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arXiv2026

Duality formulas for $\widehat{\mathcal{Q}}$-multiple zeta values

In this paper, we introduce two duality formulas for $\widehat{\mathcal{Q}}$-multiple zeta values ($\widehat{\mathcal{Q}}$-MZVs for short) which are defined by Takeyama and Tasaka. Since taking two different limits of $\widehat{\mathcal{Q}}$-MZV recovers the $\boldsymbol{p}$-adic multiple zeta value and the $t$-adic multiple zeta value respectively, finding the relation of $\widehat{\mathcal{Q}}$-MZVs partially supports the Kaneko--Zagier conjecture and its refined version. Currently, three types of duality formulas for the $\boldsymbol{p}$-adic multiple zeta values are known, and for one of them, the $q$-analogue was studied by Takeyama and Tasaka. We present $q$-analogues of the remaining two duality formulas for the $\boldsymbol{p}$-adic multiple zeta values.

math.NT↗
arXiv2026

Making Collaborative Signals Count: Graph-Aware Large Language Models for Sequential Recommendation

Large language models (LLMs) have been widely adopted as backbones for recommender systems. However, their language-centric pretraining makes it difficult to capture collaborative signals implicit in user-item interactions, which are crucial for personalized recommendation. Existing methods either inject collaborative representations produced by external recommenders or model only intra-sequence dependencies, limiting their ability to exploit global collaborative patterns. To address this limitation, we propose GALLM, a graph-aware LLM framework for sequential recommendation. GALLM constructs a collaborative graph over text tokens and item tokens, and models three types of relations: Text--Text relations for preserving semantic dependencies, Item--Text relations for aligning item tokens with their textual descriptions, and Item--Item relations derived from global item co-occurrence patterns. These relations are transformed into lightweight learnable attention biases and incorporated into the LLM attention mechanism, enabling collaborative-aware token interactions without introducing an additional graph encoder. Experiments on four real-world benchmarks show that GALLM achieves the best performance among the compared baselines, improving over the strongest baseline by 9.76\% on average in HR@5. The code is available at https://github.com/Fenglin-miku/GALLM.

cs.IR↗
arXiv2026

Reduced Arc-Weight Heterogeneity for Master Stability Analysis of Directed Networks

Master stability analysis can be applied to directed networks even when their Laplacian matrices are not diagonalizable. Nevertheless, a diagonalizable Laplacian is easier to analyse because the perturbations governing synchronization separate into independent modes. This paper asks how many different positive coupling strengths are needed to obtain this simplification without adding or removing any directed connections. We first give an elementary construction showing that suitable positive weights exist for every weakly connected directed network and explain its relationship to stronger genericity results in the literature. We then introduce a measure of the smallest number of distinct coupling strengths required for diagonalizability. If a common coupling strength already produces a diagonalizable Laplacian, only one value is needed. For directed acyclic networks, we give a constructive upper bound based on the length of the longest directed path from a source. This bound is exact for rooted outward directed trees. Consequently, an outward star requires only one coupling value, whereas a directed path requires a different value on every arc. These results reduce coupling heterogeneity while retaining the simpler modal form of master stability analysis. Diagonalizability is treated as an analytical convenience, not as a sufficient condition for synchronization.

eess.SY↗
arXiv2026

CFR without Unbiasedness: Debit-Budgeted Public Feedback

At a finite public-chance cut, partial counterfactual regret minimization (CFR) can evaluate successive outcome batches at learner states changed by earlier batches. Balanced coverage then lacks the conditional unbiasedness used by Monte Carlo CFR analyses. We introduce \emph{target debit}, the one-sided cumulative underestimation needed to transfer regret on delivered feedback to the dense target game. Our central theorem bounds weighted exploitability by delivered-row regret, target debit, and a native alternating-update correction. This yields Debit-Budgeted CFR (DB-CFR), which selects a public plan from completed history, executes it once, and settles its debit afterward. Complete coverage has zero debit and supplies exact recovery. With at most $\ell$ unsettled blocks, hidden debit is bounded by the sum of the $\ell$ largest predictable block envelopes; for fixed $\ell$ and polynomial output weights, the resulting $O(T^{-1})$ term preserves the additive-RM/RM+ rate. A finite converse gives equal-metadata plans with charges $0$ and $11/8$, proving that a nontrivial strict-budget decision requires semantic information or bounded post-execution settlement. In two released heads-up no-limit hold'em turn endgames, all 42 registered shallow comparisons favor partial coverage before complete coverage overtakes it between 32 and 64 rounds. In public Leduc, a lagged rule fixed on four development orders beats the best matched-recurrence-work fixed width on all ten unseen orders (median NashConv gain $0.0456$) without future candidate replay.

cs.GT↗
arXiv2026

ARISE: An adaptive residual-informed stability ensemble for feature selection in small-sample biomedical omics

Objective: Small-sample molecular classification requires feature selectors that identify predictive, stable, and nonredundant subsets for binary and multiclass outcomes. We propose ARISE (Adaptive Residual-Informed Stability Ensemble), which integrates complementary relevance signals, class-balanced stability assessment, residual-informed redundancy control, and multiclass pairwise coverage. Methods: ARISE combines seven percentile-normalized relevance components through 15 predefined profiles, adaptively weighted by nested inner cross-validation. It was evaluated on five molecular datasets, eight feature-set sizes, three fixed classifiers (k-nearest neighbours, support vector machine, and random forest), and six filter comparators. Generalization was estimated by five-fold outer cross-validation repeated 50 times using balanced accuracy, macro-F1, and Cohen's kappa. Results: Across 210,000 held-out assessments, ARISE ranked first in all 15 dataset-metric combinations. Equal-dataset means were 0.793 for balanced accuracy, 0.776 for macro-F1, and 0.725 for kappa, exceeding the strongest aggregate comparator by 0.022, 0.023, and 0.028, respectively. Performance remained strong across compact feature sets, although the optimal budget differed by dataset. Conclusion: ARISE provides a transparent, adaptive framework that jointly addresses relevance, stability, redundancy, and multiclass discrimination. Its consistent results across datasets, classifiers, metrics, and feature-set sizes support further evaluation for small-sample molecular classification.

stat.ML↗
arXiv2026

The Machine's Internal Clock: Do LLMs Share Human Temporal Illusions?

Human perception of time is subjective. Temporal illusions show that the brain relies on context and relational cues when judging duration. Prior studies established these effects with visual and auditory stimuli. We ask whether written narratives alone can cause these illusions, and whether LLMs respond as human participants do. We introduce a benchmark of 6,684 paired scenarios spanning five illusions, each judged from the character's and the reader's perspective. In our human study (60 participants), participants' judgments matched the predicted directions for all five illusions in at least one perspective (7 of 10 conditions). Across 14 LLMs, models reproduce every effect humans show in the same direction, but on average more strongly. Most effects persisted even after cue words were removed and after controlling for 15 lexical and semantic features. These results show that models and humans agree in direction but not in strength, which cautions against treating LLM judgments as substitutes for human responses for subjective temporal reasoning.

cs.CL↗
arXiv2026

Scaled boundary cubature scheme in higher dimensions: integration over polytopes and curved regions

We extend the scaled boundary cubature (SBC) scheme from planar regions to higher-dimensional regions described by oriented boundary patches. The resulting parametrization transforms integrals over compact regions in $\mathbb{R}^d$ into sums of integrals over the boundary-patch parameter domains and a radial coordinate. In three dimensions, this yields a direct volume-integration rule for solids bounded by affine faces, triangular or tensor-product surface patches, B-spline patches, NURBS patches, and combinations of curved and affine boundary representations. For affine polytopes, recursive application of the scaled boundary map yields nested tensor-product rules over simplex sectors; in three dimensions, these reduce to tetrahedral-sector rules that apply equally to convex and nonconvex oriented polyhedra. We also develop transformations for weakly singular integrands. Placing the scaling center at a point singularity exposes the radial power cancelled by the Jacobian, while generalized radial scalings and Gauss--Jacobi quadrature handle fractional powers. A transverse scaled-boundary map provides the analogous construction for affine singular sets, with straight-line examples in three dimensions. Numerical examples verify polynomial exactness on affine polyhedra and a four-dimensional tesseract, rapid convergence on curved B-spline and NURBS solids, and the expected convergence improvements for point and line singularities. Near-boundary singularity tests also identify when additional patch subdivision or patch-parameter transformations are required.

math.NA↗
arXiv2026

When Entropy Is Not Enough: Reclaiming Lost Semantics in LLM Output Length Prediction

Efficient LLM serving is often bottlenecked by the need to pad sequences to a fixed maximum length, and this wastes compute and degrades throughput. Output length prediction enables length-aware scheduling and reduces overhead. Existing methods, including entropy-guided token pooling, rely on token-level entropy but overlook semantic differences between tokens, causing them to underweight important tokens and overemphasize less informative tokens. We introduce ESTP(Entropy-and-Semantic Token Pooling), a lightweight framework that combines entropy representations with attention-based semantic representations. By deriving both representations directly during prefill, ESTP captures uncertainty and semantic importance while incurring negligible additional inference latency and memory overhead compared with methods using external auxiliary models. On the ForeLen benchmark, ESTP outperforms baseline methods, achieves better prediction accuracy and lower prediction errors across most scenarios. When integrated with a length-aware scheduler in end-to-end system tests, it further improves overall throughput and reduces the padding ratio.

cs.AI↗
arXiv2026

The Geometric Function Atlas: Using What We Know About Radius Problems to Solve New Ones

Usually, radius problems between Ma--Minda classes are solved one pair at a time, by fitting a disk inside the target region, providing a sufficient but not always the sharp radius. The same class appearing under different names makes comparison of results harder, with mistakes and duplication eluding detection. The Geometric Function Atlas catalogs radius problems using exact generators and a direction (source $\to$ target), ensuring unique identification. For each problem, we then compute the radius numerically, together with the point where the image first meets the target boundary. This helps us identify the sharp estimate which guides the proof we write. With this system, we were able to refine two earlier stated estimates, the disk radius for the sine $\to$ modified sigmoid and sine $\to$ rational cases from $\operatorname{arsinh} c$ to $\arcsin c$, and correct earlier stated values for the crescent and exponential classes: the sharp radius is $\sin 1$ from crescent to exponential, and $\log(1+\sqrt2)$ from exponential to crescent. All four proofs follow a common strategy: an estimate that is exact at the contact point, followed by the standard extremal function. Applying the method, we derive fifteen further sharp radii, four of them known.

math.CV↗
arXiv2026

ReRef-3D: A Benchmark for Spatial Referring Expression-Guided 3D Object Placement

We introduce ReRef-3D, a benchmark for language-guided single-object placement in controlled 3D tabletop scenes. It contains 33,826 instructions across 998 CLEVR-derived scenes, spanning 16 placement types and direct, one-hop, and two-hop references. Given that an instruction defines a region of acceptable placements rather than one coordinate, predictions are evaluated by relation satisfaction and physical validity. Each instruction also includes a verified natural rephrasing. We evaluate LLaVA-3D, 3D-LLM, 3D-LLaVA, LL3DA, and PlaceIt3D, with PlaceIt3D evaluated under both point-based and region-based supervision. Region-supervised PlaceIt3D achieves the highest placement accuracy at about 80% and LLaVA-3D reaches about 70%. Performance varies by relation type, but nearest and aligned remain the most difficult. Rephrasing has little effect on performance overall.

cs.CL↗
arXiv2026

Readiness Barrier Functions: Forward-Invariant Control Authority for Overactuated Multirotor Allocation

Allocation schemes that greedily maximize a readiness metric over the actuator fiber bundle of an overactuated multirotor produce commands that jump between disconnected optimal strata, demanding actuator rates no motor can deliver; effort-minimizing schemes are continuous but cannot guarantee that wrench-rate authority stays above any certified level. We reconcile the two by treating authority as a forward-invariant quantity: a control barrier function on the log-determinant of the drag-aware actuator-authority co-metric, enforced at torque level by a quadratic program in the allocation null space. A single design inequality renders the certified set compact and strictly interior to the actuator box, with the readiness cost of any rotor deactivation given in closed form as $\ln(n/(n{-}m))$ for symmetric designs. An explicit alignment ratio states when tracking can stay exact, otherwise the wrench error is bounded by $\mathcal{O}(ρ^{-1/2})$, and a robust variant handles motor-parameter uncertainty with a closed-form floor shift independent of the airframe matrix. On a hexarotor and a fully-actuated octorotor the closed-form gap matches simulation to machine precision. Over $300$ randomized missions, greedy maximization violates the certified floor in up to $51\%$ of authority-scarce missions, while the proposed filter never leaves the certified set and, in the hardest moment reversal, commits a $79\times$ smaller wrench error. The robust variant holds the floor on all $150$ perturbed plants. A high-fidelity simulation with measured propeller and motor data shows that the floor holds under unmodeled aerodynamics, electrical limits, and delay, and where it stops applying.

cs.RO↗
arXiv2026

Cramér-Rao Bound Analysis for Cell-Free ISAC Systems with Fluid Intelligent Metasurfaces

Fluid intelligent metasurfaces (FIMs) reshape antenna geometry to improve angular sensitivity. This paper studies their role in cell-free integrated sensing and communication, where distributed access points provide distinct observation directions. Under calibrated path gains, we derive the conditional angular Fisher information matrix, retain cross-AP coupling, and map it to a position-domain Cramér--Rao bound (CRB). A diagonal-information specialization exposes the dependence on angular diversity, while a multi-target extension quantifies the loss from jointly estimating other target positions. We use CRB-driven coordinate search to design transmit and receive shapes and evaluate sensing performance, equal-resource AP scaling, and MRT-based communication--sensing allocation. In the considered four-Tx/four-Rx configuration, shape design reduces the position root CRB from 0.300 to 0.227 m at 10 dB reference SNR. Two-target results further illustrate how cross-target coupling increases the joint localization bound at small separations.

cs.IT↗
arXiv2026

Dynamic Regime-Aware Conformal Calibration for Reliable Economic Forecast Intervals under Multiple Distribution Shifts

Conformal prediction provides distribution-free prediction intervals but relies on exchangeability, an assumption often violated in economic forecasting because of covariate shift, concept drift, local heterogeneity and latent regimes. We propose Dynamic Regime-Aware Conformal Prediction (DRACP), which combines density-ratio, localized kernel and probabilistic regime-aware weighting with a self-tuning online significance controller in a unified weighted conformal calibration framework. We distinguish three theoretical results: finite-sample validity under oracle importance weights, a coverage-gap bound for estimated weights with rates in effective sample size, and deterministic or regret guarantees for the online controller. We evaluate DRACP against six baselines on 48 real forecasting series covering euro-area and EU-27 HICP inflation, US macroeconomic and energy indicators, and daily financial series. Recent online methods (FACI, strongly-adaptive online conformal prediction and conformal PID) were verified against the authors' implementations. DRACP is not the most efficient method: strongly-adaptive online conformal prediction achieves the best interval score and intervals about 20% narrower. Instead, DRACP provides the most reliable calibration, achieving coverage closest to the nominal 0.90 (0.890), never falling below 0.80 on any series, maintaining the best coverage at all forecast horizons, and performing best during the 2021-2023 inflation surge. The strongly-adaptive method undercovers on 20 of 48 series versus 10 for DRACP. DRACP therefore offers a principled trade-off between calibration and efficiency, favoring reliable coverage when prediction intervals must satisfy coverage standards. An ablation study shows that the online controller and conditional-scale normalization provide most of the performance gain, whereas the weighting components make a smaller contribution.

cs.LG↗
arXiv2026

Optimal Loss Allocation and Reflected Free Boundaries in Systemic Risk

We study a singular mean-field control problem in which a central planner allocates losses generated by bank defaults to maximize terminal system health. Every generated loss must be borne by the surviving banks, without external capital. We prove that a cutoff, or "taxing-the-richest" rule is optimal for every non-decreasing concave terminal payoff, including the survival indicator. We construct the continuous-time optimizer by solving a time-discretized problem and passing to the limit, and establish its uniqueness in law for every non-constant payoff. The optimal flow is characterized by a novel reflected free-boundary problem. We establish well-posedness in a probabilistic solution class and prove positive-time smoothness of both the free boundary and the density of surviving banks. The main difficulty is the dependence of the limiting feedback on a moving support endpoint, which is unstable under Wasserstein convergence. We address this through stochastic-order comparisons, compactness estimates for the cutoff boundaries, and an augmented call-function formulation.

math.OC↗
arXiv2026

The impact of recombination during tidal disruption events

During a tidal disruption event, the resulting debris stream cools down adiabatically due to the tidal stretching. As the temperature drops, the gas is expected to undergo chemical processes, which can release thermal energy into the stream, potentially affecting the subsequent gas evolution. For the first time, we investigate in detail this effect and its dynamical impact on the early-time evolution of the stream by making use of three dimensional hydrodynamic simulations coupled with a realistic equation of state. We find that a few days after disruption, the energy injected by hydrogen recombination and molecular hydrogen formation causes the stream thickness to grow much more rapidly. In the bound debris, this effect stops the stream's confinement by self-gravity before the gas reaches apocentre. As a result, the maximum stream thickness increases by a factor that ranges from a few, for the most bound gas, to a few tens for the near-parabolic gas, reaching $\approx 30 \, R_{\star} $ around the peak of the mass fallback rate. We discuss how this accelerated stream expansion may affect the subsequent evolution of the gas, estimate the luminosity powered by recombination in the unbound debris, and evaluate the potential influence of non-ideal magneto-hydrodynamic effects. By characterizing the thermodynamic and hydrodynamic properties of the stream before its return near pericentre, our results provide physically motivated initial conditions to self-consistently model the later stages of tidal disruption events, offering a promising pathway to unveiling the physical origins of their observed emission.

astro-ph.HE↗
arXiv2026

A deep learning algorithm for black hole spin estimation using hot-spot secondary images

Sagittarius A* exhibits frequent flaring activity across the electromagnetic spectrum that is often associated with a localized region of strong emission known as a hot spot. We aim to train a deep learning model to provide a link between key parameters of this phenomenon - hot-spot emission radius, and black hole inclination and spin - to the observed angle difference between the primary and secondary image ($ΔPA$) that present and future interferometric arrays could resolve. Using the general relativistic radiative transfer code IPOLE, we generated a library of $\sim100.000$ models with varying system parameters and computed the position angle difference on the image plane between the primary and secondary images of the hot spot. We explore equatorial and non-equatorial circular orbits and evaluate our models against approximate observational constraints, including partial-orbit visibility and observational errors. Our algorithm STIHOS shows remarkable accuracy in calculating spin and inclination from the majority of the observational tests we perform ($σ_{a_*}=0.04,\,σ_i=2^{\circ}$), even in extreme conditions where only half of the orbit is visible. The off-equatorial estimation provides softer constraints in the absence of prior information. Our results demonstrate the importance of hot-spot observations for spacetime estimations. Given the increasing efforts to detect the photon-ring, our framework could prove valuable in interpreting the first observations of lensed emission.

astro-ph.HE↗
arXiv2026

Levine Equivalence in Aura Topological Spaces: Reachability, Alexandrov Structure, and Quotient Frames

In this paper, we study Levine equivalence in aura topological spaces. We show that the aura topology is determined by the reachability preorder induced by the scope function and is therefore an Alexandrov topology. We prove that the aura-Levine hull has the explicit representation $K_{\mathfrak a}(A)=\uparrow_{\mathfrak a}A=S_{\mathfrak a}^{\infty}(A)$, and hence two subsets are aura-Levine equivalent if and only if they have the same eventual forward spread. We also describe the quotient structure of the equivalence classes, characterize separation properties through the reachability preorder, classify scope functions that induce the same Levine equivalence, and examine preservation under aura-continuous mappings. For finite aura spaces, we provide an explicit procedure for deciding aura-Levine equivalence using the reflexive-transitive closure of the scope relation.

math.GN↗
arXiv2026

Anytime Solver Evaluation with a Normalized Signed Primal Integral and Explicit Reference Policies - Extended Version

Anytime solvers return usable solutions before they terminate and improve them while time remains. Their progress is commonly summarized by a primal integral, a final gap, or convergence curves. Each summary leaves consequential choices open: how to score a run before its first feasible solution, whether poor incumbents are truncated, and whether the reference value is updated after the experiment or version-frozen beforehand. These choices become visible when runs produce no valid incumbent or improve a published best-known value. We study a normalized signed primal integral built from a bounded relative gap. It assigns an intrinsic worst value to an empty run, requires no acceptance threshold, and assigns negative instantaneous gaps to incumbents that beat a frozen reference. We compare the smooth difference-over-sum kernel with a signed version of Berthold's max-normalized gap and use the former as a working default. We also distinguish analysis-time from version-frozen reference policies and recommend reading the score with the raw final gap, mean convergence curve, and target-attainment curve. We evaluate these choices on a five-arm routing campaign and two model-fidelity ladders. The two signed kernels preserve every panel ordering in this study, whereas a common acceptance threshold compresses the distances between arms and reverses one panel ordering. Updating 54 of the 212 reference values changes score levels and removes all negative scores, while leaving the observed panel orderings unchanged. An exploratory screen also identifies 12 panel comparisons in which similar integral scores conceal materially different endpoints or attainment rates. The implementation, frozen inputs, and generators are openly released.

math.OC↗