For a given graph $F$, a graph $G$ is said to be $F$-saturated if $G$ contains no copy of $F$ but for any edge $uv\notin E(G)$, $G+uv$ contains a copy of $F$. The saturation number $sat(n,F)$ is defined as the minimum number of edges among all $n$-vertex $F$-saturated graphs. The virus graph $K^s_t$, where $s\geq0$ and $t\geq \max\{3,s\}$, is a graph of order $s+t$ constructed by attaching $s$ distinct leaves to $s$ different vertices of a complete graph $K_t$. Hua and Peng [Discrete Math. 349 (2026) 114674] determined $sat(n,K^2_3)$ and characterized its corresponding extremal graphs. In this paper, we determine $sat(n,K^3_3)$ and $sat(n,K^2_t)$ with $t\geq 4$, together with the structural descriptions of the related extremal saturated graphs.

We report the first measurement of the semileptonic decay $D^+_s \rightarrow K^*(892)^0μ^+ν_μ$ and an improved measurement of the decay $D^+_s \rightarrow K^*(892)^0 e^+ν_{e}$ using a sample of $7.33~\mathrm{fb}^{-1}$ of $e^+e^-$ annihilation data collected at center-of-mass energies between 4.128 to 4.226~GeV with the BESIII detector at the BEPCII collider. We measure the branching fractions to be $\mathcal B({D^+_s\rightarrow K^*(892)^0 μ^+ν_μ})=(2.07\pm0.22_{\rm stat}\pm0.10_{\rm syst})\times10^{-3}$ and $\mathcal B({D^+_s\rightarrow K^*(892)^0 e^+ν_{e}})=(2.14\pm0.18_{\rm stat}\pm0.10_{\rm syst})\times10^{-3}$. Based on a simultaneous study of the dynamics in two semileptonic decays, the hadronic form factor parameters in the $D^+_s\rightarrow K^{*}(892)^0$ transition are determined to be $r_{V} = V(0)/A_1(0) = 1.63 \pm 0.14_{\rm stat} \pm 0.08_{\rm syst}$, $r_{2} = A_2(0)/A_1(0) = 0.60 \pm 0.13_{\rm stat} \pm 0.06_{\rm syst}$, and $A_1(0)=0.56 \pm 0.02_{\rm stat} \pm 0.01_{\rm syst}$, where $V(0)$ is the vector form factor and $A_{1,2}(0)$ are the axial-vector form factors evaluated at $q^2=0$. The precision of $r_V$ and $r_2$ is improved by twofold and $A_1(0)$ is measured for the first time. We also report the first model-independent measurements of the differential decay rates and the lepton forward-backward asymmetries for $D^+_s\rightarrow K^{*}(892)^0\ell^+ν_{\ell}$ decays. Based on these measurements, we perform a test of lepton flavor universality in full and separate $q^2$ intervals with $D^+_s\rightarrow K^{*}(892)^0\ell^+ν_{\ell}$ decays. No violation is found within uncertainties. Our results present for the first time a complete study of the dynamics in the $D_s^+\rightarrow K^*(892)^0$ transition, and provide stringent tests of various non-perturbative theoretical calculations.

Lagrangian generalized Nash equilibriums (LGNEs) were introduced by Rockafellar (2024) for a class of generalized Nash equilibrium problems (GNEPs) in which each player's strategy is subject to conic constraints. This paper investigates the stability properties of the LGNE solution set, specifically focusing on the Aubin property, isolated calmness, and Lipschitz continuous single-valued localization. For general conically constrained GNEPs, characterizations of the Aubin property and isolated calmness of the LGNE solution mapping under canonical perturbations are established. These characterizations are formulated using the coderivative and graph derivative of normal cone mappings. Subsequently, these general results are specialized to GNEPs with equality and inequality constraints, yielding explicit characterizations for both the Lipschitz continuous single-valued localization and isolated calmness of the corresponding LGNE solution mapping, which are described by nonsingularity of linear complementarity sytems. For GNEPs with shared conic constraints, the Aubin property and isolated calmness of the consensus LGNE solution mapping--where identical Lagrange multipliers are assigned to the shared constraint--are first characterized. We further analyze the case when the conic constraints are specialized as equalities and inequalities. Finally, for classical conically constrained Nash equilibrium problems, the Aubin property and isolated calmness of the Lagrangian Nash equilibrium solution mapping are also analyzed.

This paper establishes a structural generalization of Batchelor's theorem within the framework of $C^\infty$-superschemes. Our main result proves that any Batchelor space satisfies a global splitness condition, establishing an isomorphism between the structure sheaf and its associated graded sheaf. Although this isomorphism is non-canonical, the existence of a splitting endows the structure sheaf with a natural $\mathbb{Z}_{\geq 0}$-grading. This grading is shown to be equivalent to the data of an even superderivation, which we term an Euler vector field. Consequently, global splittings of $C^\infty$-superspaces can be characterized in terms of Euler vector fields, providing a differential-geometric formulation of the splitting.

We give an improved connectivity oracle under vertex failures. After a set of $k$ vertices fails, our oracle performs an $O(k^{6})$-time update independent of the graph size $n$, and then answers pairwise connectivity queries in optimal $O(k)$ time. For constant $k$, it uses near-linear space and can be built in near-linear preprocessing time. In contrast, all prior oracles with $n$-independent update time[PSS+22, vdBS19] either require $Ω(n^{2})$ space or incur $2^{2^{O(k)}}$ update and query time. Moreover, their preprocessing time is polynomially large in $n$, far from near-linear. Our oracle builds on the unbreakable decomposition framework of[PSS+22], but introduces three new ingredients: (i) shortcutting over the tree decomposition to reduce space from quadratic to near-linear, (ii) bootstrapping that leverages $n$-dependent oracles internally to obtain near-linear preprocessing, and (iii) a new patch set mechanism that yields conditionally optimal $O(k)$ query time.

Current merged precipitation products such as IMERG, GSMAP, and CMORPH combine satellite estimates from passive microwave (PMW) and infrared (IR) observations. However, the different information content of these sensors makes it challenging to produce consistent precipitation estimates, even for coincident observations. The resulting inconsistencies between PMW and IR retrievals can introduce artifacts in the temporal evolution of merged precipitation fields and lead to an overreliance on time-propagated PMW estimates. We introduce GPROF-IR, a novel IR precipitation retrieval that leverages a convolutional neural network to improve precipitation estimates from single-channel IR observations. We demonstrate that the proposed model is able to leverage the temporal information in half-hourly IR observations to improve precipitation estimates. GPROF-IR is designed for integration into the upcoming release of the Integrated Multi-Satellite Retrieval for GPM (IMERG V08) and produces estimates that are climatologically consistent with the GPROF-NN PMW retrieval. We evaluate GPROF-IR using independent, global reference measurements and demonstrate substantial improvements over conventional IR retrievals. GPROF-IR provides lower mean squared error and higher correlation coefficient than IMERG V07 PMW estimates over continental land masses but remains below the accuracy of PMW precipitation estimates over sea surfaces and climate regimes with a greater influence from shallow precipitation. By expoiting both spatial and temporal information content in geostationary IR observations, GPROF-IR establishes a new state of the art for single-channel IR precipitation retrievals. GPROF-IR can be used to quasi-global precipitation estimates at half-hourly resolution from 1998 onward, providing a consistent and accurate foundation for improving merged precipitation products.

This paper considers stochastic optimization problems with weakly convex objective and constraint functions. We propose Prox-PEP, a proximal method equipped with quadratic subproblems. To handle nonlinear equality constraints, we employ an exact penalty approach, transforming them into inequality constraints with auxiliary slack variables. At each iteration, we construct quadratic approximations for both the objective and the constraint functions to facilitate efficient subproblem computation. By carefully designing the second-order approximation matrices, the subproblem constructed via the augmented Lagrangian function is strictly guaranteed to be strongly convex. Furthermore, we adopt a dynamic strategy for the equality penalty parameter: it monotonically increases up to a predefined threshold and remains constant thereafter. Building upon this algorithmic framework, we establish comprehensive asymptotic complexities. We prove that Prox-PEP achieves an $\mathcal{O}(T^{-1/4})$ average expected oracle complexity for $ε$-KKT stationarity, specifically bounding the squared norm of the gradient of the Moreau envelope of the Lagrangian function, alongside constraint violations and complementarity conditions. Additionally, under standard light-tailed martingale noise assumptions, we derive an $\mathcal{O}(T^{-1/8})$ high-probability convergence bound for the norm of the gradient of the Lagrangian's Moreau envelope, as well as $\mathcal{O}(T^{-1/4})$ high-probability bounds for both constraint violations and complementarity conditions.

Channel knowledge map (CKM) has emerged as a promising technique to leverage prior propagation knowledge in low-altitude wireless networks (LAWNs), yet state-of-the-art grid-based CKM construction methods struggle to support efficient LAWN deployment due to their lack of differentiability with respect to continuous locations of unmanned aerial vehicles (UAVs). To overcome this limitation, we propose a differentiable CKM-triggered trajectory optimization framework for LAWNs. Firstly, we propose a location-oriented CKM construction method that directly maps continuous spatial coordinates to channel gain. In particular, a shared convolutional neural network (CNN) is employed to encode high-level environmental features from conditional inputs. These features are then sampled based on location information to form a fused regressor-conditional multilayer perceptron (c-MLP) or conditional Kolmogorov-Arnold network (cKAN)-for channel gain prediction. We further propose a joint power, bandwidth, and trajectory optimization (JPBTO) method for multi-UAV systems, with the constructed differentiable CKM employed to evaluate the communication performance. The formulated non-convex problem is solved via alternating optimization and successive convex approximation. Numerical results show that the proposed framework enables location-aware differentiability of the CKM, while achieving higher accuracy than the methods without environmental features. Furthermore, the proposed CKM-JPBTO achieves a significantly higher minimum throughput than the conventional statistical channel model-based JPBTO.

Training wide neural networks on sensitive data in untrusted cloud environments requires simultaneously achieving computational efficiency and rigorous privacy guarantees. Sparsification techniques, essential for scalable training of wide layers, expose input-dependent memory-access patterns (i.e., leakage) that are visible and can be exploited by a host OS/hypervisor, even when computation is protected by a Trusted Execution Environment. We present TENNOR, a system that resolves this tension by co-designing the neural network training pipeline with doubly oblivious primitives, eliminating access-pattern leakage while also utilizing adaptive sparsification. TENNOR recasts sparse neuron activation as a locality-sensitive hashing (LSH) retrieval problem, reducing secure sparsification to doubly oblivious accesses over an LSH data structure. To eliminate the prohibitive storage cost of ``multi-table'' LSH, we introduce Multi-Probe Winner-Take-All (MP-WTA): the first multi-probe scheme for rank-based LSH, achieving a 50x reduction in (hash table) memory while preserving model accuracy. We evaluate TENNOR on extreme multi-label classification benchmarks with output layers of up to 325K neurons inside an Intel TDX Trusted Domain, achieving speedups of 13x--470x over a Path ORAM baseline and reducing a 208-hour run to about 26 minutes.

Glycine-the simplest amino acid-has remained undetected in the interstellar medium despite decades of sensitive searches, motivating alternative approaches to constrain its astrochemical origin. A promising strategy is to investigate the broader $\rm C_{2}H_{5}O_{2}N$ isomer family and identify detectable members that can serve as observational anchors for glycine-related chemistry. Herein, we report the first robust interstellar detection of methyl carbamate toward the hot molecular core G358.93-0.03 MM1 using ALMA 1 mm observations. Ten unblended rotational transitions are identified, yielding a column density of (4.21$\pm0.84)\times10^{15} \rm cm^{-2}$ and an excitation temperature of $204\pm10$ K. We also searched for other $\rm C_{2}H_{5}O_{2}N$ isomers with available rotational spectroscopic data, including glycine, but none were detected, allowing us to derive upper limits on their column densities. The resulting abundance pattern deviates significantly from the Minimum Energy Principle predictions, highlighting that the $\rm C_{2}H_{5}O_{2}N$ family is shaped primarily by kinetic chemical process rather than thermodynamic equilibrium. The observed methyl carbamate abundance is consistent with a grain-surface formation scenario involving radical-radical recombination ($\rm CH_{3}$O + $\rm NH_{2}$CO), further supported by its correlated abundances with its proposed precursors, methanol and formamide, across diverse astrophysical environments. This detection establishes methyl carbamate as a new observational anchor for glycine chemistry, providing critical constraints on the formation pathways of amino-acid-related molecules in star-forming regions.

The $\mathcal{H}_2$ model reduction problem for high-dimensional linear quantum systems is studied under the constraint of physical realizability (PR). This constraint requires preservation of the canonical commutation relations and the quantum input-output structure, and therefore prevents the direct use of standard projection methods. A symplectic Petrov-Galerkin framework is presented, in which reduced-order models automatically satisfy the PR identities by construction. Within this framework, a symplectic variant of the iterative rational Krylov algorithm is developed and referred to as Quantum IRKA (Q-IRKA). At each iteration, an enriched tangential rational Krylov pool is generated from shifted linear solves. A symplectic basis is then extracted by a Gram-Schmidt-type procedure, paired with symplectic conjugates, and normalized so that the reduced trial space satisfies the canonical symplectic constraint. The interpolation points are updated from selected mirror images of the poles of the current reduced-order model, while the reduced-order matrices are obtained exclusively by structure-preserving projection. Numerical experiments on low-channel oscillator-chain systems and on a bosonic Kitaev-chain-inspired benchmark show that Q-IRKA is effective for large-scale linear quantum systems. Symplecticity and PR are preserved to machine precision, and accurate reduced-order models are obtained with moderate computational cost. The results also show that reduction quality depends substantially on dissipation geometry, channel placement, heterogeneity, and reduced order. These findings indicate that scalable $\mathcal{H}_2$ model reduction of linear quantum systems can be achieved while strictly preserving the underlying physical structure.

A particle-in-a-box model of continuous space quantum annealing is proposed and studied numerically by solving the Schrödinger wave equation directly. Three types of energy landscapes with multiple local minima are considered, namely a sinusoidal wave modulated by a concave, a convex, or a flat envelope. Both static (energy spectrum) and dynamical (residual energy) behaviors are analyzed in detail, paying particular attention to the effects of landscape roughness and annealing depth. Simulation results show that the residual energy as a function of annealing speed is largely independent of these two factors. The prevalence of diabatic transitions during annealing is observed, and the discrepancy between our numerical results and the Landau-Zener formula is discussed. An interesting feature in the energy gap spectrum, which we call flat gaps, is examined. Based on it, we propose a mechanism to explain the trapping of wave function in local minima during diabatic transitions, widely observed in our data.

Sparse solution problems play an important role in both signal processing and image restoration. In this paper, we propose a stochastic column-block nonlinear Bregman method for efficiently computing sparse solutions to nonlinear systems. Under certain assumptions, we analyze the convergence of the proposed method and derive an upper bound for its convergence rate. Numerical experiments, including an image recovery problem, are presented to illustrate the efficiency of the proposed method.

GitHub Actions is increasingly used to deploy LLM-based agents for repository-centric tasks such as issue triage, pull-request review, code modification, and release assistance. These agentic workflows extend traditional CI/CD automation with agentic capabilities but also create a new injection surface. In this paper, we introduce Agentic Workflow Injection (AWI), a workflow-level injection flaw where untrusted GitHub event context, such as issue bodies, pull-request descriptions, or comments, is incorporated into agent prompts or agent-consumed inputs and converted into attacker-influenced behavior through agent tools or downstream workflow logic. We identify two core AWI patterns: Prompt-to-Agent (P2A), where untrusted content reaches an agent prompt boundary, and Prompt-to-Script (P2S), where attacker influence propagates through model- or agent-derived outputs into later scripts. We present the first systematic study of AWI in GitHub Actions. We characterize 1,033 real-world AI-assisted actions and extract AWI-specific taint specifications, including prompt boundaries, derived outputs, agentic capabilities, and access-control interfaces. Based on these specifications, we design TaintAWI, a taint-analysis tool that tracks flows from untrusted event context to agent prompt inputs and security-sensitive workflow sinks. Applying TaintAWI to 13,392 real-world agentic workflows from 10,792 repositories, we report 519 potential AWI vulnerabilities, of which 496 are confirmed exploitable under our threat model, yielding a precision of 95.6%. Among them, 343 are previously unknown zero-day vulnerabilities. We prioritized disclosure for 187 zero-day cases, received 26 maintainer responses, and 24 cases have been accepted or fixed at the time of writing.

Code-switching in contact varieties like Singaporean English (Singlish) challenges natural language generation due to limited parallel data and rapid lexical evolution. We propose a retrieval-augmented generation (RAG) framework that externalizes dialectal knowledge into a curated lexicon, enabling controlled lexical code-switching without fine-tuning. Our approach retrieves candidate Singlish expressions and guides generation through sparse lexical substitution. Human evaluation with 164 Singaporean participants found RAG and zero-shot prompting equally natural and appropriate. Automatic analyses reveal different transformation regimes: zero-shot prompting induces extensive paraphrasing (median 23 token edits), whereas RAG performs minimal substitutions (median 1 edit) with higher semantic preservation (mean cosine similarity 0.978 vs. 0.926). Our results demonstrate that externalizing code-switching into lexical resources enables control and auditability without sacrificing perceived quality, offering practical advantages for rapidly evolving contact varieties.

When a computer algebra system fails to solve an Ordinary Differential Equation, is this a limitation of its implementation, or a genuine computational barrier? Three traditions bear on the question. Modern computer algebra algorithms can be extremely efficient: Newton-type methods solve polynomial ODEs over $\mathbb{Q}[[X]]$ in quasi-linear time. Analog models of computation has shown that polynomial ODEs and Turing machines are two presentations of the same phenomenon, with solution length acting as time and precision as space. Computable analysis shows that ODEs can be intrinsically hard -- undecidable, even $\mathsf{PSPACE}$-complete, over compact domains. Comparing these traditions is natural and necessary, yet such comparisons routinely reduce to comparisons of encodings rather than of underlying algorithmic content. We argue that reverse mathematics provides a representation-invariant lens in which algorithmic content is compared directly. We prove that every level of the Big Five hierarchy is inhabited by a natural statement from classical ODE theory, as an exact equivalence: the regularity of $f$ is an intrinsic algorithmic invariant placing the initial value problem $y'(t)=f(t,y(t))$, $y(t_0)=y_0$, into one of several computational strata, ranging from polynomial-time solvability to transfinite computation. The resulting stratification acts as a practical diagnostic common to the three traditions. By abstracting from representation, it separates fundamental barriers from the technical shortcomings of symbolic solvers, the artefacts of analog encodings, and the effectivity constraints of computable analysis, identifying the intrinsic parameters (length bounds, radii of convergence, moduli of continuity) under which feasibility is restored.

We study the temperature dependence of meson screening masses in two-flavour lattice QCD using dynamical truncated overlap fermions (TOF), a type of lattice chiral fermions. The screening masses for the $π$, $ρ$, $a_1$, $a_0$, and the sigma $(f_0)$ mesons are extracted by computing spatial correlation functions. Above the pseudocritical temperature $T_{\rm pc}$, the $π$ and $f_0$ screening masses become degenerate, consistent with chiral restoration. The $(π,f_0)$ and $(ρ,a_1)$ pairs also show the expected degeneracy. Decomposition of the $f_0$ propagator reveals that the connected contribution dominates above $T_{\rm pc}$, while the disconnected part becomes significant below $T_{\rm pc}$, explaining the reduced statistical clarity observed at low $T$. These results demonstrate that dynamical TOF simulations can capture the qualitative thermal behaviour of the scalar sector.

We investigated quantum thermal machines powered by sequential nonselective generalized measurements, taking a double quantum dot with coherent interdot tunneling as a working substance. In this platform, the competition between detuning and tunneling hybridizes the localized states and modifies the energetic response of the cycle, allowing us to analyze measurement-driven thermodynamics beyond simple diagonal qubit models. We formulate a three-stroke cycle composed of thermalization with a single reservoir and two generalized measurement channels, and derive the corresponding internal-energy and entropy variations in order to identify the operational regimes of the device. Depending on the measurement parameters, the system can operate as a heat engine, accelerator, heater, or refrigerator. We show that the introduction of tunneling not only reshapes the boundaries between these modes, but also generates refrigeration configurations that are absent in the purely detuned model. In addition, the performance maps reveal that temperature, detuning, and tunneling amplitude jointly control the most favorable regions for work extraction and cooling. Our results demonstrate that coherent interdot coupling acts as an important resource for optimizing measurement-powered quantum thermal machines and highlight double quantum dots as a promising setting for experimentally relevant implementations of measurement-assisted thermodynamic devices.

Magnetoelectric (ME) effects in antiferromagnets provide a fertile platform for exploring symmetry-driven cross-correlated responses. However, their microscopic origin remains elusive and is often obscured in simplified low-energy descriptions. In this study, we revisit the microscopic mechanism of the ME effect in a collinear antiferromagnetic zigzag chain by employing a multi-orbital tight-binding model that explicitly includes both $s$- and $p$-orbital degrees of freedom. Using analytical and numerical calculations based on the Kubo formula, we demonstrate that the ME response is governed by orbital degrees of freedom activated through $s$--$p$ hybridization, while the spin contribution vanishes due to spin conservation. To elucidate the low-energy description, we derive an effective Hamiltonian projected onto the $s$-orbital subspace using the Schur complement. We show that a naive application of the Kubo formula within this effective model fails to capture the ME response. This issue is resolved by systematically incorporating vertex corrections in terms of orbital hybridization into the response functions. Furthermore, by introducing a quasiparticle renormalization scheme, we formulate a renormalized Kubo formula that preserves conservation laws and accurately reproduces the full multi-orbital results. Our analysis revisits the conventional low-energy perspective and reveals that the ME effect originates from virtual interorbital processes encoded in vertex corrections, rather than from the bare low-energy Hamiltonian. The effective framework developed here provides a unified microscopic understanding of orbital-driven ME responses and offers a systematic route to incorporate hybridization effects beyond simple low-energy models.

When algorithmic decisions depend on data distributed across institutions, how can we ensure that an individual's outcome does not change arbitrarily based on a protected attribute? We study this question in vertical federated learning (VFL), where features are split across parties, sensitive attributes may be private, and proxies for protected characteristics can be scattered across institutional boundaries under strict privacy constraints. Our focus is on individual-level counterfactual stability, i.e., per-instance prediction consistency under protected-attribute interventions as formalized in the causal fairness literature, rather than group parity guarantees such as demographic parity or equalized odds. We propose SCC-VFL, a server-centric framework for enforcing selective counterfactual consistency (SCC) at the individual level in VFL. SCC-VFL operationalizes a given policy specification by combining three components: (i) differentially private, graph-free discovery of feature roles into non-descendants, policy-permitted mediators, and impermissible proxies using only a formally private sketch of the sensitive attribute, with a formal per-release privacy that does not extend to the full training pipeline; (ii) masked counterfactual generation that edits only mediators while fixing non-descendants and suppressing proxy leakage; and (iii) server-side enforcement via an SCC consistency loss that penalizes impermissible prediction changes under protected-attribute interventions. Across three real-world datasets spanning credit, healthcare, and criminal justice, SCC-VFL maintains or improves predictive accuracy while sharply reducing decision flip rates by up to 98% relative to strong baselines. It also lowers attribute-inference attack success and improves robustness, demonstrating favorable utility-fairness-privacy trade-offs in realistic VFL deployments.

Biological cells are able to adapt their behaviour in response to environmental cues. Durotaxis is a phenomenon in which cells adjust their migration depending on the mechanical properties of a surrounding substrate. Although durotaxis has been studied more than two decades, basic cellular-scale mechanism of how cells regulate the motility responding to substrate stiffness remains to be elucidated. We address this issue by developing a theory utilising a mechanochemical model that integrates intracellular biochemical reactions with cellular deformation and substrate adhesion. Numerical analysis reveals that the characteristic speed and diffusion constant of cells change non-monotonically with respect to substrate stiffness, indicating the emergence of an optimal stiffness for migration. In addition, by introducing a memory effect that allows feedback from cell mechanics to the intracellular chemical reactions, the persistence time increases with substrate stiffness on a substrate softer than the optimal. We further investigate theoretically the origin of the non-monotonic dependence, that is comparable to the experimental observations, in terms of cell deformation and symmetry breaking in substrate adhesion. We believe that our study provides a unifying framework to understand complex durotactic cell migration.

We report the results of a search for sub-GeV axion-like particles (ALPs) using pilot run data from the Electron Beam-dump Experiment at KEK LINAC Switching Yard 3 (EBES). The data were collected in December 2023 with a 4 GeV positron beam and correspond to $1.3\times10^{14}$ positrons on target. In the pilot run setup, a tungsten beam dump and a single PbO calorimeter were used. We consider ALP production via the Primakoff process induced by bremsstrahlung photons in the beam dump, followed by the decay $a\toγγ$. The background was estimated with a data-driven method, and a signal region was defined such that the expected background yield is below 0.1 events. No events were observed after unblinding. Upper limits at the 90% confidence level were derived in the ALP mass-coupling plane, extending the experimental coverage into a region of parameter space not explored by previous searches.

Cooperative multi-agent reinforcement learning (MARL) involves complex agent interactions and requires effective exploration strategies. A prominent class of MARL algorithms, decentralized softmax policy gradient (DecSPG), addresses this through energy-based policy updates. In practice, however, such energy-based policies are intractable to maintain and are commonly projected onto the Gaussian policy class. In this work, we show that the limited expressiveness of Gaussian policies severely hinders exploration in DecSPG, and this limitation worsens as the number of agents grows. To address this issue, we propose decentralized diffusion policy learning (DDPL), which parameterizes each agent's policy with a denoising diffusion probabilistic model, an expressive generative model that captures multi-modal action distributions for enhanced exploration. DDPL enables efficient online training of diffusion policies via importance sampling score matching (ISSM), a novel training method with theoretical guarantee. We evaluate DDPL on representative continuous-action MARL benchmarks, including multi-agent particle environment, multi-agent MuJoCo, IsaacLab, and JAX-reimplemented StarCraft multi-agent challenge, and observe consistently improved performance.

We study the three-quark ladder Bethe--Salpeter equation in Minkowski-space QCD$_2$ in the light-cone gauge. Using the quasi-potential expansion, we project the baryon equation onto the light front and show that, at leading order in the valence truncation, the resulting mass-squared eigenvalue equation is equivalent to the Bars--Durgut equation. We also derive the endpoint power-law behavior of the valence wave function in terms of the quark mass and coupling, closely paralleling the original 't Hooft analysis for mesons. The resulting three-quark equation is solved numerically for $N_c=3$, and the ground-state baryon mass is found to be in reasonable agreement with previous light-cone quantization results in QCD$_2$, suggesting that the valence sector provides the dominant contribution to the ground state. The excited-state spectrum further yields a Regge trajectory that captures the overall trend of the experimental nucleon spectrum, and we compute selected structure observables, including parton distribution functions, double distribution amplitudes, and coordinate-space densities. This framework provides a useful confining test bed for Minkowski-space bound-state methods and for future developments toward confining formulations in 3+1 dimensions beyond the valence truncation.

Photonic Chern insulators enable unidirectional light transport protected by nontrivial band topology -- essential for robust photonic integrated circuits and error-free communication. However, disorder from impurities or defects inevitably exists in practical applications, yet how weak disorder affects topological chiral edge states remains insufficiently understood. Here, we reveal a previously unrecognized mechanism by which weak disorder can disrupt robust propagation of chiral edge states in photonic Chern insulators, despite the preservation of global topological invariants. By randomly replacing a small number of magnetized rods with nonmagnetized impurities in a magnetic photonic crystal, we find that when the excitation frequency approaches the single impurity defect state frequency, weak coupling between spatially extended defect states forms a topologically trivial impurity band inside the topological gap. This enables coexistence and coupling of defect states and chiral edge states. The reciprocal "necklace state" transport channels formed by coupled defect states break the expected unidirectional propagation in topological Chern insulators with weak disorder. Our work reveals that topological chiral edge state and disorder interactions are more intricate than previously understood and provides new insights into stability and control of topological transport in realistic applications.

We study the correlation clustering problem in the node-arrival data stream model. Unlike previous work, where the stream consists of the graph's edges, we focus on the setting in which the stream contains only the nodes. This model better reflects many real-world scenarios in which the data stream naturally consists of raw objects (e.g., images, tweets), and the similar/dissimilar edges are derived through a similarity function. We present C$^4$Approx, a streaming algorithm that approximates the cost of correlation clustering using sublinear space in the number of nodes and a constant number of passes. We further complement this result with lower bounds. Experiments on real-world datasets show that by storing only 2% of the nodes, our algorithm achieves performance comparable to the classic Pivot algorithm and the more recent PrunedPivot algorithm, even on sparse graphs.

The consistent histories formalism can be used to describe histories comprised of events across many systems, times, and places, plausibly rich enough to describe our experiences of the classical world; however, many consistent history sets are nonclassical and thus not obviously relevant to our experiences. Meanwhile, the program of environmentally induced decoherence identifies dynamically privileged classical degrees of freedom, but provides no general account of when or how many such degrees of freedom consistently combine to form histories. This work shows that the strengths of these two approaches can be combined by adopting a dynamics-first perspective on decoherence. Inspired by quantum causal models and quantum Darwinism, we define the process of decoherence in terms of the causal influences through unitary dynamics required for the proliferation of information about observables. We characterise decoherence as a property of the unitary dynamics, without presupposing the existence of any quantum state. Instead, we show that the state emerges from dual decoherence, related to decoherence by time-reversal of the unitary dynamics. Indeed, for any set of systems in an arbitrary unitary circuit, decoherence and its dual single out a privileged consistent history set -- and we demonstrate through examples that states emerge from dual decoherence while outcomes emerge from decoherence. Hence the idea that quantum states emerge from the process of decoherence turns out to be the key missing ingredient for unifying environmentally induced decoherence and consistent histories. Taking this idea ontologically seriously leads to a recently proposed causal interpretation of quantum theory or a dynamics-first version of the Everett interpretation. The causal approach also sheds light on the suppression of off-diagonal terms, time asymmetry, and robustness of the pointer basis.

This paper addresses feature subset selection for Support Vector Machines (SVMs) based on the cross-validation criterion. Unlike statistical criteria such as the Akaike information criterion (AIC) and the Bayesian information criterion (BIC), cross-validation requires only the mild assumption that samples are independently and identically distributed (i.i.d.). For this reason, the cross-validation criterion is expected to work well across a wide range of prediction problems, and it has already demonstrated its usefulness as a feature subset selection method for regression. The objective of this paper is to extend the framework of best feature subset selection via the cross-validation criterion to SVM classification problems. This subset-selection problem can be formulated as a bilevel mixed-integer optimization problem. Because bilevel optimization problems are generally hard to solve, we introduce the Least Squares Support Vector Machine (LS-SVM), whose optimality conditions admit a closed-form expression, and reduce the problem to a single-level mixed-integer optimization problem. This reformulation allows us to solve the problem using standard optimization software. We evaluate the proposed framework through simulation experiments that compare it with a regularization-based method (L1-regularization), a sequential search method (recursive feature elimination), and mixed-integer optimization (MIO) based on statistical criteria. The results show that the proposed framework achieves favorable performance both in classification accuracy and feature selection accuracy.

Membership inference attacks (MIAs) have been extensively studied in large language models (LLMs) and vision-language models (VLMs), yet their implications for vision-language-action (VLA) models remain largely unexplored. VLA models differ from standard LLMs and VLMs in several important ways: they are often fine-tuned for many epochs on relatively small embodied datasets, operate over constrained and structured action spaces, and expose action outputs that can be observed as executable behaviors and temporally correlated trajectories. These characteristics suggest a distinct and potentially more informative attack surface for membership inference. In this work, we present the first systematic study of MIAs against VLA systems. We formalize two membership inference settings for VLA models: sample-level inference over individual transition samples and trajectory-level inference over complete embodied demonstrations. We further develop a suite of attack methods under multiple access regimes, including strict black-box access. Our attacks exploit both classic MIA signals, such as token likelihood, and VLA-specific signals, such as observable action errors and temporal motion patterns. Across multiple VLA benchmarks and representative VLA models, these attacks achieve strong inference performance, showing that VLA models are highly vulnerable to membership inference. Notably, black-box attacks based only on generated actions achieve strong performance, highlighting a practical privacy risk for deployed embodied AI systems. Our findings reveal a previously underexplored privacy risk in robotic and embodied AI, and underscore the need for dedicated privacy evaluation and defenses for VLA models.

This study proposes a mixture cure model that latently divides a population based on event occurrence within a finite time horizon. Conventional models rely on event occurrence over an infinite horizon, introducing untestable assumptions that often lead to issues with identifiability and interpretability. By shifting the estimand to a specific period of interest, the proposed approach reduces reliance on these infinite-tail assumptions and aligns interpretations more closely with finite-horizon decision-making objectives. Through simulation studies, we first evaluate the statistical properties of the proposed estimator, including estimation bias and variance. We further show that relying on conventional infinite-horizon models for finite-horizon decision-making can lead to erroneous judgments. Finally, we apply the model to transaction data from Mercari, a Japanese online flea market platform. The empirical results reveal that the proposed model identifies different significant variables compared to the conventional model, offering interpretations that better reflect seasonal variation in user behavior.