Completely integrable finite dimensional Hamiltonian systems are well understood thanks to the work of Liouville and Arnold. On the other hand, the Lax Pair formulation of the KdV equation marks the beginning of the extension of the completely integrable theory to infinite dimensional Hamiltonian systems. Solutions of initial value problems for systems that admit a Lax Pair formulation normally have a tame qualitative behavior if Lax Pairs give rise to an infinite complete set of conserved laws. The situation is different for initial-boundary value problems, even in one space dimension. There are problems where integrability persists and regular (long time asymptotic) behavior can be proven (and we have proven it). There are others where even irregular "fractal-chaotic-looking" behavior can appear. In this short article we review an instance of each case. We also make a connection with results from the existing theory of perturbed Lax Pair equations on the real line.

Previous work on the gravitational-wave background generated in a two-scalar-field cosmological model, in which warm inflation and the dark sector are unified within a single framework, has shown that the resulting spectrum could be potentially detectable by planned next-generation gravitational-wave observatories. In this work, we extend this analysis to the weak dissipation regime of warm inflation, highlighting how the features of the inflationary scenario play a crucial role in the production of gravitational waves. The full gravitational-wave energy spectrum is calculated using the formalism of continuous Bogoliubov coefficients. By comparing our results with those obtained in the strong dissipation regime and with the sensitivity curves of future detectors, we find that the weak dissipation regime improves the prospects for observational detection.

We study a Dirichlet--Ferguson process $ζ$ on a general phase space. First we reprove the chaos expansion from Peccati (2008), providing an explicit formula for the kernel functions. Then we proceed with developing a Malliavin calculus for $ζ$. To this end we introduce a gradient, a divergence and a generator which act as linear operators on random variables or random fields and which are linked by some basic formulas such as integration by parts. While this calculus is strongly motivated by Malliavin calculus for isonormal Gaussian processes and the general Poisson process, the strong dependence properties of $ζ$ require considerably more combinatorial efforts. We apply our theory to identify our generator as the generator of the Fleming--Viot process and to describe the associated Dirichlet form explicitly in terms of the chaos expansion. We also establish the product and chain chain rule for the gradient and an integral representation of the divergence. Finally we give a short direct proof of the Poincaré inequality.

The rapid growth of imaging and spectroscopic surveys has intensified the need for efficient tools that support visual inspection, a practice that remains essential for tasks such as classification, catalog refinement, and validation of automated methods. Existing solutions, however, often require the use of multiple platforms and complex workflows to integrate heterogeneous data. To address this challenge, we present the first release of the AstroInspect (https://astroinspect.github.io), a web-based system which ensures seamless access to several astronomical resources. The system provides an intuitive graphical user interface (GUI) through which users can upload catalogs of objects defined by celestial coordinates. AstroInspect automatically enriches these catalogs with complementary information, including imaging, spectroscopic, and photometric data retrieved in real time from surveys such as the Sloan Digital Sky Survey (SDSS), the Legacy Surveys (LS), and the Southern Photometric Local Universe Survey (S-PLUS). As an example of its scientific utility, we used AstroInspect to identify H$α$ emission-line galaxies within a 7 deg radius in the direction of the Hydra I cluster (also known as Abell 1060) by visual inspection. Using a candidate set of 981 galaxies selected from S-PLUS photometric data, we produced a catalog of 80 galaxies with confirmed H$α$ emission. These results highlight the potential of AstroInspect to support efficient visual inspection workflows.

Counterspeech offers a non-repressive approach to moderate hate speech in online communities. Research has examined how counterspeech chatbots restrain hate speakers and support targets, but their impact on bystanders remains unclear. Therefore, we developed a counterspeech strategy framework and built \textit{Civilbot} for a mixed-method within-subjects study. Bystanders generally viewed Civilbot as credible and normative, though its shallow reasoning limited persuasiveness. Its behavioural effects were subtle: when performing well, it could guide participation or act as a stand-in; when performing poorly, it could discourage bystanders or motivate them to step in. Strategy proved critical: cognitive strategies that appeal to reason, especially when paired with a positive tone, were relatively effective, while mismatch of contexts and strategies could weaken impact. Based on these findings, we offer design insights for mobilizing bystanders and shaping online discourse, highlighting when to intervene and how to do so through reasoning-driven and context-aware strategies.

Radiation detectors deployed as part of a large urban network or for homeland security monitoring must maintain reliable energy calibration even when subjected to substantial variations in temperature and ambient background radiation. Traditional calibration methods often rely on power-intensive temperature stabilization or peak-locking algorithms that are susceptible to environmental changes. This publication presents a novel software-based calibration method that eliminates the need for active temperature control by utilizing full-spectrum analysis. The method continuously updates the calibration parameters by fitting the spectral data with a series of background radiation contributions (K, U, Th series, radon progeny and cosmics) combined with a Monte-Carlo-based physical detector model that incorporates light yield non-proportionality and photomultiplier tube saturation. Performance was validated using simulated data, measurements in an environmental chamber across a wide temperature range (-25C to +50C), and data from a multi-day outdoor field deployment. Results demonstrate that the method successfully maintains stable energy calibration despite significant ambient temperature variations and precipitation events. The technique effectively decouples instrumental drift from spectral changes caused by environmental background fluctuations. This approach provides a robust, automated, and low-power alternative to conventional calibration techniques, enabling the practical deployment of large-scale, unattended networked detector systems.

Black holes described by the Kerr metric can have a theoretical maximum dimensionless spin parameter of $a_\bullet = 1$, but several effects may limit the maximum spin parameter in astrophysical systems. We perform general relativistic magnetohydrodynamics simulations of accretion flows around black holes with $a_\bullet = 0.9375$ and $a_\bullet = 0.998$, each corresponding to a proposed astrophysical limit in the literature. We then perform full polarized general relativistic ray-tracing to produce astrophysical movies of these simulations, as can be spatially resolved by the Event Horizon Telescope (EHT) and its extensions. Although many properties of black holes and accretion flows evolve rapidly as $a_\bullet \to 1$, we find that our $a_\bullet=0.9375$ and $a_\bullet=0.998$ simulations are remarkably similar, both in terms of their GRMHD fluid properties and their full-Stokes, time-variable images. This suggests that previous work using simulations with $a_\bullet \approx 0.9375$ may be representative of models with $a_\bullet \gtrsim 0.9375$ in most practical cases. Our calculations suggest that shape and size constraints on the photon ring, enabled by extensions of the EHT into space by missions such as the Black Hole Explorer (BHEX) may be the only practical way to distinguish between models with different spin parameters as $a\to 1$.

We relate general maps to bipartite maps through a bijection of type slit-slide-sew. We provide an involution on arbitrary genus maps with even degree faces. This enables a full interpretation of the relation between general and bipartite maps, in the case of genus $1$ maps with a unique face. The main tool is the use of rotations along well-chosen specific loops. Once a noncontractible simple loop is given, one slits along it, slides one notch, and sews back. This mildly modifies the structure of the map along the loop, changing the parity of the length of other loops crossing it. In the unicellular toroidal setting, the structure of noncontractible loops is simple enough to enable a full correspondence between general and bipartite maps.

We propose the protocol for preparing the maximally entangled Bell state between remote qubits at the ends of the spin-1/2 chain governed by the specially engineered nearest-neighbor XX-Hamiltonian with excited central spin as the initial state. This method does not require including optical constituent in the teleportation protocol and can be implemented in the quantum devices with solid-state architecture for teleporting unknown states or organizing quantum gates between remote qubits. A superconducting flux-qubit chain is an example of such devises.

Edge deployment of LLM agents on IoT hardware introduces attack surfaces absent from cloud-hosted orchestration. We present an empirical security analysis of three architectures (cloud-hosted, edge-local swarm, and hybrid) using a multi-device home-automation testbed with local MQTT messaging and an Android smartphone as an edge inference node. We identify five systems-level attack surfaces, including two emergent failures observed during live testbed operation: coordination-state divergence and induced trust erosion. We frame core security properties as measurable systems metrics: data egress volume, failover window exposure, sovereignty boundary integrity, and provenance chain completeness. Our measurements show that edge-local deployments eliminate routine cloud data exposure but silently degrade sovereignty when fallback mechanisms trigger, with boundary crossings invisible at the application layer. Provenance chains remain complete under cooperative operation yet are trivially bypassed without cryptographic enforcement. Failover windows create transient blind spots exploitable for unauthorised actuation. These results demonstrate that deployment architecture, not just model or prompt design, is a primary determinant of security risk in agent-controlled IoT systems.

This paper develops a general method of inference for fixed effects models which is (i) automatic, (ii) computationally inexpensive, (iii) tuning parameter-free, and (iv) highly model agnostic. Specifically, we show how to combine a collection of subsample estimators into a jackknife $t$-statistic, from which hypothesis tests, confidence intervals, and $p$-values are readily obtained.

Traditional phishing website detection relies on static heuristics or reference lists, which lag behind rapidly evolving attacks. While recent systems incorporate large language models (LLMs), they are still prompt-based, deterministic pipelines that underutilize reasoning capability. We present MemoPhishAgent (MPA), a memory-augmented multi-modal LLM agent that dynamically orchestrates phishing-specific tools and leverages episodic memories of past reasoning trajectories to guide decisions on recurring and novel threats. On two public datasets, MPA outperforms three state-of-the-art (SOTA) baselines, improving recall by 13.6%. To better reflect realistic, user-facing phishing detection performance, we further evaluate MPA on a benchmark of real-world suspicious URLs actively crawled from five social media platforms, where it improves recall by 20%. Detailed analysis shows episodic memory contributes up to 27% recall gain without introducing additional computational overhead. The ablation study confirms the necessity of the agent-based approach compared to prompt-based baselines and validates the effectiveness of our tool design. Finally, MPA is deployed in production, processing 60K targeted high-risk URLs weekly, and achieving 91.44% recall, providing proactive protection for millions of customers. Together, our results show that combining multi-modal reasoning with episodic memory yields robust phishing detection in realistic user-exposure settings. Our implementation is available at https://github.com/XuanChen-xc/MemoPhishAgent.git.

We present an updated analysis of the angular distribution for $ψ(3686) \to p\bar{p}$ decay, taking into account transverse beam polarization, to investigate potential sources of forward-backward asymmetry and azimuthal modulation beyond the simple $1+α\cos^2θ$ form. We focus on the interference between the $ψ(3686)$ resonance and the two-photon exchange continuum process, as well as the background from initial-state-final-state radiation interference. A maximum-likelihood fit to the $\cosθ$ distribution of $ψ(3686)\to p\bar{p}$ yields $α= 1.00 \pm 0.03$, consistent with previous results. Our model predicts a significant $\sin(2ϕ)$ modulation in the azimuthal angle, indicating the influence of transverse beam polarization. These findings motivate future two-dimensional angular analyses to fully disentangle the polarization and interference dynamics in charmonium decays to baryon pairs.

Modeling precipitation and its accumulation over time and space is essential for flood risk assessment. In this paper, we analyze rainfall data collected over several years through a micro-scale precipitation sensor network in Montpellier, France. A novel spatio-temporal stochastic model is proposed for high-resolution urban extreme rainfall and combines realistic marginal behaviour and flexible dependence structure. Marginally, rainfall intensities are described by the Extended Generalized Pareto Distribution (EGPD), capturing both moderate and extreme events without threshold selection. Based on peaks-over-threshold theory for spatial processes, dependence during extreme episodes is modeled by an r-Pareto process with a non-separable variogram allowing for episode-specific advection, such that the displacement of rainfall cells is represented explicitly. Based on a catalog of extreme space-time episodes extracted from observations, parameters are estimated by a new composite likelihood based on joint exceedance indicators. Empirical advection velocities are derived beforehand from a radar reanalysis dataset. We show that the model accurately reproduces the spatio-temporal structure of extreme rainfall observed in the Montpellier OMSEV network and enables realistic stochastic scenario generation for flood risk assessment.

We demonstrate that the interplay between structural geometry and Rashba spin-orbit coupling generates nontrivial topological phases in honeycomb nanoribbon heterostructures. We consider an armchair nanoribbon in which a Rashba spin-orbit coupled region is embedded between pristine segments. Increasing the Rashba coupling induces symmetry-protected interface states localized at the junction between topologically distinct regions, which remain robust against edge perturbations. For finite ribbon widths, Rashba spin-orbit coupling drives a gap closing and reopening, signaling a topological phase transition without modifying the lattice structure. Our results reveal a mechanism by which interfacial geometry and spin-orbit interaction cooperatively engineer tunable topological states in graphene-based nanostructures.

We investigate a linear diffusion equation incorporating historical effects, characterised by a finite non-negative Borel measure on \((0, \mathfrak T]\). This approach accommodates both distributed memory and discrete delays within a unified weak formulation. The measure-valued framework encompasses the memory-free scenario, absolutely continuous kernels, purely atomic delay kernels, and mixed regimes. Our principal result is a finite-time well-posedness theorem for arbitrary finite measures, including kernels with atomic components. More precisely, we prove existence and uniqueness of weak solutions on \((-τ_{\max},\mathfrak T]\) and derive stability bounds with constants depending explicitly on \(\mathfrak T\), \(μ((0,\mathfrak T])\), and the coercivity and boundedness parameters of the bilinear forms. Subsequently, we demonstrate continuous dependence on the kernel over fixed time intervals, leading to regime-consistency results such as vanishing-memory limits and concentration to a discrete delay. For a restricted dissipative subclass of absolutely continuous kernels, we identify a positive-type condition that results in an energy inequality, and we provide verifiable sufficient criteria, including complete monotonicity, along with an internal-variable representation.

We use a diffusion Monte Carlo (DMC) algorithm to solve the Schrödinger equation that describes $udsc\bar c$ pentaquarks within the framework of a non-relativistic constituent quark model. We considered only multiquark states with defined values of parity, color, spin and isospin, selected to be compatible with the experimentally favored assignment $J^P=1/2^-$ for one of the candidates, and assumed $I=0$. However, we found that, to explain the existence of the $P_{cs}(4338)$ and $P_{cs}(4459)$ pentaquarks, we need the total wavefunction to be also an eigenvector of the SU(3) {\em flavor} operator. When we impose that condition, we obtain two structures compatible with the masses extracted from the $J/ψΛ$ spectrum. In addition, two states are predicted below the $J/ψΛ$ threshold but above the $η_cΛ$ one that would not appear in that channel. If we only impose the $I=0$ condition, we obtain a {\em single} (not two) structure compatible with the experimental quantum numbers, with a mass below the $J/ψΛ$ threshold.

Average of exponential ${\rm Tr}_R e^X$, i.e. of a group rather than an algebra character, in Gaussian matrix model is known to be an amusing generalization of Schur polynomial, where time variables are substituted by traces of products of non-commuting matrices ${\rm Tr} \left(\prod_i A_{k_i}\right)$ and are thus labeled by weak compositions. The entries of matrices $A_k$ are made from extended Laguerre polynomials, what introduces additional difficulties. We describe the generic sum rules, which express arbitrary traces through convolutions of a single Laguerre polynomial $L_{N-1}^1(z_{k_i})$, what is a considerable simplification.

We study the implementation of a universal quantum gate set via multiple-braiding within $SU(2)_k$ ($k > 2$, $k \neq 4$) anyon models. The multiple elementary braiding matrices (MEBMs) are derived from the $q$-deformed representation theory of $SU(2)$. Braiding multiplicities from one to nine are examined as building blocks for $\{H, T, \text{CNOT}\}$ in $SU(2)_3$ and $SU(2)_5$. Only one case fails to support universality; high-precision $H$ and $T$ gates can be achieved by a Genetic Algorithm enhanced Solovay--Kitaev Algorithm, and expanding operations to 30 enables direct approximation of a locally equivalent CNOT for the remaining eight. Notably, even-order braiding operations offer a physical advantage by reducing the number of non-Abelian anyons required in braiding-based topological quantum computing (TQC). Our numerical results provide strong evidence that most multiple-braiding sequences in $SU(2)_k$ ($k > 2$, $k \neq 4$) anyon models are capable of universal quantum computation.

We discuss the classical elliptic Toda chain introduced by Krichever and the elliptic Ruijsenaars-Toda chain introduced by Adler, Shabat and Suris. It is shown that these models can be obtained as particular cases of the elliptic Ruijsenaars chain. We explain how the classical $r$-matrix structures are derived for these chains. Also, as a by-product, we prove that the elliptic Ruijsenaars-Toda chain is gauge equivalent to discrete Landau-Lifshitz model of XYZ type. The elliptic Toda chain is also gauge equivalent to XYZ chain with special values of the Casimir functions at each site.

We present a systematic study of non-supersymmetric type II toroidal asymmetric orbifolds with vanishing vacuum energy at one-loop in string perturbation theory. These are engineered through the conservation of a supercharge-like operator in each individual sector in the orbifold sum, despite the overall explicit breaking of spacetime SUSY. We provide a full classification of such orbifolds with finite Abelian point-group, which can only admit $\mathbb{Z}_k \times \mathbb{Z}_k$ point group with $k=2,3,4$. We present detailed constructions, alongside other examples with non-Abelian point group. For some of these models, it is possible that this cancellation persists at higher loops.

We present a temperature-dependent extension of the approximate electronic conductivity formula of Hindley and Mott that leverages time-averaged fluctuations of the electronic density of states obtained from ab initio molecular dynamics. By thermally averaging the square of the density of states near the Fermi level, we obtain an estimate of the temperature dependence of the conductivity. This approach termed the thermally-averaged Hindley-Mott (TAHM) method was applied to five representative systems: crystalline aluminum (c-Al), aluminum with a grain boundary (AlGB), a four-layer graphene-aluminum composite (Al-Gr), amorphous silicon (a-Si) and amorphous germanium-antimony-telluride (a-GST). The method reproduces the expected Bloch-Gruneisen decrease in conductivity for c-Al and AlGB. Generally, the reduction (increase) in conductivity for metallic (semiconducting) materials are reproduced. It captures microstructure-induced, thermally activated conduction in multilayer Al-Gr, a-Si and a-GST. Overall, the approach provides a computationally efficient link between time-dependent electronic structure and temperature-dependent transport, offering a simple and approximate tool for exploring electronic conductivity trends in complex and disordered materials.

Zero-knowledge circuits enable privacy-preserving and scalable systems but are difficult to implement correctly due to the tight coupling between witness computation and circuit constraints. We present zkCraft, a practical framework that combines deterministic, R1CS-aware localization with proof-bearing search to detect semantic inconsistencies. zkCraft encodes candidate constraint edits into a single Row-Vortex polynomial and replaces repeated solver queries with a Violation IOP that certifies the existence of edits together with a succinct proof. Deterministic LLM-driven mutation templates bias exploration toward edge cases while preserving auditable algebraic verification. Evaluation on real Circom code shows that proof-bearing localization detects diverse under- and over-constrained faults with low false positives and reduces costly solver interaction. Our approach bridges formal verification and automated debugging, offering a scalable path for robust ZK circuit development.

We introduce APPL (Abstract Program Property Logic), a unifying Hoare-style logic that subsumes standard Hoare logic, incorrectness logic, and several variants of Hyper Hoare logic. APPL provides a principled foundation for abstract program logics parameterised by an abstract domain, encompassing both existing and novel abstractions of properties and hyperproperties. The logic is grounded in a semantic framework where the meaning of commands is first defined on a lattice basis and then extended to the full lattice via additivity. Crucially, nondeterministic choice is interpreted by a monoidal operator that need not be idempotent nor coincide with the lattice join. This flexibility allows the framework to capture collecting semantics, various classes of abstract semantics, and hypersemantics. The APPL proof system is sound, and it is relatively complete whenever the property language is sufficiently expressive. When the property language is restricted to an abstract domain, the result is a sound abstract deduction system based on best correct approximations. Relative completeness with respect to a corresponding abstract semantics is recovered provided the abstract domain is complete, in the sense of abstract interpretation, for the monoidal operator.

Landau polaritons arising from the coupling between cyclotron resonance and terahertz split-ring resonators (SRRs) have served as a central platform for exploring ultrastrong light-matter interaction for more than a decade. Over this period, a wide variety of SRR architectures, differing in size, geometry, and even material composition, have been investigated. However, the regime of near-field coupled SRRs has remained largely unexplored. Here, we demonstrate ultrastrong coupling using photocurrent spectroscopy in two prototypical near-field configurations: a SRR dimer and a topological SRR chain. The measurements reveal hybridization not only with bright resonant modes but also with optically dark modes and topological edge modes, highlighting the exceptional sensitivity of the photocurrent spectroscopy. Moreover, the engineered near-field interactions allow the study of multi-mode ultrastrong coupling and the interplay between topological band structure and cavity quantum electrodynamics.

We analyze the quantum states of an isolated composite system consisting of two stacked quantum Ising (SQI) subsystems, coupled by a local Hamiltonian term that preserves the $Z_2$ symmetry of each subsystem. The coupling strength is controlled by an intercoupling parameter $w$, with $w=0$ corresponding to decoupled quantum Ising systems. We focus on the quantum correlations of one of the two SQI subsystems, $S$, in the ground state of the global system, and study their dependence on both the state of the weakly-coupled complementary part $E$ and the intercoupling strength. We concentrate on regimes in which $S$ develops critical long-range correlations. The most interesting physical scenario arises when both SQI subsystems are critical. In particular, for identical SQI subsystems, the global system is equivalent to the quantum Ashkin-Teller model, characterized by an additional $Z_2$ interchange symmetry between the two subsystem operators. In this limit, one-dimensional SQI systems exhibit a peculiar critical line along which the length-scale critical exponent $ν$ varies continuously with $w$, while two-dimensional systems develop quantum multicritical behaviors characterized by an effective enlargement of the symmetry of the critical modes, from the actual $Z_2\oplus Z_2$ symmetry to a continuous O(2) symmetry.

We investigate the holographic timelike entanglement entropy (HTEE) and timelike subregion complexity of a thermal CFT$_d$ deformed by a relevant scalar operator $ϕ_0$, dual to a hairy black hole in AdS$_{d+1}$. We employ the prescription of merging spacelike and timelike surfaces at the interior, constructing an extremal surface homologous to a boundary timelike subsystem with a time interval $Δt$. Consequently, this deformation breaks the invariance of the imaginary component of HTEE observed in pure AdS$_3$ and BTZ geometry, introducing a nontrivial dependence on $Δt$. At small $Δt$, we derive analytical expressions that are in agreement with numerical results, and observe partial consistency with analytic continuation to temporal or spacelike entanglement entropy at the level of the near-boundary expansion. However, analytic continuation of CFT temporal entanglement entropy fails to reproduce the HTEE calculations under boundary deformation, even in $d=2$. Furthermore, we extend the numerical calculations to higher dimensions ($d=3$). In addition, we study holographic timelike subregion complexity within the complexity=volume conjecture and find that it remains real-valued, providing a complementary geometric probe of the black hole interior. In particular, for the BTZ black hole, we analytically show that the UV-finite term of the subregion complexity receives its entire contribution from the interior region alone.

We consider the problem of sharing correlated data under a perfect information-theoretic privacy constraint. We focus on redaction (erasure) mechanisms, in which data are either withheld or released unchanged, and measure utility by the average cardinality of the released set, equivalently, the expected Hamming distortion. Assuming the data are generated by a finite time-homogeneous Markov chain, we study the protection of the initial state while maximizing the amount of shared data. We establish a connection between perfect privacy and window-based redaction schemes, showing that erasing data up to a strong stationary time preserves privacy under suitable conditions. We further study an optimal sequential redaction mechanism and prove that it admits an equivalent window interpretation. Interestingly, we show that both mechanisms achieve the optimal distortion while redacting only a constant average number of data points, independent of the data length~$N$.

Cumulative observables often exhibit saturation in systems involving propagation or spreading with local dissipation. This work shows that bounded cumulative response follows directly from local linear relaxation. Linear cumulative observables accumulated over the lifetime of a relaxing signal are limited by a scale set by the relaxation time, independent of geometry, dimensionality, or microscopic transport dynamics. When relaxation is mapped to space through transport or spreading, this temporal bound yields a corresponding spatial saturation scale determined by the transport law. The result shows that cumulative saturation follows directly from exponential local relaxation and does not depend on the specific transport mechanism.

Let $(X,x)$ be a pointed geometrically connected smooth projective variety over a sub-$p$-adic field $K$. For any given rank $n$, we prove that there are only finitely many isomorphism classes of representations $π_{1}^{EF}(X,x)\rightarrow \mathrm{GL}_{n}$, where $π_{1}^{EF}(X,x)$ is Nori's fundamental group of essentially finite bundles. Equivalently, there are only finitely many isomorphism classes of essentially finite bundles of rank $n$. This answers a question from C.Gasbarri.