We study the division of a heterogeneous good between two agents into contiguous bundles, each defined by a starting location and a quantity, in a purely ordinal framework that does not rely on cardinal valuations. We introduce a general class of monotonic preferences representable by indifference curves. We show that an allocation is Pareto efficient and envy-free if and only if it lies in a specific ``balanced region'', implying that an equal split is fair only when it belongs to this region. We further show that no rule can simultaneously satisfy Pareto efficiency, envy-freeness, and strategy-proofness.

Tensor linear systems widely arise from high-dimensional data mining and computing, for instance, natural language processing and machine learning. A class of residual-based tensor Kaczmarz method is proposed for tensor linear equations with t-product. Theoretical analyses prove the convergence and give an upper bound of the convergence rate of the proposed method. Furthermore, an accelerated residual-based Kaczmarz method with heavy ball momentum is developed. Numerical experiments verify the efficiency of the proposed methods and demonstrate that they are faster than the existing tensor Kaczmarz methods.

We prove a sharp forbidden interval for the nontrivial adjacency eigenvalues of trivially perfect graphs. More precisely, we show that if $G$ is a trivially perfect graph, then $\operatorname{Spec}(G)\cap [\sqrt{8}-4,0]\subseteq \{-1,0\}$. Moreover, we prove that the interval is best possible at both endpoints: there are connected trivially perfect graphs with eigenvalues arbitrarily close to $\sqrt{8}-4$ from below, and connected trivially perfect graphs with positive eigenvalues converging to $0$.

Let $Ω\subseteq \mathbb C^d$ be a bounded symmetric domain, $G$ a finite complex reflection group acting on $\mathbb C^d$, and $\boldsymbol θ:Ω\to \boldsymbol θ(Ω)$ the associated proper holomorphic map factored by $G.$ In this paper, we investigate commutant lifting and interpolation by Schur functions on the quotient domain $\boldsymbol θ(Ω).$ For a given quotient module of the Hardy space $H^2(\boldsymbolθ(Ω))$, we obtain equivalent criteria for a contractive module map to admit a Schur-class lift: one in terms of the contractivity of an associated functional on a subspace of $L^1(\partial\boldsymbolθ(Ω))$, and another in terms of a geometric distance formula in the same $L^1$-space. Specializing to quotient domains of the polydisc factored by imprimitive finite complex reflection groups, we obtain a commutant lifting criterion formulated in terms of inner functions. Finally, we apply these operator-theoretic results to finite-point Nevanlinna-Pick type interpolation problems on $\boldsymbol θ(Ω)$. Since the symmetrized bidisc and the tetrablock arise as quotient domains of suitable bounded symmetric domains, these criteria apply in particular to those domains.

Symbolic automata extend classical finite-state automata to handle large or infinite alphabets by labeling transitions by predicates coming from a boolean algebra. Many results from automata theory have been lifted to this model, and it has proved its usefulness for example in multiple software verification applications. Here, we tackle the passive learning problem of identification in the limit, i.e. learning a model from a sample without access to an oracle to query. We provide an algorithm, SAI, that efficiently identifies in the limit symbolic automata over any monotonic algebra where predicates labeling transitions are of the form a <= x < b. The algorithm extends the RPNI framework for passive learning of finite-state automata to symbolic automata thanks to a new splitting operation inspired by RTI, a passive learning algorithm for deterministic real-time automata, a subclass of timed automata. The learning algorithm combines merging of states and splitting of states allowing to infer the predicates on transitions in a top-down fashion. We prove that SAI admits polynomial size characteristic samples.

Non-adiabatic AC calorimetry is the most widely used technique for estimating the heating power of magnetic nanoparticles in magnetic hyperthermia. However, it is prone to systematic errors which lead to a standard deviation in the intrinsic loss power (ILP) of approximately 30-40%, as revealed by the RADIOMAG EU COST Action TD1402 round-robin study involving 21 European laboratories. In this study, we re-examine the RADIOMAG dataset to both uncover previously unreported instrumentation issues, and to explore more deeply some of the reported instrumentation issues. We identify four common sources of error: i) Insufficient temperature resolution, ii) AC-field sensitive thermometers, iii) Non-physical temperature oscillations, and iv) Apparent non-linear heat loss. Based on these findings, we propose criteria for sufficient measurement quality and apply them to re-estimate the ILP values. These results have a standard deviation of 18-30%., demonstrating that addressing instrumentation and analysis issues can improve measurement reliability and decrease the inter-laboratory deviation by up to 38%. When re-estimating ILP, we used the initial slope method, arguing that the corrected slope method, which was previously used to investigate the RADIOMAG data, could introduce misleading interpretations of systematic ILP deviations due to sub-optimal measurement conditions and the unnoticed influence of non-linear heat losses. However, we emphasise that the corrected slope method is preferred, given a linear heat loss. Based on our analysis, we introduce a diagnostic protocol by using slope curves - a simple yet effective plot type - for identifying and solving common instrumentation challenges proactively before the data acquisition phase.

This paper presents modified augmented Lagrangian block preconditioners for the mixed-dimensional coupling of three-dimensional solid bodies with embedded one-dimensional torsion-free Kirchhoff-Love beams using Lagrange multipliers for constraint enforcement. The finite element discretization of this mixed formulation leads to an indefinite saddle-point system. An augmented Lagrangian formulation is employed to regularize the linear system while maintaining exact enforcement of the coupling constraints. Starting from the corresponding ideal augmented Lagrangian block preconditioner, more practical block-triangular variants are derived in which the solid, beam, and Schur complement blocks can be treated independently. In addition, different variants of Schur complement approximations are introduced. Numerical experiments demonstrate robustness with respect to model parameters, near mesh-independent iteration counts, and favorable strong and weak scalability. These results indicate the suitability of the proposed approach for large-scale simulations of mixed-dimensional models in solid and structural mechanics, as demonstrated by an engineering example involving a composite sandwich plate.

We prove an Erdős-Ko-Rado type extremal result for tilings of a $1 \times n$ chessboard by tiles whose lengths belong to a set $Λ$. Two tilings are said to intersect if they contain a tile spanning the same set of squares. We prove that if $1\inΛ$, then the maximum size of an intersecting family of tilings is attained by the set of all tilings containing a fixed singleton tile at one of its ends. This result generalizes a theorem of Butler, Horn and Tressler, which is equivalent to the case $Λ=\{1,2\}$.

The China Jinping Underground Laboratory (CJPL), located $\sim 2,400$~m beneath Jinping Mountain, is one of the world's deepest and largest ($\sim 300{,}000~\mathrm{m}^3$) underground facilities, hosting dark matter, nuclear astrophysics, and neutrino experiments. We report the first muon radiography (muography) conducted at this extraordinary depth. Cosmic muons detected by a one-ton prototype developed for the Jinping Neutrino Experiment were used to perform non-invasive subsurface density mapping over a 3~km lateral range. The 1.3~m diameter detector provides nearly isotropic acceptance and an angular resolution of $\sim 4.5^\circ$. By correlating the predicted surface muon flux distributions with the underground measurements, we reconstruct a directional opacity map that constrains the density structure of the overburden and shows excellent agreement with satellite-derived terrain models. This work demonstrates the feasibility of muography at extreme depths with kilometer-scale overburden and establishes a robust methodology for future geophysical applications and large-scale facilities, such as the full Jinping Neutrino Experiment. Based on this validated overburden model, we further predict the total muon fluxes for the eight experimental halls in CJPL-II, providing essential input for their physics programs.

In this policy memorandum, we explain why deployers of AI models in high-stakes contexts should treat those AI models as insider risk vectors. High-stakes contexts include AI model deployment within government agencies and contractors, where AI models are privileged with access to, among others, classified and sensitive unclassified information, IL6 and IL7 network environments, cleared personnel, and other critical resources. AI models are increasingly embedded in high-stakes contexts and capable of leveraging their authorized access and permissions to execute misaligned actions that could damage national security, such as whistleblowing, sabotaging, or blackmailing. This combination of (1) privileged access to critical resources and (2) an increased ability to act autonomously and against the desire of their organization makes the potential insider risk posed by AI models functionally indistinguishable from that posed by their human counterparts. As a consequence, AI models deployed in high-stakes contexts could lead to intentional or unintentional loss or degradation of government or contractor information, resources, or capabilities via the unauthorized disclosure of information (leaks and spills), as well as sabotage, and theft, just like human insiders can. Despite this pressing concern, existing insider risk policies and mitigations have yet to adapt to AI insider risk. In order to safeguard national security while increasingly capable frontier AI models are leveraged for critical tasks and operations, we recommend that the U.S. Government adapts well-established measures, such as continuous evaluation and monitoring, to AI models deployed in high-stakes contexts.

Motion of particles across quasicrystalline surfaces exhibits peculiar features due to the presence of long-range order without translational periodicity. Under time-periodic forcing, this motion can become locked in directions thatn deviate strongly from the mean driving direction. We show that for surface potentials with a quasicrystalline pattern of minima generated by a superposition of plane waves, particle trajectories are nonperiodic, yet their mean direction and speed are determined by hidden periodic potentials. The lattice vectors of these underlying potentials define characteristic velocities that dictate both directional and speed locking. The particle motion does not synchronize with the driving, and it is possible for the mean speed to remain nonlocked even in directionally locked states. These findings are demonstrated using a model directly amenable to experimental realization.

In 1983, Henri Cohen and Hendrik Lenstra proposed a conjecture about the distribution of the N-torsion of the class group of a random quadratic field, supported by what was at the time a large amount of computational evidence. The Cohen-Lenstra heuristics, which are still almost entirely unproven, have become one of the central foundational problems in arithmetic statistics. Recent years have seen a rapidly accelerated pace of development in Cohen-Lenstra problems. I will give a tour of these developments, including the work of Wood and her collaborators developing a fully fleshed out roster of generalized Cohen-Lenstra conjectures, with support from topology; Smith's theorems proving the Cohen--Lenstra conjectures for the 2-primary part of the class group, as part of more general theorems about Selmer groups in quadratic twists, leading to a resolution of the minimalist conjecture for elliptic curves; and recent work by Koymans and Pagano in the ell-primary case, expanding on Smith's work and proving Stevenhagen's conjecture on the negative Pell equation.

Volcanism on the Moon is highly asymmetric, with the nearside having extensive mare emplacements and the farside exhibiting only sparse, localized volcanism. The Freundlich-Sharonov Basin (FS Basin), a preNectarian/Nectarian impact basin located on the central farside of the Moon (18.35N, 175.2E), hosts a limited volume of spatially restricted and isolated volcanic patches, which provide an ideal geological setting to investigate controls on the lunar magmatism in a thick, KREEP poor farside crust. In this study, detailed geological characterization of the FS Basin is provided for the first time, incorporating insights from morphological, chronological, and compositional analyses using high resolution datasets from missions such as Chandrayaan1 (Moon Mineralogy Mapper), Kaguya, and Lunar Reconnaissance Orbiter. The results of this study reveal a previously undetected ~192 km diameter inner depression ring, along with spatially aligned subsurface magmatic intrusions, and exposures of PAN and orthopyroxenes along the basin rings. Compositional analyses indicate that the FS Basin experienced at least two volcanic eruptions dominated by exceptionally high-alumina basalts (~16 to 24 wt% Al2O3) around ~3.4 Ga and ~2.1 Ga. This is the highest reported alumina content in the lunar maria, also expanding the period of known high alumina volcanism on the Moon to the late phase. We propose that the limited extent of volcanic eruptions in the FS Basin is a result of the combined effects of composition-dependent magma buoyancy, reduced magma production, and impact modified crustal structures determining the magma extrusion sites.

"Polymer quantum mechanics" is the name given to a quantization scheme inspired by loop quantum gravity in which the configuration space of the theory is chosen to have a discrete topology. Polymer quantization yields a representation of the canonical commutation relations that is genuinely distinct from the conventional "Schrödinger" representation. In this paper, we summarize the main features of polymer quantum mechanics and investigate in detail the polymer quantization of systems with configuration spaces that are classically compact. We show explicitly how using the standard construction of polymer states leads to a Hilbert space of states defined on a finite graph of points. By way of example, we find the exact energy eigenvalues and eigenfunctions for a particle on a ring and a particle in a box defined on such lattices, and discuss similarities and differences from standard Schrödinger quantum mechanics. We also explore the continuum limit of states in these systems, and demonstrate in detail how the exact eigenfunctions in the position representation approach their continuum counterparts.

We consider a two-dimensional periodic reaction-diffusion system under natural conditions on the reaction function and with initial condition $θ$. We show that on the global attractor $\mathcal A$ of the resulting dynamical system $(u_θ(t):t>0)$, a reverse Poincaré inequality holds true, and that as a consequence the map $θ\mapsto u_θ(t)$ satisfies a $L^2$-Lipschitz stability estimate on $\mathcal A$ for any $t>0$ fixed. We then show that statistical recovery of an initial condition $θ$ in the attractor $\mathcal A$, as well as prediction of the states $u_θ$, is possible from discrete measurements of the system at `fast' near parametric convergence rates.

Quantum geometry shapes the effective mass of Bloch particles through the geometric properties of single-particle states. Here we show that this principle extends to paired states. Starting from a generic multiband Hubbard model, we derive an exact effective-mass theorem for two-body bound states and its many-body counterpart for Cooper pairs near the critical temperature within Gaussian fluctuation theory. In both cases, the inverse effective mass separates into a ``conventional'' band-structure contribution and a new geometric contribution, pair quantum geometry, governed by quantum metrics on the pairing manifold, which becomes nontrivial when pairing is non-uniform across sublattices. In the many-body setting, analytic continuation renders the fluctuation kernel non-Hermitian, producing a biorthogonal pair geometry and a generally complex Cooper-pair effective mass whose imaginary part reflects Landau damping. Exact calculations on one-, two-, and three-dimensional lattice models show that pair quantum geometry can make quantitatively significant contributions to the effective mass. These results establish pair quantum geometry as a fundamental ingredient of superconductivity beyond conventional band geometry.

Wildfire monitoring and suppression require timely information on fire behavior, including fire energy release and rate of spread, to support operational decision-making and resource allocation. Active fire products from the Flexible Combined Imager (FCI) aboard the geostationary Meteosat Third Generation (MTG) satellites provide 10-min observations over Europe and Africa. Deriving fire behavior information from these observations requires associating individual hotspot detections into coherent fire events. We present a Fire Event Tracker (FET) algorithm that performs spatio-temporal clustering of hotspot detections from the LSA-SAF FCI active fire product. The algorithm assigns persistent identifiers to fire events and updates their geometry, fire radiative power, and rate of spread at each 10-min interval. The same parameterization is used for both near-real-time and retrospective processing. FET was applied retrospectively to the Mediterranean FCI hotspot archive of 2025 and operationally in two near-real-time contexts: wildfire monitoring in Portugal and support of the 2025 SILEX airborne campaign within the EUBURN project, where besides fire monitoring, FET products were also used to initialize coupled FOREFIRE-MesoNH simulations for plume forecasting. Results show that event-based clustering of FCI active fire detections provides a consistent description of fire evolution, enabling both tactical wildfire management and high-frequency seasonal fire analyses.

We present a multilevel embedding framework for quantum chemistry calculations on a quantum computer. In our framework, a quantum algorithm treats the strongly correlated active space, while a high-level wave-function method such as coupled cluster theory or multireference perturbation theory recovers the remaining correlation in the surrounding region. A sampling-based quantum algorithm, quantum-selected configuration interaction, bridges the quantum and classical treatments. The entire calculation is embedded in a low-cost density functional theory description of the surrounding environment using Manby's projection technique. We apply the framework to organic, metal-organic, and metallic systems, computing bond dissociation energies, adsorption energies, and reaction barriers using only the subset of qubits of a 144-qubit superconducting quantum computer at the University of Osaka and achieving $\sim$1 kcal/mol agreement with classical references for a Menshutkin $\mathrm{S_N2}$ reaction inside a carbon nanotube. Our results may open the way to quantitatively reliable quantum-classical hybrid calculations for large-scale chemical systems.

Cheating poses a significant threat to the Multiplayer Online Games (MOG) industry by degrading player satisfaction and undermining the fairness in competitive gaming. Despite efforts to develop mitigation techniques, cheating remains difficult to detect and prevent in practice. In particular, a class of cheats based on network flow disruption remains unsolvable. To find out how to detect such attacks we need access to representative labelled data. However, no such dataset exists. To address this gap, we leverage an experimental framework that combines a multiplayer online game with a plug-in capable of both reproducing cheating attacks and collecting logs at two levels: network and application-layer. This paper presents a dataset compiling records of game sessions played by both real players and automated game clients, with cheating actions explicitly logged. To the best of our knowledge, this is the first dataset that provides logs of network flow disruption cheats. While it includes such network-based cheats, it is not limited to them and also contains records of more commonly studied cheats, such as aimbots and wallhacks. This dataset can be used by researchers in academia and industry seeking to develop cheating detection mechanisms for online games. Furthermore, it is designed to be evolutive and can be enriched by others creating their own data traces with the proposed framework.

We establish a relativised variational principle for the Feng--Huang weighted topological entropy associated with a factor map between dynamical systems. Combined with a recent theorem of Yin, this yields an almost-everywhere equivalence between the Feng--Huang entropy and its combinatorial version on fibers. As an application, we compute the Hausdorff dimension of the intersection of random translates of two Bedford--McMullen carpets. The resulting formula extends the Kenyon--Peres formula from the self-similar to the self-affine setting, and also points to a new problem concerning random matrix products.

In a smoothly bounded domain $Ω\subset R^n$, $n\le 5$, the manuscript considers the variant of the Keller-Segel system given by \[ \left\{ \begin{array}{l} u_t = D Δu - \nabla \cdot (u\nabla v), \\[1mm] v_t = d Δv + \nabla \cdot (u\nabla v) - v + u, \end{array} \right. \] which involves an additional contribution $\nabla \cdot (u\nabla v)$ to the chemoattractant evolution, in line with refined modeling literature reflecting an anisotropic correction to the isotropic signal production term $+u$ in the classical Keller-Segel model. It is shown that for arbitrary $D>0$ and $d>0$ and any nonnegative intial data from $W^{1,\infty}(Ω)\times W^{1, \infty}(Ω)$, an associated Neumann problem admits a global weak solution $(u,v)$ which, inter alia, satisfies \[ \sup_{t \in (0,\infty)\setminus N} \int_Ωe^{u^α(\cdot,t)} < \infty \] with some $α>0$ and some null set $N\subset (0,\infty)$.

We construct canonical Steenrod square operations on the Geisser--Schmidt/Milne modified compactly supported étale cohomology of separated finite-type schemes over rings of $S$-integers in which $2$ is invertible. This lets us extend Feng's notion of the absolute étale Wu class from the finite-field setting to arithmetic bases away from $2$. A key technical input is a modified compactly supported relative Wu formula, extending Benoist's relative Wu formula to the arithmetic compact-support setting. Using this, we prove an absolute Wu formula for regular projective flat schemes over either finite fields of odd characteristic or rings of $S$-integers away from $2$: if $f\colon X\to B$ is such a scheme, then the absolute Wu class of $X$ is the product of the relative Wu class $\operatorname{Sq}^{-1}(w_{\mathrm{et}}(τ_f))$ and the pullback of the absolute Wu class of the base. In the $S$-integer case, the base contribution is $1+β_B$, where $β_B$ is the Bockstein, equivalently the Kummer class of $-1$. As an application, we obtain an infinite family of universal mod-$2$ congruences among the Chern classes of regular projective flat schemes over such bases, governed by an arithmetic deformation of Hirzebruch's $2$-Todd series; this is the generalized Hecke theorem. In low dimensions these congruences recover Hecke's theorem on the different away from $2$, Serre's Riemann--Hurwitz theorem for spin bundles, Atiyah's theorem on theta characteristics over finite fields, and the smooth $3$-manifold branched-cover analogue of the Shusterman--Sawin theorem, while yielding new higher-dimensional congruences over both finite and arithmetic bases.

Nitric oxide (NO) is important in biological, atmospheric, plasma, industrial, and astrophysical environments, where reliable electron-collision data support modelling charged-particle interactions with matter. Its well-known experimental properties make it suitable for assessing how the target electronic-structure description affects low-energy electron scattering calculations. In this work, NO properties were evaluated using B3LYP, M06-2X, PBE0, and $ω$B97X-D3, with basis sets ranging from minimal to quadruple-zeta quality. Bond length, dipole moment, ionisation potential, and polarisability were compared with experiment to assess the sensitivity of the target description to the functional and basis set. The aug-cc-pVQZ basis set was then used to generate target models for ab initio R-matrix calculations over 0.1--20 eV. The total cross sections show low-energy resonance features, with the strongest functional dependence around the broad peak near 0.8--1.0 eV. A sharper, higher-energy structure is also observed below 2 eV, shifting from 1.74 to 1.82 eV depending on the functional. Differential cross sections show modest functional sensitivity, with more noticeable angular differences at 7.5 and 10 eV. These results show that the DFT functional and basis set affect the target properties, with the resulting target description influencing low-energy electron-scattering observables of NO. The comparison supports $ω$B97X-D3/aug-cc-pVTZ geometry optimisation followed by aug-cc-pVQZ target-property calculations as a practical protocol for R-matrix modelling of NO.

We investigate the spatially-resolved ISM properties of the local ($z = 0.048$), IR-luminous ($L_{\rm IR} = 10^{11.87}$\,L$_\odot$), late-stage galaxy merger IRAS F01364-1042, combining multi-wavelength IFU observations from \textit{JWST/MIRI-MRS}, ALMA and Keck/KCWI. Using these datasets, we construct emission line maps of several key tracers of the ionized (e.g., [Ne\,II]\,12.8$μ$m, [O\,III]$\lambda5007$), warm molecular (e.g., \ce{H2}\,0-0\,S(3)), and cold molecular gas (e.g., CO (J$=2-1$)), and perform detailed decomposition of spectra extracted in resolved regions across the areas of emission. We confirm the presence of a multi-phase galactic biconical outflow along the minor axis of a highly inclined rotating disk. The inferred outflow velocities are $\sim\,$500 - 600\,km\,s$^{-1}$ $\sim\,$350\,km\,s$^{-1}$, and $\sim\,$200 - 300\,km\,s$^{-1}$, in the ionized, warm and cold molecular phase, respectively, with corresponding mass outflow rates of $\sim 0.3 - 2.3$, $\sim 31$, and $\sim 38 - 240$\,M$_\odot\,$yr$^{-1}$. The cold molecular phase dominates both the total mass outflow rate and the associated kinetic energy ($\sim\,2 - 8 \times 10^{42}$\,erg\,s$^{-1}$). We confirm, for the first time, a dust-obscured AGN in IRAS\,F01364-1042, via detection of the [Ne\,V]\,14.3$μ$m line. The low inferred AGN bolometric luminosity ($1.2 - 1.8 \times 10^{43}$\,erg\,s$^{-1}$) suggests that the nuclear starburst alone, with a star formation rate of $\sim 40 - 60$\,M$_\odot$\,yr$^{-1}$, can account for the energy required to drive the outflow, though a more active AGN phase in the recent past may have also played a role. Our work showcases the necessity of multi-wavelength observations for interpreting the gas dynamics in merger-driven dusty starbursts, and the capability of \textit{JWST/MIRI-MRS} to uncover obscured, low-luminosity AGN that may be common in these systems.

Understanding the fundamental mechanical behaviour of iron oxide phases is essential for controlling attrition and fracture during iron ore reduction process, particularly in hydrogen-based direct reduction systems. This study investigates the room temperature plasticity and fracture behaviour of single-crystal hematite, magnetite, and Wustite using nanoindentation and micro-cantilever fracture testing. Hematite exhibited the highest hardness, H and elastic modulus, E (H=18.5 GPa, E=281 GPa), followed by magnetite (H=8.7 GPa, E=165 GPa) and Wustite (H=7.5 GPa, E=145 GPa), reflecting differences in slip activity along the iron oxide reduction sequence. Furthermore, fracture toughness was measured using notched microcantilevers for all three iron oxide phases, aligned along low index and high index crystallographic planes, respectively. For the low index-oriented case hematite showed increased fracture toughness owing to crack deviation and faceting while magnetite and Wustite exhibited single plane cleavage fracture. Distinct changes in the deformation behavior in terms of plasticity and cracking of the three iron oxides were evident from both methods. Further investigation of a magnetite-gangue interface, particularly relevant to low-concentration ores, revealed significantly reduced fracture toughness compared to the magnetite phase. Overall, these results provide a comprehensive set of mechanical properties of iron oxides with potential application in material models for predicting fracture and attrition during hydrogen-based direct reduction.

It is an open question whether every topological group is precompact or ambitable. This note presents a topological group that is ambitable but does not satisfy previously known sufficient conditions for being so.

This paper employs shortfall risk to measure portfolio risk. Assume stock returns follow polynomial relations with their influence factors. We propose a moment-based distributionally robust optimization (DRO) shortfall risk portfolio model. For piecewise linear loss functions, we show that this DRO model can be transformed into a tractable linear conic optimization problem with nonnegative polynomial cones. A Moment-SOS relaxation algorithm is proposed to solve the transformed problem. Its finite and asymptotic convergence properties are studied. For optimizers computed from our algorithm, we give convenient conditions verify their global optimality for the original DRO problem. Numerical experiments involving real stock market data are given to show the efficiency of our approach.

Verbal harassment is a growing source of psychological stress for people around the world. It occurs both online and offline and relies on language to demean, threaten, or discredit its targets. Unlike other stressors such as loss or uncertainty, verbal harassment aims at silencing its targets by eroding their sense of being heard and weakening their perceived ability to respond. Many individuals lack access to adequate and timely support, however, when they experience such harassment. People increasingly turn to conversational artificial intelligence (AI) such as ChatGPT or dedicated AI companions for emotional support, raising questions about whether it can facilitate the same psychological benefits as actual human empathy. We focus on online contexts as a prevalent application of verbal harassment. We develop and test a psychological framework identifying three key linguistic signals of empathic listening (perspective-taking, emotional validation, and action orientation), that together restore a sense of feeling heard and enhance coping in the context of verbal harassment. We find that LLMs consistently produce language exhibiting stronger empathic-listening markers than human non-experts and trained mental health professionals, promoting more approach-oriented (vs. avoidance-oriented) coping strategies. A subsequent behavioral study shows that these linguistic signals boost recipients' sense of feeling heard and increase their coping self-efficacy. These findings reveal how specific linguistic features create empathic connections between humans and advanced conversational AI and can enhance people's psychological resilience. Our results highlight the potential for AI to serve as a scalable source of emotional support, especially when human support is unavailable or insufficient.

The double-directional (DD) wireless channel model is important for realistic system design since it provides complete propagation information. While stochastic and deterministic channel models are widely adopted, and existing machine learning (ML) solutions mostly aim to align future channel realizations, these solutions are often limited to short time spans that may not be statistically significant. Moreover, because the number of multi-path components (MPCs) varies with spatial and temporal variation of the receiver (RX) and/or interacting objects (IOs), typical ML solutions that require fixed, predefined input and output shapes fall short. To curb these limitations, we propose a statistics-aided ML solution that relies on a fixed subset of MPCs selection. More specifically, we first select top-$M$ MPCs, where $M\in\mathbb{Z}^+$ is much smaller than the total number of MPCs, and construct learnable graphs to train our proposed hybrid TimesNet-TimeFilter (TNTF) model. We then use a channel statistics-aided training method to generate future top-M DD channel realizations such that the statistics calculated from these realizations matches closely with those of the actual statistics from the complete time-varying DD channel realizations. We validate the proposed solution using extensive simulations on both synthetic stochastic channel model (SCM)-based and deterministic ray-tracing-based datasets, and demonstrate its effectiveness relative to state-of-the-art baselines.

Gottesman-Kitaev-Preskill (GKP) states are essential non-Gaussian resources for fault-tolerant photonic quantum computing, enabling logical qubit encoding with intrinsic robustness against errors. Several approaches to GKP state preparation have been explored, including measurement-based protocols in circuit QED and trapped-ion systems, cat-state breeding, and photon-subtraction schemes. However, these methods are either restricted to specific platforms or require deep non-Gaussian resource chains with exponentially low success probabilities. Gaussian Boson Sampling (GBS) offers a compelling all-photonic alternative by generating non-Gaussian states through measurement-induced nonlinearity, without the need for matter-based ancilla or active feedforward. Nevertheless, its practical implementation is limited by the exponential computational cost of evaluating matrix hafnians-#P-complete functions that govern photon-number probabilities. To address this challenge, we introduce a two-stage Histogram Gradient Boosting surrogate pipeline that predicts, without any hafnian computation, the optimal heralding pattern, circuit fidelity, and post-selection probability for candidate GBS circuits, while reserving exact quantum simulation exclusively for surrogate-selected candidates. Trained on circuit configurations across 3-5 optical modes, the surrogate achieves 90.0% GKP-detection accuracy on a held-out set, representing a 23.7 percentage-point improvement over the baseline, with a fidelity mean absolute error of 0.032 and a log-scale post-selection probability $R^2 = 0.837$, reducing the total simulation burden by approximately 90%.