Security vulnerabilities in software can have severe consequences; however, manual vulnerability detection is costly and does not scale, especially as agentic coding frameworks increase the rate of code production. Over the last decade, a large body of research has applied machine learning machine learning to automate vulnerability detection (ML4AVD), yet self-reported performance on the most popular datasets shows no clear upward trend. The ML4AVD research community has identified several flaws in problem formulations, datasets, and metrics, but these are discussed in isolation, leaving the overarching problems that generate and reinforce these flaws unaddressed. We first systematize the field through a survey of 87 influential works based on their problem formulation, input and detection granularity, target programming languages, evaluation metrics, datasets, and detection approach. Drawing on this corpus and prior empirical work, we identify twelve pain points spanning the ML4AVD pipeline and show that they are self-reinforcing and causally inter-meshed: feedback loops between datasets, formulations, baselines, and metrics perpetuate each other and explain the field's persistent concentration on binary classification of C/C++ vulnerabilities at the function level. Thus, the field optimizes for a narrow and artificial problem that omits vulnerability type prediction, broader language support, and separation of input from detection granularity. We pair each pain point with concrete recommendations to break these loops. Finally, we use AIxCC as a case study to assess how well a recent high-profile effort aligns with these recommendations and reflect on the relevance of ML4AVD in the era of agentic AI.

Graph neural networks (GNNs) are becoming increasingly popular for EEG-based depression detection. However, previous GNN-based methods fail to sufficiently consider the characteristics of depression, thus limiting their performance. Firstly, studies in neuroscience indicate that depression patients exhibit both common and individualized brain abnormal patterns. Previous GNN-based approaches typically focus either on fixed graph connections to capture common abnormal brain patterns or on adaptive connections to capture individualized patterns, which is inadequate for depression detection. Secondly, brain network exhibits a hierarchical structure, which includes the arrangement from channel-level graph to region-level graph. This hierarchical structure varies among individuals and contains significant information relevant to detecting depression. Nonetheless, previous GNN-based methods overlook these individualized hierarchical information. To address these issues, we propose a Hybrid GNN (HGNN) that merges a Common Graph Neural Network (CGNN) branch utilizing fixed connection and an Individualized Graph Neural Network (IGNN) branch employing adaptive connections. The two branches capture common and individualized depression patterns respectively, complementing each other. Furthermore, we enhance the IGNN branch with a Graph Pooling and Unpooling Module (GPUM) to extract individualized hierarchical information. Extensive experiments on two public datasets show that our model achieves state-of-the-art performance.

Physics seeks to uncover the laws of Nature and express them through mathematical equations. Despite the vast diversity of natural phenomena, physical equations exhibit structural regularities that set them apart from arbitrary mathematical expressions. While principles such as dimensional analysis have long guided the formulation of physical models, the exploration of more subtle statistical patterns within the equations of physics remains an open question. Here, by analysing four corpora of physics equations and applying advanced implicit-likelihood techniques, we find that the frequency of mathematical operators follows an exponential decay law, in contrast to Zipf's power law for word frequencies in natural languages. This reveals a statistical meta-law of physics, possibly reflecting a combination of communication efficiency and constraints imposed by Nature itself. The meta-law offers practical benefits for symbolic regression by drastically narrowing down the space of physically plausible expressions. More broadly, it may inform the development of language models that can generate coherent mathematical representations, advancing the automation of physical law discovery.

We study the problem of Hamiltonian structure learning from real-time evolution: given the ability to apply $e^{-\mathrm{i} Ht}$ for an unknown local Hamiltonian $H = \sum_{a = 1}^m λ_a E_a$ on $n$ qubits, the goal is to recover $H$. This problem is already well-understood under the assumption that the interaction terms, $E_a$, are given, and only the interaction strengths, $λ_a$, are unknown. But how efficiently can we learn a local Hamiltonian without prior knowledge of its interaction structure? We present a new, general approach to Hamiltonian learning that not only solves the challenging structure learning variant, but also resolves other open questions in the area, all while achieving the gold standard of Heisenberg-limited scaling. In particular, our algorithm recovers the Hamiltonian to $\varepsilon$ error with total evolution time $O(\log (n)/\varepsilon)$, and has the following appealing properties: (1) it does not need to know the Hamiltonian terms; (2) it works beyond the short-range setting, extending to any Hamiltonian $H$ where the sum of terms interacting with a qubit has bounded norm; (3) it evolves according to $H$ in constant time $t$ increments, thus achieving constant time resolution. As an application, we can also learn Hamiltonians exhibiting power-law decay up to accuracy $\varepsilon$ with total evolution time beating the standard limit of $1/\varepsilon^2$.

We study the problem of learning a local quantum Hamiltonian $H$ given copies of its Gibbs state $ρ= e^{-βH}/\textrm{tr}(e^{-βH})$ at a known inverse temperature $β>0$. Anshu, Arunachalam, Kuwahara, and Soleimanifar (arXiv:2004.07266) gave an algorithm to learn a Hamiltonian on $n$ qubits to precision $ε$ with only polynomially many copies of the Gibbs state, but which takes exponential time. Obtaining a computationally efficient algorithm has been a major open problem [Alhambra'22 (arXiv:2204.08349)], [Anshu, Arunachalam'22 (arXiv:2204.08349)], with prior work only resolving this in the limited cases of high temperature [Haah, Kothari, Tang'21 (arXiv:2108.04842)] or commuting terms [Anshu, Arunachalam, Kuwahara, Soleimanifar'21]. We fully resolve this problem, giving a polynomial time algorithm for learning $H$ to precision $ε$ from polynomially many copies of the Gibbs state at any constant $β> 0$. Our main technical contribution is a new flat polynomial approximation to the exponential function, and a translation between multi-variate scalar polynomials and nested commutators. This enables us to formulate Hamiltonian learning as a polynomial system. We then show that solving a low-degree sum-of-squares relaxation of this polynomial system suffices to accurately learn the Hamiltonian.

We study invariants of bosonic and fermionic (Grassmann-valued) matrices under the adjoint action of $U(N)$, weighted by the fermion number. Such models naturally appear as the supersymmetric indices of supersymmetric gauge theories and are captured by $U(N)$ matrix models. We discuss two features of the fermionic models that are qualitatively different from bosonic models. Firstly, the $2N^\text{th}$ power of a Grassmann matrix vanishes, which gives rise to many new trace relations. Secondly, trace relations in models involving fermions could cause an increase in the supersymmetric index as $N$ decreases, in contrast with purely bosonic models. We focus on a simple model involving one fermion and one derivative that corresponds to a $\frac14$-BPS supersymmetric index in $\mathcal{N}=4$ SYM theory, in which we find that the index is independent of $N$. We prove this rank-independence analytically, and experimentally study the cancellations between bosonic and fermionic trace relations that lead to it. Based on these observations, we make some conjectures on resulting algebraic structures, including the analogue of the polarized Cayley-Hamilton identities and the Second Fundamental Theorem of invariants in the presence of Grassmann matrices. Finally, we present various (smooth and singular) limits of the most general supersymmetric index in $\mathcal{N}=4$ SYM theory, and study some patterns in their behavior as a function of $N$.

This paper reviews recent advances in quantum learning theory for continuous-variable (CV) systems. Quantum learning theory investigates how to extract classical information from quantum systems as efficiently as possible. CV systems are ubiquitous in nature and in quantum technologies, as they describe bosonic and quantum-optical systems. While quantum learning theory for finite-dimensional systems has been extensively studied, the corresponding theory for CV systems has only recently begun to develop; here we provide a concise review. We focus on the following questions: what is the minimum number of copies (the sample complexity) required to learn a non-Gaussian state, possibly under energy constraints? What is the sample complexity for learning Gaussian states? How does the performance of CV state learning depend on non-Gaussianity? How can one test whether a state is Gaussian or far from the set of Gaussian states? And how can Gaussian processes be learned efficiently? Central to these topics, we also review several bounds on the trace distance between CV states in terms of their covariance matrices, which may be of independent interest. Overall, this work summarises selected developments in tomography of CV systems and highlights a selection of open problems.

Leptophilic sub-MeV spin-1 dark matter (DM) can be converted into a photon via inelastic scattering with a free electron or absorption by a neutral hydrogen atom in the primordial plasma. We study for the first time the impact of the energy injection resulting from such processes on cosmic microwave background (CMB) anisotropies. We obtain upper limits on the vector and axial-vector DM-electron couplings using Planck 2018 temperature, polarization, and lensing data for DM masses between 100 eV and 100 keV. We find that, due to the suppression of the hydrogen atomic form factor at high energies, inelastic scattering provides the dominant constraint for DM masses above the keV scale. At lower masses, hydrogen ionization through DM absorption is the leading channel, driven by the higher efficiency of post-recombination energy injection in modifying the free-electron fraction. Although the bounds we derive are considerably weaker than existing laboratory and astrophysical limits, they provide a robust and independent cosmological probe of leptophilic DM interactions.

The eigenstate thermalization hypothesis provides a framework for understanding thermalization in isolated quantum many-body systems by characterizing statistical properties of local observables in energy eigenstates. Here we demonstrate that distributions of matrix elements in macroscopic systems may depend not only on the macrostate parameters, such as the densities of local conserved charges, but generally also on the properties of ensembles used in sampling eigenstates. To this end, we depart from the conventional analysis of microcanonical windows and consider statistical ensembles with an adjustable scale parameter prescribing the magnitude of charge fluctuations. We specifically consider an integrable field theory that permits efficient numerical sampling of matrix elements and reliable extrapolation to the thermodynamic limit. Moreover, in this system, we identify a class of states that enables explicit closed-form computation of the suppression rate of matrix elements. Our findings reveal an underlying multiscale structure of matrix elements captured by a non-analytic fluctuation-scale dependence of algebraic exponents governing their statistical properties.

The structure of entanglement in the ground state of the harmonic chain is studied. A class of two-mode squeezed states, useful for this purpose, is identified. The entanglement of the local modes at the ends of the chain, after tracing out the centre, rapidly falls to zero as the length of the chain increases. However, if the central modes are measured, and the result communicated to systems interacting with the outer modes, the latter exhibit greatly enhanced entanglement, including in conditions where none was otherwise available. These ideas can be demonstrated in experiments in trapped ions, among other systems. The extension to the continuous case yields enhanced entanglement extracted from the vacuum state of a bosonic quantum field.

"Vibe coding" and "vibe analytics" have been framed as a democratization of technical capability. This paper argues that AI-assisted methodology more broadly, or what I call "vibe methodology," also democratizes the failure modes specific to each domain. When AI assists with methods whose validity depends on assumptions that cannot be verified from the output alone (a class I call "vibe inference"), the failure surface is structurally different: the output does not reliably signal invalidity, and when it does, recognizing the signal requires the expertise the workflow bypasses. I focus on "vibe econometrics," the subset of AI-assisted causal analysis where identification can be named faster than it can be audited. The claim of this paper is not that AI invents inferential failures that did not previously exist, but that it changes their incidence, observability, and persuasive force enough to create a practically distinct governance problem. This results in three failure modes: method-data mismatch, where AI bypasses expertise at execution; confidence laundering, where AI amplifies the credibility of formatted output; and invisible forking, which spans both. What is new is not the failure modes but AI's industrialization of their packaging. The barrier between naming a method and executing it has collapsed, and weak foundations, dressed as rigorous analysis, now reach audiences at a scale, speed, and polish that previously required expertise. I propose the Analysis Contract, a pre-commitment framework that adapts the logic of pre-analysis plans and the Causal Roadmap to the AI-assisted setting. The contract imposes three conditions before a causal claim is made: a method-data contract, a data audit, and a pre-commitment statement defining what would count as a disconfirming result. The framework generalizes across domains of vibe inference through domain-specific instantiation.

We study methods for simultaneous analysis of many noisy and biased estimates, each paired with an even noisier estimate of its own bias. The analyst's goal is to construct short calibrated intervals for each parameter. The standard debiasing approach, which subtracts the bias estimate from each biased estimate, inflates variance and yields long intervals. In this paper, we propose an empirical Bayes rebiasing strategy that starts from the fully debiased estimates and learns from data how much bias to reintroduce by estimating the unknown bias distribution. We provide convergence rates for the coverage of our intervals when the bias distribution is estimated using nonparametric maximum likelihood. Furthermore, we demonstrate substantial precision gains in prediction-powered inference, including pairwise LLM win-rate evaluations, as well as for inference of direct genetic effects in family-based GWAS.

The chiral magnetic effect (CME), arising from the chiral anomaly and enabling a mutual conversion between magnetic topology and fermionic chirality, is a key mechanism in magnetar field evolution. Previous work by Dehman & Pons (2025) demonstrated that the CME can efficiently generate dipolar fields ($B_{\rm dip} \gtrsim 10^{14}~\mathrm{G}$), consistent with magnetar timing measurements, provided that the initial magnetic field carries net helicity. However, whether neutron stars are born with magnetic helicity remains uncertain. In this work, we investigate the CME across a range of initial helicity configurations, including non-helical initial conditions. We find that the CME efficiently generates magnetar-strength dipoles on timescales of decades, independently of the initial helicity content. The instability is driven by localized helical structures that induce a residual chiral asymmetry and is primarily governed by the maximum chiral chemical potential, requiring $μ_5^{\rm max} \gtrsim \mathrm{few}\times10^{-11}~\mathrm{MeV}$ for onset in the magnetar regime. Our results further show that these dipoles may either remain stable and subsequently evolve through standard Ohmic decay, or become unstable if they acquire sufficient helicity, in which case they decay through the chiral anomaly, transferring energy to less helical modes. This outcome depends sensitively on the initial helicity distribution. These findings extend the applicability of the CME to more realistic magnetic-field configurations and underscore the importance of the helicity distribution at birth, a quantity that remains poorly constrained in neutron star formation, yet is crucial for determining neutron star magnetic evolution and magnetar formation.

Fractional magnetization plateaus provide a sensitive probe of many-body spin states in frustrated quantum magnets, yet their microscopic origin in kagome antiferromagnets remains unresolved. This is particularly true of the mysterious $1/9$ plateau, which is predicted by theory but infrequently observed in experiment. Here, we investigate this problem in the $S = 1/2$ anisotropic kagome antiferromagnet Y-kapellasite, Y$_3$Cu$_9$(OH)$_{19}$Cl$_8$, using pulsed-field magnetization measurements on single crystals and high-field $^{35}$Cl NMR. We identify a hierarchy of field-induced fractional features, including $1/3$ and $1/9$ plateaus, as well as a weaker low-field feature. Analysis of the NMR spectra and the magnetic susceptibility across the $1/9$ plateau demonstrate that it is accompanied by an ordered local spin configuration, a strong suppression of low-energy spin fluctuations and activated behavior, consistent with a gapped fractional state. These features differ from those in the only other material YCu$_3$(OH)$_6$Br$_2$[Br$_{1-y}$(OH)$_y$] in which this plateau is observed, implying a surprising robustness of the $1/9$ state to the details of the underlying magnetism.

Preventing signal detection in communication and active sensing requires careful control of transmission power. In fact, the square-root laws (SRL) for covert classical and quantum communication and sensing prescribe that the average output power per channel use scales as $1/\sqrt{n}$ for $n$ channel uses. Two strategies for achieving this are diffuse and sparse signaling. The former transmits signals with power decaying as $1/\sqrt{n}$ on all $n$ channel uses, which is convenient for mathematical analysis. The latter transmits constant-power signals rarely, on approximately $\sqrt{n}$ out of $n$ channel uses, while remaining silent on the others. This offers significant practical advantages in compatibility with modern digital transmitters. Here, we study sparse signaling over lossy thermal-noise bosonic channels, which describe quantumly many practical channels (including optical, microwave, and radio-frequency). We characterize the input signal state that minimizes detectability. We find an unintuitive optimal quantum state structure: a mixture of just two consecutive photon-number states. In particular, in the low-brightness regime, the optimal signal state is a mixture of vacuum and a single photon. Since these states are generally suboptimal for both communication and active sensing, we explore the resulting trade-off and identify input-power thresholds for transitions between optimizing for covertness vs. performance in communication and sensing tasks.

We studied the constrained Hamiltonian formulation of a supersymmetric Korteweg-de Vries (KdV) equation, which is observed to be a constrained system similar to its classical version. We found a nontrivial Lagrangian description, where we select $a=2$ for the free parameter $a$ in the supersymmetric extension. The corresponding degenerate Lagrangian requires an exclusive consideration and the utilization of the Dirac-Bergmann algorithm. We explicitly determined the full set of primary and secondary constraints and constructed the total Hamiltonian governing the dynamics of the system. In this analysis, in addition to a nontrivial constraint involving the fermionic fields, the consistency conditions give rise to a nonlocal contribution to the Hamiltonian density. This highlights a distinctive feature of this supersymmetric extension. We showed that the resulting Hamilton equations of motion reproduce the supersymmetric KdV system in the component form. Finally, we derived a compact superspace representation of the Hamiltonian and demonstrated its consistency with the component-level formulation.

A projective hyperkähler manifold of Kummer-type is said to be twisted modular if it is birational to the Albanese fiber of a moduli space of twisted sheaves on an abelian surface. We prove that, with the exception of certain cases of Picard rank 3, any projective Kummer-type manifold admitting a finite-order symplectic birational self-map that acts nontrivially on its second cohomology group is twisted modular. We provide a complete characterization of these exceptions in terms of their Néron-Severi lattices. We then investigate symplectic birational self-maps of modular Kummer-type manifolds, determining exactly which Mukai vectors allow the birational transformation induced by crossing the vertical wall, which acts on cohomology as a reflection, to correspond to a finite-order symplectic birational self-map. Additionally, we prove in an appendix several results concerning moduli spaces of twisted sheaves on abelian surfaces which were not readily available in the literature.

We consider three-dimensional Einstein gravity in Euclidean signature with a finite boundary of torus topology endowed with an induced metric of fixed conformal class and a constant trace of extrinsic curvature $K$. For vanishing, positive, and negative cosmological constant $Λ$, we analytically determine boundaries enclosing different patches of locally flat, de Sitter (dS$_3$), and Anti-de Sitter (AdS$_3$) spaces. We find solutions that depend non-trivially on either cycle of the torus, noting that some of them exhibit self-intersections. Adapting the Gibbons-Hawking prescription of interpreting the Euclidean gravitational path integral as a thermal partition function, we explore the rich semi-classical thermodynamic phase space of the problem. While most saddles are found to be either thermally unstable or metastable compared to those with uniform boundaries, we find inhomogeneous solutions that are thermodynamically favourable in the case of $Λ< 0$ and $2<K|Λ|^{-1/2}<3/\sqrt{2}$. Moreover, for all values of $Λ$, there exist patches of space with a non-contractible thermal circle and a macroscopic entropy. We further analyse the problem in both the AdS$_3$ boundary limit and the stretched dS$_3$ horizon limit, and comment on a recasting of the problem in terms of classical strings.

We consider the phase ordering problem for the low-temperature Ising dynamics initialized from a biased and disordered initialization. Work of Fontes, Schonmann, Sidoravicius (2002) showed that at zero-temperature, Ising Glauber dynamics on $\mathbb Z^d$ for $d\ge 2$ initialized from i.i.d. spins on each vertex that are $+1$ with sufficiently large probability, absorbs into the all-plus configuration quickly. We prove that analogous behavior holds throughout the low-temperature regime of the Ising model in two dimensions. Namely, there exists $p_0 <1$ such that Ising Glauber dynamics initialized from i.i.d. spins that are $+1$ with probability $p>p_0$, run at any low temperature $β>β_c$ converges rapidly to the plus phase measure $π^+$. The result is proved using a spacetime multiscale coupling valid in any $d\ge 2$, that boosts a uniform-in-$β$ quasi-polynomial bound on the mixing time of Ising dynamics with plus boundary conditions, into rapid phase ordering from biased initializations with no boundary conditions.

Asteroseismology is the study of resonant oscillations of stars to infer their internal structure and dynamics. It is also a powerful tool for precisely determining stellar parameters such as mass, radius, surface gravity, and age. The ongoing TESS mission, with its nearly complete sky coverage, presents a unique opportunity to uniformly probe stellar populations across the Milky Way. TESS is estimated to have observed more than 300,000 oscillating red giants, most of which have one to two months of observations. Given the scale of this dataset, we need a fast, efficient, and robust way to analyse the data. In this work, our objective is to develop a machine learning (ML) based method to infer asteroseismic parameters from short-duration observations. Specifically, we focus on two global seismic parameters, the large frequency separation ($Δν$) and the frequency at maximum power ($ν_{\mathrm{max}}$), from one-month-long TESS observations of red giants. Meanwhile, for K2 data, our focus extends to inferring the period spacings of dipolar gravity modes ($ΔΠ_{1}$), in addition to $Δν$ and $ν_{\mathrm{max}}$. Our findings demonstrate that our machine learning algorithm can accurately infer $Δν$ and $ν_{\mathrm{max}}$ for approximately 50% of samples created by taking one-month Kepler and K2 observations. For TESS one sector data however, we recover reliable $Δν$ for only about 23% of the stars. Additionally, we get reliable $ΔΠ_{1}$ inferences for about 200 young red-giants from K2. For these $ΔΠ_{1}$ inferences, we see a good match with the well known $Δν-ΔΠ_{1}$ degenerate sequence observed in Kepler red-giants.

Hidden multipolar orders in spin-orbit-coupled Mott insulators provide a promising setting for correlated quantum matter, yet their control and detection remain major challenges. Here, we demonstrate that circularly polarized light enables both in $4d^2/5d^2$ systems with edge-sharing octahedra. Using a Floquet Schrieffer-Wolff expansion of a driven Hubbard-Kanamori model, we derive a low-energy multipolar Hamiltonian with two qualitatively new light-driven terms. One is an effective static field that couples linearly to the magnetic octupole, realizing an octupolar inverse Faraday effect. The other is a bond-dependent anisotropic exchange interaction absent in equilibrium. These two couplings are the key result of this work: the first provides a direct optical handle on hidden octupolar order, while the second reorganizes the multipolar exchange landscape and opens an enlarged Kitaev-like multipolar liquid regime. Their interplay produces a nonequilibrium multipolar phase space inaccessible in equilibrium, enabling optical tuning among antiferro-octupolar, ferro-octupolar, partially polarized ferro-quadrupolar, Ising octupolar, and multipolar liquid phases. We further show that the induced multipolar order couples to the lattice, generating reversible trigonal and tetragonal distortions that provide structural fingerprints in pump-probe experiments. Our work establishes a general mechanism for the optical generation, control, and detection of hidden multipolar quantum states.

This paper presents a time domain (TD) formulation for modeling the transient electromagnetic response of two-dimensional (2D) metasurfaces using the Method of Auxiliary Sources (MAS) combined with the Generalized Sheet Transition Condition (GSTC). In the proposed approach, the frequency-domain impedance type GSTC is transformed into a causal, convolution-based TD representation and integrated within the MAS formulation. rfaces.

The rapid expansion of large-scale electronic health record (EHR) data offers unique opportunities to improve the accuracy and efficiency of clinical risk estimation. Yet, because clinical events may occur outside the recording health system, clinical event outcomes are frequently subject to double censoring (both left and right). Besides, gold-standard event times can often only be ascertained through labor-intensive manual chart reviews, yielding labels for only a small subset of patients. Reliance on this limited labeled set alone is limited in efficiency, whereas widely available surrogate outcomes such as the time to first diagnostic code or first disease mention are error-prone and can yield biased estimates if used directly. Semi-supervised learning (SSL) methods provide a principled way to integrate labeled and unlabeled data, and prior work has demonstrated their advantages in settings with binary or right-censored outcomes. However, existing approaches do not accommodate double censoring for risk prediction, which poses additional methodological challenges. To address this gap, we develop a novel SSL framework for risk prediction that combines a small set of gold-standard labels with large-scale surrogate information under double censoring. We establish the theoretical validity of the proposed estimator. Through extensive simulation studies, we show that our method substantially improves estimation efficiency relative to existing supervised estimators (based on the labeled data). Finally, we demonstrate its practical value by applying it to study risk factors for type 2 diabetes (T2D) using EHR data from a health system in the US.

In his 1976 paper "More about the massive Schwinger model", Coleman introduced $1+1$-dimensional Quantum Electrodynamics coupled to two charged massive fermions. By applying Abelian bosonization, he elucidated much of the physics of this two-flavor Schwinger model, but he listed three puzzles at the end of his paper. We present new analytical and numerical calculations to solve Coleman's three puzzles and thereby deepen our understanding of this model. These puzzles pertain to the theory with equal fermion masses at $θ= 0$ and at $θ= π$, as well as the size of isospin-breaking effects when the fermion masses are unequal. For the puzzle at $θ= π$, the solution is related to the structure of the zero-temperature phase diagram arXiv:2305.04437: for equal fermion masses $m$, the model exhibits spontaneous breaking of charge conjugation symmetry and absence of confinement for any value of the gauge coupling $g$, so that there is a smooth interpolation from weak to strong coupling. Using two-loop Renormalization Group and integrability methods, we show that the mass gap behaves as $\sim m e^{-0.111 g^2/m^2}$ in the strong coupling regime $m\ll g$. Our numerical results using the lattice Hamiltonian are in good agreement with this behavior. For the puzzle at $θ= 0$, the solution is related to a level crossing between two isosinglet particles with different discrete quantum numbers; we demonstrate the necessity of such a crossing by comparing integrability and weak coupling calculations, and we also exhibit the crossing numerically. Finally, we provide a new estimate for the size of isospin-breaking effects caused by different fermion masses at strong coupling.

A powerful means to understanding condensed matter that possesses a multi-constituent, non-isolated, and complex nature, with a preeminent example being two-dimensional (2D) materials, is studying many-body interactions. However, experimentally observing high-order many-body interactions is a daunting task due to its heavy reliance on the abundance of low-order complexes. Here, we report the observation of four-body hot biexcitons in an energetically unfavorable bilayer of tungsten disulfide (WS2) through creating extreme optical confinement. Specifically, we integrate a non-radiative bound state in the continuum (BIC) into a photonic crystal (PhC) defect cavity, forming a quasi-three-dimensional (q-3D) but open confinement for photons at the driving frequency. The extremely confined photons in both reciprocal and physical spaces then excite inherently unproductive two-body hot excitons situated slightly above the indirect bandgap so efficiently that they form overwhelmed higher-order four-body hot biexcitons. Distinctively, these hot biexcitons exhibit substantial valley polarization and coherence at room temperature, which we attribute to the topological nature of BICs and the associated q-3D confinement with an orbital angular momentum. Besides achieving room-temperature biexcitons, the q-3D confinement could be valuable for higher-order interactions, such as triexcitons, and many other many-body phenomena, including Bose-Einstein condensation.

We introduce ECNUClaw, an open-source framework for building learner-profiled intelligent study companions in K-12 education. The system constructs and maintains a five-dimension learner profile -- covering cognitive, behavioral, emotional, metacognitive, and contextual dimensions -- by extracting signals from student-companion dialogues at each turn. Profile updates feed directly into an adaptive strategy engine that adjusts the companion's guidance intensity, encouragement frequency, and Bloom's taxonomy scaffolding in real time. The framework design draws on three theoretical strands from the Chinese educational technology literature: Zhang's Digital Portrait Three-Layer Framework for learner assessment, the Education Brain model for educational system architecture, and the Human-AI Collaborative IQ concept for companion design philosophy. ECNUClaw is implemented in Python and supports seven Chinese LLM providers through a unified OpenAI-compatible adapter layer. We describe the system architecture, the profiling and adaptation mechanisms, and discuss limitations and next steps. The source code is available at https://github.com/bushushu2333/ECNUClaw.

Recently, the pinching antenna systems (PASS) have attracted significant attention due to their ability to exploit dynamically reconfigurable pinching points along waveguides for flexible signal transmission. However, existing work largely overlooks user mobility although the optimal pinching configuration is highly dependent on the user's location and must be continuously adjusted. In this work, we investigate a PASS-enabled system model in which a base station (BS) serves a mobile user. We formulate an optimization problem that aims to maximize the user's average sum rate over a predefined time horizon while satisfying quality-of-service (QoS) constraint. This objective is achieved by jointly optimizing the beamforming vector at the BS and the pinching locations along the waveguides. Nevertheless, the resulting problem is highly non-convex and challenging to solve using conventional optimization techniques due to the intricate coupling among variables. The difficulty is further exacerbated by environmental randomness arising from user mobility and a probabilistic blockage model. This reveals a key engineering challenge: the performance gains of PASS critically rely on the ability to track or predict user trajectories in real time. To address these challenges, we adopt a deep deterministic policy gradient (DDPG) approach within a reinforcement learning framework, which is well-suited for continuous state and action spaces. Finally, extensive simulations are conducted to validate the proposed approach and demonstrate the importance of real-time configurability.

This work concerns the design and analysis of a limiting technique that allows the preservation of invariant domains for high-order numerical approximations of nonlinear hyperbolic systems of conservation laws. The method can be applied to any conservative discretization method in space as well as to a wide range of explicit and implicit time integration schemes. The method limits the high-order solution around a low-order accurate solution that is known to preserve all the invariant domains. It generalizes the flux-corrected transport limiter [J. P. Boris and D. L. Book, J. Comput. Phys., 11, 1973; S. T. Zalesak, J. Comput. Phys., 31, 1979] to systems of conservation laws and relies on the limitation of antidiffusive fluxes, but defines the limiting coefficients so as to express the limited solution as a convex combination of invariant domain preserving quantities similarly to the convex limiting framework [Guermond et al., Comput. Methods Appl. Mech. Engrg., 347, 2019]. We give details on the derivation of this limiting technique and provide some illustration with finite volume or discontinuous Galerkin (DG) space discretizations associated to explicit or implicit Runge-Kutta methods as well as to time DG integrations. The limiter is applied iteratively to refine the limited solution around the high-order one, while preserving the invariant domains, and a heuristic is proposed to accelerate its convergence. Numerical experiments solving one- and two-dimensional problems involving scalar hyperbolic equations and the compressible Euler equations are presented to illustrate the properties of these schemes.

Let $\mathrm{Mac}(W)$ be the MacNeille completion of the Bruhat order of a Coxeter group $W$. We introduce an action of the $0$-Hecke monoid of type $W$ on $\mathrm{Mac}(W)$, which allows us to define a weak order and a descent set statistic on $\mathrm{Mac}(W)$. When $W$ is of type $A$, we recover constructions of Hamaker and Reiner, which were originally formulated in terms of monotone triangles and alternating sign matrices. Using this action, we prove that certain unions of Knutson--Miller subword complexes are vertex-decomposable. By specializing to type $A$, we prove a conjecture of Escobar, Klein, and Weigandt regarding Cohen--Macaulay ASM varieties. Along the way, we also exhibit a counterexample to a conjecture of Hamaker and Reiner regarding the poset topology of intervals in the ASM weak order. Finally, when $W$ is finite and irreducible, we use our $0$-Hecke action to introduce a noninvertible dynamical system on $\mathrm{Mac}(W)$ that we call the MacNeille pop-stack operator, and we prove that the maximum number of iterations of this operator needed to reach the bottom state is $h-1$, where $h$ is the Coxeter number of $W$. This article is meant to serve as a case study in using large language models to automate the workflow of mathematical research. The proof of the conjecture of Escobar--Klein--Weigandt and the disproof of the conjecture of Hamaker--Reiner were obtained autonomously by ChatGPT 5.4 Pro. Other aspects of the paper were obtained mostly by the author, but ChatGPT expedited the process. We provide a detailed account of this interaction, and we speculate on what allowed the model to be successful.

The celebrated Kronig-Penney model traditionally has been formulated with square well potentials representing atomic centres. Here, we use a slightly more realistic potential, the truncated harmonic oscillator, in lieu of square well potentials, and solve the model analytically. We derive the energy dispersion and wave functions for this model. This configuration has some important similarities and differences compared to the usual model. In particular, we write the governing equation in a form suggestive of the tight-binding approximation, as can be done for the usual model. In this way, it is straightforward to derive an expression for the tunneling amplitude used in tight-binding in terms of the harmonic oscillator potential parameters.