Papers

For systems with steep gradients, sharp interfaces, or severe spatio-temporal coupling, Physics-informed neural networks (PINNs) suffer from spectral bias, geometric inflexibility, and boundary constraint conflicts, which undermine accuracy and convergence. To overcome these issues, we propose a geometry-adaptive and constraint-enhanced PINN (GAC-PINN). The framework comprises four components: a gradient-driven adaptive grid mapping (AGM) for diffeomorphic point concentration with Jacobian regularization, an adaptive bandwidth hard-constraint ansatz with spatially-varying boundary transition widths, a Gaussian Fourier feature mapping as a spectral preconditioner to further enhance high-wavenumber representation, and an operator-aware router that automatically selects the appropriate hard-constraint construction based on whether the governing PDE contains temporal derivatives. An AGM callback mechanism and a three-stage training strategy ensure stable coordination. Benchmarks including the viscous Burgers equation, a sharp-peaked 2D Poisson problem, and the Allen-Cahn phase-transition equation show that GAC-PINN attains relative (L^2) errors of ((1.747\pm 0.450)\times 10^{-4}), ((2.868\pm 0.947)\times 10^{-5}), and ((1.756 \pm 0.712)\times 10^{-3}), respectively, consistently outperforming the baselines. Ablation studies further reveal that AGM alone yields a substantially lower error than residual-based adaptive refinement (RAR), while RAR becomes beneficial only when combined with FFM, demonstrating a context-dependent module interaction. Convergence analysis verifies rapid error reduction and saturation with increasing resolution, establishing a practical adaptive framework for high-fidelity simulation of problems with localized sharp features in applied mechanics and computational physics.

Accurate segmentation of post-treatment brain metastases is essential for treatment planning, longitudinal disease monitoring, and quantitative assessment of therapeutic response. The BraTS-MET 2026 Task 1 challenge introduces a clinically relevant segmentation problem involving four anatomically distinct tumor subregions: non-enhancing tumor core (NETC), surrounding non-enhancing FLAIR hyperintensity (SNFH), enhancing tumor (ET), and the resection cavity (RC). Among these, RC segmentation is particularly challenging because of its low prevalence, heterogeneous postoperative appearance, and lesion-wise evaluation protocol, leading conventional segmentation networks to prioritize dominant tumor classes during optimization. The proposed nnU-Net-based framework explicitly addresses RC segmentation through four complementary components: (i) RC-weighted Dice and Cross-Entropy optimization to alleviate class imbalance, (ii) anatomically consistent cavity augmentation to increase the diversity of postoperative cavity appearances, (iii) a residual encoder architecture for enhanced multi-scale feature learning, and (iv) lesion-aware morphological post-processing to suppress false-positive cavity predictions while preserving anatomically plausible structures. The framework is evaluated on the BraTS-MET 2026 Task 1 online validation benchmark. Among the evaluated configurations, the ensemble model (Residual Encoder nnU-Net + nnU-Net + RC-aware CarveMix) achieves the best performance, with lesion-wise Dice scores of 0.732, 0.752, 0.708, and 0.575 and corresponding NSD scores of 0.794, 0.798, 0.727, and 0.474 for ET, TC, WT, and RC, respectively. These experimental results show that integrating RC-aware optimization, anatomically consistent augmentation, and lesion-aware post-processing provides an effective strategy for improving rare resection cavity segmentation in post-treatment brain metastases.

We present the instrument description and the first on-sky observations for the new CHara ARray Integrated Optics Testbench (CHARIOT) at the CHARA Array. CHARIOT is a 2-telescope proof-of-concept instrument that utilises a fibre-connectorised beam combiner fabricated by ultrafast laser-inscription in Infrasil quartz glass, which presents low-OH contamination and high transparency over the whole K-band. With its fibre-connected architecture, CHARIOT is designed as a plug-and-play testbed instrument to test and validate fibred astrophotonic components on-sky. At this point, CHARIOT is able to measure raw fringe squared visibilities with a sub-1% precision for stars with K-mag<2. Under poor to moderate seeing conditions, the current limiting magnitude for fringe detection is K-mag = 5.212 (HD210824). These results demonstrate that CHARIOT's performance is already comparable to the former JouFLU instrument. With additional improvements, the limiting magnitude could be extended and the precision for fainter stars improved. The successful on-sky demonstration paves the way for a new high precision K-band beam combiner instrument at the CHARA array.

Understanding how two entities are connected often requires tracing multi-hop relations across documents to identify intermediate entities and supporting evidence that explain a connection. This is a task that appears frequently in scientific research and other knowledge-intensive analyses. We formalise this setting as multi-hop relation inference: given two known endpoint entities, we aim to recover the bridge entities and evidence-grounded reasoning chains that connect them across a document corpus, and to generate an explanation grounded in the retrieved evidence. Existing multi-hop RAG systems typically seek an unknown answer entity rather than explicitly recovering the connection between two known endpoints and graph-based approaches often rely on costly LLM-extracted knowledge graphs that limit scalability to large document collections. We introduce ConRAG, which builds a lightweight entity-document graph from entity co-occurrence and LLM-based entity filtering. Its connective retrieval infers and semantically ranks paths between two endpoints. On MuSiQue and 2WikiMultiHopQA, ConRAG consistently improves bridge entity and reasoning chain recovery over strong RAG baselines, while reducing graph-indexing token cost by up to roughly 1.5 orders of magnitude. Our results show that endpoint-constrained path retrieval provides an effective and index-efficient approach to evidence-grounded relation discovery.

A random assignment of n indivisible objects to n agents is specified by its assignment matrix and implemented by drawing a deterministic assignment from a Birkhoff-von Neumann decomposition. Kawase et al. observed that the choice of decomposition matters for fairness: a matrix that is envy-free in the sense of stochastic dominance (SD-EF) can be decomposed so that some agent envies another with probability close to 1. They call a decomposition Dec-EF if every agent envies every other agent with probability at most 1/2, proved that every SD-EF matrix admits a Dec-EF decomposition when n <= 3 or when there are at most two distinct preferences, and left the general case open. We settle the first open case: every SD-EF matrix with four agents admits a Dec-EF decomposition. The worst case over the SD-EF polytope of a profile is attained at a vertex, and our computer-aided proof enumerates all 26,927 vertices for the 762 profiles up to symmetry in exact arithmetic and certifies each by a rational decomposition. The same method settles five agents with at most four distinct preferences and the probabilistic serial rule for all five-agent profiles, and adversarial search up to seven agents finds no counterexample. For general n, an envy-budget identity shows that 1/2 is the best possible threshold. We prove that every SD-EF matrix with at most two distinct rows admits a Dec-EF decomposition, and that the maximum-entropy decomposition is Dec-EF whenever all agents but two share a preference; the latter proof rests on a new monotonicity lemma for weighted least-squares rankings. In general, natural decompositions fail: greedy Birkhoff-von Neumann can come arbitrarily close to envy probability (n-1)/n, and maximum entropy fails at n = 4 when all preferences differ. Deciding whether an arbitrary random assignment, not necessarily SD-EF, admits a Dec-EF decomposition is strongly NP-complete.

For a finite group $G$, let $\lambda(G)$ denote the minimum number of orbits on the elements of a finite lattice $L$ with $\operatorname{Aut}(L)\cong G$. Babai and Goodman conjectured that $\lambda(G)$ is bounded by an absolute constant. We prove that $\lambda(G)\leq 50$ for every finite group $G$, thereby confirming their conjecture. Moreover, the lattice can be chosen to have a regular orbit. The main algebraic ingredient is a decomposition of a generating set of an arbitrary finite $2$-group into an elementary abelian part and two sets in which no quotient of distinct elements is an involution.

We prove a sharp Szemerédi-Trotter estimate \[\mathcal{I}(A,\mathcal{L})\lesssim \frac{|A||\mathcal{L}|}{p}+|A|^{2/3}|\mathcal{L}|^{2/3}+|A|+|\mathcal{L}|\] for prime finite field $\mathbb{F}=\mathbb{F}_p$ by a new polynomial decomposition theorem. As applications, we first prove the sharp Furstenberg set estimate in $\mathbb{F}^2$. Secondly, we improve sum-product estimate \[\max\{|A+A|,|A\cdot A|\}\gtrsim\min\{(p|A|)^{1/2},|A|^{5/4}\},\quad A\subset\mathbb{F}.\] Finally, we improve the Fourier restriction estimate $R^*(2\to\alpha)$ holds for $\alpha>\frac{10}{3}$ in $\mathbb{F}^3$ when $p\equiv 3\mod 4$.

Post-training foundation video models on heterogeneous reward-weighted data usually assume that all data categories induce compatible updates. This assumption is fragile when categories correspond to different skills, domains, or evaluation dimensions. We study this problem in text-to-video post-training, where VBench2.0 dimensions define data buckets and an external multimodal reward pipeline assigns sample weights. We propose G$^3$-LoRA (Gradient-Guided Grouped LoRA), a data organization procedure that probes category-level gradients induced by reward-weighted video samples, removes the shared global update direction, clusters categories by residual gradient compatibility, trains group-specific LoRA experts, and consolidates them into one adapter by weight merging followed by on-policy distillation from the experts. We motivate this procedure by viewing reward-weighted flow matching as velocity-field regression: incompatible reward dimensions may prefer different denoising directions in overlapping noisy latent regions, causing shared LoRA training to average capabilities. On Wan2.1-T2V-1.3B-Diffusers, the merged grouped adapter improves the matched VBench2.0 evaluation over the base model, a joint reward-weighted LoRA baseline, and random, semantic, and raw-gradient partitions trained with the same pipeline; an independent evaluator agrees, and on CogVideoX-2B grouping avoids the negative transfer of joint training. The gain is not uniform: merging compresses the largest specialist gains, distillation recovers part of this loss, and camera motion and several local-quality dimensions remain challenging. Together, these results suggest that gradient compatibility can serve as a practical diagnostic for organizing reward-weighted video post-training data.

Autoregressive large language model inference repeatedly invokes the target model to generate one token at a time, making generation sensitive to GPU memory movement and sequential execution. This study evaluates two-token multi-token prediction (MTP) against autoregressive decoding in a controlled single-request deployment on an NVIDIA A10G GPU. A 360-request benchmark covered plain-text, reasoning-intensive, and tool-calling workloads, while runtime telemetry, Nsight Systems, PyTorch Profiler, and selected Nsight Compute measurements were used to explain the observed performance. MTP increased output throughput by \(1.91\times\) to \(2.19\times\) across all prompts and reduced time to first output by 10.0–14.2%. Median mean acceptance length ranged from 2.370 to 2.595 tokens per verification iteration. Profiling showed that MTP introduced a longer and more complex execution path, including proposal, sampling, attention, gathering, and reduction operations. However, it required 56.4–78.1% fewer executions of the selected repeating CUDA Graph per generated token. The dominant MTP GEMM kernel was not faster than the dominant autoregressive GEMV kernel, and selected instances of both approached the A10G memory-bandwidth limit. These results show that MTP improved inference through amortization: greater token progress reduced repeated GPU execution sufficiently to outweigh the additional speculative-execution cost.

Let $f$ be a Steinhaus random multiplicative function and let $g$ be a polynomial of degree $d$. Write $S_N=N^{-1/2}\sum_{n\le N}f(n)\,e(g(n))$. We prove a quantitative dichotomy for the moments of $S_N$: for each integer $s\ge 2$, either $\mathbb{E}|S_N|^{2s}$ is close to the Gaussian moment $s!$, or the coefficients of $g$ can be approximated by rationals with a small denominator. In particular, if the coefficients of $g$ satisfy a Diophantine condition, then $S_N$ converges in law to a complex normal distribution with mean $0$ and variance $1$. Lean 4 code for the proofs is provided, for convenience of verification.

Bourneuf, Charbit and Thomassé [BCT25] showed that the domination number of a tournament can be bounded as a function of its fractional dichromatic number. The function proved was exponential and the tools were based on VC-dimension. In this paper, we present two new proofs of this theorem. The first proof is based on a reduction to the problem of bounding the domination number of a $(1/2-\epsilon)$-majority tournament, for which [BCT25] and Charikar, Ramakrishnan and Wang [CRW26] gave tight bounds. This proof yields the same exponential bound on the domination number as in [BCT25]. The second proof gives a quasilinear bound for the domination in terms of the fractional dichromatic number. It was obtained via AI and was inspired by the recent book proof of the existence of a Condorcet Winning Set of size five due to Ramakrishnan [Ram26].

We study the nonlinear stability of the quadratic plane Poiseuille flow $U(y)=(y^2,0)$ for the two-dimensional incompressible Navier–Stokes equations on $\mathbb T\times\mathbb R$. We prove that for initial perturbations of size $O(\nu^{2/3})$ in a $\nu$-dependent weighted Sobolev space, the flow is globally nonlinearly stable. In particular, the nonzero streamwise modes experience enhanced dissipation and decay exponentially on the characteristic time scale $O(\nu^{-1/2})$, while the zero mode remains uniformly controlled. Thus, in this weighted Sobolev topology, \(O(\nu^{2/3})\) is a sufficient stability scale without logarithmic loss.

Semantic indexing must preserve reusable source information without committing too early to one business schema, while providing checkable premises for reasoning. We propose 5W1H+Which, a design that separates source-grounded content extraction from progressive ontology binding. The 5W1H questions organize independently addressable content units; Which records links to versioned ontology elements, mapping relations, applicability scopes, and validation states. Time, location, system environment, and participant roles constrain when facts, bindings, and rules may be used. Unbound content remains searchable, whereas formal reasoning requires explicit premise checks. The design distinguishes business valid time, system knowledge time, and operational traces, and tracks dependencies for revalidation and incremental maintenance. Worked examples illustrate cloud migration and temporal policy validity. The resulting linked corpus can support downstream training and evaluation organized around benchmarks, positive and negative examples, trajectories, and costs. Trajectories preserve steps, evidence-backed checkpoints, recovery, and local-to-global failure impact; reusable skills remain downstream abstractions requiring cross-episode validation. We specify falsifiable hypotheses and capability-matched baselines to test cross-task evidence coverage, contextual misuse, and update cost under equal information and budgets. The contribution is a proposed indexing and maintenance contract, not a new universal ontology or post-training algorithm. No experiments have yet been conducted, and no performance improvement is claimed.

For a finite group $G$, define the field $\mathbb{Q}(G) := \mathbb{Q}(\{\chi(g) : \chi \in \operatorname{Irr}(G) , g \in G\})$. In this article we compute generating sets for the fields $\mathbb{Q}(G)$ when $G$ is a finite general or special linear group, a finite general or special unitary group, or one of the simple groups $\operatorname{PSL}_n(q)$ or $\operatorname{PSU}_n(q)$. We then apply these results to classify all number fields $F$ of degree $2$ or $3$ over $\mathbb{Q}$ such that $F = \mathbb{Q}(S)$ for some non-abelian simple group $S$.

We describe AfS (Agent for Science), a platform built for long-horizon scientific work, where a project runs for tens of hours across dozens of agent runs with a human present only occasionally. Most agents for science are general coding agents with a skills folder attached, and they inherit that lineage's failure mode: under pressure to finish, they fabricate, skip, or smooth over. Our design rests on one claim: most of the credibility of machine-made research can be moved from asking the model to behave to making the non-compliant state unrepresentable. We encode research discipline as mechanically enforced laws (commitment before measurement; unforgeable freezing; reports are not facts; evidence persists but verdicts do not; negative results are first-class; mechanical questions to the framework and semantic judgment to the model), organized around three time horizons: a minimal set of research nodes within a run, an inquiry contract with frozen closure conditions and a hash-chained artifact ledger within a project, and a two-tier knowledge base with promotion by rewriting across projects. This is a system description written under one rule: each mechanism appears in exactly one place, with the invariant it enforces, the failure it prevents, the way it is realized, and the cost it imposes. It covers the node contract, the write-path gates, the two-tier memory, and the runtime substrate. Three traces walk real failure attempts through the mechanisms that catch them, and two closed campaigns are included as worked illustrations rather than as an evaluation. We report no benchmark: a process-integrity suite that would support quantitative comparison is under construction, and what we can measure today is only the operating cost of the machinery.

We study forward orbits in $\mathbb Z^2$ generated by the expanding affine maps $(x,y)\mapsto(mx+i,ny+j)$, where $m\ge n\ge2$ are integers and $(i,j)$ ranges over a nonempty digit set $\Lambda\subseteq\{0,\ldots,m-1\}\times\{0,\ldots,n-1\}$. We obtain explicit formulae for the mass, Beurling, discrete packing, and Assouad dimensions, the discrete Hausdorff dimension and its lower variant, and the lower entropy index. When $m=n$, all these dimensions equal $\log_m\#\Lambda$. When $m>n$, they can differ, and several depend on the starting point through the sizes of the endpoint columns of $\Lambda$. The two Hausdorff dimensions coincide and admit a pressure variational formula. Our proofs use finite symbolic models and approximate squares to relate digit counts to coverings in centered windows, translated windows, and annuli. We also characterize invariant lattice sets and determine their dimensions. Finally, we compare the orbit dimensions with semigroup growth and the dimensions of the compact dual attractor. In particular, the mass and Beurling dimensions need not equal the semigroup growth exponent, in contrast to the corresponding one-dimensional theory.

We employ the set-theoretic methods yielding the consistency of the existence of nontrivial pairwise disjoint covers of the unit interval (or equivalently $\mathbb{R}^n$ for $n\in\mathbb{N}\setminus\{0\}$) by less than $2^\omega$ closed sets in the context of covers of infinite dimensional Banach spaces $\ell_1(\kappa)$ for infinite $\kappa$ under geometric conditions arising in tiling theory and in approximation theory. Specifically, for $\kappa=\omega_1, \omega_2$, using side-by-side Sacks forcing we prove the consistency of an arbitrarily large continuum above $\kappa$ with the existence of a highly disconnected proximinal set in $\ell_1(\kappa)$, built from norm-compact pieces separated by a common positive distance, and the existence of a normal disjoint tiling of $\ell_1(\kappa)$ by star-shaped bodies of the form $X+B$, where $X$ is norm compact and $B$ is the unit ball. We also prove that if $\kappa$ is an uncountable cardinal of countable cofinality, then $\ell_1(\kappa)$ does not admit any normal disjoint tiling by bodies of the form $X+B$, where $X$ is closed and norm-separable and $B$ is the unit ball. These results complement a result of Klee of 1981 obtained for $\kappa$ satisfying $\kappa^\omega=\kappa$, recent results of De Bernardi, Russo, Sezgek and Somaglia, and a $\mathsf{ZFC}$ a machine-discovered result (included in the appendix) that there are no nontrivial discrete Chebyshev sets in $\ell_1(\kappa)$ when $\kappa<2^\omega$.

In this paper we study a class of 1-homogeneous solutions of the one-phase problem coming from the Cartan isoparametric cubic polynomials, which exist only in dimensions $d=5,8,14,26$. Our main result shows that they are unstable in dimensions $d=5,8,14$, and minimizing in dimension $d=26$. This provides the first example of a singular minimizing cone in the Alt-Caffarelli problem that is neither axially symmetric nor of Lawson-type.

I briefly overview the original formulation of the t-J model starting from Hubbard model, as well as stress its unique features, i.e., advantages and shortcomings when discussing its physical properties. Particular emphasis is put on a brief characterization of connection between magnetism, unconventional superconductivity, and the Mott-Hubbard localization of the correlated carriers in a narrow band. In the second part I summarize the model generalization to the three–orbital situation. The main purpose is to list some basic features of the physics associated with t–J model.

Estimating integrals of black-box, high-dimensional functions, from expectations and kernel mean embeddings to the softmax kernel in self-attention, is a basic subroutine in machine learning. Rank-1 lattice rules suit this setting: they query the integrand only at a fixed point set and need no gradients. When the $n$ points serve as a design matrix $X\in\mathbb{R}^{n\times d}$ for a feature map, however, computing $\Psi(X)^\top v$ or $\Psi(X)w$ for an elementwise nonlinearity $\Psi$ costs $O(nd)$ time and memory for any standard quasi-Monte Carlo point set. We study subgroup rank-1 lattices, whose Korobov generator $(1,t,\dots,t^{d-1})$ uses a scalar $t$ of fixed multiplicative order $m$. Splitting $\mathbb{F}_n^\times$ into cosets of $\langle t\rangle$ reduces both maps to short cyclic correlations evaluated by FFT, giving exact results for arbitrary $\Psi$ in $O(n\log m)$ time and $O(n)$ memory, without forming $X$. Since fixing $m$ falls outside classical component-by-component theory, we prove convergence directly: via resultants with the cyclotomic polynomial $\Phi_m$, the squared worst-case error in the Korobov space decays as $O(n^{-(\alpha-1)/(m-1)})$ for prime $m\ge d+1$, and this threshold is exact. Using the splitting of $n$ in $\mathbb{Q}(\zeta_m)$, averaging over the $m-1$ admissible generators improves the constant by a factor $\Theta(m-1)$. Empirically, the subgroup lattice beats Gaussian and orthogonal random features and scrambled Sobol' and Halton points in 49 of 54 synthetic kernel-estimation settings and all 45 softmax-attention settings on nine real datasets, and builds a sample set with $d=2048$, $n\approx4.1\times10^7$ in 2.3 ms.

We extend the notion of robust viscosity solutions to semilinear rough partial differential equations (RPDEs) of the form \[ \partial_t u + \mathcal{L}_t u + f(t,x,u,\sigma^{\top}\nabla_x u) + h(t,x,u)\,\diamond dW = 0, \quad u(T,x)=\xi(x), \] driven by a discontinuous path $W$ of finite $q$-variation for some $q<2$. This includes, in particular, typical paths from a broad class of Lévy processes, for instance from $\alpha$-stable Lévy processes with $\alpha<2$. Our notion of solution is formulated through a solution map that agrees with the classical viscosity solution for smooth drivers and is continuous in the terminal condition and the driver, with both the driver and the solution paths viewed in a suitable Skorokhod-type decorated-path metric \cite{chevyrev_superdiffusive_2024}. These requirements naturally imply that robust viscosity solutions must employ Marcus-type jumps, and we establish well-posedness, a flow property, and a stochastic representation in terms of the rough BSDEs with discontinuous Young drivers \cite{becherer_rough_2026}. For Lévy processes of finite $q$-variation with $q<2$, our notion of RPDE solutions provides a pathwise interpretation for corresponding SPDEs, which are seen to be Markov processes in an infinite-dimensional function space.

We prove uniqueness of the blow-up at every singular point of the one-phase free boundary problem for which one blow-up has an isolated singularity. The result applies to Lipschitz stationary solutions and does not require any integrability assumption on the cone. In this sense, our result completes the picture for uniqueness of tangent cones at isolated singularities in the one-phase problem. Inspired by Simon's work in the minimal surface setting, we prove an infinite dimensional Łojasiewicz inequality for the spherical Weiss' energy. This yields an epiperimetric inequality for non-minimizing solutions, which leads to the uniqueness result.

We propose a lifted reformulation of supervised classification that improves the final accuracy of standard classifiers without changing the architecture at inference time. A network $N=N_2\circ N_1$ is split at a single semantic interface and one learnable prototype per class is inserted there. Training combines a quadratic consensus penalty that pulls $N_1(x)$ toward the prototype of its class with a classification loss of $N_2$ evaluated on samples drawn around the prototypes, whereat no gradient crosses the interface. At inference the prototypes are discarded and the unmodified network $N_2\circ N_1$ is used. Across CIFAR-10, CIFAR-100, and TinyImageNet with ResNet and vision transformer backbones, lifted training improves test accuracy by up to five percentage points over variants without lifting under a shared tuning protocol. Moreover, we provide theoretical justification of those results.

Unmanned aerial vehicles (UAVs) serving the low-altitude economy require reliable localization in urban canyons, indoor facilities, and other GPS-challenged environments. Visual matching with a geo-tagged database provides an alternative source for absolute positioning, but onboard computation and energy limits motivate offloading the database and matching pipeline to an edge server. The resulting localization quality depends on what visual information can reach the edge in time under varying wireless-communication and edge-computing resources. In this paper, we propose a network-adaptive edge-assisted multi-view localization framework that combines scalable orthogonality-regularized variational information bottleneck (O-VIB) encoding, value-of-information (VOI)-guided request control, and value-aware edge scheduling. We design an O-VIB model that supports nested latent prefixes from 8 to 128 dimensions and four UAV view modes. Each UAV requests edge assistance when the predicted localization-risk reduction exceeds the communication and service costs. On CARLA multi-view UAV data, VOI-guided control can lower the mean and 95th-percentile (p95) route errors by 24.8% and 31.0%, respectively, relative to budgeted periodic offloading under a matched per-route traffic budget. In indoor UAV experiments with motion-capture ground truth, our design can lower the mean position error by 28.0% relative to uncompressed all-view CLIP retrieval while cutting the descriptor traffic by 98.6%, using a 0.145 KB semantic representation. Under high congestion, a VOI-weighted scheduler with waiting-age and deadline shaping can lower the edge-side p95 latency of the top-10% high-value requests from 137.7 ms to 32.8 ms.

We study a new quasilinear system of balance laws (i.e. conservative first-order PDEs with source terms) for the numerical simulation by a front-capturing approach of viscoelastic athermal multi-material flows with sharp interfaces (like a mixture of immiscible fluids and solids). It naturally extends with an energy balance that is meaningful to stability and thermodynamics. In particular, the unequivocal definition of solutions to Cauchy problems can be guaranteed in some cases, thanks to a symmetric-hyperbolic formulation.

Solana is one of the most popular blockchains, and is arguably the most widely used blockchain for smart contracts, also known as dApps. Understanding the types of smart contracts that are being executed by Solana and their interplay is therefore highly beneficial both for designers of modern blockchains and developers of smart contracts. To that end, in this paper we analyze a million recent Solana blocks. We report statistics about the size of blocks (number of transactions per block), execution time units for individual transactions and fees, and invoked Solana programs. Further, based on the declared readset and writeset of each transaction, as mandated by Solana, we analyze the conflicts and corresponding conflict graphs arising within each block. These latter statistics are important to understand the potential for parallelism in the network, which is one of the main claimed benefits of Solana. The data and code are available in open source.

Generative AI promises easier dashboard creation, raising questions about the future of dashboards and the people who create and use them. We interviewed 16 experts based in 14 countries about their practices and expectations. Almost all expected dashboards to persist for recurring questions, monitoring, and reporting. They anticipated adaptive views and combinations of language, graphical controls, and gestures, while emphasizing interaction as part of human exploration and understanding. Participants expected authors' responsibilities to shift toward specifying requirements, curating generated work, and evaluating outputs, with design knowledge and communication remaining important. Easier creation also raised concerns about validation effort, users' understanding, maintenance, and personalization weakening shared understanding. We discuss seven opportunities for research and practice concerning validation, end-user education, dashboard proliferation and rot, organizational guidance, adaptation, novel visualizations, and accountability for AI-generated content. Our findings connect dashboard evolution with the human and organizational work needed to sustain their use.

The critical current density ($J_c$) of V-Ti alloy superconductors is strongly influenced by the size and distribution of microstructural defects that pin magnetic flux lines. In this work, the effect of successive cold working and annealing (SCA) at 550{\deg}C on the microstructure, superconducting properties, and flux-pinning behaviour of the V$_{0.59}$Ti$_{0.40}$Ce$_{0.01}$ alloy is investigated and compared with the previously reported SCA at 450 and 650{\deg}C. During SCA at 550{\deg}C, the superconducting transition temperature increases gradually with successive processing steps. The first annealing after cold rolling to 50% thickness produces a significant enhancement in $J_c$ over the measured field range, whereas subsequent SCA cycles result in only marginal changes. The $J_c$ remains relatively weakly dependent on magnetic field over wide magnetic-field range, and the final cold-worked sample exhibits a finite $J_c$ up to 8.5 T. Pinning force density analysis shows that grain boundaries dominate flux pinning in low magnetic fields, whereas dislocations and $\beta$-$\alpha'$ interfaces become the dominant pinning centres in higher fields. Comparison of the different SCA temperatures shows that 650{\deg}C provides the highest low-field $J_c$, whereas 450{\deg}C gives the best high-field performance. In contrast, SCA at 550{\deg}C provides most balanced field dependence and the largest enhancement in $J_c$ relative to the corresponding as-cast alloy. Although the highest absolute $J_c$ in the high-field regime is achieved after the third SCA cycle at 450{\deg}C, a comparable value is obtained after only the first annealing at 550{\deg}C. These results demonstrate that the intermediate annealing temperature of 550{\deg}C provides an effective balance between defect generation, phase evolution, and recovery, resulting in enhanced flux pinning over a wide magnetic-field range.

Saved checkpoints record states along a training trajectory, but generally do not determine the updates at states that would be visited under a different schedule. We study how accurately these checkpoints can reconstruct the endpoint of a sequential reference with prescribed update strengths. Under a common local transition model, two checkpoint-index moment conditions characterize all convex merges that agree with this reference through second order. We then prove an information limit that for nondegenerate profiles, no algorithm using only a fixed-length gradient-descent (GD) history with step size $h$ can achieve $o(h^3)$ endpoint error uniformly over a fixed class of smooth, strongly convex losses. The lower bound follows from two losses with identical GD checkpoint histories but sequential reference endpoints separated by $\Omega(h^3)$. Quadratic-Accurate Merging (QAM) achieves a matching uniform $O(h^3)$ endpoint error bound. Its explicit coefficients also define the unique profile-dependent merge that exactly matches the sequential GD reference across all fixed quadratic objectives. Across two public Adam checkpoint trajectories (SmolLM3-3B and OpenEuroLLM-Prelude-9B), three windows and three profiles per model, and 15 tasks, QAM shows mixed results for short windows and broader advantages over Warmup-Stable and Merge (WSM) for longer windows. Matched-moment GSM8K diagnostics further show that local consistency alone does not fully determine downstream scores. These results characterize the reconstruction limits of saved histories, provide a coefficient rule that attains the optimal rate, and assess its practical utility.

Machine learning (ML) increasingly powers Internet of Things (IoT) applications at the edge. Yet producing a deployable edge ML artifact for a specific scenario requires navigating a huge search space spanning data representation, model design, training on domain-specific data, and runtime customization. This workflow is fragmented and difficult to scale across diverse edge applications. We present EdgeCraft, an LLM-driven system that turns high-level intent into deployable edge ML artifacts. Building such a system raises two challenges: (1) How can an LLM be guided to find high-quality solutions that meet dynamic SLOs for task quality, latency, and energy? (2) How can trustworthy target-device verification be obtained at low cost? EdgeCraft addresses these challenges with two designs. (1) A constraint-aware synthesis tree explores alternative candidates and uses measured SLO gaps to guide each improvement. (2) A multi-fidelity verifier progressively combines low-cost checks with full target-device verification to reduce verification cost while preserving reliable verification results. It also records verified failures for reuse, avoiding repeated device work. To support concurrency, EdgeCraft provides a multi-tenant runtime that runs cloud training and target-device verification in parallel while isolating requests. Across 50 public tasks, EdgeCraft exceeds the task-specific Reference in best-observed quality on 40 tasks and finds an SLO-feasible artifact on 45, with the two outcomes overlapping on 38 tasks. Moreover, EdgeCraft achieves competitive performance on our self-collected SEN dataset, suggesting its generalizability to real-world IoT sensing tasks.