Papers

In this paper, we investigate null geodesics in the spacetime of a Reissner-Nordström black hole pierced by a cosmic string. Analysis of the equations of motion reveals that null geodesics in this conical spacetime can be classified into three main categories, with the classification entirely determined by the ratio $|Q|/M$ (where $Q$ and $M$ denote the black hole charge and mass, respectively). Analytical solutions to the null geodesic equations are obtained for each category. Based on these solutions, we numerically simulate light trajectories and analyze in detail the effects of the black hole charge $Q$ and the cosmic string parameter $\alpha$. It is found that the cosmic string parameter $\alpha$ enhances the winding behavior of null geodesics across all three main categories. Finally, we consider light deflection in the equatorial plane and derive an expression for the deflection angle, revealing that the charge $Q$ decreases the deflection angle, whereas the cosmic string parameter $\alpha$ increases it.

For $r \ge 0$, let $\mathcal P_r=\{\binom{r}{0},\binom{r}{1},\ldots,\binom{r}{\lfloor r/2\rfloor}\}$ be the set of distinct entries in row $r$ of Pascal's triangle. We study the least possible least common multiple of $n$ entries chosen from one row, with the row itself also free: $a(n)=\min_{r\ge0,\ S\subseteq\mathcal P_r,\ |S|=n}\operatorname{lcm}(S)$. Whereas the least common multiple of an entire row is given by a classical identity of Farhi, allowing both the row and the selected coefficients to vary creates a different optimization problem. We first recast the fixed-row problem exactly as a weighted prime-power exclusion problem, which explains how omitting a few coefficients can remove expensive prime-power contributions. Our main asymptotic result is $\log a(n)=2n+O\!\left(n\exp\!\left(-c(\log n)^{3/5}(\log\log n)^{-1/5}\right)\right)$ for some absolute $c>0$, so $a(n)^{1/n}\to e^2$. A two-band refinement further shows that every optimal row satisfies $r_n=2n+O\!\left(n\exp\!\left(-c(\log n)^{3/5}(\log\log n)^{-1/5}\right)\right)$, and that the minimum prefix defect of an optimal support is $o(n)$.

Physics-informed neural networks (PINNs) require coordinated choices across representation, architecture, sampling, constraints, loss construction, and optimization, yet effective configurations can vary substantially across partial differential equations (PDEs). Existing automated design methods search over these choices, but training outcomes are still used primarily to rank candidates rather than to inform subsequent designs. We develop PINNForge, an execution-grounded large language model (LLM)-driven evolutionary framework that treats observed PINN training behavior as a cross-generation design signal. PINNForge initializes diverse configurations from PDE-related prior knowledge, executes them, retains globally strong configurations, and feeds their execution evidence and accumulated run-level experience back to the LLM. The LLM then revises and recombines coupled design components or explores new combinations within a generate–execute–evaluate–evolve loop. Across 25 PDE benchmarks, PINNForge achieves the lowest mean MSE on 24 tasks among RoPINN, PINNsFormer, PINNsAgent, and PINNForge. Removing knowledge guidance, execution feedback, or evolutionary search increases the median task-wise MSE ratio to 3.74$\times$, 12.10$\times$, and 10.10$\times$, respectively, relative to full PINNForge.

We investigate the free boundary propagation of a non-linear degenerate parabolic problem with both fourth and second order non-linearities, which may be used to model viscous thin-film flow in the regime of weak slippage with an additional contributions from a singular disjoining pressure brought forth by inter-molecular forces. By carefully treating the individual scaling behaviors of the non-linearities, we obtain asymptotically optimal upper and lower bounds on the rate of forward support propagation. These rates show that the fourth-order operator dominates the propagation rate on short time scales, but the long-term rate of propagation is controlled by the second-order operator. We estimate further the time at which this trade-off in propagation rate occurs. Lastly, we examine sufficient conditions to ensure that the free boundary does not immediately advance in a given direction, leading to a detailed picture of how the competition between the second/fourth-order operators influence the free boundary dynamics of solutions.

Rooftop photovoltaic (PV) design requires careful panel placement to make effective use of potentially limited roof space and available sunlight. Existing simplified roof models can miss objects and superstructures that shade panels. We simulate rooftop irradiance using hourly weather and a terrain horizon, computing shadows from nearby buildings, trees, and roof superstructures rendered from the Sun's viewpoint. Our method (i) infers existing panel layouts from imagery and estimates their yield, (ii) relocates these panels to improve the yield, and (iii) generates shading-aware layouts for new installations. We compare modeled yield with production records from 11 Swiss installations and evaluate new layouts in simulation on 19 additional rural roofs. Without knowledge of any electrical or system specifications, we obtain a median daily correlation with measured production of 0.982. Absolute energy estimates remain sensitive to system specifications. Comparing new layouts with equal panel counts, accounting for neighborhood and roof-detail shading changes the position or orientation of an average of 38.9% of panels per roof. These layouts increase modeled annual yield by up to 7.91% compared with layouts designed without accounting for neighborhood and roof-detail shadows. We publicly release our tool for modeling and designing rooftop PV installations with terrain, neighborhood, and roof-detail shading at https://github.com/tobiasvonarx/shading-aware-pv.

We determine the exact local precision limits for single-copy estimation of smooth multiparameter quantum statistical models contained in spin factors, a class of matrix Jordan algebras whose state spaces generalize the qubit Bloch ball. At any parameter point where the symmetric logarithmic derivative (SLD) Fisher information is positive definite, we characterize the entire attainable classical Fisher-information region over all finite-outcome positive-operator-valued measurements. After SLD normalization, this region consists exactly of the real symmetric positive semidefinite matrices with trace at most one, independently of the ambient Hilbert-space dimension. This yields a sharp weighted covariance bound for every positive definite weight, attained by an explicit locally unbiased estimator based on randomized spectral measurements of SLD directions. The proof combines a statistics-preserving positive projection onto the spin factor with the two-eigenvalue structure of its effects, revealing the Jordan-algebraic origin of the tradeoff. The result extends the qubit information tradeoff to models with more than three parameters. Since the optimal measurement depends on the unknown parameter, we simulate an adaptive scheme for a five-parameter model on a four-dimensional Hilbert space and observe performance close to the optimal local benchmark.

Soma instance segmentation, i.e., identifying and delineating individual cell somas as distinct instances, is crucial for cellular analysis and connectomic reconstruction. Three-dimensional electron microscopy (3D EM) provides nanometer-scale resolution for capturing fine-grained soma morphology. However, dense instance-level manual annotation is prohibitively costly, limiting the scalability of fully supervised methods. To address this challenge, we propose SomaNet, a weakly supervised framework for 3D EM soma instance segmentation under partial annotation constraints. SomaNet adopts a teacher–student learning paradigm tailored to partial labels. The teacher is trained using partially annotated data to generate pseudo-labels, while the student jointly learns from the partial ground-truth annotations and the generated pseudo-labels, progressively recovering dense instance segmentations. To accurately delineate cell somas under limited supervision with varying instance counts, SomaNet incorporates affinity learning, which encourages high similarity within instances and low similarity across instance boundaries. Semantic-guided affinity decoding and 2D-to-3D reconstruction then produce volumetrically consistent 3D soma instances while preserving the large receptive fields of 2D backbones. The framework is architecture-flexible and supports diverse backbones, including vision transformers and foundation models, enabling direct transfer of pretrained visual representations to volumetric EM segmentation. Experiments on 3D EM brain datasets demonstrate that SomaNet achieves accurate and robust soma instance segmentation across regions with diverse soma morphologies under partial annotation. Code is available at https://github.com/mkhateri/SomaNet.

We prove the uniqueness conjecture of Fomin and Neville for their long mutation cycles in all ranks $n\ge4$. More generally, we show that every nucleus-extension quiver has a unique simple cycle in its labeled mutation graph. These quivers allow an acyclic part of arbitrary size outside the nucleus. Our proof uses three mutation statuses determined by a closed nucleus and the full subquivers obtained by deleting one part of its nucleus decomposition at a time from the ambient quiver. We analyze transitions between these statuses to prove that every mutation leaving the prescribed cycle is performed at an exit.

Automated pollen analysis supports veterinary cytology, but brightfield microscopy is costlier and more complex than lens-less digital in-line holographic microscopy. We evaluate whether reconstructed holograms can narrow this gap and whether model explanations remain reliable under modality change. Six pollen species were imaged by brightfield and holographic microscopy. Raw, single back-propagation and iterative phase retrieval holograms were evaluated with YOLOv26s detection and MobileNetV4 classification after anchor-based annotation transfer. Six attribution methods were assessed for spatial grounding and faithfulness with the Attribution Health Inspection and Repair (AHIR) protocol, which tests model brittleness under weak noise and corrects attribution-map granularity when needed. Brightfield achieved 0.6890 mAP50-95 (0.8865 mAP50) for detection and 0.9687 macro-F1 (0.9705 accuracy) for classification. Reconstructed holograms narrowed the gap with a task-dependent split: p-type was strongest for detection at 0.5324 mAP50-95 (0.8229 mAP50), while r-type was strongest for classification at 0.7695 macro-F1 (0.7866 accuracy), both far above raw-hologram baselines. Activation-based explanations localized strongly on grains, and region-based methods retained ~60 to ~80% of faithfulness under holography. The holographic detector was highly brittle to weak perturbations, saturating deletion-based evaluation while insertion remained informative. Pixel-level gradient explanations approached random floor, yet spatial smoothing restored p-type gradient faithfulness from 0.05 to 0.51. For holographic classification, perturbation-based explanations remained faithful while gradient-based methods fell below random floor. Reconstruction improves low-cost holographic pollen analysis, while AHIR distinguishes genuine attribution failure from artifacts caused by model brittleness and map granularity.

Deep learning models are powerful but opaque. As quantum machine learning matures, the field faces a defining choice: build quantum models that are equally opaque, or exploit the mathematical structure of quantum mechanics to make them inherently interpretable. We show that the latter is possible. By tracking quantum mutual information~(MI), entanglement entropy, and state fidelity through the layers of a Quantum Transformer Block (\qtb{}), a fully-coherent variational circuit with quantum analogues of both attention and feedforward, we gain direct insight into how the model processes information: which tokens it attends to, when correlations form, and why predictions fail. On four tasks with known dependency structure we show that (i)~learned MI matrices align with ground-truth task structure (AUC$\,{=}\,0.69$ on lookup), (ii)~disabling entangling gates collapses accuracy from 100% to 15% while MI$\to 0$, proving entanglement is the mechanism, (iii)~accuracy and MI co-evolve during training ($\rho\,{=}\,0.92$ on lookup), and (iv)~per-sample MI predicts prediction correctness on the conditional task with ROC AUC$\,{=}\,0.84$. All results are validated on IBM Quantum hardware (ibm\_kingston, Heron~r2): the circuit's reasoning process, from product state through structured entanglement, is directly observable on a superconducting processor. These proof-of-concept results, obtained on small synthetic tasks, suggest that the physics of quantum computation can provide intrinsic interpretability signals with no direct classical counterpart, motivating study of whether this advantage persists at scale.

Resolution over parities, $\mathrm{Res}(\oplus)$, is the characteristic-two version of resolution over linear equations: clauses are disjunctions of affine equations over $\mathbb F_2$. Superpolynomial size lower bounds were previously known only for restricted refutations: tree-like, regular, or of bounded depth. We prove that every DAG-like $\mathrm{Res} (\oplus)$ refutation of the bit pigeonhole principle with $n+1$ pigeons and $n=2^\ell$ holes has more than $\exp(n/(32768\ell^2))=2^{\Omega(n/\log^2 n)}$ clauses, for every $\ell\ge32$, with no restriction on regularity or depth. The proof translates an arbitrary refutation with $S$ clauses into a polynomial calculus refutation of degree $O(\log n)$ over $O(S+n^2)$ groups of extension variables in the style of Buss, Impagliazzo, Krajicek, Pudlak, Razborov, and Sgall. One substitution then removes all extension variables at once and leaves a nonzero low-degree polynomial derived from the pigeonhole axioms alone at degree at most $n/2$; a degree lower bound in the style of Razborov, proved through the homology of chessboard complexes, shows that no such derivation exists. The argument also yields a general sufficient condition for $\mathrm{Res}(\oplus)$ size lower bounds. The main theorem, this condition, and all their dependencies are formalized in Lean 4, and every statement links to its formal proof. The proof was developed with substantial AI assistance within an open research framework described in the final section.

We investigate the equilibrium structure of electrically charged quark stars within the framework of energy-momentum-squared gravity (EMSG), adopting a unified interacting quark-matter equation of state that incorporates perturbative QCD corrections, color superconductivity, and finite-strange-quark-mass effects. By solving the modified Tolman-Oppenheimer-Volkoff equations over a broad range of EMSG coupling strengths and interaction parameters, we show that the inclusion of electric charge substantially increases both the maximum mass and radius compared with neutral configurations. For strong negative couplings and pronounced interaction strengths, the resulting stellar models reach masses close to $3,M_{\odot}$ with compactness ratios of order $0.34$, placing them within the mass range inferred for the secondary component of GW190814, whose nature remains observationally undetermined. The presence of charge reduces the central density at maximum mass by approximately $10$–$15\%$ while maintaining full compliance with causality requirements. Furthermore, comparisons with observational constraints from PSR J1614$-$2230, J0348$+$0432, J0740$+$6620, J0952$-$0607, and recent NICER radius measurements indicate that charged EMSG configurations remain consistent with current astrophysical bounds over a wide parameter space. These results demonstrate that a moderate electric charge, when combined with nonlinear matter-geometry coupling, can support quark stars that are significantly more massive than those predicted in general relativity, underscoring the potential observational relevance of charged compact objects in modified gravity and multimessenger astrophysics.

Mechanical systems are traditionally designed as passive assets, where sensing, analysis, and control are treated as decoupled and externally prescribed processes. Reliance on predefined mechanistic models and supervised learning with offline optimization further limits their adaptability in changing environments. Drawing inspiration from biological cognition, we introduce a computational framework enabling mechanical systems to learn, adapt, and make decisions through interactions with partially observable environments. Perception, action, and learning are integrated through active inference within a perception-action loop. Sensor data are assimilated through a neural reservoir to support continual belief updating, while actions actively probe and influence the physical system, becoming an integral part of the inference process. Through self-directed interaction, adaptive behavior emerges from the continual refinement of internal representations to explain varying observation patterns while pursuing mechanical objectives. Across simulated case studies involving multiple mechanical systems, static and dynamic sensing, and objectives ranging from deformation maximization to vibration mitigation, we demonstrate the potential of the proposed framework as enabling paradigm for autonomous mechanical systems.

Generative vision-language models (VLMs) offer a counting paradigm in which one model produces both a count and a natural-language account of the scene, yet their raw counting accuracy sits in the range of sub-million-parameter specialist regressors. The open question is whether auxiliary guidance from a pretrained specialist can lift them into useful territory, and through which channel that guidance is best routed. We evaluate Qwen2.5-VL-7B on four widely used crowd counting benchmarks (ShanghaiTech A and B, UCF-QNRF, NWPU-Crowd). Zero-shot prompting rarely produces a parseable count, so LoRA supervised fine-tuning establishes the baseline at overall MAE 81.64. Conditioning on a P2PNet-derived density heatmap as an auxiliary visual signal fails in every encoding we tested, and an adversarial-swap protocol shows the model reads the heatmap but applies it counterproductively. We propose CrowdCue, a family that supplies the same specialist's already-integrated integer count to the VLM as a discrete symbol. The text-channel variant reaches MAE 72.04. The visual-channel variant, which renders the integer as printed digits and supplies it as a second image, reaches MAE 62.65, the strongest result in this paper and well ahead of the cue-supplying specialist alone (84.45 on the same split). In the late-fusion VLM we study, the binding constraint is not the channel but the abstraction level at which the specialist signal is delivered.

Multi-user multiple-input multiple-output (MU-MIMO) is a key technology that improves wireless capacity through multiple antennas. In MU-MIMO downlink precoding, vector perturbation (VP) is a representative nonlinear method that achieves high performance. However, its search for the integer perturbation vector reduces to a closest vector problem, whose complexity grows rapidly as the number of users increases. We propose a method that relaxes the discrete structure of the integer perturbation into a continuous mixture of $t$-distributions, enabling efficient search via gradient-based Hamiltonian Monte Carlo (HMC). Complexity analysis and numerical experiments demonstrate the effectiveness of the proposed method. Its search complexity scales as O(N^2) in the number of users N. At a symbol error rate of 10^-3, it performs within 2.4 dB of a hypersphere approximation benchmark, which approximates the performance limit of VP. This paper reframes the VP perturbation search as a probabilistic inference problem, providing a general formulation for handling high-dimensional discrete search in a continuous space.

Iterative text-to-motion generation delivers high-quality and semantically aligned motions but requires multiple network evaluations, resulting in substantial inference latency. We present MixiMotion, a strict one-step text-to-motion generation framework based on offline set distillation. Instead of distilling a single teacher trajectory for each text prompt, MixiMotion constructs an offline bank of multiple teacher motions and aligns teacher and student sample sets through asymmetric bidirectional matching. The teacher-to-student direction promotes coverage of diverse teacher-supported motions, while the student-to-teacher direction suppresses unsupported generations. We further introduce differentiable decoded-space kinematic supervision to complement normalized representation matching with constraints in the decoded motion space. At inference, MixiMotion generates a complete motion sequence with a single network evaluation, without teacher queries, iterative sampling, or candidate ranking. On ViMoGen, MixiMotion achieves a semantic alignment score of $0.835$, outperforming the evaluated one-step baselines and approaching the $0.858$ score of its 50-step HY-Motion-1.0-Lite teacher. In blinded human evaluation, MixiMotion obtains an overall rating of $4.33$, compared with $4.50$ for the teacher, while outperforming the evaluated one-/few-step baselines. Meanwhile, generation latency is reduced from $829.58$\,ms to $9.30$\,ms, corresponding to an $89.2\times$ speedup. These results demonstrate an effective quality–efficiency trade-off for strict one-step text-to-motion generation.

LispBM is a Lisp dialect for microcontrollers and embedded systems. This paper is about the changes made to LispBM resulting from it being integrated into the VESC family of firmware and thus gaining a userbase. As a surprise to Author 1, the new users of LispBM wrote programs larger than ever imagined. This used up all available heap space and we were forced to find a way to evaluate Lisp programs partitioned across RAM and flash memory. This story and a couple more, like the one about the Lisp-image system for fast boots, are the core contribution of this paper. When the first versions of the VESC firmware with a built-in Lisp runtime system were released, there was some grumbling here and there about Lisp and its syntax, as expected. To our delight, most seemed very excited about a scripting language in the firmware. To the engineer and builder users, the choice of syntax seemed to matter less than the potential it opened up for them.

Multi-class open-set anomaly detection requires a model to characterize the normal acceptance domain formed by multiple heterogeneous subdistributions using only class-labeled samples from known normal classes, and to identify previously unseen anomalies at test time. Existing single-hypersphere methods cannot explicitly represent class-specific locations and acceptance ranges, while current multi-hypersphere or multi-class approaches do not fully integrate inter-class boundary constraints, learnable acceptance ranges, and interpretable decisions. To address these limitations, we propose Interpretable Multi-Hypersphere Deep Anomaly Detection (IMHD-AD). IMHD-AD constructs an independent hypersphere for each known normal class in a shared feature space. With target-inside and non-target-outside constraints, IMHD-AD embeds the class-specific hypersphere centers and radii directly into the final network layer and jointly optimizes them with the shared representation. The minimum signed boundary score across hyperspheres simultaneously determines open-set acceptance or rejection and provides a faithful geometric explanation of each decision. On MNIST, Fashion-MNIST, and CIFAR-10, IMHD-AD achieves the highest AUC in 28 of 30 open-set comparisons. A two-dimensional synthetic study further shows that model architecture must balance the compactness of known normal classes against the separability of unknown anomalies.

We study the Bregman proximal point method for the obstacle problem, a fundamental variational inequality arising in contact mechanics, optimal design, and mathematical finance. Each Bregman proximal step regularizes the energy through a Bregman divergence generated by a Legendre function, leading to a semilinear elliptic subproblem. We first establish a well-posedness and strict feasibility theory for these subproblems. We then analyze the convergence of the resulting iteration in the $H^1$-norm. Our convergence analysis is based on a sequential strict local minimality inequality. We show abstractly how the order of minimality determines the convergence rate. Assuming that the initial guess lies above the exact solution and a one-sided Bregman growth condition holds, we establish sequential strict local minimality of order $s \geq 2$ and derive sublinear convergence rates in the $H^1$-norm of the form $O(k^{-\zeta})$, where $\zeta\in(1/2,1]$ depends on the choice of Legendre function. For the Shannon and Tsallis entropies, we show that these rates are sharp in a uniform worst-case sense. Under additional assumptions on the free boundary and the obstacle, we establish sequential strict local minimality of order $s = 1$ with the Shannon and Spence entropies. This yields linear convergence of the form $O(\varrho^k)$ for some $\varrho\in(0,1)$.

We establish interior Hessian estimates for $k$ convex solutions of $\frac{\sigma_k(D^2u)}{\sigma_l(D^2u)}=1$, where $1 \leq l < k < n$, $k-l \in \{1,2\}$, and $2k > n$.The proof combines a concavity inequality with a pointwise doubling argument.

3D Gaussian Splatting (3DGS) enables high-quality novel view synthesis but incurs high storage and transmission costs due to dense Gaussian primitives. Recent anchor-based compression reduces per-primitive redundancy, yet redundancy across anchors remains largely unexploited. We propose CRP-GS (Cross-Representation Priors for Gaussian Splatting), a rate-distortion optimized compression framework that leverages cross-representation priors to improve anchor-level entropy modeling. First, a Correspondence-Oriented Hierarchical Structure (COHS) organizes anchors by feature correspondence rather than spatial proximity, constructing root-leaf dependencies so that selected anchors can act as informative priors to conditionally encode others, yielding more accurate likelihood prediction and lower conditional entropy. Second, Shared Feature Aggregation (SFA) extracts globally shared features from a contextual hash grid and injects them into anchor representations, factoring out scene-consistent low-frequency information that would otherwise be redundantly embedded in individual anchors. Both modules are trained under a unified rate-distortion objective to balance bitrate reduction and rendering fidelity. Experiments across multiple benchmarks show that CRP-GS achieves a favorable overall rate-distortion trade-off, yielding around 30% average bitrate reduction compared to anchor-based baselines while maintaining comparable rendering quality.

We develop a quantitative approach to quasi-local operators with bounded block-rank. Our main results are a quantitative decomposition for quasi-local operators into block-rank-one pieces and a quantitative finite-propagation approximation in the block-rank-one case, leading to a quantitative proof of the bounded block-rank rigidity result for Roe and quasi-local algebras.

We present M3GA-Wild, the first benchmark for multi-modal, multi-session ground-to-aerial place recognition in forests. M3GA-Wild unifies and extends existing forest localisation datasets, providing a holistic benchmark with synchronised RGB imagery and LiDAR from ground traversals spanning 36 km, aligned high-resolution aerial imagery and multi-altitude LiDAR covering 370 hectares, and accurate geo-referenced 6-DoF poses for precise evaluation. M3GA-Wild captures diverse forest scenes with varying viewpoints, occlusion, and environmental conditions, enabling systematic evaluation of visual, LiDAR, cross-modal, and multi-modal methods. Baseline experiments show that LiDAR-based approaches significantly outperform vision-only methods under severe viewpoint differences, while current multi-modal fusion strategies yield limited gains due to poor cross-modal alignment. By pairing aerial RGB imagery with geo-referenced aerial LiDAR, M3GA-Wild also enables evaluation of foundation models for monocular depth estimation as a cheap source of 3D geometry from forest imagery, with initial experiments revealing shortfalls of current methods. These results highlight key challenges in cross-platform localisation, including modality misalignment and severe domain gaps. M3GA-Wild establishes a new benchmark to support research in robust multi-modal localisation and long-term autonomy in unstructured natural environments. The dataset and code will be available upon acceptance.

This paper investigates the stability of strong global and exponential attractors for a semilinear beam equation with memory and fractional damping, where $\alpha\in[0,2]$ denotes the fractional damping exponent and $\beta\in[0,1]$ the memory parameter. After showing the existence of a strong global attractor, we prove its upper semicontinuity in the parameter pair $(\alpha,\beta)$. We then construct a family of strong exponential attractors and establish its continuity in $(\alpha,\beta)$. Here, “strong" means that the compactness, attraction, and parameter-robustness properties are established in a topology stronger than that of the phase space. Compared to existing $\beta = 0$ results, our findings hold in a stronger topology. The analysis draws upon our recent higher-order regularity results for global attractors.

We introduce Neural $S$-Transform Reconstruction (NeSTR) for Gaussian stochastic partial differential equations (SPDEs). The learned object is not the random solution itself, but its $S$-Transform on a finite dimensional subspace of the white noise test space. For Wick type SPDEs, NeSTR yields a deterministic parametric PDE for the restricted $S$-Transform, and the stochastic solution is recovered from the Taylor coefficients of this transform at the origin. Thus the neural approximation is tied directly to the Wiener chaos expansion of the solution. The main novelty of NeSTR is an inverse $S$-Transform reconstruction principle combined with finite mode learning: we prove consistency of the recovered chaos coefficients, separate noise mode, chaos truncation, deterministic solver, and neural approximation errors, and give a deterministic learning formulation for the restricted transform. Numerical tests on an additive stochastic heat equation and a multiplicative Wick heat equation show that polynomial spectral representations in the transform variables provide stable access to higher order chaos coefficients. The resulting reconstruction separates the equation dependent deterministic coefficient fields from a reusable Gaussian–Hermite basis. Consequently, NeSTR learns an analytic generating function whose derivatives recover the Wiener chaos coefficients, rather than learning stochastic trajectories directly.

Short-circuit protection is vital for ensuring the safe operation of high-power-density power converters using Silicon Carbide (SiC) MOSFETs. However, adapting conventional desaturation (DESAT) protection, originally designed for Silicon (Si) IGBTs, is challenging due to the significantly shorter shortcircuit withstand time of SiC devices, typically less than 3{\mu}s. Nevertheless, DESAT protection can be adapted for SiC MOSFETs through certain circuit modifications. This article provides a comprehensive analysis and design guidelines for the three architectural variants of DESAT protection circuits, specifically for adjusting the short-circuit detection time suitable for SiC MOSFETs. Further, this article establishes a quantitative framework to evaluate the noise induced into the DESAT protection circuits during turn-off dv/dt switching transients. From this analysis, a design methodology and safe operating boundary are derived for each DESAT configuration, guiding the systematic selection of component values to balance dv/dt noise margin and short-circuit detection speed for SiC MOSFETs. Experimental results are presented to validate the analysis.

We explore the quasinormal modes of a massless test scalar field in the gravitational background of a non-extremal dilatonic dyonic black hole. The dyon-like black hole solution is considered within a four-dimensional gravitational model that includes two scalar fields and two 2-forms. It is governed by two dilatonic coupling vectors $\vec{\lambda}_s$ (with $s=1,2$) that satisfy $\vec{\lambda}_1 = \vec{\lambda}_2 = \vec{\lambda}$ and $\vec{\lambda}^2 = 1/2$. We derive and examine the quasinormal modes of a massless scalar test field in the eikonal limit. These modes are governed by the solution parameters $\mu > 0$, $P_1 > 0$, and $P_2 > 0$. In the two limiting scenarios – namely $P_1 = P_2 = 0$ and $P_1 = P_2 = P > 0$ – our results reduce exactly to the known (eikonal) quasinormal spectra for the Schwarzschild and Reissner-Nordström black holes, respectively. Numerical higher-order WKB analysis of quasinormal frequencies for two lower levels (for various values of parameters) is also presented.

The no-signalling principle lies at the heart of Bell-type experiments involving spacelike-separated parties. Although not all no-signalling correlations can be realized within quantum theory, the no-sinalling principle itself remains fundamental even for post-quantum theories, since its violation would imply superluminal signalling. In the spirit of device independent nature of the Bell inequalities, there has recently been growing interest in causal inequalities, which identify correlations admitting no causal explanation. Such correlations have been rigorously studied within the process-matrix formalism, which is built upon a constraint analogous to spacelike separation in Bell scenarios. We refer to this constraint as the single-interaction constraint, whereby each party interacts with the environment only once. Despite considerable effort, no fundamental guiding principle is currently known that characterizes the restrictions this constraint imposes on the correlations generated by Process Matrices. In this work, we address this gap by proposing a generalized causality principle for the bipartite case. We show that for certain cases, the generalised causality principle defines a strict subset of the set of all signalling correlations. This principle thus provides a fundamental limit on quantum and even post-quantum theories subject to the single-interaction constraint. By analogy with no-signalling, whose violation excludes certain causal structures among the parties, a violation of the generalised causality principle rules out a corresponding class of causal structures(causal structures with the single interaction constraint). More broadly, our techniques provide a general framework for deriving generalised causal constraints, applicable to a wide class of indefinite-causal-order scenarios.

Exact calculations for smooth toric Fano varieties in dimensions at most seven suggest a sharp dimension-dependent lower bound for the positive difference between the rational and integral Gongyo indices. We compute both indices for the smooth toric Fano models obtained from blow-ups of projective space at torus-invariant points by the anticanonical minimal model program. For pseudo-symmetric smooth toric Fano varieties, we prove the proposed lower bound and determine all equality cases. We also apply a dimension-raising construction to obtain an explicit infinite family of smooth toric Fano varieties with positive gap from odd-dimensional weak Fano varieties with zero gap. For the standard models considered, we determine the smallest dimension increase needed to obtain a Fano variety by iterating this construction and compute both indices of the minimal lifts. Finally, every positive rational number occurs as a Gongyo-index gap, even within the pseudo-symmetric class.

We establish a Demailly-type approximation theorem for singular Finsler metrics satisfying the multiple coarse \(L^p\) extension property on holomorphic vector bundles. As an application, we obtain a new proof of the fact that the multiple coarse \(L^p\) extension property characterizes Griffiths positivity, as shown by Deng–Wang–Zhang–Zhou.