Papers

Immersive computing is poised to become a major paradigm for future human-computer interaction (HCI), enabling spatial and embodied experiences across applications such as education, healthcare, manufacturing, emergency response, and scientific discovery. However, today's Internet and computing infrastructure were not designed for real-time, multi-user, sensor-rich, and privacy-sensitive immersive applications. They require coordination across sensing, representation, compression, networking, edge/cloud computing, rendering, security/privacy, and human experience. This report summarizes key findings from the NSF Workshop on Networking and Systems Challenges in Immersive Computing. The workshop brought together researchers from networking, systems, extended reality (XR), artificial intelligence (AI), graphics, HCI, security, privacy, and applications to identify challenges and opportunities. We conclude that immersive computing cannot be enabled by isolated advances in network bandwidth, device capabilities, AI models, or rendering alone. The field needs end-to-end architectures that adapt to user behavior, application requirements, resource constraints, and social expectations. We organize the agenda into six themes: networked systems for immersive computing; real-time edge-cloud orchestration for XR applications; AI for immersive experiences; privacy, security, and trust in XR systems; human-centered design and user experience in XR; and scalable infrastructure, testbeds, and open ecosystems for XR. We further identify key research questions, future trends, risks, ten-year success metrics, and action items for academia, industry, government, and research community. The report calls for coordinated investment in open platforms, reproducible benchmarks, privacy-preserving systems, and human-centered evaluation to build trustworthy, scalable, and broadly impactful infrastructure.

In this Letter, we develop a graph-geometric framework and prove that the pentagonal bipyramid (PBP) is the unique global minimiser of both the seven-particle Lennard-Jones energy in $\mathbb{R}^3$ and the seven-charge Thomson energy on $S^2$, up to rigid symmetries and particle relabelling. For the Thomson problem, this strengthens a recent deterministic global-optimality certificate to numerical tolerance into an exact global-optimality and uniqueness theorem. A weak-interaction graph, defined by thresholding pair geometry, organises configuration space without imposing symmetry or discarding any pair interaction. For Lennard-Jones, pair-energy counting, graph classification, subset bounds, and force balance reduce all possible minimisers to 29 bounded domains; exact geometric certificates exclude 28, localise the survivor near the PBP, and a uniform restoring-energy estimate proves uniqueness. The Thomson proof follows the same progression: graph reduction, geometric localisation, and rigidity, but finalises through whole-domain coercivity and a global localisation theorem. The same fivefold order therefore emerges in two very different physical settings: an unconstrained cluster with a preferred bond length and purely repelling charges confined to a sphere, showing a common geometric organising principle for seven particles that is not tied to either interaction.

Understanding how transmission varies across age groups is important for epidemic surveillance and targeted intervention, but estimating age-specific transmission in near real time is challenging when infections are only partially observed, observations are delayed, and transmission varies across age groups. We develop a Bayesian age-stratified renewal model that jointly estimates latent infections, time-varying age-specific susceptibility, and age-specific contributions to transmission within an empirically specified contact structure. To enable sequential inference under these processes, we use a block particle filtering approach embedded within a sequential Monte Carlo squared framework, with fixed-lag smoothing to account for temporal dependence and delayed observations. From the inferred transmission process, we derive a next-generation matrix, effective reproduction number, and reproduction contributions. Applied to age-stratified COVID-19 surveillance data from Ireland during the Omicron dominant period, the framework reveals heterogeneity in susceptibility and transmission, with older adults exhibiting higher susceptibility, while younger and working-age groups make larger contributions to transmission because of their higher contact rates. These results demonstrate how statistical inference can provide age-specific transmission estimates to support targeted epidemic monitoring and intervention.

Layer pruning reduces the size and inference cost of vision-language-action (VLA) models, but selecting a deployable configuration requires deciding both which layers to remove and how to recover task performance. These decisions depend on the model and task, and a failed trial can reflect either the deletion set or insufficient recovery. We present AutoPruner, an agent-driven framework that jointly searches pruning structures and recovery recipes through closed-loop experimentation. Offline layer interventions measure changes in action output to provide functional evidence. An LLM agent combines this evidence with evaluation history and retained diagnoses to propose deletion sets and recovery recipes within a search budget. Each proposal is executed and evaluated on the target tasks, and the resulting feedback guides the next experiment. Across OpenVLA-OFT, StarVLA, and FastWAM on four LIBERO suites, AutoPruner removes 16.7–87.5% of backbone layers while maintaining task success above 90%, with measured inference speedups of up to 2.50$\times$. Further analysis shows that functional probes identify action-sensitive layers despite high representation similarity, and that recovery can make previously failing structures viable.

This article focuses on defining the Euler class group of stably free module and analyzes the condition for existence of unimodular element in corresponding projective module.This is an improvisation of work by Banerjee and Das, On a question of Nori:Obstructions,improvements and appliaction. If A is a smooth affine algebra over certain affaine algebras.

How many equilateral points can $\ell_p^n$ contain beyond $n+1$? For every fixed real $p>4$, we construct equilateral sets for which the number of points beyond $n+1$ grows at least linearly with $n$. For every fixed dimension, we prove that the maximum is $n+1$ at all sufficiently large finite $p$, with an explicit threshold. The least dimension admitting any fixed number of extra points is $p^{1+o(1)}$ as $p\to\infty$. The constructions and finite bounds are formalised in Lean. Thus $p=4$ marks the boundary: $n+1$ is exact in every dimension for $2\leq p\leq4$, while at every fixed finite $p>4$ the excess grows at least linearly with dimension.

Mixture-of-Experts (MoE) models have emerged as an effective paradigm for scaling large language models, yet their massive parameter footprint poses severe memory challenges for deployment. Existing compression methods typically treat expert pruning and merging as disjoint operations and rely on greedy heuristics, often leading to irreversible information loss or representational pollution. In this paper, we propose PRIME, a unified optimization framework for MoE compression via adaptive PRunIng and MErging. PRIME casts the discrete prune-merge assignment step as a global Integer Linear Programming over a frequency-weighted surrogate objective, jointly selecting pruning and merging decisions while accounting for expert usage. We motivate the frequency-aware objective through an error-bound analysis under fixed representative assignments, and show that the formulation favors high-frequency experts as centroids, promoting routing stability. Extensive experiments on Qwen3-30B-A3B and Qwen3.5-122B-A10B demonstrate that PRIME achieves strong accuracy retention across knowledge, coding, math, and long-context tasks, while serving benchmarks of merged models quantify the memory and throughput benefits of expert compression in vLLM.

Jiao and Ren proved that the varieties generated by the matrix semirings $\M_n(S_7)$ form an ascending chain of nonfinitely based varieties, and asked whether consecutive members are equal for all $n\geq2$. We give a negative answer by exhibiting an identity in five variables that holds in $\M_2(S_7)$ and fails in $\M_3(S_7)$. Consequently, $\V(\M_2(S_7))$ is a proper subvariety of $\V(\M_n(S_7))$ for every $n\geq3$. The proof uses the cubic-power property established by Jiao and Ren and a description of products equal to the constant matrix $[a]_n$. The identity forces two distinct indices to exhaust the index set in dimension two; an additional index yields an explicit counterexample in dimension three.

Compositional generalization remains challenging when language models must combine familiar reasoning operations in unfamiliar ways. The Scenario-Based Commonsense Reasoning Evaluation (SCoRE) 2026 tests this ability on three mixed domains absent from training and requires models to identify the complete set of correct options for each question. We introduce Route-Verify-Vote (RVV), a framework for procedure-conditioned self-consistency that uses language models without parameter updates. Route uses the provided domain label to select a reasoning procedure that guides the model in representing and applying the relevant constraints. Verify prompts the model to assess each option against those constraints. Vote aggregates complete answer sets and allocates additional samples to questions with a small vote-count margin between the two most frequent sets. Samples for each question follow the same domain-specific procedure. On the official test set, voting over 16 sampled answer sets per question achieves an exact-set accuracy of 74.6%. Adaptive RVV reaches 77.3%, and combining models on selected domain routes raises accuracy to 79.4%. The final system ranked second among participating systems. These results support domain-specific reasoning procedures and answer-set disagreement as useful tools for allocating inference-time computation in mixed-domain reasoning.

X-ray image-based Radiology Report Generation (RRG) constitutes a critical research direction within medical artificial intelligence, with great potential to alleviate clinicians' diagnostic workload and shorten patient waiting periods. Despite substantial advances over recent years, the field faces evident bottlenecks stemming from insufficient standardized benchmarks and inadequate domain adaptation of generic large models. Notably, the newly released CheXpert Plus dataset is provided without accompanying baseline implementations and evaluation results, which impedes standardized training, quantitative evaluation and fair comparison among follow-up algorithms. To mitigate this limitation, we establish a comprehensive benchmark encompassing prevailing X-ray report generation models and Large Language Models on CheXpert Plus. This benchmark delivers a reliable comparative foundation for upcoming methods and enables researchers to rapidly identify state-of-the-art approaches within this domain. Beyond benchmark construction, we rethink X-ray RRG under the paradigm of large models and propose a novel framework termed MambaXray-PRB. Our framework improves report generation performance and enhances model interpretability via multi-stage large-model pre-training and multi-modal Chain-of-Thought reasoning. The pipeline consists of three successive phases: self-supervised auto-regressive modeling, X-ray-report contrastive learning, and post-training optimization for reasoning and report generation. Extensive experiments on IU X-ray, MIMIC-CXR, and CheXpert Plus datasets validate the effectiveness of MambaXray-PRB for radiology report generation. The source code of this paper is available on https://github.com/Event-AHU/Medical_Image_Analysis

We present Go2-DrivoR, a goal-conditioned adaptation of the end-to-end autonomous driving trajectory planning framework DrivoR for urban navigation with quadrupedal robots. By conditioning trajectory generation on a local-frame subgoal through a goal token and adapting the vehicle-centric scoring formulation, the method extends DrivoR to short-horizon goal-conditioned local planning without redesigning its core decoders. Specifically, we redefine drivable-area compliance for sidewalk-oriented navigation and reformulate the original ego progress term as goal-conditioned ego progress. Trained exclusively on TartanGround simulation data, Go2-DrivoR improves waypoint-conditioned planning performance on unseen simulation environments and transfers zero-shot to open-loop real-world trajectory prediction.

As context windows scale to tens or hundreds of thousands of tokens, KV cache compression has become essential for efficient LLM inference. Existing methods fall into three families: score-based eviction, summary compensation, and offload-and-recall. Yet all three decide what to keep or recall by content relevance to the current query. We show this shared design is structurally incomplete. A cache supports two access modes: associative lookup by content and sequential traversal by position; current compressors implement only the first. The gap matters in practice: retrieval-augmented generation, code completion, and structured-data extraction all require the model to reproduce identifiers, field values, or code tokens verbatim from the context. Under compression, content-based eviction retains the head of such a sequence but discards its continuation, causing verbatim copying to break irreversibly midway, a failure we call sequential forgetting. This failure resists better scoring, larger budgets, summary compensation, and dynamic re-scoring; it is the dominant source of remaining quality loss under compression. We propose KVFetch, a training-free, drop-in framework that opens a temporal recall channel for any score-based compressor. It demotes evicted candidates to a quantized cold tier, detects active copying through a monotone read pointer, and prefetches positional successors into fixed-size hot-tier slots without increasing attention cost. On RULER-16K under an iso-budget control, KVFetch recovers verbatim copying from 0.8 to 78.4 and raises the 13-task average by +8.4, with gains concentrating on tasks that require sequential access. On LongBench, where no task requires sequential access, the channel remains dormant and imposes no cost.

We study the application of large language models (LLMs) to the visual exploration of textual corpora. We introduce zero-shot visualization (ZSV), a task in which users specify concepts in natural language and documents are mapped onto the corresponding concept axes for visualization. Building a ZSV system of practical value is non-trivial, as it requires choices at the intersection of feature functions, efficient implementation tradeoffs, and pre/post-processing decisions affecting visualization quality. To that end, we establish a benchmark that compares methods spanning embedding similarity, direct semantic judgments, and conditional likelihood estimation in this setting. Across multiple datasets and use cases we evaluate the properties of different scoring methods and design choices in terms of semantic faithfulness, score fidelity, and computational cost. Our results identify that scoring based on next-token probabilities offers the strongest practical trade-off among the evaluated methods. We further apply this approach to unlabeled corpora to examine its behavior in realistic exploratory settings. These experiments highlight additional design considerations, including the use of graded axes together with binary relevance filtering, and reveal a compositional sentiment bias in off-topic documents. Based on these findings, we provide practical guidelines for constructing end-to-end ZSV baselines.

We study complex rank-two pinor fields on the flat Möbius band and the relation between their deck equivariance and Dirac boundary realizations. With explicit Clifford conventions, the two lifts for each Pin type are represented by $R=c\sigma_1$, where $c=\pm1$ for Pin+ and $c=\pm i$ for Pin-. The relevant longitudinal monodromy is $cJ$, with $J\phi(w)=\sigma_1\phi(-w)$, rather than the fiber matrix alone. Its eigenspaces give shifts $0,1/2$ in the positive case and $1/4,3/4$ in the negative case. We identify the resulting geometric Sobolev spaces and construct self-adjoint elliptic realizations of $D=-i(\sigma_1\partial_x+\sigma_2\partial_w)$ with a local boundary condition defined by the longitudinal tangent field. An exact graph estimate gives compact resolvent and Fredholm mappings on nonnegative Sobolev levels. The spectrum consists of a single unpaired transverse branch and paired branches whose longitudinal shifts alternate with transverse parity. Consequently, the kernel and spectral symmetry depend on the lift and boundary condition; the two negative Pin lifts have eta values $1/2$ and $-1/2$ in the stated convention. We also give a secular equation and an exact kernel criterion for the full translation-invariant family of local self-adjoint elliptic boundary lines.

Carbon credits, offsets and index insurance rest on counterfactuals: what the land would have done under the same weather without management, or what a bad season cost. Current baselines fail in two ways: some ignore rain, others condition on rain linearly and annually. But the true response lags the rain, depends on hidden state such as moisture from other sources, and responds differently from pixel to pixel. Focussing on grassland pasture as a proof of concept, we fit a temporal world model of MODIS greenness conditioned on CHIRPS rain over two 45 km^2 sites in Laikipia, Kenya: a transition density map for greenness given recent and current rainfall. We use it, conceptually, as Black-Scholes is used. Inverting the model on observed greenness it yields an implied residual, everything the land did that the rain does not explain. Two capabilities drop out of this solution: 1) attribution, what the land did beyond the rain; 2) sensitivities, derivatives of the rollout with respect to rain and state, close analogues of the Greeks. On Laikipia test sites, our learned model recovers three-month greenness with 23% less error than a history-only baseline and 13% less than the best hand-written model on unseen years. In the 2022 drought, the land ended 0.17 NDVI below normal; the rain that failed explains roughly half of that, and under normal rain with the same residual it would still have ended 0.10 below. Delta, the derivative of greenness with respect to rain, is computed at every pixel and averages 0.075 NDVI per extra 100 mm of rain. A Delta at every pixel is an exposure to rain that can be hedged, allowing efficient pricing of contracts and accurate attribution.

We characterize the regret attainable in online convex optimization when access to the feasible set is limited to an exact linear optimization oracle. The learner is given an inscribed ball and a diameter bound and must remain feasible on every consistent instance. For convex $G$-Lipschitz losses, diameter at most $D$, a total allowance of $Q$ oracle calls, and a strict limit of $B$ calls per round, the dimension-free minimax expected regret is $\Theta(GD\max\{\sqrt T,T/(1+\min\{Q,BT\})^{1/4}\})$. The lower bound applies to arbitrary randomized learners. Universal feasibility first forces each action into the hull of the supplied ball and the preceding oracle replies. A fixed-body construction then couples fresh phase directions to a shared simplex, making useful replies costly repeatedly even though all losses have a common minimizer. A counted approximate-gradient method with interleaved blocks attains the matching rate. Total-budget and strict per-round guarantees follow as special cases, including the $T^{3/4}$ rate with one call per round and the quadratic total budget needed for $\sqrt T$ regret. For prescribed smoothness $\beta$, an analytic construction yields a curvature-dependent lower bound and identifies the threshold above which the general characterization remains sharp.

Audits of AI visibility summarise the brand recommendations of deployed language models into per-system profiles. We test whether such a profile describes the system on one corpus of 6,475 stored responses (6,324 analysable) collected between December 2025 and February 2026 from five deployed endpoints across gift-recommendation, corporate-reputation and category-ownership queries. The collection harness cut many answers short: 83.1% of Gemini 3 Flash answers in category ownership end mid-sentence under a 1,024-token output cap. With every answer cut to its first 800 characters, a character n-gram classifier cross-validated by prompt attributes one response to GPT-5.2, Gemini 3 Flash, Gemini 3 Flash with search, Grok or Perplexity sonar-pro with 97.84% accuracy (5,028 responses, 383 prompts, majority class 31.5%, 30 split seeds). Length alone falls to the majority rate, 24 formatting statistics reach 95.79%, and masking brand names and capitalised tokens leaves 97.72%. Held-out query conditions keep 97.43% weighted by size and 88.0% unweighted; in a retrieval-grounded arm that changes the harness, no Grok answer is attributed to Grok (0/120). Aggregated into 50 model-by-domain-by-condition units, twelve behavioural features separate four systems at 66.53% under grouped cross-validation, against a label-permutation null with mean 33.71% and 95th percentile 46.0%. Across domains the aggregate profile fails: a forest trained on category-ownership units assigns all 22 gift units to the wrong system, consistent with a reversal in brand volume (8.41 against 0.94 brands per response in gifts, 3.01 against 3.91 in category ownership), while single responses transfer at 89.92% balanced accuracy. The surface form of an answer carries the system across the query domains tested; aggregated brand behaviour does not, and the uncrossed design cannot separate the system from the domain or the harness.

The Hilbert matrix operator $H$ is bounded on the standard weighted Bergman spaces $A^p_\alpha,\, p>\alpha+2>1$. We examine the limiting case when $\alpha=p-2$, and for $p\leq 2$, we characterize the logarithmic modification of the standard weight needed for the domain $A^p_{v_{\gamma,p}}$ and codomain $A^p_{v_{\beta,p}}$ to ensure boundedness. In particular, we prove that $H:A^2_{\log^\gamma} \to A^2_{\log^\beta}$ is bounded if and only if $\gamma-\beta\geq 2$ and $\gamma>1$, solving an open problem posed by B. Karapetrović and M. Jevtić. We also settle the situation for $p>2$ in all cases, except when the logarithmic exponents $\gamma$ and $\beta$ satisfy $\gamma-\beta=p$. Moreover, we completely solve the same problem when the domain and codomain are certain weighted reflexive $\ell^p$ spaces. All results are extended to the generalized Hilbert operator $H_g$.

Memorization audits of generative models read similarity scores against thresholds, with no null distribution, and the conclusions they support can be wrong. By MemBench's rule, the benchmark's mitigations roughly halve Stable Diffusion's memorization; audited with false-discovery control, two thirds of the certified images are no longer detected under random prompt perturbations, five sixths under attention rescaling, and all of them under embedding optimization. The field's data-copying test, read against its own null, flags ten of twenty-four generators that reproduce nothing. We argue that for memorization the null is the hard part, and supply two. For a whole model, training and held-out images are exchangeable given its samples, and relabelling them is a permutation test, exact for any statistic when the held-out images are a random split; under it, a nearest-neighbour preference still fires on seven of those twenty-four, and a count restricted to the near-duplicate scale on none (McNemar p=0.016). For single images, the natural nulls fail twice, measurably: ranking an image among random images yields 596 false discoveries among 2,365 controls, and resampling independent generations makes the null three times too narrow. Calibrated against matched controls, the audit certifies 36 of 61 MemBench images at 5% false-discovery rate, held-out controls are certified in 0.01% of calibration splits, and on this benchmark two generations per image recover that count. A calibrated maximum, which reads occasional rather than typical copying, certifies 46. As the scale-restricted statistic we recommend the small-scale mass of the Intersection Euler Characteristic Profile, which also counts distinct images copied and tests whether two models copy the same ones.

Alpöge constructed a complex structure on $S^6$ through a torus fibration with exactly three special fibres. We prove that every member of the associated admissible period family is Oka and that the family projection over each relatively compact parameter disc is an Oka map. The Oka property survives the deletion or simultaneous blow-up of any finite set of distinct points in any member. Blowing up a single point therefore produces an Oka complex manifold diffeomorphic, but not biholomorphic, to $\mathbb{P}^3$. The proofs combine explicit cyclic coverings with analytic extension and the invariance of the Oka property under holomorphic coverings.

We study an optimal control problem for the two-dimensional Navier-Stokes equations projected onto the tangent space of the $\mathbb{H}$-unit sphere manifold $\mathcal{M} := \{\boldsymbol{u} \in \mathbb{H} : \|\boldsymbol{u}\|_{\mathbb{H}}=1\}$. This geometric projection yields a constrained evolution system of finite codimension, ensuring that the state remains on $\mathcal{M}$ for all times. Using a Faedo-Galerkin approximation technique, we establish the global existence and uniqueness of strong solutions to the constrained Navier-Stokes equations with external controls $\boldsymbol{U} \in \mathrm{L}^2(0,T;\mathbb{H})$, together with uniform energy estimates. The associated optimal control problem, minimizing a quadratic cost functional subject to the manifold constraint, is shown to admit at least one optimal pair $(\boldsymbol{u}^*,\boldsymbol{U}^*)$. We derive the first-order necessary optimality conditions by formulating an optimal control system whose state-control pair $(\boldsymbol{u}^*,\boldsymbol{U}^*)$ evolves on the tangent bundle $T\mathcal{M}$ of the constraint manifold $\mathcal{M}$. In this setting, the control satisfies $\boldsymbol{U}^*(t)\in T_{\boldsymbol{u}^*(t)}\mathcal{M}$ for all $t\in[0,T]$, ensuring that the dynamics remain confined to the tangent bundle $T\mathcal{M}$. Furthermore, we establish the Fréchet differentiability of the control-to-state mapping $\boldsymbol{U}\mapsto \boldsymbol{u}_{\boldsymbol{U}}$ in $\mathrm{C}([0,T];\mathbb{H})\cap\mathrm{L}^2(0,T;\mathbb{V})$, with the corresponding linearized state characterized as the unique weak solution of a linearized constrained Navier-Stokes system preserving the tangency condition. These results provide a rigorous analytical foundation for the optimal control of fluid flows constrained to nonlinear manifolds.

We study the Kuramoto–Sivashinsky (KS) equation in one, two, and three spatial dimensions subject to a codimension-one constraint. The constraint preserves the \(L^2\)-norm of the solution and consequently provides a uniform a priori bound that plays a central role in the higher-order energy estimates. In one spatial dimension, we establish global well-posedness by means of a Fourier–Galerkin approximation and compactness arguments. In two and three dimensions, we first prove the existence and uniqueness of local strong solutions using analytic semigroup theory and the Banach fixed-point theorem. In two dimensions, the preserved \(L^2\)-norm, combined with the Agmon inequality and suitable higher-order energy estimates, allows us to control the nonlinear terms and obtain global-in-time a priori bounds. Consequently, we establish the existence and uniqueness of global strong solutions for arbitrary sufficiently regular initial data, without any smallness assumption. This provides a global well-posedness result for the constrained two-dimensional KS equation, in contrast with the corresponding unconstrained problem, for which global well-posedness of strong solutions remains open in general. In three dimensions, although the constraint yields a uniform \(L^2\)-bound, the available interpolation and Agmon estimates are insufficient to close the higher-order energy estimate. This identifies a genuine dimension-dependent obstruction to extending the global regularity argument to three dimensions.

We obtain restrictions on the geometry and topology of minimal equatorial fillings in $\mathbb{S}^3$ of the lowest possible Morse index.

Jarzynski's equality recovers an equilibrium free-energy difference from nonequilibrium work trajectories, but its exponential average can converge very slowly because rare trajectories carry large weight. We show that coarse thermodynamic information measured at the nonequilibrium endpoint can reduce this sampling burden while keeping the same microscopic trajectories and the same free-energy target. The endpoint mean energy and a coarse spatial record define a maximum-entropy state and select one member of an exact family of fluctuation relations. That physically selected member provides an exact statistical control for the ordinary Jarzynski estimator, even when the final energy and retained record do not commute. In a finite Bose–Hubbard system, this control substantially lowers the finite-confidence sampling cost, while a small controlled departure from exact endpoint matching produces a square-root information–sampling tradeoff.

We establish a randomized first-order lower bound for finding an $\epsilon$-stationary point, $\|\nabla f(x)\|\le \epsilon$, of a nonconvex function with initial gap at most $\Delta$, $L_1$-Lipschitz gradient, and $L_2$-Lipschitz Hessian. Each oracle call returns the exact function value and gradient. Let $Q_{\mathrm{rand},\mathrm{FO}}^{\infty}(\epsilon;\Delta,L_1,L_2)$ denote the minimax number of calls, maximized over finite dimensions, for arbitrary adaptive randomized algorithms with per-instance success probability at least $2/3$. In the regime $\epsilon\lesssim L_1^2/L_2$ and $\Delta L_2^{1/2}\epsilon^{-3/2}\gtrsim 1$, we prove $ Q_{\mathrm{rand},\mathrm{FO}}^{\infty}(\epsilon;\Delta,L_1,L_2) \ge c\,\Delta L_1^{1/2}L_2^{1/4}\epsilon^{-7/4}, $ where $c>0$ is an absolute constant. This matches the deterministic restarted accelerated-gradient upper bound of Li and Lin (2023) and extends the sharp deterministic lower bound of Zhou (2026) to unrestricted randomized algorithms. Thus, randomization does not improve the high-dimensional worst-case query rate. The construction keeps quadratic curvature visible while revealing the forcing directions sequentially. Large eigenspaces limit preprocessing, and a scheduled-disclosure coupling makes each fresh direction incur a separate cost.

Edge-localized modes (ELMs) are transient magnetohydrodynamic instabilities commonly observed in tokamak plasmas. Although deep time-series models can learn complex dynamic patterns from multi-diagnostic signals, their predictions are mainly data-driven and lack explicit utilization of ELM physics, plasma operating states, and historical discharge experience. As a result, they may confuse categories with similar temporal patterns, particularly under severe class imbalance. To address this issue, we propose KGF-ELM, a Knowledge Graph Fusion Network for ELM Recognition, and introduce a Knowledge Graph Collaborative Fusion Module (KGCFM) that organizes physical evidence from the current time window, ELM prototypes, relational knowledge graph representations, and similar historical discharge cases into complementary multi-source knowledge representations. KGCFM collaboratively models these knowledge sources through physics prototype matching, graph-structured knowledge encoding, historical case retrieval, cross-evidence consistency analysis, and reliability estimation, thereby generating knowledge representations for enhancing temporal features and correcting classification results. Based on this module, KGF-ELM employs a dual-level reliability-aware fusion mechanism. At the feature level, physical residuals and graph-guided knowledge representations are adaptively incorporated into temporal features according to their reliability. At the decision level, reliability gating, minority-class protection, and bounded knowledge correction are used to safely refine the classification results and reduce the negative influence of unreliable knowledge on the base model.

Ion temperature Ti and electron temperature Te are fundamental kinetic parameters for evaluating tokamak plasma confinement, turbulent transport and magnetohydrodynamic stability. Reliable prediction of their spatiotemporal profiles is essential for long-pulse steady-state operation on the Experimental Advanced Superconducting Tokamak (EAST). However, existing EAST diagnostic systems have obvious measurement limitations, including narrow applicable conditions of charge exchange recombination spectroscopy and severe signal degradation of edge temperature diagnostics during long discharges. Classical physics-based transport codes suffer from high computational cost and error accumulation, while existing data-driven models only separately predict Ti or Te relying on spectral data, lacking joint Ti/Te modeling and failing under missing spectral measurements. In this work, we propose a multi-modal (i.e., global macroscopic diagnostic signals and spectral data) fusion attention neural network for simultaneous reconstruction of Ti/Te profiles on EAST. It leverages an adaptive attention module to weight global diagnostic features and suppress noise interference, employs convolutional layers to extract deep spectral representations, and utilizes multi-head self-attention to facilitate cross-modal feature interaction. Two separate prediction heads are constructed to output full radial distributions of Ti and Te. This work builds the first EAST-oriented joint Ti/Te prediction model compatible with operating scenarios without spectral diagnostics. Hierarchical attention mechanisms excavate nonlinear multi-modal correlations to realize high-performance dual-temperature profile prediction. The source code of this paper is available on https://github.com/Event-AHU/OpenFusion/tree/main/TiTe_Prediction

In this paper, we construct primitive KMS-symmetric quantum Markov semigroups for which the $p$-logarithmic Sobolev constant vanishes at $p=1/2$ and a correlated graph-based example for which the $p$-logarithmic Sobolev constant tends to $-\infty$ as $p\to 0^+$. These examples obstruct a positive uniform reverse-hypercontractivity rate on $(0,1)$. By contrast, we show that every primitive KMS-symmetric quantum Markov semigroup satisfies quantum reverse hypercontractivity for $1/2< p\leq q < 1$ with explicit sufficient times. For each fixed $\delta>0$, a sufficiently strong dephasing perturbation satisfies a uniform positive logarithmic Sobolev inequality on $[\delta, 1]$ and hence quantum reverse hypercontractivity for $\delta< p\leq q<1$ with fixed $0<\delta<1/2$. Furthermore, we establish reverse hypercontractivity for graph-based KMS-symmetric quantum Markov semigroups for $\delta< p\leq q< 1$ with fixed $0<\delta<1$ for connected graphs when $n \geq 3$.

We construct a smooth solution of the focusing cubic nonlinear Schrödinger equation on a square two-dimensional torus which is global in both time directions and concentrates at one point as time tends to positive infinity. Its mass is the mass of the Euclidean ground state and its energy is zero. If $\lambda(t)$ denotes its concentration scale and $L$ the period, then $L/\lambda(t)=2\log t+\frac{11}{2}\log\log t+O(1)$. The solution approaches a phased, periodized ground state with an error tending to zero in every fixed Sobolev space. In particular, its $H^s$ norm is asymptotic to an explicit constant times $(\log t)^s$ for every $s>0$. We also prove uniqueness, up to constant phase and time translation, within the quantitative single-profile asymptotic class used in the construction. The mechanism is the exponentially small interaction of the profile with its periodic images. Exact mass and energy constraints select the concentrating branch, while a positive energy on the moving constrained space controls the terminal-value problem at every fixed regularity order.

In the setting of the previously reported degree-seven counterexample of ani, we present an explicit monic polynomial with real rational coefficients and a direct proof by certified separators. The polynomial has seven simple zeros in the open unit disk. Every continuous path joining distinct zeros in its closed unit sublevel set has image of one-dimensional Hausdorff measure greater than $2+10^{-8}$. Five piecewise-linear graphs exclude twenty of the twenty-one zero pairs; two short forbidden segments force a quantitative detour for the remaining pair. Exact rational Bernstein certificates verify the graph inequalities on forty-four terminal intervals and their unbounded tails. The proof does not require critical-point counting or analytic inverse branches. We separately record the general continuum and dilation arguments that transfer path-length obstructions to Hausdorff measure and to closed sublevel sets. Those transfers are not asserted as new principles. The focus is the explicit real-coefficient construction, its separation certificates, and its verified numerical margin, rather than a first negative answer to the length-two question or a disproof of every larger universal bound.