Published: 2026-07-26 16:54:31
Authors: Arman Kolozyan, Tom Sorger, Alexander Hicks, Stefanos Chaliasos
Categories: cs.CR
Abstract:
Zero-knowledge proofs (ZKPs) have become a core technology for privacy and verifiable computing. They are used to secure blockchains that handle billions of dollars and identity applications dealing with sensitive personal data. However, ZKP systems are complex, and subtle implementation errors can completely break their guarantees, letting attackers forge money or false proofs of identity. Researchers and practitioners have therefore developed a growing set of bug detection and formal verification methods to secure these systems. Yet their real-world effectiveness and adoption remain unclear. In this paper, we aim to shed light on the state of ZKP security tooling. We first systematize the landscape of these tools and observe that most target Circom, leaving newer DSLs and zkVMs with limited support. We then evaluate six tools across 70 real-world vulnerabilities and find that while the tools detect 45.7% of bugs on isolated targets, their effectiveness drops to 19.6% on full codebases, with important vulnerability classes left unaddressed. We also present the first systematic analysis of formal verification efforts, revealing that current work focuses primarily on constraint correctness and identifying key gaps and risks. Finally, we survey 48 practitioners, showing that development and security remain human-led, LLMs are widely used, and practitioners prioritize tools with clearer guarantees and lower integration effort. Overall, our results highlight the need for better integration of security tooling with the development and auditing process, and we provide actionable insights for researchers and practitioners.
Published: 2026-07-26 16:41:43
Authors: Peyman Nasehpour
Categories: math.AC, math.RA
Abstract:
In this paper, we investigate the subtractive closure operator in commutative hemiring theory. While this operator satisfies standard closure properties, it does not distribute over ideal addition, intersection, or multiplication in general. We introduce Kuratowski hemirings (where closure preserves joins) and nucleus hemirings (where closure preserves meets), providing explicit counterexamples and positive results for each. Key findings include: the standard semiring $\mathbb{N}_0$ and the max-plus algebra are nucleus hemirings with multiplicative distributivity; the interval semiring $T = [0,1]$ is Kuratowski and multiplicatively distributive but not nucleus; and polynomial hemirings $S_0[X,Y,Z]$ over zerosumfree hemirings form a broad class of non-nucleus counterexamples. We also correct a recent claim regarding distributivity over arbitrary intersections.
Published: 2026-07-26 16:38:35
Authors: A. Montañés, E. Ruiz
Categories: econ.EM
Abstract:
It is obvious to say that an adequate estimation of the autocorrelation function is central in time series analysis. In this paper, we propose three new robust estimators based on ratios of observations, which offer strong resistance against outliers. While the first estimator, which is based on the median, is not efficient, the second is a Quasi Maximum Likelihood (QML) estimator with better efficiency properties. The third estimator is a plug-in estimator, which does not require numerical optimization and, consequently, is extremely simple from a computationally point of view, having similar efficiency to that of the ML estimator. We derive the asymptotic distribution of the first two estimators, when the true autocorrelations are zero. Furthermore, we also show that the asymptotic distribution of the plug-in estimator is rather close to that of the QML estimator, allowing for inference and, in particular, for the construction of point-wise significance bands for the autocorrelations. Using Monte Carlo simulations, we analyse the finite sample properties of the proposed estimators and compare them with those of the sample autocorrelations and alternative extant robust estimators based on ranks. Although the proposed estimators have larger dispersion than the sample autocorrelations in uncontaminated time series, they are highly robust in the presence of outliers. Also, they have better properties than popular alternative robust estimators based on ranks when estimating autocorrelations of order larger than one. The results are illustrated by estimating the correlogram of daily IBEX35 returns, quarterly US economic growth and monthly US inflation.
Published: 2026-07-26 15:53:43
Authors: Roumen Anguelov, Charlise Basson, Yvette N. Hlophe, Avulundiah Edwin Phiri, June C. Serem, Tivoli Visser, Priyesh Bipath
Categories: q-bio.QM
Abstract:
This paper presents a robust mathematical framework for quantifying antiproliferative effects from noisy in vitro cell viability experiments. The methodology is demonstrated using crystal violet assay measurements of quinolinic acid-induced growth inhibition in B16-F10 murine melanoma, RAW264.7 macrophage, and HaCaT keratinocyte cells through parametric cell viability models. Experimental data exhibited substantial variability and violated the independence assumptions underlying classical inferential statistics. To address these challenges, the proposed framework combines minimal statistical analysis, comprising model-free confidence intervals and pooled within-replicate variability, with deterministic approximation based on least-squares fitting to experimental means and leave-one-replicate-out cross-validation. While all three cell types were described by a common mechanistic framework, each required a distinct parameterisation to capture its characteristic response to quinolinic acid. The resulting one- and two-parameter models accurately described dose- and time-dependent inhibition, with predictive errors close to the intrinsic experimental variability. The models also yielded explicit expressions for time-dependent IC50 values, enabling reliable prediction of inhibitor concentrations required to achieve specified levels of growth inhibition. The proposed framework provides a practical and robust approach for analysing noisy preclinical cell viability data and can be readily extended to other antiproliferative agents and experimental systems.
Published: 2026-07-26 15:51:46
Authors: Evgeniy Khain, Rohan Sukumar
Categories: q-bio.PE, cond-mat.stat-mech
Abstract:
We consider the spatial spread of epidemic into an unstable, healthy state. When the transmission rate depends on the fraction of infected, the propagating pulse of infection can be either a pulled front or a pushed front. We determined the phase space of parameters for the pulled and pushed regions both by numerically solving the spatial SIR partial differential equations and by a theoretical analysis of the front propagation phenomenon. We found both a continuous and a discontinuous transition between the pulled and pushed front solutions; in the latter transition, the front speed undergoes a jump as a certain parameter crosses the critical threshold. The behavior of the propagating pulses near the transitions has been analyzed and a good agreement between the theory and numerics has been observed. Finally, a bistable region where both pushed and pulled propagating pulses can be realized has been discovered.
Published: 2026-07-26 15:41:52
Authors: Zahra Abdalla Elashaal, Afef Hfaiedh, Nahla Khraief, Issmail Ellabib, Giansalvo Cirrincione
Categories: cs.RO, cs.LG
Abstract:
Exploration in sparse-reward long-horizon tasks poses significant challenges for reinforcement learning. To address these challenges, we propose a two-level Hierarchical Reinforcement Learning (HRL) framework. The first level handles high-level strategic planning, while the low-level uses the continuous-control Soft Actor-Critic (SAC) algorithm, and they utilize entropy-regularized policy optimization. The proposed framework was trained and evaluated using the Search-and-Rescue-2 (SAR-2) dataset. HRL-SAC effectively addresses sparse-reward long-horizon search problems characterized by delayed rewards and continuous control, and its outperforming the flat SAC baseline reinforcement learning in terms of success rates, coverage efficiency, and convergence. These findings indicate that hierarchical entropy-regularized policies are a promising solution to tackle long-horizon sparse-reward reinforcement learning tasks.
Published: 2026-07-26 15:41:48
Authors: Haidong Li, Henry Lam, Yijie Peng
Categories: stat.ME
Abstract:
We study stochastic gradient estimation in black-box environments where only noisy simulation observations of function values are available. Finite-difference (FD) methods are among the most widely used zeroth-order gradient estimators in such settings, by measuring the change in function values against a perturbation size. While the optimal order in choosing this perturbation size with respect to the simulation budget is well understood, the optimal constant factor relies on model characteristics that are typically unknown and viewed to be as difficult to estimate as the gradient itself. Consequently, FD estimators are often based on ad hoc tuning of the perturbation size, which may exhibit highly unstable performance across problem instances. In this paper, we challenge this conventional wisdom from both theoretical and practical perspectives. We show that, by pilot-estimating these model quantities using a negligible fraction of the simulation budget, substantial robustness is attained in the resulting FD estimators. Theoretically, we show that using a perturbation size governed by this pilot estimation can already achieve an MSE that is first-order identical to the ``oracle" MSE as if the optimal perturbation size is known in advance. Moreover, we show how such an approach is competitive against any choices of prescribed perturbation size, even if they are designed to be minimax-optimal over reasonable classes of target functions and FD schemes. Our proposed pilot estimation is practically easy to run, and a variety of numerical experiments demonstrate both the robustness and near-oracle optimality of our estimator relative to conventional FD schemes based on ad hoc tuning.
Published: 2026-07-26 15:37:30
Authors: Silas Koemen
Categories: stat.ML, cs.LG, stat.ME
Abstract:
Distributional random forests replace mean-based CART splitting with criteria that compare the full conditional response distribution in candidate children. We implement and systematically study a family of such criteria inside a single honest-forest implementation: isotropic random-Fourier-feature maximum mean discrepancy (MMD), an anisotropic diagonal-bandwidth variant, an adaptive per-split frequency-selection variant, and a non-kernel sliced-Wasserstein criterion, together with post-hoc kernel-mean shrinkage of the forest weights. Using paired-seed comparisons across synthetic quantile mechanisms, real univariate benchmarks, a California-housing subsample curve, and multivariate synthetic and real responses, we characterize where each extension pays. Three findings recur. First, among distributional criteria ordinary isotropic MMD is already close to best in class: the anisotropic, adaptive-frequency, and sliced-Wasserstein extensions, and post-hoc shrinkage, do not systematically improve on it. Second, on scalar tabular regression mean-based CART splitting remains the robust default and wins many cells. Third, multivariate responses are the regime where distributional splitting clearly earns its keep, most sharply on a pure-dependence copula where the energy score separates the criteria even though marginal CRPS does not. The evidence supports a simple allocation story: distributional splitting helps only when non-location structure is both present and estimable; otherwise it dilutes split-selection power away from the mean. All criteria, the honest forest, and the paired-comparison harness are implemented in the open-source \texttt{drforest} library, whose Rust-backed split search makes broad criterion sweeps inexpensive.
Published: 2026-07-26 15:30:48
Authors: Shijia Wang, Da Guo, Qiang Xiao, Fanghui Bi, Weisheng Li, Dongjing Wang, Chuanjiang Luo
Categories: cs.IR
Abstract:
We describe Melo, an LLM-powered music recommendation agent deployed on NetEase Cloud Music. Melo is structured as a deterministic five-node state graph over heterogeneous tools, with a prompt- and state-machine-driven orchestration policy rather than a fine-tuned controller. At industrial scale, the bottleneck is not how smart the brain is but how the system detects and recovers from the mistakes that brain makes. Two production failure modes drove the design: entity hallucination, where the agent commits to interpretations unsupported by the live catalog or user-behavior index, and long-tail degradation, where over-constrained requests collapse to generic popular fallbacks. We address them with two complementary mechanisms. Inference-time entity grounding repurposes the production search index as a verification primitive that gates entity decisions before they propagate downstream. Reflective retry verbalizes failure reasons from a broken tool chain and feeds them into the next planning step, so the system can relax or revise constraints rather than fall back blindly. A one-month online A/B test across NetEase Cloud Music's playlist surfaces reports an over 2 pp lift in a primary playlist retention metric and a lift of over one minute in a core playlist engagement metric. Offline ablation isolates a 7.8 pp reduction in entity misidentification from the three-layer grounding stack on our evaluation set, and a triggered-session analysis on our evaluation set shows reflective retry firing on 5.8% of sessions with 59% process-level recovery. Our deployment experience suggests that progress on LLM-powered music recommendation at this scale depends as much on the named, ablatable runtime machinery that catches and corrects the brain's mistakes as on the brain itself: a hypothesis we offer for the community to test.
Published: 2026-07-26 15:29:16
Authors: Pankaj Bhagwat, William E. Strawderman, Edward I. George
Categories: math.ST, stat.ME
Abstract:
For the canonical problem of estimating a multivariate normal mean under squared error loss, we demonstrate, for the first time, the existence of proper Bayes minimax multiple shrinkage estimators by introducing a general approach for their explicit construction. As opposed to minimax shrinkage estimators that shrink towards a single prespecified target, minimax multiple shrinkage estimators adaptively shrink towards the more promising of a set of prespecified targets, substantially increasing the region of potential risk reduction while maintaining the protection of always being at least as good as the maximum likelihood estimator. These estimators are particularly useful in practice as they address the challenge of selecting a minimax shrinkage estimator when prior information suggests more than one viable shrinkage target to choose from. In contrast to previous formal Bayes minimax multiple shrinkage estimators, which were built on mixtures of superharmonic marginals, these proper Bayes minimax multiple shrinkage estimators are obtained via mixtures of square-root superharmonic marginals. Examples of such proper Bayes minimax multiple shrinkage estimators include an adaptive convex combination of the classical Strawderman shrinkage estimators.
Published: 2026-07-26 15:26:00
Authors: Shuqing Zhao
Categories: cs.CL, cs.PL
Abstract:
We report the design and end-to-end verification of first-class IEEE-754 binary32 (FP32) and bfloat16 (BF16) arithmetic for ARCH, a hardware description language intended to be generated by language models. Every operator - comparisons, conversions, add, sub, mul, and fused multiply-add (FMA) - is described once against a single bit-vector IR and rendered three ways from one source: synthesizable SystemVerilog, an SMT-LIB model, and a Lean 4 proof model. The three artifacts cannot drift apart structurally, and the residual per-node printer correspondence is machine-checked: a Yosys-to-SMT miter proves the emitted SystemVerilog equivalent to the SMT model for all 24 operators. Verification splits at the solver-tractability frontier: multiplier-free operators (comparisons, add/sub over all 2^64 inputs, conversions, and all binary BF16 arithmetic) are proved exhaustively equivalent to the SMT-LIB FloatingPoint theory; the SAT-hard multiplier-bearing operators (FP32 mul and FMA) are proved correctly rounded in Lean, sorry-free, against a value-level round-to-nearest-even specification over exact dyadic values. Physical characterization exposed the FMA as the timing outlier: its exact-wide 470-bit datapath does not pipeline in our flow. We reimplemented it as a bounded 98-bit guard/round/sticky datapath that pipelines to 268 MHz on Nangate45, and proved, in Lean and over all 2^96 inputs, that it is bit-identical to the exact-wide reference, so it inherits the reference's proven correct rounding. The equivalence is tractable precisely because the shared multiplier appears on both sides and cancels: neither a SAT solver nor the proof ever solves a multiplier equivalence. (The BF16 FMA is deliberately an FP32-accumulating fusion, characterized as exactly that.) All machine-checked claims are pinned to a tagged open-source release.
Published: 2026-07-26 15:08:41
Authors: Rui Ding, Tianshu Zhang, Jiarui Yu, Namitha Nandakumar, Quanlong Yang, Mudi Wang, D. Y. Wang
Categories: physics.optics
Abstract:
Subdiffraction imaging serves as a novel technique to enhance the optical imaging resolution, where a backscattering-free approach remains so far unavailable. Here, we theoretically predict and experimentally demonstrate that the gyromagnetic photonic crystals applied with staggered magnetic fields support nonreciprocal light propagation beyond the diffraction limit. Broadband subdiffraction imaging was experimentally observed to span the frequency window traversing a pair of spectrally separated Dirac points, where near-flat equi-frequency contours (EFCs) emerged while experiencing an enforced shape transition. Our findings establish a practical paradigm for constructing backscattering-immune super-resolution imaging systems based on topological photonic crystal platforms.
Published: 2026-07-26 14:47:47
Authors: Wendi Deng, Hang Du, Guoshun Nan, Haokun Tian, Jiaqi Yu, Xinlei Cao, Jaile Li, Jingfeng Chen, Ling Deng, Ting Li, Hao Yang, Jun Liu, Xudong Jiang, Sicong Leng
Categories: cs.AI
Abstract:
Multimodal large language models exhibit capabilities on reasoning tasks, yet often produce flawed intermediate steps while yielding correct final answers. This behavior undermines interpretability and reliability, suggesting reliance on spurious shortcuts rather than faithful reasoning. Although efforts have explored step-level supervision, distinguishing decisive steps from redundant ones remains challenging. We propose $O^2$-CritiCuRL, a novel curriculum reinforcement learning framework that introduces critical-step awareness through an iterative offline-online paradigm. In the offline stage, $O^2$-CritiCuRL conducts multi-rollout analysis over step-annotated trajectories to estimate step-level importance, allowing the framework to distill critical reasoning steps and filter out redundant ones. In the online stage, we employ a progressive step-level reinforcement learning strategy, where truncated chains guide the model to infer missing steps and refine its reasoning, thereby sharpening its focus on critical steps and overcoming the limitations of static supervision. Extensive experiments on multimodal reasoning benchmarks show that our method achieves state-of-the-art performance while delivering superior training and inference efficiency. Code is available at https://github.com/kk0013/CritiCuRL.
Published: 2026-07-26 14:45:15
Authors: Kevin Lee, Benjamin Letham, Zhiyuan Jerry Lin, Elodie Samson, Eric Onofrey, Poppy Zhang, Shawndra Hill, Eytan Bakshy
Categories: cs.AI, cs.LG
Abstract:
Ad creative optimization is increasingly constrained by evaluation rather than generation. Generative models can produce many plausible creatives, but reliable evaluation requires online experiments, in which only a limited slate can be tested. We study how to use data from historical A/B tests to generate and select the candidates in that slate. We developed and deployed a performance-driven offline-to-online workflow that guides creative generation with a predictive model as an inference-time critic. In the offline phase, we use a predictive model trained on historical experiments to rank and refine variants created by a generative model. A final test slate is then deployed in an online adaptive experiment. In a 50-arm field experiment, we found that the best creative generated with this method yielded 45.1% higher engagement than the best human-authored creative. Two additional experiments showed the same upper-tail pattern, with lifts of 46.7% and 36.2%. We found that despite the predictive model being too noisy to directly identify the best creative offline, it effectively guides the generative model toward creating strong candidates that can be efficiently evaluated in an adaptive experiment. The results suggest a design principle for creative optimization with generative models: use predictive models to guide generation of a slate to test, judge the slate by whether it contains high-performing candidates at a feasible test size, and use adaptive experiments to select among candidates while limiting traffic lost to weak arms.
Published: 2026-07-26 14:37:46
Authors: Yirui Luo, Yihang Xie, Yao Ge, Yong Liang Guan, David Gonz{á}lez G
Categories: eess.SP
Abstract:
In high-mobility orthogonal frequency division multiplexing (OFDM) systems, rapid channel variation can make the channel state information (CSI) estimated from pilots inaccurate for data subcarriers, leading to a mismatch with their effective channel. To address this issue, this paper proposes a CSI RefineNet receiver, where the CSI is iteratively refined using soft symbol decisions in a data-aided manner. Specifically, a pilot-driven initialization module is first employed to obtain a coarse CSI estimation and the corresponding symbol posterior probabilities. Based on these posteriors, soft data-aided channel observations are constructed over all subcarriers and fused with the initial CSI to refine the channel estimation. The refined CSI is subsequently fed back to the equalization and detection modules, thereby forming an iterative receiver structure. To improve training stability and fully exploit the refinement capability, a two-stage training strategy is also developed. Simulation results demonstrate that the proposed CSI RefineNet receiver achieves superior BER performance and strong robustness under different velocities, modulation orders, and pilot spacing configurations in high-mobility OFDM systems.
Published: 2026-07-26 14:28:49
Authors: Wei-En Lin, Li-Chieh Hsiao, Chen-Hsun Ma, Erh-Hsiang Yeh, Wei-Lun Peng, Hsi-Sheng Goan, Cen-Shawn Wu, Yueh-Nan Chen, Yung-Fu Chen, Chung-Ting Ke, Chii-Dong Chen
Categories: quant-ph
Abstract:
High-fidelity and rapid qubit readout is essential for superconducting quantum processors, typically realized through the quantum non-demolition (QND) dispersive interaction within a qubit-resonator architecture. However, the achievable readout speed and fidelity are fundamentally limited by measurement-induced state transitions (MIST). For a transmon qubit, MIST is highly sensitive to the offset charge $n_g$ due to the charge dispersion of its higher-lying energy levels. In this work, we systematically investigate $n_g$-dependent MIST dynamics governed by the diabaticity and symmetry of pulse shaping within a charge-sensitive transmon architecture. We engineer fast-load and fast-clear pulses that effectively suppress resonator photon overshoots, thereby demonstrating a highly practical strategy to mitigate MIST without requiring complex waveforms or real-time feedback. Utilizing active gate-voltage control and rapid feedback, the measurement-induced transition probability is precisely mapped against $n_g$ and the steady-state resonator photon number, exhibiting strong agreement with numerical Floquet branch analysis. Ultimately, we evaluate the $n_g$-averaged total error probabilities for both readout and post-readout stages, verifying that a straightforward three-step pulse scheme consistently minimizes overall readout errors. Within the framework of large-scale superconducting quantum processors, this practical, hardware-free approach inherently offers a better trade-off between the readout signal-to-noise ratio and QND preservation.
Published: 2026-07-26 14:22:15
Authors: Kezhao Lai, Yutao Lai, Hai-Lin Liu
Categories: cs.AI
Abstract:
LLM-based automated heuristic design (AHD) typically scores executable programs on complete instances or within fixed solver components. In large-scale routing problems, localized reconstruction reduces the size of each optimization task, but repair regions within the same incumbent can exhibit substantially different structures. One construction rule must therefore compromise across them. In this paper, we propose SpecAHD, a coupled bilevel framework for within-instance specialization. An upper-level search learns where to expose bounded repair regions, while a lower-level search evolves a complementary repertoire of executable heuristics for the induced repair tasks. The upper-level program determines the repair tasks seen by the lower level, while checked repair outcomes determine how upper-level programs are evaluated. The lower-level objective favors heuristics that perform well on average or solve tasks that the current repertoire handles poorly. For the repair tasks induced by a fixed upper-level program and a fixed lower-level candidate pool, this objective is monotone submodular, allowing greedy repertoire selection with a (1-1/e) approximation guarantee. Across four routing problems and multiple LLM backbones, SpecAHD reduces held-out objective cost by up to 57.7% against the strongest competing AHD baseline and outperforms the per-instance baseline envelope on most public instances.
Published: 2026-07-26 14:21:32
Authors: Kazuhiro Sato
Categories: math.OC
Abstract:
We study convex optimization over a compact convex set when the objective is smooth and convex only on an open domain. Under a boundary-blow-up condition, every feasible initialization yields a compact invariant sublevel set separated from the complement of the objective domain, and an optimal solution exists. For a domain-aware Armijo projected-gradient method, a safe-neighborhood analysis establishes well-defined objective evaluations, finite backtracking, sufficient decrease, and a run-specific but iteration-independent positive lower bound on the accepted step sizes. These properties yield explicit sublinear objective and stationarity guarantees, together with convergence of the full iterate sequence. Positive curvature restricted to feasible displacement directions further guarantees uniqueness and linear convergence. We apply the framework to controllability scoring with prescribed input directions and compact convex allocation constraints. Feasibility is characterized exactly by controllability of the input directions eligible for positive allocation, while restricted injectivity of the Gramian map guarantees uniqueness of the optimal allocation and provides explicit strong-convexity bounds. A directed-network example illustrates how candidate exclusion can preserve or destroy feasibility and alter the optimal allocation in a criterion- and horizon-dependent manner.
Published: 2026-07-26 14:07:38
Authors: Andrew M. Pitts
Categories: cs.LO
Abstract:
We give a new notion of displayed setoid (family of setoids) in intensional type theory. It is used to give a semantics for extensional type theory with universes (ETU) within safe Agda, which serves as a machine-checkable formalization of intentional type theory augmented with a universe closed under inductive-recursive definitions (IRU). The syntax of ETU is defined in IRU in a traditional extrinsic form, using a well-scoped locally nameless representation of its terms. Giving its semantics in terms of displayed setoids is complicated by the very limited means of expression afforded by IRU. As a corollary we obtain a proof within IRU of the consistency of ETU.
Published: 2026-07-26 13:59:28
Authors: Mikko Fischer
Categories: math.CO
Abstract:
We exhibit a connected graph on 24 vertices with maximum degree 3, independence number 9 and zero forcing number 11, refuting a 2017 conjecture of TxGraffiti recorded as Conjecture 2 of the survey of Davila, Brimkov and Pepper. The same construction with a different gadget gives a connected cubic graph on 36 vertices with independence number 15 and zero forcing number 17; the conjecture therefore fails also in the cubic form in which the survey's Lean 4 appendix states it. In particular Z <= alpha + 1 is not a universal bound for connected cubic graphs, and the value Z = alpha + 2 is attained.
Published: 2026-07-26 13:58:28
Authors: Qian Bao, Yaojun Chen, Yanbo Zhang
Categories: math.CO
Abstract:
Let $\mathcal{F}$ be a $k$-uniform hypergraph. The famous Erdős--Ko--Rado (1961) theorem determines the maximum size and extremal structure for $\mathcal{F}$ being $t$-intersecting, that is, $|F_1 \cap F_2| \ge t$ for any two edges $F_1, F_2$ of $\mathcal F$. The codegree squared sum $\mathrm{co}_2(\mathcal{F})$ is the square of the $\ell_2$-norm of the codegree vector of all $(k-1)$-sets in $\mathcal{F}$, which was initially introduced for Turán problems of hypergraphs. Recently, Brooks and Linz (2026), as well as Wu and Zhang (2026) investigated the maximum value of $\mathrm{co}_2(\mathcal{F})$ and corresponding extremal structures for $\mathcal{F}$ being $t$-intersecting. Moreover, Brooks and Linz asked if the classical results on intersecting families can be extended to $\mathrm{co}_2(\mathcal{F})$. In this paper, by developing the spectral techniques for incidence matrices, we study the extremal problems of $\mathrm{co}_2(\mathcal{F})$ for $\mathcal{F}$ being intersecting families in finite vector spaces, affine spaces, and attenuated spaces, and establish the Erdős--Ko--Rado theorems in $\ell_2$-norm for the three finite spaces.
Published: 2026-07-26 13:44:09
Authors: Shuai A. Chen, Qianqian Chen, Guangyu Yu, Zheng Zhu
Categories: cond-mat.str-el
Abstract:
Pair-density-wave (PDW) superconductivity is a state in which the superconducting order parameter modulates at a finite wavevector. Using large-scale density matrix renormalization group, we study the doped altermagnetic Mott insulator in the checkerboard $t$-$J$ model, where altermagnetic exchange anisotropy is encoded microscopically through anisotropic ferromagnetic next-nearest-neighbor exchange. By mapping the ground-state phase diagram as a function of doping and altermagnetic anisotropy, mainly on six-leg cylinders, we identify a transition from a uniform $d$-wave superconducting regime with charge modulation to a PDW regime coexisting with stripe order. In the PDW regime, we report an unconventional wave-vector locking $\mathbf Q_{\mathrm{PDW}}\approx 2\mathbf Q_{\mathrm{Stripe}}$ along the cylinder direction, in contrast to the conventional relation. Pair correlations reveal a two-scale structure, consisting of short-distance local $d$-wave pairing and long-distance finite-momentum PDW correlations. A symmetry-based Ginzburg--Landau analysis is presented for the observed locking. Our results identify altermagnetism as a strong-coupling, microscopically grounded route to finite-momentum superconductivity in doped Mott insulators.
Published: 2026-07-26 13:35:06
Authors: Mohammad Sabouri
Categories: eess.SY, cs.RO
Abstract:
This paper develops an observer-assisted control architecture for 3D trajectory tracking of torpedo-type underactuated AUVs with non-minimum-phase sway/heave dynamics under unknown ocean currents. A three-stage state-current observer provides relative-velocity estimates to a nonlinear feedforward term for dominant current rejection and to an LMI-certified LPV-$\mathcal{H}_\infty$ correction layer. Feedback-linearising cancellation yields a constant input matrix, enabling convex synthesis without pairwise cross terms. A residual-level break-even law shows that the effective surge disturbance depends on current-estimation error, while a singular-perturbation analysis proves local practical uniform ultimate boundedness on the embedded LPV model. REMUS simulations over three trajectories and four current scenarios show 89-96% current-estimation reduction, about 99% translational residual reduction, and RMS tracking-error reduction from 4.04 m to 0.24 m.
Published: 2026-07-26 13:28:36
Authors: Chong-Bin Chen, Jia-Xi Feng, Fu-Wen Shu, Linjie Song
Categories: astro-ph.CO
Abstract:
We investigate scalar-induced gravitational waves (SIGWs) in an inflationary model with symmetry breaking, in which charged scalar fields are coupled to an isotropic triplet of Abelian gauge fields through a kinetic function. Such SIGWs can be enhanced to a detectable level when the mixing between the inflaton and gauge-field perturbations is sufficiently large. We find that the longitudinal mode and the charge-dependent mixing between perturbations become relevant only when the gauge-field excitation occurs sufficiently late during inflation. In this regime, the corresponding SIGWs are shifted to ultra-high frequencies, typically can around the GHz band. We show that the parameters characterizing the effects of the longitudinal mode and charge-dependent mixing affect the signal in qualitatively different ways. This provides characteristic signatures for distinguishing the neutral case from the charged one through the frequency profile of the stochastic gravitational-wave background.
Published: 2026-07-26 13:12:58
Authors: George A Kevrekidis
Categories: math.OC, cs.LG, math.DS
Abstract:
Discrete optimization algorithms are often analyzed through continuous-time limiting ODEs, but a convergence certificate for the ODE is not automatically one for the discrete algorithm. We develop contact Hamiltonian systems as a setting where the transfer can be made precise. A contact Hamiltonian $H$ on $J^1(\mathbb{R}^n)$ obeys the intrinsic decay identity $\dot H = -H\,\partial_s H$, so an augmented energy $\mathcal{E}$ built from $H$, together with the conformal rate $\partial_s H$, is a continuous-time rate certificate whenever $\mathcal{E}$ controls the objective gap. Our main theorem states, under three named and independently checkable hypotheses, that an order-$r$ contact splitting with step $h$ transfers this certificate over the finite horizon set by backward error analysis. The discrete decay envelope is governed by the modified conformal factor up to $O(h^r)$ perturbations plus a backward-error shadowing defect, and the mechanism is inherited exactly because the modified Hamiltonian is itself a contact Hamiltonian. Quadratic heavy ball is a fully solvable example: its projected dissipative-leapfrog spectrum agrees with established conformal-symplectic optimization theory, while the augmented contact Hamiltonian yields a sharp objective-to-certificate comparison that verifies the transfer hypotheses. For strongly convex objectives with state-dependent damping, an explicit Bregman-type Lyapunov certificate instead transfers by an auxiliary-shadowing corollary. The decomposition $H=K+V+D$ into kinetic, objective-encoding potential, and dissipation terms serves as a design template, with a catalogue of closed-form sub-flows including contact-specific damping families. Numerical experiments confirm the predicted conformal-factor tracking orders and show competitive performance on ill-conditioned benchmarks and deep-learning tasks.
Published: 2026-07-26 13:02:39
Authors: Yair Hayut, Assaf Rinot, Zhixing You
Categories: math.LO
Abstract:
Foreman and Magidor showed that the continuum hypothesis implies the existence of a countably-closed $\aleph_2$-cc forcing notion $\mathbb P$ for adding $\square_{\aleph_1}$. Here, we show that $\mathbb P$ may consistently be realized as an $\aleph_2$-Souslin tree. More generally, we prove that $\square_λ$ may be added by a $λ^+$-Souslin tree, providing the first analog of the Foreman--Magidor forcing at the level of successors of singular cardinals. Our construction is uniform and extends to inaccessible cardinals as well.
Published: 2026-07-26 13:01:48
Authors: Ilia Barutkin, Maxim Fofanov, Sergey Belokonny, Vladislav Makeev, George Chernishev
Categories: cs.DB, cs.AI, cs.CE, cs.LG
Abstract:
Data profiling aims to extract complex patterns from data for further analysis and use that data in domains such as data cleaning, data deduplication, anomaly detection, and many more.
Functional dependencies (FDs) are one of the most well-known patterns. However, they are poorly suited for these tasks, as real data is usually dirty, and the rigid definition of FDs does not allow algorithms to locate them. For this reason, there are several formulations aimed at relaxing FDs to support dirty data, with approximate functional dependency (AFD) being the most popular one. Another formulation is the Probabilistic Functional Dependency (pFD), which we aim to support inside Desbordante - a science-intensive, high-performance and open-source data profiling tool implemented in C++. However, pFDs are relatively poorly studied, compared to AFDs.
In this paper we study pFDs, both analytically and empirically. We start by assessing how different pFDs and AFDs are by studying cases in which pFDs have an edge over AFDs. Then, we implement the algorithm for pFD discovery, as well as study its run time and memory consumption. We also compare it with an AFD discovery algorithm. Lastly, we study the output of both algorithms to learn whether or not it is possible to use AFD discovery algorithm to get pFDs and vice versa.
Published: 2026-07-26 12:38:06
Authors: Oshadha Samarakoon, Dushan Herath, Ishara Ranmandala, Dilshara Herath, Roshan Godaliyadda, Parakrama Ekanayake, Vijitha Herath
Categories: eess.IV, cs.CV
Abstract:
Sky-image irradiance studies often compare forecasting systems in which the image encoder, temporal model, fusion block, target definition, and training recipe all change together. We use a narrower protocol: the multimodal forecasting pipeline is fixed, and only the visual backbone is varied. The shared setup keeps preprocessing, clear-sky-index normalization, weather-history encoding, fusion, regression head, loss, optimizer schedule, seed, and chronological split policy unchanged. We compare ConvNeXt, Swin Transformer, VMamba, Spatial Mamba, and MambaVision backbones for 10min-ahead forecasting on Folsom and a strict matched NREL split. Forecast skill is measured against clear-sky-index smart persistence, and temporal-only rows are reported as weather-history diagnostics rather than as the main ranking criterion. On the Folsom strict split, all evaluated visual-backbone runs improve over smart persistence. In the evaluated single-seed strict runs, VMamba Small and Swin Base reach matched Folsom RMSE values of 65.39 W/m^2 and 65.50 W/m^2; the temporal-only diagnostic reaches 69.51 W/m^2. On the 313-sample NREL strict split, smart persistence remains strongest at 17.48 W/m^2, while the lowest visual RMSE is obtained by Swin Tiny at 23.76 W/m^2. These results provide a reproducible encoder comparison under one fixed multimodal operating point rather than establishing architecture-level dominance, statistically resolved ranking, or fully optimized forecasting performance. Code available here: https://github.com/Oshadha345/irradiance_benchmark
Published: 2026-07-26 12:30:10
Authors: Zehavit Zvi
Categories: math.RT
Abstract:
Brauer tree algebras are important and fundamental blocks in the modular representation theory of groups. Aihara develped an algorithm, which we call a mutation reduction, for getting from a Brauer tree algebra to the simpler Brauer star algebra using a sequence of mutations centered on edges. Schaps and Zvi, using the Schaps-Zakay theory of pointing the tree, showed that different algorithms for the sequence of mutations give permutations of the edges.
We give a modification of Aihara's algorithm and tested it against the original algorithm for computational efficiency. We prove that all versions of Aihara's algorithm are the fastest possible in the sense of requiring the least number steps to reach the Brauer star, when compared to all possible complete mutation reduction algorithms.
Published: 2026-07-26 12:13:56
Authors: Olga Buntina, Hamidreza Golmohammadi
Categories: math.CO
Abstract:
A set $D$ of vertices graph $G$ is a total outer-independent dominating set (TOIDS) of $G$ if every vertex of $G$ is adjacent to at least one vertex in $D$, and $V(G)\setminus D$ is an independent set of $G$. A TOI-coalition in $G$ comprises two disjoint sets of vertices $A$ and $B$ of $G$, neither of which is a TOIDS but whose union $A\cup B$ is a TOIDS of $G$. We say that the sets $A$ and $B$ form a TOI-coalition, and are TOI-coalition partners. A TOI-coalition partition in $G$ is a vertex partition $Ψ=\{V_1, V_2,..., V_k\}$ in which every set forms a TOI-coalition with another set in $Ψ$. The TOI-coalition number $C_t^{oi}(G)$ is the maximum cardinality among all TOI-coalition partitions of $G$. In this work, the above-mentioned concepts are introduced and studied. The existence of a TOI-coalition partition is investigated. Several sharp upper bounds on $C_t^{oi}(G)$ are established. Finally, the exact values of $C_t^{oi}(G)$ for some graph classes are obtained.
Published: 2026-07-26 12:02:53
Authors: Philipp Steigerwald, Eric Rudolph, Mara Stieler, Jennifer Burghardt, Jens Albrecht
Categories: cs.CL, cs.CY
Abstract:
This paper presents GEMCo, a releasable, human-written proxy for inaccessible counselling data: 86 complete German e-mail counselling conversations (728 messages), expert-authored cases and counsellor sessions with trained role-players. It is validated against a held-out reference of 124 real counselling conversations. The proxy and the real conversations are measured against each other in counsellor strategies and client emotions. The gap is detectable but small. A generative validation supports the analysis. The validation method itself generalises to any domain where real data cannot be shared but a human-made proxy can. Privacy and ethics keep real counselling data closed. GEMCo carries none by design and can be released -- a first step toward language research in this domain.
Published: 2026-07-26 11:54:16
Authors: Dragan Mašulović, Veljko Toljić
Categories: math.CO
Abstract:
In this paper we show that the Hall's universal group does not have finite big Ramsey degrees. Our strategy consists of piggybacking on the recent result of Hubička, Konečný, Todorčević and Zucker (announced at EUROCOMB~2025) that the Fraïssé limit of the class of all finite complete edge-labelled graphs with where the set of labels is countably infinite does not have finite big Ramsey degrees. We then use our categorical machinery to transport their result from the context of edge-lebelled graphs to the context of groups.
Published: 2026-07-26 11:14:08
Authors: Makoto Suda, Edan Lerner, Eran Bouchbinder
Categories: cond-mat.dis-nn, cond-mat.mtrl-sci, cond-mat.soft, cond-mat.stat-mech
Abstract:
A recently formulated mean-field model of glasses features an equilibrium, zero-temperature Replica-Symmetry-Breaking (RSB) transition in some parameter range. In this range, the model's solution in the Replica-Symmetric phase is expressed in terms of an effective, self-consistent random potential for uncoupled degree of freedoms, where the transition to the RSB phase is characterized by the emergence of spectral-edge localized modes and a pseudogapped quartic vibrational spectrum, resulting in a finite spin-glass susceptibility. These properties are preserved in numerical solutions of the model under non-equilibrium conditions, i.e., upon an instantaneous quench. Inspired by recent advances in computer glasses, we define a micromechanical response function --- the linear response to local force monopoles --- in the framework of the mean-field model. We establish exact relations between the force monopole stiffness and global susceptibilities, which suggest a close correspondence between the non-equilibrium RSB phase of the model and the above-mentioned effective random potential description. As such, the obtained micromechanical observables constitute a concrete realization of the collective degrees of freedom of the model, offering a bridge between a glassy mean-field model and finite-dimensional glasses. We show that the model's vibrational spectrum can be computed solely from the monopole response statistics and, by employing a marginal stability criterion, we extract a characteristic frequency/stiffness scale of soft glassy modes, which is related to the boson peak in finite-dimensional, laboratory glasses.
Published: 2026-07-26 11:00:10
Authors: Guo Yurong, He Yufei, Li Yonghao, Chang Dongliang, Zhang Ke, Ma Zhanyu
Categories: cs.CV
Abstract:
Controllable infrared-visible image fusion aims to integrate complementary thermal and structural information with flexible region-aware modulation, producing fused images that adapt to diverse user requirements and downstream tasks. However, existing methods typically rely on predefined discrete control conditions, leading to a sparse space that fails to support fine-grained modulation demands. To address this, we propose ConFusion, a novel framework that learns the continuous fusion space via Gaussian-conditioned spatial-aware modulation, enabling instance-level fine-grained controllable infrared and visible image fusion. ConFusion employs a dual-branch architecture to disentangle modality-invariant and modality-specific representations under joint reconstruction and text-guided semantic alignment. Gaussian-conditioned instance modulation variables coupled with Grounded SAM-based instance masks guide instance-level fine-grained modulation through the Mask-Guided Specific Feature Modulator, while the Text-Driven Invariant Feature Enhancer improves semantic consistency and enhances fusion. During inference, the multimodal large language model parses user intents into instance-level modulation variables to guide image fusion. Extensive experiments show that ConFusion achieves state-of-the-art performance across multiple metrics in both fusion quality and downstream tasks, while supporting fine-grained controllable image fusion. Our code is available at https://github.com/HeyufeiAnto/Confusion
Published: 2026-07-26 10:49:08
Authors: Yu-Hao Mu, Zhihuan Zhou, Enkun Li
Categories: astro-ph.CO
Abstract:
DESI DR2 BAO combined with CMB and Type~Ia supernovae in the Chevallier--Polarski--Linder (CPL) parameterisation prefers evolving dark energy over $Λ$CDM at roughly $2.8$--$4.2σ$. We reconstruct the same late-time expansion history with a hierarchical Gaussian process (GP) that co-samples the kernel hyperparameters $(σ_f,l)$ together with $(H_0, Ω_m, Ω_k, ω_b h^2)$, coupling BAO, compressed Planck distance priors, and Pantheon+ through a Monte-Carlo effective likelihood conditioned on 37 cosmic-chronometer $H(z)$ points. The baseline posterior gives $w(z\simeq 0)=-0.80^{+0.26}_{-0.23}$ (68\%~C.L.), about $0.8σ$ from $w=-1$, with $l=3.79^{+0.81}_{-1.12}$. A CPL fit on the identical compressed Planck pipeline improves nested $Λ$CDM by only $Δχ^2\sim 1$ ($\sim 1σ$). Ablations that fix $(σ_f,l)$, drop SN or LRG1/2 BAO, replace the radial-basis kernel by Matérn-$5/2$, or tighten the prior on $l$ leave the median $w(0)$ within $\lesssim 1σ$ of $-1$. The mild preference reported here is therefore specific to this compressed-CMB analysis and does not address DESI's full Planck-likelihood result.
Published: 2026-07-26 10:39:52
Authors: Yanbo Qiao, Sariah Al Saati, Jean-Eric Wegrowe
Categories: cond-mat.mes-hall
Abstract:
The stationary state of a spin Hall bar connected to an external load circuit is investigated through a variational approach based on the principle of minimum power dissipation generalized to the two-spin-channel model. The self-consistent distributions of longitudinal and transverse current densities, alongside the corresponding spin and charge accumulations and dissipation power in the resistance, are derived. Surprisingly, it is shown that the Joule dissipation vanishes when the load resistance is placed at a sufficiently large distance compared with the spin-relaxation length. Such a highly non-trivial global stationary state appears as the most striking characteristic of the injection of pure spin current compared with more usual current injection.
Published: 2026-07-26 10:32:18
Authors: Konstantin Loginov
Categories: math.AG
Abstract:
Let $G=(\mathbb{Z}/4)^4$. We prove that if $X$ is a rationally connected threefold with a faithful action of $G$, then $X$ is $G$-birational to the Fermat quartic threefold. If $X$ is a terminal $G\mathbb{Q}$-Fano threefold, this birational equivalence is biregular. Consequently, the group $G$ acts faithfully on a rationally connected threefold but does not embed into $\operatorname{Cr}_3(\mathbb{C})$. Combined with earlier results, this yields a complete classification of the pairs $(m,r)$ for which $(\mathbb{Z}/m)^r$ embeds into $\operatorname{Cr}_3(\mathbb{C})$, and of those for which it embeds into $\operatorname{Bir}(X)$ for a rationally connected threefold $X$.
Published: 2026-07-26 10:29:20
Authors: Zhaoxi Zhang, Xiaomei Zhang
Categories: cs.AI, cs.CR
Abstract:
Long-lived AI agents increasingly evolve after deployment by retaining experience, acquiring skills and tools, revising workflows, delegating work, and moving across task phases. This improves adaptation but creates a distinct authorization problem. Tool-enabled agents can turn model errors and prompt injections into consequential external actions; when evolution occurs under a live grant, the subject exercising that authority or the context in which it acts may no longer match what the user evaluated. Evolution can change both the effects reachable under an old grant and the authority required by the task, which may rise, fall, or become incomparable. Existing tool policies constrain actions but do not determine when a grant survives this change.
We formulate authorization continuity: when does an existing grant remain valid, how may active authority change, and what boundary must never move? Our state-bound model fixes a transition envelope and an immutable effect ceiling at grant time. The envelope determines whether the grant survives a mutation; below the ceiling, authority may contract freely and expand only under specified evidence conditions. We distinguish requested from realized effects and prove that, under complete mediation, sound effect abstraction, attenuating delegation, and monitor integrity, mutation cannot amplify protected effects beyond the user-issued ceiling. Agent-produced evidence may allocate authority below the ceiling but cannot raise it. Finally, we map six mutation classes to their authorization consequences.
Published: 2026-07-26 10:26:10
Authors: Bohao Ji
Categories: math.DG, math.GT
Abstract:
In this paper, we study three-dimensional combinatorial Yamabe flows on locally finite infinite triangulations in Euclidean and hyperbolic background geometries. Under suitable non-degeneracy and bounded-degree assumptions, we establish the short-time existence and uniqueness of the original flows. We further introduce the extended flows by using the continuous extension of solid angles, and prove long-time existence for both extended flows under suitable initial assumptions.
Published: 2026-07-26 09:59:57
Authors: Jianing Li, Dianze Li, Arren Glover, Xiaopeng Fan, Guoqi Li, Chiara Bartolozzi, Ryad B. Benosman, Yonghong Tian
Categories: cs.CV
Abstract:
Conventional frame-based cameras face significant challenges in detecting objects under high-speed motion blur or in low-light environments. Neuromorphic cameras provide asynchronous visual streams with high temporal resolution and a wide dynamic range, offering a promising solution for object detection under challenging conditions. Despite the development of numerous models and the emergence of various applications in neuromorphic object detection, there is still a lack of deep understanding and standardized benchmarks to assess progress and address key challenges. In this paper, we provide a comprehensive survey and benchmark of existing neuromorphic object detection algorithms. Specifically, we first present a problem description, review the available datasets, and revisit the evaluation metrics. We then explore existing neuromorphic object detection approaches from various perspectives, including event representation, temporal modeling, multimodal fusion, asynchronous processing, low-latency processing, and energy-efficient computing. Furthermore, we evaluate a wide range of representative neuromorphic object detection models and offer detailed analyses of the comparative results. Finally, we discuss unresolved issues in neuromorphic object detection and propose potential future research directions. We hope this survey and benchmark will be a valuable resource for researchers and provide guidance for future advancements in neuromorphic object detection.
Published: 2026-07-26 09:35:08
Authors: Yoo Jin Cha, Omar Duran, Nicola Castelletto, Victor A. P. Magri, Hamdi A. Tchelepi
Categories: math.NA
Abstract:
The mimetic finite difference (MFD) method provides a robust discretization for flow simulation on general polyhedral meshes, but its computational cost can become significant due to dense local operators and reduced global sparsity. While the two-point flux approximation (TPFA) offers a substantially cheaper alternative, its accuracy is generally restricted to $K$-orthogonal grids. To balance these competing considerations, we present an adaptive MFD framework based on a residual-based consistency indicator derived from the discrete constitutive equations. The indicator measures local inconsistency and enables adaptive TPFA/MFD stencil selection through a user-prescribed tolerance $τ$. Because the adaptation is performed within a mimetic framework, arbitrary TPFA/MFD partitions remain stable and structure preserving. Theoretical analysis establishes uniform coercivity and proves explicit tolerance-controlled convergence of the relative flux error. Numerical experiments on challenging polyhedral reservoir benchmarks demonstrate accuracy comparable to full MFD discretizations while substantially reducing matrix density and computational cost.
Published: 2026-07-26 09:27:09
Authors: A. Dezhakam, A. Sheykhi, A. Dehyadegari
Categories: gr-qc
Abstract:
We investigate ghost dark energy (GDE) in a cosmological framework derived from Kaniadakis entropy. By applying the first law of thermodynamics to the FRW apparent horizon, we obtain modified Friedmann equations that include a correction term characterized by the Kaniadakis parameter $λ$. We then study the evolution of a flat universe containing pressureless matter and interacting GDE within this modified gravity setup. Our numerical analysis reveals that the Kaniadakis correction mildly affects the dark energy equation of state and shifts the transition to cosmic acceleration. Stability analysis via the squared sound speed shows the model remains generally unstable, though the instability is moderated for larger $λ$. Statefinder diagnostics indicate that the model approaches the $Λ$CDM fixed point in the future, with deviations decreasing as $λ$ increases.
Published: 2026-07-26 09:25:43
Authors: B. N. J. Persson
Categories: cond-mat.soft
Abstract:
We present an analytical theory for the flash temperature for viscoelastic solids sliding on rigid and randomly rough surfaces. The theory takes into account the surface roughness on all relevant length scales.
Published: 2026-07-26 09:24:20
Authors: Andrew Parry, Emmanouil Georgios Lionis, Debasis Ganguly, Sean MacAvaney
Categories: cs.IR
Abstract:
Modern information retrieval systems typically operationalise relevance as a query-conditional score computed at inference time. This design choice has become dominant such that alternative decompositions of relevance are rarely discussed, despite the long history of document and query priors in probabilistic retrieval and large-scale search. As neural ranking models grow more computationally expensive and retrieval pipelines expand to include multi-stage ranking, recommendation, and retrieval-augmented generation, this monolithic view of query-time scoring becomes increasingly limiting. We argue that modern information access systems are more naturally understood as performing approximate posterior inference, in which relevance is refined through a staged combination of query-dependent likelihoods and query-independent priors. We extend classical probabilistic retrieval formalisms to contemporary learned systems and show how explicit likelihood-prior decomposition exposes new opportunities to shift computation offline while disentangling document-level and interaction-level beliefs. We present empirical evidence that incorporating query-independent document utility can complement existing rankers and improve effectiveness with minimal query-time computation (solely score fusion). Concretely, a learned prior improves first-stage retrieval through rank fusion (up to 0.046 nDCG@10 on TREC DL-2019 and 0.029 nDCG@10 on TREC DL-2020) and also improves downstream re-ranking, with the largest gains observed for the LLM re-ranker RankZephyr (up to 0.054 nDCG@10 on TREC DL-2020). Finally, we discuss how this decomposition connects to broader information access and outline research directions for designing retrieval systems that explicitly allocate modelling capacity between offline priors and online interaction.
Published: 2026-07-26 09:23:23
Authors: Yi Xu, Yi-Zheng Fan
Categories: math.CO
Abstract:
We establish a tensor spectral stability theorem for uniform hypergraphs with bounded matching number. More precisely, for fixed integers $k\geq 3$ and $β\geq2$, and sufficiently large $n$, we prove that every $n$-vertex $k$-uniform hypergraph $H$ with matching number at most $β$ and tensor spectral radius close to the maximum possible value among all such hypergraphs must be structurally close to the extremal hypergraph $S_{n,k,β}$, whose edges consist of all $k$-sets intersecting a fixed set of $β$ vertices. Furthermore, we show that every edge of $H$ intersects this distinguished vertex set and that $H$ contains all but a small proportion of the edges of $S_{n,k,β}$. As an application, we obtain a new proof of the spectral version of the Erdős matching conjecture for sufficiently large $n$.
Published: 2026-07-26 09:10:23
Authors: Noraiz Tahir, Mubasher Jamil, Kaynat Fatima, Tajammal Hussain Khokhar
Categories: gr-qc
Abstract:
An additional term of the form $λ\mathbf{T} \cdot \mathbf{C} \cdot \mathbf{T}$ in the Einstein-Hilbert Lagrangian was introduced to explain the interaction between matter and pure gravitational field [H. W. Lee and A. Qadir, Motion of test particle for Weyl-interaction gravity, {\it Int. Jour. Mod. Phys. D} {\bf 28}(16) (2019) 2040014], the modified relativistic dynamics (MORD). In this paper, we estimate the shadow parameters of black hole in a spherically symmetric static spacetime within the MORD framework. As a first approximation, we assume that the black hole is surrounded by a constant-density baryonic matter halo. The analysis is then extended by introducing a homogeneous plasma background. We compute the shadow radii for various black hole masses and analyze their dependence on the WIG coupling parameter $λ$. In addition, we compute the fundamental quasi-normal mode (QNM) frequencies under test-field approximation, and perform a time-domain integration analysis.
Published: 2026-07-26 08:58:26
Authors: Anneke Reinold, Laur Peedu, Kirill Amelin, Urmas Nagel, Toomas Rõõm, Sven Luther, Hannes Kühne, Dirk Wulferding, Kingshuk Mukhuti, Maarten W. de Dreu, Peter C. M. Christianen, Dennis Kudlacik, Dmitri Yakovlev, Zhiying Zhao, Taro Nakajima, Yoshimitsu Kohama, Thomas Lorenz, Franco Lisandrini, Corinna Kollath, Marcin Raczkowski, Fakher F. Assaad, Zhe Wang
Categories: cond-mat.str-el, quant-ph
Abstract:
By appropriately perturbing a critical transverse-field Ising chain away from its critical point, the system can develop a finite correlation length with a characteristic purely massive spectrum, whose ratios and correlations are precisely described by an integrable field theory and an infinite set of integrals of motion corresponding to the $E_8$ Lie algebra. In this work, we report on experimental observation of a characteristic massive spectrum close to transverse field-induced dimensional reduction in a quasi-two-dimensional quantum magnet Cu$_2$(OH)$_3$Br, providing evidence for an emergent $E_8$ symmetry and the corresponding excitations of bound states in the sublattice of its ferromagnetic chains. These results demonstrate the power of integrable field theory in describing emergent many-body quantum critical phenomena in condensed matter systems.
Published: 2026-07-26 08:50:28
Authors: Jiwon Moon, Yerin Hwang, Kyomin Jung
Categories: cs.CL
Abstract:
Instruction hierarchy (IH) requires models to prioritize instructions by source, ensuring that higher-priority instructions override lower-priority ones. Despite its importance for safe and controllable deployment, existing evaluations have focused almost exclusively on English, leaving it unclear whether IH compliance remains stable in multilingual settings. We introduce XIH-Bench, a benchmark for multilingual IH evaluation with both same-language and cross-language conflicts across six languages, four domains, and three IH settings. Across models, we find two consistent patterns. First, IH compliance exhibits a clear language-dependent asymmetry: a language that strengthens compliance in the higher-priority position can become disruptive in the lower-priority position. Second, cross-language conflicts yield higher compliance than same-language conflicts, a phenomenon we term the Language Boundary Effect. We further show that language specialization can make lower-priority instructions in model-favored languages harder to override, creating multilingual reliability and security risks.
Published: 2026-07-26 08:48:05
Authors: Songnian Xu, Xiaoya Li, Dein Wong, Wenhao Zhen
Categories: math.SP
Abstract:
In this paper, \( G \) is a simple connected graph, and \( m_G(λ) \) denotes the multiplicity of \( λ\) as an eigenvalue of the Laplacian matrix \( L(G) \). Let \( p(G) \) denote the number of pendant vertices of \( G \), \( q(G) \) the number of quasi-pendant vertices of \( G \), and \( c(G) \) the dimension of the cycle space of \( G \).
Li et al. [Discrete Mathematics, 2026] proved that if \( G \) is a tree with \( G \not\cong K_{1,n-1} \) and \( λ\neq 1 \), then \[ m_G(λ) \le q(T) - 1. \] Moreover, for a general graph \( G \) with \( λ\neq 1 \), Li et al. also proved in the same paper that \[ m_G(λ) \le c(G) + q(G), \] with equality if and only if \( G \cong K_{1,n-1} \) or \( G \cong C_n \) with \( λ\notin \{0, 4\} \).
A natural consequence is that if \( c(G) + q(G) \ge 2 \), then \[ m_G(λ) \le 2c(G) + q(G) - 1. \] When \( c(G) = 0 \), this reduces to the result of Li et al. for trees. In this paper, we give a complete characterization of graphs \( G \) attaining the equality \[ m_G(λ) = 2c(G) + q(G) - 1. \]
Published: 2026-07-26 08:41:03
Authors: Alain Komaty, Luis S. Luevano, Vidit Vidit, Anjith George, Zeina Al Amine, Sébastien Marcel
Categories: cs.CV
Abstract:
Efficient border control is becoming a significant global challenge, mainly due to severe congestion and extended passenger waiting times. To mitigate these bottlenecks and facilitate passenger flow, biometric technologies are increasingly deployed to streamline identity verification and enhance crossing efficiency. Technical limitations frequently impede biometric identification, particularly in long-range surveillance, where systems must deal with adverse atmospheric conditions and degraded image quality. While high-quality frameworks like BRIAR exist, they are frequently restricted to specific government agencies. This paper introduces GaitFace, a new public dataset that contains face and gait data captured at long distances. To ensure that the research reflects authentic border scenarios, we use Pre-Enrollment data, where a traveler registers via a mobile device, and "In-the-Wild" captures, which records individuals at a distance across multiple viewing angles and different cameras. Benchmarking SOTA face and gait models reveals that current architectures fail under low-resolution and elevated viewpoints despite success with optical assistance. GaitFace exposes these critical vulnerabilities, providing a rigorous public benchmark to drive more robust, unconstrained biometric research.