Papers

This study formulates individual route reproduction as a shortest-path problem over learned driver-specific latent link costs. The central idea is that, once such latent costs are inferred from contextual information, observed routes can be reproduced without enumerating alternative route sets. We propose a neural pipeline that includes a perception model that embeds context covariates, which comprises individual characteristics, trip-specific attributes, and network-level traffic states, into the personalized link costs. A constrained optimization (CO) layer, which determines the shortest path (SP) based on these estimated costs, follows the perception encoder. To enable end-to-end training, we employ decision-focused learning to align the predicted shortest paths with observed routes. The implicit maximum likelihood estimation (iMLE) provides an approximate gradient of the loss function that contains the non-differentiable CO layer. Furthermore, a regularization term anchors the latent cost distribution to the empirical scale of observed link travel times, mitigating the scale ambiguity inherent in shortest-path supervision. Empirical evaluations demonstrate that the proposed framework outperforms baseline route choice models in path reproduction. The learned latent costs, interpreted as proxies for perceived travel costs, provide plausible explanations for heterogeneous route choices.

We investigate single-excitation quantum walks across the one-to-two-dimensional crossover in diluted power-law hopping models. Using arrays of $\ell$ coupled chains of length $L$, we identify the finite-size localization crossover from the longitudinal spreading of an initially localized excitation. The crossover filling is well described by an exponential approach to its two-dimensional value with increasing $\ell$, defining a characteristic transverse scale $\ell_e$, and effectively two-dimensional behavior emerges already for $\ell\ll L$. An independent spectral analysis shows that $\ell_e$ is set by the transverse extent of the eigenstates participating in the dynamics, providing a microscopic interpretation of the dimensional crossover. Our results reveal an intrinsic eigenstate scale governing emergent dimensionality in diluted systems with power-law hopping, a regime directly relevant to recently developed arrays of polar molecules, Rydberg atoms, and other quantum simulators with long-range interactions.

Phylogenetic networks generalize phylogenetic trees as models of evolutionary history, allowing lineages to merge as well as to diverge. For many types of genetic data the root position of such a network cannot be recovered, so that only a semi-directed network can be inferred: a mixed graph in which only the edges entering a reticulation vertex are directed. A common strategy for inferring such a network is to first infer the subnetwork it induces on each set of $k\geq 3$ of its leaves, called a $k$-net, and then to assemble these pieces. This can only succeed if the $k$-nets determine the network, in which case that network is said to be encoded by its $k$-nets. Semi-directed networks of level-1 and 2, those whose biconnected components contain at most one, respectively two, reticulations, are known to be encoded by their $4$-nets, or quarnets, whereas level-3 networks are not. Even so, in this paper we show that level-3 semi-directed networks are encoded by their $5$-nets, or quinnets, and we characterize the limitation of quarnets exactly: we show that a single previously reported counterexample captures the only obstruction, every other level-3 network being encoded by its quarnets. Our proofs rest on a collection of encoding results for individual structural features of a network, which we establish for networks of arbitrary level and which are of independent interest.

Ransomware continues to encrypt files during the interval between attack onset and detection. Real-time backups can mitigate this damage by preserving files before they are modified. The previously proposed Real-Time Open-File Backup System (ROFBS) triggers backups primarily on file-open events. However, the file lifecycle offers several candidate trigger points, including open, read, write, and rename operations. Triggering backups too early may create unnecessary backup files, whereas triggering them too late may allow ransomware writes to race with backup creation and prevent the preservation of clean file contents. Consequently, it remains unclear which trigger timing best balances recoverability and the number of backups created. In this study, we design and evaluate real-time backup triggers for mitigating ransomware damage from a file-lifecycle perspective. Specifically, we compare four strategies: Open-time backup, Read-time backup, Write-time backup, and Rename-time backup. We implement these strategies in an ROFBS-style prototype on XFS and evaluate them using five ransomware samples: Conti, Sodinokibi, AvosLocker, REvil, and HelloKitty. Our results clarify how trigger timing affects both damage mitigation and the number of backups created, providing design guidance for selecting effective triggers in real-time backup systems against ransomware.

Ternary language models such as BitNet b1.58, Falcon-E and BitCPM are fine-tuned through higher-precision latents and deployed as ternary codes by an export that, in the labs' documented pipelines, first casts latents to bf16. We audit releases from three labs. In released checkpoints, fp32 quantization of the shipped latents disagrees with deployed codes on 0.83-1.77% of codes (Falcon-E, BitCPM) and 1.530% (2B-4T); most Falcon-E and BitCPM disagreements are bf16 products exactly on the threshold, which ties-to-even maps to zero, and the unmodified onebitllms exporter reproduces all four Falcon-E releases byte for byte. At fine-tuned endpoints with ULP-matched rates, the documented export lowers greedy GSM8K strict accuracy from 58.79% to 0.78% (Falcon-E-1B-Base) and 36.13% to 0.39% (BitCPM-CANN-0.5B), and a bf16 save and reload lowers 2B-4T's by 27.54 points while its last-number accuracy rises at that endpoint. The strict decrease recurs at each of three new seeds in all three models and has the same direction on 607 reserve test rows, but it is recipe-dependent: at Falcon-E's online-loss-selected rate the export was non-inferior, and after a longer recipe no difference was detected. Two remedies, writing the trained codes directly or adjusting bf16 inputs so unchanged tools emit them, met an inherited 4-point strict-accuracy non-inferiority criterion in all three models, also for the pooled mean over three fixed new trajectories per model and, separately, on the reserve rows. In a frozen study of bf16 latents in fine-tuning (one task, one trajectory per arm), native bf16 writes left 2B-4T's endpoint codes unchanged and changed one Falcon-E code; emulated stochastic-rounding and compensated writers changed codes and were non-inferior to fp32 training at that margin. In two model families, randomized threshold-distance interventions support distance-dependent selection of changed codes.

In current work, we delve into the study of complex Hessian equations on compact Kähler manifolds. By imposing a constraint on both the bisectional curvature and the oscillation of the solution, we demonstrate that the Laplacian estimate can be linearly controlled by its gradient estimate. Consequently, we are able to derive gradient estimate for the solution using a standard interpolation argument, without the need to employ the blow-up technique. As an application, we demonstrate that when the right-hand side of the complex Hessian equations approximate 1 in the $L^1$ norm, the desired gradient estimate is obtained.

Agentic workflows enable large language models (LLMs) to solve complex tasks by coordinating reasoning, tool use, and verification. However, a workflow optimized for an entire task collection can overlook differences in the reasoning strategies that individual queries need, while searching for a new workflow for every query repeats costly optimization. To address this tradeoff, we introduce RA-MoWE, a framework that uses workflow-affinity embeddings to cluster queries and guide the generation of reusable expert workflows. Each embedding records how well a fixed set of reference workflows solves a query, revealing similarities in which reasoning strategies are effective. RA-MoWE uses each cluster's queries and average embedding to initialize and refine a specialized workflow through execution feedback. An embedding encoder predicts these embeddings from query text, allowing new queries to select a generated expert without first executing the reference workflows. On a 300-query test set drawn from four benchmarks spanning mathematics, science, and programming, RA-MoWE improves average task score by 4.04 percentage points over selecting among the reference workflows, while using 27.7% fewer language-model calls at inference.

We study how the spin of a compact secondary and a gravitational-decoupling deformation of the Kerr geometry are imprinted on gravitational waves from strong-field eccentric motion around a rotating black hole. The orbit is evolved with the Mathisson–Papapetrou–Dixon equations under the Tulczyjew spin supplementary condition, and the radiation is computed with the numerical-kludge method. The deformation describes a black hole only below a critical curve in the plane of the two hair parameters. The spin of the secondary pulls the pericenter inward and, above a critical value, carries the particle into the black hole. The hair raises this capture threshold, from $S\simeq0.66$ in Kerr to $0.9$ and above close to the horizon boundary, because it reduces the effective mass near the black hole. The emitted signal remains a discrete comb of orbital harmonics: the spin strengthens the pericenter bursts and shifts power toward higher harmonics, while both the spin and the hair leave their main imprint through an accumulated dephasing. The imprint of the hair is controlled by the parameter that sets the radial reach of the deformation, disappears in the Kerr-like limit of the family, and is amplified by the spin of the secondary. For a source at $2$ Gpc with $M=10^6M_\odot$ and $\mu=10M_\odot$, a $6.8$ h segment of the signal carries a signal-to-noise ratio of about $1.4$ in LISA, $2.7$ in Taiji and $0.9$ in TianQin. Within the same segment the more extended deformations become distinguishable from Kerr, first in Taiji; since this holds for a nonspinning secondary, it applies directly to astrophysical EMRIs. The spin-induced frequency shifts are linear in the spin, so the large spins used here are a magnified illustration of a dephasing that, for realistic secondaries, accumulates to a phase of order a radian over an inspiral.

Interactions between two nuclei in nuclear reactions are calculated by applying the energy density method to nuclear energy density functionals. We particularly focus on the effects of nuclear mat- ter properties on fusion reactions by using the Korea-IBS-Daegu-SKKU (KIDS) density functional. Uncertainty of the equation of state in symmetric nuclear matter is accounted for by using different values of the incompressibility and the effect is explored with the 40Ca+40Ca system. Though not prominent, a systematic dependence on the incompressibility can be inferred from the fusion cross sections. The effect of asymmetric nuclear matter is described by adopting the symmetry energy parameters that are consistent with the neutron star data, but still have large uncertainties. In the application to the 48Ca+48Ca and 16O+208Pb systems, we observe a systematic dependence on the stiffness of the symmetry energy. We also consider the uncertainty of the effective mass of the nucleon in nuclear medium. We employ models that have isoscalar and isovector effective masses varying from minimum to maximum values in the allowed ranges. Contrary to incompressibility and symmetry energy, fusion cross sections are insensitive to the isoscalar and isovector effective masses. Without any phenomenological adjustment or modification of the model, fusion processes are described accurately by applying the interaction potentials derived from nuclear structure mod- els

Parameter-efficient fine-tuning (PEFT) has become a standard approach for adapting large language models to downstream tasks. However, most existing PEFT methods rely on uniform and static adaptations, without accounting for the structured heterogeneity of attention across dimensions, heads, layers, and input tokens. In practice, attention representations exhibit non-uniform behavior, and positional encoding mechanisms such as rotary positional embeddings (RoPE) induce dimension-dependent positional structure, making uniform adaptation suboptimal. In this work, we propose DyPAM (Dynamic Positional Attention Modulation), a PEFT method that adapts how positional information contributes to attention by operating directly on the query and key representations. DyPAM combines input-conditioned, dimension-wise modulation with head-wise and layer-wise structural modulation, performing fine-grained adaptation of positional attention aligned with the RoPE-induced structure without modifying the pretrained backbone. Extensive experiments on mathematical and commonsense reasoning benchmarks across multiple backbone models demonstrate that DyPAM consistently outperforms existing strong PEFT baselines.

As LLMs increasingly assist in moral reasoning, omission bias, the tendency to prefer inaction even when equivalent framings reverse substantive outcomes, poses a significant risk of skewed decision-making. Yet omission bias remains underexplored in LLM evaluation, with the few existing studies limited in scale and focused largely on utilitarian-deontological conflicts. To address this gap, we introduce OMIT, a benchmark consisting of 218 paired-frame scenarios across 10 conflict types, constructed by leveraging disagreement patterns from an LLM-based, five-perspective philosophical persona panel (utilitarianism, deontology, virtue ethics, care ethics, and contractualism). Evaluating eight LLMs, we find that omission bias is pervasive but inversely correlates with model size within families. We further evaluate four inference-time interventions and find that interventions encouraging models to consider moral principles before committing to a yes/no answer reduce omission bias and increase frame-consistent responses, although lower omission bias rates can also coincide with shifts toward action-biased responses. Ultimately, this work contributes not only the OMIT benchmark, but also a methodology for using diverse philosophical disagreement signals to evaluate framing-sensitive inaction preferences and the distributional effects of mitigation attempts in LLMs under complex moral conflicts.

The scenario approach is a well-established statistical framework for data-driven decision-making. In particular, in data-driven optimization, the scenario approach unveils how the problem structure governs out-of-sample generalization, and offers a principled basis for assessing and certifying the reliability of the optimal solution as per constraint satisfaction. Despite its strong theoretical development and wide applicability, no software toolbox has been available to date that enables user-friendly, data-driven convex optimization within the scenario-approach framework. In this paper, we introduce Scen-Opt, an open-source software tool that integrates convex programming with data samples while providing statistical guarantees grounded in scenario theory. Scen-Opt is implemented in Python, supporting data-driven linear, quadratic, and semidefinite programming, and offers a Python-based web application with an intuitive and reactive graphical user interface (GUI) built using modern web technologies. Scen-Opt can be used directly through its online interface or installed locally, accommodating both manual input and data-file uploads (CSV, JSON, TXT, TSV, MAT, Excel, NPY, NPZ, Parquet). Built on a Python backend with a modern JavaScript frontend, Scen-Opt offers a highly user-friendly experience and efficient usability across desktops, laptops, tablets, and mobile devices. In this paper, Scen-Opt is applied to a set of representative benchmarks, demonstrating its practical effectiveness for data-driven convex optimization with guaranteed performance.

A normalized analytic function $f(z)=z+\sum_{k=n+1}^{\infty}a_kz^k$ defined on the unit disk $\mathbb{D}$ is called Ma–Minda starlike or Ma–Minda convex if $zf'(z)/f(z)$ or $1+zf''(z)/f'(z)$, respectively, is subordinate to a Ma–Minda function $\varphi$. In this paper, we investigate the radii of Ma–Minda starlikeness and convexity for functions satisfying $|f''(z)|<M$ in $\mathbb{D}$. We first develop a unified approach for determining these radii and then apply it to obtain explicit radius estimates for several important choices of the Ma–Minda function~$\varphi$.

We build on EndoWake, an endogenous wake model that links the wind speed at every grid cell to its upwind neighbors by linear constraints, so that wake field, siting decisions and project constraints share one mixed-integer model. Its four parameters are calibrated once on the single wake of a Reynolds-averaged Navier-Stokes (RANS) simulation, and a graphics processing unit (GPU) scores over a million layouts per second per wind direction. At Lillgrund, we compare searches guided by EndoWake and by PyWake under a RANS judge that no search calls: the fidelity of a wake model is not the quality of the layouts optimized under it. Two diagnostics separate a quadrature error between the sampled wind directions from a surrogate bias localized off each wake edge, not reported before to our knowledge; at random directions, five paired starts detect no difference between the pipelines. The main result puts the speed to use: EndoWake ranks the moves of a local search on the GPU, and PyWake confirms every accepted move. On twenty unseen starts, with one GPU and thirty CPU processes, screen-and-confirm reaches similar mean gains to a search on PyWake alone, 7.9 times faster at one wind speed and 14.9 times faster on the annual energy (3.0 and 4.7 with a proof of local optimality charged to the timed search); on a second site it keeps its speed, and its local optima fall slightly short of those of PyWake alone. Code and data are deposited on Zenodo.

In digital pathology, compact evidence is often used to explain or audit predictions made by whole-slide image multiple instance learning models. In hierarchical compact-evidence pipelines, candidate filtering introduces a strategy-specific candidate-conditioned prediction alongside the original full-bag prediction. If the evaluation reference changes while the intended target remains the original full-bag prediction, however, not only can the measured fidelity of the same compact evidence change, but comparisons between competing candidate strategies can also change. To make this dependence explicit, we introduce CHARTER, a reference-aware evaluation charter that asks researchers to DECLARE the intended target and reference, QUANTIFY candidate-induced prediction shift, and AUDIT the stability of comparative conclusions. Across the 15 comparisons in our main five-seed Random-K audit, 4 showed determinate reversals; in a matched native-ranking stress test, the ACMIL comparison changed from REVERSED to PRESERVED. CHARTER turns otherwise implicit candidate-filtering and reference choices into an auditable evaluation specification, helping distinguish genuine preservation of the intended prediction from apparent gains induced by changing the prediction being explained.

On-policy self-distillation (OPSD) trains a language model to match a copy of itself conditioned on privileged context. Existing work varies what privileged context contains and how it is produced while also changing models, data, and training setups, making the effects of privileged context design difficult to isolate. Motivated by efforts in continual learning to reduce catastrophic forgetting, we study how the choice of privileged context affects policy drift. Specifically, we vary two axes: content (a demonstration, feedback, or rephrase) and source (external, self-generated with a verifier, or self-generated without a verifier). We train Qwen2.5-7B with OPSD across these nine combinations and three datasets, measuring target-task accuracy, prior-task retention, reverse KL from the base policy, and parameter-update geometry. Holding source fixed, changing content spans a wider median KL range than holding content fixed and changing source. The ratio between these ranges is $5.1\times$ for per-token KL and $2.2\times$ for per-sequence KL. Parameter-update geometry shows the same pattern: updates from adapters that share content are more closely aligned (mean cosine $0.571$) than updates from adapters that share source ($0.255$). For continual learning, these findings suggest that privileged context should be treated as part of OPSD's stability design because it is associated with how far and in what direction the policy moves.

Electrifying space heating with heat pumps (HP) and backup electric-resistance heaters (ERH) is incentivized to support decarbonization but increases voltage and thermal issues in distribution networks. Direct load control (DLC) of smart thermostats (ST) provide grid support, yet, to the best of our knowledge, existing methods do not co-optimize this flexibility with grid-scale battery energy storage systems (BESS) and voltage-regulation devices, and do not use ERH for preheating, limiting peak demand reduction and undervoltage mitigation. We propose a mixed-integer linear programming (MILP)-based model predictive control (MPC) framework that coordinates ST setpoints for preheating and setback, grid-scale BESS, on-load tap changers, switched capacitor banks, and step voltage regulators. The framework is evaluated on 23-node and 733-node distribution networks, including a real-data-based feeder, across multiple realized days. On the 23-node feeder with 50% HP penetration and 50% DLC participation, the proposed framework reduces the feeder peak by 23.1%, and by 27.1% with the co-optimized BESS. Rolling-horizon setpoint optimization contributes 6.5 percentage points beyond a day-ahead ST schedule (16.6%), and dispatching the ERH for preheating adds 2.7 percentage points beyond backup-only operation (20.4%). On the 733-node feeder, where thermal congestion is the binding constraint, the framework reduces overloaded branches by 94% and overloaded transformers by 47%. These results demonstrate the potential of coordinated demand flexibility and voltage regulation to accommodate heating electrification.

In the 1960s, Erdős and Gallai conjectured that the edges of every $n$-vertex graph can be decomposed into $O(n)$ cycles and edges. We prove this conjecture. Equivalently, every Eulerian graph on $n$ vertices can be decomposed into $O(n)$ cycles, which confirms Hajós' conjecture up to a constant factor.

The standard Novikov-Thorne model for geometrically thin accretion disks assumes a zero-torque inner boundary condition at the innermost stable circular orbit (ISCO). Relaxing this assumption to allow a finite viscous torque—driven by magnetic stresses bridging the plunging region—can significantly enhance the radiative efficiency and high-frequency spectral emission of black hole accretion flows. While this mechanism is well-established for Kerr spacetimes, its thermodynamic viability around exotic, horizonless compact objects remains largely unexplored. In this article, we investigate the application of the inner viscous torque boundary condition to a thin disk embedded in a regular mini-boson star spacetime. By numerically integrating the coupled Einstein-Klein-Gordon field equations and employing the Lense-Thirring slow-rotation approximation, we generate an exact, horizonless background that strictly satisfies the weak energy condition. We demonstrate that the topological absence of a coordinate ISCO fundamentally alters the accretion dynamics. Without a sudden geodesic plunge, stable circular orbits penetrate deep into the dense scalar core, causing the physical inner boundary of the disk to be determined dynamically by the peak of the Keplerian angular velocity. Because the specific angular momentum of the fluid approaches zero at this deep microscopic boundary, the standard viscous torque is mathematically quenched. Consequently, the enhanced radiative flux divergence typically associated with boundary torques in black holes is naturally suppressed around regular boson stars. This torque quenching offers a robust phenomenological discriminator between standard black holes and horizonless ultralight scalar structures.

Phase-field models offer an efficient alternative to self-consistent field theory (SCFT), but quantitative predictions of block-copolymer phase behavior remain challenging. We develop a quadratic-connectivity entropic (QCE) density functional and its adaptive extension (AQCE). QCE combines quadratic nonlocal connectivity with a nonlinear binary relative-entropy term, while AQCE adds bounded interfacial stiffness that preserves the homogeneous response. In lamellar benchmarks, QCE gives the lowest mean profile error among the tested models and AQCE the lowest mean period error. Compared with the optimized phase-field (OPF) model fitted to SCFT force and stress data, AQCE reduces strong-segregation period and profile errors by more than fivefold and sixfold, respectively. AQCE further reproduces the topology of the SCFT phase diagram for AB diblocks, a more demanding test of free-energy rankings among competing morphologies. Because architecture enters through ideal-chain correlations, the same nonlinear construction extends to other A/B architectures. We demonstrate this transfer for symmetric linear ABA lamellae, accurately predicting their profiles, periods, and ordering threshold.

Phase-contrast microscopy enables rapid, nondestructive observation of threading dislocations in GaN, but the relationship between dislocation contrast and the Burgers vector has not been established. Here, we demonstrate that the in-plane Burgers-vector direction of threading edge dislocations in GaN can be determined from the arrangement of bright and dark contrast in phase-contrast microscopy images. The relationship was first established for threading edge dislocations in ammonothermal GaN whose Burgers vectors were independently determined by X-ray topography and was subsequently applied to hydride vapor phase epitaxy-grown GaN. The Burgers vector predicted from the phase contrast was verified by weak-beam dark-field TEM and large-angle convergent-beam electron diffraction. For the threading edge dislocations examined, the direction obtained by rotating the direction from the minimum of the dark contrast to the maximum of the bright contrast by 90{\deg} counterclockwise coincided with the Burgers-vector direction. Analysis based on the photoelastic effect further suggests that the phase contrast primarily reflects the sum of the two in-plane normal strain components, {\epsilon}xx + {\epsilon}yy, around the dislocation. These results demonstrate that phase-contrast microscopy can be used as a nondestructive optical method for determining the in-plane Burgers-vector direction of threading edge dislocations in GaN.

We develop a graph-based deep learning model, GAMANet, to predict galaxy and halo properties using the GAMA DR4 dataset. Multiple catalogues are combined to construct a unified sample of 19,469 galaxies and derive a set of photometric, spectroscopic, morphological, and environmental features. The galaxy sample is represented as a graph, with galaxies as nodes and physically motivated connections based on spatial proximity and group membership as edges. A Graph Attention Network with GATv2 layers is then used to learn information from the galaxy neighbourhood while assigning different weights to neighbouring galaxies. The model simultaneously predicts halo mass, stellar mass, and a specific star formation rate proxy. On the test set, GAMANet achieves $R^2 = 0.958$, $0.985$, and $0.982$ for halo mass, stellar mass, and SSFR proxy, respectively, with an RMSE of $0.237$ dex for halo mass. These results demonstrate that graph-based learning can extract useful information about galaxy and halo properties directly from observational data while incorporating the environmental relationships encoded in the galaxy graph.

LLM-based multi-agent systems (MAS) have demonstrated strong capabilities in solving complex problems across diverse domains. Recently, the dynamic orchestration of agent systems has become an important research direction. However, existing methods suffer from limited composition, misaligned dependencies, and inflexible scale, restricting their ability to adapt to reasoning requirements during execution. To address these limitations, we reframe MAS design as a partially observable Markov decision process, in which both the composition and scale of the MAS are dynamically determined. We propose DHCG, a novel framework that coordinates three modules (Planner, Worker, and Generator) to progressively construct a dynamic hierarchical collaboration graph from scratch based on the query and evolving execution feedback. At each step, guided by feedback, the Planner generates a set of distinct and complementary roles tailored to the current reasoning needs and selectively routes relevant information to each role. It can also finalize the hierarchical collaboration graph early or progressively expand it when additional reasoning is required. We further introduce action-aware preference optimization to train the Planner to make more effective decisions when constructing hierarchical collaboration graphs. We systematically evaluate DHCG across code generation, mathematical reasoning, and domain-specific reasoning benchmarks. DHCG achieves state-of-the-art average performance among the compared methods, improving over the single-agent baseline by 13.06 points and outperforming both static and dynamic MAS baselines by 2.77-8.02 points. Additional experiments further demonstrate its generalization across different Planner backbones and unseen Worker models.

Retrieval-augmented forecasting for Web and online services supplements a forecaster with the continuations of historical segments that resemble the current context. Most existing methods build the retrieval memory once from the training segment, leaving observations revealed after deployment unavailable as references, and generally do not calibrate how much retrieved information should influence a frozen forecaster. We identify two key determinants of retrieval utility for a frozen forecaster: the timeliness of the retrieved history and its complementarity, i.e., whether the correction it induces aligns with the forecaster's residual errors; this alignment can shift between validation and deployment when the memory becomes stale. We propose FreshCast, a plug-in retrieval framework for frozen forecasters: a non-parametric streaming memory keeps writing in new observations, relational kernel regression weights candidate readouts into a memory forecast, and its correction weight is calibrated in closed form on the validation segment. Under a simplified generative model, we characterize the optimal combination gain through the second-order relation between forecaster error and memory correction, and show that periodic memory information can become redundant once the forecaster captures it. Across seven datasets, ten forecasters, and three input lengths, FreshCast reduces average MSE for every forecaster and input length, by 14.0% and 5.7% at L = 96 and 720, and achieves lower average MSE than the evaluated retrieval-augmented and online updating baselines in their comparison settings. Ablations show that post-training observations are a primary source of the gain: freezing the memory at the end of training removes most of it. For a frozen forecaster, similarity alone is not enough: useful retrieval must stay timely and provide information that the forecaster still misses.

For a proper cocompact action of a finitely generated discrete group $\Gamma$ on a spin manifold $M$, the higher localised $\widehat{A}$-genera $\widehat{A}_g(M,\omega)$ introduced earlier by the author and Mathai were shown to be an obstruction to $\Gamma$-invariant metrics of positive scalar curvature, for $\omega$ arising from the subring of $H^*(\underline{B}\Gamma,\mathbb{R})$ generated by elements of degree at most $2$, under the assumptions that the fixed-point set $M^g$ is connected and that $g$ is regular with respect to a certain real group $2$-cocycle. We show that both assumptions can be dropped.

Large language models (LLMs) equipped with terminal access have demonstrated strong capabilities in automating software engineering tasks. However, existing agents remain brittle on long-horizon workflows, where they must repeatedly reconstruct program state scattered across source files, configurations, tests, dependencies, and runtime behavior, leading to increasingly long interaction histories, context explosion, and semantic drift. Large repositories further complicate the identification of task-relevant components. To address these challenges, we introduce Dev-Primitives (Development Primitives), a modular and executable abstraction that transforms repository components from passive software artifacts into active participants in software engineering. Each Dev-Primitive pairs a repository artifact with a resident LLM, which gives the artifact an agent-native interface grounded in its own implementation and dependencies, enabling natural-language reasoning, inter-component communication, and localized self-modification. Building on Dev-Primitives, we propose HERMES, a Harness Engineering framework for software engineeRing via Modular Executable Dev-PrimitiveS, which instantiates these primitives at repository scale through a dependency-aware dynamic activation mechanism and a bug diagnosis mechanism that maps execution evidence back to the components that must be revised. Extensive experiments on four software engineering benchmarks demonstrate that HERMES outperforms matched baseline harnesses by 12.4% on average. Moreover, when paired with strong activation and diagnosis models, HERMES, even with Qwen3-8B Dev-Primitives, remains within 4.5% of the homogeneous GPT-5.6 Sol configuration across all four benchmarks, while reducing inference cost by 26.2% on Terminal-Bench 4.0, highlighting the importance of harness design in software engineering agents.

Online multifactorial experiments requires early stopping for practically negligible effects while controlling false stopping under continuous monitoring and retaining precise treatment-effect estimation. We develop a design-driven framework that chooses allocation and the evidence rule jointly, treating allocation as evidence collection and testing and estimation as complementary uses of the same evidence. For multifactor experiments with nuisance block effects and treatment-by-block interactions, we show that block-orthogonal designs remove nuisance contamination from the treatment score and form a complete class for worst-case evidence growth. Under a fixed information budget, an isotropic allocation and an explicit radial e-value jointly attain the minimax rate optimal for directionally unknown alternatives. The same allocation is universally optimal for maximum likelihood estimation of treatment effects, simultaneously achieving A-, D-, and E-optimality and establishing double optimality for testing and estimation. Batchwise replication yields an anytime-valid e-process, retains minimax rate optimality for cumulative conditional worst-case evidence growth, and preserves universal estimation optimality for the prespecified complete experiment. Simulations and a large language model prompt experiment illustrate gains in stopping efficiency and estimation precision.

Let $E_{\tau}:=\mathbb{C}/(\mathbb{Z}+\mathbb{Z}\tau)$ be a flat torus and $G(z)=G(z;\tau)$ be the Green function on $E_{\tau}$ with the singularity at $0$. Consider the multiple Green function $G_{n}$ on $(E_{\tau})^{n}$: \[ G_{n}(z_{1},\cdots,z_{n}):=\sum_{i<j}G(z_{i}-z_{j})-n\sum_{i=1}^{n}G(z_{i}). \] A critical point is called trivial if $\{z_{1},\cdots,z_{n}\}=\{-z_{1},\cdots,-z_{n}\}$ in $E_{\tau}$. Lin and Wang (Ann. Math. 2010) proved that $G_1=-G$ has exactly three trivial critical points and at most one pair of nontrivial critical points (depends on the choice of $\tau$). For general $n\geq 2$, Chai, Lin ang Wang (Camb. J. Math. 2015) proved that $G_n$ has at most $2n+1$ trivial critical points, but how many nontrivial critical points might exist remained completely open there. In this paper, we prove that $G_n$ has at most $n$ pairs of nontrivial critical points, and this upper bound is optimal at least for $n=2,3$. The key idea is to show that nontrivial critical points (if exist) are always non-degenerate and contribute the same degree $(-1)^{n+1}$. Applications to the curvature equation $\Delta u+e^{u}=8\pi n \delta_{0}$ and the integral Lamé equation $y''=[n(n+1)\wp(z)+B]y$ will be given. In particular, we show that the kernel of the linearized operator is one-dimensional for any solution of the curvature equation.

Semantic sensing (SemS) acquires task-relevant information rather than reconstructing complete physical information. Existing SemS formulations typically operate open loop: sensing configurations and observation schedules are fixed before inference and cannot respond to evolving task-level evidence. We propose Agentic SemS, a closed-loop framework for AI-enabled radio access networks (AI-RANs) that controls sensing within a communication-feasible profile set. A profile-conditioned causal Transformer updates the semantic belief from streaming observations, while key-value caching enables efficient state updates across profile changes without repeatedly processing the complete history. A semantic utility network estimates the task-level benefit of acquiring the next observation block under each feasible profile after accounting for sensing cost. The resulting continuation utilities jointly support next-profile selection and semantic early exit, adapting sensing configuration and duration to evolving evidence. The expected semantic gain is further related to conditional mutual information, providing a value-of-information interpretation of continued online sensing. Experiments on Widar3.0 with six emulated sensing profiles show that, in comparison with full-sequence High, the resource-efficient Agentic setting reduces normalized cumulative sensing cost by 25.33% while achieving 85.79% Macro-F1. At the same utility checkpoint, semantic early exit provides a further 12.35% cost reduction over adaptive sensing without early exit, with a 0.97-percentage-point Macro-F1 decrease.

Experiments on binary run-length differentiability lead to sharp computer-assisted criteria for shuffle squares. Every $C^3$-word of length greater than $16$ is a shuffle square exactly when both letter multiplicities are even. All $34$ nonempty even-Parikh exceptions are smooth and persist in every higher differentiability class. For $C^2$ the sharp threshold is $48$, with $212$ nonempty exceptions. At level $C^1$ no global parity threshold exists, but every even-Parikh non-shuffle-square of length at least $36$ has proper nonempty shuffle-square prefixes and suffixes. Exactly $230$ nonempty even-Parikh $C^1$-words have no nonempty shuffle-square prefix. The full tree avoiding such prefixes eventually consists of $422$ periodic rays. Consequently, a nonempty Kolakoski prefix is a shuffle square exactly when both multiplicities are even, apart from lengths $4$ and $8$. We also characterize classes of morphisms reflecting shuffle squares. For doubly binary words, we determine the exact deletion distance and largest twins, and prove sharp bounds for single local repairs. Exact recurrences, residual-state checks, and separate Python programs make the finite computations reproducible.