Papers

An empirical comparison of high resolution M4,5 X-ray Absorption Spectroscopy (XAS), based upon High Energy Resolution Fluorescence Detection (HERFD), with Bremsstrahlung Isochromat Spectroscopy (BIS), the high energy variant of Inverse Photoelectron Spectroscopy (IPES), of various actinide materials is presented here. It will be shown that XAS-HERFD is essentially the j-specific version of BIS, providing a direct measure of the separate 5f5/2 and 5f7/2 Unoccupied Density of States (UDOS).

The transition from titanium-sapphire to ytterbium-based laser technology enables turnkey implementations of high-order harmonic generation (HHG) setups at high repetition rates, opening up new applications, e.g., in semiconductor metrology. This, however, requires exploring and understanding the impact of new experimental conditions. Here, we study HHG in neon over the spectral range 8-17 nm with high spectral resolution, using a post-compressed ytterbium laser. Our measurements reveal a large pulse-energy- and pressure-dependent spectral shift, spanning more than two harmonic orders. The femto-chirp of the harmonic emission combined with the blueshift of the fundamental field allows us to relate the observed spectral shifts to the temporal window of harmonic generation, which is determined by phase-matching. To understand these dynamics, it is essential to consider the reshaping of the driving laser field inside the plasma, despite the low driving intensity and long pulse duration. We introduce an on-axis phase-matching description that captures these effects and reproduces the experimental and simulated trends. These results demonstrate the central role of plasma-induced laser reshaping in phase-matching of HHG, which should be accounted for when optimizing sources in a multi-parameter landscape.

Transferable adversarial attacks are arguably the most practical black-box threat model. Under the same perturbation budget, stronger transfer attacks attain higher attack success rate (ASR), yet their imperceptibility also tends to degrade. Under such a fixed-budget protocol, transferability and imperceptibility therefore appear to trade off against each other. We argue that this conflict is an artifact of fixed-budget evaluation, not an intrinsic trade-off. When attacks are compared on the ASR–imperceptibility Pareto frontier obtained by sweeping $\epsilon$, stronger transfer attacks already attain better imperceptibility at matched ASR than weaker ones. To exploit this latent advantage, we introduce the stealthy transfer attack ST, a plug-in primal-dual wrapper that adds an $L_\infty$ saturation regularizer to the standard constrained objective and resolves it through a two-step primal-dual update: a projected primal step on the perturbation coupled with an $L_1$-ball projection on a dual variable that absorbs the regularizer through Fenchel duality, requiring no auxiliary models or handcrafted perceptual priors. Empirically, ST extends the Pareto frontier across different base attacks and additional surrogate architectures. At $\epsilon{=}16/255$, average imperceptibility gains over each base attack are $17\%$ on LPIPS and $14\%$ on NIQE while ASR is preserved or improved. At matched high-ASR levels, the strongest ST variants further Pareto-dominate dedicated stealth-oriented transfer attacks, confirming that the latent imperceptibility advantage of strong transfer attacks can be unlocked by a primal-dual optimization wrapper without sacrificing transferability. Code will be made available at \url{https://github.com/AndssY/ST}.

Neural audio codecs compress waveforms into compact discrete tokens that underpin speech language models, real-time communication, and large-scale audio storage. Almost every dominant design, including residual vector quantization, finite scalar quantization, and single-codebook variants, follows the VQ-VAE template by partitioning the encoder latent through a learned codebook or a fixed scalar grid. We ask whether this partition is necessary. We introduce GS-Codec, a neural speech codec whose bottleneck is a parametric signal decomposition rather than a quantizer. We adapt Gaussian splatting from 3D scene reconstruction to one-dimensional latents. An inner optimization loop fits each encoder segment as a weighted sum of 1D Gaussian primitives. The decoder then reconstructs the waveform from the rendered sum. To avoid the cost of this iterative inner loop at inference time, we additionally train a lightweight GS Predictor Net that regresses the primitive parameters in a single forward pass. The encoder and decoder are trained end-to-end through the inner loop, with no quantizer anywhere in the training pipeline: the bottleneck is the decomposition itself, and scalar quantization is applied only post-training to the fitted parameters. Rather than relying on discrete codebook stages for bitrate control, our representation exposes a fine-grained rate-quality tradeoff: a single trained checkpoint supports post-training bitrate control by varying the number of primitives and the per-parameter bit depth, with no retraining required. GS-Codec matches or exceeds well-established open-source codecs such as EnCodec and DAC on speaker similarity (SIM), intelligibility (STOI), and perceptual quality (UTMOS) at comparable bitrates, while achieving comparable semantic performance (WER). Code and audio samples are available at https://ronaluf.github.io/gs-codec/

The paper studies a classical non-relativistic particle moving in $\mathbb{R}^{N}$, $(N\geqslant2)$, in the presence of the Kepler-Coulomb force $\boldsymbol{F}(\boldsymbol{r})=\alpha\boldsymbol{r}/r^{3}$, $(\alpha\neq0)$. It is shown that the extended-configuration-space transformation involving the projective transformation of the radius vector $\boldsymbol{r}\to\boldsymbol{R}=\boldsymbol{r}/(1+\boldsymbol{c}\cdot\boldsymbol{r})$ and the differential time scaling $\mathrm{d}t\to\mathrm{d}T=\mathrm{d}t/(1+\boldsymbol{c}\cdot\boldsymbol{r})^{2}$, where $\boldsymbol{c}$ is a real vector-valued parameter with dimensions of inverse length, constitutes a dynamical quasi-symmetry in the sense that it maps Newton's equation of motion $m(\mathrm{d}^{2}\boldsymbol{r}/\mathrm{d}t^{2})=\alpha\boldsymbol{r}/r^{3}$ into the equation $m(\mathrm{d}^{2}\boldsymbol{R}/\mathrm{d}T^{2})=(\alpha\boldsymbol{R}/R^{3}) \operatorname{sgn}(1-\boldsymbol{c}\cdot\boldsymbol{R})$. This quasi-symmetry is independent of, yet complementary to, the well-known Kepler-Coulomb dynamical symmetry, which is SO($N+1$) for negative energies and SO($N,1$) for positive energies. A detailed analytical and graphical analysis of induced mappings between non-degenerate conic trajectories associated with the original and transformed systems is presented. Mappings between velocity hodographs are also briefly discussed. It is then proved that the conservation of energy in the transformed motion implies the conservation of the Laplace-Runge-Lenz vector in the original dynamics.

Continual learning is typically framed as acquiring new knowledge without catastrophically forgetting previous tasks. However, a flexible continual learner should also be able to reuse and recombine previously acquired knowledge to rapidly solve novel task compositions. We introduce Gated Target Propagation (GaTaP), a continual learning algorithm in which task-specific gating variables—learned through a closed-form inner loop update—selectively suppress or enhance network modules. Network parameters are learned in a slower timescale outer loop, using the same local difference target propagation error signal as is used for adapting gating variables. We provide tractable experiments on class-incremental learning scenarios for both multilayer perceptron and convolutional network architectures. We show strong performance retention on previously learned tasks, as well as compositional generalization to unseen tasks, achieved through few-shot gain adaptation at inference. We analyze learned gating patterns and find that related tasks exhibit similar gating patterns, suggesting that inferred gates capture meaningful, reusable task structure. Overall, GaTaP provides a powerful framework for jointly ameliorating catastrophic forgetting and enabling few-shot compositional generalization in neural network models.

Bell nonlocal correlations cannot be reproduced by local hidden-variable models without communication, making classical communication cost a natural quantitative measure of nonlocality. Although finite communication always suffices to simulate any correlation in a fixed finite Bell scenario, determining the minimum amount needed to (exactly) simulate any given nonlocal correlation remains challenging, especially in the average-cost setting. Here, we derive lower bounds on input-average communication cost from nonlocal games, allowing variable-length, fully interactive two-way protocols. When applied to parallel games, these bounds yield explicit finite quantum correlations for which the exact simulation cost exceeds any prescribed finite input-average communication budget. For $n$ parallel Magic-Square-winning correlations, we prove a lower bound of $n\log_2(3/2)$ bits and give a one-way communication protocol that attains this rate asymptotically. For the quantum correlation maximally winning the $n$-copy of the Clauser–Horne–Shimony–Holt nonlocal game, we obtain an input-average lower bound of approximately $0.04627n$ bits for exact simulation. Finally, we formulate a hierarchy of lower bounds and complementary upper bounds using deterministic correlations up to chosen communication costs. Both recover the exact input-average cost at their final levels, and if the bounds agree at lower levels, their common value yields the exact input-average cost without needing to consider all communication strategies.

Astrocytes are increasingly recognized as active regulators of neural dynamics, yet their role in large-scale synchronization remains incompletely understood. Building on the discovery of breathing cluster synchronization in neuron-astrocyte networks, we investigate whether this phenomenon persists under more biologically realistic conditions by incorporating thermosensitive neuronal dynamics, intrinsic electric-field interactions, stochastic perturbations, and delayed astrocytic feedback. Through systematic numerical simulations of a network containing structurally symmetric neuronal subsets, we show that breathing clusters characterized by intermittent alternations between synchronized and desynchronized states, remain robust across a broad range of biophysical conditions. The results reveal a non-monotonic dependence on astrocytic attenuation and feedback parameters, with intermediate values maximizing rhythmic switching through a slow push-pull regulatory mechanism. Temperature and electric-field effects primarily modulate neuronal excitability and the tolerance of the breathing state to noise, while elevated stochastic perturbations progressively destabilize cluster coherence. In contrast, the phenomenon exhibits remarkable robustness to biologically realistic astrocytic delays. Importantly, our findings indicate that the emergence of breathing synchronization remains fundamentally governed by the interplay between network symmetry and astrocyte-mediated feedback, whereas temperature, electric fields, and noise act as modulators of its stability and temporal organization. These results establish breathing cluster synchronization as a robust organizing principle of astrocyte-regulated networks and provide a quantitative framework for understanding how glial regulation shapes cortical state-switching under realistic physiological conditions.

Inference systems determine how fast and how cheaply language models can be served, so making them faster has direct practical value. However, prior work focuses mostly on optimizing certain parts such as kernels or memory within the large system. In this work, we take a holistic approach and apply agentic self-evolution to optimize the whole system end-to-end. Our SEIS (Self-Evolving Inference Systems) autonomously optimizes the entire mini-sglang engine without human intervention through iterative sessions with inherited experiences and code changes. Serving Qwen3-0.6B on H100, the resulting engine reaches 3.27X the throughput of the original mini-sglang implementation and beats SOTA engines like vLLM, TensorRT-LLM, and SGLang in the single-request workload. The correctness of the optimized inference engine by SEIS is tested in terms of numerical difference and downstream accuracy on math and long-context retrieval tasks. The code and session histories show that the speedup comes from redesigning the whole engine and that building on earlier sessions beats independent attempts. These results suggest that agentic self-evolution can optimize a complex system end-to-end. The evaluation also has to evolve with the engine, and letting agents evolve it is a natural next step.

For a finite graph $G$, the maximum average degree $\operatorname{mad}(G)$ is the largest average degree of a nonempty subgraph of $G$. Hendrey, Norin and Wood asked whether this parameter is partitionable, that is, whether for all positive reals $a,b$ every graph $G$ with $\operatorname{mad}(G)<a+b$ admits a vertex partition $V(G)=A\cup B$ with $\operatorname{mad}(G[A])<a$ and $\operatorname{mad}(G[B])<b$. In this note, we answer this question affirmatively. Moreover, we generalize this to an arbitrary number of partition classes. The clustered chromatic number $\chi_\star(\mathrm{G})$ of a graph class $\mathrm{G}$ is the minimum integer $k$ such that, for some integer $c$, every graph in $\mathrm{G}$ has a $k$-coloring in which every monochromatic component has at most $c$ vertices. We apply this result to show that $\chi_\star(\mathrm{A}_m)=\left\lfloor\frac{m}{2}\right\rfloor+1$, where $\mathrm{A}_m$ is the family of graphs $G$ with $\operatorname{mad}(G)\leq m$. This solves an open problem posed in Wood's survey and highlighted by Hendrey and Wood. As another application of our general partition result for $\operatorname{mad}$, we obtain a bound for relaxed colorings. Namely, for non-negative integers $d_1,\ldots,d_k$, every graph $G$ with \[\operatorname{mad}(G)<\sum_{i=1}^k \frac{2d_i+2}{d_i+2}\] admits a partition $V(G)=V_1\cup\ldots\cup V_k$ such that $\Delta(G[V_i])\leq d_i$ for each $i\in[k]$. In particular, this provides the first non-trivial bounds for $k\ge3$ with arbitrary $d_i$ and improves the previously known bound for $(d+1,d)$-colorings with $d \ge 2$.

Neural approaches to Graph Edit Distance (GED) have achieved strong results under standard within-dataset evaluation, but much less is known about how well these models transfer across graph collections. We conduct a systematic study of this problem using exact GED supervision across diverse graph datasets and a broad set of representative learning-based methods. Our results reveal a pronounced gap between within-collection performance and cross-collection transfer. Models that perform well on their training collections often lose this advantage when evaluated on structurally different data. Training on multiple source collections substantially improves zero-shot transfer and provides a better starting point when limited supervision is available for a new target collection. Further analysis shows that transfer behavior varies with the source–target direction and the structural characteristics of the collections involved. These findings suggest that conventional within-collection evaluation provides only a partial view of the generalization behavior of neural GED models and motivate broader evaluation across heterogeneous graph collections.

Neuroscience treats the brain as a control hierarchy, with cortical systems governing subcortical mechanisms. We argue that this mistakes a configuration for an architecture. Local asymmetries of influence are real, but control is relational and process-specific; because neural elements constrain one another across concurrent processes, relations can form cycles that resist a stable ranking. Evidence from learned action, cortico-cerebellar and thalamocortical loops, and defensive behavior shows that control changes with practice, task phase, urgency, viability demands, and affordances. Hierarchical order therefore characterizes time-bounded configurations, whereas heterarchy characterizes the architecture's repertoire across occasions. We propose a spectrum of control indexed by dynamical decoupling: how far behavior can depend on history, internal state, and anticipated consequences. The account yields experimentally testable predictions.

Detecting responses that retrieval-augmented generation does not ground in its context trades speed against accuracy: surface checks miss paraphrased fabrication, sampling-based methods cost extra generations. Hidden-state probes sit between the two, but every existing one reads the generating model's own activations, so a change of generator invalidates the detector and a closed-weight generator is out of reach. This paper removes that coupling. The Grounding Probe is logistic regression over the mean-pooled middle-layer hidden states of an observer language model that reads the context, question, and response in one forward pass and generates nothing, with the recipe it needs: pool over response tokens, read a middle layer, and control capacity, which closes the train-test AUROC gap from 0.087-0.202 to 0.009-0.013. Asking the observer outright, rather than reading its hidden state, costs at least +0.166 AUROC in every one of four models. Fitted on 15,090 annotated responses it reaches 0.879-0.894 AUROC on RAGTruth test across four observers, and 0.924 AUROC with 0.820 F1@0.5 averaged with a supervised span detector, 0.060 above that detector alone. One probe holds across six generators, and hold-out controls, including one in which no evaluation prompt appears in training, bound the cost of removing a generator at about 0.02 AUROC. Code, probes, and predictions are released.

Code readability supports software understanding, review, and maintenance. As AI coding agents become more widely used, readable code helps both humans review agent-generated output and agents maintain code within limited context windows. Yet existing readability models do not consistently agree with human judgements across datasets. We introduce BTTF (Back To The Future), pairing linear regression with information-theoretic features. Rather than using language models as black-box judges, BTTF uses them as measurement instruments. It combines traditional code measurements, embedding-based semantic organisation, and causal-LM predictability to capture source structure, semantic coherence, and contextual surprise. We evaluate BTTF on five publicly available human-rated readability benchmarks and our manually annotated MBJP development set, totalling 1,100 samples. BTTF improves average Spearman correlation over the strongest baseline by up to 0.101. Across 13 controlled readability-reducing transformations on production code, it achieves response rates of 93.8% in Java and 87.6% in Python, outperforming Dorn by 14% and 19.2%. It performs best among local models and trails the strongest cloud-LLM response by 1.7% in Java and 5.1% in Python. The direct-LLM baselines require an average of 1,083 prompt tokens per evaluation while remaining opaque. BTTF combines state-of-the-art benchmark performance and strong transformation robustness with feature-granular interpretability: every feature coefficient matches its theoretical directional effect across all evaluated model configurations.

Hypergraphs record multi-way interactions among entities. Extracting information from the combinatorial structure underlying observed multi-way interactions is a central task in many real-world problems. Existing methods face several limitations. First, many deep architectures for hypergraphs do not explicitly exploit the potential low-rank structure, which can sacrifice parsimony and interpretability in the learned representations. Second, many low-rank-based methods operate on tensor representations, which typically require hyperlinks to have uniform sizes and thus limit their applicability to general hypergraphs with non-uniform hyperlink sizes. Third, many methods ignore the fact that hyperlinks often arise from heterogeneous mechanisms. For example, medical symptoms may co-occur in the profiles of patients with very different conditions, and such heterogeneity should be incorporated into the learning process. In this work, we develop a general framework for hypergraph representation learning using hyperlink random effects while exploiting the low-rank structure in hypergraphs. The proposed framework accommodates latent heterogeneity in hyperlink formation while preserving entity interaction patterns. We establish identifiability of the model parameters and theoretical guarantees of representation-level recovery under this framework. The framework allows flexible specifications for the hyperlink random effects; in this paper, we study three choices: categorical, Gaussian mixture, and score-based effects, and develop corresponding estimation algorithms. Through simulation studies, we demonstrate the effectiveness of the proposed method in recovering latent structure and capturing heterogeneous interaction patterns. Empirical studies on real-world hypergraph datasets further illustrate the practical utility of our approach.

LLMs are used both to simulate network protocol implementations, as honeypots do, and to write them. Prior work evaluates the two uses separately, from a model's answers or conversations in one case and from its generated code in the other. We observe that a knowledge probe (asking the model which security checks an implementation needs) and a conversation can credit security checks that the generated program lacks, but no study has compared them with the code the same model writes. To fill this gap, we present the first such comparison between simulation mode (S-mode), where the model plays the implementation in a conversation, and development mode (D-mode), where the model writes the program and the program is attacked, with a knowledge probe as a baseline. We design and implement a harness that judges all three with one attack suite and one oracle, and evaluate 15 LLMs on four protocol implementations. We find that with the full security specification, the median model's attack success is at most 4% on reassembly, HTTP, and firewall implementations in both modes, but 13% in S-mode and 15% in D-mode on DNS. In D-mode, adding the missing DNS requirement to the specification cuts that attack from 100% to 34% and changes only that check, whereas deleting a stated rule weakens the program on other checks too. Asking the model beforehand does not predict which checks a program has, since 13 of the 14 models that write a DNS resolver name the check, yet all 42 programs lack it. S-mode is a useful first filter, flagging 82% of the real DNS vulnerabilities and leaving 96% of the safe cases unflagged. It errs in both directions, over-reporting security checks that D-mode does not implement and under-reporting checks that D-mode does. S-mode can screen but not replace D-mode testing, and security requirements should be written down even when a model can recite them.

Actor-critic methods reuse past experience to improve sample efficiency. However, historical data are typically regarded as off-policy samples for the current policy-improvement update. This work introduces Regularized Dual Averaging Actor Critic (RDA2C), which assigns a distinct role to replay. In regularized dual averaging, the subsequent policy is determined by accumulated policy-improvement feedback, so historical advantage estimates contribute directly to the actor objective rather than solely to the most recent update. RDA2C stores state-action samples with critic-estimated advantage labels, fits a dual score model $Z_\theta$ to the aggregated dataset, and derives the current policy from the accumulated score model using the entropy mirror map. In this way, replay defines an empirical dual objective from which the policy is computed. To analyze RDA2C, we establish a finite-time value-gap decomposition, separating the regularized dual-averaging term from errors due to stale-replay supervised fitting, critic bias, finite-buffer variance, and replay coverage, and stating the assumptions under which each error is bounded. RDA2C accepts advantage labels from any critic. With GAE labels, RDA2C outperforms PPO on six of eight MuJoCo tasks and eight of twelve Atari games. RDA2C also outperforms AAPDA, the closest dual-averaging baseline, on six of eight MuJoCo tasks. With twin-$Q$ labels, RDA2C matches SAC at matched batch size and update frequency.

In this paper, we present an operator representation for Herglotz-Nevanlinna functions in several variables using self-adjoint linear relations. Moreover, a description of the reproducing kernel Hilbert space corresponding to a Herglotz-Nevanlinna function of several variables is also presented, along with a comparison to some existing result concerning the class of Loewner functions.

Increasing architectural complexity is often assumed to improve health misinformation detection, yet reported gains are difficult to interpret when studies use different corpora, preprocessing pipelines, data splits, and leakage controls. This study provides a controlled cross-corpus benchmark of five compact neural architectures (1D-CNN, LSTM, BiLSTM, CNN-LSTM, and CNN-BiLSTM), a soft-voting neural ensemble, and three classical machine-learning baselines using COVID19-FNIR and CONSTRAINT. Exact-text duplicate controls were applied before modelling; all neural systems used a common preprocessing and optimisation protocol, and neural results were repeated across three random seeds. On COVID19-FNIR, the deep ensemble achieved a mean macro-F1 of 0.9963 and ROC-AUC of 0.9994, while individual neural models ranged from 0.9945 to 0.9957 macro-F1. On CONSTRAINT, the ensemble achieved macro-F1 of 0.9272 and ROC-AUC of 0.9811, whereas a linear SVM achieved macro-F1 of 0.9574 and ROC-AUC of 0.9931. Architecture rankings changed across corpora, and simple sparse linear models remained highly competitive. The findings show that model complexity does not provide a stable performance advantage and that benchmark construction can dominate architecture choice. The study contributes a reproducible, leakage-controlled basis for evidence-driven model selection in health misinformation classification

Sparse attention reduces core-attention computation, but its indexers still incur repeated selection work and per-layer key-cache storage. Reusing selected indices across layers reduces this overhead but constrains multiple layers to the same token set. We introduce LatentIndex, which extends the latent-sharing principle of Multi-head Latent Attention across indexer layers. Each layer group constructs a shared latent cache from its first layer's hidden states, while layer-specific scoring enables independent token selection. Absorbing key decoders into queries enables direct scoring of the shared cache without reconstructing historical per-layer keys. We develop training-free calibration and investigate a training-aware instantiation of this principle. To balance quality and computation, a hierarchical selection (HS) variant lets followers independently refine a shared candidate set proposed by the anchor. With four-layer sharing, LatentIndex reduces logical indexer-cache storage by 61.1% on DeepSeek-V3.2. Across DeepSeek-V3.2 and GLM-5, training-free LatentIndex improves head-wise attention-mass recall over IndexCache by up to 3.28 percentage points while maintaining RULER and LongBench performance close to native DSA. HS further achieves 2.30-2.72 times decode indexer speedups over DSA across 8K-128K contexts, retaining most of LatentIndex's recall. LatentIndex offers a new perspective on cross-layer indexing: sharing continuous representations rather than discrete selections enables efficient reuse while preserving layer-specific token selection.

We show that two infinite families of homology $S^2\times S^2$'s presented in \cite{FPS, AP}, originally proposed as exotic candidates, are aspherical. In particular, none of these manifolds is an exotic $S^2\times S^2$. We prove this by reconstructing them from aspherical building blocks, following Edmonds. The same arguments apply to and rule out further candidates for simply connected exotica. We also give counterexamples to the conjecture that Luttinger surgery preserves symplectic asphericity.

Genome-wide association studies (GWAS) have greatly advanced the discovery of genetic variants underlying complex traits and diseases. Yet in heterogeneous populations, existing GWAS strategies typically either pool all individuals under an assumption of population homogeneity or perform meta-analysis across predefined subgroups, both of which are limited when latent genetic heterogeneity attenuates subgroup-specific effects and masks true associations or subgroup labels are imprecise. Here we present UCALM, a unified unsupervised framework that infers genetically homogeneous subgroups directly from the data and integrates subgroup-specific GWAS with a novel layered meta-analysis method to capture both shared and subgroup-specific association signals. Through extensive simulations and analyses of large-scale human and livestock cohorts, including the UK Biobank ($n \approx 487{,}000$) and a heterogeneous pig cohort ($n \approx 85{,}000$), we demonstrate that UCALM substantially alleviated the mean genomic inflation across 24 UK Biobank traits to 1.17 compared with 1.43 for GLM and 1.37 for LDAK-KVIK, and further revealed 74 loci in the pig cohort that were previously obscured by conventional approaches. Our results establish a robust and broadly applicable strategy for association mapping in structured populations and improve the resolution of genetic signals across diverse species.

In this paper, we revisit a multi-dimensional nonlocal transport equation of the form \begin{eqnarray*} \partial_t\rho+g\mathcal{R}_a\rho\cdot \nabla\rho= 0,~\rho(\cdot,0)=\rho_{0}, \end{eqnarray*} where the transform $\mathcal{R}_a$ is defined by \begin{eqnarray*} \mathcal{R}_a\rho(x,t)=\frac{\Gamma(\frac{n+1}{2})}{\pi^{\frac{n+1}{2}}}P.V.\int\limits_{\mathbb{R}^n}\Big(\frac{x-y}{|x-y|^{n+1}}-\frac{x-y}{(|x-y|^2+a^2)^{\frac{n+1}{2}}}\Big)\rho(y,t)dy. \end{eqnarray*} This model was first introduced in [W. Zhang, J. Differential Equations 467 (2026) 114275] as a natural generalization of the well-known Kiselev-Sarsam equation proposed in [A. Kiselve and N.A. Sarsam, Nonlinearity 38 (2025) 055018]. By using an improved pointwise inequality for the transform $\mathcal{R}_a$, we obtain a better and more natural version of a nonlinear integral inequality proved in Zhang [31] for the transform $\mathcal{R}_a$. In addition, we also establish a new weighted nonlinear inequality for the transform $\mathcal{R}_a$ implying the finite-time blow-up for a class of smooth radial initial data.

Numerical Linear Algebra (NLA) has consistently played a vital role in advancing science by providing tools to solve fundamental problems encountered in scientific and engineering applications. Over the decades, it has continually evolved to meet the demands driven by successive waves of scientific discovery. For instance, during the 1950s and 1960s, substantial efforts were devoted to developing methods for solving eigenvalue problems that emerged from the rapidly growing field of aerodynamics. This led to the discovery of the LR and QR algorithms. Later the attention turned to the solution of sparse linear systems that were common in applications like computational aerodynamics. Today we are experiencing yet another wave of major scientific advancement and NLA is once more at the heart of its development. This Machine Learning (ML) wave is proving to be utterly disruptive in science and engineering. Many tools in ML particularly Large Language Models (LLMs) are grounded in matrix and tensor methods. As we are approaching Artificial General Intelligence (AGI), it is clear that matrix methods will be called to play an even more significant role. For the numerical linear practitioner the speed of the current change makes it particularly challenging to adapt. This is a survey article that centers on machine learning techniques, with a particular focus on large language models. It has two main objectives. The first is to clarify the core concepts behind Large Language Models in a manner accessible to specialists in numerical methods. The second is to examine the key Numerical Linear Algebra concepts employed by LLM techniques, while also highlighting several significant recent contributions of NLA to the field.

The escalating energy demands of modern wireless networks make energy-efficient system design a central challenge for future 6G deployments. Relay-assisted communication has long been recognized as a powerful tool for improving coverage and throughput, tracing its roots to early repeater communication systems and the foundational relay channel models in information theory. Meanwhile, modern relay selection and routing strategies are primarily driven by rate-based or transmit-power-centric metrics, which often neglect hardware-level losses that is independent of the transmitted signal. As networks grow denser and more heterogeneous, signal-independent hardware inefficiencies and circuit power consumption increasingly dominate the total energy consumption and fundamentally alter the optimality of relay assignment decisions. To address the challenge of modeling signal-independent power consumption in relay-assisted systems, the Waste Factor (WF) framework is adopted: a hardware-aware, unifying metric that explicitly captures signal-independent power losses across cascaded transceivers and wireless channels. Using WF, the energy consumption of multi-user, multi-relay wireless systems is quantified and minimized under practical hardware and network constraints. The formulation jointly accounts for component inefficiencies, propagation losses, and relay-selection constraints. The proposed framework demonstrates that the WF formulation provides a fundamentally new way to model relay-assisted communication, enabling hardware-aware energy-per-bit minimization and a structured representation that enables computationally efficient analysis. Simulation results confirm that WF-based relay assignment reduces total energy per bit while improving the ability of users to satisfy minimum received-power requirements, outperforming conventional formulations across both metrics.

Context. Modeling the global dynamics of the Sun requires numerical frameworks capable of simulating the highly turbulent convective envelope and its coupling with the stable radiative interior. Simulating such spherical domains in standard cartesian finite-volume codes presents significant topological challenges. Aims. The goal is to extend the cartesian Adaptive Mesh Refinement (AMR) framework Dyablo to non-cartesian geometries in order to perform global solar convection simulations that extend all the way down to the stellar core. Methods. We introduced a mapped grid approach within the Dyablo framework to build Dyablo Whole Sun (DWS) code. We implemented an $\alpha-\beta$ well-balanced scheme to preserve hydrostatic equilibrium. Furthermore, we present a robust methodology to generate fully integrated solar background profiles from $r=0$ to the surface. Results. We validated the implementation using standard hydrodynamic tests and ran high-resolution 2D global solar convection simulations on a disk grid. Conclusions. Our models successfully capture the turbulent convective broad slow upflows and narrow fast downflows and the excitation of acoustic waves and p modes. The interaction of strong downflowing plumes with the top of the radiative zone, successfully excites internal gravity waves in the radiative interior.

Let $G$ be a Lie group equipped with commuting left and right linear representations on a vector space $V$, and let $G\Join V$ be the associated centered semidirect product. We develop a reduction scheme for covariant field theories on principal bundles with structure group $G\Join V$ from both Lagrangian and Hamiltonian perspectives, obtaining the reduced Euler-Poincaré and Lie-Poisson field equations decomposed into their $\mathfrak g$- and $V$-components, where $\mathfrak g$ is the Lie algebra of $G$. We also derive the reduced multisymplectic form formula, as well as the Noether and energy-momentum balance laws. Our reduction results are compared with those for principal bundles with standard semidirect-product structure groups, and the role of the centered variables is investigated: they retain the original two-sided geometric data and separate the left and right contributions via the heart and diamond operators. The framework is then applied to a two-sided matrix microstructural model and to the second-order jet group on $\mathbb R^r$, $G_r^2$. For the matrix model, the conjugation representation decomposes $\operatorname{Mat}(3)$ into scalar, vector, and symmetric-traceless sectors, clarifying its precise relation to director and alignment-tensor variables without identifying it with standard nematodynamics. For the one-dimensional jet group on a $(1+1)$-dimensional Minkowski base, we obtain a semilinear symmetric-hyperbolic system and an exact traveling conversion front with explicit energy-momentum exchange between the linear- and quadratic-jet sectors. Its hyperbolic-target interpretation yields a conserved positive energy for the linearized perturbations. A nonlinear numerical experiment illustrates the reduced evolution and reconstruction of the group-valued field, with consistency assessed through mesh refinement and an independent wave-map computation.

Object detection under image degradation can benefit from clean-image supervision, but aggregate gains do not imply that transferred representation changes are uniformly useful. We study how clean task knowledge affects degraded-image representations and whether local responses to structured representation directions can be characterized geometrically. Using paired clean and Gaussian-degraded BDD100K images, we show that clean-teacher distillation improves observed detection accuracy while producing heterogeneous object-level transfer. We isolate a representation component complementary to direct clean-teacher alignment and map it into the distilled student space through an orthogonal bridge. Controlled interventions rescue 13.22% of objects lost under the distilled representation, versus 4.30% under norm-matched random perturbations, with very low harm on preserved objects. We introduce task-sensitive geometry, a gradient-derived channel-space geometry constructed from normalized detection-loss gradients. On a reserved cohort, mapped-complement orientation within this frozen geometry is positively associated with local intervention-response magnitude after controlling for intervention magnitude (partial Spearman $\rho$ = 0.242, 95% CI [0.108, 0.359]). The relationship eplicates on independent data ($\rho$ = 0.180) and with RT-DETR-L ($\rho$ = 0.227), but not for the direct clean-teacher residual family, and it weakens for large interventions. Routing rules and specialized distillation objectives based on these signals do not yield statistically reliable gains over CLEANKD. These results support a local, direction-family-dependent task-sensitive geometry while showing that converting such structure into improved global training remains an open problem.

We present the first calculation showing that a material-asymmetric Sagnac speed meter can improve quantum-noise-limited sensitivity to $B-L$ vector dark matter by nearly two orders of magnitude over a Fabry–Perot Michelson position meter at the low-mass end of the band. We introduce material contrast into a dual-ring interferometer to probe composition-dependent $B-L$ forces and compare the two configurations at equal incident power, input-mirror transmissivity, and cavity round-trip length. For sapphire mirrors and a one-week benchmark, the quantum-noise-only median expected $95\%$ CL upper limit reaches $1.2\times10^{-27}$ at $m_A=4.1\times10^{-14}\,\mathrm{eV}/c^2$ ($10\,\mathrm{Hz}$), a factor-$57$ improvement. This band-edge forecast assumes negligible classical noise; sensitivity at $10\,\mathrm{Hz}$ is not established for a realizable suspension and isolation system. The material-induced displacement is essentially identical in both configurations, with the gain arising from reduced low-frequency quantum backaction. These results identify speed-meter readout as a promising route to lower-mass vector-dark-matter searches.

Fluid antenna systems (FAS) have recently emerged as a promising technology for future wireless networks due to their ability to access a large number of channel realizations using a single radio-frequency chain. This capability creates new opportunities for physical-layer security beyond conventional beamforming and artificial-noise approaches. In this paper, we propose a novel Fluid Antenna Secure Channel-driven Constellation (FASCC) framework for downlink communications, in which information is conveyed through channel-domain constellation points generated by FAS port selection and phase adaptation. Two complementary FASCC schemes are developed, depending on the availability of eavesdropper's channel state information. Numerical results demonstrate that the proposed FASCC framework achieves significant secrecy gains in terms of bit error rate and mutual-information secrecy performance, even when Eve is significantly closer to the base station than Bob.