Papers

We prove the localization dichotomy conjecture for non-periodic Hall insulators on the lattice. That is, we show that the Fermi projector $P$ of a gapped exponentially local Hamiltonian on $l^2(\mathbb{Z}^2) \otimes \mathbb{C}^n$ admits an exponentially localized Wannier basis if and only if $P$ has vanishing Chern number.

Deciding whether two samples come from the same distribution is a classical problem in statistics, and generative transport offers a new way to approach it. We build a stochastic interpolant directly between the two samples and observe that, for a symmetric schedule, its law is invariant under the time reflection $t \mapsto 1-t$ whenever the two distributions coincide. We therefore test whether the marginals at times t and 1-t agree by computing their Jensen–Shannon divergence. Both marginals are explicit mixtures over all cross-pairs of observations, so nothing is learned, and permutation calibration gives an exact finite-sample level. For Gaussian noise, this divergence equals a time integral that pairs the reflection defects of the velocity field and of the score, so the test compares transport dynamics rather than endpoints alone. With a narrow-plus-broad noise design, the test attains the minimax separation rate n^{-2s/(4s+d)} over bounded, compactly supported densities whose difference has Sobolev smoothness s > 3d/4, with no lower bound on the densities. Fusing a dyadic grid of noise scales through their permutation ranks, without sample splitting, preserves exact level and adapts to unknown s at an iterated-logarithmic cost. Empirically, the test matches or outperforms state-of-the-art kernel two-sample tests.

Voice anonymization aims to conceal speaker identity while preserving linguistic and paralinguistic information, yet many existing methods require dedicated training. We propose a training-free, two-stage anonymization method for pretrained flow-matching voice conversion systems. In the condition-construction stage, the source content representation is regenerated under a randomly selected speaker context to reduce residual source-speaker information while preserving linguistic content. In the speech-generation stage, the source speech is used to identify the generation direction associated with the original speaker, and the source-aligned component is suppressed while useful content guidance is retained. The proposed method modifies only inference-time conditioning and guidance, without updating any pretrained parameters. Experiments on VoicePrivacy 2026 Track 1 show that the two-stage method improves speaker privacy while maintaining competitive word error rate and emotion recognition performance.

Algorithmic recommendations can help participants navigate large matching markets. For example, recommendations for school and college choices may reduce information frictions and disparities in access to high-performing programs. At scale, however, recommenders in capacity-constrained settings can be self-defeating: if they steer too many users toward the same items, then even users who were originally predicted to have a high chance of matching to an item may not, due to increased competition. In this paper, we formalize this phenomenon of recommendation-induced congestion; motivated by the NYC high school match, we show that naive recommendations can cause sharp decreases in program acceptance rates, most affecting applicants with the fewest nearby options. Next, we propose and theoretically analyze a congestion-aware, bilevel optimize-and-simulate approach to allocate recommendations and improve match outcomes safely, in equilibrium. Finally, we deploy this approach in the 2025-26 admissions cycle of the NYC high school match, aiming to reduce disparities by highlighting personalized lists of nearby, high-performing programs where an applicant has a high predicted offer likelihood. In a randomized controlled trial, we find that 16.4% of treatment applicants ranked a recommended program, versus 10.5% of control applicants who ranked a program they would have been recommended (57% relative increase; $p$=0.011); 5.6% of treatment applicants matched to such a program, versus 3.3% of control applicants (71% relative increase; $p$=0.071); further, no treatment applicant was rejected from a recommended program. Our findings suggest that recommenders should be analyzed and designed as market-shaping interventions.

Comprehensive visibility into Internet Background Radiation (IBR) requires diverse measurement infrastructure. Recent work showed that cloud IBR depends on the provider making single-provider telescopes systematically biased. These studies relied entirely on Western providers and left the Asia-Pacific region as a blind spot. In this report we extend a multi-cloud network telescope onto Tencent Cloud inside mainland China. We detail how Internet fragmentation, geo-politics, and provider rules complicate global measurement through strict onboarding barriers and an unreliable management plane. Once deployed, our nodes captured high-volume regional scanning invisible to our Western vantage points. We conclude by connecting our findings to the Responsible Internet framework. This framework relies on independent global observation to build a transparent Network Inspection Plane. We show that building this plane is bottlenecked by sovereign ecosystems and requires a collaborative community effort.

Giant impacts (collisions between planet-sized bodies) are violent events that fundamentally alter the properties of planets and the structure of planetary systems. Observations of these events provide important constraints on the role of giant impacts in the formation of planetary systems. However, relating such observations to the specifics of the impact responsible is challenging, since numerical simulations struggle to resolve the expected extreme low densities of observable material at the edge of ongoing impact structures. In particular, lower limits on density are often enforced in SPH codes for computational efficiency. Here, we present a method of post-processing output from smoothed particle hydrodynamics (SPH) simulations of giant impacts, that emulates realistic physical properties in multi-phase and multi-material collisions, in order to better understand these low-density outer regions. We apply our novel post-processing pipeline to determine the direct thermal emission and potential observational signatures of giant impacts, and obtain consistent photic surface geometries for an example impact simulated for a range of resolutions and code parameters. We find that during the first days after this terrestrial giant impact event, the emission from hot, unbound ejecta can be comparable in temperature and luminosity to that of an M-Dwarf star, and as such can be astronomically observable. Our work begins to bridge the gap between observations and theoretical models, and could allow high cadence, large-sky surveys, such as that to be carried out by the Vera C. Rubin Observatory, to place constraints on the frequency and properties of giant impacts in our local neighbourhood.

Many social applications of machine learning exhibit performative effects: population behavior changes in response to deployed models. Performative prediction studies this interaction through a distribution map that relates each model to the population distribution it induces. One of the main results in this framework showed that repeated risk minimization (RRM), which updates models by retraining on the most recent data, can converge to a stable model that minimizes risk on its own induced distribution. However, existing analyses typically assume access to the complete distributions of features and labels after model deployment, ignoring the possibility of selective labels: observing labels only for the accepted subset of the population. In this work, we formalize performative prediction with selective labels and show that retraining only on observed data can misguide the retraining procedure and undermine the guarantees of convergence to a stable solution. We then propose a worst-case objective based on knowledge of a confidence interval on the probability of a positive label. Applying RRM to this objective permits us to remain within a bounded distance to the true stable point. Under a sensitivity assumption on the conditional label distribution, we further show how previously accepted data can tighten these confidence intervals over time. Experiments in a lending application with fairness regularization show that our robust optimization approach closely matches the performance of RRM with complete label access.

Classical reinforcement learning (RL) assumes that a reward is observed for every visited state-action pair. However, in real-world applications such as autonomous driving, such fine-grained feedback can be costly or difficult to collect, whereas trajectory-level feedback may be too sparse for efficient learning. To provide a general feedback model bridging these two extremes and handle large state spaces, we study RL with segment reward feedback under linear function approximation. Our work answers how the granularity of segment feedback and the choice of segmentation influence learning. For equal-length segments with known transitions, we design algorithms $\bitssegd$ and $\edlinucbsegd$ for binary and sum feedback types, respectively. They adopt posterior sampling with planning to achieve computational efficiency and the E-optimal experimental design to attain near-optimality. Nearly matching lower bounds are established. For equal-length segments with unknown transitions, we develop a unified $\seglsvits$ framework with two instantiations for binary and sum feedback, which carefully integrates the posterior estimated reward parameters into least-squares value iteration. These results reveal a fundamental insight: under binary feedback, increasing the number of segments significantly reduces the regret through an exponential factor, while surprisingly, under sum feedback, the granularity of segments does not affect learning much. Finally, to investigate whether segmenting according to state-action features can further expedite learning, we design an algorithm $\uneqsegbitsd$ that allows arbitrary segmentations. The resulting regret bound shows that under the usual elliptical potential analysis, the influence of state-action features on the regret appears only through logarithmic factors, and equal segmentation achieves the best performance.

We study the graphical forced mean curvature flow in a planar strip subject to Robin boundary conditions. The normal velocity is prescribed by $V=H+b$, where $b>0$ is constant and $H$ denotes the curvature of the graph. We consider positive even solutions and reduce the problem to the half interval. The main results describe the degeneration produced by the Robin condition: the height, the instantaneous velocity, and the spatial gradient diverge, while the normalized slope $u_x/u$ converges to one away from the symmetry axis. The normalized velocity $u_t/u$ converges to the forcing parameter $b$. The curvature converges to zero in the interior in an integral sense, whereas its horizontal curvature measure concentrates at the symmetry axis.

We proposed to boost the photon bunching effect of classical light via a modified Fabry-Pérot cavity with one of the cavity mirrors being replaced by a spatial light modulator, through which multiple independent transverse modulations, each was to encode independently spatially correlated phase on the wave front of the light field, was cascaded in sequence in the longitudinal propagation direction in the cavity. The two-photon bunching peak and the three-photon bunching peak of the generated superbunching light field were measured to be $36.9\pm2.0$ and $\rm (2.46\pm0.12)\times10^{3}$, respectively, which, as compared to those of thermal light, were improved by one-order and three-order of magnitude, respectively. Correspondingly, the ghost image visibility reconstructed with the superbunching light was demonstrated experimentally to be improved by $\sim 40$ times as compared to that with the pseudo-thermal light. Such classical superbunching light field is of essential importance not only for fundamental physics but also for potential applications such as correlated imaging, ghost interference and nonlinear optics.

Pervasive intelligent applications are increasingly deployed on mobile and Internet of Things (IoT) edge devices. Consequently, Large Language Models (LLMs) are increasingly used to support these applications. Yet, due to their high resource demands, LLMs are mostly deployed in the cloud. Layer-wise edge-cloud inference lets resource-constrained edge devices contribute computation to LLMs they cannot host in full. However, heterogeneous split points introduce two coupled inefficiencies. First, edge execution and communication create idle gaps between cloud invocations. Second, requests arriving at different model depths cannot be conventionally batched. We present DySCo, a collaborative runtime that keeps KV caches local and introduces dyForward, a model-aware layer-range executor that runs configurable contiguous layer ranges from resident model shards without reloading weights. For multi-edge serving settings, we introduce depth-synchronized batching (DSB), which advances heterogeneous requests to the deepest cut and batches their common suffix. Experiments across heterogeneous devices, two model families, and local and wide-area links show that idle gaps increase the latency of subsequent GPU forward calls even when waiting time is excluded, adding up to 25 ms of additional cloud-side suffix latency per decoding step in our measurements. At an average concurrency of eight, DSB improves throughput by 275% over FIFO, 48% over exact-match batching, and 79% over round-robin interleaving while reducing mean per-session latency. Together, these results show that requests with different edge-cloud splits can reuse resident cloud weights and share batched suffix computation. The artifact repository for this work is publicly available at: https://github.com/Large-scale-Sustainable-Computing-LSC/dysco-artifact

Dynamic blockage severely degrades vehicular integrated sensing and communication (ISAC), since narrow millimeter-wave beams must be adjusted before the line-of-sight (LoS) link is blocked or misaligned. This paper proposes WM4ISAC, a proactive ISAC framework built on a world model that learns a reusable latent dynamics model of the traffic environment from downlink radar heatmaps, rather than directly mapping observations to beam indices. The proposed framework uses a vision (V) module to compress sensing observations, an action-conditioned memory (M) module to predict latent environment evolution, and lightweight event heads to evaluate LoS alignment, blockage, and scatter-assisted non-line-of-sight (NLoS) alignment for candidate beams. A codebook-level controller then uses these event predictions to proactively switch between LoS and NLoS beams without knowing the future user or blocker states. Simulations under dynamic blockage show that WM4ISAC improves the mean rate by $28.9\%$ over current LoS tracking, raises the 5%-tile rate from $0.9$ Mbps to $30.5$ Mbps, and reaches $88.7\%$ of the perfect-information upper bound.

We investigated the microscopic magnetic state of the itinerant-electron ferromagnet LuInCo4 with a cobalt pyrochlore lattice by means of powder and single-crystal neutron diffraction measurements. The powder neutron diffraction profiles at zero field are well described by a simple q = 0 collinear ferromagnetic structure with an ordered Co moment of 0.9 uB. Single-crystal neutron diffraction experiments further suggest the absence of both antiferromagnetic order and long-period helical magnetic modulation. In addition, diffuse magnetic scattering was observed around q = 0, with its intensity distribution gradually broadened in reciprocal space upon cooling. Based on these observations, we propose a possible microscopic origin of the low-temperature metamagnetic transition in terms of a ferromagnetic instability enhanced by gradual localization of the itinerant Co-3d electrons. These results suggest that LuInCo4 provides a model system for investigating the interplay between electron localization and itinerant-electron ferromagnetism in cobalt-based metallic pyrochlore compounds.

The hard disk model is a fundamental reference system for excluded volume physics, liquid structure, and 2D ordering. Yet, despite its apparent simplicity, an analytical formulation of its thermodynamics has remained difficult because the free volume available to disks centers has a highly nontrivial many-body geometry. Here we show that this geometry admits a closed and exact representation: for any given hard disk configuration, the free volume can be analytically expressed through intersection areas of up to five exclusion disks. This provides a direct geometrical route from particle coordinates to the configurational partition function and entropy. We prove that the N disk partition function factorizes into a product of conditional free volumes and identify its two limiting asymptotic forms: the low density fluid regime controlled by extensive cavities and the high density fluid regime controlled by intensive private cells. Using the geometric measures computed from representative equilibrium particle configurations, the resulting theory reproduces the established hard disk equation of state over almost the entire density range up to close packing. At intermediate densities, the analysis reveals a mixed fluid regime in which localized caged defects provide an additional configurational entropy within the density interval preceding liquid hexatic coexistence. Finally, the five disk intersection area is shown to be a sensitive local scalar measure of hexagonal ordering, complementing the orientational order parameter and emphasizing the central role of many-body correlations.

Artificial intelligence capabilities are often measured as resources accumulated within firms, yet they also circulate across organizational boundaries through worker mobility. Drawing on a database of approximately 535 million employment records across 58 countries, we reconstruct the inter-firm network of AI talent flows over 2010–2022. We find that AI talent inflows are becoming increasingly concentrated among a small set of leading firms, with stronger preferential attachment than in general labor mobility. Yet the network core remains contestable: central positions in AI networks change hands far more often than in non-AI networks. Network position also carries information that goes beyond workforce size. This network position is economically consequential: AI network centrality is associated with higher enterprise value, after accounting for workforce scale, assets, and fixed effects. Event-study estimates further indicate that sharp improvements in network position are followed by higher enterprise value relative to matched firms with similar pre-event trajectories. Together, these findings suggest that corporate AI advantage depends not only on how much talent firms accumulate, but also on where they sit in its circulation.

In a previous paper, we investigate the control problem of discrete event systems under cyber attacks, where CA-controllability and CA-observability are proposed. We prove that a discrete event system can be controlled to generate a specification language K if and only if K is CA-controllable and CA-observable. While CA controllability can be "converted" to (conventional) controllability, CA-observability cannot be "converted" to (conventional) observability. In this paper, we further investigate CA-observability. We develop a method and an algorithm to check CA-observability. The method involves constructing an augmented automaton whose states are pairs of the current state and state estimate of the supervised system. We prove that K is CA-observable if and only if the language generated by the augmented automaton is equal to K. An algorithm is then developed to check CA-observability. We also investigate the properties of CA-observability. We show that CA-observability is not closed under (set) in tersection. Note that (conventional) observability is closed under intersection. We further show that CA-observability is not closed under union. This is similar to observability. If K is not CA-controllable and CA-observable, we pro pose a method to calculate a CA-controllable and CA observable sublanguage. We first calculate the supremal CA-controllable sublanguage for K which can be described by a sub-automaton of the automaton for K. We then propose a state-estimate-based supervisor based on the subautomaton, which ensures the supervised system stays within K.

Can authentication make memory, rather than computational hardness, the attacker's bottleneck? Contextual Chain is a lightweight continuity protocol for intermittently connected devices that share evolving physical or operational context. An honest device follows one realized history, updating a compact accumulator and fixed hash-based readiness lanes; outages cause pause or bounded rollback, not branch search. After the epoch is frozen, a fresh challenge selects one lane under a short deadline. An outsider that missed context may therefore need to prepare for many mature histories before learning which one will be tested. In the standard random-oracle model, a causal counting theorem lower-bounds the deadline-accessible retained state required for a target success probability against arbitrary nonlinear preselection encoding and adaptive post-selection queries, accounting for sequential depth, candidate queries, and cross-target protected information obtained online. Honest readiness memory remains fixed and independent of the number of plausible histories. Contextual Chain thus converts shared-experience uncertainty into a tunable preparation requirement without transferring combinatorial complexity to lightweight devices.

We consider site percolation on general graphs and give a sufficient condition on the escape probability of a certain random walk with degree-dependent conductances, such that the number of minimal vertex cutsets of size $n$ separating a given vertex from infinity is bounded above exponentially in $n$. This result extends an analogous theorem of Easo, Severo and Tassion under slightly stronger assumptions. Moreover, we give an alternative sufficient condition in terms of the isoperimetric dimension or, more specifically, an isoperimetric-type inequality. Furthermore, our theorem is sufficient to extend the results of Panagiotis and Severo, and show that there exists a universal positive constant $\varepsilon_1$ such that site percolation on every infinite, connected, locally finite, vertex-transitive graph satisfies $p_c = 1$ or $p_c \leq 1-\varepsilon_1$.

The density dependence of four-quark condensates is a major source of uncertainty in operator product expansion analyses of hadrons in nuclear matter. Their determination is particularly relevant to the $N$–$J/\psi$ interaction, whose long-range attraction appears to be well described by two-pion exchange in lattice QCD. We evaluate the pion-coupled four-quark condensates using one-nucleon intermediate-state insertions and incorporate them into the QCD sum rule analysis for the $J/\psi$ meson in nuclear matter. At normal nuclear matter density, we find a mass shift of $-1.75$ MeV, which is of the same order as the approximately $-5$ MeV attraction inferred from a two-pion exchange potential fitted to lattice QCD results. A previous factorization-based treatment required the introduction of unnaturally large phenomenological parameters to obtain a comparable shift. Our result shows that one-nucleon intermediate states provide a significant contribution to the in-medium four-quark condensates and improve the connection between the operator product expansion and the long-range $N$–$J/\psi$ interaction.

Auditing the claimed outcomes of large language model (LLM) training is challenging when model weights and training data are private, while cryptographically proving the full training process is prohibitively expensive at Transformer scale. We present zkLLMPoT, a zero-knowledge framework that certifies auditor-defined properties of a trained checkpoint through forward evaluation rather than verification of its optimization trajectory. zkLLMPoT includes 2 phases: 1) The trainer fixes the architecture and the model weights are committed. Then the auditor selects challenge sequences, preventing the trainer from modifying the checkpoint in response to the audit data. 2) Then the trainer proves the objective value attained by the committed model on those sequences. This formulation makes the certification cost independent of the number of training iterations, without revealing model weights or requiring access to private training data. We build on sumcheck- and lookup-based arguments to certify Transformer computations, while supporting next-token loss and task-specific audit objectives. Across four model families, operator-level benchmarks yield proving times of 41-59 seconds for 1.1-1.5B-parameter models and 131 seconds at 13B for the covered operators, with verification below half a second at a sequence length of 512.

The strong universality conjecture of Bobrowski and Skraba asserts that, under a prescribed data-dependent additive centering, the empirical laws of log-log transformed persistence ratios of random geometric complexes share a universal limit across sampling models, dimensions, filtrations, and homological degrees. They conjectured a left-skewed Gumbel limit and used it as a null law for testing topological significance. We show that, when the uncentered empirical laws and the centerings have deterministic limits, the conjecture forces a second-order quantity of each model's limiting law, determined by ratios close to one and unchanged by additive shifts, to agree across models and dimensions. To compute this quantity for degree-one Čech persistence, we bypass the global persistence pairing with a local proxy based on edges and their first incident triangles in the equivalent alpha filtration. In dimensions two and three, a Palm-Mecke calculation evaluates the proxy intensity exactly for stationary Poisson processes, and two-sided topological bounds show that it agrees with the true normalized persistence intensity through second order. After transfer to finite samples, the quantity equals $\pi^2/32$ and $4/\pi^2-1/4$ for the limiting laws of independent uniform samples from the unit square and the unit cube, respectively. The centered empirical laws converge weakly in probability to distinct deterministic limits, and their mean laws, the expectations of these random laws, also converge weakly to these limits. Hence the conjecture fails even for mean laws. Neither limiting law belongs to the left-skewed Gumbel location-scale family.

We consider approximate message passing (AMP) with discontinuous denoisers, such as hard slicers, quantizers and hard thresholding, for which the classical state evolution (SE) analysis does not apply. It is first shown that the standard Onsager coefficient; i.e., the average pointwise derivative of the denoiser, misses a boundary term, namely, the sum over the jumps of the jump size times the density of the denoiser input at the jump. Then, for real independent and identically distributed (i.i.d.) Gaussian matrices, a positive noise variance, a fixed number of iterations and a prior with finite second moment, we transfer the Lipschitz SE theorem directly to denoisers, fixed in advance, that are continuously differentiable with bounded derivative except at finitely many jumps, by bounding the distance between the iterates of AMP and of AMP on Lipschitz ramps of the denoisers through the fraction of inputs that cross a jump. It is thereby proven that AMP follows SE, also for test functions such as symbol errors, if its Onsager coefficient contains the boundary term, evaluated either along SE or, as we propose, at the noise level estimated from the residual, with the density computed from the known prior. Simulation results with 4- and 8-level pulse amplitude modulation (PAM) demonstrate that AMP with a hard slicer, whose standard coefficient is identically zero, fails with this coefficient, while with the proposed one, it follows SE and comes close to Bayes-optimal AMP.

Many organizations adapt large pretrained models to their own tasks by fine-tuning on private data. Several of these parties often hold data for the same task and wish to fine-tune a model together without pooling that data. Federated learning (FL) enables joint fine-tuning, but reconstruction attacks on shared intermediate values (the model or its gradients) remain a privacy risk. A one-shot protocol that exchanges one encrypted contribution exposes no intermediate value. Such a protocol still gives the trained model to every participant, which is not permitted where the model is a regulated or proprietary asset. We present HE-OFT, the first cryptographically secure one-shot federated fine-tuning protocol in which no party receives the trained model. Each client fine-tunes a low-rank adapter and a classifier head on a frozen public backbone and keeps the adapter. The client uploads one encrypted head displacement, which the server combines under multiparty CKKS and never decrypts. A quorum of clients returns only the predicted label to the querier. On four text classification tasks and one vision task, HE-OFT reaches 61 to 79 per cent accuracy, against 20 to 48 per cent for a client training alone. HE-OFT keeps 85 to 96 per cent of the accuracy of a disclosed model. A test-time query takes 443.1 to 1713.1 s on one core, or 56.1 to 255.1 s with level restoration on a GPU. Restoring levels at the server cuts the traffic per query from up to 1.6 GiB to 13.5 MiB.

Skyrmion lines and semi-local strings are examples of infrared-finite cosmic strings that arise in theories with spontaneously broken global symmetries. Unlike global $U(1)$ strings, they do not support the long-range Nambu-Goldstone boson (NGB) profile responsible for a logarithmically infrared-divergent string tension. We argue that NGB emission from their low-frequency oscillations is strongly suppressed. Consequently, their gravitational-wave signals may be comparable to those from local strings.

We develop a theory of distributional Riesz fractional gradients in variable exponent Lebesgue spaces and introduce the associated nonlocal Sobolev spaces. Moreover, Sobolev, Hardy, Morrey, and Trudinger-type inequalities are established, and a fractional fundamental theorem of calculus is derived. As an application, we study nonlinear variational problems with nonstandard growth and establish existence and Euler–Lagrange equations for minimizers.

We describe a Segre-Veronese construction of polynomial solutions to the interpolation conditions of the numerators of tree-level MHV gravity amplitudes given by Hodges' formula. The five- and six-point Hodges numerators arise from Segre determinants, while for every $n\geq7$ suitable Segre determinants lead to solutions linearly independent of the Hodges numerator. The existence of such independent elements for $n=7,8$ was recently established by Mai and Zhang.

We obtain recurrence relations for formal characters of Feigin-Stoyanovsky type subspaces of standard $B_2^{(1)}$-modules at fixed level. The recurrences are derived directly from the combinatorial bases described by difference and initial conditions. Unlike in type $A_\ell^{(1)}$, the right side in general involves several shifted characters. We give explicit polynomial coefficients and prove that the resulting system, together with the constant term normalization, determines all formal characters at fixed level uniquely. At level $1$ we solve the recurrence system explicitly and obtain fermionic formulas for all three characters. We also relate these characters to the multigraded generating functions for exponent triples parametrizing the Meurman-Primc monomial basis of standard $A_1^{(1)}$-modules.

Large language models are increasingly used to simulate clients for counselor training and psychological counseling research, but reliable simulation requires clients to remain psychologically coherent across extended interactions. Existing role-playing methods largely rely on static profile prompts and may exhibit persona drift, unrealistic cooperativeness, or inconsistent psychological states, communicative actions, and emotions. Existing evaluations also lack a unified testbed for both stable client characteristics and evolving psychological dynamics. We propose MASC, a Multi-Agent Self-Calibration framework with latent construct alignment for consistent client role-playing in psychological counseling. MASC combines construct-guided generation, collaborative refinement, consistency verification, and memory-based revision in a closed calibration loop that detects and corrects inconsistencies as dialogue unfolds. We further introduce CRPC-Bench, a benchmark covering session-level profile information and Big-Five personality traits, as well as turn-level psychological state, communicative action, and emotion expression. CRPC-Bench contains 38 motivational interviewing client profiles augmented with personality and emotion annotations. Experiments show that MASC outperforms existing methods across profile, personality, receptivity, and turn-level consistency, with the heterogeneous configuration achieving the strongest overall performance. MASC and CRPC-Bench provide a unified foundation for developing and evaluating psychologically coherent client simulations for AI-assisted counseling research and training.

Accurate transport properties calculations in transition metals require treating inter-orbital hybridization, which is often poorly captured by simplified single-band models. We propose an ab initio approach combining maximally localized Wannier functions and the Allen's method to correctly account for this mixing, overcoming the artifacts inherent to the Souza-Marzari-Vanderbilt scheme. Our method enables efficient orbital-resolved analysis of transport spectral functions. Applied to face-centered cubic Pd and body-centered cubic Mo, we reveal universal scattering mechanisms despite distinct electronic structures in these metals. Crucially, the parallel addition of distinct scattering channels perfectly reproduces full Allen's method calculations, rigorously validating this decomposition. We show that the absence of a $d$-peak at Fermi level in Mo enhances $s$-$s$ scattering, while the same contribution to resistivity and electron thermal conductivity of Pd is close to the experimental data for Ag. Ultimately, the proposed method provides a universal and efficient tool for the microscopic analysis of electron-phonon scattering mechanisms in systems with strong hybridization between localized and delocalized electron states.

We study the computation of mixed volumes of convex sets given as rational subspace sections of bodies described by membership oracles. The sets need not have nonempty interior. For positive multiplicities $\alpha_1+\cdots+\alpha_k=n$, we give a randomized algorithm that computes a relative $\varepsilon$-approximation with probability at least $1-\delta$. Its running time is polynomial in Gurvits' factor $\Gamma_\alpha=(n^n/n!)\prod_i\alpha_i!/\alpha_i^{\alpha_i}$, the input presentation length, and $\varepsilon^{-1}$, and linear in $1+\log\delta^{-1}$, with degree independent of $k$. The running-time bound holds for every choice of the random bits, and zero mixed volumes are detected exactly. We extend the capacity-scaling and sampling method of Narayanan–Roy by using rational projections and a smooth mixed Monge–Ampère representation. In particular, the algorithm runs in randomized polynomial time when the number of distinct convex sets is bounded above by a constant.