Synchronization is the spontaneous alignment of the dynamics of weakly-coupled oscillators. In addition to temporal dynamics like periodic and chaotic oscillations, also the spatio-temporal dynamics of spatially-extended systems like wildlife populations can synchronize. We exploit here the intrinsic spatio-temporal complex dynamics of broad area lasers to demonstrate such synchronization at lab-scale. Broad-area vertical-cavity surface-emitting lasers (BA-VCSELs) exhibit chaos from the nonlinear coupling between laser modes with different spatial profiles and polarization. When coupling two BA-VCSELs, several synchronization and anti-synchronization regimes are observed, highlighting the complex interplay between oscillating modes with different frequencies and spatial patterns. The correlation coefficient varies between 0.2 and 0.9 depending on the dynamics and on the time scale under analysis. Besides its fundamental interest, our experiment with commercial devices marks the first step towards real-world spatial multiplexing in multiple user physical-layer secure communication based on chaos synchronization.

Quantum neural networks (QNNs), as currently formulated, are near-term quantum machine learning architectures that leverage parameterized quantum circuits with the aim of improving upon the performance of their classical counterparts. In this work, we show that some desired properties attributed to these models can be efficiently reproduced without necessarily resorting to quantum hardware. We indeed study the expressibility of parametrized quantum circuit commonly used in QNN applications and contrast it to those of two classes of states that can be efficiently simulated classically: matrix-product states (MPS), and Clifford-enhanced MPS (CMPS), obtained by applying a set of Clifford gates to MPS. In addition to expressibility, we assess the level of primary quantum resources, entanglement and non-stabilizerness (a.k.a. "magic"), in random ensembles of such quantum states, tracking their convergence towards the Haar distribution. While MPS require a large number of parameters to effectively reproduce an arbitrary quantum state, we find that CMPS approach the Haar distribution more rapidly, in terms of both entanglement and magic. Our results on states with up to 20 qubits indicate that high expressibility in QNNs is attainable with purely classical resources.

The mid-infrared spectral region holds growing importance for applications such as gas sensing and spectroscopy. Although compact ultrashort pulse laser sources are essential to enable these applications, their realization in this spectral range remains an open challenge. We demonstrate an integrated approach to generate pulses in the mid-infrared based on chirped Bragg gratings engineered to compensate for the group delay dispersion of quantum cascade laser frequency comb sources. SiGe graded-index photonic circuits are used for operation around 8 μm wavelength. With this approach, pulses as short as 1.39 picoseconds were obtained, marking a key step towards fully integrated ultrashort pulse sources in the mid-infrared.

There has been significant recent interest in studying how the number of numerical semigroups of genus $g$ behaves as a function of $g$. Bras-Amorós has shown how to organize the collection of numerical semigroups of genus $g$ into a rooted tree called the ordinarization tree. The ordinarization number of a numerical semigroup $S$ is the length of the path from $S$ back to the root of the tree. We study the problem of counting numerical semigroups of genus $g$ with a fixed ordinarization number $r$. We show how this can be interpreted as a counting problem about integer points in a certain rational polyhedral cone and use ideas from Ehrhart theory to study this problem. We give a formula for the number of numerical semigroups of genus $g$ and ordinarization number $2$, building on the corresponding result of Bras-Amorós for ordinarization number $1$. We show that the ordinarization number of a numerical semigroup generated by two elements is equal to the number of integer points in a certain right triangle with rational vertices. We consider the analogous problem for supersymmetric numerical semigroups with more generators. We also study ordinarization numbers of numerical semigroups generated by an interval.

Various deep learning-based approaches utilizing pre-trained language models (PLMs) have been proposed for automated vulnerability detection. With recent advancements in large language models (LLMs), several studies have begun exploring their application to vulnerability detection tasks. However, existing studies primarily focus on specific programming languages (e.g., C/C++) and function-level detection, leaving the strengths and weaknesses of PLMs and LLMs in multilingual and multi-granularity scenarios largely unexplored. To bridge this gap, we conduct a comprehensive fine-grained empirical study evaluating the effectiveness of state-of-the-art PLMs and LLMs for multilingual vulnerability detection. Using over 30,000 real-world vulnerability-fixing patches across seven programming languages, we systematically assess model performance at both the function-level and line-level. Our key findings indicate that GPT-4o, enhanced through instruction tuning and few-shot prompting, significantly outperforms all other evaluated models, including CodeT5P. Furthermore, the LLM-based approach demonstrates superior capability in detecting unique multilingual vulnerabilities, particularly excelling in identifying the most dangerous and high-severity vulnerabilities. These results underscore the promising potential of adopting LLMs for multilingual vulnerability detection at function-level and line-level, revealing their complementary strengths and substantial improvements over PLM approaches. This empirical evaluation of PLMs and LLMs for multilingual vulnerability detection highlights LLMs' value in addressing real-world software security challenges.

Quantum guessing games offer a structured approach to analyzing quantum information processing, where information is encoded in quantum states and extracted through measurement. An additional aspect of this framework is the influence of partial knowledge about the input on the optimal measurement strategies. This kind of side information can significantly influence the guessing strategy and earlier work has shown that the timing of such side information, whether revealed before or after the measurement, can affect the success probabilities. In this work, we go beyond this established distinction by introducing the concept of metainformation. Metainformation is information about information, and in our context it is knowledge that additional side information of certain type will become later available, even if it is not yet provided. We show that this seemingly subtle difference between having no expectation of further information versus knowing it will arrive can have operational consequences for the guessing task. Our results demonstrate that metainformation can, in certain scenarios, enhance the achievable success probability up to the point that post-measurement side information becomes as useful as prior-measurement side information, while in others it offers no benefit. By formally distinguishing metainformation from actual side information, we uncover a finer structure in the interplay between timing, information, and strategy, offering new insights into the capabilities of quantum systems in information processing tasks.

We introduce the time glass, a non-periodic analogue of the discrete time crystal that arises in periodically driven dissipative quantum many-body systems. This phase is defined by two key features: (i) spatial long-range order arising from the spontaneous breaking of an internal symmetry, and (ii) temporally chaotic oscillations of the order parameter, whose lifetime diverges with system size. In other words, a time glass is a state of matter in which all components evolve in a synchronized yet chaotic manner. To characterize the time glass phase, we focus on the spectral gap of the one-cycle (Floquet) Liouvillian, which determines the decay rate of the slowest relaxation mode. Numerical studies of periodically driven dissipative Ising models show that, in the time glass phase, the Liouvillian gap remains finite in the thermodynamic limit, in contrast to time crystals where the gap closes exponentially with system size. We further demonstrate that the Liouvillian gap converges to the decay rate of the order-parameter autocorrelation derived from the classical (mean-field) dynamics in the thermodynamic limit. This result establishes a direct correspondence between microscopic spectral features and emergent macroscopic dynamics in driven dissipative quantum systems. At first glance, the existence of a nonzero Liouvillian gap appears incompatible with the presence of indefinitely persistent chaotic oscillations. We resolve this apparent paradox by showing that the quantum Rényi divergence between a localized coherent initial state and the highly delocalized steady state grows unboundedly with system size. This divergence allows long-lived transients to persist even in the presence of a finite Liouvillian gap.

We characterize the s-parabolic Lipschitz caloric capacity of corner-like $s$-parabolic Cantor sets in $\mathbb{R}^{n+1}$ for $1/2<s\leq 1$. Despite the spatial gradient of the s-heat kernel lacking temporal anti-symmetry, we obtain analogous results to those known for analytic and Riesz capacities.

We study generic graded contractions of Lie algebras from the perspectives of group cohomology, affine algebraic geometry and monoidal categories. We show that generic graded contractions with a fixed support are classified by a certain abelian group, which we explicitly describe. Analyzing the variety of generic graded contractions as an affine algebraic variety allows us to describe which generic graded contractions define graded degenerations of a given graded Lie algebra. Using the interpretation of generic $G$-graded contractions as lax monoidal structures on the identity endofunctor of the monoidal category of $G$-graded vector spaces, we establish a functorial version of the Weimar-Woods conjecture on equivalence of generic graded contractions.

Agent-based models (ABMs) are widely used in biology to understand how individual actions scale into emergent population behavior. Modelers employ sensitivity analysis (SA) algorithms to quantify input parameters' impact on model outputs, however, it is hard to perform SA for ABMs due to their computational and complex nature. In this work, we develop the Simulate, Summarize, Reduce, Cluster, and Analyze (SSRCA) methodology, a machine-learning based pipeline designed to facilitate SA for ABMs. In particular, SSRCA can achieve the following tasks for ABMS: 1) identify sensitive model parameters, 2) reveal common output model patterns, and 3) determine which input parameter values generate these patterns. We use an example ABM of tumor spheroid growth to showcase how SSRCA identifies four common patterns from the ABM and the parameter regions that generate these outputs. Additionally, we compare the SA results between SSRCA and the popular Sobol' Method and find that SSRCA's identified sensitive parameters are robust to the choice of model descriptors while Sobol's are not. This analysis could streamline data-driven tasks, such as parameter estimation, for ABMs by reducing parameter space. While we highlight these results with an ABM on tumor spheroid formation, the SSRCA Methodology is broadly applicable to biological ABMs.

We study the dynamics and intervention strategies of a rumor using the modified Maki-Thompson model. A key challenge in social networks is distinguishing between natural increases in transmissibility and artificial injections of rumor spreaders, such as through broadcast events or astroturfing. Using stochastic simulations, we compare two scenarios: one with organic growth in transmissibility and another with externally injected spreaders. Although both lead to high autocorrelation, only the organic growth produces oscillatory patterns in autocorrelation at multiple lags, an effect we can analytically explain using the $N$-intertwined mean-field approximation. This distinction offers a practical tool to identify the origin of rumor virality and also infer its transmissibility. Our approach is validated analytically and tested on real-world data from Twitter during the announcement of the Higgs boson discovery. In addition to detection, we also explore control strategies. We show that the average lifetime of a rumor can be manipulated through targeted interventions: placing spreaders at specific locations in the network. Depending on their placement, these interventions can either extend or shorten the lifespan of the rumor.

Accurate relative orbit determination is a significant challenge in modern space operations, particularly when relying only on angular measurements. The inherent observability limitations of this approach make initial state estimation difficult, directly impacting mission safety and performance. This work proposes a hybrid estimation and control strategy for autonomous rendezvous. An active learning (AL) based algorithm designs the initial input control sequence by maximizing the exploration of the output space, thereby enhancing the observability of the initial relative state for the angle-only initial relative orbit determination (IROD) problem. The IROD solution provides a batch estimate of the initial relative state and its analytical covariance, which quantifies the estimation quality and determines the transition point to recursive filtering. Once the uncertainty is sufficiently low, an Extended Kalman Filter (EKF) is initialized with the IROD solution and takes over for sequential estimation, providing state estimates to a Model Predictive Controller (MPC) to complete the rendezvous. The proposed framework is validated through numerical simulations, demonstrating its ability to reliably resolve the scale ambiguity, outperform baseline excitation strategies, and successfully execute an end-to-end rendezvous from initial estimation to final approach.

Starting from a microscopic description of weak system-bath interactions, we derive from first principles a quantum master equation that does not rely on the well-known rotating wave approximation. This includes generic many-body systems, with Hamiltonians with vanishingly small energy spacings that forbid that approximation. The equation satisfies a general form of detailed balance, called KMS, which ensures exact convergence to the many-body Gibbs state. Unlike the more common notion of GNS detailed balance, this notion is compatible with the absence of the rotating wave approximation. We show that the resulting Lindbladian dynamics not only reproduces the thermal equilibrium point up to a small renormalization of the system Hamiltonian, but it also approximates the true system evolution with an error that grows at most linearly in time, giving an exponential improvement upon previous estimates. This master equation has quasi-local jump operators, can be efficiently simulated on a quantum computer, and reduces to the usual Davies dynamics in the limit of a coarse-graining time much larger than the inverse of the smallest frequency difference. With it, we provide a rigorous model of many-body thermalization relevant to both open quantum systems and quantum algorithms.

This paper presents a scalable and robust solver for a cell-by-cell poroelasticity model, describing the mechanical interactions between brain cells embedded in extracellular space. Explicitly representing the complex cellular shapes, the proposed approach models both intracellular and extracellular spaces as distinct poroelastic media, separated by a permeable cell membrane which allows hydrostatic and osmotic pressure-driven fluid exchange. Based on a three-field (displacement, total pressure, and fluid pressure) formulation, the solver leverages the framework of norm-equivalent preconditioning and appropriately fitted norms to ensure robustness across all material parameters of the model. Scalability for large and complex geometries is achieved through efficient Algebraic Multigrid (AMG) approximations of the preconditioners' individual blocks. Furthermore, we accommodate diverse boundary conditions, including full Dirichlet boundary conditions for displacement, which we handle efficiently using the Sherman-Morrison-Woodbury formula. Our theoretical analysis is complemented by numerical experiments demonstrating the preconditioners' robustness and performance across various parameters relevant to realistic scenarios. A large scale example of cellular swelling on a dense reconstruction of the mouse visual cortex highlights the method's potential for investigating complex physiological processes such as cellular volume regulation in detailed biological structures.

In this article we describe all possible infinite linear configurations that can be found in a shift of any set of positive upper Banach density. This simultaneously generalizes Szemerédi's theorem on arithmetic progressions and the recent density finite sums theorem of Kra, Moreira, Richter, and Robertson.

Non-stabilizerness, alongside entanglement, is a crucial ingredient for fault-tolerant quantum computation and achieving a genuine quantum advantage. Despite recent progress, a complete understanding of the generation and thermalization of non-stabilizerness in circuits that mix Clifford and non-Clifford operations remains elusive. While Clifford operations do not generate non-stabilizerness, their interplay with non-Clifford gates can strongly impact the overall non-stabilizing dynamics of generic quantum circuits. In this work, we establish a direct relationship between the final non-stabilizing power and the individual powers of the non-Clifford gates, in circuits where these gates are interspersed with random Clifford operations. By leveraging this result, we unveil the thermalization of non-stabilizing power to its Haar-averaged value in generic circuits. As a precursor, we analyze two-qubit gates and illustrate this thermalization in analytically tractable systems. Extending this, we explore the operator-space non-stabilizing power and demonstrate its behavior in physical models. Finally, we examine the role of non-stabilizing power in the emergence of quantum chaos in brick-wall quantum circuits. Our work elucidates how non-stabilizing dynamics evolve and thermalize in quantum circuits and thus contributes to a better understanding of quantum computational resources and of their role in quantum chaos.

High-precision positioning in GPS-denied environments is a demanding but challenging technology. Resonant Beam Positioning (RBP) utilizes a resonant beam with properties such as energy focusing, self-establishment, self-alignment, and passive operation, offering a promising solution for this task. However, traditional RBP algorithms require a fixed number of resonant beam base stations, which can be costly to expand coverage. To address this limitation, we propose a distributed resonant beam positioning (DRBP) system that simultaneously estimates the base station and mobile target (MT) positions. Firstly, the MT receives resonant beam samples to locate the base station in the limited field of view (FoV) region. Subsequently, it estimates self-position based on the known locations of the base stations. During moving, the DRBP system facilitates self-positioning on the MT side, enabling dynamic expansion of both the number of base stations and the coverage area. Numerical results demonstrate that DRBP achieves a positioning root mean square error (RMSE) of $0.1$ m and a rotation RMSE of 2$^\circ$, validating the system's high accuracy.

In this paper we introduce a graded bracket of forms on multicontact manifolds. This bracket satisfies a graded Jacobi identity as well as two different versions of the Leibniz rule, one of them being a weak Leibniz rule, extending the well-known notions in contact geometry. In addition, we develop the multisymplectization of multicontact structures to relate these brackets to the ones present in multisymplectic geometry and obtain the field equations in an abstract context. The Jacobi bracket also permits to study the evolution of observables and study the dissipation phenomena, which we also address. Finally, we apply the results to classical dissipative field theories.

In this note, we consider the space $H(Ω)^{\mathbb N}$ of sequences of holomorphic functions on an open set $Ω\subset {\mathbb C}$. If $H(Ω)$ is endowed with its natural topology and $H(Ω)^{\mathbb N}$ is endowed with the product topology, then it is proved the existence of two closed infinite dimensional vector subspaces of $H(Ω)^{\mathbb N}$ such that all nonzero members of the first subspace are sequences tending to zero pointwisely but not compactly on $Ω$ and all nonzero members of the second subspace are sequences tending to zero compactly but not uniformly on $Ω$. This complements the results provided in a recent work by the same authors.

This paper expresses the Chern character for topological K-theory based on the formulation of the family of Fredholm operators, by using the points at which the Fredholm operator becomes singular (Fermi points). In particular, we explain that the odd Chern character can be thought of as a generalization of the spectral flow. As applications, we give elementary proofs of the evenness of the edge index and the bulk-edge correspondence for four-dimensional topological insulators with time-reversal symmetry of class AI.

We develop a continuous-time stochastic model for optimal cybersecurity investment under the threat of cyberattacks. The arrival of attacks is modeled using a Hawkes process, capturing the empirically relevant feature of clustering in cyberattacks. Extending the Gordon-Loeb model, each attack may result in a breach, with breach probability depending on the system's vulnerability. We aim at determining the optimal cybersecurity investment to reduce vulnerability. The problem is cast as a two-dimensional Markovian stochastic optimal control problem and solved using dynamic programming methods. Numerical results illustrate how accounting for attack clustering leads to more responsive and effective investment policies, offering significant improvements over static and Poisson-based benchmark strategies. Our findings underscore the value of incorporating realistic threat dynamics into cybersecurity risk management.

Detecting individual spins--including stable and metastable states--represents a fundamental challenge in quantum sensing with broad applications across condensed matter physics, quantum chemistry, and single-molecule magnetic resonance imaging. While nitrogen-vacancy (NV) centers in diamond have emerged as powerful nanoscale sensors, their performance for single-spin detection remains constrained by substantial environmental noise and restricted sensing volume. Here, we propose and demonstrate an entanglement-enhanced sensing protocol that overcomes these limitations through the strategic use of entangled NV pairs. Our approach achieves a 3.4-fold enhancement in sensitivity and a 1.6-fold reduction in spatial resolution relative to single NV centers under ambient conditions. The protocol employs carefully engineered entangled states that amplify target spin signals through quantum interference while suppressing environmental noise. Crucially, we extend these capabilities to resolve metastable single-spin dynamics, directly observing stochastic transitions between different spin states by identifying state-dependent coupling strengths. This dual functionality enables simultaneous detection of static and dynamic spin species for studying complex quantum systems. The achieved performance establishes entanglement-enhanced sensing as a viable pathway toward atomic-scale characterization of quantum materials and interface.

We present SPDL (Scalable and Performant Data Loading), an open-source, framework-agnostic library designed for efficiently loading array data to GPU. Data loading is often a bottleneck in AI applications, and is challenging to optimize because it requires coordination of network calls, CPU-bound tasks, and GPU device transfer. On top of that, Python's GIL (Global Interpreter Lock) makes it difficult to gain performance improvement from multi-threading. We found that when data preprocessing functions release the GIL entirely, it is possible to execute them concurrently in a thread pool, thereby improving the workflow performance. Our benchmark shows that compared to the PyTorch DataLoader, SPDL can iterate through the ImageNet dataset 74% faster while using 38% less CPU and 50GB less memory. When training ViT-B/16 model, SPDL can send data to the GPU at a speed that does not starve the training. Additionally, when using SPDL on Python 3.13t, without changing any code, the throughput is further by improved by 33%, thanks to the disabled GIL. SPDL can improve the performance of current AI model training, and receives further performance improvements when Free-Threaded Python is adopted in production systems. SPDL is available at https://github.com/facebookresearch/spdl.

Let $Z$ be a noetherian integral excellent regular scheme of dimension 2. Let $Y$ be an integral normal scheme endowed with a finite flat morphism $Y \to Z$ of degree 2. We give a description of Lipman's desingularization of $Y$ by explicit equations, leading to a desingularization algorithm for $Y$.

In this paper, we consider the hyperbolic nonlinear Schrödinger equations (HNLS) on $\mathbb{R}\times\mathbb{T}$. We obtain the sharp local well-posedness up to the critical regularity for cubic nonlinearity and in critical spaces for higher odd nonlinearities. Moreover, when the initial data is small, we prove the global existence and scattering for the solutions to HNLS with higher nonlinearities (except the cubic one) in critical Sobolev spaces. The main ingredient of the proof is the sharp up to the endpoint local/global-in-time Strichartz estimates.

The predictive power of cosmic inflation hinges on the existence of a conserved quantity at very large scales, called the primordial curvature perturbation, which is therefore insensitive to the details of reheating and the physics of the hot Big Bang. Whether the classical spacetime symmetries responsible for this conservation law can enforce it at the quantum level is an old debate. Although this was never explicitly proven, cosmologists often assume that this freezing holds at all loop orders and that inflationary predictions can always be propagated to the radiation era, with primordial fluctuations playing the role of seeds for the large-scale structures that we observe in our universe today. In this work, by consistently using the effective field theory of inflationary fluctuations, we explicitly prove for the first time that the renormalized one-loop power spectrum of the primordial curvature perturbation freezes exactly on scales larger than its sound horizon.

We numerically investigate the application of the path-sum-based causal set scalar propagator construction to (1+1)-dimensional Anti-de Sitter (AdS) spacetime. Building upon a generalization of Johnston's path sum approach, we simulate Poisson-sprinkled causal sets in AdS$_{1+1}$ and numerically evaluate the retarded scalar propagator, comparing it to the known continuum result. Our results confirm that even in curved spacetimes with constant negative curvature, the discrete causal set path sum reproduces the continuum propagator without modification of the flat-spacetime jump amplitudes, thereby providing further numerical support for former analytical results and the applicability of the path sum formalism to curved Lorentzian manifolds.

The identification of Partial Differential Equations (PDEs) has emerged as a prominent data-driven approach for mathematical modeling and has attracted considerable attention in recent years. The stability and precision in identifying PDE from heavily noisy spatiotemporal data present significant difficulties. This problem becomes even more complex when the coefficients of the PDEs are subject to spatial variation. In this paper, we propose a \textbf{W}eak formulation of \textbf{G}roup-sparsity-based framework for \textbf{IDENT}ifying PDEs with varying coefficients, called \textbf{WG-IDENT}, to tackle this challenge. Our approach utilizes the weak formulation of PDEs to reduce the impact of noise. We represent test functions and unknown PDE coefficients using B-splines, where the knot vectors of test functions are optimally selected based on spectral analysis of the noisy data. To facilitate feature selection, we propose to integrate group sparse regression with a newly designed group feature trimming technique, called GF-Trim, to eliminate unimportant features. Extensive and comparative ablation studies are conducted to validate our proposed method. The proposed method not only demonstrates greater robustness to high noise levels compared to state-of-the-art algorithms but also achieves superior performance while exhibiting reduced sensitivity to hyperparameter selection.

The toroidal geometry of tokamaks and stellarators is known to play a crucial role in the linear physics of zonal flows, leading to e.g. the Rosenbluth-Hinton residual and geodesic acoustic modes. However, descriptions of the nonlinear zonal flow growth from a turbulent background typically resort to simplified models of the geometry. We present a generalised theory of the secondary instability to model the zonal flow growth from turbulent fluctuations in toroidal geometry, demonstrating that the radial magnetic drift substantially affects the nonlinear zonal flow dynamics. In particular, the toroidicity gives rise to a new branch of propagating zonal flows, the toroidal secondary mode, which is nonlinearly supported by the turbulence. We present a theory of this mode and compare the theory against gyrokinetic simulations of the secondary mode. The connection with other secondary modes -- the ion-temperature-gradient and Rogers-Dorland-Kotschenreuther secondary modes -- is also examined.

We establish a correspondence between the gravitational phase space at null infinity and the subleading phase space near a finite-distance null hypersurface, such as a black hole horizon. Within this framework, we identify the celestial $Lw_{1+\infty}$ symmetries in the subleading phase space at the horizon by constructing their canonical generators and imposing self-duality conditions. This leads to an infinite tower of conserved charges in the absence of radiation, revealing new gravitational observables relevant to black hole physics.