Papers

We study the dark-matter phase space distribution of Milky Way-mass halos in the Auriga simulations, considering both hydrodynamic and dark-matter-only runs. In a spherically averaged potential, we test whether the coarse-grained distribution function can be approximated as a function of the integrals of motion $E$ and $L$. We find that $f(E,L)$ provides a useful description of the simulated halos: although the deviations from this form are formally statistically significant, the median fractional residuals between radial shells are typically $\lesssim 15\%$, with 90th-percentile residuals of order tens of percent. An energy-only approximation, $f(E)$, gives similar median residuals but is systematically disfavored by $\chi^2$ tests, indicating that angular momentum dependence is statistically preferred. Ultimately we find that neither $f(E)$ nor $f(E,L)$ fully describes the particle data at high precision. The remaining residuals likely reflect departures from spherical equilibrium, including anisotropy, triaxiality, substructure, and baryonic effects.

This study develops a projection-based descent method for minimizing weakly semismooth functions over polyhedral sets, taking an initial step toward extending projection-based descent algorithms to nonsmooth, nonconvex optimization problems. At each iteration, the method considers an inner approximation of the Clarke $\varepsilon$-subdifferential at the current iterate over the feasible region and uses its least-norm element to generate a search direction. An exponential limited backtracking line search is then developed to assess the quality of the generated direction, while a projected variant of Mifflin's line search is proposed to identify nonredundant subgradients that enrich the Clarke $\varepsilon$-subdifferential approximation when necessary. To quantify stationarity, a characterization of stationary points based on the projection operator yields a computable optimality measure for the proposed method. The convergence properties of the proposed method are established under mild assumptions. If the algorithm generates infinitely many serious steps, we identify two subsequences such that every cluster point of each subsequence is stationary. If the number of serious steps is finite, we show that the final serious step generates a stationary point. Numerical experiments demonstrate the efficiency and broad applicability of the proposed method across a wide range of test problems, including applications in image denoising, multiobjective optimization, and data clustering. To extend the applicability of the proposed method to problems with general smooth nonlinear constraints, we propose a heuristic approach based on sequential linearization.

Deep forecasters predict from a fixed-length lookback window, and lengthening it gives diminishing returns at a growing cost. Retrieval augmentation instead shows the model how similar past situations continued. Retrieving a whole past window gives every variate the continuation of the same past moment. In multivariate series, however, the best past match differs from variate to variate. We present GNA (Granular Neighbor Assembly), a retrieval layer for forecasting backbones that assembles neighbors at two granularities: whole past windows, which keep the variates coherent, and per-variate neighbors, in which each variate takes its future from its own best-matching past. A learned gate decides, per forecast step and variate, how much to trust these futures against a persistence forecast, next to the backbone's own forecast. Candidates come from an embedding trained to predict each window's future, and retrieval is strictly causal: a past window is used only once its future has been observed. With the same lookback for every model and the same retrieval constants for all datasets, GNA improves two Transformer backbones in 85 of 96 dataset-horizon settings, gives the lowest MSE on 8 of 12 standard benchmarks and beats its backbone in every seed on 10 of them. Both granularities are needed, and neighbors of mismatched queries are worse than none. Retrieval helps most where the lookback says least: the gate shifts trust to retrieved futures further ahead. Where it fails, on hourly non-stationary series at long horizons, the loss is consistent with a drifting level of the retrieved futures.

Seasonal adjustment is fundamental to economic analysis, but uncertain because seasonal components are inherently latent. This article introduces a probabilistic model discovery method that decomposes a time series into seasonal and nonseasonal components. The method returns a posterior distribution over the structure and parameters of a seasonal component. In simulation studies, the method can improve point forecasts, interval predictions, and recovery of seasonal components relative to X-13ARIMA-SEATS. In a study of eight U.S. macroeconomic series during the COVID-19 recession, the method surfaces significant ex-ante uncertainty about current seasonal adjustments in real time, well before many X-13 revisions reach their eventual peaks.

The shallow embedding of higher-order modal logic in classical higher-order logic, used in Benzmüller and Scott's Notes on Gödel's and Scott's variants of the ontological argument, reaches beyond the modal object language: its quantifiers range over domains containing the nominals and satisfaction operators of hybrid logic. A proof using one proves a theorem of the embedding, not necessarily of the modal logic. Whether a result is one of the modal logic can be settled by replaying it in an explicit calculus, or, more cheaply and for all results at once, by analysing what the embedding's proofs substitute. Every statement the Notes prove has a proof in the embedding substituting nothing outside the object language, 294 of them explicit. The Notes' own proofs substitute none either; what it flags are terms a prover introduced. A soundness theorem over general models closed under the object language, and a sentence of that language the embedding proves but which fails in such a model, fix what the certificate says. The Notes' three open questions are settled too, without nominals, but by the empty instance of the conjunction axiom, too cheaply to convince. Generalised to Gödel's "any number of summands", the axiom covers the empty conjunction and the singleton. This article restricts it to at least two different conjuncts, a non-degenerate reading of Gödel's footnote, and settles them again without nominals. In effect only the empty conjunction is excluded; the singleton comes back with the other axioms. In one variant the restriction refutes the possible existence of a God-like being; the answers return, with no side condition, once the Notes' non-emptiness clause is confined to Gödel's essence. Every theorem here is verified in Isabelle/HOL and independently in Lean 4, the separating model in its propositional part; the countermodels are Nitpick's, checked by the build.

Generative agent-based models (GABMs) are increasingly used to simulate social media dynamics, including misinformation spread. For such social simulations to be valid proxies of human behavior, LLM agents should replicate established human cognitive biases, among them the Illusory Truth Effect (ITE), where repeated exposure to a claim increases its perceived truth value. We investigate whether and how the ITE manifests across four LLMs (Gemma-3-4b-it, Qwen2.5-7B-Instruct, Llama-3.1-8B-Instruct, and GPT-5-nano) in a social media simulation context. We propose a two-phase within-context experimental design that embeds the repetition manipulation inside a realistic news feed interaction. Using this design, we collect 336,000 truth, importance, sentiment, and interest ratings across 100 statements, 10 feed variants, and 3 replications. The key comparison is between ratings assigned to repeated statements, seen throughout a simulation phase, and completely unseen ones, rated within the same experimental context window. We distinguish genuine ITE (truth-specific repetition boost) from mere exposure effects. We run an OLS regression followed by a Linear Mixed-Effect Model to account for differences across models and ratings. Our results reveal four qualitatively distinct patterns: Gemma-3 exhibits a genuine ITE; Qwen2.5 shows a mere exposure effect; GPT-5-nano displays no repetition effect on truth and mild skepticism toward repeated content; Llama-3.1 shows a small truth boost alongside decreases in evaluative dimensions. Crucially, temperature has no effect on these findings, and a variance decomposition highlights the high context-sensitivity of LLM rating behavior. Our findings caution against assuming uniform ITE replication across LLMs in social simulations, while suggesting that Gemma-3-4b-it may offer the most behaviorally realistic approximation for misinformation-related simulations.

Existing protein geometry models typically represent molecular surfaces using local geometric features such as sampled points, normals, and curvature. While effective for capturing exposed molecular shape, these representations do not explicitly model the volumetric organization beneath the surface or provide a consistent coordinate system for residue-wise volumetric structure. We introduce Protein-TetSphere, a registered residue-wise volumetric representation for proteins. Each protein chain is tetrahedralized to obtain local volumetric regions associated with individual residues, which are then registered to a shared fixed-topology tetrahedral reference and represented in a common Laplacian basis. This registration establishes consistent volumetric coordinates across residues, enabling local three-dimensional deformation to be integrated with surface and chemical information in a multimodal protein representation. We evaluate Protein-TetSphere on ligand-binding pocket classification, protein–protein interface prediction, and de novo protein binder design. Across the three tasks, Protein-TetSphere improves ligand-binding pocket balanced accuracy from $0.795$ to $0.826$, Pinder-Pair/Site AUROC from $0.914/0.852$ to $0.932/0.866$, and binder-design success from $14.95\%$ to $19.90\%$ on the BoltzGen Challenge Set and from $27.62\%$ to $32.19\%$ at the ProtDBench backbone level. These results show that registered volumetric geometry provides complementary spatial information beyond molecular surfaces across protein recognition, interaction, and design.

Transporting droplets along cylindrical surfaces is an emerging area of research with a wide range of practical applications such as fog collection and filtration. Recent experimental studies by Feng et al. (2024) have revealed a wealth of new droplet coalescence dynamics on a pre-wetted cylindrical fibre, illustrating the need for more advanced theory. In this paper, we study both the early-stage and late-stage dynamics of droplet coalescence on a sloped cylindrical fibre. In the early stage, when the minimum thickness of the liquid bridge connecting two droplets is small, we propose a lubrication-based model to analyze the capillary-driven self-similar dynamics of the liquid bridge. Our theory predicts the bridge growth rate and demonstrates that asymmetry in the adjoining contact angles contributes to the migration of the merged droplet, showing good agreement with experimental observations. In the late stage, as droplet merging progresses, inertia effects become significant and lead to rapid mass transfer. To capture this regime, we develop a weighted residual model for liquid films flowing on a sloped pre-wetted cylinder, incorporating key physical effects such as gravity, low-to-moderate inertia, surface tension, and intermolecular forces. This model explains the experimentally observed directional self-propelled transport during droplet coalescence, where the larger droplet migrates toward the smaller one. Numerical simulations based on this model further support these findings, showing good agreement between the predicted coalescence-induced droplet migration and experimental observations.

We propose an algorithmic framework for solving adaptive robust optimization with provable guarantees on both tractability and solution accuracy. The framework introduces soft separation, a probabilistic mechanism for identifying worst-case uncertainty realizations via a time-inhomogeneous Markov chain. Rather than solving an exact separation problem in each iteration, which is intractable in general, the chain carries adversarial information across iterations, co-evolves with the optimization iterates, and recovers exact separation at terminal iterates with high probability. For continuous first-stage (here-and-now) decisions, we design a first-order method that uses soft separation to produce adaptive gradient estimates. Notably, we prove polynomial-time convergence in expectation to the global optimum. For mixed-integer here-and-now decisions, we embed soft separation within a branch-and-cut framework to generate valid cuts for the robust objective and obtain a high-probability certificate of global optimality. Numerical experiments demonstrate that the proposed methods scale favorably with problem dimension and scenario size relative to state-of-the-art approaches. The instances and code are available online at https://github.com/xuqy2002/SoftSeparationARO.

Disk-level scattering amplitudes involving one Ramond–Ramond and two NSNS states on a D-brane obey nontrivial identities among scalar world-sheet integrals imposed by gauge and T-duality Ward identities. We investigate the cohomological organization of these relations using twisted de Rham cohomology and show that the Ward identities admit twisted-exact representatives. In the $I/J$ sector, the unique generic linear dependence among the Ward identities is realized one degree lower in the same twisted de Rham complex, revealing a common cohomological origin for the identities and their syzygy. We also identify independent pointwise algebraic relations among the integrands. An independent cohomological rank computation then establishes that the physically selected $I/J$ family spans a five-dimensional subspace of the top twisted cohomology at generic complexified kinematics. Extending the construction to the $K$-family, including the exceptional double-pole representative $K_3$, introduces no additional cohomology direction. Hence the complete $I/J/K$ family considered here spans the same five-dimensional subspace.

Quantum error-correcting codes are essential for reliable quantum communication. The achievable parameters can be improved by using entanglement-assisted stabilizers at the cost of consuming pre-shared Bell pairs. If the availability of such Bell pairs is intermittent, the ability to adapt the code to available resources is beneficial. That is, to pick a single mother code that can be adapted to different entanglement budgets. To achieve this, we extend an existing puncturing construction for standard/unassisted stabilizers to the entanglement-assisted setting through a three-step procedure: Interpreting the code as an unassisted stabilizer, puncturing a receiver-side qubit, and recovering an entanglement-assisted representation. This procedure reduces the number of required Bell pairs by one while preserving the number of transmitted and logical qubits. We derive a bound on the resulting distance loss and establish conditions for preserving the original code distance. Finally, we analyse distinct, randomly generated, entanglement-assisted stabilizers with five to eight transmitted qubits. Of these codes, 14.75% have a greater distance than their associated unassisted representations. Among this subset, 81.4% admit at least one puncturing choice that preserves the original entanglement-assisted distance. These results illustrate how puncturing can reduce entanglement requirements while maintaining code distance.

Cochlear neural degeneration (CND) can impair suprathreshold coding without elevating pure-tone thresholds, complicating its diagnosis when it coexists with hair cell loss. We present a unified comparison of temporal and noise-based probes for CND detection using low-context vowel-consonant-vowel (VCV) syllables to reduce linguistic and contextual cues. Using a phenomenological auditory nerve model, we simulated responses to 21 VCV tokens under time compression, reverberation, and speech-in-noise conditions across presentation levels and seven CND profiles. We computed mutual information (MI) between inner hair cell potentials and auditory nerve neurograms and quantified information loss relative to a normal-hearing baseline. Time compression and amplitude-modulated (AM) noise produced the largest modeled information losses. We then evaluated these stimuli in a consonant-identification study involving 36 listeners with normal audiograms, 12 of whom reported difficulty understanding speech in noise. Neither 40 percent time compression in quiet nor AM noise alone distinguished listeners with and without these difficulties. However, compressed speech presented in AM noise separated the two groups. This partial agreement between model predictions and behavior supports our MI-based stimulus design framework and motivates further evaluation of combined temporal and noise-based probes for CND detection.

Recent work has established that power-law spectral conditions on data enable tight convergence bounds for deterministic gradient descent, resolving the conflict between classical exponential bounds and observed power-law learning curves. In this work, we extend this result to the stochastic regime of high-dimensional machine learning. We provide two main contributions: (1) We generalize the power-law spectral theory to Stochastic Gradient Descent (SGD), showing that the same spectral exponents govern stochastic dynamics; (2) For the fundamental case of isotropic Gaussian data, we provide a precise analysis of data shuffling, deriving exact constants that prove Single Shuffle is strictly superior to Flip-Flop and IID sampling. Our results bridge the gap between abstract spectral theory and practical stochastic training choices, offering a unified picture of how data geometry drives optimization speed.

As scientists seek to transcend traditional material property relationships, novel structures with artificial periodicity, configurational complexity, and disorder are increasingly being explored. For phonons, these architectures can induce significant phase correlations, which strongly shifts lattice heat conduction away from the conventional framework of particle-like scattering. This thermal phonon coherence can develop in space and time separately, resulting in distinct wave-like phenomena. Here we rigorously outline the theories of phonon spatial and temporal coherence. Crucially, this review focuses on demystifying and building conceptual understanding of the fundamental principles linking the various thermal conductivity and phonon property results reported in the literature. Furthermore, we use this understanding to establish a comprehensive physical picture of the wave nature of thermal phonons, unifying the spatial and temporal coherence theories. Altogether, the theoretical dissections in this review provide an extensive knowledge base for understanding and engineering thermal phonons in complex materials.

We study one-sided, two-sided and reflected exit problems for a finite-state Markov-modulated additive-increase and multiplicative-decrease process. For upward passage, a first-jump decomposition and a spatial Laplace transform lead to a recursion indexed by finite words of phases and to a convergent Green series. For downward passage, the first-jump operator is a strict contraction and the known contribution from $[p_i b,b]$ becomes an explicit boundary forcing term in the same spatial recursion. These allow to derive the corresponding Green representation of the first passage matrix and its finite-dimensional compatibility condition. The derivation of the two-sided exit identity is based on the Markov property, which in this context is equivalent to the cocycle property of the Laplace transform, together with the recursive equation at the upper level. For reflection at the running infimum, a finite $\bar p$-geometric method of steps realizes a certain Picard map that allows to find the exit matrix. As a result, we construct a Doob martingale related to the first passage time of the reflected Markov-modulated AIMD.

Crash counts on urban road networks exhibit spatial dependence driven by road connectivity rather than Euclidean proximity alone. We propose a Bayesian negative binomial model that represents spatial variation through a parsimonious combination of spectral components defined directly on road segments. The model combines the normalized random edge neighborhood Gaussian (RENeGe) operator with a continuous spike-and-slab prior, with mixture indicators marginalized out. Eigenvalue-dependent slab variances link spectral regularization to network-supported smoothness, while posterior slab-membership probabilities quantify support for individual components and uncertainty in effective spectral complexity. Segment length is used as an exposure offset, so fitted rates describe crash frequency per unit road length rather than traffic-adjusted risk. In a simulation study with 1,200 datasets and 4,800 Bayesian fits, the proposed model achieved the lowest mean spatial-field recovery error and highest mean test log predictive density under sparse RENeGe truth. Under alternative generating mechanisms, its predictive performance remained close to dense spectral models and exceeded that of a nonspatial model. Applications to Barcelona and central Bogota showed distinct posterior spectral patterns. Exploratory leave-one-segment-out comparisons found similar predictive accuracy for the proposed model and a low-rank edge CAR model, both outperforming a nonspatial negative binomial model, while a spectral BYM2 model achieved the highest exploratory predictive score. These results support probabilistic summaries of spectral complexity without a detectable predictive penalty relative to the corresponding CAR model.

Two-dimensional phase unwrapping can dominate computation and memory usage in wide-area Interferometric Synthetic Aperture Radar (InSAR) processing. Here we present Whirlwind, a minimum-cost-flow (MCF) unwrapper tailored for large interferograms of surface deformation. We derive fixed likelihood-ratio costs using multilook interferometric phase statistics, marginalizing uncertainty in the local phase-gradient and coherence estimates. A compact integer lookup table and parallel-augmenting successive-shortest-path solver with Dial bucket queues make the MCF solve efficient while avoiding flow-dependent cost relinearization. We test whether these improvements in speed and memory can be obtained without a loss of solution quality using multiple evaluation criteria for individual interferograms, at mission-production scale, and in end-to-end displacement time series solutions. On a 74-Mpixel Sentinel-1 interferogram of the 2019 Ridgecrest earthquakes, Whirlwind runs in 209 s, 28x faster than single-tile SNAPHU, while using 40% of the peak memory. Across 6,014 provisional NISAR geocoded unwrapped (GUNW) products, 93% agreed with the SNAPHU-derived results on more than 99% of valid pixels; on seven challenging 77-MHz Antarctic frames, Whirlwind ran a median 21x faster than SNAPHU while matching 99.4% of its integer-cycle assignments. Finally, in a complete Sentinel-1 time series experiment, Whirlwind improved the network-inversion consistency over SNAPHU, and in a high-resolution Capella time series of the Portuguese Bend landslide, it achieved the highest correlation with a dense GPS network among five unwrapping configurations. Whirlwind is provided as an open-source library capable of handling the growing volume of globally available InSAR data.

Distributed quantum computing (DQC) has been proposed as a way to scale quantum algorithms for practical applications beyond monolithic quantum processor architectures. Among these applications, quantum chemistry is widely regarded as one of the most promising use cases for quantum computing. In this work, we estimate the distributed-resource requirements of unitary coupled-cluster (UCC) ansätze for quantum chemistry, focusing on unitary coupled-cluster singles and doubles (UCCSD), unitary pair coupled-cluster doubles (UpCCD), and unitary pair coupled-cluster with generalized singles and doubles (UpCCGSD) circuits for hydrogen chains. We focus on a teleportation-based approach to DQC, quantitatively comparing a naive distribution method to the output of the TeleSABRE algorithm. For both approaches, we estimate the cost of handling nonlocal two-qubit gates across a fixed midpoint or quarter-point partition, reporting Bell-pair/classical-communication costs in teleportation. Across Jordan-Wigner and Bravyi-Kitaev, we find that UpCCD with spin-blocked Jordan-Wigner ordering gives the most favorable scaling, while UCCSD incurs substantially larger distributed-resource requirements.

Large language models can learn abstract rules from just a few in-context examples, but how their internal mechanisms activate as examples accumulate is not well understood. We trace a three-stage symbolic reasoning circuit (abstraction, induction, retrieval) across shot counts in three model families and find it is detectable and functional well before the model achieves high accuracy. Per-head causal contribution grows up to 8x from 1- to 10-shot, and cross-shot activation patching raises accuracy from 1% to 56% at 0-shot and 17% to 88% at 1-shot. Function vectors scaled and injected at 0-shot rescue accuracy up to 86%, largely substituting for the induction stage but depending critically on an intact downstream retrieval stage. The infrastructure for abstract rule-following is present in the weights before any demonstrations; in-context examples, function vectors, and related interventions appear to supply input to the same latent circuit.

Reliable evaluation of large language models (LLMs) is essential for their development and deployment, yet is often costly, risky, and difficult to perform safely online. We study off-policy evaluation for LLMs, where limited human-labeled data from a behavior model are used to evaluate a newer target LLM. This setting is challenging because labels are scarce, behavior–target distribution shift is common, and response likelihoods are often unavailable for black-box LLMs. We propose the Optimal Transport-based Robust Off-Policy Evaluation (OTROPE), a likelihood-free evaluation that performs distributional correction in a semantic space via optimal transport to align labeled behavior-policy samples with unlabeled target-policy samples. OTROPE combines corrected human-labeled residuals with proxy predictors, yielding a doubly robust-style evaluation without behavior-policy modeling or density-ratio estimation. We theoretically characterize why baseline evaluators fail under LLM distribution shift, and establish consistency and convergence rates for OTROPE when either the reweighted behavior distribution or the proxy predictor converges. Experiments on synthetic and real LLM evaluation tasks show that OTROPE consistently outperforms baselines while enabling ensembles of weaker LLM evaluators to approach and sometimes surpass stronger evaluators. Code is available at https://github.com/LinerXiang/OTROPE.

Existing multimodal scaling laws fit multimodality terms empirically after testing and never vary how much data is multimodally paired at fixed data budgets. We investigate how, under the same total data per modality, changing the number of paired data affects loss curves in multimodal classification tasks. We train models in three different environments and run experiment sweeps varying data sizes and pairing budget. Pairing ratios have a dramatic impact on loss and this impact is directly tied to how much information synergy the task contains. Only paired data is able to reduce synergistic loss, while unpaired data can reduce redundant or unimodal information up until unimodal floors. Unlike traditional scaling laws where loss drops immediately in power law decay, synergy acquisition is gated, requiring a critical threshold of paired data before synergistic loss falls at all. We introduce a new family of multimodal scaling laws where total data-attributable loss is the sum of four individual power laws corresponding to the four different information channels of redundancy, a unique channel per modality, and synergy, and show how this law is both more theoretically sound and empirically valid across our experiments. This law predicts multimodal loss in our experiments more accurately than existing laws, with 3.2% error on fit tests versus 10.4% error for the best pairing extension of published laws.

Recent studies have observed that parameter changes during language-model post-training can be concentrated in a small subset of coordinates. This phenomenon has been reported in reinforcement learning, on-policy distillation, and supervised fine-tuning on near-policy data. Its recurrence across different post-training paradigms suggests shared structure in training dynamics. In this paper, we examine this pattern through the diagonal model Fisher, which measures the sensitivity of the model's output distribution to individual parameters and is independent of any particular reward or teacher signal. Theoretically, we show that small diagonal Fisher leads to small expected gradients across a range of training objectives, providing a common explanation for sparse gradient updates. Empirically, we test this connection in RL and OPD. We find that Fisher identifies where gradients are concentrated, and fixed sparse masks selected from the initial Fisher retain a large proportion of the improvement from full training. Finally, we investigate the mechanisms underlying low Fisher in on-policy training. Our results show that high-probability next tokens tend to have similar parameter sensitivities, contributing to low Fisher. Together, these results establish the diagonal model Fisher as a unifying perspective linking update sparsity to on-policy training dynamics in LLM post-training.

Magnetic skyrmions represent vortex-like spin configurations that provide a robust platform for next-generation spintronic technologies. Although they are often treated as two-dimensional objects with integer topological charge, their extension into three-dimensional strings realizes other composite structures with unique device functionalities that transcend planar frameworks. Unfortunately, a lack of bulk probes has failed to realize such higher-dimensional topological structures and their implementations. Here, we report the first experimental visualization of three-dimensional topological $Q = 0$ skyrmion structures using neutron scattering tomography techniques across the equilibrium phase of a Co$_8$Zn$_8$Mn$_4$ sample. Disordered skyrmion states reveal metastable skyrmioniums and composite topological objects novel to bulk systems. Vortex-antivortex lattices mediate changes in topology, with unprecedented transition pathways via a coupling of merons and monopoles. The present realization of bulk Q = 0 quasiparticles and meron-mediated dynamics paves the way for higher-dimensional spintronic frameworks through multi-bit encoding architectures, unidirectional transport schemes, and monopole-mediated controls.

We derive the Fokker-Planck equation and its entropy production from the master equation. To this end we consider a discrete space of states where the master equation is defined and appropriate transition rates are introduced. A transition rate has two parts, one of which is the ordinary term proportional to the inverse of the spacing and the other is inversely proportional to the square of the spacing corresponding to the variance of the independent stochastic variable. In the continuous space limit, we obtain the Fokker-Planck as well as the rate of entropy production and the flux of entropy. We also consider the case where the space of states is the phase space and discuss the equations appropriate for systems in contact with several heat reservoirs and for isolated systems.

Linear RNNs offer linear-time sequence processing and constant-memory decoding, but their fixed-size recurrent states must accommodate all past key–value associations. Existing forgetting mechanisms and Delta Rule updates reduce interference by selectively clearing or correcting the state, yet earlier associations can still become difficult to retrieve. We introduce CyFA (Cyclic Flow Attention), a Linear RNN with relative-time-partitioned memory. At each step, a learned clock controls the cyclic transport applied jointly to the key and value states before the current key–value pair enters the age-zero slot, thereby organizing stored associations across relative-time slots. We further derive an exact change to absolute-clock coordinates that expresses CyFA as two scalar-decay linear attention recurrences and enables efficient chunk-wise training. Across 400M–1.4B pretraining experiments with matched recurrent-state sizes, CyFA improves recall-intensive performance while maintaining competitive language modeling and high computational efficiency. At 400M, CyFA outperforms KDA on FDA (42.60 vs. 26.07) while requiring only 46.7% and 48.3% of KDA's forward and backward core-operator execution times, respectively. Our code is publicly available at \href{https://github.com/Chyxx/CyclicFlowAttention}{this https URL}.

We report a study of the magnetic properties and Fermi-surface topology of the kagome magnet HoV$_6$Sn$_6$ using magnetization and tunnel-diode-oscillator (TDO) measurements. The temperature-dependent magnetization exhibits Curie-Weiss behavior at high temperatures and reveals long-range magnetic order below $T_c$ $\approx$ 2.4 K. Below Tc, the field-dependent magnetization reveals pronounced magnetic anisotropy, with saturation moments of $\approx$ 9.5 and 7 $\mu_B$ /Ho for fields applied along the out-of-plane and in-plane directions, respectively. To probe the Fermi surface, we perform TDO measurements in magnetic fields up to 41.5 T and at temperatures down to 0.35 K. The TDO signal exhibits well-defined quantum oscillations with multiple frequencies extending up to $\sim$ 9 kT. Angular- and temperature-dependent measurements are used to determine the Fermi-surface geometry and cyclotron effective masses, respectively. To elucidate the electronic structure, we perform first-principles calculations of the electronic bands, density of states (DOS), and Fermi surface. The calculated band structure exhibits flat-band features, van Hove singularities, and Dirac-like crossings near the Fermi level. The DOS near the Fermi level is dominated by the V-d orbitals, indicating that the V kagome layers play a major role in determining the low-energy electronic properties of HoV6Sn6. Our calculations further support a ferromagnetic ground state with the Ho moments oriented along the c axis, consistent with neutron-scattering measurements. The calculated quantum-oscillation frequencies from the Fermi-surface pockets of HoV6Sn6 are in overall good agreement with the experimentally observed frequencies. Our combined experimental and theoretical results provide insight into the magnetic anisotropy and electronic structure of HoV$_6$Sn$_6$ and reveal its multiband Fermi-surface topology.

Hedging a derivative by trading the underlying asset changes the payoff that the hedging intended to replicate. We study this phenomenon when trading generates price impact and execution costs. In a binomial model, we characterize replication through a fixed-point equation. In continuous time, we derive a nonlinear pricing PDE whose implicit terminal condition captures the nature of the moving target problem of the hedger. For monotone convex Lipschitz payoffs (such as calls and puts) we establish exact replication under midpoint execution costs. Numerical experiments illustrate: (i) how price impact shifts the effective strike, (ii) the non-linear dependence of the option price on the number of contracts, (iii) how execution costs smooth terminal holdings, (iv) the extent to which the hedger's own trading can bring an otherwise worthless option into the money, and (v) we explain the spread and the shape of the limit order book in the options market based on the price impact and the shape of the limit order book of the underlying.

We exhibit two vector fields on $S^2$, which generate the entire Lie algebra of algebraic vector fields. Compositions of the flows associated with these two vector fields enable us to approximate every diffeomorphism of $S^2$ isotopic to the identity in the $\mathrm{C}^r$-sense for any $r\geq 0$.

We consider an infinite array of graphene disks in a square unit cell, where every disk of the quadrumer is excited in the dipole regime. Hybridization of plasmonic eigenmodes belonging to different IRREPs of the point group of symmetry C4v is discussed. It is shown that the hybridization of the pair of 1D IRREPs modes A1 and B2 as well as the pair A2 and B1 can exist in this symmetry. For the cell period p0 and the quadrumer period P, the relation P/p0 = 2 defines polarization independence of these pairs of modes. The discussed modes are dark ones and require for their excitation breaking the point symmetry of the quadrumer and, for breaking their degeneracy, i.e. separation in the two pairs, a modification of the discrete translation symmetry, i.e. change the parameter P/p0. The separated modes can be excited by normally incident plane wave with orthogonal polarizations.

Large Reasoning Models (LRMs) are commonly trained with reinforcement learning (RL) to improve their generation of chain-of-thought (CoT) reasoning before producing final answers. However, RL rewards are typically assigned based on final answers, providing little or no direct supervision over intermediate reasoning. This can lead to deceptive safety alignment, where the reasoning trace and final answer convey inconsistent safety signals. To systematically investigate this phenomenon, we introduce DSAR (Deceptive Safety Alignment Rate), a metric that jointly assesses reasoning traces and final answers to quantify their safety inconsistency. Across multiple LRMs and benchmarks, we find that deceptive safety alignment is pervasive under standard prompting conditions and is substantially amplified under prefilling attacks. We further provide a hidden representation analysis showing that models exhibit stronger safety discrimination at the final-answer stage than during intermediate reasoning. To close this gap, we propose SARA (Safety-Aware Reasoning Alignment), an RL-based method that rewards both safety-aware reasoning and safe final answers, encouraging early harmful intent recognition and enforcing reasoning-answer consistency. Experiments show that SARA significantly mitigates deceptive safety alignment under both standard and adversarial settings while preserving helpfulness and utility. Code is available at https://github.com/xzhou98/SARA.