Papers

On-policy distillation from multiple teachers combines expertise from different domains in a single student, but conflicting gradients can hinder this integration. Gradient corrections directly constrain parameter updates under plain SGD. With optimizers such as AdamW, however, momentum, adaptive scaling, and weight decay can turn a corrected gradient into an update that increases a domain loss to first order. To address this gap, we propose Update Projection for Multi-Teacher On-Policy Distillation (UP-MOPD). UP-MOPD lets the original mixed gradient update the optimizer state and generate a candidate displacement, then projects only violating candidates before they are committed to the parameters. The projection gives the unique feasible update closest to the candidate in Euclidean distance. In experiments combining medical and general domains, UP-MOPD improves IFEval-loose accuracy late in training by 2.96 points over vanilla M-OPD. It achieves an average score of 60.03 across eight metrics, compared with 59.00 for gradient projection and 59.15 for update rejection. On a public benchmark covering mathematics, code, and instruction following, it achieves the best average across six tasks (32.67), leads on LiveCodeBench v5, and ties for the best IFEval result.These results support projecting optimizer updates to reduce interference between domains.

We develop a computational framework for the quantum relative entropy based on the replica trick and apply it to analyze the evaporation process method of Jackiw-Teitelboim black holes. We show that the relative entropies between the exact radiation state and the Hawking saddle state and the replica wormholes saddle state quantify information-theoretic costs inherent to coarse-grained semiclassical descriptions. During evaporation, the relative entropy for the Hawking saddle increases monotonically, reflecting a progressively higher thermodynamic cost of sustaining the Hawking description. Conversely, the relative entropy associated with the replica wormholes saddle decreases, which indicates that the description of connected geometries becomes progressively more accurate. Moreover, the sign of the difference between the two quantities reverses precisely at the Page time, providing an information-theoretic diagnosis for the transition between competing gravitational saddles. Our results recast the Page transition as a flow of relative entropy costs between competing semi-classical descriptions, revealing an information-theoretic structure underlying the emergence of effective irreversibility in coarse-grained black hole evaporation.

Knowledge of the structure and evolution of cosmic magnetic fields is indispensable to understand how primordial magnetic fields were generated and amplified during the lifetime of the Universe. Polarisation studies over significant redshift ranges are an important tool in understanding cosmic magnetic fields. We aim to understand the structure and evolution of cosmic magnetic fields, utilising the polarised spectra and depolarisation characteristics of (background) radio sources. Using radio polarisation data at two different frequencies from the LOFAR Rotation Measure (RM) grid catalogue at 144\,MHz and new Apertif data at 1.4\,GHz, we investigate the source statistics of a common sample of polarised sources, deriving the depolarisation ratio between these two frequencies. We utilise this to disentangle depolarising effects local to the source from those along the line of sight. We compile a catalogue of 598 polarised radio components, most of which are located in low-density environments. Fractional polarisation decrease for both wavelengths with redshift. We attributed the main depolarisation at 1.4\,GHz to effects occurring close to the sources, while the depolarisation measured at 144\,MHz is most likely generated by cosmic filaments along the line-of-sight. We were able to get a first redshift dependent upper limit estimate of the RM dispersion in cosmic web filaments.

We study the structure of finitely ramified henselian valued fields of mixed characteristic with arbitrary residue fields via their residue rings of higher length, where a residue ring of length $n$ is the quotient ring of the valuation ring by the $n$-th power of its maximal ideal. We prove an approximate lifting theorem for homomorphisms between residue rings of higher length and explicitly determine the optimal bound of error of lifting. As applications, we obtain several Ax-Kochen-Ershov principles for relative completeness, relative existential completeness, and existential closedness using the pure ring structures on the residue rings. And we show that any formula on a residue ring of length $k$ is equivalent to a normal form of sentences in pure ordered group structure and special formulas at level $n$, uniformly for all finitely ramified henselian valued fields of mixed characteristic $(0,p)$ and the same initial ramification index $e$. Here, for $n\ge k$, a special formula at level $n$ represents a definable set on a residue ring of length $k$ given by a projection image of a definable set in pure ring structure on a residue ring of length $n$. Also, such $n$ is optimally computed from the precise estimation of error of lifting and depends only on $k$, residue characteristic $p$, and initial ramification index $e$.

The classical More Sums Than Differences (MSTD) problem studies finite sets $A\subset\{0,1,\ldots,n\}$ for which $|A+A|>|A-A|$, where $A+A=\{a_1+a_2:a_1,a_2\in A\}$ and $A-A=\{a_1-a_2:a_1,a_2\in A\}$. As addition is commutative and subtraction is not, it was conjectured that as $n\to\infty$ almost all subsets $A$ chosen uniformly from the power set of $\{0,1,\ldots,n\}$ are difference-dominated, and it was thus a surprise when Martin and O'Bryant proved a positive percentage of sets are sum-dominant. We greatly generalize this model by introducing a Markov-chain framework, where the classical MSTD model is now just a special case. Let $(X_i)_{i=0}^n$ be a stationary two-state Markov chain on $\{0,1\}$ with transition probabilities $P(0,0)=p$ and $P(1,1)=q$, where $p,q\in(0,1)$. We include $i$ in $A$ exactly when $X_i=1$, and define $A=\{i\in\{0,\ldots,n\}:X_i=1\}$. The usual independent Bernoulli model is recovered when consecutive inclusion decisions are independent, equivalently when $p=1-q$. In particular, the uniformly random subset model corresponds to $p=q=1/2$. Using the fringe-middle method from the MSTD literature, we show that the middle sums and differences are filled with high probability, so the comparison between $|A+A|$ and $|A-A|$ is again governed by endpoint fringes. By fringe manipulation, we prove that the probabilities of sum-dominant, difference-dominant, and balanced sets tend to strictly positive limits as $n\to\infty$. We also give numerical estimates of these three probabilities for finite $n$ over a range of values of $p$ and $q$. Through combinatorial methods, we find a closed-form expression for $\mathbb{E}[|A-A|-|A+A|]$ as $n\to\infty$.

Visualization dashboards are widely used interactive tools, but a disconnect exists between the dynamic data they display and their static structure. End-users cannot modify the dashboard to answer new questions. We introduce Living Dashboards, whose views are born, wither, revive, and die in response to how they are used. Rather than requiring manual reconfiguration, a living dashboard observes interaction and natural-language queries to autonomously wither neglected views and revive those used again. More consequential decisions, such as adding or retiring views, are deferred to the user. We formalize the concept as a four-dimensional design space and implement it in Living Dashboard, a web-based prototype. We evaluate it in an exploratory between-subjects study (N = 12) against an AI-supported baseline on analytical tasks. Living Dashboard participants answered more tasks correctly, reported lower workload, and rated the system higher on usability, though the two conditions differed in more than adaptive behavior alone.

Electrophysiological recordings provide powerful tools for characterizing the dynamics of neuronal networks. In vitro neuronal cultures offer a controlled setting for investigating network responses to diverse interventions, including pharmacological and optogenetic stimulation. However, conventional analyses often reduce electrophysiological activity to aggregate measures calculated over fixed temporal windows, providing only a static representation of the network state. Here, we introduce a comprehensive, multiparametric analytical framework designed to characterize both the temporal evolution of network activity and the transitional states induced by external interventions. The framework combines multiple network discriminators with a compositional analysis that resolves electrode-level responses into excited, inhibited, and unchanged states over successive temporal segments. We apply the framework to electrophysiological recordings obtained under pharmacological interventions with 4-aminopyridine (4-AP), optogenetic stimulation, and additional benchmark conditions. The results demonstrate that the proposed analysis can reveal subtle and transient responses that may be difficult to detect using conventional aggregate measures, including responses to low-dose pharmacological interventions. These findings highlight the value of temporally resolved and compositional analyses for characterizing heterogeneous neuronal network responses in vitro.

Space-Time Wave Packets (STWPs) have enabled numerous nontrivial properties, such as tunable group velocities, nondiffraction and nonlocal spin textures in optical fields. However, this has not been properly studied in matter waves. Here, we investigate free-electron STWPs, which are propagation-invariant and group-velocity-tunable matter wave packets, constructed by constraining the spatiotemporal spectrum of the electron wavefunction in momentum space. Due to the unique dispersion of free-electrons, the electron STWP can carry two different topologies, and host both meron and skyrmion topological textures in momentum space. We demonstrate the topological phase transitions and tunable skyrmion numbers by spectral geometry tuning. We also show the topologically robust propagation of the electron pulses and corresponding real-space skyrmionic expectation value textures encoded within each single electron wavefunction. Our results open a platform for topological free-electron wavepackets uses in sensing and information transfer.

Computing is conventionally implemented by hardware engineered for information processing. Here we investigate infrastructure-native computing: the use of a physical system built for another primary function as a fixed computational operator. In time-domain simulations of an IEEE 14-bus electrical network, Kirchhoff's current law and Ohm's law relate voltage-reference perturbations applied at distributed controllable nodes interfaced by power electronics converters to current responses through a topology-dependent transformation. A trained digital encoder and decoder exploit this transformation for image classification, reaching 91.5% accuracy on MNIST and 82.25% on Fashion-MNIST. The modeled operator is represented by 933 surrogate parameters, compared with 12,340 task-trained parameters for an accuracy-matched fully connected core transformation. Current superposition further supports concurrent spatial sharing of the operator and sequential temporal reuse, with per-stream accuracies above 85% and 93%, respectively, in surrogate-model evaluations. Evaluations on CIFAR-10 and repeated 10-class tasks sampled from a Butterflies-and-Moths dataset show that the incremental utility of the physical operator depends on the representation supplied by upstream digital feature extraction. These results provide a simulation-based proof of concept for infrastructure-native computing with electrical networks and identify topology, accessible control channels, and input representation as determinants of its computational utility.

We consider the following class of singular elliptic problems \[ \begin{cases} -\Delta u = -\dfrac{u}{|u|^{\beta+1}}\chi_{\{|u|>0\}} +\lambda |u|^{p-1}u, & \text{in }\Omega,\\[1mm] u=0, & \text{on }\partial\Omega, \end{cases} \] where $\Omega\subset\mathbb R^N$ is a bounded smooth domain, $N\geq3$, $0<\beta,p<1$, and $\lambda>0$. The energy functional is not of class $C^1$ in $H_0^1(\Omega)$, and the standard critical point theory does not apply. We prove that a nontrivial nonnegative weak solution exists if and only if $\lambda$ exceeds a critical value $\bar\lambda$, which we identify and locate strictly between two Rayleigh-type parameters $0<\lambda_*<\bar\lambda<\lambda^*<+\infty$. This gives a sharp existence threshold. We also prove that for every $\lambda$ in a neighborhood on the left of $\lambda^*$, there exist at least two distinct nontrivial nonnegative weak solutions. The first is a minimizer on the Nehari manifold, with an energy changing sign at $\lambda^*$. The second has a strictly positive energy. For $\lambda<\lambda^*$ sufficiently close to $\lambda^*$, both solutions have positive energy. This contrasts with previous multiplicity results for the same problem, in which the two solutions obtained have energies of opposite signs.

Large language models (LLMs) have demonstrated strong capabilities in question answering, yet they still frequently suffer from hallucinations on knowledge-intensive tasks. Knowledge graphs (KGs) provide LLMs with structured, interpretable, and updatable factual grounding, making them a promising external knowledge source for reliable reasoning. However, existing LLM-guided graph reasoning methods typically rely on hop-wise greedy or beam-style pruning during evidence retrieval. Such local decision processes are inherently myopic: evidence that appears weak near the source may become crucial only after deeper graph context is explored, causing answer-critical branches to be discarded prematurely and making the reasoning chain difficult to recover. To address this limitation, we propose Foresight-over-Graph (FoG), a foresight-aware evidence retrieval framework for knowledge base question answering (KBQA). FoG iteratively constructs a question-relevant evidence subgraph and uses far-to-near feedback to guide path exploration, and maintains a compact memory subgraph to support continued exploration. Extensive experiments on widely used KBQA benchmarks demonstrate that FoG achieves state-of-the-art performance, with a particularly large improvement of 16.58% in Hit on CWQ, while also reducing LLM calls and token usage. Our code is available at https://github.com/yhong7/FoG .

The inherent non-convex minimum-separation constraints introduced by movable antennas present a formidable challenge to the joint optimization of antenna positions and transmission strategies, rendering conventional methods computationally infeasible, particularly in large-scale cell-free massive multiple-input multiple-output (MIMO). In this work, we propose the graph-based learning individual intrinsic reward heterogeneous-agent proximal policy optimization (GLIIR-HAPPO) algorithm, a novel heterogeneous multi-agent reinforcement learning (MARL) framework that fundamentally overcomes this impasse by systematically decomposing the original coupled optimization into coordinated subproblems. To ensure tractability, we embed the non-convex geometric constraints into a penalty-augmented reward structure and develop a specialized geometric solver that enables the positioning agents to efficiently navigate the high-dimensional action space. Specifically, we propose an architecture featuring a dynamic-interaction graph critic for adaptive cross-role coordination, together with role-conditioned federated distillation that synchronizes same-role policies through compact actor-output statistics. Beyond architectural design, we establish a rigorous theoretical analysis that derives monotonic performance improvement bounds and establishes convergence guarantees for the proposed bi-level optimization. Numerical simulations demonstrate that our framework yields significant sum-rate improvements over state-of-the-art MARL schemes. Moreover, the performance of our advanced architecture closely approaches its fully centralized counterpart, while drastically reducing communication overhead.

Predicting the shapes of entire curves requires accounting for nonlinear geometry and unknown alignments between curves. We develop elastic kernel ridge regression, a nonparametric method for planar curve responses with scalar, multivariate, or functional covariates. Using square-root velocity representations, we formulate penalized conditional Fréchet mean estimation in a shape space invariant to translation, rotation, scaling, and reparametrization. A vector-valued reproducing kernel Hilbert space provides a flexible nonlinear link through the spherical exponential map. We use an alternating algorithm to align each observed curve to its current fitted value, and updates the regression function. To facilitate this, we provide a new Euclidean quasi-Newton solver that exploits scale invariance of the reparametrization objective; this accelerates alignment while retaining accuracy in a numerical comparison. Simulations demonstrate the benefits of estimating alignment within the regression and respecting spherical geometry. Applied to vocal tract contours from a real-time magnetic resonance imaging recording, the method recovers missing frames and reconstructs shape trajectories from downsampled data. A speech inversion proof of concept on the same recording predicts tongue shapes from acoustic features, illustrating the method's potential. The method is implemented in the R package sphereg2.

Given a cycle type, the corresponding conjugacy class of $S_n$ generates either $S_n$ or $A_n$ for sufficiently large $n$. We prove that the sequence of diameters of Cayley graphs is eventually polynomial on residue classes for any fixed cycle type. This result is also extended to finite unions of conjugacy classes.

In this work, we consider decision-focused learning (DFL) for a Markov decision process (MDP), where existing methods differentiate through the KKT conditions of the Bellman equation and require solving a linear system over all state-action pairs, limiting its scalability. We address this by reformulating the MDP as an occupancy measure-based linear program (LP), whose feasible region is induced by predicted dynamics, and we derive a closed-form gradient by identifying the active constraints in the feasible polyhedron via the pivoting algorithm. This occupancy measure-based LP layer raises two challenges: (1) LP's solution gradient is discontinuous when active constraints change, and (2) the LP backward cost still scales with the state size, which is costly for large or continuous state spaces. We address the challenges with an augmented Lagrangian surrogate and smooth the boundary jumps by random row sketching of the constraints, and a learnable soft state-aggregation layer and its function-approximation generalization that scales the LP to large finite and continuous-state MDPs. Across multiple tasks, our methods reach lower regret than KKT-based DFL and two-stage baselines with significantly lower computation cost. The source code for all experiments is available at https://github.com/A-Eshragh/State_Aggregation_Project.

We study a random walk in $\mathbb{Z}^d$ in a dynamical random environment constituted of independent null recurrent birth-and-death chains, and establish a scaling limit result for the position of the walker in terms of a sublinear time change of Brownian motion, thus establishing subdiffusivity, in contrast to a diffusivity result established previously in an ergodic version of the model.

We introduce new techniques to study mixed-characteristic special loci in moduli spaces and give several applications, focusing in particular on the moduli space $\mathsf{M}_g$ of curves. These applications include Zariski density results for split Jacobians, non-density results for supersingular loci, and lifting results for algebraic cycles, all under appropriate numerical conditions. Our methods generalize to more-or-less arbitrary moduli spaces mapping to Hodge-type Shimura varieties (and even some settings beyond the Shimura case), and relate to questions raised by Oort and de Jong.

Human video offers a scalable source of robot demonstrations, yet most human-to-humanoid retargeting methods assume a legged robot with human-like kinematics. This assumption does not hold for mobile-base humanoids equipped with a wheeled base, vertical lift, and two arms. Human walking must be expressed through base motion, while torso bending may require coordinated lift and arm motion. We address this mismatch with a task-conditioned framework that assigns reconstructed human motion to base, lift, and arm responsibilities before robot-specific realization. The allocator preserves the human-derived path, stabilizes heading, separates turn and translation when needed, retimes commands to satisfy base limits, and repairs lift and arm trajectories. A deployment adapter then converts the reference to 50 Hz commands using stationary-base detection, deadband and slew-rate filtering, time-consistent playback scaling, and separate linear and angular gains. We evaluate the resulting references with human-derived task-space comparisons, policy-free simulation replay, and a qualitative execution on a physical robot.

In this report we analyze charasteristics of structural symmetry of small AkBlCm nanoclusters (A - Rb, Cs; B - Pb, Sn, Bi; C - Cl, Br, I), binding energies, stability, and, ultimately, applicability as building blocks for construction of larger-size nanoclusters. Preliminary spatial modeling of ternary compound nanoclusters has been carried out on the basics of geometrical approach, namely interatomic distances taken as a sums of corresponding ionic radii. The geometry optimization and binding energies of the modeled structures have been determined through quantum-chemical calculations. Geometry optimization has been performed with Gaussian09 software package using Density Functional Theory (DFT) within the generalized gradient approximation of the Perdew-Burke-Ernzerhof (PBE) and hybrid approximation of the Becke-3-Lee-Yang-Parr (B3LYP) exchange-correlation functionals. The Stuttgart/Dresden (SDD) and Los Alamos National Laboratory 2 Double Zeta (LANL2DZ) scalar-relativistic effective basic potentials were employed throughout the calculations. As a result of these calculations, a clear relationship between the atomic radii, their ratios within the nanoclusters and their stability has been obtained and analyzed.

Visual counting is commonly formulated as counting a single specified target, with a model receiving an image-specific exemplar, text query, or target category and returning a single count. We instead study fixed-vocabulary image-query-free multi-category counting. A global vocabulary is fixed for each run, and, given only an RGB image, the model predicts a complete category–count vector without being told which categories appear. We present UniCounting, which casts counting as instance-aware structural inference over an over-complete proposal set. Generic segmenters produce duplicate masks, partial views, and proposals from neighboring instances; semantic scores can name them but cannot determine which denote the same object. Frozen SAM~2.1 generates masks, while frozen DINOv2 and OpenCLIP provide relation and category features. A 3,267-parameter category-shared relation head predicts same-instance affinities from instance-mask-derived supervision. Sparse graph construction, representative selection, labeling, and background-margin admission then convert each admitted component into one count with replayable group evidence. Only the relation head is trained, without count or density-map targets. On COCO clean500, UniCounting obtains lower point-estimate vector $\ell_1$ error and absent-class false mass than calibrated OWLv2-All80, with comparable micro presence F1. Under a matched decoder, the learned relation reduces both errors relative to mask containment, mask IoU, CLIP, and DINO, while revealing a fragmentation–merge trade-off. We also report transfer diagnostics on OmniCount-sub, FSC-147, and CARPK.

Large language model (LLM) serving is increasingly dominated by agentic workloads, in which agents and their sub-agents accumulate context as KV cache across many requests, consuming substantial memory. High-bandwidth flash (HBF) is a promising solution, providing an order of magnitude greater capacity at HBM-class read bandwidth, but its finite write endurance is the key limiting factor. Our key insight is that KV cache should be placed across HBM and HBF by its lifetime. Placing shorter-lived data in HBM lets HBM absorb more of an agent run's writes and sends less of them to HBF. As the lifetime of KV cache in agentic serving is dictated by the harness, the program that orchestrates the agents, we analyze its behavior and identify three axes along which lifetime diverges, temporal, structural, and inter-worker. Guided by these observations, we present Lachesis, a lifetime-aware KV cache placement layer between the agent harness and the serving engine. At write time, it places each segment in HBM or HBF according to its lifetime, and frees its blocks once the segment is no longer read. In trace-driven simulation, Lachesis extends HBF lifetime by 1.19-3.13x over HBM-first placement, reaching 3.3-12.2 device-years. Even under continuous 24x7 operation at the full load a tight SLO admits, HBF outlasts its five-year warranty on the multi-agent trace.

Across scientific domains, empirical data often give rise to positive semidefinite matrices that encode similarities, couplings or interactions and induce natural geometries. We investigate whether changing the geometry used to compare the same empirical representations preserves subject-level performance and the local structures from which explanations are derived, a question we term the prediction explanation invariance problem. We address this problem across morphometric MRI, fMRI and EEG data by comparing Frobenius and trace geometries applied to the same empirical matrices. Predictive performance was broadly preserved across geometries, but comparable performance did not imply agreement in subject-level decision scores or predicted labels. Predictive similarity also masked geometry-dependent differences in local neighbourhoods, perturbation sensitivities and explanatory rankings. Dimensionality reduction made the two subject-space geometries progressively more concordant, while classification performance and decision-level agreement declined. These results identify data geometry as a hidden degree of freedom in explainability: similar performance does not guarantee invariant decisions or explanations.

Motivation: Plant disease resistance genes, particularly those encoding NB-LRR proteins, are important targets for crop improvement. Proteome-based domain or motif searches can only identify NB-LRRs among existing gene models, meaning they cannot recover loci that have been missed or incorrectly predicted by the reference annotation. The full-length, homology-based R-gene prediction (HRP) method circumvents this issue by reconstructing gene models directly on the genome. However, the original implementation of this method requires several separate phases of classification, comparison and filtering operations. Results: HRPv2 is an automated, enhanced version of the original strategy. The labour-intensive, step-by-step curation process used in HRP has been replaced by a reproducible filtering framework. Enhancing two steps of the homology search process has enabled HRPv2 to better account for the specific NB-LRR variability of the genome. Performance validation confirmed that the number of full-length NB-LRRs annotated in both the automatically predicted gene set of the respective genome assembly and the final NB-LRR repertoire has increased in HRPv2 compared to HRP. Availability and implementation: HRPv2 and its associated documentation and reproducible test data are available at https://github.com/AndolfoG/HRPv2. Detailed installation and dependency information is provided in the repository README. A version-pinned Conda package has also been developed and locally validated to provide a reproducible execution environment.

Let $L$ be a number field containing a CM field $K$. We compute an explicit current representing the $\mathrm{GL}_{\mathcal{O}_K}(\mathcal{O}_L)$-equivariant algebraic Eisenstein-Kronecker classes constructed by Kings-Sprang. In the Bianchi case, where $K$ is imaginary quadratic and $[L:K]=2$, this yields a purely algebraic construction of Eisenstein cohomology classes, even though the associated locally symmetric space is not an algebraic variety. We express their constant terms at the cusp in terms of partial Hecke $L$-values of $K$.

We develop a spatially explicit nonlinear biomass model for exploited fish populations incorporating density-dependent Beverton-Holt production, natural mortality, diffusion driven spatial movement, and harvesting. Starting from a reduced biomass model motivated by spawning stock biomass data, we derive a reaction-diffusion model with Neumann boundary conditions and spatially distributed harvesting. We establish positivity, boundedness, and well-posedness of the biomass dynamics, and identify a critical harvesting threshold separating persistence and extinction regimes of spatially homogeneous equilibria. A distributed optimal harvesting problem is then formulated, and the corresponding state-adjoint optimality system and pointwise projection characterization of the harvesting control are derived. The adjoint variable provides a measure of the marginal future value of biomass within the harvesting objective and offers a diagnostic that complements biomass abundance alone. Numerical simulations examine the coupled evolution of biomass, the adjoint variable, and optimal harvesting effort. The results show that diffusion progressively reduces the initial spatial heterogeneity in biomass, while the computed adjoint and optimal harvesting fields exhibit limited spatial variation under the parameter regime considered. These results illustrate how the coupled state-adjoint-control framework links spatial biomass dynamics with future management value and harvesting decisions.

Energy-efficient LLM serving requires minimizing serving GPU energy while meeting latency and throughput service-level objectives (SLOs). Attention–FFN disaggregation (AFD) enables separate resource allocation and operating controls for attention and expert computation, but their energy effects remain coupled through the execution pipeline. Realizing its energy-saving potential therefore requires navigating a hierarchical configuration space in which deployment structures constrain admissible controls and shape their end-to-end effects. Finding low-energy configurations that meet SLOs is challenging because physical evaluations are costly and only a small fraction of candidates can be measured. We present Energy-Oriented Configuration Optimization (ECO), which jointly searches deployment structures and their admissible operating controls under a limited measurement budget. ECO constructs a structure-aware energy prior from calibrated stage behavior and pipeline dependencies, then learns residual prediction errors with a Gaussian process. Its cost-aware constrained Bayesian optimization prioritizes measurements according to expected energy improvement while accounting for SLO feasibility, execution success, and evaluation cost, and returns the lowest-energy measured feasible configuration. Across all 16 scenarios on A6000 and A100 with Qwen and DeepSeek, ECO's frozen configurations, evaluated on disjoint requests, reduce serving energy by 40.5% and increase output token rate by 20.7% on average relative to baselines while meeting target SLOs. Across the 8 A6000 scenarios, its selected feasible energy averages 33.1% below generic constrained Bayesian optimization and 25.8% below genetic search.

The semantic gap between tensor-centric software models and signal-level hardware testbenches creates significant productivity bottlenecks in verifying Domain-Specific Accelerators (DSAs). Existing frameworks like Cocotb suffer from prohibitive synchronization overheads due to fine-grained interactions. To address this, we propose vTen, a data-centric framework that strictly decouples verification intent from execution mechanics. By leveraging a declarative DSL and kernel-granular batching, vTen minimizes host-simulator interaction frequency. Evaluation on a production-scale 3D U-Net accelerator demonstrates that vTen achieves a 2x performance improvement in simulation latency and a 60.3% reduction in code complexity compared to Cocotb.

We study the Dunkl–Schrödinger operator $L=-\Delta_k+V$ on $\mathbb R^N$, $N>2$, where $V$ is a nonnegative potential in the reverse Hölder class ${\rm RH}^q(dw)$, $q>\mathbf N/2$, and $\mathbf N$ is the homogeneous dimension. We establish decay estimates for the resolvent kernel in terms of the critical radius and the orbit distance. For reflection-invariant potentials, we obtain $L^p(dw)$ bounds for $VL^{-1}$, second-order Dunkl derivatives of $L^{-1}$, and the Riesz transform $\nabla_kL^{-1/2}$, together with fractional potential and mixed estimates. The proofs combine local estimates for weak solutions, the Dunkl Fefferman–Phong inequality, and kernel estimates adapted to the Euclidean and orbit distances.

Let $E/F$ be a CM extension and let $1\le r<n$. We determine primitive Fourier coefficients of Hermitian Klingen-Eisenstein series on $\mathrm{U}_{n,n}$ induced from cusp forms on $\mathrm{U}_{r,r}$, at principal congruence level. Using the pullback formula for Hermitian Eisenstein series, we express a normalized primitive Fourier coefficient of a Klingen-Eisenstein series as the corresponding primitive Fourier coefficient of a Siegel Eisenstein series multiplied by a Petersson inner product with an explicitly constructed holomorphic automorphic form. The automorphic form in the Petersson inner product is a finite sum of products of Hermitian theta series and Siegel Eisenstein series of degree $r$. Under some hypotheses, we also prove the $p$-integrality of these normalized primitive Fourier coefficients.

We give an introduction to the time-fractional stochastic heat equation driven by 1+d-parameter fractional time-space white noise, in the following two cases: (i) With additive fractional time-space white noise (ii) With multiplicative time-space Brownian noise The fractional time derivative is interpreted as the Caputo derivative of order $\alpha \in (0,2]$ and we assume that the Hurst coefficient $H=(H_0,H_1,H_2, ...,H_d)$ of the time-space fractional white noise is in $(\tfrac{1}{2},1)^{1+d}$. We find an explicit expression for the unique solution in the sense of distribution of the equation in the additive noise case (i). In the multiplicative case (ii) we derive the correct space–time convolution equation and its Wiener chaos expansion. For $1<\alpha\leq2$ a second initial condition is required. The endpoint $\alpha=2$ is treated separately and yields a stochastic wave equation with finite propagation speed. A solution $Y(t,x)$ is called mild if $E[Y^2(t,x)] < \infty$ for all $t,x$. In the multiplicative case the random-field condition is expressed by the square integrability of the forcing kernel. For the classical Laplacian and space–time white noise, the endpoint $\alpha=2$ admits a random-field solution only in space dimension $d=1$. This paper is partly a survey paper, explaining the concepts and methods behind the results. It is also partly a research paper, in the sense that some results are new, to the best of our knowledge.