Reliability-based topology optimization (RBTO) requires repeated estimation of small failure probabilities and their gradients, making conventional nested Monte Carlo approaches computationally prohibitive for large scale structural problems. We propose an RBTO framework that integrates large deviation theory~(LDT) with stochastic gradient descent~(SGD) to address this challenge. LDT provides closed-form exponential rate estimates of rare event probabilities, enabling accurate gradient computation without parametric assumptions on the failure density and without evaluating a full nested reliability loop at every iteration. These LDT-based gradient estimates are used directly to drive a mini batch SGD update of the design variables using only a few random samples per iteration. The framework is validated on three benchmarks, namely, a two-dimentional (2D) simply supported rectangular beam, a 2D L-shaped beam, and a three-dimentional (3D) cantilever beam, under both compliance-based and stress-based failure criteria. Across these examples, the RBTO designs achieve failure probabilities lower than their robust topology optimization counterparts, demonstrating that optimizing for performance under uncertainty alone does not guarantee the satisfaction of explicit reliability constraints. Therefore, the proposed framework offers a computationally efficient route to reliable structural design under uncertainty, with direct relevance to safety-critical engineering applications.

Short-term load forecasting for AI data centers presents new challenges because it is computing-driven, with heterogeneous job arrivals, sizes, and durations exhibiting bursty, non-stationary dynamics. Compared with traditional load types, data center loads are less researched and can pose greater threats to the efficiency and stability of power grids. To close the gap, this paper proposes a regime-adaptive ensemble learning forecasting algorithm to predict computing-driven dynamic workloads in AI data centers. A weight-learned neural network within an ensemble learning framework is developed to exploit the complementary strengths of two machine learning (ML) submodels across varying operating regimes. Furthermore, a novel feature engineering strategy is developed to incrementally learn from a non-stationary data stream. Thus, the ensemble weights are dynamically optimized to facilitate adaptive calibration of inter-submodel contributions. Comparative case studies on the MIT Supercloud dataset demonstrate that the proposed method significantly enhances load forecasting accuracy and adaptivity across various regimes, and the selected combination of ML models for ensemble learning outperforms other possible combinations. To the best of our knowledge, our method is the first to reduce minute-class forecasting errors for AI data center loads to below 1%, highlighting its potential for grid-interactive coordination and demand response.

Upon the introduction of the Metropolis algorithm, the question of how many steps in the Markov chain were needed to achieve convergence to stationarity became apparent. The convergence was rather slow, i.e. for a process on $n$ states the number of steps needed to achieve convergence to stationarity was found to be on the order of $n^2$ if the underlying distribution is uniform. The obvious problem with Metropolis et. al is that the Markov chain is reversible. In other words, for any state $j$ we can move from $j$ to $j + 1$ and back to $j$ in two steps. To correct for this, Diaconis, Holmes, and Neal improved Metropolis et. al by introducing a non-reversible Markov chain. The Diaconis-Holmes-Neal sampler, as it is known, is a Markov chain on two copies of $n$ states, a $+1$ copy and a $-1$ copy. Applications of the Diaconis-Holmes-Neal sampler include Markov chain sampling and situations in statistical physics, among others. However, an answer to the question of how many steps are needed to achieve convergence to stationarity was required. Hildebrand showed that if the underlying probabilities are log-concave then the sampler achieves convergence to stationarity in at least a constant multiple of $n$ steps. Nonetheless, the question of whether a similar convergence exists when the underlying probabilities are instead unimodal was posed in Hildebrand. While Lange answered the question in the three simplest cases - the simple case, the function of $n$ case, and the asymmetric function of $n$ case - and Lange answered the question in the general symmetric unimodal case, the general unimodal case is left to this paper.

As LLMs are increasingly integrated into systems that browse, retrieve, summarize, and act on web content, webpages have become an untrusted input vector for downstream model behavior. This enables site owners, contributors, and adversaries to embed instructions directly in web resources, i.e., indirect prompt injections. While prior work demonstrates such attacks in controlled settings, their prevalence, deployment, and real-world impact remain unclear. We present one of the first large-scale empirical analyses of indirect prompt injections in webpages and HTTP responses. Analyzing 1.2B URLs from 24.8M hosts, we identify 15.3K validated instances across 11.7K pages. These are not isolated cases: a small number of recurring templates account for most cases. We characterize their objectives, delivery mechanisms, visibility, persistence, and impact, revealing a heterogeneous ecosystem spanning disruptive prompts, reputation manipulation, content-protection directives, and AI-bot detection, targeting systems such as crawlers, search pipelines, customer-support agents, and hiring workflows. A key finding is that most instructions target machines rather than humans: about 70% appear in non-rendered HTML (e.g., headers, comments, metadata), and many visible cases are hidden via rendering techniques. To assess practical risk, we run 5,200 controlled experiments across 13 models and four webpage representations. Our results show compliance is limited but non-negligible, reaching up to 8% for smaller models on plain-text inputs, while structured representations reduce compliance by preserving structural cues. Overall, prompt-based interference is already present in the web ecosystem and represents a growing source of tension between LLM-driven automation and the sites it consumes.

We demonstrate a micro-Fabry-Pérot cavity array through laser etching of high-surface-quality mirrors onto a single fused silica substrate. A cavity finesse of $4750\pm 200$ was achieved with a simple array design with $500~μm$ cavity length, $100~μm$ diameter micromirrors and $300~μm$ transverse separation. Arrays with up to 12 cavities were simultaneously tested for single mode operation, and absolute frequency measurements correlated strongly with the etched depth as measured by profilometry. Simultaneous measurements of the absolute resonant frequency for neighboring cavities showed a factor of 5 common-mode cavity drift reduction. Arrays of such cavities can be employed in chip-scale cavity QED networks (current cooperativity estimates are at the border of strong coupling for $^{87}$Rb atoms, $C=1$) as well as for precise laser stabilization at nearby wavelengths on a chip.

In Alzheimer's disease research, for individuals who remain dementia-free through a given follow-up time, an important clinical question is how much longer they are likely to remain dementia-free. Quantiles of this remaining time provide clinically interpretable prognostic milestones and can help characterize prognostic heterogeneity across baseline groups. We address this question in the Alzheimer's Disease Neuroimaging Initiative (ADNI), focusing on baseline amyloid status as the exposure. Estimation is challenging because amyloid status is observed rather than randomized, requiring adjustment for confounding, and because time to dementia onset is heterogeneous and heavily right-censored. We estimate causal contrasts in quantile residual life using a Bayesian nonparametric enriched Dirichlet process mixture model for the joint distribution of event times, exposure, and baseline covariates, with inference via Bayesian g-computation. The approach accommodates ignorable missing baseline covariates through data augmentation, supports inference across clinically relevant landmark times, and allows sensitivity analysis for residual unmeasured confounding. Simulation studies show good performance under complex heterogeneity and heavy censoring. In ADNI, elevated baseline amyloid was associated with shorter quantiles of remaining dementia-free time than non-elevated baseline amyloid among individuals who remained dementia-free through relevant landmark times, overall and within baseline diagnostic subgroups.

Orbital data centers are being evaluated as solar-powered compute constellations and relay-integrated processing platforms. Their feasibility is not set by orbital solar flux alone, but by simultaneous closure of photovoltaic generation, eclipse recharge, radiative heat rejection, sustained space-to-ground communications, utilization, replacement cadence, and delivered compute-years over finite mission life. This paper derives necessary cluster-level competitiveness conditions using delivered information-technology (IT) electrical power $P_{\rm IT}$, deployed mass per delivered IT power $m_{\rm kW}$ in kg/kW, communication intensity $Γ=D_{\rm sg}/E_{\rm IT}$, sustained communication ceiling $Γ_{\max}$, effective utilization $U_{\rm eff}$, and lifetime penalty $Π_{\rm life}$. For a representative $P_{\rm IT}$=1 MW high-sunlight anchor, the base case gives beginning-of-life photovoltaic area $A^{\rm BOL}_{\rm PV}=5.64 \times 10^3 {\rm m}^2$, radiator area $A_{\rm rad}=2.50 \times 10^3 {\rm m^2}$, and 29.4 kg/kW for photovoltaic, storage, and radiator mass; fixed spacecraft mass raises the total to 34-59 kg/kW. At m_kW ~ 40 kg/kW, a terrestrial infrastructure benchmark of 10-40 k\$/kW allows only 250-1000 \$/kg for the combined launch and spacecraft-build cost before space-to-ground communications, operations, utilization, and lifetime terms are included. That allowance is 3.4-13.5 times below the current public Falcon 9 dedicated low-Earth-orbit launch-price benchmark alone, before spacecraft build is included. Space-native preprocessing and communications-integrated edge compute are credible early regimes; terrestrial-user general compute closes only for low Earth-coupled communication intensity, high effective utilization, long delivered lifetime, and very low combined launch-plus-build cost.

Recent results have shown that for a linear tilt to a reference measure, the scores that would be produced under convolution with a normal variable can be expressed in terms of convolutions of the original density. Here, we extend that result to include constant negative diagonal tilts as well. The relationship follows from relating the denoisers of the two densities, which define the scores via Tweedie formula. A linear tilt results in a location shift to the score operator, while a quadratic tilt results in both a location shift and a time shift. Thus the scores of the tilted density can be understood as the scores of the original convolution process at a different location and noise level. These results are of interest to those in the score based diffusion community, and may lead to better score estimators which take advantage of these tilted score relationships.

Thin liquid films exhibit rich instability and rupture dynamics that critically impact coating performance across many applications. In this work, we use the lattice Boltzmann method (LBM) simulations within a lubrication-theory framework to systematically quantify how film thickness, surface energy, wettability, and intermolecular forces govern dewetting kinetics and long-time morphology. Master-curve scalings are identified for the time to dewet, revealing a strong power-law sensitivity to film thickness and a comparatively weak dependence on moderate variations in the contact angle. Following rupture, the film reaches a physically meaningful coverage plateau, whose magnitude correlates with material parameters and provides a practical window for morphological stabilization prior to coarsening. Long-time evolution obeys classical coarsening scaling laws, with surface energy controlling domain density. These results demonstrate that lubrication-based models can deliver predictive design guidance for evaluating coating robustness and forming materials and surface engineering strategies. Source code is available at https://github.com/Zitzeronion/Swalbe.jl.

Recent advances in occupancy extrapolation (OE) show that potential of orbital-occupation based energy functions can describe electronic excitations. Here, the OE method in the particle-hole channel is extended to an effective quasiparticle Hamiltonian, enabling a multi-configurational description beyond single-determinant OE and $Δ$SCF. The method performs comparably to the Bethe-Salpeter equation for valence singlet and charge-transfer excitations, and better for valence triplet and Rydberg states, supporting its accuracy and broad applicability.

Success-driven social learning, in which individuals preferentially adopt the ideas and methods that appear most successful, is a foundational principle of collective behavior across systems ranging from ant colonies to scientific communities. But science is a particular kind of collective search -- one in which the quality of an explanation is itself difficult to assess. Is success bias adaptive in this setting? In agent-based simulations of collective theory building, we find that it is not. Scientists in our model systematically overestimate the quality of their own theories, creating an illusion of understanding: a persistent gap between perceived and actual performance. Success bias amplifies this illusion; communities that favor apparently successful theories explore a narrower range of possibilities, efficiently filtering out poor explanations but failing to discover better ones. This effect intensifies with problem complexity, as scientists in more complex environments become increasingly unable to assess how well their theories actually perform. Most strikingly, when agents optimize their social behavior to maximize the perceived success of their theories, they paradoxically undermine their actual performance, and produce levels of inequality that mirror those found in real scientific communities.

This paper studies the interactive fixed effects (IFE) estimator in a panel-data setting with heterogeneous treatment effects. We show that, if the treatment-effect heterogeneity admits a linear factor structure, the IFE estimator could fail to recover the average treatment effect on the treated units. The problem arises because the interactive fixed effects absorb the heterogeneity in the treatment effect, creating a \textit{bad-control} problem. With time-invariant factors or unit-invariant loadings in the treatment effect heterogeneity, identification may further break down due to multicollinearity. These problems are not present in alternative estimation methods that exclude treated units in post-treatment periods from the factor estimation.

Gravitational Wave (GW) data bring an exceptional avenue to test the underlying models of coalescing compact objects. In the regime of strong gravity and high curvature, they allow the exploration of minute deviations from the best-fit models, which are difficult to uncover with other observational modalities. These deviations can stem from departures from General Relativity (GR) or unaccounted astrophysical effects. They may not be explainable within the current description of GW strain data, or may simply be difficult to model. However, they are expected to be correlated between detectors and across the population of observed events. The recently developed SCoRe analysis pipeline leverages these properties by focusing on the correlated power between detectors and combining results from multiple events. In this paper, we apply the framework on the Third Gravitational-Wave Transient Catalog to search for source-dependent deviations. In particular, we explore whether there is evidence for a mass-scale in the observed events, which can act like a line of demarcation in their physical properties by exhibiting a deviation that is different above and below this mass-scale. This mass scale dependency naturally arises in gravitational theories described through effective field theories, due to environmental effects or in scenarios involving exotic compact objects, where the GW signature can differ from the standard binary black holes in GR. Using the 30 highest Signal-to-Noise Ratio events in the catalog, we find Bayes factors ranging from 0.16--0.5 (depending on where the threshold mass is set), thus disfavoring the hypothesis of existence of any mass-scale between $\sim 2.5$ M$_\odot$ and $60$ M$_\odot$. We also compute the distribution of excess cross-correlated power across events and find a Bayes factor of $0.07$, which agrees with expected noise statistics.

Rotating calorons were introduced in the context of rotating quark-gluon plasmas. They are anti-self-dual gauge fields on $\mathbb{R}^4$ that are invariant under a glide rotation. We formulate a Nahm transform which identifies rotating calorons with solutions of a delayed-differential equation. Using this transform, we prove existence of an eight-parameter family of charge 1 rotating calorons with nontrivial holonomy and rotational angle $π$, which we construct and visualise using a numerical implementation of the Nahm transform.

As quantum computers continue to increase in size and topological complexity, benchmarking crosstalk becomes more complex and resource-intensive. This limits the ability to obtain relevant crosstalk metrics for applications such as error mitigation, quantum computer security, and circuit transpilation. There applications benefit from accessible metrics on how each gate contributes to crosstalk. However, crosstalk metrics are rarely provided by quantum computer providers and can be expensive to obtain on modern large NISQ devices. In this work, we propose CrossBench, a customizable system that generates crosstalk benchmarks for finitely large NISQ devices with arbitrary topologies. CrossBench uses a custom graph labeling algorithm to generate crosstalk benchmarks for a given quantum topology and gate set. These benchmarks can be used to estimate the average contribution of each gate's crosstalk to qubit error rates. We evaluate the effectiveness of CrossBench by generating and running benchmarks on multiple IBM quantum computers with different topologies. Our results show that CrossBench can identify gates that introduce significant crosstalk across all tested devices, with strong statistical significance (p < 0.05). These promising results show that CrossBench can give simple and accessible crosstalk benchmarks for modern NISQ systems.

We prove the $\frac{2d}{d+1}$-Sidon inequality for a system of functions representing the most general extension of the Rademacher $d$-chaos to the $p$-ary case.

This paper presents an optimal network topology control framework using cutting-plane methods for efficient network partitioning with controllable edges. The objective is to enable real-time reconfiguration of interconnected sub-networks while ensuring radial connectivity, resource feasibility, and structured leader allocation, which are essential for distributed control, stability, and coordination. The problem is formulated as a mixed-integer program that integrates graph-theoretic constraints, resource flow, and network structural properties to enforce an operational hierarchy. To address the combinatorial complexity of cycle elimination and leader assignment, we propose an iterative cutting-plane framework that ensures convergence to an optimal and feasible network topology. Theoretical guarantees on optimality preservation, feasibility, and convergence are established, ensuring systematic elimination of infeasible configurations while maintaining distributed controllability. Simulations on a modified Iowa 240-bus power distribution grid demonstrate the framework's effectiveness in network reconfiguration under resource constraints. The approach achieves median and best-case speedups of 57.5x and over 64x in a 46-switch configuration, highlighting its applicability to other networked control systems.

In this article, we propose a simple and efficient hyperreduced strain-space model order reduction (MOR) approach for hyperelastic representative volume elements (RVEs), called Empirical Material Sampling and Linearisation (EMSL). The approach is conceptually motivated by the Empirically Corrected Cluster Cubature (E3C) of Wulfinghoff and Hauck [36], but also draws on ideas from previous work on incremental variational structure-preserving strain-space model order reduction techniques to achieve rapid evaluations in the online phase. As in E3C, we group the material domain into regions of similar behaviour, and query the material routine at one reference strain value per region. However, we sample these strains only once per load increment, at empirically estimated expected strain values. We use the reference material tangent and strain modes obtained via the Proper Orthogonal Decomposition (POD) to compute a linearised estimate of the stress response in the remainder of the material cluster. In contrast to E3C, which approximately integrates the exact material law, EMSL could therefore be said to exactly integrate an approximation of the material behaviour.The resulting reduced problem is affine in each load step, allowing for integration over the entire computational domain via operations which can readily be preprocessed in the offline phase. Since a linear equation system is obtained in each load increment, no Newton iterations are required in the online phase. For benchmark comparisons, we pose a variant of two popular reduced cubature schemes in strain space and recall the E3C algorithm proposed by Wulfinghoff et al. On an example hyperelastic RVE problem with a porous geometry, we show that EMSL Pareto-dominates competing strain-space approaches in terms of the tradeoff between accuracy and runtime.

The detection of CO2 on the Jovian satellite Europa by Galileo NIMS and recent mapping of the leading side by JWST has revealed that it is most concentrated in geologically young terrains, and its v3 asymmetric stretch appears as a spectral doublet centered at 4.25 and 4.27 um. Since crystalline CO2 is unstable at Europan surface conditions, this observation implies an active source and a trapping medium, which may be separate. To this end, several hypotheses have been proposed, but no laboratory work has successfully reproduced the spectral features of CO2 on Europa so far. Radiolyzed carbonates have also been discussed as plausible precursors and host materials for CO2, though their role has not been experimentally validated in a Europa-like environment. Here, we report the first laboratory experiments investigating CO2 production from carbonate salts exposed to 10 keV electron irradiation at 50, 100, and 120 K in ultrahigh vacuum. Using diffuse reflectance FTIR spectroscopy, we observe the emergence, growth, and saturation of an absorption doublet centered near 4.25 and 4.27 um, consistent with the CO2 v3 band. Postirradiation thermal desorption studies using residual gas analysis reveal that the radiolytically formed CO2 is stable at temperatures beyond Europa's surface. This work provides the first experimental evidence that low-energy electron irradiation of carbonates in cryogenic, vacuum conditions can produce and retain CO2, and suggests that carbonates can serve as endogenous reservoirs of CO2 on irradiated icy bodies in the outer solar system.

We report the discovery of six new variable stars identified through an exploratory analysis of several sky fields observed by the author using a small telescope and a CMOS camera. The search employed simultaneous photometry of hundreds of objects with AstroImageJ, supplemented by custom Python-based tools developed by the author to generate aperture lists and visualize light curves across the full field of view. The variables were further characterized using TESS data, and their properties are presented. We also describe the data analysis workflow, including the software packages LCV and VS-fit, developed by the author for periodogram analysis and light-curve modelling.

Hyperledger Fabric (HLF) is a modular, permissioned blockchain widely adopted in enterprise settings. Enhancing its throughput and latency remains challenging, as optimization decisions made in one phase of the transaction lifecycle can adversely affect other phases. In this work, we present a systematic, phase-level and end-to-end study of HLF optimizations along three fronts, combining production-grade testbed experiments with calibrated SimPy simulations. First, we introduce two novel optimization techniques that target commit-phase bottlenecks: block-level pipelining and strategic waiting. In pipelining, we overlap validation and private-data acquisition of successive blocks with state-consistency checks and ledger updates improving commit throughput by up to 1.9x. Strategic waiting coordinates commit progress by temporarily pausing fast leaders and boosting laggers to sustain endorsement parallelism, yielding up to a 1.2x higher throughput. Second, we conduct micro-benchmarking of three configuration levers: private-data dissemination, block-size selection, and endorsement peer selection. Our results reveal that: (i) Relaxed quorums for private-data dissemination significantly reduce latency in both endorsement and commit phases; (ii) Under light workloads, smaller blocks yield lower end-to-end latency, whereas, under heavy workloads, larger blocks are necessary to improve throughput and reduce latency; and (iii) Relaxed leader selection dramatically reduces dropped transactions and boosts endorsement throughput, with a modest increase in MVCC invalidations. Finally, we analyze the interplay among private-data dissemination, VSCC parallelization, and pipelined commits. Interestingly, the throughput gains over a serial commit path are maximized at a moderate level of parallelization. Together, our findings provide phase-aware and protocol-level refinements for optimizing HLF.

Trotterization is a standard approach for simulating quantum time evolution on quantum computers, where the Hamiltonian is split into local terms and each term is applied in sequence. The order of these terms affects the fidelity of the simulation when they do not commute, so the choice of ordering directly impacts the accuracy of the simulation. We study this problem for one-dimensional XXZ Heisenberg Hamiltonians using a structured set of 24 candidate orderings derived from colorings of the Hamiltonian's commutation graph and their group permutations. Finding the best candidate for large systems becomes prohibitive because fidelity evaluation is computationally expensive. In this work, we train a transformer encoder on smaller systems to predict the best candidate ordering for larger systems directly from Hamiltonian and Trotter-configuration features, without computing candidate fidelities at inference time. The model is trained on in-range systems of 3 to 14 qubits with 15-qubit systems held out for validation. Experimental results show that the model reaches a mean test fidelity gap of 0.00115 relative to the best of the 24 candidates on out-of-range systems of 16 to 20 qubits. A training-size sweep further shows that generalization emerges once training includes systems up to L=8 qubits, with validation at L=9, and the gap continues to decrease as the training range grows. To our knowledge, this is the first application of a learned model to Trotter ordering, and it motivates future work on AI-guided Trotter ordering with generalization across Hamiltonian families and system types.

The standard architecture for a high-peak-power femtosecond laser is chirped pulse amplification using diffraction gratings for compression; the damage threshold of the compression gratings limits current lasers to multi-petawatt peak power. Plasma gratings have orders-of-magnitude higher damage tolerance than conventional optics, so plasma gratings with sufficiently high optical quality could allow the construction of ultra-high-power femtosecond lasers. Here, we present experimental measurements of the angular dispersion, angular bandwidth, and diffraction angles of ionization-based plasma transmission gratings and show that both the dispersive and the diffractive properties of these gratings are in close agreement with optical theory and simulations. Gratings with a period of 10.2 microns are found to have an angular dispersion of approximately 0.005 degrees/nm. The dispersion and bandwidth of these gratings suggest plausible designs for a plasma-grating-based compressor and indicate a pathway to compact lasers with petawatt to exawatt peak power.

We compute exact finite-rank BPS generating functions for the fermionic matrix model with single-trace supercharge $Q_p=\operatorname{tr}(Ψ^p)$ at $(p,N)=(5,3),(5,4),(5,5),(7,4)$, together with partial data at $(7,5)$. In all complete computed cases, the charge-resolved spectrum exhibits an overdetermined factorization -- a power of $p$, times an onset monomial $x^{q_{\min}}$, times $(1+x)^N$, times a palindromic reduced polynomial -- despite the loss of Casimir solvability at $p\ge 5$. We prove rank palindromicity $r_R=r_{N^2-p-R}$ from the exterior top-degree pairing; at $(5,5)$, the ten low-charge ranks and the minimal divisibility condition $(1+x)\mid\mathcal{R}_{5,5}$ determine the remaining middle rank, and direct computation confirms the full generating function. For fixed $p$, the mod-$p$ Witten indices give a closed-form index floor; together with the trivial Hilbert-space upper bound, this places any accumulation point of $N^{-2}\log Z_{\mathrm{BPS}}^{(p,N)}$ in the window $[\log(2\cos\fracπ{2p}),\,\log 2]$. A rank-projection tower gives rigorous lower bounds on the projection-fortuitous cohomology. In matched $\mathcal{N}=2$ SYK examples at $N_f=16$, the BPS count saturates the index floor, whereas the single-trace matrix model has nonzero index excess and broader charge support.

Let $G = \mathrm{SL}(n,\mathbb{C})$, let $B$ be a fixed Borel subgroup, and let $P \supset B$ be a parabolic subgroup determined by a composition $(c_1,\dots,c_k)$ of $n$. Write $P'$ for the derived group of $P$ and $\mathfrak{m}$ for the Lie algebra of the nilradical of $P$. By Richardson's theorem the algebra of semi-invariants $\mathscr{I} := \mathbb{C}[\mathfrak{m}]^{P'}$ is polynomial; in type $A$ its generators may be taken to be the Benlolo--Sanderson (BS) invariants. The \emph{nilfibre} is the common zero locus $\mathscr{N} := V(\mathscr{I}_{+}) \subset \mathfrak{m}$. A set of \emph{component tableaux}, each encoding combinatorial data summarised in a multi-set called the \emph{Red Set}, was constructed in earlier work by Y. Fittouhi and A. Joseph in The reverse tableau: a gateway to the surjectivity of the component map. The resulting \emph{component map} $ϕ: \{\text{component tableaux}\} \to \Irr(\mathscr{N})$ was shown to be injective. In the present article, we develop the Factorization Principle for Benlolo--Sanderson invariants in order to give a rigorous proof of the surjectivity of the component map $ϕ$. While the combinatorial framework of reverse tableaux was introduced in a work by Y. Fittouhi and A. Joseph cited above, the surjectivity of $ϕ$ remained conjectural: the linearization method used there did not exclude the possible loss or merging of irreducible components. The present paper resolves this geometric difficulty by showing that the relevant invariants factorize into products indexed by pseudo-neighbouring column pairs, thereby ensuring that every component is reached in a controlled and accountable way.

XRISM observations to date have shown that gas kinetic pressures in the intracluster medium (ICM) tend towards the low end of predictions from cosmological simulations. Here, we present a XRISM observation of the merging cluster Abell 2034, which exhibits the broadest emission lines yet observed in a galaxy cluster. We measure a velocity dispersion of ~470 km/s, corresponding to a kinetic pressure fraction of ~15%. This places A2034 at or above the high end of the theoretical predictions for similar-mass clusters. This large velocity dispersion may reflect Mach ~0.5 turbulence in the ICM and/or result from a core disruption driven by the ongoing head-on merger. We also detect a ~380 km/s gas bulk velocity gradient along the merger axis with an opposite sign to the galaxy velocity gradient, indicating a decoupling of the cluster galaxies (and dark matter) from the ICM. Finally, we report tentative evidence of several spectral anomalies, including a suppressed Fe He$α$-z line, an enhanced Fe Ly$α$-2 line, and a potential absorption feature at ~8.7 keV. The first two features may be explained by the combination of a multi-phase ICM and a non-equilibrium ionization state in the wake of a merger shock. Deeper XRISM observations of this cluster are required to confirm these features. This work highlights the importance of kinematic measurements across a large sample of merging clusters as well as the need for deep XRISM observations to unveil more exotic physics in the ICM.

We study embeddings between reproducing kernel Hilbert spaces $H(K)$ of functions of $d \in \mathbb{N} \cup \{\infty\}$ variables. The kernels $K$ are superpositions of weighted finite tensor products of a fixed univariate kernel. The basic idea for the embeddings is to compensate a change of the univariate kernel by a suitable transformation of the weights. For the proofs we employ ($d \in \mathbb{N}$) and develop ($d = \infty$) a discrete calculus on the cone of all weights, where completely monotone weights play a particular role. We sketch how to apply the embedding results to computational problems, as, e.g., numerical integration or function recovery.

We present Northern Extended Millimeter Array (NOEMA) observations of the CO (2-1) molecular gas kinematics in the nearby Compton-thick Seyfert 2 galaxy NGC 3079, with an angular resolution of 0.5" ($\sim$40 pc). To interpret the observed CO (2-1) kinematics, we model the rotating disk using two software tools, 3D-Barolo and DysmalPy, to generate mock 3D data cubes. Both models indicate, in addition to the rotating disk, the presence of a spatially unresolved nuclear component characterized by high velocity dispersion. Analysis of the visibility data reveals that the blue-shifted, high-velocity component is spatially offset from the continuum peak by 0.17" ($\sim$ 14 pc) and exhibits line-of-sight velocities of $v$ - $v_{sys}$ = -350 to -450 km s$^{-1}$, which we interpret as a nuclear molecular outflow. We calculate a molecular gas mass outflow rate of 8.82 $M_\odot$ yr$^{-1}$, with a kinetic power ($\dot{E}_{\text{out}}$) of 3.8 $\times$ 10$^{41}$ erg s$^{-1}$ and a momentum rate ($\dot{p}_{\text{out}}$) of 2.05 $\times$ 10$^{34}$ Dyne. The momentum rate exceeds the AGN radiation momentum rate by a factor of $\sim$15, suggesting an energy-driven outflow. Furthermore, we argue that the derived kinetic power of the nuclear molecular outflow favors a jet-powered scenario that explains the slowdown and brightening of the parsec-scale radio source observed with the Very Long Baseline Array.

We propose an accelerated computational fluid dynamics framework based on a hybrid Fourier Neural Operator-Lattice Boltzmann Method (FNO-LBM) for steady and unsteady weakly compressible flows. FNO-based initialization significantly accelerates LBM in reaching steady-states of porous media flows across all macroscopic fields, achieving up to 70% speed-up in convergence of density and more than 40% of pressure-drop while preserving the final steady-state accuracy. Simulations of unsteady flows can be accelerated by hybrid coupling strategies that employ FNO rollouts embedded into LBM time advancement in a way of super-time-stepping. Global and time-resolved error metrics across 100 trajectories for generic 2D flows demonstrate that hybridization consistently improves accuracy and stabilizes long-horizon rollouts. Best efficiency is achieved for a lightweight 2.6M-parameter FNO, which diverges under pure autoregressive rollout but achieves 96-99.8% error reduction under hybrid coupling, matching the predictive capability of a much more expensive 11.2M-parameter model. The hybrid framework enhances predictive fidelity, suppresses error accumulation, and enables small and cheap surrogate models to operate effectively within the same error regime as larger surrogates. These results demonstrate that hybrid neural-operator coupling achieves robust and computationally efficient accelerated LBM while maintaining physically consistent flow evolution.

We study stochastic differential games with $N$ players, where interactions are determined by sequences of graphs in which the number of neighbours of each node remains bounded as $N$ grows, such as chain graphs or lattices. Our main goal is to quantify the phenomenon of the "unimportance of distant players" in such a large population, sparse regime: we show that, in order to determine the optimal trajectory in open-loop strategies of a given player with an arbitrarily small error, it suffices to consider a reduced game involving only the players at a certain distance in the graph, assigning arbitrary trajectories to the farther ones. Our main result provides an explicit non-asymptotic estimate in terms of the graph distance, valid independently of the time horizon $T$, under suitable convexity and monotonicity assumptions on the costs. Similar results are obtained for games in distributed strategies.