Papers

DC microgrids are low- or medium-voltage networks designed to connect and manage DC-based sources and loads. A key challenge in operating DC microgrids is maintaining the DC voltage within certain predefined limits while ensuring its stability. Droop control, the most common method towards addressing this challenge, enables decentralized voltage control and power sharing, but suffers from poor transient performance, resulting in voltage dips and overshoots in applications with fast varying loads such as AI datacenters. This paper introduces an improved droop control method based on voltage-locked loop synchronization, which ensures DC voltage stabilization with significantly improved transient response and achieves the desired load sharing between the available source converters. The core design principle is reflected in the functional separation of the control scheme into a virtual DC machine (VDCM) that operates as a spinning wheel and a virtual current source connected in parallel. The transient response is provided by the VDCM to damp and stabilize DC bus voltage variations, while the slow droop response is provided by the virtual current source to ensure steady-state power balance. The performance of the proposed method is validated in an experimental microgrid setup.

While background expansion data alone cannot discriminate among cosmological models, the growth of large-scale structures directly probes the underlying theory of gravity, offering a path to distinguish General Relativity from its modifications. In this work, we constrain three representative $F(R)$ modified gravity models (Starobinsky, Hu-Sawicki, and $R^2$-corrected Appleby-Battye) using measurements of the growth rate $f(z)$ and the matter fluctuation amplitude $\sigma_8(z)$. Our analyses combine MCMC parameter estimation, Gaussian Process reconstructions, and goodness-of-fit statistics including Akaike information criterion (AIC) and Bayesian information criterion (BIC). All investigated models provide statistically comparable fits to the current growth data, with information criteria differences too small to establish a preference for any particular scenario. To overcome this degeneracy, we reconstruct the effective gravitational coupling $\mu(z)$ from the MCMC posterior samples, providing a physically motivated diagnostic that complements standard goodness-of-fit criteria. The Starobinsky and Hu-Sawicki models predict moderate departures from General Relativity, remaining compatible with constraints on both $\mu(z)$ and $S_8$. In contrast, the $R^2$-AB model predicts $\mu_0 \sim 3.5$ and $S_8 = 0.638$, a $3.2\sigma$ tension with Planck 2018, rendering it physically disfavored despite its competitive statistical performance.

Sample identification (SI) is the task of matching pairs of tracks, where one track is created by musically transforming an element of the other. In the absence of sample annotations at scale, the dominant training paradigm has depended on artificially creating sample pairs. Although a recently released dataset provides annotations of real sample pairs at scale, an effective training recipe is missing. In this work, we present SI Embeddings (SIE), an SI model that achieves state-of-the-art results on three benchmarks, including a large-scale test set. We show that the previous state of the art trained on artificial pairs generalizes only partially to real pairs, and that its training data limits its performance. We also show that real pairs do not fully account for SIE's performance: its architecture and training recipe contribute substantially. We provide the first fully supervised training recipe for real-world SI, establishing a strong foundation for future research in the field.

We consider nonparametric tangent vector field regression on a Riemannian manifold without boundary. Because responses at different points lie in different tangent spaces, the proposed kernel estimator first parallel transports nearby responses to the target tangent space and then forms a volume-corrected local average. We first derive its uniform second-order bias, finite-bandwidth covariance, and stochastic rate. For simultaneous inference, the tangent norm is written as a supremum over the unit tangent bundle. Exact covariance whitening gives a unit-variance Gaussian field whose correlation length is of order $h$ along the base manifold and of order one along the fibre. Its local covariance geometry leads to a Gumbel limit with an explicit intrinsic constant. Combining this limit with Gaussian approximation and cross-fitted covariance estimation yields a feasible simultaneous confidence tube for the regression field. We further discuss improved finite-sample inference with bandwidth selection and high-order bias corrections. Simulations on various manifolds support the proposed inference procedure. A randomized reconstruction of global wind data illustrates how the tube's cross-sections describe spatially varying uncertainty.

In this work, we conduct a systematic comparison of two state-of-the-art motion-imitation reinforcement learning (MIRL) pipelines, one built on SCONE/HyFyDy and one built on MuJoCo/MyoSim. HyFyDy emphasizes physiological realism through detailed musculotendon modeling, while MuJoCo prioritizes computational efficiency and scalable policy learning. While recent work has demonstrated that both pipelines reproduce human kinematics with high fidelity, it remains unclear if they accurately capture the underlying neuromuscular behavior that produced the movement. This limitation is particularly important for robotic assistive-device design and control, where outcome measures such as muscle activation patterns and metabolic cost are often used as optimization targets. To conduct a systematic comparison, our work compares both pipelines using a common set of human motion-capture and electromyography (EMG) measurements. The results find that while both pipelines produce similar kinematics with relative accuracy, the muscle activations from HyFyDy are more aligned with the experimental EMG, as supported by the average pooled (RMSE, r) values for muscle activations from HyFyDy and MuJoCo: (0.164, 0.4) and (0.344, 0.11), respectively. While we conclude that the more advanced physiological realism of HyFyDy currently makes it more suitable for musculoskeletal modeling, both require further development to bring physiological realism to GPU-parallelizable simulation environments and advance robotic assistive device design.

Although vision-language-action (VLA) policies have advanced rapidly, long-horizon execution may still progress to the next task stage before the required physical effect has been established. We call this a mismatch between semantic commitments, physical conditions that a stage must establish or maintain, and the actual physical state. Because an action command alone cannot confirm such a condition, local deviations can propagate and cause task failure. To address this problem, we present CommitFlow, a closed-loop execution framework that combines commitment monitoring with local correction while keeping the base policy frozen. CommitFlow integrates three components. A Semantic Commitment Monitor (SCM) compares stage requirements against current state evidence and holds back dependent actions when a required condition is unmet or violated. BoundaryFlow then generates a local correction conditioned on the current state and base action, and Relation and Gain Calibration (RGC) selects the smallest correction strength that satisfies the relevant constraints. Across the ten common RoboTwin 2.0 benchmark tasks, CommitFlow achieves a mean success rate of 75.9 percent, improving on the base policy pi0.5 by 22.7 percent. Cross-policy experiments show consistent gains, pointing toward reliable long-horizon robot execution.

Heating matter can restore symmetries spontaneously broken at low temperature. The axial $U(1)$ symmetry of quantum chromodynamics (QCD) is different: it is present in the classical theory with massless quarks but is broken upon quantization by the axial anomaly. The anomaly persists at every temperature, yet its observable effects can weaken. Can hot matter nevertheless behave as though this symmetry were restored at long distances? Whether such effective axial $U(1)$ restoration occurs depends on how microscopic quark and gluon dynamics governs the strength and spatial range of axial breaking. This review brings together theoretical developments and first-principles lattice QCD calculations. We examine how gluon-field topology shapes the low-lying Dirac modes and their correlations, how these modes contribute to axial breaking at different spatial scales, and what this implies for the order and critical behavior of the chiral phase transition as quark masses approach zero.

Counterfactual simulation with a clinical world model means fixing a patient's history, changing the treatment, and reading off the predicted response. Doing so requires deciding what counts as one intervention. In clinical settings, interventions are documented as bundles: a co-occurrence audit of 945,707 patient-hours from MIMIC-IV shows groups of components, such as every parameter of a dialysis circuit, that never appear apart, so an edit that changes one component on its own describes an hour that never occurs in the data. We hypothesize that the granularity at which an intervention is edited changes how a world model responds, and test this with Clin-JEPA, a latent world model of patient trajectories conditioned on hourly treatment text. At 1,019 documented onsets of invasive ventilation, we keep the patient's history and other treatments fixed and compare editing one ventilator setting with editing the complete configuration recorded for a real patient with the most similar recent trajectory. The complete bundle moves the predicted next state further than any single setting, consistently across all five settings, and the difference remains after accounting for how much each edit changes the model's input. Intervention granularity therefore materially affects the response of a clinical world model: single-component edits may understate treatment sensitivity, and bundle-aware editing may offer a better-supported basis for counterfactual treatment simulation.

We study the oracle complexity of finding $\epsilon$-stationary points of smooth bilevel optimization problems with a nonconvex upper-level objective and a strongly convex lower-level problem. We consider a stochastic first-order oracle that returns unbiased stochastic gradients of both the upper- and lower-level objectives, with variance bounded by $\sigma^2$. We prove that, for any initial optimality gap $\Delta>0$ and all sufficiently small $\epsilon>0$, every adaptive randomized first-order algorithm requires $\Omega\!\left(\Delta \kappa_y^2 \epsilon^{-2}\max\{1,\sigma^2\kappa_y^6\epsilon^{-4}\}\right)$ oracle queries to find an $\epsilon$-stationary point of its hyper-objective function, where $\kappa_y$ denotes the condition number of the lower-level problem. In particular, in the noise-dominated regime, the lower bound is $\Omega\!\left(\Delta\sigma^2\kappa_y^8\epsilon^{-6}\right)$. This establishes the optimality of the $\epsilon^{-6}$ dependence achieved by the best-known first-order stochastic methods.

We present a didactic treatment of compartmental disease spread modeling centered on the SIR framework, aimed at mathematics education. Our focus is on how modeling choices encode transmission mechanisms and data-collection practices. We begin by stating the structural hypotheses of compartmental models, including population partitioning, homogeneous mixing, flow closure, and Markovian transitions. We then derive the basic SIR dynamic equations in both continuous-time (differential equations) and discrete-time (difference equations) settings. A key goal is to clarify the distinction between density-dependent and frequency-dependent transmission. We do this by constructing the force of infection from the contact rate, prevalence, and per-contact transmissibility while tracking units and interpretations. We go beyond the usual mass-balance SIR model by introducing the discrete Kermack-McKendrick perspective through the cumulative force of infection. This naturally leads to discrete SIR updates with an exponential escape probability term. We also derive Bernoulli-based exponential formulations for both density- and frequency-dependent transmission, interpret these probabilistically over observation intervals, and obtain the associated discrete infectivity kernel. This highlights how geometric infectious survival emerges from per-step removal. The paper includes reproducible, introductory-level Python code to implement the basic discrete SIR model, the continuous SIR model, and the exponential discrete variants. We provide instructors with an example of parameter estimation from prevalence data using least squares, along with guidance on interpretation and limitations. This framework is designed to help teachers integrate model assumptions, units, simulation, and inference in a coherent introduction to infectious disease modeling.

Leaf-wood segmentation of individual trees from LiDAR point clouds is essential for quantitative structure models (QSMs) used in non-destructive biomass estimation. Existing segmentation methods typically exclude radiometric features (e.g., intensity, return number) to maximize cross-sensor compatibility. We challenge this design choice by evaluating cross-site and cross-platform generalization: training on the public Heidelberg dataset (terrestrial TLS, 1550nm) and testing on a novel dataset from Ontario, Canada (RPA-LS, 905nm). Results show that geometry-only methods - including state-of-the-art deep learning models trained on high-density LiDAR datasets - fail to generalize to the sparse, top-down geometry of aerial scans, achieving F1 scores <= 0.56. Incorporating radiometric features (intensity, return number, number of returns) improves F1 to 0.61, but more critically, increases wood recall by 119% from 0.16 to 0.35. Furthermore, geometry-only approaches often result in fragmented stem and branch components. We find that leveraging radiometric features preserves greater structural connectivity, resulting in more coherent architectures that are better suited for QSM reconstruction. We demonstrate that while geometric patterns are view-dependent and prone to overfitting scan patterns, radiometric features encode physical material properties that generalize across disparate sensors and environments.

Covariate matching between treatment and control groups remains a foundational methodology in observational causal inference, designed to replicate the covariate balance of randomized controlled trials. Despite substantial methodological advancements, applied researchers continue to face an inherent trade-off between achieving rigorous balance and preserving the statistical power of the matched sample. We introduce a novel framework for a matching method named Optimal Study Interior Partitioning (OSIP). OSIP frames observational matching as a joint optimization problem governed simultaneously by a maximum cardinality constraint on the number of strata, and a strict fine balance threshold on the matching carried out in each strata. OSIP is based on two-stage optimization algorithm. In both stages it considers a projection of the (high-dimensional) data into one-dimensional space by evaluating an estimated propensity score for each unit. The method is based on enforcing a partition of the input to subsets of consecutive intervals of estimated propensity scores. The novelty arises because we consider this task as a global optimization problem. In the first stage, we employ an optimal partitioning algorithm with respect to an auxiliary (one-dimensional) goal function. In the second phase, we go back to the original distance function and apply heuristics approaches locally optimizing the solution from the first stage. We compare our framework with established methodologies from the literature across well-studied empirical benchmarks. We use the standard benchmark of Lindner cardiovascular dataset to demonstrate that OSIP provides a highly efficient sweet spot solution for the corresponding multi-criteria goal. This conclusion is verified by considering also other benchmark datasets.

NiO is one of the most important p-type oxide contact materials used in many semiconductor technologies. However, current NiO growth methods can induce interfacial damage that diminishes device performance. Fine control of interfaces is especially important in implementing NiO heterojunction diodes and transistors based on ultra wide band gap (UWBG) semiconductors such as AlGaN and Ga_{2}O_{3} used for power electronic applications. Here, we report on how molecular beam epitaxy can be used to achieve low-defect, lightly doped NiO contact layers for a \beta-Ga_{2}O_{3} diodes. Although high-temperature growth does not measurably decrease the on-state resistance of the diode, increased growth rates up to 600 nm/hr lower on-state resistance in p– NiO / \beta-Ga_{2}O_{3} heterojunction diodes without reducing film quality. At a NiO growth rate of 380 nm/hr, unoptimized diodes with 35 nm thick p– NiO layers demonstrate a device-average specific on-state resistance of 1.46 \Omega-cm^{2} and an ideality factor of 1.46. Individual devices grown at this condition show specific on-state resistance as low as 25 m{\Omega}-cm2 with a rectification ratio of 2.7x106. Scanning transmission electron microscopy imaging reveals the (100) NiO/ (100) \beta-Ga_{2}O_{3} interface is coherent and atomically abrupt. These results open a new avenue to optimizing the NiO interface to produce robust, competitive kV-class power electronic devices based on \beta-Ga_{2}O_{3} and other UWBG semiconductors.

In this paper, we resolve the quantum KKL conjecture of Montanaro and Osborne \cite{MO2010} for quantum Boolean functions on the $n$-qubit hypercube. More precisely, for every self-adjoint unitary $T$, we bound the largest $L_2$-influence from below by a constant multiple of $\mathrm{Var}(T)\log(n)/n$. The proof heavily depends on upper and lower commutator estimates on the Hilbert space.

Best-of-$n$ (BoN) sampling is a simple yet effective inference-time alignment method, but hard maximization provides only coarse control over the trade-off between reward and distribution shift. Soft Best-of-$n$ (Verdun et al. 2025) provides smoother control and converges to the optimal distribution associated with KL-regularized reward maximization. In this paper, we introduce ExpBoN, an alternative soft BoN method based on the exponential-noise report-noisy-max mechanism. It admits an exact finite-$n$ decomposition, which yields exponentially fast convergence in total variation, expected reward, and both directions of KL divergence. We provide comprehensive theoretical analyses of its convergence and regret behavior. We further integrate ExpBoN into the guided speculative inference (GSI) framework (Geuter, Mroueh, and AlvarezMelis 2025), resulting in ExpGSI, for efficient reward-guided LLM alignment. ExpGSI yields substantial reductions in computational cost while maintaining comparable accuracy. Experiments on MATH500, MMLU-STEM, and Minerva Math with the Qwen2.5-Math and Qwen3 model families show that ExpGSI reduces estimated computation by $14\%$-$39\%$ across candidate budgets for Qwen2.5-Math and by up to $45\%$ at $n=16$ for Qwen3. Overall, our results provide a theoretical and algorithmic foundation for exponential-noise BoN and efficient test-time LLM alignment.

Speech enhancement (SE) models degrade under domain shifts and have to adapt to unseen target domains during deployment. Most existing test-time adaptation (TTA) methods for SE do so by adapting a subset of the model weights using a self-supervised loss, which requires backpropagation at test-time and permanently alters the model. We instead recalibrate the prediction itself and propose BLINC, a training-free TTA method that remaps the predicted time-frequency mask onto a bimodal target distribution by histogram matching. At test-time, the target distribution is parameterized from blind features of the noisy recording, so neither a reference distribution from a classical algorithm nor online metric optimization is involved. BLINC improves the overall quality of both evaluated SE models on almost every target condition and matches or exceeds the loss-based TTA baselines at minimal overhead.

Path sampling methods enable the computation of thermodynamic and kinetic properties through Monte Carlo (MC) moves that generate trajectories from short forward and backward molecular dynamics (MD) segments. Recently, the wire-fencing move was developed to achieve near-unity acceptance while also rapidly decorrelating successive paths, two properties that are usually in conflict in conventional MC schemes. However, in large systems, such as biomolecular simulations, the frame-saving frequency is often kept low to reduce storage requirements. Likewise, when evaluating the order parameter is expensive, frames are saved less frequently to reduce the associated cost. In either situation, this can severely limit the number of available shooting points, in extreme situations leaving only a single point, typically the one with the highest order parameter value, accessible for shooting. Repeated shootings may then originate from the same configuration, reducing sampling efficiency. Here, we introduce a multi-resolution variant of the wire-fencing move in which selected subtrajectories are propagated at higher temporal resolution than the stored trajectories. This refinement affects only the MC move and does not alter the structure or storage of the generated paths, but enhances the diffusion of shooting points along the trajectory and thereby improves sampling efficiency. The approach is demonstrated on two model systems and a realistic protein–ligand unbinding process, with the latter showing an estimated efficiency improvement of more than an order of magnitude.

For every integer $n\ge 2$, we introduce a new combinatorial condition PP$(n)$ inspired by paradoxical decompositions of groups. As $n$ increases, the property PP$(n)$ weakens, and the resulting hierarchy interpolates between group-theoretic manifestations of negative curvature and proper proximality. More precisely, we prove that a countable group is properly proximal if and only if it satisfies PP$(n)$ for some $n$. On the other hand, every acylindrically hyperbolic group satisfies PP$(2)$; furthermore, finitely generated PP$(2)$-groups admit a geometric characterization: they are precisely the groups containing strongly quasi-convex, non-cyclic, free subgroups. In particular, we obtain that every countable acylindrically hyperbolic group is properly proximal. Finally, for every $n\in\mathbb N$, we provide examples of finitely generated properly proximal groups that do not satisfy PP$(n)$, thus proving that our hierarchy is indeed infinite.

In the 1960s, Erdős and Hajnal conjectured that every graph with sufficiently large chromatic number contains a subgraph of large girth (size of a smallest cycle) and large chromatic number. In this paper, we prove that every tournament with sufficiently large dichromatic number contains a subdigraph of large digirth (size of a smallest directed cycle) and large dichromatic number. We investigate the same statement when replacing digirth by girth (of the underlying graph). We show that it implies the conjecture of Erdős and Hajnal, and prove it for a particular family of tournaments.

We introduce an iterative framework that automates the extraction of interpretable, schema-bound categorical features from unstructured text for tabular prediction models. To navigate the feature space, a generator LLM proposes semantic definitions, a separate extractor LLM materializes the features, and a downstream tabular model evaluates their predictive performance. We optimize this search by translating explicit model errors, such as AUC ranking inversions, into natural-language feedback, steering the LLM to resolve specific predictive failures. Evaluated across three public datasets, this error-driven loop accelerates feature discovery by up to $3\times$ compared to unguided search. Empirically, the generated features demonstrate strong multi-view complementarity, strictly outperforming any subset when combined with TF-IDF and dense embeddings. Finally, the framework guarantees instance-level interpretability: the discovered features dominate SHAP importance rankings and provide a fully transparent, semantic audit trail for every prediction.

We prove that, on closed three-manifolds, the limit interface of a sequence of stable abelian Higgs critical points with uniformly bounded energy is a finite union of smooth closed immersed geodesics, possibly with multiplicity and self-intersections. This follows from an integral estimate for the diffuse curvature, derived from an integral bound on the discrepancy.

We prove that Stark–Shintani ray class invariants (Stark units) associated to real quadratic fields are algebraic numbers. These invariants are given by special values of Faddeev's modular quantum dilogarithm, introduced by Garoufalidis–Kashaev–Zagier. Our main discovery is that special values of the modular quantum dilogarithm satisfy an explicit overdetermined system of polynomial equations, matching a variation on the defining equations of Andersen–Kashaev's notion of a quantum dilogarithm on a product of two cyclic groups. We give two and a half proofs that this system of equations defines a zero-dimensional variety. The simplest follow from an uncertainty principle for finite Fourier transform and $2$-adic valuation bounds. The last proof is more involved and shows finite quanatum dilogarithms can be used to categorify fusion rings introduced by Izumi, and the algebraicity of the special values then follows by Ocneanu's rigidity theorem. As a byproduct, we obtain an explicit infinite family of irrational near-group fusion categories. As a further application, we prove a family of quadratic relations for Stark units recently conjectured by Appleby, Flammia, and Kopp motivated by Zauner's conjecture about SIC-POVMs (complex equiangular lines).

The presence of a dark energy (DE) core, made of a Chaplygin dark fluid, is capable of influencing the diverse observable properties of neutron stars (NSs). However, there is also the possibility that NSs could contain a mixture of ordinary nuclear matter and DE. In this perspective, we propose an equation of state (EoS) that includes both normal matter and DE, where a free parameter $f$ quantifies the ratio of DE density with respect to the total energy density. As expected, in the limit $f \rightarrow 0$ we recover the already known results corresponding to pure nuclear matter. Remarkably, increasing this fraction $f$ leads to a softer EoS and thus strongly favors the fulfillment of the causality condition. As a consequence of our mass–radius results, the central compact object in HESS J1731-347 can be satisfactorily described as a DE admixed NS. For sufficiently high stellar masses, our calculations further indicate that both the gravitational redshift and the fundamental nonradial oscillation frequency increase significantly with an increasing DE fraction, whereas the opposite trend is observed for the total gravitational mass and tidal deformability. As is typical for compact stars composed purely of ordinary matter, we find that in our DE admixed stellar models the central density corresponding to the maximum-mass configuration coincides with the point at which the squared radial vibration frequency vanishes. Moreover, higher DE concentrations lead to enhanced stability of these configurations.

We revisit a classic topic in probabilistic combinatorics, the lower-tail large-deviation problem for triangles in the random graph $G(n,p)$. Here we aim for first-order asymptotics for the quantity $\mathbb{P}[X=k]$ with $X$ the number of triangles in $G(n,p)$ and $0 \le k \le (1-\epsilon) \mathbb{E}X$, in the sparse regime in which the logarithmic asymptotics are Poissonian. When $k=0$ (the case of triangle-freeness) and $p = p(n)$ is sufficiently small, first-order asymptotics are known via Janson's inequality and results of Stark and Wormald; when $k$ is sufficiently close to $\mathbb{E}X$, first-order asymptotics are known via local central limit theorems. Our main result gives first-order asymptotics for all $k$ in the above range when $p = o(n^{-2/3})$, improving upon the result of Frieze that required $p = o(n^{-4/5})$. We also characterize, up to vanishing total variation distance, the distribution of the $k$ triangles in the corresponding conditional distribution and give an efficient algorithm to approximately sample from this conditional distribution. Notably, when $k = \Theta(\mu)$ there is a transition at $p = \Theta(n^{-4/5})$ from an asymptotically uniform triangle distribution to a distribution asymptotically singular to uniform.

Suppose an online algorithm is given an unbiased $p$-sample of its input as offline advice; can the algorithm exploit the sample to achieve beyond-worst-case performance? We study this online algorithms with a sample (OAS) model. We show a tight $O\left(\log (1/p) \cdot \log m + \log n\right)$-competitive algorithm for set cover, exponentially improving upon the $O\left(1/p \cdot \log (mn)\right)$ guarantee of Gupta et al. (SODA'24) and answering an open question therein. Our techniques extend to covering integer programs and non-metric facility location, also yielding tight bounds for these problems. Further, we give an $O(\log (1/p)/ \log \log (1/p))$-competitive algorithm for metric facility location, answering an open question of Argue et al. (NeurIPS'22). We then introduce and study the robust variant of the OAS model, in which an adversary is allowed to arbitrarily modify $k$ elements of the $p$-sample. For set cover, covering integer programs, and non-metric facility location, we obtain a tight competitive ratio of $O\left(\log (k/p) \cdot \log m + \log n\right)$. For metric facility location and Steiner tree, we obtain tight competitive ratios of $O\left(\log (k/p) / \log \log (k/p) \right)$ and $O\left(\log (k/p)\right)$ respectively. To the best of our knowledge, these are the first results for robust algorithms in the OAS setting.

Detecting pretraining data in large language models is challenging because high likelihood can reflect either training exposure or strong generalization. In the joint space of prediction loss and predictive entropy, a likelihood-only detector uses a horizontal boundary and can mistake predictable non-members for members. Motivated by this, we introduce an inclined boundary that evaluates prediction loss relative to predictive entropy. Our analysis shows that entropy correction can preserve the expected membership signal while reducing its variance, thereby improving standardized member–non-member separation. We further extend the mean–variance analysis to the more general setting with a nonzero mean entropy gap. Interestingly, this entropy-adjusted score admits a Helmholtz free-energy interpretation, leading to Energy Transfer Detection (ETD), which views pretraining data detection from a macroscopic residual free-energy transfer perspective. Extensive experiments show that ETD achieves the best average detection performance, improving average AUROC by up to 3.5% and TPR@5%FPR by up to 5.1%, while remaining robust across diverse settings.

The gold standard datasets for mapping connectomes are electron microscopy volumes of densely labeled neural tissue at nanometer resolution. Yet reconstructing and proofreading neuronal arbors and annotating all synapses requires pipelining multiple software tools that are often fragmented, inconsistently maintained, or proprietary, hindering reproducibility and automation. Here, we introduce Catena, an open-source, comprehensive, developer-centric software suite for connectomics that integrates modules for 3D neuron and organelle segmentation, synapse detection, microtubule tracking, and neurotransmitter inference. Catena organizes its modules in composable, chunk-wise processing pipelines in a completely documented, extensible, and adaptable design. We further reduce compute and ground-truth data requirements with pretrained machine learning models, facilitating fine-tuning. Catena ships fully containerized modules that encapsulate evolving dependencies for consistent execution across workstations and clusters. By consolidating open components, shareable models, and containerized runtimes, Catena delivers a reproducible and scalable approach to mapping cellular connectomes from electron microscopy volumes. Code and documentation: https://github.com/Mohinta2892/catena.git

In thermodynamics it is common to assume that the choice of ensemble (e.g., micro-canonical, canonical, or grand-canonical) should not affect the underlying physics in the thermodynamics limit. We show that this does not necessarily hold for critical exponents. Examining a simplified model of quantum error correction (single step encoding and decoding by a random unitary) and the behavior of both the fidelity and magic at the corresponding threshold, we find different exponents when using generic channels or supposedly equivalent quantum trajectories. Interestingly, the obtained exponents saturate a recently derived information theoretic bound by Feldman et al. (2026), which we extend from the grand-canonical to the canonical case, including intermediate ensembles which we define. Moreover, even the existence of the transition is shown to be ensemble-dependent.

We discuss the application of $L^2$-based velocity averaging to the Wigner kinetic equation governing the quantum evolution of the Wigner transform of a density operator of a particle subjected to an external electromagnetic field. This extends the $L^2$-based averaging lemma from [F. Golse, J. Möller: Commun. Math. Sci. (2026)] to electromagnetic fields. We make use of the magnetic or gauge-invariant Wigner transform due to Stratonovich [Sov. Phys. D., (1)414-418, 1956] which differs from the usual definition by a phase factor involving the circulation of the magnetic vector potential along a line segment. The magnetic Wigner transform obeys the Wigner equation in the generalized phase space variables $(x,v=\xi-A(t,x))$, which is a more natural setting for the application of velocity averaging. Since the magnetic Wigner equation contains a first order derivative in the spatial variable, we obtain compactness in $L^2$ but no gain in regularity.

Nanoscale self-heating involves phonon transport across confined geometries, material interfaces, and temperature fields over which the scattering rates can vary substantially. We develop PhonoMC, an occupation-based deviational Monte Carlo method for solving the phonon Boltzmann transport equation within the relaxation-time approximation. A fixed equilibrium state is retained as the deviational reference, while the local temperature reconstructed from the represented energy is used to evaluate mode-dependent scattering rates. Collisions are updated with a separately determined relaxation temperature to conserve energy over each time step, and prescribed lattice heating is introduced by changing carrier occupations rather than continuously adding computational particles. For cross-plane transport through a 100-nm Si film, the deviational formulation reproduces the full-population heat flux while reducing its standard deviation by a factor of approximately 3.3 at \(\Delta T=100\)~K with \(10^5\) carriers. In contrast, keeping the scattering rates fixed at 300~K overestimates the heat flux by 23.7% at \(\Delta T=250\)~K. Calculations of Si thin films distinguish finite-length effects from surface-scattering suppression, and Si/3C-SiC bilayers are used to examine interfacial thermal resistance. The method is further applied to localized heating in FinFET-like structures, where replacing the lower Si substrate with higher-conductivity 3C-SiC leads to a higher hotspot temperature because of the additional resistance associated with the confined Si region and the Si/SiC interface. These results show that a fixed deviational reference can be combined with local temperature-dependent scattering and sustained heat deposition in a mode-resolved Monte Carlo description of nanoscale thermal transport.