Papers

With the launch of the Imaging X-ray Polarimeter Explorer in 2021, recent observations have provided X-ray polarization data for several rotation-powered pulsars. To fully exploit these data, it is important to better understand the relationship between polarization properties and the magnetospheric structure. In this paper, we investigate polarization properties in the outer gap model, incorporating both outward emission and inward emission toward the rotation axis, which has not been considered previously. We find that the polarization position angle varies at the intensity peaks, typically accompanied by a high polarization degree, as is in the case for outward emission. Moreover, the variation in the polarization position angle tends to exceed 50 degrees when the intensity peaks of outward and inward emissions overlap, compared to cases with only outward emission. We compare the polarization model including inward emission with IXPE observations. For example, for PSR B1509-58 where inward emission is proposed to be dominant in the outer gap model, we find that observed PA swing prefers a line of sight from the southern hemisphere rather than the northern hemisphere.

Recent innovations in deep learning have significantly enhanced the diagnosis of medical images, although they are based on the use of centralized data storage that pose severe threats to patient privacy and medical data security. To address this issue, this research proposes a Federated Learning (FL) model that is coupled with an optimized YOLOv8 network to detect the kidney stones on a computed tomography (CT) image and at the same time, protect privacy of the patients. The suggested system can help various medical organizations to jointly train a common model without exchanging the information about the patients. This is to ensure that data protection laws like GDPR and HIPAA are adhered to. The residual feature fusion and DropBlock regularization among other architectural improvements are also included in YOLOv8 to enhance detection robustness and minimize overfitting. Experimental analysis carried out on a distributed CT dataset demonstrated that the federated YOLOv8 model has a mAP at 50 of 0.733 and is able to keep the data confidential. Moreover, its lean design facilitates fast edge deployment and real-time inference across a clinical setting. Altogether, these findings indicate that Federated Learning is a safe and efficient solution to AI-assisted diagnosis in contemporary healthcare when combined with the use of sophisticated object detection models.

Locally commuting multiple radial Schramm-Loewner evolutions ($\mathrm{SLE}_{\kappa}$) are encoded by partition functions satisfying the radial Belavin-Polyakov-Zamolodchikov (BPZ) equations and a conformal Ward identity with spectral parameters $\lambda,\nu\in\mathbb{R}$. For $\kappa>0$ and $\lambda\in\mathbb{R}$, we show that the solution space of the radial BPZ system has dimension $2^n$, where $n$ is the number of variables. We then determine all admissible Ward parameters $\nu$ and the exact dimensions of the subspaces selected by the conformal Ward identity, covering both generic and degenerate cases. The classification reveals a parity difference: nonzero rotation-invariant solutions exist for every $\lambda$ when $n$ is even, but only at finitely many exceptional values when $n$ is odd. When $0<\kappa\leq4$, $\lambda>0$ for odd $n$ or $\lambda>-3/2$ for even $n$, we construct a basis of positive solutions using multiple SLE, providing global realizations of the locally commuting SLEs. At $\kappa=4$, we identify a family of explicit solutions as partition functions for level lines of a Gaussian free field with suitable boundary data and interior singularities.

Local asymptotic minimax (LAM) risk is a foundational efficiency criterion in statistics and econometrics. The literature uses two definitions of LAM risk: one which appears in classical lower bounds and another which appears in arguments establishing attainment of those bounds. Conventional efficiency arguments are consistent with any estimator-dependent weighted average of the two, and consequently do not reveal which of these generalized $\alpha$-LAM risk indices describes researchers' actual preferences. We take a decision-theoretic approach to systematically resolve this ambiguity. We axiomatically characterize the set of preferences with a generalized $\alpha$-LAM representation, and we document that such preferences may violate basic rationality requirements such as Monotonicity. Motivated by this, we axiomatically characterize the subset with constant-weight representations. Within this class, a Sample Uncertainty Aversion axiom uniquely selects attainment LAM. We argue that Sample Uncertainty Aversion is normatively appealing, and we therefore recommend attainment LAM as the functional form for LAM risk.

Flow state, characterized by deep engagement and immersion during challenging activities, represents a valuable mental state with significant implications for learning, performance, and rehabilitation outcomes. While flow has been extensively studied behaviorally, objective neurophysiological detection methods suitable for real-world deployment remain limited. Electroencephalography (EEG) offers a promising avenue for flow detection due to its accessibility, portability, and superior temporal resolution; however, the utility of consumer-grade EEG devices for robust, and subject independent flow classification has been insufficiently explored. This study validates entropy-based biomarkers for flow state detection using two wearable EEG headsets, Muse-S and Emotiv Insight, across 45 participants performing adaptive Tetris gameplay. After denoising, we applied the Discrete Wavelet Transform (DWT) to decompose the signals into multiple frequency sub-bands. From each sub-band, entropy-based features, combining channel-wise measures (Slope Entropy, Distribution Entropy, Spectral Entropy) with cross-channel descriptors (Cross Distribution Entropy, Cross Spectral Entropy) were extracted. These features were then used as input to a Random Forest classifier (RF), evaluated with two validation schemes: Random Sampling (RS) and Leave-One-Subject-Out (LOSO). Under random sampling cross-validation, Random Forest classifiers achieved 97% mean accuracy; under the more rigorous leave-one-subject-out (LOSO) scheme, average accuracy reached 75%, demonstrating genuine cross-subject generalizability. Comprehensive multi-classifier validation (SVM-RBF, GentleBoost, k-NN, Fitted Discriminant, Naive Bayes) confirmed that entropy biomarkers are robust across diverse modeling frameworks.

This paper proposes a phonemically comprehensive, ASCII-only romanization scheme for Thai and Lao, treating the two closely related languages as a unified cross-lingual design problem. The scheme represents segmental contrasts, vowel length, and lexical tone while maintaining one-symbol-one-phoneme transparency and systematic correspondence between Thai and Lao. The scheme prioritizes synchronic phonetic correspondence, including correspondence with Pinyin and Jyutping where applicable, while preserving historical-phonological correspondence where it does not conflict with phonetic transparency. Tone uses a compact single-digit default notation, supplemented by optional tone-value and historical tone-category representations. The resulting scheme provides a readable, keyboard-friendly, and machine-processable phonemic representation for language learning and cross-lingual speech processing.

SMT solvers are essential in various domains, including program verification and synthesis. Although their correctness and performance have been extensively studied, performance testing for the floating-point theory remains limited, particularly for real-world queries. We propose a metamorphic testing approach that uses semantics-preserving rewrite rules, focusing on floating-point special values and peep-hole optimizations, to uncover meaningful performance issues in SMT solvers' handling of floating-point formulas. Using real-world test inputs, our approach is able to identify for every solver tested SMT queries for which solving time increases when the queries are simplified; we see slowdowns of up to 33.4x for Z3, 5.6x for MathSAT, 4.5x for cvc5, and 1.8x for Bitwuzla. We further observe that the approach is less successful when using input files that were randomly generated from a grammar.

Circulant digraphs form a prominent class of Cayley digraphs defined on finite cyclic groups. Building on the existing classification of $2$-arc-transitive circulant graphs, this paper presents a complete classification of $2$-distance-transitive circulant digraphs. Our main theorem establishes that every connected $2$-distance-transitive circulant digraph is isomorphic to one of the following: the undirected cycle $C_n$, the complete bipartite graph $\K_{\frac{n}{2},\frac{n}{2}}$, the complete multipartite graph $\K_{m[b]}$ with $m\geq 3,b\geq 2$, the graph $\K_{\frac{n}{2},\frac{n}{2}}-\frac{n}{2}\K_2$ for odd $\frac{n}{2}$, prime-order Paley graphs, the directed cycle $\overrightarrow{C}_n$, the oriented graph \(G(p^m,r)\) satisfying Condition~\ref{p-power-normal-2dt-cond}, the oriented graph \( C_r(b,1)\) with $r\geq 3,b\geq 2$ and $rb=n$, the lexicographic product oriented graph \( G(p^m,r)[\overline{\K}_d]\) where \(G(p^m,r)\) obeys Condition~\ref{p-power-normal-2dt-cond}.

We investigate the relationship between weak asymptotic symmetry ($\mathrm{WAS}$) and asymptotic symmetry ($\mathrm{AS}$) for quasisymmetric maps associated with planar quasilines. To this end, we introduce a formally weaker condition, called equidistant weak asymptotic symmetry ($\mathrm{EWAS}$), and prove that, for quasisymmetric embeddings of $\mathbb{R}$ into $\mathbb{C}$, the three conditions $\mathrm{AS}$, $\mathrm{WAS}$, and $\mathrm{EWAS}$ are equivalent. We then establish that $\mathrm{WAS}$ implies $\mathrm{AS}$ for quasisymmetric homeomorphisms from an arbitrary quasiline onto $\mathbb{R}$. More generally, if $h\colon\Gamma_1\to\Gamma_2$ is a quasisymmetric homeomorphism between quasilines and $\Gamma_1$ is asymptotically conformal, then $\mathrm{WAS}$ implies $\mathrm{AS}$. A formally dual statement holds when $\Gamma_2$ is asymptotically conformal, provided that $h$ is uniformly continuous. In the compact setting of bounded quasicircles, these results yield an answer to the $\mathrm{WAS}$-$\mathrm{AS}$ problem posed by Brania and Yang.

We use a kinematical model including circular rotation of the Milky-Way disk incorporating effects produced by a spiral density wave with constant radial and vertical components of the velocity dispersion tensor and adopted solar Galactocentric distance R_0=8.277kpc (inferred by GRAVITY collaboration in 2022) to derive the velocity field parameters for a sample of 2384 open clusters from the Hunt and Reffert (2024) catalog having ages no greater than 100 Myr almost all of which reside at Galactoaxial distances between 5 and 14 kpc. We estimate the velocity-field parameters using maximum-likelyhood method and the affine-invariant variant of the Markov chain Monte-Carlo method proposed by Goodman and Weare (2010) with both methods yieilding almost identical parameter values. The inferred rotation curve, on the whole, is consistent with the results based on our kinematical analysis of a sample of Galactic masers. We find the linear rotation velocity at the solar distance to be V=242.3+/-1.1~km/s; it reaches its maximum V~244 km/s at Galactoaxial distance of about R_g~7 kpc followed by a slow and smooth decline with V~227 km/s at R_g=14 kpc. The inferred radial and vertical components of the velocity dispersion tensor are (sigma U_0, sigma W_0)~(10.63+/-0.15, 4.56+/-0.15) km/s. We find the pitch angle and the phase of the Sun for a four-armed spiral pattern to be i~-11.7+/-0.3 degrees and chi_0~138+/-5 degrees, respectively, and the amplitudes of radial and tangential perturbations, f_R=-3.0+/-0.4 and f_{theta}=-3.1+/-0.4 km/s, respectively.

Talagrand asked whether the Rademacher cotype of an operator is universally controlled by the maximum of its Gaussian cotype and its $(q,1)$-summing norm. We give a negative answer already for $q=2$. The counterexample was discovered by ChatGPT (GPT-5.6).

Accurate estimation of left ventricular ejection fraction (EF) from echocardiography is central to cardiovascular care, and deep learning enables automated EF prediction from echocardiographic video. Because EF is clinically derived from left-ventricular (LV) volumes, a widely held intuition is that explicit LV segmentation should improve prediction. We introduce a quantitative criterion, the segmentation ceiling, that makes this testable: from EF as a normalized difference of end-diastolic and end-systolic volumes, we derive in closed form how per-frame segmentation area error propagates into EF error, and thus the accuracy a mask must reach before it can improve on direct regression. Using EchoNet-Dynamic, a UniFormer-S backbone, and the empirically measured within-patient error correlation, the criterion places the break-even near 10% per-frame area error, whereas a representative segmenter operates at roughly 14%, above the ceiling. Consistent with this, four strategies for injecting segmentation or area information (a predicted-mask channel, end-diastolic/end-systolic clip sampling, and per-bin and amplitude area-consistency objectives) fail to beat a raw-video baseline; ground-truth masks help only through label leakage. Input representation thus not being the limit, we identify generalization as the practical lever: weight averaging with strong augmentation attains a test R^2 of 0.806 (MAE 4.08) under a matched dense-clip protocol, comparable to an R(2+1)D baseline (0.811) while tightening the validation-to-test gap. Finally, a heteroscedastic beta-NLL formulation yields informative, well-calibrated per-prediction uncertainty, larger for clinically harder low-EF cases, where Monte-Carlo dropout does not. The segmentation ceiling gives a concrete design criterion for when mask-guided EF estimation is worthwhile, plus a simple, uncertainty-aware recipe for EF regression.

Autoregressive (AR) video generation degrades over long horizons due to an overlooked train-inference discrepancy we term KV eviction mismatch: models train on short clips where all context frames reside in the KV cache, but at inference, memory constraints force distant frames to be evicted from the KV cache - removing context the model was conditioned on. Rather than simulating eviction via context truncation - which discards temporal information the model still needs and degrades motion coherence - we keep the context but while progressively reducing the influence of distant frames, making their eventual eviction negligible. To guide this design, we introduce the positional response $R( \Delta, \, t_{\text{denoise}})$, a perturbation-based sensitivity measure revealing that context influence decays steeply with temporal distance and varies systematically across denoising steps. Motivated by this analysis, we propose Recency Forcing, which applies a non-positive, timestep-dependent bias, termed Temporal Response Bias (TRB), on pre-softmax attention logits derived directly from $R$, closing the train-inference gap without modifying context length or training objectives. We further introduce Biased Attention Reparameterization (BAR), an exact reformulation that moves the bias outside the softmax, making TRB a standard FlashAttention call at zero overhead. Recency Forcing operates in both training-free mode and training-based mode. Experiments on VBench and VBench-Long demonstrate state-of-the-art long-horizon generation quality at no additional inference cost.

We prove that a path maximizes the expected range of a uniformly chosen graph homomorphism into the integers, with one vertex pinned at zero, among all connected bipartite graphs of the same order. This establishes the expectation form of the Benjamini–Häggström–Mossel conjecture. The proof restricts and rescales a homomorphism on each bipartition class, then contracts the edges on which the resulting height function is constant. A quantitative estimate for the rank of these zero edges compensates for a parity term in the expected range of a simple random walk, allowing an induction on the number of vertices. We then prove that the BHM inequality implies the Loebl–Ne\v set\v ril–Reed inequality for uniformly chosen integer 1-Lipschitz functions on arbitrary connected graphs, and hence obtain the LNR conjecture as a corollary of BHM. The proof was obtained through interaction with OpenAI GPT-6 Astra and verified by the author. The main results have also been formalized and checked in Lean~4.

Injection of pure spin current into superconductors remains a major challenge in superconducting spintronics. Previous studies have primarily focused on spin-polarized quasiparticles and spin-triplet supercurrents, while vortices, ubiquitous topological defects in type-2 superconductors, have been theoretically proposed as alternative carriers of spin angular momentum, yet direct experimental evidence is still lacking. Here, we report the vortex-mediated spin current injection in NbSe2/LiAl2Fe3O8(LAFO) bilayer, an Ising superconductor/ferrimagnetic insulator heterostructure. Under an out-of-plane temperature gradient and an in-plane magnetic field, the NbSe2/LAFO bilayer shows a pronounced thermoelectric peak near the upper critical magnetic field, which has the opposite sign to the conventional vortex Nernst signal observed in a single-layer NbSe2. The sign reversal suggests that the vortex flow induced by spin current injection is opposite to the flow driven by the temperature gradient, which is consistent with theoretical mechanisms including spin-vorticity transmutation and the inverse vortex spin Hall effect. By mapping the field temperature phase diagram, we reveal that the spin current injection occurs exclusively in the vortex liquid phase of NbSe2. Absence of the thermoelectric signal above the superconducting transition temperature further rules out the quasiparticle contribution. Our results establish vortices as efficient carriers of spin information in superconductors, opening a new route towards vortex-mediated superconducting spintronic devices.

The existing singularity-free guiding vector field (SF-GVF) with an additional virtual coordinate can eliminate singular points (i.e., points where the vector field vanishes) inherent in conventional GVFs and guarantee global convergence of robot trajectories to closed and self-intersecting desired paths. However, the desired speed given by the GVF along the desired path in the original lower-dimensional space cannot be arbitrarily specified but depends on path parameterizations. One possible workaround is to partially normalize the physical projection of the SF-GVF and assign a user-designed speed. However, we show that this workaround may introduce new singularities since the normalization denominator can become zero. To address this issue, we propose a new SF-GVF with prescribed physical speed (PPS). The integral curves of the new SF-GVF converge exponentially to the desired path from any initial condition in the higher-dimensional space (including virtual dimension); more importantly, the robot's physical speed converges to the PPS, while the path-error dynamics remain invariant under regular reparameterizations of the desired path. We further develop a saturated acceleration control law for second-order kinematic models. Finally, comparative simulations and 3D path-following experiments with a quadrotor under different PPS profiles validate the theoretical results and demonstrate the effectiveness of the proposed approach.

Let $\mu$ be a finite positive Borel measure on $[0,1)$ and let $\gamma>0$. We establish sharp mapping criteria for the generalized Cesàro operator \begin{equation*} \mathcal C_{\mu,\gamma}f(z) =\sum_{n=0}^\infty \mu_n \left(\sum_{k=0}^n \frac{\Gamma(n-k+\gamma)}{\Gamma(\gamma)(n-k)!}a_k\right)z^n,\qquad z\in \mathbb{D},\end{equation*} between Hardy spaces, including the source and target $H^\infty$ endpoints. For $0<p<q<\infty$, for $0<p=q<1$, and for $0<p\le1$ with $q=\infty$, the boundedness of $ \mathcal C_{\mu,\gamma}: H^p \to H^q$ is equivalent to $\mu$ being a $(\gamma+1/p-1/q)$-Carleson measure, without further restrictions on $\gamma$. For $1\le q<p\le\infty$, set $1/r=1/q-1/p$. In this range, boundedness and compactness are equivalent to \[ \int_0^1 \left(\frac{\mu([t,1))}{(1-t)^{\gamma-1/r}}\right)^r \frac{dt}{1-t}<\infty. \] This condition is also equivalent to $F_{\mu,\gamma}\in H^r$ and to $\sum_{n\ge0}(n+1)^{r\gamma-2}\mu_n^r<\infty$, where $F_{\mu,\alpha}=\mathcal C_{\mu,\alpha}(1)$ and $\mu_n=\int_{[0,1)}t^n\,d\mu(t)$. For $1<p<\infty$, boundedness and compactness from $H^p$ to $H^\infty$ are characterized by the shifted condition $F_{\mu,\gamma+1}\in H^{p'}$, where $p'=p/(p-1)$. We therefore obtain a complete boundedness classification of the generalized Cesàro operators $\mathcal C_{\mu,\gamma}$ between Hardy spaces $H^p$ and $H^q$ for the full range $0<p,q\le\infty$.

We study a natural way to deform area-preserving maps between compact Riemann surfaces. Specifically, we evolve the metrics on the two Riemann surfaces by the normalized Ricci flow and the graph of the area-preserving map by the mean curvature flow. We prove that the flow exists for all time, remains the graph of an area-preserving map, and converges smoothly and exponentially to a minimal Lagrangian graph with respect to the product of the limiting metrics. This generalizes earlier results of Wang and Smoczyk, in which the Riemann surfaces have constant scalar curvature.

Time-resolved electroluminescence has been a central methodology in the development of LED devices. However, it still lacks quantitative theoretical descriptions of time-resolved electroluminescence. By combining the equivalent circuit models of semiconductor devices and the carrier dynamics of electroluminescence processes, we here developed a Voltage-Current-Emission framework to illustrate time-resolved electroluminescence from the pulse voltage as input, to injection current and finally generate electroluminescence as output. The features of different LED devices can be quantitatively interpreted, confirming the universal applicability across LEDs with different materials and device structures. Importantly, the curves of time-resolved electroluminescence can be simulated to quantitatively describe the dynamics of current and carriers of LED operation. In all, the Voltage-Current-Emission framework offers theoretical guidance for achieving advanced LED devices for AI technology.

Large language models are being integrated into malware triage workflows as reasoning components that summarize static evidence and produce analyst-facing verdicts. This paper shows that the same reasoning capability introduces a new attack surface. We present ALIBI, a semantic cover story attack against frontier LLM-based malware analyzers. ALIBI adds a small, non-executed read-only section to a compiled binary, containing a coherent but false security product narrative, without altering imports or executable behavior. Instead of issuing direct instructions to the model, it reframes suspicious evidence as expected behavior of a benign endpoint security tool. On a frozen PE set of 50 malicious samples, the payload flips 30 of the 35 baseline-malicious samples to benign on Gemini 2.5 Pro, while GPT-5.5 Pro and Claude Opus 4.7 produce substantial severity downgrades with significant confidence reductions even when verdict labels are preserved. The attack transfers to ELF binaries, where Gemini flips 16 of 40. A verification-guided defense prompt roughly halves the benign verdicts, but 42.9 percent of malicious samples still reach benign. LLM malware analyzers therefore require provenance checks that separate verified facts from attacker-controlled claims, not narrative trust.

Clinical coding agents repeatedly encounter the same failure modes, including unsupported codes, missed documented conditions, specificity errors, and procedure-coding convention mismatches. We introduce Learn-Then-Act, an inference-time adaptation framework that converts errors from a small labeled LEARN batch into a structured Mistake Knowledge Database (MistakeKDB). False-negative lessons are routed to a recall-oriented Coder, while false-positive lessons are routed to a precision-oriented Judge. We instantiate the framework in LearnActCoder, a Coder-Judge clinical coding pipeline with lookup-table grounding where available. On 150 matched MIMIC-III notes, structured MistakeKDB improves CPT F1 by 5.9 percentage points, while raw-example and reflection-style memories remain near the no-memory baseline; the ICD-9 improvement is not significant. On a matched MIMIC-IV cohort, memory shifts ICD-10 coding toward higher precision at a recall cost, leaving F1 statistically unchanged. Applying the same memory to 1,000 held-out MIMIC-III notes maintains a stable ICD operating point, providing scale/stability evidence. Overall, the results are consistent with structured, feedback-derived error memory being useful for adapting clinical coding behavior across cases without weight updates or changes to the underlying workflow. Absolute CPT/HCPCS performance remains low, and the system is evaluated retrospectively rather than in clinical deployment.

Containment decisions – where to put a firewall, which links to monitor, what a program may reach – are computed from an observed structure, and observation is a snapshot. We ask what a snapshot misses when the wiring changes over time. On a hypercube whose active dimension rotates, a balanced split shows zero crossing edges at 93% of instants, yet 8,192 edges must be blocked permanently; adding one always-on ring, a defender sees 2 where 8,194 must be blocked, a factor of 4,097. A time-aware defender holds 585 blocks on average, but one step of clock lag drops its containment to 0%. On the real Internet the same gap is only x1.8-2.0 (1997-2000) and x1.5-1.6 (2024-2026) once growth is removed, so the blind spot is introduced by design, not inherited from the world – and it has been designed: the round-robin schedules of optical datacentre fabrics have a gap equal to their period. A declared capability map, checked by static reachability over a real application's call graph, catches all 8 planted holes; the string deny-list previously in place catches 2. One calculation generates every number from one parameter, the period, and reads three boundaries not usually called schedules: frequency hopping, whose standard results are these closed forms with channels in place of edges; the air gap, whose always-on crossing set is empty and whose known breach came at the one phase a snapshot misses; and the tool surface of a coding agent, inventoried from the inside. Turning the cuts on that agent: idle, its instantaneous state cut is zero, while 6 channels carry it across a context reset, none of them the network, so severing the network removes 0. The channel that spawns copies is a branching process with a sharp threshold at approval rate 1/b, below which denial is unnecessary and above which denial is insufficient. Contain by the paths that exist, not by the behaviour that was seen.

Automated visual analysis opens new avenues for behavior–based psychological measurement. Nevertheless, existing technological modules are typically scattered across task specific systems with heterogeneous interfaces and disparate deployment requirements. In this work, we present SeetaPsych v1.0, an open source, unified and extensible computer vision toolkit designed to extract psychologically relevant signals from facial images and/or face based videos. The current release encompasses four major core modules aiming at behavior–based physiological perception: unified face based emotion analysis (simultaneous facial expression recognition, facial action unit detection, and valence–arousal estimation), camera based heart rate estimation, screen point–of–gaze estimation, and scene gaze following. A suite of auxiliary preprocessing modules for human centric visual analysis is also included, comprising face detection, facial landmark detection, and head detection. These functionalities are encapsulated within a modular Pipeline/Runner architecture that automatically resolves attribute dependencies, constructs computation graphs, and support intermediate result sharing among modules. SeetaPsych provides standardized Python APIs to facilitate reproducible, large scale analyses, alongside an interactive WebUI for rapid, code–free method evaluation. Overall, SeetaPsych offers an integrated and accessible visual measurement platform for research in psychology, behavioral science, human computer interaction, and related fields.

Matrix graphical models aim to characterize conditional dependence structures in matrix-variate data under a separable covariance assumption. In this framework, the precision matrix is decomposed as a Kronecker product, enabling separate modeling of undirected graphs across row and column domains. Existing methods have been developed for this problem, including likelihood-based approaches and regression-based procedures for graph estimation. Likelihood-based methods estimate precision matrices directly and recover graph structures indirectly, whereas regression-based approaches directly target estimating edges among variables, thus outperforming the former. However, existing regression-based methods are based on multiple penalized regression problems, which naturally yields asymmetry in estimated graphs and computational difficulty in selecting tuning parameters. To address the limitations, we propose a joint estimation of partial correlations in matrix graphical models. The proposed method estimates all partial correlations simultaneously within a unified optimization framework, thereby preserving symmetry and easing the pain of selecting the best models. Numerical studies demonstrate that the proposed method improves graph recovery performance compared to existing approaches. We also analyze protein expression data collected from patients with pulmonary tuberculosis, measured repeatedly at multiple time points, where the proposed method compares protein networks between two groups of patients and recovers the temporal dependence structure.

Large Language Models (LLMs) have achieved remarkable reasoning capabilities by utilizing chain-of-thought (CoT) as a scratchpad for intermediate stages of thinking. However, CoT techniques require explicit supervision on thinking tokens, which requires rich, task-specific data. In this work, we propose Abstract Token Curriculum (ATC), a novel curriculum learning framework that elicits effective continuous intermediate representations without direct supervision or manual scratchpad design. ATC gradually increases problem complexity through a sequence of distributions, training the model to develop internal abstract “thoughts” in the continuous representation space. This paper provides both theoretical and experimental evidence for the benefits of ATC and its advantages over previous methods for training continuous thoughts. Theoretically, we show that for learning parity functions with single-layer softmax attention using ATC, attention naturally focuses on the CoT tokens in the context that provide the “easiest path” to predicting the next token. Experimentally, we show ATC's effectiveness on graph reachability and arithmetic learning tasks.

Pre-trained 3D vision models have substantially advanced point cloud analysis, yet adapting them to downstream tasks via full fine-tuning is computationally expensive and storage-intensive. Parameter-Efficient Fine-Tuning (PEFT) offers a promising alternative by reducing both adaptation cost and storage burden. However, existing prompting-based approaches ignore the intrinsic geometric structures of point clouds, thereby limiting their adaptation capability. This limitation stems from their inability to encode both fine-grained geometric cues and coarse-grained structural semantics, as well as failing to propagate such information effectively through the model hierarchy. To address these challenges, we propose GAPrompt++, a multi-granular geometry-aware prompting method that provides richer geometric guidance for efficient 3D task adaptation. Specifically, we introduce a Point Shift Prompter that extracts multi-granular geometric features across different scales, enabling instance-specific geometric adjustments during adaptation. Next, a Keypoint Prompter adaptively generates point-level prompts to highlight local geometric saliency and fine-grained structural details. Furthermore, a Prompt Propagation mechanism injects these multi-granular geometric cues throughout the feature extraction hierarchy, strengthening the ability to capture essential geometric characteristics. Extensive experiments show that GAPrompt++ achieves state-of-the-art performance among prompting-based PEFT methods and even surpasses full fine-tuning across diverse benchmarks, while requiring less than 2% trainable parameters. In addition, to address the saturation of existing evaluation datasets, we construct two more challenging benchmarks derived from 3D Gaussian Splatting and Multi-View Stereo reconstruction, offering diverse and realistic point cloud scenarios to promote future research.

Building on the point interaction method developed in our previous work, this paper studies inverse eigenvalue problems for regular Sturm-Liouville problems with Dirac weights. More precisely, we explicitly reconstruct the potential of regular Sturm-Liouville problems with the single-point and two-point Dirac weights from the solutions of a class of Cauchy problems which is completely determined by the first eigenvalues of a family of perturbed problems originating from moving point interaction models in quantum mechanics. Finally, the multi-point Dirac weighted case is also discussed.

We give an efficient algorithm with improved algorithmic guarantees for the (offline) Beck–Fiala problem when the sets have bounded size. Let $A$ be an arbitrary matrix $A\in\{0,1\}^{m\times n}$ with at most $d$ ones per column and at most $s$ ones per row. Let $\log^*$ denote the iterated logarithm and $\ell_j$ denote the $j$-fold composition of log. Assume $s\le\exp(O(\sqrt d))$. We provide an efficient algorithm that, for arbitrary sparsity $d$, gives $O(\sqrt d(1+\log^*n))$ discrepancy. Moreover, if $d\ge\ell_j(n)$ for a fixed integer $j\ge1$, the algorithm gives $O_j(\sqrt d)$ discrepancy. The proof is a bootstrapping scheme using the Bansal-Jiang algorithm.

We introduce the notion of a unitary disk-like $n$-category, which is a disk-like $n$-category equipped with a reflection structure and a sphere trace inducing positive-definite pairings. Since a finite unitary disk-like $n$-category is defined to be the local field data of a fully extended $(n+1)$D unitary TQFT, we propose a complete finite unitary disk-like $n$-category as the definition of a finite $(n+1)$-Hilbert space for all $n$. For $n=1$ and $n=2$ we verify this proposal, proving that complete finite unitary disk-like 1- and 2-categories are isometrically equivalent to finite 2- and 3-Hilbert spaces respectively, and that these equivalences are functorial. For $n=1$ we recover a unitary refinement of Schommer-Pries' classification of oriented $(1+1)$D TQFTs in terms of $\mathrm{H}^*$-Morita equivalence classes of $\mathrm{H}^*$-algebras, and for $n=2$ we categorify this to classify oriented $(2+1)$D unitary TQFTs by $\mathrm{H}^*$-Morita equivalence classes of $\mathrm{H}^*$-multifusion categories. Along the way, we investigate fully incomplete 3-Hilbert spaces, prove a strictification result for pivotal dagger 2-categories, and define functors and higher transformations between disk-like $n$-categories.

We study the convergence of the vanilla stochastic policy gradient method applied to the linear quadratic regulator (LQR) problem. The method is cheap in the following sense: (1) at each iteration only $\tilde{O}(1)$ interactions with the environment are needed, therefore allowing frequent policy improvement steps, and (2) to ensure stability throughout and convergence to an $\epsilon$-optimal policy with probability $1-\delta$, only $O(\mathtt{Polylog}(1/\delta)/\epsilon)$ interactions are needed. To the best of our knowledge, this appears to be the first time that a stochastic model-free policy optimization method for LQR converges with high probability with $\tilde{O}(1)$ per-iteration computation and polylogarithmic dependence on the confidence level. The convergence analysis presented here is agnostic to LQR specifics and hence could be potentially generalized to a broader class of problems.