Papers

Let $I\subseteq S$ be a monomial ideal with minimal generator degrees between $e$ and $d$, where $2\leq e\leq d$. We prove that if $t_a(S/I)<ea$, then $$ t_{a+b}(S/I)\leq t_a(S/I)+ \left\lceil\frac{(2d-1)b}{2}\right\rceil $$ for $a\geq2$, $b\geq0$, and $a+b\leq\operatorname{pd}_S(S/I)$. Consequently, $$ t_{a+b}(S/I)\leq ae+db-1-\left\lfloor\frac b2\right\rfloor. $$ In particular, if $t_2(S/I)<2e$, then $$ t_i(S/I)\leq \left\lceil\frac{(2d-1)i}{2}\right\rceil-2(d-e) $$ for $2\leq i\leq\operatorname{pd}_S(S/I)$. We also obtain a regularity bound and give a quadratic family in which our estimate for the last shift is smaller than every bound obtained from ordinary subadditivity. The constant $2d-1$ is sharp for $d=2$.

When a language-model audit finds no leak, what is needed to certify non-leakage? We study guarantees over a declared prompt domain under an executable leakage criterion and decoding rule. For general bounded polynomial-time evaluators, a supplied leaking execution is polynomial-time checkable, while leak existence is \NP-complete and deterministic certification is \coNP-complete. Exact stochastic certification is $\coNP^{\PP}$-complete at every fixed rational cutoff in $(0,1)$. Restricting the computation can change these bounds. For example, certification is in \coNP\ when all randomness is a terminal draw from an efficiently computed finite probability table. Attention models admit polynomial-time certification when local dependency windows of logarithmic length precede one global head, given deterministic decoding, fixed vocabulary, exact rational weighted means, a direct binary affine readout and finite-automaton prompt domains. A construction with two global layers instead makes certification \coNP-complete over template domains, with one head per layer, polynomial width, logarithmic precision and an inverse-polynomial logit margin. Planted-secret experiments measure what finite audits miss relative to complete references. Among 30 secret–model-state pairs that leak under greedy single-prompt execution on their secret's 4,096-prompt domain, uniformly selecting 256 recorded evaluations per pair misses every leak for an expected $41.06\%$ of these pairs. Batched and single-prompt checks disagree on one complete-domain decision among all 48 fine-tuned pairs, while a same-order repeat reproduces every single-prompt output. These results distinguish computational conditions for certification from the coverage and execution conditions needed to interpret a negative audit.

An $\mathfrak{N}$-semigroup is an archimedean, idempotent-free, cancellative and commutative semigroup. For example, the additive semigroup $\mathbb{R}_{>0}$ of strictly positive real numbers is a $\mathfrak{N}$-semigroup. Hewitt-Zuckerman showed that every $\mathfrak{N}$-semigroup admits a semigroup homomorphism to $\mathbb{R}_{>0}$. We show that every uniquely divisible $\mathfrak{N}$-semigroup $S$ admits enough semigroup homomorphisms to $\mathbb{R}_{>0}$ to detect divisibility in $S$. %They were studied by Tamura and Kobayashi. The main ingredient is a version of the Eidelheit and Kakutani hyperplane separation theorem for vector spaces over $\mathbb{Q}$. A counterexample due to Ravsky explains why this result does not generalise to the larger class of $\mathfrak{N}$-semigroups.

In cross-silo split learning, Parallel Split Learning with Global Sampling forms representative pooled batches when class distributions differ across clients, but ignores client delay when several clients can supply the same class. We introduce Latency Budgeted Parallel Split Learning with Global Sampling, which separates each pooled batch's integer class target from the choice of clients that supply its examples. The flow variant formulates this assignment as an integral network-flow problem and minimizes modeled client-side completion time for the current target. The fast variant uses a greedy next-completion rule to reduce schedule-construction cost. Both preserve the target stream and use every local example once per epoch. A planning rule selects between the variants while accounting for the cost of constructing both candidate schedules. On CIFAR-10, the flow variant reduces modeled training time by 6.75%, with a 0.30 percentage-point decrease in final accuracy. On Tiny ImageNet with 20 candidate classes per client, the fast variant reduces modeled time by 16.87% and reaches all four validation targets earlier than the latency-unaware baseline. Across 405 schedule comparisons, the planning rule stays within 2% of the lower realized cost in 96.54% of cases. In our evaluation, latency-aware provider assignment reduces modeled training time without changing the prescribed class targets, while the preferred variant depends on whether assignment savings outweigh schedule-construction overhead.

2D Gaussian-based image representation is becoming increasingly popular, and our work proposes a new approach to steganography by embedding information within Gaussian parameters rather than image pixels. We first fit the parameters of this representation to the target image and employ a secret key to select a subset of these parameters for fine-tuning, allowing us to embed an 8-bit message while maintaining high visual fidelity in the reconstructed image. Thirty fitting experiments on three synthetic images show that the correct key can recover the message without error, while decoding with incorrect keys yields a Bit Error Rate (BER) of $0.543$, close to random guessing. Compared with random selection using the key, selecting the least-disturbing edits recovers the message more reliably (one-sided $p=0.031$), and the average PSNR cost is only $0.091$ dB in visual quality. The embedding method transfers to 112 natural images at $256\times256$ using 4,096 Gaussians. The correct-key BER is $0.000$, and decoding under a wrong key stays close to random guessing at $0.520$. Our method embeds the payload through three Gaussian parameter types: log-anisotropy, opacity, and color luminance. In a separate nine-fit reduced setting, color luminance is removed, so the payload uses two instead of three parameter types, a $33.3\%$ reduction; all 256 Gaussians remain in the fitted representation. The correct key still recovers the message without error. However, wrong-key BER rises from $0.514$ to $0.571$, moving farther from random guessing ($0.5$).

A graphical user interface (GUI) agent that ships on a phone runs a small model and reuses experience: action paths recorded on earlier runs and cached from the cloud. When an app updates, part of this experience becomes silently wrong. On nine real app version pairs, an agent carrying experience recorded on the old version succeeds 10.1 points less often than one carrying none, and it does not notice the mismatch until 3 steps after acting on it. We propose REBASE, a protocol that keeps the device copy and the cloud copy of the experience coherent across updates. When a version changes, the cloud replays its copy on the new version and the device verifies each recorded step before executing it; when a step still fails, the device sends the cloud evidence in increasing size, starting from an accessibility-subtree diff, until the cloud re-derives an executable patch, keyed by version so that one repair serves the whole fleet. On two Jetson devices, REBASE restores the success rate of stale experience to that of fresh experience recorded on the new version within one episode, at 708x fewer bytes and 47.3x fewer cloud calls than uploading screenshots to the cloud, and 2.5x less device energy than running without experience.

Pretrained robot policies offer strong manipulation skills but are typically limited to single-agent settings, where a robot acts in isolation. In this work, we study how to adapt pretrained single-agent diffusion policies to multi-agent settings using minimal collaborative data, co-optimizing for two key objectives: high coordination performance and single-agent skill retention. To this end, we introduce ALTER, an adaptation method for coordination on demand: the adapted policy coordinates with other robots when deployed in a team while remaining capable of acting independently when operating alone. Execution is decentralized: each robot acts only on its own visual observations, without explicit inter-agent communication. Our method trains a coordination head that predicts a residual denoiser to transform single-agent behavior into coordinated multi-agent behavior when necessary while also preserving single-agent capabilities. To preserve single-agent capabilities, we augment a small number of collaborative demonstrations with self-distilled data generated by the base policy during training of the residual denoiser. In simulation, ALTER achieves higher coordination success over our baselines while retaining much higher source-skill retention. In our hardware experiments, we find similar trends where ALTER better co-optimizes for coordination success and single-agent skill retention than the baselines.

In this article, we investigate the stochastic Camassa–Holm equation driven by additive noise, which models nonlinear shallow-water waves under random external forcing. We establish that, almost surely, any finite-time breakdown occurs through wave breaking: the wave amplitude and the positive part of the slope remain bounded, whereas the minimum slope tends to $-\infty$. Under an additional moment assumption, we derive an initial-slope condition ensuring wave breaking with positive probability. We also formulate the equation as a stochastic Hamiltonian PDE, establish its stochastic multi-symplectic conservation law, and derive the evolution law for the averaged $H^1$ energy. Combining the Fourier–Galerkin method, symplectic Runge–Kutta integration, and exact solution of the linear stochastic subsystem, we propose a fully discrete method which preserves an integrated discrete stochastic multi-symplectic conservation law and the linear growth of the discrete averaged \(H^1\) energy. Under suitable regularity and resolution assumptions, we present that the fully discrete dynamics retain the slope-steepening mechanism responsible for wave breaking, providing a discrete counterpart of the continuous behavior.

The magnetic field geometry in the near-horizon region is very important in shaping polarimetric signatures of black hole images. With a hybrid magnetic field consisting of an axisymmetric split-monopole field and a tilted uniform external field, we investigate the effects of external magnetic field inclination on the polarimetric signatures of Sgr A* by employing a stationary semi-analytical radiatively inefficient accretion flow (RIAF) model and general relativistic polarized radiative transfer simulations. Our results show that the external magnetic field tilt significantly modifies the electric vector position angle (EVPA) pattern and brightness distribution. The induced non-axisymmetry from the tilted magnetic filed component renders polarization morphology dependent on the observer's azimuthal angle, which is a novel behavior absent in purely axisymmetric magnetic field configurations. In combination with Event Horizon Telescope (EHT) data, we analyse the possibility of such hybrid magnetic fields around Sgr A*.

Molten pool flow significantly influences bead geometry, defect formation, and solidification microstructure in wire-arc directed energy deposition (DED). However, direct flow sensing remains an open challenge due to extreme temperatures, intense arc illumination, and complex flow patterns. Traditional research has relied either on computationally intensive fluid dynamics simulations, which require assumed boundary conditions and lack empirical anchoring, or on vision-based tracer particle tracking, which yields sparse, noisy, and physically unconstrained velocity estimates. This work bridges these two paradigms by reconstructing physics-constrained 2D surface flow fields from high-speed imaging of a GTAW-based wire-arc DED process under distinct flow regimes: quasi-steady convection and periodic droplet impact. The pipeline begins with homography correction to calibrate the oblique camera view, followed by dense optical flow extraction to provide raw velocity observations. For quasi-steady pools, a physics-informed neural network (PINN) reconstructs the surface velocity field by jointly enforcing data fidelity, incompressible Navier-Stokes momentum equations, no-penetration boundary conditions, and an arc-forcing prior through composite loss minimization. For pools subject to periodic droplet impact, a phase-conditioned time-dependent PINN is further developed to resolve the cyclic flow evolution throughout the impact period. This work provides a unified framework that bridges high-speed visual sensing and fluid mechanics, enabling physics-grounded flow diagnostics for wire-arc DED processes.

Bound states in the continuum (BICs) provide a mechanism for preserving entanglement in waveguide quantum electrodynamics. Here, using quantum control techniques in a configuration of two braided giant atoms, we propose a robust approach to create high-fidelity entangled BICs. The protocol combines quasi-Floquet modulation of the effective atom–waveguide couplings with an independent phase-controlled atomic exchange, which provides restricted counterdiabatic assistance for preparing the complete dressed BIC. In the lossless effective model, we obtain a full-state BIC fidelity of $0.99992$ and an unconditional atomic Bell fidelity of $0.99588$ using a fast control protocol. Microscopic finite-mode simulations validate the central-sideband description during the passage, while static calibration-error scans quantify its control tolerances. A separate microscopic study with relaxation and dephasing, using experimentally motivated component scales, identifies a finite useful entanglement window and a benefit from shaping the coupling envelopes. These results support controlled preparation, retention, and retrieval of dressed entanglement within the stated control and noise assumptions.

When adapting pre-trained models through fine-tuning, freezing weights alone might not preserve performance, as updates elsewhere can change the inputs to the frozen core, ultimately affecting overall performance. We first analyse the case where a selected frozen core can be isolated and propose removal-value, a capacity-based score that approximates HOPE's removal cost averaged over removal orders. We show that in VGG-8, cutting paths from trainable neurons into a frozen core makes selection using this score useful: $70\%$ frozen preserves $5.22\pm0.51$ percentage points more old-task accuracy than DEFT at similar new-task accuracy. In transformers, shared residual streams leave paths into frozen neurons open. For this case, we derive drift-value, a forward-only proxy for the output disturbance from updating each weight entry under a local update model. In language models, at 40 epochs, this policy exceeds adapted Wanda and RIA freezing scores in settings with substantial retention loss, while its differences from Fisher remain unresolved. After 160 epochs on Qwen2.5-1.5B, it retains $0.0433\pm0.0102$ more than static Fisher. In DINOv3 vision-transformer adaptation to point clouds, drift-value retains $0.440$ image accuracy versus $0.187$ for a random mask of the same count. These results motivate Guarded Freezing: select by removal-value when incoming paths are cut, and by drift-value when they remain.

Time-series diagnostic systems rarely rely on retrieving relevant historical cases, and when they do, retrieval is evaluated only indirectly through downstream prediction. We introduce READ-Bench, a benchmark for historical-case retrieval across 12 diagnostic datasets, centered on multivariate time series, that defines relevance by shared fault or event type rather than signal shape, so visually different traces of the same fault count as relevant while similar-looking traces of different faults do not. Treating retrieval as a base retriever followed by a reranker, we evaluate classical distances, symbolic retrievers, self-supervised and foundation-model embedders, and their fusion, plus label-aware and language-model rerankers, under one protocol that varies supervision, pollution, and corpus scale with significance testing. Under a common channel-independent interface, pretrained representations offer no statistically detectable advantage over strong classical and symbolic baselines for search alone. The decisive factor is a small amount of resolved-case supervision at reranking, namely a Gaussian-process reranker that propagates a few neighbor labels in embedding space, which helps far more than more sophisticated representations or language-model reasoning and holds under pollution and at full corpus scale. Guided by these findings, we fuse a normal-residual-scored embedder with a dynamic time warping leg via reciprocal-rank fusion, then rerank with the Gaussian-process reranker, improving NDCG@10 over its own search stage on all 12 datasets, by +0.11 from reranking and +0.16 over the strongest single base retriever.

Ultra-low-leakage memories are attracting increasing attention for in-memory sensing and computing. However, achieving sufficiently long retention in silicon memories for analog signal processing remains challenging because of leakage through the access transistor. In this work, we demonstrate an all-silicon independent-dual-gate memory whose leakage current, inferred from single-electron counting statistics, is below $10^{-22}$ A, giving a measured retention time exceeding 1000 s. Owing to the extremely low leakage, the subthreshold nonlinearity of the access transistor can be exploited without disturbing the stored charge, enabling in-memory amplitude-modulation (AM) demodulation. The proposed memory provides a CMOS-compatible platform for ultra-low-power signal processing and in-memory sensing.

Magnetoresistive materials have been tremendously important for the development of magnetic memory storage and spintronic devices. Recently, the antiferromagnetic EuX2Pn2 compounds, with X being a transition metal and Pn being a pnictogen, have seen intensive research interest due to their unusual anomalous Hall effect behavior and pronounced resistive anomaly near the Neel temperature (TN). These magnetotransport phenomena have been interpreted in the context of shortranged ferromagnetic Structuations, magnetic polaron formation, canted spin configurations, and temperature dependent metal insulator transitions in the electronic structure. Here, we report the observation of such a pronounced resistivity anomaly in EuZn2As2 near TN = 19 K. We demonstrate the suppression of this anomaly using applied magnetic fields, both in plane and out of plane. To further interpret the origin of the observed transport behavior, we studied the temperature dependent electronic structure using combined angle resolved photoemission spectroscopy (ARPES) and first principles density functional theory (DFT) calculations, which exhibits limited modifications to the bands across TN away from the Fermi energy. This lack of involvement of the electronic structure indicates a spin-scattering origin of the aforementioned transport properties, rather than a reconstruction of the Fermi surface.

Nested sampling estimates the evidence by assigning prior volumes to an ordered sequence of likelihood contours. Markov chain constrained-prior samplers, which are used in high-dimensional problems, generate many intermediate states before producing the next classic sample. These intermediate states are discarded because their correlation prevents them from being inserted into the ordered NS sequence without changing its order-statistic law. This paper introduces a novel method of using them to improve evidence estimation, by formulating NS in a Bayesian way and conditioning on phantom samples as Monte Carlo observations. We then present the open-source software package, JAXNS v3, and its implementation choices. We validate the approach on a set of problems, and identify its limitations via ablation. In our experiments, when problem structure is well resolved, conditioning on all retained phantom samples reduces log-evidence RMSE by at least $30\%$, with larger improvements at higher dimensionality. For the tested problems with unresolved structure, full phantom conditioning produces no detectable improvement or deterioration in evidence accuracy. Phantom conditioning produces overconfident evidence uncertainties. We also introduce two dynamic nested sampling allocation schemes. Evidence-improving allocation approximately halves the number of likelihood evaluations required to achieve comparable evidence accuracy relative to uniform allocation. Posterior-improving allocation doubles the classic posterior's Kish effective sample size for $17.5\%$ additional likelihood evaluations.

Language models (LMs) are often used as a tool to model human language processing. Recent studies suggest that severely restricting LMs' context window improves their fit to human psycholinguistic data by simulating human working memory constraints. However, it is possible that this strict memory-decay approach overlooks humans' reliance on long-range structural representations, such as discourse structre. In this work, we systematically vary the context window size of GPT-2 across four large-scale naturalistic English reading-time datasets and observe a U-shaped relationship: Although restricted contexts (< 20 tokens) successfully capture local memory limitations, expanded contexts (500–1,000 tokens) ultimately yield the highest overall psycholinguistic fit. To investigate the mechanism driving this benefit, we conduct a counterfactual inference-time experiment that disrupts cross-sentential entity chains by pronominalizing repeated discourse entities. Obscuring these structural linkages significantly degrades the predictive power of larger context windows by 20% to 40%. Our experiments demonstrate that tracking long-range coreference relations is one important factor for the alignment between LM surprisal and human reading behavior, and approximate the extent to which human comprehenders use global discourse relations during language processing.

The design of optimal causal linear feedback schemes for additive white Gaussian noise (AWGN) channels with noisy output feedback has remained an open problem for over 60 years. Prior work has focused on restricted policy classes, especially passive (uncoded) noisy output feedback, where only the transmitter performs feedback coding. However, passive noisy output feedback fundamentally lacks the degrees of freedom required to attain the information-theoretic performance limit in general. In this paper, we consider the active (coded) noisy output feedback setting, where both the transmitter and the receiver perform feedback coding. We then develop a constructive KKT-optimal active linear feedback design that asymptotically attains the Elias-Butman SNR converse bound, thereby establishing MSE/SNR optimality over the entire class of causal linear schemes. Furthermore, we prove that the optimal passive feedback solution is recovered as a special case of the active design. This passive solution admits a Geometric Toeplitz (GT) structure with a Chance-Love (CL)-style one-shot polynomial characterization, and can be computed with O(log T) complexity. Thus, our results provide an affirmative answer to the long-standing optimality question for noisy output feedback under causal linear feedback coding, and our numerical results support the theoretical findings.

Smartphone motion sensors support interactive applications, but their readings may also reveal touchscreen input beyond their intended use. Assuming known drawing intervals, we study whether handwritten digits remain predictable across users and devices, as a 10-class problem on 19,628 HuMIdb recordings from 481 participants. We compare handcrafted features with classical machine learning algorithms, MiniRocket kernels, and a compact sensor patch transformer on accelerometer, linear acceleration, gyroscope, and gravity signals. The transformer achieves 57.74% accuracy and 82.64% top-3 accuracy on 75 unseen participants, and 58.77$\pm$0.95% over 3 seeds for unseen participants on 9 unseen phone models. Low motion recordings remain informative, accuracy is not monotonic in motion level, and the tested contrastive pretraining, augmentation, and derived signals give no consistent gains. Digits are thus predictable beyond familiar users and phone models under assumed segmentation, while acquisition-order shortcuts limit conclusions about practical privacy exposure. Code available at: https://github.com/Arritmic/motion-digit-leakage.

Best-of-$N$ jailbreaking (BoN) bypasses safeguards of aligned models by drawing $N$ independent augmentations of an unsafe prompt and sampling $M$ completions of each. Previous works have shown that the attack success rate (ASR) seems to follow a power-law in $N$, which we challenge. The exponent drifts with $N$, with an exponential crossover which is a finite-size artifact of the adversarial dataset. Little work has been done to explore the entire two-budget ($N, M$) attack surface as well as its dependence on the generation temperature $T$. We introduce a simple barrier model where each prompt has a baseline safety level and each augmentation a random thermally activated barrier. Then four numbers, each backed by an interpretable safety mechanism, determine the entire ($N, M$) attack surface. They extrapolate predictions from $N \leq 100$ to $N = 10^4$, collapse five distinct models on the same scaling function and predict ASR at different temperatures from the one they were fitted at.

Rewriting in proof assistants spans a strict hierarchy. Equational rewriting substitutes based on extensional equality; subequational rewriting substitutes based on homogeneous relations such as $\leq$ or $\subseteq$, justified by monotonicity lemmas; and generalized rewriting relates different operations across different types, justified by transfer rules. All three are specializations of one schema, the function relator $(R \Rightarrow S)\,f\,g$. Lean 4's rw and Mathlib's grw/gcongr implement the first two levels, but the third has had no Lean implementation. We present one: a transfer tactic family over a tagged rule database, benchmarked using Mathlib's own test suites, of which 112 of 178 ported tests close through the transfer engine. An evaluation of the design's three motivating hypotheses returns a mixed result: generality holds, authoring effort wins in its amortized form (averaged per use), but on dependency footprint, transfer only ties a mature library and loses on coercions. This shows that transfer's value is concentrated on transferring into domains where few theorems exist.

Hybrid attention models have emerged as a crucial architecture for Large Language Models (LLMs) (e.g., the Qwen3.5 and Kimi series). Their memory and computational efficiency make them highly attractive for on-device inference, forming a promising synergy with edge Neural Processing Units (NPUs). However, naive execution of these hybrid models on edge NPUs fails to deliver these benefits, often bottlenecking the prefill stage due to severe memory-system inefficiencies and architectural mismatches within the linear attention (LA) layers. We present HA-NPU, the first system to enable efficient hybrid attention LLM inference on edge NPUs without modifying the underlying algorithms. HA-NPU enhances execution efficiency by reorganizing the dataflow of the LA components across three levels: (1) At the core level, it partitions workloads by the head dimension and fuses dependent operators, eliminating cross-core global memory accesses; (2) At the operator level, it reorders execution to consume intermediate tensors immediately, drastically minimizing local-buffer pressure; (3) At the tensor level, it employs dataflow-aware layout planning to minimize transformation overhead between matrix and vector processing units. Compared to competitive baselines, HA-NPU achieves up to 35.95$\times$ LA kernel speedup and 36.14$\times$ energy reduction, delivering up to 2.03$\times$ faster end-to-end request latency. The source code will be made publicly available at https://github.com/yinyuanzhang/HA-NPU

In this paper, we develop a mixed quantization technique for graph vector bundles that combines semiclassical analysis and quantum cat maps. We apply it to study the Kesten–McKay law and quantum ergodicity.

This work investigates how negative differential resistance (NDR) can be utilized to enhance conversion gain in superconducting niobium nitride (NbN) hot-electron bolometer (HEB) mixers. Conventional HEB operation avoids NDR regions due to parasitic oscillations caused by interactions between thermal inertia and bias-line reactance. Recent experimental results show that reducing the bias-T inductance suppresses these oscillations and enables stable biasing within the NDR regime, thereby increasing the mixer conversion gain beyond levels achievable under positive differential resistance (PDR) bias. Using a lumped thermal-electrical model, we interpret these experimental findings, derive stability conditions for NDR-biased operation, and predict the future performance limits achievable through optimized bias circuit designs. Our results indicate that further reductions in bias inductance, combined with appropriate load-line conditions, could yield several decibels of additional gain while maintaining practical IF bandwidths.

Complementary waveform libraries yield impulse-like aggregate delay responses at zero Doppler, but pulse-dependent Doppler phases degrade their sidelobe cancellation. This paper develops a linear-algebraic formulation for coordinating a (D)-ary transmission schedule and slow-time receive weights for paraunitary MIMO waveform libraries. Using a modal decomposition of the CPI ambiguity matrix, prescribed-order Doppler-nulling conditions for the (D-1) nonzero modes are expressed as homogeneous linear constraints on the receive weights for a fixed schedule. This representation gives the SNR-optimal fixed-schedule weights by subspace projection and reduces the remaining design to a discrete schedule search. Degrees-of-freedom and modal-growth analyses relate the design to the CPI length, null order, and waveform dimension. Numerical examples compare the resulting designs with established binary constructions and demonstrate Doppler suppression across the full ambiguity matrix of a four-waveform configuration.

Comet nuclei preserve a record of planetesimal formation, but their sizes are difficult to measure because the nucleus is usually blended with its coma. We present a catalog of nucleus sizes for 523 comets (235 long-period and 288 short-period comets; LPCs and SPCs) from the 14.5-year WISE/NEOWISE archive, supplemented by Spitzer photometry. A coma-nucleus decomposition of the radial profiles yields conservative upper limits for all 523 comets and diameters with uncertainties for 301 (107 LPCs and 194 SPCs), with median diameters of 5.3 and 2.5 km, respectively. Nucleus colors across the four WISE bands follow the heliocentric trend expected from the transition between reflected and thermal emission, with no measurable difference between the two dynamical classes. The cumulative size-frequency distribution of the SPCs has a slope of $\gamma = 1.45_{-0.13}^{+0.15}$ (68% confidence interval) over $D = 2$–15 km, steepening to $2.05_{-0.38}^{+0.47}$ for the perihelion $q < 2$ au subset. The LPC distribution is smoothly concave down: a broken power law places a break near 35 km, with slopes of $0.92_{-0.12}^{+0.13}$ below and $3.68_{-1.24}^{+1.96}$ above, while the $q < 2$ au subset gives $1.39_{-0.28}^{+0.35}$ over $D = 4$–20 km. All distributions flatten below the fitted ranges and level off near 1 km. We discuss the implications of our results and their connection with models of the destabilized trans-Neptunian population.

We study whether benchmarks reliably guide model selection as developers adapt to evaluation feedback across multiple criteria. We find that the worst-case test-set size needed to estimate the best score among $k$ adaptively chosen models, under any convex combination of the criteria, grows exponentially with the number of criteria, reaching the $\Theta(\sqrt{k})$ cost of answering $k$ adaptive statistical queries with only $O(\log k)$ criteria, at fixed accuracy and confidence. In attacks on multi-task large language model benchmarks with five to ten criteria, feedback restricted to nondominated task profiles produces large reused-to-held-out score gaps and frequent false winners. These results challenge a prominent explanation for prior observed reliable benchmark reuse—that developers mainly respond to convincing improvements over the current best—in rich-feedback settings, while leaving open how often ordinary model development encounters this vulnerability.

Vision-Language-Action (VLA) models leverage large-scale pretraining to ultimately achieve generalist manipulation. Deployed VLA policies must support continual learning to acquire new tasks over time. Teaching a VLA a new task generally requires finetuning it on demonstrations of that task. However, naively finetuning on downstream tasks causes the policy to forget earlier tasks and degrades generalist capabilities. This failure is known as catastrophic forgetting. Most continual learning methods counter it by replaying data from earlier tasks. However, the old task demonstrations are not always readily available. In this paper, we introduce SAMBAR, a continual learning algorithm that prevents catastrophic forgetting during VLA finetuning without requiring access to the demonstrations of any previously learned task. We propose to cast continual learning as a constrained optimization problem and solve it with the method of multipliers. In our approach, the method of multipliers drives the policy to learn the new task without the model parameters drifting far away from their previous values. In contrast to a standard regularization penalty, the method of multipliers raises the penalty as the constraint violation accumulates by using a dual variable. We also selectively anchor the parameters critical to previous tasks to preserve past knowledge, leaving other parameters free for new task acquisition. The combination of dual variable and selective anchoring, therefore, balances knowledge acquisition with knowledge retention. We evaluate our method, SAMBAR, on the LIBERO simulation benchmark and on hardware. When sequentially finetuning on a VLA, every replay-free baseline we compare against completely forgets the first task it learned, whereas SAMBAR retains every task it has learned.

We analyse a discontinuous Galerkin method for two-dimensional scalar conservation laws on curved domains. Small intersections of a Cartesian grid with the domain are combined by rectangular cell merging. The local space is the restriction of $\mathbb Q_k$ to each physical merged cell. An entropy-conservative flux is supplemented by face viscosity and, for odd degrees, a skew derivative-jump correction on unmerged interior squares. We prove exact semidiscrete $L^2$ dissipation and an optimal error estimate for every fixed $k\ge1$. For smooth solutions with homogeneous trace on the entire boundary, the semi-discrete method satisfies an $O(h^{k+1})$ error bound. The constants are independent of the original cut-cell area fractions. The proof combines a physical-cell $L^2$ projection and cancellation of regular-face projection errors. A separate semidiscrete result covers linear transport with upwind inflow data. Computations for Burgers' equation on a disk and linear advection on a smooth star exhibit orders close to $k+1$ for $k=1,2,3$.

The global transition to a cashless economy has placed credit cards as the key element of digital transactions, acclaimed for their easy use, speed, and acceptance in most places. However, the growing dependence on this payment method has led to an escalation of the risks associated with credit card (CC) fraud. Detecting this type of fraud is a difficult task because the patterns are constantly changing, there is a data imbalance, and it is necessary to identify the legitimate transactions and the fraud ones at the same time. This study addresses this challenge by proposing a credit card fraud detection (CCFD) framework using a data balancing technique and a deep learning (DL) model. The proposed fraud detection model is trained and evaluated by collecting the dataset called Credit Card Fraud Detection from the Kaggle repository. As the dataset is highly imbalanced, we utilized the Synthetic Minority Oversampling Technique (SMOTE)-Tomek technique to balance the dataset. Further, the balanced dataset is classified using the Heterogeneous Graph Neural Network (HGNN) model. The HGNN model represent various transactions using a heterogeneous graph architecture and by using an attention based message passing technique, it managed to consider the complex relationships, time factors, and user behavior. The integration of SMOTE-Tomek in the model further boosted its capacity to identify fraudulent transactions, while lowering the rate of false positives. The HGNN model attained a 99.97% accuracy, a 99.48% F1-score, a 99.15% precision, and a 98.97% recall. The findings indicates that this model is effective and can be applied to real-world CCFD scenarios.