Papers

We prove that plane waves are the only gravitational pp-wave spacetimes which are distinguishing; in particular, they are the only strongly causal ones. This is used to prove a null version of Anderson's rigidity theorem, conjectured by Costa e Silva and Flores: every geodesically complete, transversally complete, strongly causal, Ricci-flat Brinkmann spacetime of dimension $4$ is isometric to a quotient of a plane wave spacetime.

Ultra-high-volume slag-cement (UHVS) blends can substantially reduce clinker ratio, but slow slag reaction limits strength development; Na2CO3 is a less caustic and lower-carbon activator for alkali-activated materials, yet its moderate alkalinity can similarly delay strength development. Here, dry-blended Na2CO3 (0-20 wt.% relative to water) was incorporated into a one-part binder with 90 wt.% ground-granulated blast-furnace slag and 10 wt.% Portland cement (PC) to determine whether this integration could mitigate slow strength development in both systems. Compressive strength testing, isothermal calorimetry, time-resolved quantitative X-ray diffraction, Fourier-transform infrared spectroscopy, aqueous solution analysis, and thermodynamic modeling were combined to determine how Na2CO3 controls phase assemblage, alkalinity, calculated porosity and strength development. At 5-10 wt.% Na2CO3, calcite-dominated carbonate reactions promoted a rapid alkalinity increase and accelerated early-age reaction and strength development; however, subsequent alkalinity decline limited later-age slag reaction and gel formation. In contrast, 20 wt.% Na2CO3 favored substantial early formation of gaylussite and carbonate-AFm phases, which moderated the initial pH rise and delayed early gel accumulation. The larger alkali inventory and evolving phase-solution partitioning helped sustain alkalinity at later ages, enabling continued slag dissolution and gel formation. This pathway produced higher reaction extent and lower calculated porosities, with compressive strength approaching that of neat PC. Screening-level cradle-to-gate life-cycle assessment indicates a 66-72% reduction in global warming potential relative to PC, depending on Na2CO3 production pathways. These results identify carbonate-mediated control of alkalinity persistence as key to sustaining slag reaction in UHVS systems.

We investigate how parameter-efficient adaptation of an atmospheric foundation model affects downstream regional precipitation in a controlled Aurora-WRF coupling experiment over the Beijing-Tianjin-Hebei region. A single-step, precipitation-weighted LoRA adaptation of AuroraPretrained is trained on May-September 2020-2021 and selected using 2022 validation data. Five inference-time adaptation strengths are coupled to an unchanged 9-km WRF configuration and compared with a GFS-driven control under common ERA5 initialization and auxiliary-field rules. Evaluation uses 17 initializations in 2023, hourly ERA5 precipitation, and conservative remapping to a fixed 356-cell, 0.25-degree verification grid. Heavy rainfall is defined exclusively as at least 50 mm in a continuous 24-hour window, advanced hourly. For window starts from 0 to 48 hours, unadapted Aurora attains the highest mean critical success index (CSI), 0.216, compared with 0.144 for the GFS control. An intermediate LoRA strength of 0.75 reduces the Aurora-driven 24-hour precipitation mean squared error by 30.7% and brings pooled frequency Bias from 1.510 to 1.024, but lowers CSI to 0.182. GFS retains the lowest whole-domain error. These results characterize a trade-off between rainfall detection, frequency calibration, and intensity error, showing the importance of evaluating adaptation strength against multiple downstream criteria within a common coupling framework.

In the year $1977,$ while developing the theory of modules arising in the context of Serre's problem on projective modules in the paper “On Stably Free Modules" (see \cite{AS}), A. A. Suslin constructed matrices inductively using unimodular rows. Our aim is to connect these matrices to the current and applicable field of coding theory. To this end, we construct Suslin-Rao codes, by using looking at certain unimodular all one vectors over the finite field $\mathbb{F}_2$. Comparative analysis with standard families such as Hamming, Simplex and BCH codes shows that the Suslin-Rao codes achieve better performance than Hamming and Simplex codes in terms of code rate and error correction capability, though BCH codes may outperform them for large code lengths. Bit error rate (BER) versus signal-to-noise ratio (SNR) simulations further support the practical applicability of these codes in noisy channels. The recursive nature of the construction allows efficient encoder design, making the proposed codes attractive for real-time communication systems and hardware implementation.

Physics-informed neural networks (PINNs) often converge to inaccurate solutions for conservation laws with shocks, because uniformly distributed collocation points undersample localized features and let the residual be dominated by regions that are already well resolved. We propose a feature-tracking PINN (FT-PINN) in which the solution network is defined on a fixed reference domain and composed with a diffeomorphic deformation map from a parameterized nonlinear manifold. The deformation and solution-network parameters are trained jointly by minimizing the pulled-back conservation-law residual. This lets collocation points concentrate along features of essentially arbitrary geometry, including curved, oblique, and merging shocks, without prior knowledge of their locations. The framework is agnostic to the choice of parameterization. Boundary preservation is enforced exactly through a tangential projection of the displacement, and folding is discouraged by a one-sided penalty on the Jacobian determinant. On four test problems (space-time viscous Burgers with merging shocks, a decelerating Burgers shock, the space-time Euler shock tube, and steady 2D Euler regular shock reflection), FT-PINN resolves shocks at their correct locations with a limited collocation budget. A vanilla PINN with the same architecture, budget, and training either misplaces the shocks or fails to form them.

On Blackwell, normalization and operand movement can limit attention kernels whose matrix multiplications are already deeply pipelined. We implement an FA4-style pipeline in Triton TLX with fixed-shift dense softmax and a saved inverse denominator for backward. The fixed shift removes recurrent accumulator corrections; the saved reciprocal moves row normalization from the quadratic backward loop into linear preprocessing. The guarded causal path uses a first-block anchor with selective recovery, and fully masked diagonal contractions are skipped. A packed BF16 exponential approximation and pipelined dQ publication reduce per-element work and on-chip movement. On B200 at 1,000 W, using prepared launches and the original FA4 timer, TLX improves geometric-mean throughput by 7.3 percent across the 24 cases in FA4's BF16 variable-batch grid through 32,768 tokens at head dimension 128. Dense forward and backward improve by 13.0 and 10.4 percent, respectively. Causal backward improves by 8.0 percent, while causal forward is 1.5 percent slower. The TritonBench comparison has geometric- mean gains of 13.4 percent in forward and 24.4 percent in backward

Compression trees have been historically a key component of several arithmetic units, most notably multipliers. The latter have been for the most part standalone units and in common situations synthesis tools can generate very close to optimal solutions. With large matrix multiply structures taking more of a central role in the compute industry, the need for a better understanding of these compression trees is apparent. Furthermore, the boundary of its usage needs to be redefined: dot products, polynomial fitting of non-linear operators, are all sums of products. And since products are sums of partial products, in the end, we are just adding many things together as bit heaps; i.e. the fundamental role of a compression tree. Therefore, we must see them as more than just a component of a multiplier. This paper presents a delay-aware compression-tree methodology based on a weighted bit heap. Each bit is described by its significance and relative arrival time, and the generator uses technology-independent normalized delay units to estimate Boolean logical pressure. By exploiting the commutativity of addition within each column, the method reorders bits across reduction stages and uses a Dadda-style maximum-bandwidth topology with flexible CSA3:2 operators. For Radix-4 Booth multipliers from 11 to 64 bits, the resulting trees show lower modeled delay and estimated logic volume than the evaluated Wallace-style maximum-compression trees. Fused four-way integer dot products further demonstrate how the same representation can evaluate the cost of microarchitectural constraints, such as preserving individual product redundant formats. These results show that weighted bit-heap generation provides a practical technology-independent basis for exploring compression trees beyond standalone multiplication.

Conventional FPGA routing optimizes timing, congestion, and routability but does not distinguish routes with similar nominal performance and substantially different susceptibility to configuration-induced delay degradation. This paper presents a vulnerability-weighted routing methodology for SRAM-based field-programmable gate arrays (FPGAs) that incorporates predicted routing-fault severity directly into the routing objective. A continuous vulnerability cost relates delay perturbations caused by electrically attachable dormant routing resources to the available downstream timing slack, while a complementary configuration-concentration term discourages excessive localization of vulnerable resources. To limit implementation disruption, only the highest-risk nets are selectively ripped up and rerouted while unaffected routes remain fixed. The method is implemented on a Zynq UltraScale+ XCZU7EV using a Vivado/RapidWright-based flow and evaluated across four routed benchmarks against commercial timing-driven routing, vulnerability-agnostic rerouting, and binary vulnerable-resource avoidance. Controlled configuration-equivalent perturbations provide hardware-level validation. The proposed method reduces aggregate configuration-induced timing vulnerability by 41.7% with approximately 1.0% nominal timing degradation and captures 85.8% of the vulnerability reduction obtained at the expanded routing budget by rerouting only the highest-risk 5% of eligible nets. The results demonstrate that continuous vulnerability information can improve configuration-upset resilience with limited impact on nominal routing quality.

A world model learns to forecast how a physical system evolves from recorded trajectories, yet the systems it imitates obey physical laws that are neither fully supplied nor reliably respected. The model may create energy, drift or diverge over long rollouts, and answer a changed law query using the law observed during training. We ask how much general physical structure must be hard coded into a world model, and how much system-specific physics can then be learned from data, for four properties to hold simultaneously: second law compatible dissipation, correct responses to interventions on physical parameters, stability out to one hundred times the training horizon, and robustness to disturbances. The imposed structure is general: dynamics are generated from the gradient of a learned energy through a fixed reversible operator, the energy is restricted to a confining class, a one way port can remove energy but never inject it, the drive channel is known, and the intervened parameter enters through a separable map. The model learns the energy functional, constitutive relations, dissipation rate, and couplings. Across an electromagnetic cavity, a particle in cell grid, and a shallow-water fluid, models with roughly nine thousand parameters recover constitutive functions with unit slope, separate conserving from dissipating worlds by four orders of magnitude using a single set of weights, and transfer changes in sign, magnitude, rate, and gravity to unseen values, where equal-capacity models without the same structure perform at chance or worse. A nonlinear constitutive law is recovered with its curvature preserved and predicts a held-out intervention $2$-$17\times$ better than a converged linear model.

The segmentation of anatomical structures in medical images and particularly in MRI scans, is essential for clinical diagnosis and monitoring disease progression. While Deep Learning (DL) architectures, such as U-Net and its extensions are very effective in medical image segmentation tasks, they often struggle with preserving fine-grained details and global contextual information. This is especially challenging for MRI data segmentation, where anatomical structures are characterized by irregular boundaries and variations in shape, contrast, and scale. To address this challenge, we propose a novel DL architecture for MRI segmentation across different anatomical structures. Specifically, the architecture introduces a module, named Multi-Resolution Feature Fusion (MRFF), that can be easily integrated into any U-Net-like architecture. The MRFF is integrated in all levels of an encode-decoder structure, along with attention mechanisms and skip connections to extract features at multiple resolutions, enabling the model to capture both fine-grained details and global contextual information. We evaluate the MRFFU-Net on two publicly available benchmark MRI datasets of different anatomical targets; one for Cerebrospinal Fluid (CSF) segmentation in spinal MR scans, and one for left atrium cardiac segmentation, from the Medical Segmentation Decathlon (MSD) challenge. Experimental results indicate that MRFFU-Net outperforms state-of-the-art models across multiple evaluation metrics, demonstrating its effectiveness in MRI segmentation.

The one-dimensional planar compressible magnetohydrodynamic system is studied on unbounded domains. The longitudinal viscosity obeys a power law of the specific volume, which permits it to degenerate as the density approaches vacuum, and the heat conductivity follows a power law of the temperature. For any fixed non-negative exponent in the heat conductivity term, the existence and uniqueness of global strong solutions are established for arbitrarily large initial data, provided that the positive exponent for viscosity is sufficiently small. The specific volume and temperature possess time-independent upper and lower bounds. Moreover, for each admissible viscosity exponent, the solution converges uniformly in space to the equilibrium state as time tends to infinity.

Federated multimodal graph foundation models (GFMs) aim to adapt pretrained multimodal models to decentralized graph data, where each client owns a private multimodal graph and cannot share raw information. These models typically combine a multimodal Encoder that extracts semantic evidence from heterogeneous modalities and a graph neural network (GNN) that performs relational reasoning over graph structures. However, existing federated GFM adaptation methods mainly update graph-side modules while keeping the multimodal Encoder frozen, limiting adaptation to how information is propagated while fixing what information is extracted. Through empirical studies, we reveal that Encoder and GNN adaptations are not independent: Encoder adaptation is affected by graph relations, while cross-client module swapping reveals substantial pairing sensitivity between separately parameterized Encoder and GNN updates. Motivated by this observation, we propose FedCORE, a federated adaptation framework that represents Encoder and GNN updates through a shared low-dimensional latent state. FedCORE jointly optimizes this core from multimodal and structural signals and performs federated evolution directly in the shared state space, preserving compatibility between perception and reasoning adaptations. Extensive experiments demonstrate that FedCORE reduces the Encoder–GNN pairing gap from $30.6$ to $5.9$, corresponding to an $80.7\%$ reduction over independent joint adaptation.

We determine the minimax dimension dependence of noisy zeroth-order optimization for globally strongly convex functions with higher-order smoothness in multilinear operator norm. Each query returns one function value with fresh independent Gaussian noise. For dimension $d$, query budget $T$, and any fixed finite smoothness order $\beta>2$, the minimax expected objective error satisfies $\mathcal{E}_{\beta}(T,d)=\Theta_{\beta}\left(\min\left\{1,(d^2/T)^{(\beta-1)/\beta}\right\}\right)$, with dimension-independent strong-convexity, gradient-smoothness, higher-order-smoothness, noise, and minimizer-radius bounds. Thus, for sufficiently small target error $\varepsilon$, the necessary and sufficient number of noisy values is $\Theta_{\beta}(d^2\varepsilon^{-\beta/(\beta-1)})$, with no logarithmic loss. The new lower bound matches the dimension and budget dependence of the upper bound of Akhavan et al. (2024), and holds for arbitrary randomized adaptive algorithms with unrestricted query points. Its key step localizes a normalized hypercube with one radial cutoff: a query can emphasize one hidden coordinate, but the aggregate information about all coordinates remains small. A self-contained multiscale spherical estimator attains the matching upper bound by cancelling lower-order bias terms. Constants in the rates depend only on the fixed smoothness order under the stated normalization.

We prove a joint stochastic zeroth-order lower bound for Goldstein stationarity on a Euclidean query ball, even when the ball is guaranteed to contain a stationary point. In dimension $d$, let $f=\mathbb{E}[F(\cdot;\xi)]$, assume $\mathbb{E}[\operatorname{Lip}(F(\cdot;\xi))^2]\le L_0^2$, and bound the initial objective gap over the ball by $\Delta$. For neighborhood radius $\delta>0$ and residual tolerance $\varepsilon>0$, our smooth hard family requires $\Omega(dL_0^2\Delta/(\delta\varepsilon^3))$ scalar evaluations for success probability $1/2$, against randomized adaptive algorithms that may retain and repeatedly query each sampled function. The result holds for $\varepsilon\le cL_0$, $\Delta\ge C\delta\varepsilon$, and $d\ge C[1+\log(2+\Delta L_0^2/(\delta\varepsilon^3))]$, on a constructed ball of radius $\Theta(\Delta/\varepsilon)$. A sequence of localized regions forces repeated direction estimation, and an adaptive Gaussian posterior argument controls sample reuse. The result establishes a joint dimension and accuracy obstruction on solvable bounded-domain instances. The gap is local to the query ball; a matching minimax characterization at a common radius and the corresponding unrestricted global-gap lower bound remain open here.

We ask whether Kochen-Specker contextuality is Lorentz invariant. On the full Hilbert space, it is, since boosts act unitarily. Restricted to spin, it is not: momentum acts as an environment applying momentum-dependent Wigner rotations, leaving spin observables unsharp and breaking the operator identities behind state-independent contextuality. For spin $1/2$ one scalar governs the loss, the packet average $\Delta$ of $\sin^2(\theta_W/2)$ (where $\theta_W$ is the Wigner angle); for any spin, a ray degrades at a rate set by its spin variance transverse to the boost. In the spin-only account, the Free Will Theorem's SPIN axiom fails for every $\Delta>0$; the Yu-Oh set loses contextuality between $\Delta\approx0.008$ and $0.016$, with state independence going first; the Peres-Mermin square loses contextuality at $\Delta\approx0.059$ or $0.074$ by orientation; singlet CHSH loses nonlocality for $\Delta\geq0.159$; and a GHZ-state OR gate loses Raussendorf's contextuality certificate at $\Delta\approx0.206$. A $q$-plate implements the channel exactly on photon polarisation, with a retardation in place of the rapidity, so the nonlocality, GHZ and aimed-source results are testable without motion.

Quantum networks composed of loop-like structures provide a rich platform for exploring electronic transport phenomena and have been widely studied in various contexts. However, their thermal response remains relatively unexplored, motivating us to investigate it in the present work. We consider a tight-binding (TB) quantum network composed of a finite number of triangular plaquettes, where neighboring plaquettes are connected through single bonds and each triangular loop is threaded by an Aharonov-Bohm (AB) flux $\phi$. The interplay of nonuniform site coordination, hopping asymmetry, and quantum interference gives rise to both dispersive and completely flat energy levels. We derive an analytical condition involving the TB parameters under which one of the energy branches becomes independent of the electronic momentum. We further show that the AB flux $\phi$ provides a direct means of tuning the position of the flat band. The characteristic features of the energy spectrum associated with this quantum geometry are reflected in the thermal response, which we investigate through the electronic specific heat (ESH). In particular, we demonstrate that the position of the flat band manifests itself as a distinct feature in the ESH, establishing a direct connection between the flat-band formation and the thermal response of the system. Thus, the ESH provides an alternative route for identifying the presence of a flat band, consistent with the analytical condition and the corresponding energy dispersion. Moreover, the AB flux allows the ESH to be selectively regulated through the tuning of the flat-band position. The proposed approach provides a simple complementary means of identifying momentum-independent energy levels and may be extended to other simple and complex quantum networks supporting flat bands.

Native full-duplex speech models can respond before a user finishes speaking, making the behavior of the model depend on both the final utterance and when intent-defining information arrives. Existing benchmarks primarily evaluate turn-taking mechanics, whereas safety evaluations typically assume that the complete request is observed prior to response generation. We introduce LateIntent-Bench, a matched-pair benchmark for delayed intent revelation. A shared ambiguous prefix precedes either a benign or a harmful continuation, using a controlled pause to delay when the branches become distinguishable. We define the Premature Response Rate (PRR) to measure whether response onset precedes the revelation of intent. Joint evaluation of harmful and benign engagement distinguishes changes in safety selectivity from general losses in responsiveness. Across 3,136 sessions, four native full-duplex models exhibit distinct response-timing patterns under delayed intent. Three models show increased harmful engagement while maintaining benign responsiveness, whereas one loses engagement with both branches. Inserting a 1.5s silence after intent revelation keeps PRR near the no-pause baseline and substantially reduces changes in harmful engagement. These results demonstrate that evaluating fully specified requests alone fails to capture emerging timing patterns, highlighting the necessity of assessing delayed intent revelation in full-duplex models. The code will be publicly released soon.

We prove that every $p$-absolutely Cesàro bounded operator with constant $K>1$ is $q$-absolutely Cesàro bounded for $1\leq q<pK/(K-1)$. This range is optimal, even for positive weighted shifts. On Banach spaces of type $s\in (1,2]$, we prove that every absolutely Cesàro bounded operator is $q$-absolutely Cesàro bounded for every $1\leq q<s$, with a logarithmic estimate at $q=s$. We also prove the polynomial growth bound $\| T^n \| =O(n^{1/s-\varepsilon})$ for some $\varepsilon>0$. On $L^p$-spaces, $1<p<\infty$, we extend the implication from absolute Cesàro boundedness to $p$-absolute Cesàro boundedness from positive to individually eventually positive operators. Finally, for every $1\leq p<\infty$, we construct a $p$-absolutely Cesàro bounded operator $T$ on $\ell^1$ such that $\sigma(T)\subseteq\mathbb D\cup\{1\}$ but $\limsup_{n\to\infty}\|T^n(I-T)\|=\infty$. We also observe that the construction yields a single operator which is $p$-absolutely Cesàro bounded for every $1\leq p<\infty$.

Multimodal graph learning faces a fundamental challenge: new classes may emerge after deployment, while models are trained with a fixed label space. Existing approaches typically detect unknown nodes and use LLMs to generate candidate class descriptions, but they do not determine whether existing classes are insufficient to cover these nodes or whether a generated class is reliable enough to expand the class space. Our empirical study reveals three challenges: multimodal information beyond individual modalities is required for unknown-node identification, LLM-generated class descriptions may not fully capture multimodal class characteristics, and directly adding candidate classes can introduce redundant categories. Based on these observations, we propose MOVE, a multimodal open-world class verification and expansion framework. MOVE identifies nodes that cannot be assigned to existing classes by jointly considering visual tokens, textual attributes, and graph context, leverages a multimodal LLM to generate candidate classes, and selectively expands the class space only when candidates are consistently supported by multimodal evidence without introducing unnecessary categories. Experiments demonstrate that MOVE achieves an average improvement of 11.87% across unknown recognition, open-domain annotation, and downstream graph learning tasks.

Compact edge system-on-chip (SoC) platforms increasingly run sustained LLM inference under thermal constraints, while their CPU, GPU, and RAM share a cooling path. Prefill and decode therefore consume shared, time-varying thermal headroom, yet vendor governors react only near hardware throttling thresholds without knowledge of request state or upcoming work. A control decision that improves current performance can thus consume headroom too quickly and degrade subsequent service. In this paper, we present ThermE, a runtime system that predicts and jointly manages shared thermal headroom for sustained LLM inference on edge SoCs. Its Fast LLM-to-Heat Compiler maps the model, requests, runtime state, and candidate actions to domain heats without executing LLMs. A partial differential equation (PDE)-constrained Headroom Predictor uses ThermPINN for offline thermal identification and a Reduced Headroom Predictor (RHP) for low-overhead online uncertainty-calibrated headroom forecasts. An Uncertainty-Aware Action Scheduler then selects actions that balance serving quality and future headroom. We implement ThermE atop vLLM and evaluate it across four LLM inference workloads. The results show that ThermE reduces TTFT and TPOT by 40.55% and 12.17%, respectively, relative to vLLM. It achieves a 5.70% SLO violation rate, compared with 12.30% for the strongest baseline, while its predictor obtains a 1.94 $^\circ$C MAE with 11.50 ms overhead.

The sample complexity of identifying an unknown pure stabilizer state has been a longstanding problem in quantum information. In this paper, we resolve the entire exact critical crossover for the uniform ensemble of pure $n$-qubit stabilizer states under arbitrary collective measurements and without side information. For $k=n+c$, with fixed integer $c$, the optimal success probability converges to an explicit positive series $P_{\infty}(c)$. In particular, $P_{\infty}(0)=0.1760837896\ldots$, while its two tails obey a quadratic-exponential law below threshold and $1-P_{\infty}(c)\sim2^{-c}$ above threshold. The pretty-good measurement is exactly optimal for every finite $n$ and $k$. The proof diagonalizes the stabilizer Gram operator through Clifford tensor-power duality and a defect filtration, including the exceptional binary sectors. The resulting integer-scale law quantifies the $n+O(1)$ copy threshold.

Large Language Bayes (LLB) answers an informal modelling question by sampling candidate probabilistic programs from a language model, running approximate inference on each, and averaging them with weights proportional to an exponentiated evidence bound. We show that this weighting depends on how a model is written. The log marginal likelihood is invariant to reparameterisation; the evidence bound is not. On eight schools the centered and non-centered programs are the same measure to $5.7\times10^{-14}$, yet their weights differ by $6.1\times$; importance weighting reduces this only to $2.2\times$, and reproducing the inference LLB actually runs, a full-covariance Gaussian matched to the posterior moments, still leaves $1.9\times$ on eight schools and $8.9\times$ in $64$ dimensions. Across likelihood families, dimensions and funnel severities the discrepancy reaches $31.9\times$ and reverses sign, so no single writing is uniformly preferable. It inverts Bayes factors against eight natural competitors, and the induced error in the model posterior, and in any downstream target, is controlled by the spread $\Delta$ of the bound shortfalls through a known sharp Hilbert-distance bound. Across $360$ programs from six language models the parameterisation written ranges from $0\%$ to $100\%$ centered and is stable within a model. Detecting equivalent programs statistically can falsely merge genuinely different models at practical sample budgets; verifying reparameterisations we generate ourselves cannot, and closes the window.

Energy imbalance remains a key challenge in Wireless Sensor Networks (WSNs), as nodes near the base station deplete their energy faster due to heavy forwarding loads. While mobile agents (MAs) have been employed for either data collection or sensor charging, existing approaches lack adaptability and fail to integrate both functions under realistic hardware constraints. This paper introduces a unified mobile agent framework that performs both data collection and wireless charging sequentially under single-antenna limitations. The agent's decision-making is formulated as a two-layer Hierarchical Reinforcement Learning (HRL) problem, where the upper layer optimizes movement planning and the lower layer determines the appropriate service based on real-time network states. This hierarchical structure enables the agent to learn adaptive task scheduling policies without predefined rules. Extensive simulations demonstrate that the proposed method achieves up to 15% longer network lifetime and more balanced energy distribution compared with state-of-the-art mobile agent and deep RL approaches.

We associate to finite block size data \[ \bm n=(n_d)_{d\ge1},\qquad n_1>0, \] a positive definite cyclotomic form and a Householder reflection representation. Writing \[ N=\operatorname{lcm}\{d:n_d\ne0\},\qquad \wt=\sum_d d^2n_d, \] the form on the cyclic group $C_N$ is \[ B_{\bm n}(g,h)=\frac1{\wt}\sum_{(g^{-1}h)^d=1}d^2n_d. \] Its labelled Fourier spectrum reconstructs the complete multiplicity sequence by Möbius inversion. If the $n_d$ are the Wedderburn multiplicities of a split semisimple algebra $S=\prod_d M_d(k)^{n_d}$, the divisibility widths are dimensions of characteristic sums of Wedderburn blocks, and the form together with $\dim_kS$ recovers the isomorphism type of $S$. The main theorem is an arithmetic rigidity result. For $N\ge2$, the reflection group is finite if and only if it preserves a full rank lattice, equivalently \[ \supp(\bm n)=\{1,N\},\qquad n_1=N^2n_N. \] In this case $B_{\bm n}=\frac12(I+J)$ and the group is $W(A_N)\cong S_{N+1}$. In semisimple algebra terms, finiteness is equivalent to \[ S\cong k^{N^2m}\times M_N(k)^m \] for some $m\ge1$. For $N=2$, every nonfinite case is a dense copy of $D_\infty$ in the corresponding orthogonal group. For contraction algebras of threefold flops, Toda's width formulas identify the total scale and primitive Fourier mode with $\dim A_{\con}$ and $\dim A_{\con}^{\ab}$. This yields infinitude for all irreducible flops of length at least three and, in length two, \[ \Gamma_f\text{ finite}\quad\Longleftrightarrow\quad \dim A_{\con}=2\dim A_{\con}^{\ab}. \] The final part gives a complementary BPS/Riemann–Hilbert realization of the same reflection matrices.

Selective intent routing allows an assistant to act on reliable predictions while deferring uncertain requests. Standard confidence scores primarily reflect the base model's representation, leaving an opportunity to incorporate complementary evidence without changing its decisions. We introduce a signed lexical gate that combines a sentence classifier's logit margin with a sparse lexical model's support for the classifier's predicted intent. By assigning positive evidence to lexical agreement and negative evidence to a lexically favored competing intent, the gate retains more information than either unsigned lexical confidence or a hard agreement rule. An independent binomial calibration stage selects an operating threshold for a specified risk target. Across ten runs on BANKING77, CLINC150, and HWU64, the proposed score reduces area under the risk-coverage curve by 15.8%, 15.1%, and 11.8% relative to a learned semantic-only gate. At a nominal 5% error target, it increases accepted coverage by 1.83 and 5.14 percentage points on BANKING77 and HWU64, while CLINC150 is already near full coverage. At a stricter 2% target, the simultaneous binomial procedure yields a nonempty policy in all 30 dataset-run combinations at the available calibration budgets. Matched controls show that the proposed feature improves average error ranking over the tested unsigned lexical-confidence feature, with dataset-dependent gains over binary agreement. The resulting two-feature gate provides a compact, interpretable confidence enhancement for risk-calibrated intent routing while preserving the base classifier's predictions.

The spectral weight with which a many-body eigenstate contributes to a given channel is not fixed by the smooth one-point ETH envelope, and its higher-order correlations—the connected cumulants of three and more channel-resolved spectral functions—have lacked a systematic organization. We construct one. In random free fermions, where every channel overlap is a squared Slater minor of a Haar-orthogonal one-body eigenvector matrix, the $r$-resolvent moment admits an exact replica-sector decomposition: a sum over the double-coset sectors of the orthogonal Weingarten algebra, in which the permutation sectors are the replica contraction classes and each sector value is determined by the overlap pattern of the channels and of the eigenstates. The sector coefficients follow from an exact occupancy-matrix assembly—a signed convolution over the slot permutations, a decomposition into connected blocks, and a finite-state chain transfer matrix whose local transition rules are independent of $r$ and $k$—so the sector theorem holds at arbitrary finite multiplicity, realized exactly at $r=3$ ($k=2,3,4$), $r=4$ and $r=5$ ($k=2$). The structure carries the physical hierarchy: the fully coincident sector is the projection that yields the Selberg moment ratios $q_r$, the levels are nested by exact marginalization, and the sectors are the multi-energy spectral cumulants behind the resolvent cumulants, with the irreducible self-energy vertices of the Feshbach ladder as the connected kernel. The multi-resolvent correlations of random free fermions are therefore organized, level by level, by one replica-sector algebra—an exact microscopic benchmark for the higher-order fluctuation sector of eigenstate thermalization, with its microscopic sector geometry made explicit.

We establish sharp high-probability statistical rates for nonsmooth stochastic convex optimization under heavy-tailed noise, closing the confidence-dependence gap in both general convex and strongly convex settings. We consider composite objectives with a Lipschitz convex loss and a known proximal regularizer, accessed through fresh unbiased stochastic subgradients. The centered noise has conditional norm and directional $p$th moments bounded by $L^p$ and $s^p$, respectively, where $1<p\le2$ and $0<s\le L$. For $T$ oracle calls and failure probability $0<\delta<1/10$, set $q=1-1/p$, $\ell=\log(3/\delta)$, and $A=s(L^2/s^2)^q$. With initial distance bound $D$, the minimax objective error is $\Theta(D(A+s\ell^q)/T^q)$ in the nonsaturated statistical regime. For a $\mu$-strongly convex regularizer, the corresponding quadratic-regime rate is $\Theta((A^2+s^2\ell^{2q})/(\mu T^{2q}))$. These rates require domination of the deterministic and finite-variance terms; matching lower bounds require $d\ge\lceil L^2/s^2\rceil$, while the upper bounds hold in every finite dimension. The new upper bounds attain known statistical lower-bound orders, replacing the previous confidence coefficient $s^{1/p}L^{1-1/p}$ by $s$, and its square by $s^2$ under strong convexity. The key is an online inequality that separates directional fluctuations from the total second moment created by rejection sampling. Localization preserves this separation under strong convexity without additional horizon logarithms. The results characterize oracle complexity with unrestricted internal computation.

We determine the dimensions of all derivative loci and all higher multiplicity loci of an elementary symmetric polynomial over an algebraically closed field of positive characteristic. For the degree-d polynomial in n variables, set Q = p^{v_p(n-d+1)}. The common zero locus of its order-q derivatives has dimension d - q - 1 + 1_{Q>d-q}, whereas the locus of zeros of multiplicity at least s has dimension d - s + 1_{Q>d}. The order-two case settles the dimension question in a conjecture of Orzel, with a necessary correction when d is a power of p. We classify all components attaining the larger dimension and prove that they are generically smooth. Along the coordinate components in the smaller-dimension cases, we determine the local rings and obtain generic multiplicity exactly Q. Finally, we identify the full translation stabilizer scheme and derive a Frobenius normal form. These results distinguish dimension jumps from infinitesimal thickening and give a uniform description of their dependence on the characteristic.

Smart manufacturing needs to move sensor data off the plant floor, react to it, and feed decisions back to actuators within bounded time. Programmable logic controllers (PLCs) handle fast, deterministic, safety-critical actuation, but they are not designed for the higher-level functions required by Industry 4.0, such as predictive maintenance, machine learning inference, and cross-facility analytics. These functions need a scalable, durable, and observable communication substrate. We present the communication architecture of a production system that provides this substrate and closes the loop back to the plant in near real time. The design is built from industry-standard components: Apache Kafka as the streaming backbone, OPC-UA for PLC connectivity, a relational time-series database for persistence, and JSON for serialization. The novelty is architectural. We show how these standards are integrated for closed-loop industrial control through four design choices: a single event stream per production line serves control, monitoring, machine learning, and durable recording, allowing one producer to serve many independent consumers; a protocol bridge converts polled OPC-UA traffic into publish/subscribe streams, aligns per-signal timestamps to a common time base to remove cross-signal jitter, and provides a symmetric actuation path; a transport technique carries sub-second process dynamics at a coarser publication cadence by packing timestamped samples into fixed-order arrays; and an edge-to-cloud replication scheme keeps the edge authoritative, so local control continues during wide-area network outages while cloud analytics operate on replicated data. We describe the loop latency budget, report measured broker transport latency, and discuss operational experience. The system provides soft, near-real-time behavior rather than hard real-time guarantees.

In standard transformer attention, a source token sends the same value vector to every receiver. The query determines how much to attend but not what to extract. This work introduces attention manifolds: learned 2D B-spline surfaces $S_d(q_d, k_d)$ that modulate each value dimension based on the query-key interaction. Each surface is a tensor-product cubic B-spline initialized to zero, preserving pretrained behavior. Applied to LLaMA 3.2-1B-Instruct and 3B-Instruct, attention manifolds reduce WikiText-2 validation perplexity by 2–2.5 points with 0.3% parameter overhead. Across 112 diverse prompts, surfaces change greedy-decoded output for 69% (1B) to 83% (3B) of cases, with the strongest effects on ambiguous and polysemous inputs (94–100% change rate). The surfaces improve output quality: correcting factual errors (“the CAP theorem has three main components” $\to$ “it is impossible to guarantee all three”), increasing precision (“impossible to know certain properties” $\to$ “impossible to know both position and momentum”), and adding specificity (a generic quote $\to$ an attributed Saint Augustine citation, consistently at both scales). The learned surfaces are also mechanically editable: inverting a layer's coefficients changes greedy output for 9/10 prompts (KL~0.010), providing a geometric mechanism for model steering. Setting surface coefficients to $-1$ creates “attention walls” that block value flow through specific dimensions. In a preliminary experiment, a layer-wide wall redirects an explosive-device prompt from specific instructions to general educational content, suggesting a path toward safety-oriented manifold shaping.