linear channel remains uncharted, since it is conventionally considered forbidden in inversion symmetric quantum materials. Here, we harness strong coupling between magnons and Raman-active phonons to achieve both linear and quadratic excitation regimes of magnon-polarons, magnon-phonon hybrid quasiparticles. We demonstrate this by driving magnon-polarons with an intense terahertz pulse in the van der Waals antiferromagnet $\mathrm{FePS_3}$. Such excitation behavior enables a unique way to coherently control the amplitude of magnon-polaron oscillations by tuning the terahertz field strength and its polarization. The polarimetry of the resulting coherent oscillation amplitude breaks the crystallographic $C_2$ symmetry due to strong interference between different excitation channels. Our findings unlock a wide range of possibilities to manipulate material properties, including modulation of exchange interactions by phonon-Floquet engineering., Comment: 15 pages, 4 figures

High-harmonic generation (HHG) is a nonlinear process in which a material sample is irradiated by intense laser pulses, causing the emission of high harmonics of the incident light. HHG has historically been explained by theories employing a classical electromagnetic field, successfully capturing its spectral and temporal characteristics. However, recent research indicates that quantum-optical effects naturally exist, or can be artificially induced, in HHG. Even though the fundamental equations of motion for quantum electrodynamics (QED) are well-known, a unifying framework for solving them to explore HHG is missing. So far, numerical solutions employed a wide range of basis-sets and untested approximations. Based on methods originally developed for cavity polaritonics, here we formulate a numerically accurate QED model consisting of a single active electron and a single quantized photon mode. Our framework can in principle be extended to higher electronic dimensions and multiple photon modes to be employed in ab initio codes. We employ it as a model of an atom interacting with a photon mode and predict a characteristic minimum structure in the HHG yield vs. phase-squeezing. We find that this phenomenon, which can be used for novel ultrafast quantum spectroscopies, is partially captured by a multi-trajectory Ehrenfest dynamics approach, with the exact minima position sensitive to the level of theory. On the one hand, this motivates using multi-trajectory approaches as an alternative for costly exact calculations. On the other hand, it suggests an inherent limitation of the multi-trajectory formalism, indicating the presence of entanglement. Our work creates a road-map for a universal formalism of QED-HHG that can be employed for benchmarking approximate theories, predicting novel phenomena for advancing quantum applications, and for the measurements of entanglement and entropy., Comment: 10 pages, 7 figures

The field of Quantum Computation is plagued by issues that limit the implementation and development of quantum systems and quantum algorithms. Issues which force the development of Hybrid Quantum-Classical algorithms, such as the quantum DisCoCat implementation for Natural Language Processing. These require a high processing cost and are susceptible to errors due to Out of Vocabulary words. In this work, we develop a framework to implement Few Shot Learning for Quantum Natural Language Processing, by modifying the encoding ans\"atze and dividing it into two parts, the first one leveraging the vast corpus of classical training already available, and the second variationally training on the task. This framework is then put to the test to explore its behaviour and its power in extracting as much useful work from each call to a quantum system as possible.

This work provides a vision on how to tackle the underutilization of compute resources in FPGA SoC devices used across 5G and edge computing infrastructures. A first step towards this end is the implementation of a resource management layer able to migrate and scale functions in such devices, based on context events. This layer sets the basis to design a hierarchical data-driven micro-orchestrator in charge of providing the lifecycle management of functions in FPGA SoC devices. In the O-RAN context, the micro-orchestrator is foreseen to take the form of an xApp/rApp tandem trained with RAN traffic and context data., Comment: Article accepted in the IEEE International Conference on 6G Networking (6GNet 2024)

Engineering phases of matter in cavities requires effective light-matter coupling strengths that are on the same order of magnitude as the bare system energetics, coined the ultra-strong coupling regime. For models of itinerant electron systems, which do not have discrete energy levels, a clear definition of this regime is outstanding to date. Here we argue that a change of the electronic mass exceeding $10\%$ of its bare value may serve as such a definition. We propose a quantitative computational scheme for obtaining the electronic mass in relation to its bare vacuum value and show that coupling to surface polariton modes can induce such mass changes. Our results have important implications for cavity design principles that enable the engineering of electronic properties with quantum light., Comment: 5 pages, 3 figes + Supplement: 4 pages, 1 figure

Recently, Gheibi, Jorgensen, and Takahashi introduced a new homological invariant called quasi-projective dimension, which is a generalization of projective dimension. They proved that the depth formula holds for two finitely gene\-rated Tor-independent modules over a Noetherian local ring when one of the modules has finite quasi-projective dimension. In this paper, we extend this result by pro\-ving that for finitely generated modules \( M \) and \( N \) over a Noetherian local ring \( R \) with \( \operatorname{qpd}_R M < \infty \), the equality \( \operatorname{depth} N = \operatorname{depth}(\operatorname{Tor}_q^R(M,N)) + \operatorname{qpd}_R M - q \) holds, where \( q := \sup\{ i \geq 0 : \operatorname{Tor}_i^R(M,N) \neq 0 \} \), provided that \( q < \infty \), and either \( q = 0 \) or \( \operatorname{depth}(\operatorname{Tor}_q^R(M,N)) \leq 1 \). This outcome generalizes a celebrated theorem by Auslander and allows us to derive new consequences and applications, for instance, we recover an important theorem of Araya and Yoshino., Comment: 10 pages, comments and suggestions are welcome. In this new version, Corollary 4.4 has been added, which recover a theorem of Araya and Yoshino

Polaritonic chemistry has garnered increasing attention in recent years due to pioneering experimental results, which show that site- and bond-selective chemistry at room temperature is achievable through strong collective coupling to field fluctuations in optical cavities. Despite these notable experimental strides, the underlying theoretical mechanisms remain unclear. In this focus review, we highlight a fundamental theoretical link between the seemingly unrelated fields of polaritonic chemistry and spin glasses, exploring its profound implications for the theoretical framework of polaritonic chemistry. Specifically, we present a mapping of the dressed electronic structure problem under collective vibrational strong coupling to the iconic Sherrington-Kirkpatrick model of spin glasses. This mapping uncovers a collectively induced instability in the dressed electronic structure (spontaneous replica symmetry breaking), which could provide the long-sought seed for significant local chemical modifications in polaritonic chemistry. This mapping paves the way to incorporate, adjust and probe numerous spin glass concepts in polaritonic chemistry, such as frustration, aging dynamics, excess of thermal fluctuations, time-reversal symmetry breaking or stochastic resonances. Ultimately, the mapping also offers fresh insights into the applicability of spin glass theory beyond condensed matter systems and it suggests novel theoretical directions such as polarization glasses with explicitly time-dependent order parameter functions.

We report the first ab initio, non-relativistic QED method that couples light and matter self-consistently beyond the electric dipole approximation and without multipolar truncations. This method is based on an extension of the Maxwell-Pauli-Kohn-Sham approach to a full minimal coupling Hamiltonian, where the space- and time-dependent vector potential is coupled to the matter system, and its back-reaction to the radiated fields is generated by the full current density. The implementation in the open-source Octopus code is designed for massively-parallel multiscale simulations considering different grid spacings for the Maxwell and matter subsystems. Here, we show the first applications of this framework to simulate renormalized Cherenkov radiation of an electronic wavepacket, magnetooptical effects with non-chiral light in non-chiral molecular systems, and renormalized plasmonic modes in a nanoplasmonic dimer. We show that in some cases the beyond-dipole effects can not be captured by a multipolar expansion Hamiltonian in the length gauge. Finally, we discuss further opportunities enabled by the framework in the field of twisted light and orbital angular momentum, inelastic light scattering and strong field physics., Comment: 31 pages, 9 figures, supporting information appended

This work extends our previous study from S. Shrestha et al. (2024) by introducing a new abstract framework for Variational Multiscale (VMS) methods at the discrete level. We introduce the concept of what we define as the optimal projector and present an approach where the infinite-dimensional unresolved scales are approximated in a finite-dimensional subspace using the numerically computed Fine-Scale Greens' function of the underlying symmetric problem. The proposed approach involves solving the VMS problem on two separate meshes: a coarse mesh for the full PDE and a fine mesh for the symmetric part of the continuous differential operator. We consider the 1D and 2D steady advection-diffusion problems in both direct and mixed formulations as the test cases in this paper. Moreover, we demonstrate the working of this method using the Mimetic Spectral Element Method (MSEM), however, it may be applied to other Finite/Spectral Element or Isogeometric frameworks. Furthermore, we propose that VMS should not be viewed as a stabilisation technique; instead, the base scheme should be inherently stable, with VMS enhancing the solution quality by supplementing the base scheme.