Papers

Market-making strategies in real limit order book markets face substantial model uncertainty and regime-shift risk. Existing adversarial reinforcement learning approaches improve robustness by formulating the Avellaneda–Stoikov market-making problem as a zero-sum game between a market maker and an environmental adversary. However, these approaches typically rely on Poisson order arrivals and neglect trade-induced price impact, limiting their ability to capture important high-frequency market microstructure effects such as clustered order flow, self-excitation, and post-trade price feedback. We extend adversarial reinforcement learning for market making to a more complex environment with Hawkes self-exciting order arrivals and trade-induced price impact. To mitigate the increased non-stationarity introduced by the expanded regime space, we incorporate an LSTM module that explicitly models the temporal structure of recent observations. We further characterize the equilibrium properties of the proposed framework through both game-theoretic analysis and numerical experiments, and introduce a robustness evaluation protocol focused on improvements in the left tail of the return distribution. Experimental results across a range of market regimes show that the proposed method achieves improved left-tail performance in most complex microstructure environments. In particular, the gains are pronounced in regimes with strong Hawkes excitation and low-to-moderate price impact. Bootstrap tests provide no evidence that these improvements are obtained through a stronger terminal directional inventory bias. These results suggest that combining adversarial training with temporal state representation can improve the robustness of reinforcement-learning-based market-making strategies under order-flow self-excitation, price impact, and regime uncertainty.

Let $m\geq 1$ be a fixed integer, $a$ an integer satisfying $(a,m)=1$, and $z\geq 1$ a real parameter. Denote by $\omega_{z}(n;m,a)$ the number of distinct prime divisors $p$ of $n$ satisfying $p\equiv a\, (m)$ and $p\leq z$. We study an asymptotic behaviour of $\sum_{n\leq x}\left(\omega_{z}(n;m,a)-\frac{1}{\varphi(m)}\log\log z\right)^{k}$ as $x\to\infty$ for a wide range of positive integer $k\geq 2$, where $\varphi(\cdot)$ is the Euler function. Following a method of Granville and Soundararajan we lead an asymptotic formula for the above. Also, we investigate $\sum_{n\leq x}\left(\omega(n;m,a)-\frac{1}{\varphi(m)}\log\log x\right)^{k}$, where $\omega(n;m,a)$ denotes the number of distinct prime divisors $p$ of $n$ such that $p\equiv a\, (m)$.

We study differentially private covariance estimation in operator norm for mean-zero sub-Gaussian distributions with unknown covariance support and at most $k$ nonzero entries per row. We develop a multiscale random-threshold algorithm with sample complexity $\ot(k^2/\alpha^2+k\sqrt d/(\alpha\varepsilon))$ for $(\varepsilon,\delta)$-differential privacy and error at most $\alpha\sigma^2$, where $d$ is the dimension and $\sigma$ is a known sub-Gaussian scale. The bound improves the privacy-dependent term of the existing $\ot(k^2/\alpha^2+k^{3/2}\sqrt d/(\alpha\varepsilon))$ \citep{kumar2026curse} upper bound by a factor of $\sqrt k$, and matches the lower bound of $\widetilde{\Omega}(k^2/\alpha^2 + k\sqrt{d}/(\alpha\varepsilon))$ in its applicable parameter regime. Our key technical ingredient is a direct operator-norm bound on the centered fluctuations of an ideal reconstruction, exploiting conditional independence rather than accumulating entrywise errors across each row. A multiscale allocation of threshold tests balances reconstruction variance against query sensitivity. Together, these ingredients sharpen the trade-off between approximation error and privacy protection, removing the additional $\sqrt{k}$ factor from the privacy-dependent sample complexity.

Steering with SAE features requires per-feature coefficient tuning, which currently demands intervention sweeps. We ask whether properties of the SAE itself, computable before any forward pass, predict which features will be cheap or expensive to steer. We show that variation in SAE feature steerability is partially predicted by decoder-space geometry: neighbor density and maximum cosine similarity to nearby decoder directions, both computable from the SAE weight matrix before any intervention, rank features by how much steering they require for a fixed behavioral effect ($\rho$ up to $-0.546$, $p < 10^{-6}$, AUROC 0.610-0.822 across conditions; the signal is rank-based, consistent with grid discreteness). This geometry-steerability relationship replicates across two Gemma-2 model scales (2B and 9B), two SAE widths (16K and 65K), and is detectable cross-architecturally on Llama-3.1-8B-Instruct ($\rho = -0.266$, $n = 300$). On Qwen3-8B with BatchTopK SAEs, geometry predicts whether a feature is steerable at all but not the continuous ordering among responsive features, revealing a boundary condition tied to SAE training regime. The signal weakens at deep proportional layer depth in both models, where the cost of steering exceeds our intervention budget, a consistent depth boundary. These results provide preliminary evidence that pre-steering geometry can partially inform coefficient selection, offering a path toward screening features for controllability before deployment.

We describe the integration of io_uring into Oracle Database's storage layer and the architectural decisions required to deploy it in a production multi-process RDBMS. Our design uses per-process ring contexts that eliminate inter-process synchronization, a shared buffer registration mechanism now part of the mainline Linux kernel, and a transparent fallback to libaio on error. Evaluation on an internal development build of Oracle Database 26ai shows that io_uring's benefits concentrate on asynchronous batched I/O paths: on a mixed OLTP workload (TPC-C), io_uring delivers identical throughput while reducing server CPU utilization by 1.2 percentage points through more efficient background writes; on analytical queries (TPC-H), CPU per query drops by 8.5% (geometric mean). Isolating the write path alone shows 29% lower CPU per write and 34% higher throughput. Synchronous read paths – the dominant I/O in OLTP – show no improvement and even increased CPU usage for very large I/O sizes. These results motivate a hybrid I/O architecture that retains pread/pwrite for synchronous operations, adopts io_uring for asynchronous batched I/O, and falls back transparently to libaio – a selective strategy that may also be relevant to other database systems facing the same integration question.

We study regular $\mathbb{N}$-graded vertex operator algebras $V=\bigoplus_{n\geq 0}V_n$ whose weight-zero algebra $V_0$ is a nontrivial finite-dimensional local Gorenstein algebra, asking which structural features of strongly rational vertex operator algebras persist without the CFT-type condition $V_0=\mathbb{C}{\bf 1}$. For semisimple Lie subalgebras of the left Leibniz algebra $V_1$, assuming $\ker\left(\left.L(-1)\right|_{V_0}\right)=\mathbb{C}\mathbf{1}$, the product $u_1v$ induces an invariant symmetric bilinear form. Under $C_2$-cofiniteness and a nondegeneracy condition, each simple component with nonzero form generates an affine vertex operator algebra at positive integral level and acts integrably on $V$. When $V_1$ is solvable, the Frobenius structure of $V_0$ yields a distinguished nondegenerate subspace $M\subset V_1$. Under a quasi-primary condition, $M$ is abelian and generates a Heisenberg vertex operator algebra. With additional semisimplicity, full-rank integrality, and cocycle compatibility assumptions, $V$ contains a conformally embedded lattice vertex operator algebra $V_K$, where $K$ is positive-definite and even, with rank $\dim_{\mathbb{C}}M$ and minimum norm at least $4$. Conformally shifted lattice vertex operator algebras provide explicit models illustrating the distinction among weight-one Lie, mode-generated Lie, and lattice structures. They also show that regularity alone does not ensure semisimplicity of arbitrary Heisenberg zero-mode actions, so the additional lattice-theorem hypotheses represent genuine structural obstructions.

At an $O(2)$-equivariant Hopf bifurcation, the real parts $\zeta_R$ and $\xi_R$ of the two cubic normal-form coefficients govern selection between traveling and standing waves. In a fourth-order regularized $p$-system, $\xi_R$ was observed to vanish and the cubic nonlinearity to shift only frequencies. We show that both observations are structural: variational nonlinearities enforce them even when the linear part is dissipative and non-Hamiltonian. We consider a class of two-component PDEs on the circle whose quadratic and cubic nonlinearities are generated by reflection-invariant local Hamiltonians of the fields and finitely many of their spatial derivatives, through a common constant-coefficient Poisson operator. Then $\xi_R=0$ for every admissible linear part, while $\zeta_R$ depends only on the quadratic nonlinearity. For variational nonlinearities the direct cubic terms are purely imaginary. The mixed cascade term loses its real part because its second harmonic has zero temporal frequency and the resolvent keeps its parity, while the self-cascade at the doubled critical frequency keeps a real part. When $\zeta_R\ne0$, the bifurcating traveling waves are saddles, while the standing waves are supercritical and orbitally asymptotically stable for $\zeta_R<0$ and subcritical and unstable for $\zeta_R>0$. When the nonlinearities are the Poisson operator applied to polynomials in the fields alone, and its symbol does not vanish at the critical and second-harmonic wavenumbers, cancellation for every admissible linear part conversely characterizes variationality. In a dissipatively regularized Boussinesq family, as dissipation tends to zero, $\zeta_R$ vanishes linearly off resonance and diverges inversely at the 2:1 resonance. The Hamiltonian limit of the cubic coefficient is therefore singular.

Multimodal large language models (MLLMs) are increasingly used as evaluators, yet their reliability in professional assessment tasks that require expert judgment remains unclear. We investigate this challenge in the context of assessing psychotherapeutic interpersonal skills and introduce MIS-Bench, a Multimodal Interpersonal Skills (MIS) benchmark comprising 996 psychotherapy response videos annotated across 8 dimensions of Facilitative Interpersonal Skills. Across 9 MLLMs with multiple modality and prompting settings, we find that current models show only modest agreement with human experts, inconsistent gains from multimodal input, and limited benefits from reasoning-based prompting. To mitigate this gap, we propose MIS-RAFT, a regression-aware fine-tuning method inspired by RAFT and tailored to fine-grained interpersonal skill scoring at one-decimal precision. MIS-RAFT addresses the mismatch between autoregressive token prediction and scalar-valued expert assessment, significantly improving agreement with human ratings. Overall, MIS-Bench reveals a clear gap between general multimodal capability and expert-level interpersonal judgment, while MIS-RAFT offers a promising path toward more reliable model-based assessment.

Denote by $\omega(n)$ the number of distinct prime divisors of the natural number $n$. In 2007, Granville and Soundararajan gave a quite new method to compute the higher moments $\sum_{n\leq x}(\omega(n)-\log\log x)^{k}$, for a wide range of integers $k\geq 2$. In this notes, we shall apply the method for $\omega_{z}(n)$ which denotes the number of distinct prime divisors $\leq z$ of $n$. Especially, for odd integers $k\geq 3$, we lead asymptotic formulas for $\sum_{n\leq x}(\omega_{z}(n)-\log\log z)^{k}$, under certain restrictions on $k$, $z$, and $x$. Also, we refer to a framework of the approach.

Angle-resolved photoemission spectroscopy (ARPES) and scanning tunneling spectroscopy have established surface superconductivity in the Weyl semimetal t-PtBi$_2$, whereas O'Leary et al. concluded from an independent ARPES experiment that superconducting signatures are absent above 3 K. Here we reanalyze the complete deposited data of O'Leary et al. Using only experimentally determined momentum-distribution-curve (MDC) maxima, energy-distribution-curve (EDC) peak positions, and leading edges, we find a strongly anisotropic low-energy gap and dispersion back-bending that closely reproduce the magnitude and angular dependence reported independently by Changdar et al. We further show that the temperature-dependent data of Ref.~\cite{Oleary} originate from the other surface termination and were presented using temperature-dependent energy translations, momentum translations, and momentum rescalings. Registering the original temperature-dependent datasets using the metallic bulk Fermi cutoff reveals finite gaps of approximately 2, 2, 1, and 0.8 meV at the four Fermi crossings. Thus the independently acquired data of O'Leary et al., obtained on different samples and with a different photon energy, confirm rather than contradict the previously reported anisotropic superconducting gap and additionally show that an anisotropic low-energy suppression persists to 19 K.

Spiking Neural Networks (SNNs) offer a promising path toward ultra-low-power artificial intelligence inference by emulating the event-driven computation of biological neurons. However, two challenges limit their practical deployment. First, fixed-parameter Leaky Integrate-and-Fire (LIF) neurons lack the adaptation mechanisms observed in biology, where neurons modulate their excitability based on firing history. Second, scaling from single neurons to multi-neuron networks introduces challenges in synaptic weight distribution and inter-neuron spike routing that are absent in isolated designs. This paper addresses both issues through the extension, verification, and physical implementation of adaptive LIF neurons at three architectural scales. This work contributes: a 2nd-order neuron with two-stage synaptic filtering for richer temporal dynamics; a fully-connected 6-neuron spiking network with configurable weights (100 to 5) demonstrating weight-based inter-neuron communication; and a direct verification methodology enabling per-cycle observation of all internal states. All designs were synthesized targeting Selected Area Electron Diffraction (SAED) 14 nm Complementary Metal-Oxide-Semiconductor (CMOS) technology at 1 GHz and verified with Cocotb-based Python testbenches under pulsed current stimuli (amplitude 80, ISI=3). The results show that adaptation effectively modulates firing: 31% suppression in the 2nd-order neuron (25 vs.\ 36 spikes) and 31% reduction in postsynaptic firing in the network (18 vs.\ 26 spikes). Physically, the 2nd-order neuron costs 1.77x more area and 1.52x more power than the 1st-order baseline, while the 6-neuron network demonstrates near-linear scaling (5.7x area, 5.3x power). Seven verification bugs spanning testbench connectivity, fixed-point overflow, and Verilog expression-width semantics are documented.

This paper presents our system for Track 2 of the NLPCC 2026 Shared Task 10 on citation-level faithfulness in AI-assisted scientific reporting. Given an atomic scientific claim and the structured full text of its cited paper, the task requires both a four-way relation label and up to three evidence paragraph identifiers. The label head ensembles a paragraph-aware cross-encoder with a document-level DeBERTa-large classifier, followed by class-wise decision calibration. Probability-level fusion is motivated by an out-of-fold tendency to over-predict Topical Match. The evidence head combines paragraph scores from top-20 and top-30 joint models with BM25 scores. The system runs fully offline without external retrieval or LLM prompting. On the final leaderboard, our system achieved 82.9898 overall (89.5491 Macro-F1 and 76.4305 Joint@3), ranking second in Track 2. Ablations and error analysis show that model complementarity and calibration drive the label gains. Gold-evidence inference changes label Macro-F1 negligibly, whereas evidence ranking remains important for Joint@3.

Synthetic biology enables the design of genetic circuits that act as feedback controllers. These controllers are typically designed using computational models, but mismatch between model and real dynamics can lead to controllers that fail in practice. While methods to address this issue exist, synthetic biology introduces additional structural constraints. Genetic circuits are often highly constrained by experimental limitations, reducing controller design to selection among a limited set of implementable circuits rather than an optimization over a continuous space. As a result, multiple system hypotheses may lead to the same optimal controller within the implementable set. Reducing model uncertainty may therefore be irrelevant when the models lead to the same optimal controller. In this paper, we exploit this structure to develop an algorithm for controller selection in synthetic biology, formulating the problem as a decision-oriented experimental design problem over a finite controller set. We represent plant uncertainty using a set of hypotheses and select experiments to minimize the posterior controller selection risk, rather than global model uncertainty. Across three mechanistic case studies, our method reaches the stopping criterion in fewer experimental rounds than model uncertainty and random experiment selection policies, while maintaining a comparable success rate.

For all $0< s \le 1$, we provide a new deterministic construction of Cantor sets whose Fourier dimension and Hausdorff dimension are both equal to $s$. The construction is based on a straightforward Cantor-Moran construction with contraction ratios given by reciprocals of integers. The key tool to obtain the fast Fourier decay is due to the Weil bound in analytic number theory. Furthermore, we show that the natural equal-weighted Cantor-Moran measure is the desired measure admitting the near optimal Fourier decay and the measure admits an exponential orthonormal basis $\{e^{2\pi i \lambda x}: \lambda\in \Lambda\}$ for its $L^2$ space. This gives the first examples of singular Salem spectral measures in ${\mathbb R}^1$.

Recent advances in Audio LLMs have achieved human-level speech recognition, yet existing systems struggle to capture paralinguistic aspects such as speaker traits, expressive variations, and environmental acoustic conditions. To address this, we design a framework of 22 paralinguistic characteristics and create a dataset of over 1.2M Audio-QA pairs. We develop ParA-LLM, trained with a two-stage curriculum: first on single-attribute questions to build foundational knowledge, then on multi-attribute questions for joint reasoning over speaker and acoustic characteristics. We also release ParA-Bench, a benchmark of 6,000 multiple-choice questions across speaker-speech, acoustic, and mixed categories, where frontier models like GPT-4o-Audio achieve only 36% accuracy. ParA-LLM surpasses state-of-the-art Audio LLMs like GPT-4o-Audio by 7.5% on ParA-Bench, with additional gains of 1.13% on MMAU-Pro Speech and 7.49% on MMAR Speech.

We study a parameterized hybrid ranker that fuses a dense embedding list and a sparse lexical list. The method has a small, explicit parameter vector: a dense prior $\alpha \in [0,1]$, a score-versus-rank mix $\lambda \in [0,1]$, an RRF smoothing parameter $\kappa > 0$, optional list-geometry coefficients that move $\alpha$ per query, and a router margin $\tau$ that can turn sparse search off. We grid-search those ranges on SciFact train (809 queries) and freeze the chosen values on SciFact test (300). The tuned rank-score mix ($\alpha = 0.8$, $\lambda = 0.75$, $\kappa = 20$) reaches 0.753 nDCG@10 and 0.889 recall@10, outperforming dense BGE (0.742 / 0.871) and equal-weight RRF (0.707 nDCG@10) on that test split. A list-conditioned $\alpha$ adds +0.0006 nDCG; a sparse-off router is rejected by the same train split (any $\tau$ that skipped approximately 50% of queries lost nDCG). These coefficients are dataset-specific. Equal RRF with the same models does not beat dense on a nine-zip BEIR macro-average (0.479 vs. 0.519 nDCG@10). Repeating the same train-then-freeze sweep independently on all 20 indexed units beats equal RRF on 20/20 and dense on 16/20 (unit-mean nDCG@10 0.467 vs. 0.462 dense vs. 0.420 RRF). Other corpora should reuse the ranges, not a copy of the SciFact point.

We construct a family of finite local rings whose annihilating-ideal graphs are naturally described by orthogonality of subspaces of $\mathbb{F}_2^n$. For $n=4$ we determine the clique and chromatic numbers exactly and obtain \[ \omega(\AG(R_4))=5<6=\chi(\AG(R_4)). \] Thus $\AG(R_4)$ is not weakly perfect, and the Behboodi–Rakeei conjecture fails for non-reduced commutative rings.

Quantum entanglement is a crucial resource in quantum information processing, yet its efficient, scalable and robust classification in multipartite systems remains theoretically challenging. Although supervised machinelearning has been applied to this task, most existing methods still suffer from high measurement costs, computational consumption, and weak noise robustness. In this work, by incorporating multipartite uncertainty relations as prior guidance, we propose a neural network approach to classify distinct Stochastic Local Operations and Classical Communication (SLOCC) multipartite entanglement classes based on states sampled from their local unitary (LU) orbits. Compared with traditional techniques, our method reduces experimental measurement-resource requirements and computational overhead, showing high adaptability to large-scale systems. The classification accuracy of our method reaches 99.5% in 20-qubit systems. The numerical validation is performed on states generated by random LU transformations, which preserve the SLOCC class. Within this setting, the proposed method offers strong effectiveness, scalability, and robustness for multipartite entanglement classification.

The IEEE BigData Cup benchmark combines three prediction problems with different output structures: ordinal suicide-risk classification, multi-label psychosocial factor detection, and extraction of supporting phrases. We introduce heterogeneous readout decomposition (HRD), which separates semantic verification from output realization. A locally deployed Qwen3.8-27B model, adapted with task-specific QLoRA adapters, produces both answer-token margins and layer-63 answer states for card-conditioned queries. HRD compares four latent scores for ordinal risk, retains token margins for most factors while routing seven labels through one shared latent probe, and constructs evidence sets from verbatim span candidates with calibrated, risk-conditional constraints. On two held-out user-grouped confirmation folds, the latent risk readout improves weighted F1 from 0.8237 to 0.8372 and macro F1 from 0.7965 to 0.8185. Selective factor routing improves macro F1 by 0.0105 and tail-label macro F1 by 0.0189; in contrast, global latent replacement and independent label-specific probes fail. The constrained evidence decoder raises pooled phrase F1 from 0.7488 to 0.7609 in row-level out-of-fold evaluation. Lenormand's best public result is 0.8052 on Subtask 1 and 0.6636 on Subtask 2, giving a composite score of 0.7627. These results identify the answer-token boundary, rather than semantic representation alone, as a measurable source of error in this benchmark.

Ozaki proved that every finite $p$-group occurs as the Galois group of a maximal unramified $p$-extension of a number field. Hajir, Maire and Ramakrishna made this theorem effective, obtaining a base-field degree of order $|G|$. In this article, we reduce that degree by taking the Frattini structure of $G$ into account. More precisely, for an odd prime $p$ and a finite $p$-group $G$ of order $p^n$, we prove \[ \tau_p(G) \leq p^{\ell_\Phi(G)+ \left\lceil\log_p\left(\binom{n+2}{2}+1\right)\right\rceil}. \] Here $\tau_p(G)$ is the least degree of a number field realizing $G$ as its $p$-class tower group, and $\ell_\Phi(G)$ is the iterated Frattini length of $G$. Thus, for groups of bounded Frattini length, the order-scale bound $p^n$ is replaced by the quadratic bound $O_p(n^2)$. For $E_m=(\Z/p\Z)^m$, we further prove the sharp estimate $\tau_p(E_m)\asymp_p m^2$.

Large Language Models (LLMs) have shown remarkable potential in Verilog code generation, yet existing datasets contain con siderable noise and redundancy. Prior data selection methods address only isolated quality aspects, neglect the global diversity of the training set, and cannot capture Verilog-specific structural semantics. To bridge this gap, we propose VeriSelector, the first data selection framework for Verilog code generation that jointly optimizes quality and diversity. We formulate the selec tion problem as a constrained bi-objective subset selection problem and solve it via a three-stage approximation. For quality, a multi-granularity pipeline first verifies functional correctness through testbench simulation and then filters misaligned samples via Instruction-Following Difficulty (IFD) scoring. For diversity, 109-dimensional Verilog-specific structural features (AST, CFG, and Netlist) are fused with textual embeddings for clustering-based diversity modeling. A proportional adaptive sampling strat egy then allocates per-cluster quotas guided by IFD ranks, with a provable distribution preservation guarantee. Experiments on three LLMs and three benchmarks show that VeriSelector outperforms full-dataset training and state-of-the-art baselines us ing only 20%-25% of the data, achieving Performance Retention Rates above 118% and reducing training time by over 80%. Notably, VeriSelector improves average Pass@1 by 18.49%-29.43% over full-dataset training and by 1.36%-7.95% over the best-performing baseline across all evaluated models.

We give a negative answer to Problem 17.39 of the Kourovka Notebook. For every odd prime power $q$ and every $m\geq1$, we construct a finite metabelian group $G_{m,q}$ with $Z_\infty(G_{m,q})=1$ and $|\Phi(G_{m,q})|=q$ for which the least number of system normalizers with trivial intersection is $m+1$. Thus the number is unbounded even when the order of the Frattini subgroup is fixed.

This paper investigates the $c$-differential uniformity of power functions over finite fields, an important class of cryptographic functions with favorable differential properties. Specifically, for finite fields $\mathbb{F}_q$ satisfying $q-1=en$ with $e\ge 3$ and $e\mid n$, we prove that there exists $c\in\mathbb{F}_q\setminus\{0,1,\epsilon,\dots,\epsilon^{e-1}\}$, where $\epsilon$ is an $e$-th primitive root of unity in $\mathbb{F}_q^*$, the constructed power functions $f(x)=x^{ln+1}$ with $1\le l\le e-1$ and $\gcd(l,e)=1$ satisfy the upper bound $\Delta(f,c)\le e$, provided that certain cyclotomic conditions hold. We show that our conditions are mild; namely, such power functions can be constructed over infinitely many extension fields $\mathbb{F}_q$ of $\mathbb{F}_p$ for any given $e\ge 3$ and prime $p$ with $p\nmid e$. Furthermore, based on the Weil bound for multiplicative character sums, we prove that the obtained upper bound is tight for sufficiently large $q$, demonstrating the optimality of our results. We also analyze the special case $c=-1$ and derive simplified explicit conditions. In particular, we explicitly characterize the admissible parameters for the case $e=3$ and present concrete function examples for practical validation.

Generative world-action models (WAMs) jointly generate future video and vehicle actions, while their action branches remain primarily optimized by expert imitation. Yet imitation provides no explicit closed-loop geometric verdict for generated trajectories, making verification important during both training and deployment. Closed-loop evaluators can check collision and drivable-area violations, but require privileged scene state unavailable at deployment. Existing approaches often close this gap by learning a verifier from sensor features. For these geometric checks, the rule itself is explicit. For example, collision is determined by whether the rolled-out ego footprint overlaps occupied vehicle space. What is unavailable at deployment is the scene state needed to apply the rule. We introduce DriveReferee, which uses a learned geometry readout to predict the scene representation from camera observations and executes the geometric safety rule directly rather than learning it. The resulting analytic referee evaluates collision and drivable-area safety from a scene state and candidate trajectory. During training, it scores self-sampled trajectories on ground-truth state and distills the resulting preferences into the WAM policy. At deployment, the same referee evaluates generated trajectories on this predicted state and selects a safer alternative when needed. The analytic referee requires no verdict-specific training, and its decisions follow an explicit geometric rule. Under matched candidates and inference budgets, it matches or outperforms all learned-verifier and heuristic baselines. Given the same predicted state and trajectory, learning the verdict provides no measurable downstream gain despite requiring tens of thousands of evaluator-labeled training examples. On the full NAVSIM navtest, DriveReferee reaches 92.02 PDMS with single-camera visual input and no external training data.

We study randomized experiments involving two interacting populations, such as buyers and sellers in a marketplace. In the two-sided experiments we consider, we randomize the two populations separately and independently. For a pair consisting of one member from each population, the two assignments jointly determine one of four exposure conditions. Under a local interference assumption, we consider a broad class of linear estimands, including total, interaction, and buyer- and seller-side spillover effects. Our first main result establishes that researchers can estimate these effects using ordinary least squares and conduct asymptotically valid design-based inference using the conventional two-way cluster-robust variance estimator, clustered at the buyers' and sellers' levels. Our second main result develops a sharper variance estimator for a single linear estimand that better preserves dependence within the buyer and seller dimensions and is asymptotically less conservative than the two-way clustered estimator and existing alternatives. Our third main result establishes the theory for covariate adjustment and recommends a two-way analysis-of-variance-type covariate representation to ensure efficiency gains.

Purpose: A vertebra at the lumbosacral junction is named by counting caudally from C2 on whole-spine imaging, but a lumbar case is planned on lumbar-only imaging (T12 to S1), without C2. Abdominopelvic CT holds that span plus the lowest ribs and pelvis. Where a lumbosacral transitional vertebra (LSTV) alters the count, the local anatomy is ambiguous: four rib-free vertebrae may be an L1 with a lumbar rib or an L5 assimilated to the sacrum, and six may be a sixth lumbar vertebra, a T12 with aplastic ribs, or a lumbarized S1. CTSpinoPelvic1K asks whether local morphology resolves it without the count. CTSpine1K's vertebrae and CTPelvic1K's pelvis covered these patients but were never joined; this release joins them on one series and adds the bones neither had. It provides 802 CT records with per-level ribs and femora, levels anchored on the lowest rib-bearing vertebra and S1, and classes for L6, T13, a separate S1 and lumbar ribs, so anomalies are recorded as such. Acquisition and Validation Methods: Records pair CTSpine1K and CTPelvic1K labels on each patient's bone-richest series under a VerSe-native scheme. Validation covered geometric invariants (802/802 pass), rib-vertebra incidence across 5,749 ribs (0.035% offset), and spinopelvic measures matching published values. Data Format and Usage Notes: NIfTI image/label pairs with patient-grouped LSTV-stratified five-fold splits and a loader; archived at https://doi.org/10.5281/zenodo.22139642. Potential Applications: Classifying a vertebra from local features; updating cadaveric morphometry; spinopelvic assessment; opportunistic screening; and, absent a public preoperative lumbar cohort, surgical planning research (377 records prone). Limitations: thoracic ground truth is field-of-view limited; postural angles supine; no held-out test set; ribs are triaged-review pseudolabels; Castellvi grades two-reader consensus on 33 records.

Motivated by the work of M. L. Lapidus and M. van Frankenhuisjen on fractal explicit formulas for generalized fractal strings, we develop in this paper a distributional fractal Taylor's formula with error term and an exact distributional fractal Taylor series representation for generalized fractal strings. The explicit formulas that the aforementioned authors developed provide a way of expressing a generalized fractal string $\eta$ in terms of the underlying fractal complex dimensions, under suitable growth assumptions on its geometric zeta function, $\zeta_{\eta}$, known as the languidity assumptions. This involves a sum indexed by the complex dimensions of the generalized fractal string, summing over all residues of $\zeta_{\eta}$, multiplied by the Mellin transform of a tempered or Schwartz test function $\phi$, denoted by $\widetilde{\phi}$. Under languidity assumptions, there is an error term present. Under stronger assumptions, that is, in the case of strong languidity, no error term is present and the resulting fractal explicit formula is said to be exact. In this paper, we express the residue term in the fractional distributional explicit formulas as the fractional $(-\omega)^{\mathrm{th}}$-ordered distributional derivative of the Dirac $\delta$ distribution, denoted by $Y_{\omega}$, applied to modified test functions of the form $\phi(x) \ln^{k-1}(x)$, where $k$ runs from $1$ to the multiplicity of the pole $\omega$ of $\zeta_{\eta}$. The coefficients in this sum are written in terms of the coefficients in the principal part of the Laurent expansion at $\omega$ of the geometric zeta function $\zeta_{\eta}$, multiplied by the gamma function evaluated at $\omega$. The results obtained in this paper contribute to the broader program of characterizing fractals in terms of fractal Taylor series expansions involving their underlying fractal complex dimensions.

While the gravothermal collapse of self-interacting dark matter (SIDM) halos provides a compelling mechanism for seeding supermassive black holes (BHs), the post-collapse macroscopic co-evolution of the BH and its host halo remains largely unexplored. In this paper, we introduce a novel N-body framework to dynamically model the dark matter accretion onto the central BH. By bracketing the accretion rate with two complementary phenomenological schemes—a `multi-round core-collapse' scenario and a `continuous accretion' scenario—we establish bounds on the BH mass growth trajectory. We find that the BH mass reaches $5\%-12\%$ of the total halo mass within $\lesssim2$ Gyr post-collapse. Concurrently, this sustained mass depletion drives a `gravothermal supply chain' that forces outer dark matter inward, severely depleting the inner halo density ($\lesssim 2r_s$). This unique structural imprint qualitatively matches the recently detected anomaly in the strong lens JVAS B1938+666 (detection V), where the best-fit lens model consists of an unresolved central point mass and a shallow, uniform-surface-density extended disk, offering a distinct observational signature for SIDM-seeded BHs.

A (coarse) correlated equilibrium (CE) is information-value-free (IVF) if a player can match the payoff obtained from recommendations by committing to a fixed action. Motivated by the problem of regulating algorithmic collusion, this refinement was introduced by Hartline, Wang, and Zhang [EC'26], who showed that it can be computed in polynomial time in explicitly represented normal-form game. In this paper, we examine the complexity of IVF(C)CEs in succinct games, which model more realistic strategic interactions that feature either many players or exponentially many pure strategies. We first show that computing an information-value-free CE is PPAD-complete in many-player polymatrix games or two-player Bayesian games, even when the approximation is a constant. We also prove an unconditional exponential query lower bound. Our results establish that IVFCEs are intractable, even in the centralized model, and rule out the existence of any efficient learning dynamics. This significantly strengthens the impossibility result of Hartline, Wang, and Zhang, which concerns a particular class of learning algorithms, and furnishes strong computational critiques of recent regulation on algorithmic collusion. To sidestep these hardness results, we examine the complexity of information-value-free CCE. Certain no-regret algorithms—such as regret matching or FTRL—provide a fully polynomial-time approximation scheme (FPTAS) for this problem. The complexity when the approximation is exponentially small turns out to be nuanced. On the one hand, leveraging no-regret dynamics, we establish membership in $\text{CLS} = \text{PPAD} \cap \text{PLS}$. On the other hand, we show that it is at least as hard as the P-matrix linear complementarity problem, and hence as hard as simple stochastic games. This shows that even IVFCCEs are unlikely to admit a polynomial-time algorithm barring a major breakthrough.

To meet the increasing demands for high data rates and large capacity, next generation wireless communication systems require transceivers equipped with a large number of antennas. Massive multiple-input multiple-output (MIMO) with metasurface antennas has emerged as a promising solution. In this paper, we investigate the channel estimation problem for the emerging reconfigurable intelligent metasurface antenna (RIMSA) array systems. Specifically, we develop a two-stage refinement (TSR) channel estimation method based on the compressed sensing (CS) principle. In the first stage, we exploit the antenna structure of RIMSA to receive pilots by setting identical phase response vectors across all RIMSAs. In this manner, the coherence of the measurement matrix under the CS framework is reduced and the channel estimation performance is improved. However, this special design introduces channel direction-of-arrival (DoA) estimation ambiguity and yields an ambiguous candidate DoA set. In the second stage, we optimize the phase responses of the metamaterial elements to resolve the ambiguity and accurately estimate the DoAs and channel coefficients. Overall, the estimation accuracy is improved in the first stage at the cost of ambiguity, and this ambiguity is eliminated in the second stage. We illustrate the performance advantages of the TSR method by presenting the numerical results and comparing it with the existing methods.