We present the exact analytical paraxial propagation of structured light beams that transition from Ring annular profiles to top-hat intensity distributions. The initial field is defined as a superposition of a Gaussian-weighted power-law core and a singular inverse-quadratic modulation term, both carrying an azimuthal phase factor. By solving the Fresnel diffraction integral in cylindrical coordinates, we obtain exact closed-form expressions for the propagated field at arbitrary planes. The paraxial evolution is shown to be governed by a Cauchy-Riemann beam term and an infinite series of modified Bessel functions of the second kind weighted by an azimuthal phase factor. This analytical framework demonstrates how tuning the source parameters enables a continuous transition from ring-dominated annular profiles to uniform top-hat beams. For the fundamental mode ($l=0$), the singular component fills the central intensity null, producing a flat transverse plateau.

We investigate the atomic transition probabilities in atom-mirror set-ups that are in circular motion. In one scenario, the atom is in circular motion inside a static cylindrical mirror. In the other scenario, the cylindrical mirror rotates around its central axis while the atom remains static. We report structural similarity in the atomic transition probabilities between these two cases -- these probabilities are equivalent upon interchanging the field frequencies between the two scenarios. We interpret such an observation as a semi-classical phenomenon analogous to the classical Mach's principle.

In this paper we establish sharp global $C^{1,α}$ regularity for a class of degenerate/singular fully nonlinear elliptic equations featuring Hamiltonian structures. The results presented in this paper serve as the boundary counterpart to the interior regularity estimates recently derived in \cite{AN25b, HJMZ26}, and substantially generalize the existing regularity theory developed in \cite{BBLL24b, BSRR23, BD14}. The optimal regularity is established within the framework of Caffarelli's perturbation argument \cite{C89, CC95}.

A time-reversal characteristic-mode decomposition is developed for reciprocal lossy electromagnetic structures. The formulation is built on a transmit--receive interpretation of reciprocity: the far-field pattern radiated by a mode determines the time-reversed incident field that is optimally matched to couple energy back into that same mode. This physical picture leads to an antilinear characteristic-mode equation whose solutions remain radiation-power orthogonal even in the presence of material loss, lossy loading, or matched absorption. As a result, the modal expansion coefficients directly represent the radiated-power contributions of the corresponding modes and avoid the singular biorthogonal normalization that may arise in nonnormal classical characteristic-mode expansions. Equivalent formulations are derived in the scattering-operator, T-matrix, and method-of-moments (MoM) frameworks, thereby connecting external wave-channel descriptions with current-space and port-excitation descriptions. The proposed modes reduce to classical characteristic modes in the lossless limit. Numerical examples involving a lossy two-sphere system and a loaded folded antenna demonstrate the radiation-power orthogonality, modal-expansion stability, and power interpretability of the proposed decomposition near exceptional points, where classical characteristic-mode expansions become singular or lose their radiated-power meaning.

Tensor train (TT) decomposition is a powerful method to acquire low-rank tensors. However, the computational process is frequently obstructed by the large-scale matrix singular value decomposition (SVD). The sketching algorithm serves as an efficient data compression technique that can quickly derive low-rank matrix approximations. In this paper, we propose a randomized algorithm to obtain the TT approximation of tensors using a one-pass sketching algorithm and subspace iteration, and offer thorough error-bound and robustness analysis. Numerical experiments on synthetic and real-world datasets demonstrate the effectiveness and efficiency of the proposed algorithm.

This paper proposes an epistemic foundation for aggregating sets of probabilistic beliefs by retaining only shared beliefs. It develops a model of belief formation under information-acquisition costs and capacity constraints. In this model, different information technologies rationalize different belief-aggregation rules, such as the familiar linear, geometric, power, and multiplicative pooling. Since the ranking of uncertain policies depends on these aggregation rules, failing to base collective beliefs on the underlying technologies can cause welfare losses. An application to financial markets demonstrates how these technologies translate conflicting beliefs into equilibrium prices.

Interpersonal communication requires building shared semantics that enable listeners to understand speakers' meanings from their unfolding language, but the dimensional structure of this shared neural representation remains unclear. LLMs increasingly approximate human language capability and neural responses, raising the question of whether they capture the same semantic structure shared between human brains. Here, we combined storytelling-listening pseudo-hyperscanning MEG with dimension-resolved interbrain encoding modeling to compare human- and LLM-derived accounts of shared neural semantic representations. Content words from the speaker's narratives were rated by humans and five recent LLMs along ten semantic dimensions (i.e., perception, motor, space, time, socialness, animacy, emotion, attention, causality, and drive). We tested whether these dimensions explained speaker-listener neural synchronization (NS) beyond acoustic and phonological features. Both human- and LLM-derived semantic spaces explained NS, but these shared semantics are better characterized as a multidimensional neural structure rather than a single global signal. These patterns also predicted individual differences in listeners' story comprehension, linking neural alignment to cognition. However, comparable overall prediction concealed systematic differences in representational geometry. Larger LLMs aligned more closely and showed greater overlap with humans in semantic structure and NS, but this was incomplete and dimension-dependent. The largest divergences emerged for dimensions closely tied to agency, affect, and social experience. These findings show that LLMs capture substantial components of human shared neural semantics, but their alignment is selective. Larger or more capable models improve the approximation, whereas socially and affectively grounded dimensions are captured only partially.

Soft glassy materials display rich and complex flow behaviors across both macroscopic and molecular scales, and a fundamental understanding of these phenomena remains an outstanding challenge. Here, we propose a theoretical model for the flow of supercooled liquids -- a typical class of glassy fluids -- based on a two-state paradigm that conceptualizes the flow as a dynamic coexistence of transient solid-like and liquid-like regions. The model rests on two essential physical ingredients: a correlation length that captures medium-range structural order, and a localized elasticity-mediated interaction that restricts stress propagation within solid-like regions. Remarkably, with all parameters determined solely from equilibrium state, the model quantitatively reproduces rheological responses -- including both steady-state and start-up shear -- for a broad range of shear rates. Furthermore, it simultaneously captures the evolution of molecular dynamic heterogeneity. This dual success -- spanning macroscopic rheology and microscopic spatiotemporal fluctuations -- underscores the pivotal role of structural and dynamic heterogeneities in governing the rheological response. Moreover, it provides a direct understanding of how the flow behaviors of a supercooled liquid are embedded in its equilibrium properties.

Gravitational-wave interferometers exhibit a wide variety of short-duration non-Gaussian transients, commonly referred to as glitches, that complicate the detection of astrophysical signals, bias parameter estimation, and detector characterisation. Existing machine-learning approaches classify glitch morphologies but do not provide a complete mechanism to segment and extract these disturbances from the strain data. We introduce a wavelet-based, saliency-guided framework for the supervised extraction of transient noise. Candidates are first pre-tagged using Uniform Manifold Approximation and Projection, which is also used as a diagnostic of the learned representations. A traditional learning model operating on Continuous Wavelet Transform spectrograms then identifies relevant time-frequency regions through saliency maps. These saliency patterns are transferred to an invertible multiresolution representation via the Discrete Wavelet Transform, where adaptive coefficient masking enables exact reconstruction of both glitch-only and glitch-suppressed waveforms. We demonstrate effective extraction across several representative glitch families, including 'Whistle' and 'Scattered-Light' transients, and show robustness in challenging regimes such as low signal-to-noise events and partially overlapping structures, where classical thresholding or band-limited filtering methods typically fail or introduce leakage. The proposed framework offers an interpretable and computationally efficient approach to transient-noise extraction, establishing a foundation for scalable applications to larger glitch catalogs and future observing runs.

Reliable estimates of stellar effective temperature ($T_{\mathrm {eff}}$) are fundamental to stellar population studies and Galactic astrophysics. However, the majority of stars observed in modern large-scale photometric surveys lack spectroscopic measurements, making empirical colour--$T_{\mathrm {eff}}$ relations essential tools. In this work, we present updated empirical colour--$T_{\mathrm {eff}}$ calibrations based on Sloan Digital Sky Survey (SDSS) $ugriz$ photometry combined with 2MASS $JHK_{\mathrm s}$ data. Effective temperatures are determined on a homogeneous InfraRed Flux Method (IRFM) scale using a combined sample of 3902 GALAH and 2535 APOGEE stars with high-quality photometry and well-characterised atmospheric parameters. Using this dataset, we establish empirical relations between $T_{\mathrm {eff}}$ and colour indices constructed from SDSS and 2MASS combinations. We provide both colour--metallicity--$T_{\mathrm {eff}}$ and colour--$T_{\mathrm {eff}}$ relations for dwarfs and giants. The calibrations are derived using low-order polynomial models with iterative $3σ$ clipping. Their performance depends on the adopted colour index, with long-baseline colours such as $(g-K_{\mathrm s})_0$ and $(g-z)_0$ achieving internal precisions of $\sim$30--50~K. Comparisons with previous calibrations show general agreement, with differences attributable to sample selection, photometric zero-points, and functional form. The resulting relations provide a homogeneous and internally consistent framework for estimating $T_{\mathrm {eff}}$ from SDSS and 2MASS photometry alone, and are well suited for application to large photometric surveys lacking spectroscopic information.

Using a dataset of 7.33 fb$^{-1}$ of $e^+ e^-$ annihilation data collected with the BESIII detector at center-of-mass energies from 4.128 to 4.226 GeV, we report an updated measurement of the branching fraction of $D_s^+ \to τ^+ ν_τ$ via four $τ^+$ decay modes: $τ^+ \to e^+ ν_e \barν_τ$, $μ^+ ν_μ \barν_τ$, $π^+\barν_τ$, and $π^+ π^{0} \barν_τ$. The branching fraction is determined to be $\mathcal{B}({D_s^+ \to τ^+ ν_τ}) = (5.37 \pm 0.08_{\rm stat} \pm 0.06_{\rm syst})$ %. The product of the modulus of the Cabibbo-Kobayashi-Maskawa matrix element $|V_{cs}|$ and the $D_s^+$ decay constant $f_{D_s^+}$ is measured to be $f_{D_s^+} |V_{cs}| = (248.2 \pm 1.9_{\rm stat} \pm 1.4_{\rm syst} \pm 0.6_{\rm input} \pm 0.8_{\rm EM})$ MeV. Both the branching fraction and the product $f_{D_s^+} |V_{cs}|$ are the most precise results yet obtained. Then, taking $f_{D_s^+}$ from lattice quantum chromodynamics calculations results in $|V_{cs}| = 0.993 \pm 0.008_{\rm stat} \pm 0.006_{\rm syst} \pm 0.003_{\rm input} \pm 0.003_{\rm EM}$. Conversely, one finds $f_{D_s^+} = (255.0 \pm 1.9_{\rm stat} \pm 1.4_{\rm syst} \pm 0.6_{\rm input} \pm 0.8_{\rm EM})$ MeV when taking $|V_{cs}|$ from the CKMfitter group as an input. Combining with the world average value of $D_s^+ \to μ^+ ν_μ$, the ratio of the branching fractions between $D_s^+ \to τ^+ ν_τ$ and $D_s^+ \to μ^+ ν_μ$ is estimated to be $10.04 \pm 0.29$, which is consistent with the Standard Model prediction of lepton flavor universality.

Collaborative edge-cloud inference enables resource-constrained devices to leverage large language models (LLMs) by offloading partial computation to cloud servers. However, transmitting intermediate activations exposes sensitive user prompts to prompt inversion attacks, where an adversary reconstructs the original input from shared representations. Existing defenses rely largely on heuristic perturbations or empirical tuning, offering limited theoretical understanding of privacy leakage and its interaction with utility and latency constraints. We propose an information-theoretic defense framework for prompt inversion in collaborative LLM inference. Our approach learns privacy-preserving representations by explicitly minimizing the mutual information between intermediate activations and the input prompt while maintaining task utility under computational constraints. We derive theoretical guarantees on prompt reconstruction error, characterize fundamental privacy-utility tradeoffs, and establish token-level accuracy bounds for downstream inference. We then propose a novel defense based on privacy adapters implemented via low-dimensional information bottlenecks. Extensive experiments across multiple settings demonstrate that our method achieves superior privacy-utility-latency tradeoffs compared to existing defenses (up to 35% reduction in attack success), providing a principled foundation for private and efficient collaborative LLM inference.

The ultimate speed limit of magnetic recording and spintronic devices is set by the efficiency of angular-momentum transfer during ultrafast demagnetization, yet its microscopic pathway in Rare-Earth-Transition-Metal (RE-TM) ferrimagnets remains debated. Here, we establish an orbital-mediated framework in which 3d spin-orbit coupling (SOC) governs angular momentum (AM) dissipation. Strong 3d-SOC in RE-Co enables sub-picosecond, single-step demagnetization via direct orbital-to-lattice transfer, whereas weak 3d-SOC in RE-Fe redirects AM into 4f orbitals, producing slower two-step dynamics. The second-stage rate scales with 4f-SOC strength, revealing a distinct orbital-mediated dissipation channel. Using time-resolved magneto-optical Kerr measurements, supported by an extended four-temperature model, corroborate this picture across diverse RE-TM systems (RE = Sm, Gd, Tb, Dy, Ho and TM = Fe, Co, CoNi). Our results identify the SOC-driven competition between 3d and 4f orbital channels as the universal mechanism governing ultrafast demagnetization in RE-TM ferrimagnets, enabling rational design of the switching speed for next-generation spintronic devices.

The Circular Electron Positron Collider (CEPC) distributes a reference clock distributed to 192 control nodes along its 100~km underground tunnel. The required synchronization precision is 30~ps (standard deviation). We present an enhanced White Rabbit (WR)-based clock synchronization system designed to meet this requirement. A noise-budget analysis of the standard WR slave loop identifies the analog actuation chain (DAC + VCXO + multiplier PLL) and restart-induced timing uncertainty as the dominant limitations. In our redesigned node, the DAC+VCXO chain is replaced by a Si5345A DSPLL clock generator with DCO-based phase control, removing the board-level analog tuning stage. GTX transceiver phase alignment and manual byte-alignment fixing reduce restart uncertainty from 88.8~ps to 12~ps peak-to-peak. For multi-node operation, we introduce a cascaded global-control architecture with PC-side PID auto-tuned by TD3 reinforcement learning, on-chip-temperature feed-forward calibrated to $-0.76\,\mathrm{ps}/^\circ\mathrm{C}$. The measured point-to-point synchronization precision is 3.38~ps over 1~m fiber and 3.92~ps over 50~km. In a 12-level cascade, the end-node precision reaches 6.66~ps at constant temperature and 7.30~ps under a 13$\,^\circ$C temperature swing. Synchronized-clock TIE jitter stays below 1~ps regardless of cascade depth. Restart uncertainty is 2.82~ps (std.\ dev.). A 4-level cascade operated stably for 25 hours of continuous monitoring. All measured metrics fall well within the CEPC 30~ps budget.

Large Language Models (LLMs) have rapidly emerged as tools of interest across engineering disciplines, and Process Systems Engineering (PSE) is no exception. This survey provides a systematic review of LLM applications in PSE, organizing the literature into seven categories: (1) process design and engineering, (2) molecular design and synthesis, (3) process modeling and simulation, (4) time-series forecasting, (5) optimization and scheduling, (6) process control, and (7) fault detection and diagnosis. For each category, we summarize the state of the art, identify common methodological approaches, and critically assess demonstrated capabilities versus aspirational claims. We find that LLMs show genuine promise for tasks involving natural language, including querying documentation, synthesizing unstructured knowledge, and enabling flexible human-machine interaction. However, applications requiring real-time execution, constraint satisfaction, or formal safety guarantees remain challenging. We conclude by identifying open problems and productive research directions for the PSE community.

Pixel antennas enable antenna coding, a technique that can provide more degrees of freedom in wave manipulation, to enhance wireless communications. However, acquiring full channel state information (CSI) at the transmitter incurs prohibitive overhead due to the unique hardware constraints from pixel antennas. This paper thus proposes a limited feedback multi-input multi-output (MIMO) system using pixel antennas, where the antenna coder and digital precoder are designed based on pre-defined codebooks and efficient index feedbacks. We first derive the optimal digital precoder under practical power constraints that provides insights on simplifying the joint codebook construction for antenna coder and digital precoder. We then develop a low-complexity offline codebook construction algorithm that enables subsequent codebook designs for the antenna coder and digital precoder. Simulation results demonstrate that the proposed scheme significantly outperforms unconstrained MIMO systems using conventional antennas with fixed configurations.

Accurate photometric zero-points are essential for translating observed magnitudes into physical fluxes, from comparing with models to ensuring consistency across surveys. We determine the zero-points needed to place the Sloan Digital Sky Survey (SDSS) $ugriz$ system on its nominal AB definition, by exploiting the sensitivity of the Infrared Flux Method (IRFM) to broadband flux calibration. Using benchmark effective temperatures for over 6,000 FGK-type stars, we invert the method to identify the zero-point corrections required for SDSS photometry to reproduce the adopted temperature scale. The $r$ band is found to be very well standardized, while the $i$ and $z$ bands show offsets of a few hundredths of a magnitude, consistent with previous studies. We also find a small offset in the $g$ band. The largest discrepancy occurs in the $u$ band, where the derived offset depends strongly on the adopted filter transmission curves, in particular whether one uses the original definition commonly adopted in the literature or the updated measurements that account for the presence of a red leak. This effect introduces a colour-dependent zero-point offset that becomes apparent when using a sample of late-type stars. Independent comparisons with CALSPEC spectrophotometric standards and Gaia XP spectra broadly support the offsets derived from the IRFM analysis. Our results provide a revised set of SDSS zero-points anchored to the IRFM temperature scale and demonstrate that large stellar samples can be used to constrain photometric calibration. The methodology presented here offers a complementary approach to traditional spectrophotometric calibration and may prove useful for future large-scale surveys.

For a uniformly locally finite coarse space $(X,\mathcal{E})$, we prove that for every $p\in\{0\}\cup[1,\infty]$, the lattice of geometric ideals in the $\ell^p$ uniform Roe algebra $B^p_u(X,\mathcal{E})$ is isomorphic to the lattice of ideals of $\mathcal{E}$ (equivalently, to the lattice of ideals in the associated family of controlled partial coverings of $X$). In particular, the lattices of geometric ideals for different values of $p$ coincide. Using limit operators, we establish a canonical isometric isomorphism between $B^p_u(X,\mathcal{E})$ and the reduced $L^p$ operator algebra of the coarse groupoid for $p\in[1,\infty]$, and show that it induces an isomorphism between lattices of ideals that preserves inner support. In particular, geometric (resp. ghostly) ideals correspond precisely to dynamical (resp. restrictive) ideals under this isomorphism. Using equivalent formulations of property A for coarse spaces, we prove that for $p\in(1,\infty)$, property A implies that $B^p_u(X,\mathcal{E})$ admits a multiplier approximate identity with controlled propagation, that all ideals are geometric, and that all ghosts are trivial. For the extreme cases $p\in\{0,1,\infty\}$, these properties hold for every uniformly locally finite coarse space without assuming Property A. Finally, for $p\in[1,\infty)$, a Morita equivalence between the $\ell^p$ uniform Roe algebra and the $\ell^p$ uniform algebra is shown to preserve the lattice of geometric ideals.

Altermagnetism establishes momentum-dependent spin splitting through non-symmorphic crystal symmetries, yet whether these same symmetries simultaneously govern spin and lattice collective excitations remains open. Here we show, using first-principles calculations and linear spin-wave theory, that monolayer CuF$_2$ hosts both chirality-split magnons and cycloidal phonons controlled by the same $P2_1/c$ symmetry operations. The altermagnetic order drives strongly anisotropic magnon chirality via symmetric anisotropic exchange, with Dzyaloshinskii--Moriya interactions acting as a weak secondary modulation. Crucially, the phonon and magnon chiral responses are directionally complementary: cycloidal phonon angular momentum emerges precisely where magnon chirality is symmetry-suppressed, and vice versa. The magnon bands further carry quantized Chern numbers $C^M = \pm 2$, confirming non-trivial altermagnetic topology. These results establish monolayer CuF$_2$ as a platform where a single symmetry framework engineers magnonic, phononic, and topological responses, providing a direct connection between altermagnetism and spin-lattice chirality in two-dimensional materials.

Recent advances in temporal graph research have redefined traditional static graph concepts such as triangles, motifs, and $k$-cores. Inspired by this, we introduce a novel $(k,δ)$-truss for temporal graphs, requiring triangles to exist within sufficiently short time windows. The $(k,δ)$-truss ensures both static and temporal cohesion, while the original $k$-truss is a special case when $δ= \infty$. To address $(k,δ)$-truss queries, we propose index-free and index-based approaches. Utilizing the dual containment relation of $(k,δ)$-trusses, our indexes losslessly compress all $(k,δ)$-trusses into map or tree structures, significantly reducing space while enabling optimal-time retrieval. To scale to large temporal graphs, we develop two index construction algorithms based on truss decomposition and truss maintenance, respectively, which substantially reduce redundant computations. Moreover, we present techniques for the dynamic maintenance of the proposed indexes. The experimental results demonstrate that index-based approaches process queries in interactive time and outperform the index-free approach by 2$\sim$4 orders of magnitude, while the indexes achieve compression ratios of up to $10^{-4}$ and can be updated efficiently without rebuilding from scratch.

We study superspace concentration as a quantum resource, formalized through the focus measure F(\r{ho}) = λ_max(\r{ho}_super) - the largest eigenvalue of the reduced superspace state - which quantifies the capacity of a quantum system to concentrate informational weight into a preferred subspace of an extended degree-of-freedom space. We develop a complete resource-theoretic framework around this measure and validate its properties through GPU-accelerated numerical simulation. Analytic decoherence predictions are confirmed to machine precision (1.11 x 10^{-16}) for superspace dimensions dS in {2,4,8,16,32}. Focus monotonicity holds across 10,000 random states with zero violations under four focus-non-generating channels across six system configurations. Focused quantum states resist coherent unitary attacks with significantly greater resilience than standard fidelity predicts, with focus remaining above 0.9 at attack strength ε = 0.302 versus ε = 0.174 for fidelity. We further demonstrate that the focus measure and the U(dS)-asymmetry measure are operationally distinct: asymmetry remains near zero and provides no robustness signal under coherent and targeted attacks while focus tracks spectral concentration and remains robust until ε > 0.3. The connection between Grover's algorithm and superspace concentration is made explicit via the identity F(|ψ_k><ψ_k|) = P(marked), providing a resource-theoretic interpretation of oracle query complexity. Finally, we provide the first numerical characterization of the focus capacity gap ΔF, identifying a log_2(dS) scaling law confirmed for both product and correlated noise channels.

We present an approach based on tensor networks for distributed quantum computing simulation of chemical wavepacket dynamics in a continuous variable representation. The central idea is that the tensor-network representation of the multidimensional time-evolution operator naturally induces an elevated Hilbert space where the dynamics decomposes into a set of independent lower-dimensional propagations. This transformation converts an entangled quantum evolution into a set of parallel computational tasks that can be executed asynchronously across heterogeneous quantum and classical computing architectures. The resulting formalism establishes a direct connection between tensor-network decompositions, uniformly controlled quantum circuits, and asynchronous distributed quantum computing. The approach is developed with a goal towards hybrid quantum/classical implementation, and is appropriate for a general heterogeneous mixture of quantum hardware systems. The experimental realization of the asynchronously distributed quantum processes that arise from the tensor-network decomposition are carried out on the Sandia National Laboratories' trapped-ion quantum computer, where the circuits are compiled using native partial-entangling $XX(θ)$ gates, reducing the expected two-qubit gate infidelity by more than 30\% relative to conventional fully entangling decompositions. We demonstrate the methodology by quantum computing the vibrational spectra of a small protonated water cluster that shows critical quantum nuclear behavior. Such water cluster systems have been found to be challenging for experimental action spectroscopy and for theory, and here, for the first time, we provide results for vibrational spectroscopy that are in agreement with the respective classical results to within 4cm$^{-1}$, thus allowing for the potential for spectroscopic accuracy from quantum computations.

This paper investigates the three-dimensional compressible Navier--Stokes system with a polytropic pressure law and its pressureless counterpart arising from the high Mach number limit. We focus on the different critical scaling structures of these two models. In the presence of the pressure term, the pressure gradient is balanced with the inertial and viscous effects, and thereby selects a fixed critical scaling for the pressure system. In contrast, once the pressure term is ignored, the pressureless system admits a more flexible one-parameter family of invariant scalings. For both systems, we establish the global well-posedness of strong solutions under low-regularity assumptions on the initial data, allowing vacuum and large oscillations. This improves the global result of Wen (Adv. Math. 482 (2025), Paper No. 110628), where higher regularity assumptions on the initial data are required. A central feature of our result is that the smallness conditions are {\it exactly invariant} under the intrinsic critical scalings of the corresponding systems. These scaling structures differ from the usual parabolic scaling used in the critical-space framework of Danchin (Invent. Math. 141 (2000), pp. 579--614), where the system is reformulated around a reference state. We also derive uniform a \textit{priori} estimates and obtain exponential decay estimates for the global strong solutions. The results show that the pressure term not only changes the analytic estimates, but also plays a decisive role in selecting the critical scaling structure and in determining the dynamical behavior of compressible flows.

We develop a new technique to upgrade relative biexactness in general von Neumann algebras: suppose that $\{N_i\}_{i\in I}\subset M$ are mixing and biexact subalgebras of a separable von Neumann algebra with expectation, and if $M$ is biexact relative to $\{N_i\}_{i\in I}$, then $M$ is biexact. This result yields several new examples of biexact von Neumann algebras, notably including amalgamated free products. By generalizing the relative biexactness results of Hoshino to the von Neumann algebra setting and applying our result above along with certain bimodule computations, we in fact obtain, as an application, a new classification result for biexactness for graph products of finite dimensional von Neumann algebras. This yields significant extensions of prior works of Caspers-Borst, and Blufstein-Goldman-Oyakawa.

Recent breakthrough studies of nonlinearities at extreme pump intensities ($\sim$1 $\text{TW/cm}^2$) in transparent conducting oxides (TCOs) have rewritten our understanding of the dynamics in these materials. However, exploring TCO dynamics beyond these intensities is prohibited by the damage threshold of the material. In this work, we overcome this problem by using a few-cycle pump laser pulse (sub-8\,fs) to maximize the intensity while keeping the optical fluence below the damage threshold. We observe a reversal in the optical response trend starting at optical pump laser intensities of $\sim$5 $\text{TW/cm}^2$ similar to Segal et al. At the highest pump pulse intensities, we obtain a complete change in the sign of the modulation for both transmission and reflection, producing a full-cycle oscillation of the refractive index modulation within 300\,fs. The amplitude of the sign reversal scales quadratically with the intensity. We therefore propose a simple two-photon absorption (TPA) model to explain the observed behaviour. The TPA, which is normally forbidden by the Pauli blocking, is enabled here by intraband excitations from the lower to the upper non-equilibrium states of the conduction band (CB). Such excitations vacate the states at the bottom of the CB, lifting up the blocking and thus making interband TPA possible. The model is in good agreement with experimental results, capturing the essential trends in the observed data and revealing the dynamics of competing channels caused by the interplay between interband and intraband transitions. This intensity-controlled mechanism could be the key to unlocking new applications of TCOs for time-varying photonics such as photonic time crystals.

Why do similar funding shocks generate sharply different credit outcomes across countries? We develop and estimate a dynamic structural model in which intermediary credit capacity governs the transmission of funding disruptions to lending. Using supervisory data on U.S. banks and credit unions and Brazilian banks and cooperatives from 2002--2025, we recover institution-level credit capacity and its dynamics across major crisis episodes. Credit capacity is three to six times larger in the United States than in Brazil, while persistence is similar across countries. As a result, funding shocks generate substantially larger and more persistent lending contractions in Brazil. Counterfactual analysis shows that differences in baseline credit capacity, rather than persistence, account for most cross-country variation in crisis propagation and policy effectiveness.

Digital forensic investigations increasingly depend on preprocessing heterogeneous network evidence from intrusion detection systems, IoT devices, and enterprise traffic logs. Incompatible schemas and timestamp formats hinder evidence correlation and timeline reconstruction, while current ad hoc approaches offer no mechanism to verify consistency across runs or analysis, creating reproducibility gaps that challenge evidence admissibility. This paper introduces a deterministic forensic preprocessing framework that converts heterogeneous network datasets into a reproducible canonical form. The framework formalises three preprocessing transformations: schema normalisation, temporal normalisation, and provenance tracking. These transformations are specified using set-theoretic definitions and supported by four theorems establishing determinism, information preservation, and provenance completeness. A chunk-based architecture provides O(c) bounded memory. Empirical evaluation across UNSW-NB15, IoT-23, and TON_IoT demonstrates 100% output consistency across repeated runs, robust temporal normalisation completeness over heterogeneous timestamp formats, and scalable performance from millions to hundreds of millions of records.

We investigate whether a minimal $\mathbb{Z}_4$-symmetric fermion-scalar extension of the Standard Model can simultaneously realise viable dark matter, a strong electroweak phase transition, and a stochastic gravitational-wave signal. The model contains a real scalar singlet and a Dirac fermion, allowing thermal two-component dark matter, mixed WIMP-FIMP histories, and an effectively fermionic relic abundance generated by scalar decays. We impose theoretical consistency, the correct electroweak vacuum, and dark-matter constraints from relic density, direct detection, and invisible Higgs decays before using the surviving points as input for the finite-temperature analysis. This reveals that the compatibility between dark matter and a strong first-order electroweak phase transition is highly selective. After current dark-matter constraints are imposed, the strong-transition criterion along the Higgs direction is satisfied only in two viable regimes: the thermal two-component case with $M_ψ<M_S<2M_ψ$ and the decay-driven WIMP-FIMP case with $M_S>2M_ψ$. By contrast, the thermal regime with $M_S<M_ψ$ and the stable mixed WIMP-FIMP scenario with $M_S<2M_ψ$ are largely concentrated at small portal couplings or near the Higgs-resonance region, and do not yield a strong transition in the parameter space considered. The successful transitions typically proceed through an intermediate singlet-like phase. For representative nucleating benchmark points in the viable strong-transition regions, we compute the gravitational-wave spectra from sound waves and turbulence. Some spectra enter the projected reach of future space-based interferometers, showing that detectable signals arise only in selected dark-matter-compatible regions where a sufficiently active Higgs portal appears in correlated combination with the scalar mass and the remaining dark sector parameters.

Participation entropy (PE) quantifies the spread of a many-body wavefunction across configuration space. While PE relaxes rapidly in generic chaotic systems, we show that $\mathrm{U}(1)$ conservation laws slow it down by imprinting with the slow hydrodynamic modes. Using a cluster expansion around equilibrium, we show that, after local density inhomogeneities decay, the leading PE deficit is dominated by squared connected density correlations. The long time relaxation is therefore controlled by diffusive correlation spreading, giving $ΔS(t)\sim t^{-1/2}$ in the hydrodynamic regime and crossing over to $\sim \exp[-O(t/L^2)]$ when $t\geq L^2$. We confirm this entropy correlation relation using exact computation and infinite system tensor network simulations in various quantum $\mathrm{U}(1)$ conserving circuits. Our results establish PE as a sensitive probe of hydrodynamic memory and suggest that slow relaxation is a generic consequence of conservation laws.

Let $G$ be a locally finite multigraph that is bipartite and "unbalanced," meaning that it has a nontrivial bipartition $(A,B)$ with $°(x) > °(y)$ for all $x \in A$ and $y \in B$. We explore matchings in such graphs through the lens of descriptive set theory. In particular, we show that when $G$ is Borel and $μ$ is a Borel probability measure on its vertex set, there is a Borel matching in $G$ that covers $μ$-almost every vertex in $A$. This was previously known only under the assumption that $μ$ is $G$-invariant, which we eliminate using a novel probabilistic approach. We also describe various extra conditions that imply the existence of a Borel matching covering every vertex in $A$. Along the way, we confirm a conjecture of the first and third named authors concerning the existence of Borel independent complete sections in Borel graphs of finite asymptotic separation index. In addition to their intrinsic interest, our results have applications to various other topics, such as edge-colorings, balanced orientations, and equidecomposition theory for group actions. For example, we show that the measurable edge-chromatic number of every Borel multigraph with finite maximum degree $Δ$ is at most $\lfloor\frac{3Δ}{2}\rfloor$, matching Shannon's optimal bound for finite multigraphs. Another example is that paradoxical Borel group actions with finite asymptotic separation index admit paradoxical decompositions with Borel pieces. This refines a result of Marks and Unger.