Papers

We examine the consistency of the equilibrium magnetic field $\mathbf{B}_0$ used in the analytical calculation of the sideways wall force by A. A. Martynov and S. Yu. Medvedev [Phys. Plasmas 27, 012508 (2020)] and the subsequent reformulation presented in [Phys. Plasmas 27, 054702 (2020)]. In these attempts, the current density $\mathbf{j}_0 = \nabla \times \mathbf{B}_0$ must vanish in the vacuum regions adjacent to the wall, making $\mathbf{B}_0$ curl-free as a complement to the natural $\nabla \cdot \mathbf{B}_0 = 0$. Since the cited works incorporate selected toroidal corrections without explicitly specifying the corresponding differential operators, we test $\mathbf{B}_0$ adopted in these models against Maxwell's equations using both toroidal and quasi-cylindrical formulations. We show that the divergence-free requirement is violated in the toroidal interpretation, while the curl-free condition is not satisfied in the quasi-cylindrical limit. The reformulation likewise fails to define a self-consistent equilibrium field with toroidal effects because the accompanying field corrections required for consistency with Maxwell's equations are not specified. Since the sideways force calculations are built upon these inconsistent field prescriptions, their analytical derivations are consequently compromised. The resulting arguments therefore cannot serve as a valid basis for revising either the earlier results established by D. V. Mironov and V. D. Pustovitov [Phys. Plasmas 24, 092508 (2017)] or those obtained within the single-harmonic analysis [Phys. Plasmas 22, 052502 (2015)].

Stiff chemical kinetics is a major computational bottleneck in reacting-flow simulations, while data-driven solvers remain sensitive to training-state coverage and chemical dynamics. This work combines conditional diffusion sampling with a thermochemically constrained multiscale Laplace neural operator (TC-MLNO) for chemistry ODE integration. The diffusion model learns the equivalence-ratio-conditioned joint distribution of temperature and species from low-dimensional flame data, augmenting the state space without independent perturbations. TC-MLNO represents transient, non-periodic responses through pole-residue Laplace layers and assigns fast, medium, and slow species to separate branches. Thermochemical constraints are imposed through losses for mass and elemental conservation and heat release rate. The framework is evaluated in 1D premixed flames, a 2D developing jet, and a 3D turbulent burner flame. With equal-sized datasets, diffusion sampling reduces the 95th-percentile distance to the base flame manifold by up to 37.5% and the a posteriori full-species macro-average error by up to 92.7% versus random sampling, especially for minor species and radicals. TC-LNO yields smaller errors than the DeepONet baseline for 84.9% of retained modes and reduces the 95th-percentile error for the most attenuated modes from 0.372 to 0.081. In multidimensional flames, TC-MLNO better preserves reaction-zone locations, heat-release structures, and chemically sensitive species than DeepONet. Errors of representative radical and nitrogen-containing species in the 3D flame decrease by 88.0%-88.9%. Compared with direct CVODE integration, TC-MLNO reduces mean chemistry and total solution times by 90.1% and 62.6%, respectively. These results show that distribution-aware sampling and Laplace neural operator learning provide an accurate and efficient alternative for stiff chemical ODE integration.

We study a family of special numbers and polynomials introduced by Simsek whose exponential generating function has as denominator a falling factorial in the exponential variable. Using the partial fraction decomposition of this denominator, each member of the family is expressed by a single finite sum involving Bernoulli polynomials, Apostol Bernoulli polynomials and two variable Fubini polynomials evaluated at reciprocals of integers. A second expansion, around the point where the denominator vanishes, expresses the same numbers through Stirling numbers of the second kind and generalized harmonic numbers, and yields closed formulas for the first few members. We construct a function, built from the Hurwitz zeta function and Lerch s transcendent, which interpolates the polynomials at the negative integers and gives a closed form of a multiple series recently introduced by Pokaz, Ribicic Penava and Simsek, we give an Euler type integral representation for it, and show that the numbers are signed combinations of moments of geometric random variables. Recurrence relations, asymptotics and an extension to arbitrary distinct nodes are also given.

We extend Mark Kac's kinetic framework from single-species Euclidean spaces to a two-species, non-linear interaction space on the open cone $(0, \infty)^2$ governed by the Matsumoto–Yor rational collision involution. We identify a non-linear conserved energy $E(x,y) = x + y + 1/x$ and an invariant conic metric measure $d\mu = \frac{dx \, dy}{x(x+y)}$. By establishing a two-species $H$-theorem, we prove that entropy production vanishes if and only if post-collision velocities are statistically independent ($I(U;V)=0$). In contrast to the transform-domain proof of Letac and Wesołowski~\cite{letac2000}, which relies on joint Laplace transforms of general measures, our approach yields a direct physical derivation in state space via the transformation law for logarithmic gradients and separation of variables. This uncouples the functional-differential system to uniquely characterize the Generalized Inverse Gaussian (GIG) and Gamma distributions as the non-equilibrium thermodynamic equilibria.

The semiconductor workforce shortage has renewed interest in making chip design accessible to students without conventional very-large-scale integration (VLSI) training. We present the AI Hardware Design League (AI-HDL), an international, project-based competition in which students use Large Language Models (LLMs) to generate and iteratively refine Verilog while simulation, synthesis, timing analysis, security review, and physical verification provide the engineering feedback needed to validate the result. Across two annual cycles, AI-HDL grew from 172 to 604 participants and from 40 to 108 teams, reaching 30 universities, six community colleges, and 19 countries. In the 2026 cohort, 68.7% of participants reported no prior Verilog experience. Twenty-two teams completed the four design phases and reached final evaluation. Two division-winning designs completed physical sign-off in the SkyWater 130 nm (Sky130) process, passing design-rule checking and layout-versus-schematic verification with zero violations before being submitted for fabrication. These results show that an LLM-assisted, tool-grounded workflow can be deployed at substantial scale while also revealing that completion, rather than initial access, remains the principal challenge. AI-HDL materials and finalist artifacts are released to support replication and future study.

Block-wise varying exposures are effective for cap- turing appearance of a real-world high dynamic range (HDR) scene via a single-shot. However, brightness order reversal (BOR) artifacts, blocking artifacts and loss of details in highlight/shadow regions are possible issues for block-wise varying exposures. In this paper, a novel neural block-wise auto-exposure algorithm is proposed to address the issues. The proposed algorithm maps a temporary image and its exposure time to the exposure times of all non-overlapping 16 X 16 blocks. The temporary image can be either an sRGB or a raw image. Although the sRGB image is widely adopted in existing auto-exposure algorithms, exposure times of blocks in the highlight and shadow regions might not be accurately learned due to the limited radiance measurement capability of the sRGB image. This paper thus also explores the feasibility of temporary image as a raw image. Due to the better radiance measurement capability of the raw image, the exposure times of blocks are learned more accurately, and more details in the highlight/shadow regions of the real-world HDR scene are captured by the resultant HDR imaging system. Experiment results validate the proposed neural block-wise auto-exposure algorithm.

We present a suite of 50 unpublished research-level theoretical physics problems with verifiable answers. Without AI assistance, a typical problem in our collection could be solved by a world expert in about a day or less but would take considerably longer for experts in adjacent specialties. We test the ability of off-the-shelf AI agents to tackle these problems autonomously, without human hints. When given access to tools available in a realistic setting, including the ability to search the literature and write scripts for numerical and symbolic work, the best-performing agent, GPT-6-Astra harnessed in Codex, obtains the final answers with a near-perfect accuracy of 98% at an average cost under USD 3 per problem. On average, agents show only small changes in accuracy when denied web search and access to background research papers, suggesting significant memorization of the literature. These results suggest that state-of-the-art agents can accurately perform concrete calculations required across theoretical physics research. We comment on the broader implications of these findings and discuss possible explanations for the current lack of agent-led breakthroughs in theoretical physics despite their outstanding problem-solving abilities.

What does it mean to measure the replicability of scientific results? Is it merely determining whether results are consistent across studies? Much of the existing literature on replicability draws conclusions exclusively from the comparison of study results, in terms of observed estimates, uses a variety of different metrics, and ultimately collapses the comparison into a binary verdict of success or failure. This fails to differentiate between repeated errors and corroboration of the shared generative effect. We develop a unified Bayesian framework in which distinct but related notions of replicability are formally defined and jointly embedded within a single inferential structure. A single model answers four complementary questions: agreement among independent studies; consistency between the individual studies and the shared generative effect; agreement between an existing body of evidence and a new study from the same super-population; inference on the shared generative effect. In practice, we suggest quantifying replicability through posterior probabilities relative to regions of practical relevance. We illustrate these ideas in an eQTL (expression quantitative trait locus) analysis assessing the replicability of a regulatory effect across human ancestral groups.

It is widely appreciated that robotic policies require long-term memory to perform complex tasks. However, directly conditioning policies on all past observations leaves policy learning susceptible to learning spurious shortcuts, and introduces large latency at policy deployment. As such, today's memory-augmented policies curate what to remember, either by retaining only recent frames, selected keyframes, or textual summaries, or by learning latent representations of the visual stream alone. In this work, we propose an alternative approach IMPRINT, a policy-agnostic latent memory framework that augments vision-language-action (VLA) models with multi-stream memory without explicitly constraining what the policy should remember. IMPRINT compresses different streams into a latent memory that is updated incrementally at inference, enabling low latency. To avoid shortcut learning, IMPRINT adopts a two-stage training procedure, first supervising memory to reconstruct multiple streams (observations, actions, proprioception) of past information, as well as estimate current task progress, followed by end-to-end finetuning, jointly with the policy, on action prediction. Across both simulation and real-world tasks demanding memory, IMPRINT improves average success over the base VLA by at least 26%, outperforming popular alternatives, and maintaining lowest inference latency among memory-augmented VLAs. Through careful ablations, we demonstrate the utility of incorporating diverse information streams into robotic memory, validating the advantages of foregoing history curation. Project website: https://yilin-wu98.github.io/imprint_website/.

Reinforcement learning (RL) has driven substantial progress in coding agents by relying on verified successful trajectories as learning signals. However, such trajectories are scarce in long-horizon software engineering tasks, where a minor error can invalidate the entire rollout. Repeatedly restarting from the initial state is commonly used yet inefficient, and resetting only the context with working directory misses state changes such as installed dependencies. Therefore, branching from intermediate steps to preserve earlier progress requires restoring both the agent context and execution environments. In this paper, we present SPROUT (SnaPshot-based RollOUT), an agentic RL rollout framework that scales long-horizon coding tasks by resuming and branching from intermediate states. Specifically, SPROUT was built on top of a lightweight infrastructure that checkpoints both the filesystem and the agent context after each assistant turn. A verifier-guided backtracking policy then selects where to resume a failed attempt and how to proceed. Extensive experiments on long-horizon coding tasks show that SPROUT achieves up to 23.6% improvement over pass@k across various LLMs, while using $32$–$52%$ of their tokens. For RL training of Qwen3.8-27B, SPROUT stably outperforms standard GRPO by $13.9$ points on three long-horizon coding benchmarks while cutting the time per training step by $39.5%$. SPROUT thus makes RL on long-horizon coding tasks both more effective and cheaper to scale.

System One models offer typed judgments that applications can turn into decisions. Their answers, however, are conditional on the state and question supplied by surrounding components, and on how the application uses the response. We study this boundary in a Jev-based pipeline with bounded substitutions at three adapter outputs: state extraction, question generation, and output interpretation. Across three small synthetic studies, each adapter can change the final decision while Jev and its authentic API responses remain outside attacker control. The cases expose distinct failures of source fidelity, answer meaning, and response relevance. Checks that bind these relationships stopped the corresponding interventions we tested, although source verification also rejected some valid clean decisions. The pilot identifies where correct request-level judgments can lose their connection to the original task; it does not estimate the prevalence of these failures in deployed systems.

Learning reusable skills can improve visual reasoning agents, yet applying a skill still requires the agent to implement or invoke a procedure and produce the final answer. Errors and hallucinations at these steps can prevent acquired experience from translating into reliable single-run performance. We propose VisualCoding, which combines execution-guided acquisition of reusable visual programs with direct adoption of their answers on applicable inputs. Execution-Guided Program Acquisition composes visual primitives and additional code into family-level solvers, then iteratively tests and revises them on labeled training instances. Scope-Aware Direct Execution runs a retained solver and returns its valid in-scope answer. We evaluate VisualCoding on four models across four benchmarks spanning 69 task families. VisualCoding exceeds the strongest evaluated baseline in mean accuracy by 4.45 percentage points with Gemini-3.1-Pro and by 14.78 points when reusing the frozen Pro-acquired artifacts with Flash-Lite. Ablations support execution-guided acquisition and show that direct execution outperforms textual or callable reuse of the same programs. Code is available at https://github.com/jiaq-liu/VisualCoding.

Large language models (LLMs) have achieved strong performance in mathematical and logical reasoning, yet they still suffer from the curse of complexity and struggle as problem difficulty increases with the number of constraint interactions and the size of the search space. In contrast, satisfiability solvers such as Z3 provide scalable and verifiable reasoning through constraint solving under formal theories, but lack the flexibility to interpret natural-language problem descriptions. In this work, we propose SAT-RL, a reinforcement-learning (RL) framework that trains LLMs to interact with symbolic solvers through multi-turn tool execution. SAT-RL leverages synthetic data generation with verifiable solutions, supervised warm-up on solver-augmented traces, and solver-grounded reinforcement learning with tool-aware rewards. Experiments show that SAT-RL substantially improves symbolic reasoning with tools on both in-domain and out-of-domain logic tasks. Our code is available on https://github.com/sunjia72/SAT-RL.

Based on first principles calculations, we show in hole-doped La2-xSrxCuO4, the Sr dopants prefer to form dimers, rather than be isolated as generally believed. Same trend applies to other superconductors such as Na-doped Ca2CuO2Cl2, and electron type Nd2-xCexCuO4. The dimer structure makes the two doped holes (electrons) bound up and form a singlet which is also polarized. Another type of dopant in cuprates is oxygen which behaves similarly. So, we propose that, for all oxide high TC superconductors, the holes (electrons) are pre-paired (Z-pairs) during the preparation of the superconductor. The spontaneously formed Z-pairs are conceptually different from not only the Cooper pairs, but also the Zhang-Rice singlets. The attraction force in a Z-pair originates basically from the strong antiferromagnetic exchange energy. We also found that the on-site Coulomb repulsion (U) is no longer a constant due to doping. Around a doping site, U can reduce its value discontinuously, which plays a key role in stabilizing the Z-pairs against isolated holes (electrons). A Z-pair is a p-wave like localized state which breaks the symmetry of the CuO2 plain and attracts each other along the direction perpendicular to the polarization. The Z-pairs may be popular in all of the unconventional superconductors and the periodic assembly can result in the emergence of coherence states and superconductivity.

Successor-feature-based zero-shot reinforcement learning methods pre-train a task encoder and successor-feature predictor on offline, reward-free data, then recover a policy at test time by solving a closed-form linear regression over a small labeled dataset. We identify an underexplored limitation of this approach: when the task encoder produces dense representations, the inferred reward signal becomes diffuse across the state space, reducing the contrast between goal-relevant states and the background and providing a weaker signal for the policy to follow. We address this limitation by introducing an l1 sparsity penalty that concentrates reward-predictive structure into a smaller effective subspace of the task encoder's latent space. The penalty is applied only during training and requires no architectural change or modification to the closed-form inference procedure. We instantiate this approach as Sparse-TD-JEPA, a single-line of code addition based on Temporal-Difference Joint-Embedding Predictive Architecture (TD-JEPA) that significantly improved its performance in zero-shot reinforcement learning. We evaluate Sparse-TD-JEPA on 65 tasks across the DeepMind Control (DMC) Suite and OGBench, covering locomotion, navigation, trajectory stitching, puzzle solving, and robotic manipulation. Sparse-TD-JEPA improves over TD-JEPA in all 13 domain-level comparisons. On DMC, it increases the average return from 661 +- 6 to 714 +- 3. On OGBench, it increases the average success rate from 38.0 +- 0.8 to 48.4 +- 2.3, with improvements of 13.4-18.0 percentage points on the evaluated antmaze navigation and stitching domains. Overall, Sparse-TD-JEPA achieves the highest mean performance among established zero-shot baselines in nine of the 13 domains. Analysis further shows that sparsity produces a sharper and more task-informative inferred reward landscape.

Andrews, Ganchev, Kuyper, Lempp, Miller, A.\ Soskova, and M.\ Soskova conjectured that skip-cototality coincides with weak cototality. We show that the conjecture is false by constructing a $\Pi^0_2$ set whose skip does not have a cototal degree. We further adapt this construction to obtain additional results. We prove that for each odd $n$, there is a $\Pi^0_{n+1}$ degree whose $n$-iterated skip does not have a cototal degree. We show that there is a $\Pi^0_2$ degree which does not contain an introenumerable set.

Biomolecular condensates are micron-scale, membraneless compartments that concentrate proteins and nucleic acids by liquid-liquid phase separation (LLPS). Condensates play critical roles in transcription, mRNA metabolism, stress responses, and signaling across the cell, with their dysregulation increasingly correlated with several pathologies spanning neurodegeneration, cancer, cardiometabolic disease, and viral infections. The emergent biology of condensates can be cohesively viewed through the framework of colloidal, interfacial, and transport phenomena. Here we review the condensate literature through this joint lens, treating each condensate as a biological colloid whose behavior is captured by four measurable physical quantities: a Flory–Huggins interaction parameter that determines whether the dense phase forms at all, a partition coefficient that dictates the degree of client molecule accumulation, a viscoelastic relaxation time that sets whether the dense phase responds as a liquid or a solid, and an interfacial tension that governs droplet shape and interfacial dynamics. Each quantity is traced to its physical origin, its measured range in biological condensates, and the techniques that quantify it, for both three-dimensional droplets and two-dimensional membrane-tethered condensates. Interpreting disease as the displacement of these physical quantities from their functional ranges, we reorganize condensate pathologies into a small set of physical failure modes — saturation concentration dysregulation, aberrant aging and liquid-to-solid transitions, disrupted partitioning, interfacial aggregation, and pathogen hijacking — and show how the same parameters become design variables for condensate-targeted drugs and engineered coacervate delivery vehicles. The review concludes with open questions at the interface of condensate biology and colloidal and interfacial science.

Augmenting worker capabilities in the physical world through guidance has been a decades-long goal for AI agents. One key supporting capability is to understand what the worker is doing, seeing through the human's camera or smart glasses, and assist them in documentation. Despite advances in vision language models, their capabilities in these settings remain uncertain and are challenging to benchmark because most physical work data is proprietary, and involves too much variability to study in a principled manner. Unlike structured settings such as kitchens and warehouses that have predictable lighting, geometry, and objects, field-facing tasks such as rooftop solar installation and vehicle repair are unconstrained and high variance. Here, we model real-world physical work in Blender across eleven environments, incorporating variants in both image acceptability and documentation. The acceptability task asks whether a particular view would be suitable proof-of-work and documentation asks whether an agent can understand the task-relevant state of the environment from that view. Across 26 vision-language models, we find that top models largely solve documentation when the answer is text in frame, but are weak at reading measurements and at judging small parts and spatial relations, such as whether a tape measure leans. Acceptability is harder to pin down because human raters disagree with each other. Measured against a scorer that agrees with the raters' majority about as often as a single rater does, the best models cannot be distinguished from a single non-author rater, at a cost within the range of a human pass. In the three environments where we can trace acceptability errors, most wrong rejections come from misreading the scene rather than the requirement. On the three documentation questions for which we have real images, model rankings on rendered frames transfer to real images.

Reversed toroidal field (RTF) coils introduce a new degree of freedom in stellarator coil design. While the total plasma-linked current is fixed by Ampere's law, compensating RTF currents allow the modular-coil current to exceed this value without altering the net linkage. This redistribution decouples key coil constraints and modifies the external coil geometry without significantly compromising the confining magnetic field. As a result, the achievable coil-plasma separation can be increased in the configurations studied, potentially enabling more compact stellarator designs.

Multimodal prediction models add a data source, such as imaging or an assay, to clinical information, and health systems must decide whether that added test is worth acquiring. We audited 177 studies comparing multimodal with unimodal models: 81 from a systematic review and 96 from a probability sample of 2025-2026 PubMed records. Gains in the area under the receiver operating characteristic curve (AUROC) were smaller when a study fitted a separate model for every data source (adjusted difference, -0.030; 95% CI, -0.056 to -0.005). Within 78 such studies, leaving out the strongest source's model would have raised the average gain from 0.046 to 0.108. This complete benchmarking fell from 69.1% of review studies to an estimated 46.0% of recent ones. An estimated 22% assessed decision utility and none evaluated a model prospectively, yet most claimed potential clinical usefulness or improved care (84.0% and an estimated 87.7%).

Training large-scale recommender systems on dynamic industrial platforms, such as Short-Form Video (SFV) services with billions of daily interactions, faces critical stability challenges. Rapid distribution shifts in user data and increasing model complexity frequently trigger a divergence cascade, typically initiating with gradient explosion, propagating to weight explosion, and culminating in loss explosion. This G-W-L cascade severely impedes model convergence and performance. This paper provides a systematic analysis of this G-W-L cascade within an industrial SFV recommender context. We then propose and evaluate a structured mitigation framework where interventions are explicitly mapped to counteract specific stages of the cascade: gradient (G) control, weight/activation (W) stabilization, and loss (L) shaping. Our contribution provides a structured framework for understanding and tackling training divergence, offering practical insights for deploying robust, continuously updated recommenders in large-scale, non-stationary settings. We empirically validate the effectiveness of these strategies on a major industrial SFV recommendation system.

Scientific research increasingly depends on curating experimental data from literature. Scientific data curation requires verifying exact experimental conditions (e.g., specific assays, clinical outcomes, and data availability) across long, heterogeneous files, which is a highly time-consuming process. Existing benchmarks evaluate only broad relevance on short queries, failing to capture this complexity. We introduce SciCurateBench, a benchmark of 200 expert-annotated papers from major life-science journals that challenges systems to verify conjunctive biological experimental criteria from raw, unprocessed scientific literature. We show that plain LLMs and popular reasoning, tool-using, and feedback-based agents all struggle with this task. To study what makes the task tractable, we further propose LangPoli, an integrative system in which a policy agent generates natural language action guidelines that actor agents convert into executable tools. LangPoli showed strong performance on both Paper Classification (83.16% F1 vs. 58.22% for its base LLM) and Structured Information Retrieval, and also improves re-ranking on the public benchmarks of LitSearch, BEIR, and TREC. We further explore curriculum transfer, a method that distills generalizable strategies from solved tasks to accelerate the solving of related problems. We hope this work facilitates research in truly practical scientific AI assistance. The anonymized pre-release can be found from https://anonymous.4open. science/r/scicuratebench-D885/.

General-purpose machine-learning force fields (MLFFs) for materials are now trained on the order of $100$ million structures, assuming transferability requires such scale. We test this premise on OMat24, the largest available materials dataset, by training MACE models on subsets of $6.5$ million atoms, less than $1\%$ of OMat24, selected in three complementary ways: at random, by latent-space clustering of a pretrained MLFF (DIRECT), and by a new model-free method maximizing the diversity of discrete, interpretable local environments (EnvTok). All three models approach the full-data reference MACE-OMAT-0 model to within a few tens of $\mathrm{meV}/\mathring{\mathrm{A}}$ in forces, and remain close to or exceed it on formation energies, elastic moduli, heat capacities, Li$^{+}$ migration barriers, and molecular-dynamics stability up to $3000\,$K and $500\,$GPa. This near-independence from the selection strategy shows that chemical environment diversity, not size, defines OMat24's information content: the remaining $99\%$ of structures are largely redundant. Broad sampling of chemical space thus remains essential, but reference labels are needed only for structurally and chemically distinct configurations. Using atomic positions and species, optionally augmented by magnetic moments, EnvTok identifies these before any labelling or training, yielding compact, architecture-independent datasets. This hundredfold reduction makes hybrid-DFT or higher-level relabelling of general-purpose training sets feasible, and frees computational budget for extending environmental coverage and multi-fidelity learning.

We study the optimal sequential aggregation of randomly arriving votes from a finite population to identify an unknown majority preference before a fixed deadline, trading off decision accuracy against the cost of delay. The optimal policy is a dynamic majority-quorum rule: a joint, time-varying threshold on vote lead and count, in which quorum and supermajority requirements emerge as the solution to an inference problem about non-participants' preferences. At each date, the continuation region is lens-shaped: the lead required to stop grows with turnout until too few voters remain to overturn it, and it vanishes at the deadline. We characterize conditions under which the boundary is monotone in the stakes, the arrival process, and time. Because the exact boundary admits no closed form, we derive a large-population approximation that reduces the two-dimensional rule onto a single sufficient statistic, and express the rule as a sequential significance test set by a single error tolerance. Calibrated on Polkadot governance data, an out-of-sample evaluation finds that our rule with a 2% error tolerance halves decision times relative to the incumbent mechanism.

In this work, we develop and analyze a splitting mixed finite element method, combined with a fully implicit Euler time discretization, for a stochastic Keller–Segel system with general polynomial logistic growth and multiplicative noise. The proposed splitting formulation allows the use of standard finite element spaces without requiring the LBB inf–sup condition associated with traditional mixed finite element methods and, at each time step, avoids the need for solving a coupled nonlinear system. We first establish the well-posedness of the variational solution and derive new high-moment, higher-order regularity, and exponential stability estimates. These estimates provide the key analytical foundation for the strong convergence analysis of the numerical method. A principal contribution of this work is the derivation of error estimates directly in full expectation, without the use of localization arguments. By combining the new stability and regularity estimates with a stochastic Gronwall framework, we overcome the difficulties arising from the interaction between the nonlinear chemotactic coupling and the multiplicative noise. As a result, we establish strong convergence in high-moment norms and obtain optimal convergence rates with respect to both the temporal and spatial discretizations. In particular, the proposed method achieves the optimal rates of order $k^{\frac{1}{2}}$ in time and $h$ in space in the relevant $L^2$- and $H^1$-based error norms. These results provide, to our knowledge, the first optimal strong convergence analysis in full expectation for a splitting mixed finite element approximation of this class of stochastic Keller–Segel systems.

Benchmark scores tell us what an LLM can do, but not how much energy is required to deliver that capability. We directly measure this trade-off for 86 open-weight model checkpoints, evaluated on seven benchmarks and six hardware platforms ranging from a consumer GPU to an eight-GPU server. We find large differences in energy efficiency even among models with similar capability. Most configurations lie away from the score–energy Pareto frontier: they use a median of 2.6–4.8$\times$ more energy than another configuration that scores at least as well, with differences reaching 27$\times$. Reasoning can improve capability, but enabling thinking increases energy by about 3.7$\times$ on average, and the benefit depends strongly on the model family and output budget. Generated-token count is also an imperfect proxy for energy, misordering 18–24% of model pairs. In contrast, FP8 reduces energy by roughly a quarter with little change in score, while changing hardware largely rescales energy without changing the relative ranking of models. These results show that capability alone gives an incomplete picture of efficiency. We argue that benchmark scores should be reported together with measured energy consumption under a specified serving regime and output budget.

Neural learners for classification and regression are often criticized as black boxes. We propose a probabilistic decomposition of neural learners that accounts for heterogeneous predictability across the feature space. A training procedure combining the EM algorithm, stochastic gradient descent, and maximum likelihood estimation is developed to jointly learn the predictable component and an input-dependent reliability score. We show that the optimal decomposed learner recovers the response distribution within the predictable component, while the reliability score characterizes the predictability of individual observations. We further extend the framework to incorporate localized feature transformations. Experiments on synthetic and real-world datasets demonstrate the effectiveness of the proposed framework.

We propose two new decoding algorithms for low-density parity-check (LDPC) codes. The Consensus and Return residual belief propagation (C&R-RBP) algorithm reduces the number of iterations required to achieve a target decoding error rate over an AWGN channel by exploiting the availability of updated information, thereby mitigating the performance degradation caused by the greedy behavior of RBP-based algorithms and reducing error propagation. The Consensus and Delayed Return RBP algorithm (C&DR-RBP) achieves better performance in the early decoding iterations than C&R-RBP, making it particularly suitable for low-latency applications. Both proposed methods maintain the same computational complexity as the original RBP algorithm in terms of residual calculations. We also provide a formal analysis showing that the Consensus mechanism increases the probability of correct bit decisions under initial decoding conditions and in the presence of severe bit transmission errors, providing insight into the performance gains observed in the simulations. Numerical results based on the rapidly growing 5G New Radio (NR) standard, considering different code lengths, code rates, and channel models, demonstrate that both methods outperform competing RBP-based algorithms with similar overall computational complexity in terms of frame error rate (FER) and bit error rate (BER).

At sufficiently high temperatures, lattice Quantum Chromodynamics (QCD) calculations predict that nuclear matter undergoes a rapid crossover to a novel, deconfined state known as the quark-gluon plasma (QGP), in which quark flavors essentially behave like independent particles. Here we explore the nature of this transition by introducing two new thermodynamic observables which we refer to as the diagonality and the rescaled curvature of the QCD equation of state (EoS). By comparing these observables in the case of lattice QCD calculations with those of simple toy models and more sophisticated hadronic resonance models, we show that both the diagonality and the rescaled curvature provide complementary insights into the degree of independence between different quark flavors and the underlying degrees of freedom in the system as functions of temperature. We propose that these observables may help to clarify the nature of the transition region and the onset of deconfinement in nuclear matter.

This article offers an overview of recent developments in deep learning from a control vantage point. It reviews several classes of models including feedforward and residual neural networks, transformers, large-language models, and selective state space models while explaining how control theory plays an important role in understanding their training, properties, or architecture design. The article explains how residual neural networks can be interpreted as the discretization of a continuous-time control system thereby enabling the use of control theoretic techniques for its analysis. To illustrate the power of this bridge between control and deep learning, two technical results are discussed: 1) the ability of a residual neural network to approximate arbitrary continuous functions is a non-standard controllability problem that can be solved using geometric nonlinear control and 2) transformers, the key architectural component of most large language-models, can be seen the discretization of a consensus algorithm and thus large language-models exhibit consensus. Another point of contact between control theory and deep learning is the connection between backpropagation, the algorithm used to train neural networks, and optimal control. The article addresses how the older connection between these problems, established in the 80's using discrete-time models can be reconciled with the more recent approach using continuous-time models. Several open problems and directions for future research are discussed, including selective state-space models, a recent class of models inspired by the models used in control.