For a field $k$ of characteristic $0$, we compare $k$-linear chain complexes, semisimplicial vector spaces, augmented semisimplicial vector spaces, semicubical vector spaces, and arboreal vector spaces through small differential categorical algebras. We prove that semisimplicial modules and augmented semisimplicial modules are equivalent to appropriate chain-complex homotopy theories, both at the Gabriel--Zisman localization and the Quillen model-categorical level. The semicubical sign embedding gives a natural comparison from semicubical modules to augmented semisimplicial modules and induces a Quillen adjunction, but not a Quillen equivalence on the full semicubical category since there is an obstruction in augmented homology at degree $-1$.

In this paper, we rely on the additive decomposition in law satisfied by a class of stochastic processes, combined with the well-known regulariy properties of fractional Brownian motion, to establish Besov-Orlicz regularity of their sample paths. This provides a unified and direct proof for a broad class of processes, including bifractional Brownian motion with parameters $H\in (0, 1]$, $ K\in (0, 2)$ such that $HK \in (0, 1)$, subfractional Brownian motion with Hurst parameter $H\in (0, 1)$, and certain class of self-similar processes. %associated with the stochastic heat equation.

In the coordinated motion planning problem, we are given a graph together with the starting and destination vertices of $k$ robots. At each time step, any subset of robots may move, each traversing an edge of the graph, provided that no two robots collide. The goal is to compute a schedule that routes all robots to their destinations while minimizing some objective function. In this paper, we focus on the well-studied objective of minimizing the total travel length of all robots. This problem is known to be NP-hard, and it has been shown to be fixed-parameter tractable (FPT), when parameterized by the number $k$ of robots, on full grids (SoCG 2023) and on bounded-treewidth graphs (ICALP 2024). We present a fixed-parameter algorithm for coordinated motion planning, parameterized by the number $k$ of robots, on graphs arising from discretizations of simple polygons. Such graphs are of particular interest in real-world applications, where planar motion is often constrained to discretized representations of polygonal environments. Moreover, these graphs generalize rectangular grids; consequently, our result constitutes a significant step toward resolving the parameterized complexity of coordinated motion planning on subgrids and, ultimately, planar graphs -- two prominent open problems in the field.

Long-context training of large language models (LLMs) is commonly distributed with Context Parallelism (CP) and Head Parallelism (HP), but existing training systems largely assume homogeneous GPU meshes. This paper extends CP and HP to heterogeneous GPU clusters with mixed GPU models and non-uniform network bandwidths, a common setting in production training. We introduce HexiSeq, a system that supports fully asymmetric CP--HP partitioning by assigning sequence shards and attention heads according to device compute, memory, and communication capabilities. We formalize heterogeneous CP--HP allocation as a constrained optimization problem and develop an efficient hierarchical scheduler for finding optimal schedules. We evaluate HexiSeq against state-of-the-art CP and HP baselines on both real and simulated heterogeneous clusters. Across models from 3B to 70B parameters and context lengths up to one million tokens, HexiSeq improves throughput by $1.11\times$ on average and up to $1.19\times$ on mixed H100--A100 testbeds, and by $1.36\times$ on average and up to $1.72\times$ in simulations with 32--128 GPUs spanning up to four GPU models. On FLOP-comparable pairs against homogeneous clusters, HexiSeq reaches throughput close to the strongest homogeneous baseline, showing that heterogeneous clusters can be used efficiently for long-context LLM training.

Stimulated Brillouin scattering in integrated photonic waveguides enables coherent coupling between optical photons and gigahertz acoustic phonons, providing a powerful mechanism for on-chip microwave photonics and opto-acoustic signal processing. Despite theoretical predictions of ultra-strong Brillouin interactions arising from enhanced light-sound coupling at device boundaries, most state-of-the-art integrated demonstrations remain governed by bulk photoelastic effects. This limitation stems from trade-offs between optical loss, interaction with waveguide boundaries and accessible phonon frequencies associated with the use of transverse-electric optical modes coupled to horizontally breathing mechanical modes. Here we demonstrate a new approach based on transverse-magnetic optical modes coupled to vertically breathing mechanical modes in suspended silicon membranes engineered with subwavelength metamaterial claddings. In this geometry, the interaction is dominated by the moving-boundary effect occurring at smooth top and bottom interfaces, while the phonon frequency is set primarily by the membrane thickness rather than its width. We observe forward Brillouin interactions at a record frequency of 12 GHz with a gain of 7200 W$^{-1}$ m$^{-1}$ and a mechanical quality factor of 620, yielding the highest Brillouin gain-to-quality-factor ratio reported in silicon waveguides. The devices exhibit net Brillouin amplification in millimeter-scale waveguides with pump powers below 15 mW, establishing a scalable platform for high-frequency integrated opto-acoustic signal processing.

This document details the dataset release of simulated $0νββ$ and background events originating from the decay of $^{214}$Bi in high-pressure xenon gas, describing events similar to those produced in the NEXT detector. This release is part of the Neutrinoless Double Beta Decay ($0νββ$) AI Summer School held on June 20-21 2026 at the University of California, Irvine.

We characterise the Schur bounded patterns of ideals of compact operators that are not closed under submajorisation, in particular the Schatten ideals $\mathcal{C}_p$ with $0<p<1.$ Conversely we characterise the ideals that are not closed under submajorisation by their Schur bounded patterns.

Let $B$ be an unilateral weighted backward shift on $\ell_p$, $1 \leq p < \infty$, that admits a $\mathscr{U}$-frequently hypercyclic subspace. We prove that $B$ admits such a subspace free of frequently hypercyclic vectors. The proof technique we develop also allows us to prove that $B$ admits a hypercyclic subspace free of $\mathscr{U}$-frequently hypercyclic vectors, and to solve a question posed by Bès and Menet in 2015 on the existence of common $\mathscr{U}$-frequently hypercyclic subspaces.

This paper refutes the claim that the expected rate of return of the underlying asset plays no role in the Black-Scholes-Merton option pricing model.

In this paper we consider a family of nested t-structures given by silting objects and construct a silting object corresponding to the intersection of aisles of these t-structures as a homotopy colimit. The dual construction for the cosilting case is given as a homotopy limit. The results are applied to construct two-term large silting objects corresponding to the numerical torsion pairs and the limiting walls in the wall and chamber structure of the real Grothendieck group of a finite dimensional algebra. In particular, in case the algebra is tame we can describe any numerical torsion pair in this way by combining our results with results of Plamondon and Yurikusa.

Many physical and chemical processes of interest evolve on timescales that push the limits of conventional spectroscopic instrumentation. Indeed, the temporal resolution of standard spectrometers is often insufficient to track these dynamics, which is connected to the fact that most systems rely on frame-based sensors, imposing fundamental constraints on acquisition speed, sensitivity, and data efficiency, frequently limiting practical operation to the kHz regime. In this work, we present an approach to circumvent this limitation by developing an event-based spectrometer to enable spectral reconstruction with microsecond temporal resolution by leveraging a Czerny-Turner configuration combined with asynchronous and event-driven sensing. A dedicated signal processing pipeline converts the resulting stream of binary events into calibrated spectra through temporal accumulation, geometric correction, and vertical spatial integration of the spectral line, covering a 234nm bandwidth in the visible range with a spectral resolution of approximately 0.18nm per pixel. Performance characterization under temporally modulated illumination demonstrates that the event-based spectrometer can reconstruct spectra at probing rates of up to tens of kilohertz, far exceeding the practical limits of a conventional frame-based spectrometer operated in parallel, while accurately preserving spectral peak positions and relative spectral features. Finally, to further illustrate its potential applications, the system is validated in a microfluidic experiment integrated into an inverted microscope, where spectral changes induced by an absorbing dye are tracked with higher temporal fidelity and resolution compared with the frame-based approach. These results establish event-based spectroscopy as a promising paradigm for real-time, high-temporal-resolution spectral measurements in dynamic and low-light applications.

Novel confidential computing technologies such as Intel TDX, AMD SEV, and Arm CCA have recently emerged. In practice, due to its minimal trust boundaries, Intel SGX still remains widely used for enclave-based applications in cloud environments, including confidential cloud services, privacy-preserving communication, secure payment processing, and privacy-focused advertising. With the growing adoption of Arm CPUs in cloud systems, however, existing SGX applications face a significant portability challenge: they are tightly coupled to SGX-specific APIs and execution semantics. In this paper, we present the design and implementation of CCX, a framework that enables existing SGX applications to run on Arm CCA without source code modification. To this end, CCX redesigns SGX functionality within Arm CCA firmware, adapting SGX abstractions to CCA's architecture design while preserving full compatibility with existing applications originally developed for SGX. We implemented a prototype of CCX on both the QEMU emulator and a Nitrogen8M development board. Our evaluation shows that CCX is capable of executing existing SGX applications without requiring source code changes, while providing security guarantees comparable to Intel SGX and achieving performance improvements in our evaluated settings.

AI-RAN consolidates AI services and Radio Access Network (RAN) functions onto a unified, GPU-accelerated infrastructure at the network edge. However, compute sharing between real-time RAN functions and highly heterogeneous AI services requires coordination of scheduling decisions at mismatched timescales, and placement adaptation may require service migration across nodes with non-negligible interruptions. This paper proposes a hierarchical agentic framework (HAF) for compute sharing in AI-RAN that combines a large language model (LLM)-based agent for slow-timescale placement of AI services and RAN functions with a closed-form, deadline-aware convex algorithm for fast-timescale GPU/CPU allocation. The LLM agent is further equipped with a predictive critic that filters out migrations when the induced service interruption outweighs the expected service-level objective (SLO) benefit. Experimental results show that HAF reaches 90.0% overall SLO fulfillment, a 20.5% improvement over the strongest baseline, and raises AI service request fulfillment from 51% to 85.3%. Further evaluations show that HAF retains its advantage under diverse load conditions, while the critic consistently improves SLO fulfillment across multiple open-source LLM agents.

We consider the isoperimetric inequality involving the $s$-perimeter and the $t$-perimeter with $0<s<t<1$, and show that the ball is a local minimizer of the (scale-invariant) isoperimetric ratio $\mathcal{F}(E):=P_t(E)^{\frac{1}{n-t}}/ P_s(E)^{\frac{1}{n-s}}$ among sets $E$ that are nearly spherical. To this end, we rewrite $\mathcal{F}$ as a functional of $u$, where $u$ is a scalar function on the unit sphere in $\mathbb{R}^n$ that parametrizes the boundary of $E$, and prove a quantitative stability result for $\mathcal{F}$ around $u=0$ with respect to a suitable Sobolev norm. This parallels known results where the $s$-perimeter is replaced by the volume.

We study the properties of the sequence of words $(B_i)$, where $B_1 = 101$ and $B_{i+1} = B_i C_i$ for $i \geq 1$, where $C_i$ is $B_i$ with the first $i$ symbols removed, and the infinite binary sequence ${\bf b} = 10101101011011101 \cdots$ of which all the $B_i$ are prefixes. We show that $\bf b$ is recurrent, but not uniformly recurrent; it has exponential factor complexity; it is not morphic; and the density of $1$'s exists and is transcendental.

Falsification of hybrid dynamical systems remains challenging due to mode-dependent dynamics and discrete transitions. In this work, we propose a surrogate-based falsification approach that enables hybrid systems by learning a differentiable hybrid automaton model from data. This extends previous surrogate-based falsification methods, which were limited to purely continuous dynamics. Specifically, we employ neural hybrid automata to learn both a latent mode encoder and the corresponding mode-conditioned vector fields. Once the surrogate has paired each mode with an associated vector field, the transition guards are inferred using existing trajectory data. The learned surrogate is subsequently subjected to a gradient-based optimal control formulation, which minimizes a smooth approximation of the safety specification to find safety violations. In the last step, an experiment with the optimal control solution is carried out on the original system to ensure soundness. The proposed method consistently uncovers counterexamples on a majority of evaluated benchmark specifications; on these cases, it achieves competitive or improved sample efficiency than other tools while using a reduced simulation budget.

CrRhAs was theoretically proposed to be a kagome metal with unusual magnetic ground states; however, little is known about its magnetic structure and physical properties experimentally. Here, we present an experimental investigation of CrRhAs with ZrNiAl-type structure and a distorted Cr kagome lattice. CrRhAs is an antiferromagnet with TN = 149 K. Powder neutron diffraction analysis reveals a noncollinear antiferromagnetic structure with propagation vector k = (1/3, 1/3, 1/2), which features a ferromagnetic second nearest neighbor coupling in the kagome plane that is different from the prediction in previous density functional theory calculations. Furthermore, CrRhAs exhibits anomalous electrical transport properties which are possibly related to multiband effects and strong spin fluctuations. For the temperature-dependent longitudinal resistivity \r{ho}xx, it is semiconductinglike above TN and becomes metallic below TN . The Hall coefficients exhibit two sign changes near 70 and 300 K. Combined with the results of heat capacity measurements, a large Kadowaki-Woods ratio α = 33.9 μΩ cm mol2 K2/J2 is obtained. The above results suggest CrRhAs is a strongly correlated kagome metal with multiband and noncollinear magnetic structure features.

Interfacial friction in nanofluidic systems can arise from fluctuation-induced coupling between liquid charge fluctuations and the internal excitations of the confining solid. Here, we develop a microscopic theory of exciton-mediated solid-liquid friction based on the coupling between optically generated excitons and charge fluctuations in water. We distinguish between static excitons, localized by disorder or functionalization, and dynamic excitons, which interact with water through polarization fluctuations. In both cases, we derive analytical formulas for the excitonic friction, which is experimentally tunable and can significantly reduce the slip length and thereby the hydraulic permeability of nanochannels. Applying our framework to carbon nanotubes, we quantitatively reproduce the recent measurements of Kistwal et al., showing a reduction of nanotube diffusion under optical excitation, without fitting parameters. More broadly, our results establish excitons as a mechanism to optically control nanofluidic transport and suggest that excitonic photoluminescence could provide an optical probe of flow velocity inside nanochannels.

We establish the nonlinear stability threshold $O(ν^{3/2})$ for the three-dimensional Couette flow governed by the compressible Navier--Stokes equations. While stability thresholds are well understood in two dimensions for both compressible and incompressible flows, and in three dimensions for incompressible flows, the three-dimensional compressible case remains open due to additional structural features, strong mode interactions, and wave coupling. The proof is based on a refined frequency-space approach. For zero modes, we improve upon two-dimensional methods by clearly separating and precisely estimating the main contributions from diffusion waves, acoustic waves, and the lift-up mechanism, leading to a systematic way to handle their nonlinear coupling. For the non-zero modes, we introduce new multiplier estimates and a decomposition based on the structure of the compressible system, which allows us to track the interaction between dissipation and acoustic effects.

This paper assesses the resilience of IEC 61850 digital substations under False Data Injection Attacks (FDIAs) targeting the Sampled Values (SV) protocol. The multicast nature of SV, while enabling time-critical automation, exposes substations to cyber intrusions capable of disrupting protection functions and causing large-scale outages. To evaluate these risks, coordinated attack vectors involving both physical and cyber access at the bay level are experimentally analyzed using an advanced setup based on industrial-grade intelligent electronic devices (IEDs). The proposed attacks simultaneously manipulate multiple electrical parameters in a coordinated and physically consistent manner. Experimental results confirm the feasibility of stealthy multi-vector FDIAs that can trigger false protection actions, conceal real faults, or block protection mechanisms while maintaining realistic signal behavior. The Power Hardware-in-the-Loop (PHIL) testbed enables closed-loop evaluation under strict timing, communication, and protection logic constraints, reflecting real device behavior beyond simulation and controller-level HIL environments. The findings reveal critical vulnerabilities in SV-based protection schemes that directly affect grid reliability, particularly under realistic attacker positioning. To address these challenges, a defense strategy covering deterrence, prevention, detection, mitigation, and resilience is analyzed, with emphasis on bay-level infrastructure. Furthermore, a resilience-oriented method based on trusted independent channels and cross-verification of SV data within the protection logic is outlined as a complementary countermeasure for scenarios where existing standardized security mechanisms are insufficient.

Virtual Reality (VR) applications are increasingly being integrated across a wide range of domains, including surgical training and industrial marketing. However, the long-term adoption and maintenance of VR applications remain limited, particularly due to the lack of effective, systematic, and reproducible software testing approaches tailored to their unique characteristics. To address this issue, we introduce UltraInstinctVR, a novel testing approach for VR applications. Relying on predefined VR models (scenarios), it automates the generation and execution of concrete VR system tests. In our empirical evaluation, we compare UltraInstinctVR with state-of-the-art automated VR testing approaches in terms of coverage and failure detection on 10 open-source VR applications. The results show that UltraInstinctVR outperforms existing automated tools for detecting unique failures and provides valuable insights for identifying real-world bugs in VR applications.

It has been observed that the dynamics of the Toda lattice can be well described by solutions of the Korteweg-de Vries (KdV) equation in the continuum limit. We show that, under the KdV scaling and a suitable translation, the solution of the Toda lattice with H^1 initial data converges to that of the KdV equation globally in time. Our proof relies on tools from harmonic analysis and also on the construction and the conservation of mass and energy of the Toda lattice, the latter of which are derived from the completely integrable structure of the Toda lattice. As a consequence, we obtain long-wave KdV limits for the Toda lattice.

We propose an aggregate notion of non-transferable utility (NTU) stability for decentralized matching markets with fixed prices, where market clearing is achieved through one-sided money burning, which can be interpreted as waiting. Agents are grouped into observable types and are indifferent among individuals within type; equilibrium is defined at the type level and delivers equal indirect utility within each type. We introduce money burning into two types of NTU models: In a deterministic model, we relate our notion to classical Gale--Shapley stability and show how money burning decentralizes stable outcomes under aggregation. We then introduce separable random utility, obtaining an NTU counterpart to Choo and Siow (2006). We prove the existence and uniqueness of equilibrium and provide a stationary queueing interpretation. Finally, we develop a generalized deferred acceptance algorithm based on alternating constrained discrete-choice problems and prove its convergence to the unique equilibrium.

We present the yield, average transverse momentum, and collective flow measurement of $K^{*0}$ resonances in Au+Au collisions at $\sqrt{s_{NN}} = 19.6$, 14.5, and 7.7~GeV using the AMPT model. It is found that, due to hadronic rescattering, the decay daughters of $K^{*0}$ interact with other particles in the medium, causing the yield of reconstructable $K^{*0}$ to be significantly suppressed, especially at low transverse momentum. The model results are compared with recent experimental data from Phase-II of the Beam Energy Scan (BES-II) program at the Relativistic Heavy-Ion Collider. The string-melting version of the AMPT model successfully reproduces the measured $K^{*0}/K$ ratios at all three analysed collision energies. Interestingly, AMPT calculations that exclude the hadronic phase nevertheless provide a reasonable description of the data, thereby challenging the conventional interpretation that hadronic rescattering is the primary mechanism responsible for suppressing the $K^{*0}/K$ ratio in central heavy-ion collisions. In addition, we find that the $K^{*0}/K$ ratio appears to be largely insensitive to the lifetime of the hadronic phase, whereas the average transverse momentum, $\langle p_{T} \rangle$, of the $K^{*0}$ shows a strong dependence, increasing significantly as the lifetime of the hadronic phase becomes longer. We further show that the directed flow ($v_1$) of $K^{*0}$ mesons is strongly influenced by hadronic rescattering, whereas the elliptic flow ($v_2$) exhibits only weak sensitivity to hadronic effects. These results establish $K^{*0}$ directed flow as a sensitive probe of the late-stage hadronic medium in heavy-ion collisions. These model calculations therefore provide valuable insight into the underlying physics governing the observed experimental results at RHIC.

This paper studies low-complexity soft-output decoding of turbo product codes with extended Bose--Chaudhuri--Hocquenghem component codes. Recent soft-output from covered space (SOCS) decoding substantially improves the quality of extrinsic information compared with the conventional Chase--Pyndiah decoder, but its probabilistic-domain implementation is less attractive for hardware-oriented realizations. We therefore propose a log-domain approximation of SOCS based on max-log approach. The proposed soft-input soft-output rule replaces probability-domain operations with a piecewise-linear function of reliability gaps between competing Chase-II decoding list and out of the list hypotheses, which preserves compatibility with the standard iterative TPC decoding loop. Numerical results for a TPC built from (256,239) eBCH component codes show that the proposed decoder clearly outperforms the baseline Chase--Pyndiah decoder with the same list size and approaches the performance of SOCS decoder.

The quantum circuit model essentially treats every quantum algorithm as a straight-line program. While this view is universal, recent work has shown that it is inconvenient for using different-length quantum subroutines in superposition. Using the quantum walk formalism of quantum algorithms, it is possible to model such branching behaviour, and get better composition in this setting. We apply the above branching composition to Grover's algorithm, which gives a variable-time quantum search algorithm that is worse than previous work. The reason it is worse is because branching composition does not take into account another deviation from straight-line programs: looping. We show that by modifying branching composition to also include looping, we can get a complexity that matches previous work. This highlights the importance of properly modeling the program control flow when designing quantum algorithms.

A major challenge in electrochemistry is to decouple the reactive intermediates of a catalytic cycle to optimise their energies independently. During the oxygen evolution reaction (OER), such energy interdependence results from the need to generate multiple adsorbates at the same site and sets the minimum overpotential. Here, we show that an external stimulus, such as a magnetic field, can relax the scaling relationships between intermediates during the OER. Spectroscopic measurements and Density Functional Theory simulations in Ni-Fe oxyhydroxides reveal that applying a magnetic field alters surface chemisorption and injects structural flexibility at the interface. We interpret these observations as a consequence of stimulated changes in the spin-lattice coupling, which allow access to quasi-degenerate oxygenated intermediates that modulate the reaction energy demands. Our findings redefine the scaling limitations as state-projected rather than intrinsic and establish external stimulation as a strategy to navigate multi-state energy landscapes in electrocatalysis and sensing applications.

We show that every proper minor-closed class of graphs admits a $(1+o(1))\log_2 n$-bit adjacency labelling scheme. Equivalently, for every proper minor-closed class $\mathcal{G}$ and every positive integer $n$ there exists an $n^{1+o(1)}$-vertex graph $U$ such that every $n$-vertex graph in $\mathcal{G}$ is isomorphic to an induced subgraph of $U$. Both results are optimal up to the lower order term.

We investigate core/shell GaAs/(Pb,Sn)Te nanowire nanoheterostructures with wurtzite (wz) GaAs cores and (Pb,Sn)Te topological crystalline insulator shells. The nanostructures have been grown by molecular beam epitaxy using two distinct MBE systems dedicated to III-V, and IV-VI semiconductors. The interface structure of wz-GaAs/(Pb,Sn)Te nanowires is investigated using high resolution transmission electron microscopy, scanning transmission electron microscopy and geometric phase analysis. Misfit dislocations and moiré fringes are observed as a direct result of the lattice mismatch between the core and the shell materials, and used to estimate strain in crystalline topological insulator shells. Our results point to a possibility of using moiré patterns analysis as an alternative, for estimating strain in the core-shell nanowire structures.

The John equation serves as the mathematical foundation of the X-ray transform, describing the intrinsic compatibility conditions that projection data must satisfy. In this paper, within three-dimensional (3D) Euclidean space, an innovative mixed parameterization scheme is adopted: the source point is represented using cylindrical coordinates a=(s cosθ,s sinθ,z_0), and the ray direction is represented using spherical coordinates d=\{rho}(-cos\{beta}sinα,cos\{beta}cosα,sin\{beta}). The specific form of the John equation under this geometric parameterization is systematically derived. Through detailed partial differential operator transformations, application of -1 homogeneity, and algebraic simplification, a complete system of constraint equations is obtained. In particular, under the special configurations where the ray direction is perpendicular to the radial direction of the source point in the horizontal plane (i.e., the so-called alignment condition:α = θ) and the ray has no tilt (\{beta} = 0), the constraint equations simplify to differential relations with clear physical meanings. This paper not only establishes a bridge between abstract mathematical theory and concrete imaging geometry, but also provides rigorous mathematical tools for data consistency verification, geometric parameter calibration, and incomplete-data reconstruction in 3D Computed Tomography (CT) systems. The research results are of great significance for advancing the mathematical theory and practical applications of CT imaging.