We propose a novel tensor-on-tensor modeling framework that flexibly models nonlinear voxel-level relationships using Gaussian process (GP) priors, while incorporating the spatial structure of the output tensor through low-rank tensor-based coefficients. Spatial heterogeneity is captured through patch-to-voxel mappings, enabling each output voxel to depend on its spatial neighborhood. The proposed interpretable and flexible Bayesian tensor-on-tensor framework is able to capture nonlinearity, spatial information, and spatial heterogeneity. We develop an efficient Markov chain Monte Carlo (MCMC) algorithm that exploits parallel structure to sample voxel-specific GP atoms and update low-rank tensor coefficients. Extensive simulations reveal advantages of the proposed approach over existing methods in terms of coefficient estimation, inference, prediction, and scalability to high-dimensional images. Applied to longitudinal image prediction with T1-weighted MRIs from the Alzheimer's Disease Neuroimaging Initiative (ADNI), the proposed method can accurately forecast future cortical thickness. The predicted images also enable reliable prediction of brain aging, underscoring their biological relevance. Overall, the ADNI analysis highlights the model's ability to forecast future neurobiological changes that has important implications for early detection of AD.

The classical Kapitza instability of a gravity-driven falling film requires finite inertia to operate. We show that a surface-mode instability can arise in the complete absence of inertia when the film possesses a continuous viscosity stratification, a feature relevant to particle-laden films with shear-induced migration, thermally stratified coatings, and concentration-graded flows. The viscosity field, prescribed as a linear profile across the film thickness, evolves through an advection-diffusion equation characterized by a P$é$clet number. Using long-wave asymptotics and Chebyshev spectral computations, we solve the coupled eigenvalue problem for the perturbation streamfunction and viscosity fields and demonstrate that viscosity stratification destabilizes the surface mode in the zero-inertia (Stokes) limit. The instability is confined to a finite window of P$é$clet numbers. Increasing the stratification parameter lowers the critical P$é$clet number, broadens the range of unstable wavenumbers, and increases the growth rate. The instability mechanism is traced to the phase relationship between perturbation vorticity and the interface displacement: viscosity stratification shifts the vorticity to a lagging configuration, which reinforces interface deformation, following the framework of Hinch (1984). The mechanism bears a structural resemblance to the surfactant-driven Marangoni instability in creeping two-layer flows, extending this class of scalar-mediated, inertialess instabilities to bulk viscosity stratification.

We describe and analyze a distributed compute architecture for SSO computational satellites that can potentially provide >100 kW compute power per launched metric ton (including deployment and station keeping mass). The architecture co-locates and integrates the solar cells, radiator, and compute functions into multiple small panels arranged in a large array. The resultant large vapor chamber radiator area per panel should permit ICs to operate at junction temperatures near 40*C with benefits in compute efficiency and reliability. Using the structure of the radiator to support the solar cells may also yield a specific power of about 500 W/kg compared to less than 100 for existing conventional implementations. Assuming development of custom solutions for all components, a 16 MW computation, 150 ton satellite comprising a 20 m x 2200 m grid of 16,000 panels can fit in a single Starship hold. The concept is scalable to much larger satellites with higher mass payloads or using on-orbit assembly. We consider panel sizes from 1 to 4 m2 to allow trading vapor chamber heat transport with compute efficiency and inter-panel communication. Assuming a 1 kW/panel design, 512-panel subarrays of the satellite can run a representative inference-only LLM with 500,000 token context window and 128 attention blocks, at a rate of 553 tokens/sec/session, across 256 simultaneous in-flight sessions. A full satellite could support 31 such subarrays, for >7900 inferences at a time.

In this paper, we consider a class of stochastic differential equations driven by symmetric non-degenerate $α$-stable processes (including cylindrical ones) with $α\in (1,2)$. We first establish a quantitative estimate for the Euler scheme under bounded drift $b(x)$, with an explicit dependence on $ \| b \|_{L^\infty}$. Then we obtain the weak convergence rates for the case where the drift coefficient belongs to a Besov space of negative order.

This article investigates the model-robustness of fixed-effects models for analyzing a broad class of longitudinal cluster trials (CTs) such as stepped-wedge, parallel-with-baseline and crossover designs, encompassing both randomized (CRTs) and quasi-experimental (CQTs) designs. We clarify a longstanding misconception in biostatistics, demonstrating that fixed-effects models, traditionally perceived as targeting only finite-sample conditional estimands, can effectively target super-population marginal estimands through an M-estimation framework. We comprehensively prove that linear and log-link fixed-effects models with correctly specified treatment effect structures can broadly yield consistent and asymptotically normal estimators for nonparametrically defined treatment effect estimands in longitudinal CRTs, even under arbitrary misspecification of other model components. We identify that the constant treatment effect estimator generally targets the period-average treatment effect for the overlap population (P-ATO); accordingly, some CRT designs don't even require correct specification of the treatment effect structure for model-robustness. We further characterize conditions where fixed-effects models can maintain consistency by adjusting for both cluster-level and individual-level time-invariant confounding in longitudinal CQTs. Altogether, supported by simulation and a case study re-analysis, we establish fixed-effects models as a robust and potentially preferable alternative to mixed-effects models for longitudinal CT analysis.

Network coordination games are widely used to model collaboration among interconnected agents, with applications across diverse domains including economics, robotics, and cyber-security. We consider networks of bounded-rational agents who interact through binary stag hunt games, a canonical game theoretic model for distributed collaborative tasks. Herein, the agents update their actions using logit response functions, yielding the Log-Linear Learning (LLL) algorithm. While convergence of LLL to a risk-dominant Nash equilibrium requires unbounded rationality, we consider regimes in which rationality is strictly bounded. We first show that the stationary probability of states corresponding to perfect coordination is monotone increasing in the rationality parameter $β$. For $K$-regular networks, we prove that the stationary probability of a perfectly coordinated action profile is monotone in the connectivity degree $K$, and we provide an upper bound on the minimum rationality required to achieve a desired level of coordination. For irregular networks, we show that the stationary probability of perfectly coordinated action profiles increases with the number of edges in the graph. We show that, for a large class of networks, the partition function of the Gibbs measure is well approximated by the moment generating function of Gaussian random variable. This approximation allows us to optimize degree distributions and establishes that the optimal network - i.e., the one that maximizes the stationary probability of coordinated action profiles - is $K$-regular. Consequently, our results indicate that networks of uniformly bounded-rational agents achieve the most reliable coordination when connectivity is evenly distributed among agents.

We prove an explicit finite-sample version of the Borel--Cantelli lemma under $m$-dependence. Given any $m$-dependent sequence of events $(A_k)_{1\leq k\leq N}$, we show that \[ \mathbb{P}\Bigl(\bigcup_{k=1}^N A_k\Bigr) \ge 1 - \exp\Bigl(-\frac{1}{m+1} \sum_{k=1}^{N} \mathbb{P}(A_k)\Bigr). \] The proof splits the index set into residue classes modulo $m+1$, so that each class consists of mutually independent events, and then applies an elementary product--to--exponential bound. We further derive a quantitative windowed corollary: if the partial sums satisfy \(\sum_{k=1}^{ϕ(n)}\mathbb{P}(A_k)\ge n\) for all \(n\ge1\), then for every \(N\ge1\) and \(i\ge0\), \[ \mathbb{P}\Bigl(\bigcup_{k=i+1}^{ϕ(i+N)} A_k\Bigr) \ge 1-\exp\Bigl(-\frac{N}{m+1}\Bigr). \] Finally, we present a complementary second-order refinement involving local pairwise intersection probabilities. These results complement the asymptotic and rate results of Lu, Shi and Zhao (2026) by providing explicit finite-$N$ bounds and a simple comparison framework for the baseline and second-order estimates.

Understanding interphase mass transfer is essential for a variety of applications in porous media, ranging from groundwater remediation to geologic energy storage. While X-ray micro-Computed Tomography (microCT) provides critical in situ observations, analyzing mass transfer requires models and workflows compatible with the limited spatial and temporal resolution. Current literature presents three analytical frameworks for evaluating interphase mass transfer using microCT data: the Slice-Averaged Concentration (SAC) approach, the Non-Classified per-Cluster (NPC) approach, and the Classified per-Cluster (CPC) approach. This study evaluates the results of all three approaches across four sets of time-lapse tomography sequences that observe hydrogen dissolution at varying solvent injection rates. To mitigate biases arising from dissolution-driven cluster remobilization, we introduce a volume-ratio filtering technique to all workflows to ensure that estimates more accurately reflect true mass transfer events. Our analysis finds that all three analytical approaches estimate average mass transfer coefficients within one order of magnitude of one another at the same solvent injection rate. However, the similarity between the estimates of each approach diverges when approximating more complex phenomena, such as aqueous solute concentration profiles. Ultimately, the utility of one approach over another is determined by the desired level of system detail, at the cost of the computational resources required to achieve it. Higher phenomenological resolution requires greater computational processing and refinement due to increased sensitivity to measurement and processing noise, as well as outlier events. We anticipate that the findings will provide a framework for researchers to match analytical approaches to their available computational resources and desired level of physical detail.

We report new results from a nulling study of PSR~B0751+32 (PSR J0754+3231), observed at 1250~MHz with the Five hundred meter Aperture Spherical radio Telescope (FAST). Our analysis confirms the presence of periodic nulling in this pulsar. Using the recently developed mixture model method, we obtained a nulling fraction (NF) of $35.1\% \pm 0.6\%$. Three independent approaches were employed to estimate the nulling periodicity, and the results reveal significant temporal evolution of the modulation both within individual observations and across different \textbf{observing} essions. The pulsar exhibits an asymmetric two-component mean pulse profile, with the leading component brighter and narrower than the trailing one. Pulse energy analysis shows that both components remain stable immediately after the onset of the burst state, but subsequently undergo a progressive decline, with the trailing component most severely affected prior to burst termination. Notably, no evidence of the previously reported subpulse drifting was detected in our data. Our results challenge previous models that ascribed periodic nulling to purely geometric effects.

Recent shifts in global health priorities have positioned Population Health Management (PHM) as a central area of focus. However, optimizing PHM strategies presents several challenges: managing high-dimensional patient covariates, tracking their evolution and long-term response to interventions, and accounting for the inflow and outflow of individuals within the population. In this paper, we propose a novel approach based on Measurized MDPs that integrates these components. We consider a setting in which a treatment with population-level benefits is available but scarce, and model an MDP that optimizes the long-term distribution of the healthcare population under expected capacity constraints. This formulation allows us to bypass both the dimensionality and practical challenges of handling and tracking individual patient covariates across the population. To ensure ethical compliance, we introduce a non-maleficence constraint that limits the allowable mortality rate. To solve the resulting infinite-dimensional problem, we use ADP and reduce the task to identifying a finite set of high-performing treated and untreated patients. Despite the complexity of the underlying structure, our approach yields a simple, clinically implementable index policy: a patient is selected for treatment if their adjusted impactability exceeds a specified threshold. The adjusted impactability captures the long-term consequences of receiving or not receiving treatment. While straightforward to apply, the policy remains flexible and can incorporate general machine learning models. Using CMS data, we show that our policy yields a statistically significant improvement over a myopic benchmark. This advantage increases with the time horizon, consistent with the forward-looking nature of our policy. At the longest horizon tested, this corresponds to over 1,500 additional home days annually per 1,000 patients.

Adaptive impedance matching between antennas and radio frequency front-end modules is critical for maximizing power transmission efficiency in mobile communication systems. Conventional numerical and analytical methods struggle with a trade-off between accuracy and efficiency, while deep neural network (DNN)-based supervised learning approaches rely heavily on large labeled datasets and lack flexibility for dynamic environments. To address these limitations, this paper proposes a deep reinforcement learning (DRL)-based approach for adaptive impedance matching. First, we model the impedance tuning problem as an optimal control problem, proving the feasibility of solving the optimal control law via reinforcement learning. Then, we design a tailored DRL framework for impedance tuning, which employs a compact state representation that integrates key frequency characteristics and matching quality metrics. Additionally, this framework incorporates a piecewise reward function that accounts for both matching accuracy and tuning speed. Furthermore, a test-phase exploration mechanism is introduced to enhance tuning stability, which effectively reduces local optimal trapping and high-frequency tuning variance. Experimental results demonstrate that the proposed method achieves superior performance in terms of tuning accuracy, efficiency, and stability compared with conventional heuristic and gradient-based methods, making it promising for practical impedance tuning systems.

A unified analytical framework for joint design of communication and control (JDCC) is proposed. Within this framework, communication transmission delay and steady-state control variance are derived as the two fundamental JDCC performance metrics. The Pareto boundary is then established to characterize the optimal communication-control trade-off in JDCC systems. To further obtain closed-form expressions, their performance regions are derived under maximum-ratio transmission (MRT) and zero-forcing (ZF) beamforming. For system reliability evaluation, the communication-only and control-only outage probabilities are first derived. Based on these, the JDCC outage probability is defined to quantify the probability that the communication-delay and control-error requirements cannot be simultaneously satisfied. Its analytical expressions are then derived under both MRT and ZF schemes. Finally, numerical results validate the theoretical results and reveal that: (1) the Pareto boundary characterizes the trade-off frontier and performance limit of JDCC systems and (2) the JDCC reliability is jointly determined by the uplink-downlink closed-loop control and its coupling with communication.

The magnetar 1E 1841-045 exhibited a new active episode starting on August 20, 2024, marked by X-ray bursts and enhanced persistent emission. Using data from the Einstein Probe (EP), we report on the timing and spectral results following the onset of this outburst. The pulse profile displays a multi-peaked structure, with notable phase shifts in the secondary peak. Energy-resolved pulse profile analysis indicates a transition in the dominant peak of the pulse profile above 5.8 keV. The 0.5-10 keV X-ray spectrum is well-modeled by a combined blackbody and power-law (BB+PL) model, showing a $\sim 20\%$ flux increase following the outburst. Phase-resolved spectroscopy indicates a correlation between BB temperature and pulse profile intensity, along with spectral hardening at a specific pulse phase. The high spatial resolution of EP enables effective separation of the supernova remnant emission, which is crucial for measuring the intrinsic pulse emission of the source. These findings underscore the intricate relationship between magnetar outbursts, pulse profile evolution, and spectral characteristics.

We investigate a class of nonminimal derivative couplings between fermions and electromagnetic fields that generate Rashba-like spin--orbit interactions in one-dimensional quantum rings. Starting from a generalized Dirac Lagrangian containing two independent axial structures built from the field strength $F_{μν}$ and its dual $\tilde{F}_{μν}$, we perform a systematic nonrelativistic expansion and show that both couplings induce effective Hamiltonians of the form $\boldsymbol{\mathcal{F}}\cdot(\boldsymbol{p}\times\boldsymbolσ)$. This reveals that magnetic as well as electric background fields may give rise to Rashba-type interactions, in contrast with standard condensed-matter scenarios. Before passing to the nonrelativistic limit, we analyze the relativistic content of the model in detail: the canonical structure of the deformed Dirac operator, the admissible background classes, the effective bilinear current, and the branch splitting of the relativistic dispersion relation, which constitutes the primary relativistic signature of the theory. We derive exact analytical energy levels and normalized eigenspinors for the resulting ring Hamiltonian, compute Aharonov--Anandan geometric phases, and analyze persistent spin currents together with the associated differential spin response $\mathcal{G}_s = \partial\mathcal{J}_φ^z/\partialξ$. Exploiting the analytical control offered by the model, we derive the first systematic order-of-magnitude bounds on the two Lorentz-invariant couplings $\mathfrak{g}_1$ and $\mathfrak{g}_2$ from both spectroscopic and mesoscopic scenarios, identifying the experimental channels most sensitive to the new physics encoded in these operators. We discuss physical implications, signatures, and possible experimental analogs, and outline several promising directions involving disorder, noise, and nonequilibrium spin dynamics.

The binary asymmetric channel is a model for practical communication systems where the error probabilities for symbol transitions $0\rightarrow 1$ and $1\rightarrow0$ differ substantially. In this paper, we introduce the notion of asymmetric Hamming bidistance (AHB) and its two-dimensional distribution, which separately captures directional discrepancies between codewords. This finer characterization enables a more discriminative analysis of decoding the error probabilities for maximum-likelihood decoding (MLD), particularly when conventional measures, such as weight distributions and existing discrepancy-based bounds, fail to distinguish code performance. Building on this concept, we derive a new upper bound on the average error probability for binary codes under MLD and show that, in general, it is incomparable with the two existing bounds derived by Cotardo and Ravagnani (IEEE Trans. Inf. Theory, 68 (5), 2022). To demonstrate its applicability, we compute the complete AHB distributions for several families of codes, including two-weight and three-weight projective codes (with the zero codeword removed) via strongly regular graphs and 3-class association schemes, as well as nonlinear codes constructed from symmetric balanced incomplete block designs (SBIBDs).

Based on the backward ray-tracing method, this paper numerically investigates the shadow and polarization images of rotating Einstein-Gauss-Bonnet (EGB) black hole within the framework of a thin disk model. We systematically analyze the effects of the main model parameters and the observation inclination angle $θ_o$ on both types of images. The results show that, as an intrinsic property of the black hole, the inner shadow undergoes significant deformation with increasing $θ_o$. The increase of the GB coupling constant $ξ$ only reduces the size of the inner shadow, while the spin parameter a does not alter its size but also its shape. And, the photon ring is more sensitive to variations in $θ_o$, while it is less affected by $ξ$ and $a$. For polarization images, the influence of $ξ$ on the polarization intensity is generally consistent with that observed in the accretion disk images. However, the polarization direction near the region of the inner shadow and photon ring changes significantly with $ξ$. This feature can provide an additional and effective observational tool for extracting information about the spacetime structure in Einstein-Gauss-Bonnet (EGB) gravity. Finally, we conclude that, compared to previous reliance on either accretion disk or polarization images alone, the simultaneous combination and synergistic analysis of both can more profoundly reveal the optical properties of rotating EGB black holes, providing a stronger theoretical basis for identifying such black holes through future high-resolution observations.

A torus-covering $T^2$-link of degree $n$ is a surface-link consisting of tori, in the form of an unbranched covering of degree $n$ over the standard torus. We focus on a torus-covering $T^2$-link of degree 3, which is determined by a pair $(a,b)$ of 3-braids satisfying $ab=ba$, denoted by $\mathcal{S}_3(a,b)$. We investigate to what extent the chirality of $\mathcal{S}_3(a,b)$ is detected by invariants such as the triple linking numbers, the number of Fox $p$-colorings, and the quandle cocycle invariant associated with $p$-colorings. In particular, we determine the quandle cocycle invariant for $\mathcal{S}_3(a,b)$ associated with tri-colorings.

Content creation for major video-sharing platforms demands significant manual labor, particularly for long-form documentary videos spanning one to two hours. In this work, we introduce Sima 1.0, a multi-agent system designed to optimize the weekly production pipeline for high-quality video generation. The framework partitions the production process into an 11-step pipeline distributed across a hybrid workforce. While foundational creative tasks and physical recording are executed by a human operator, time-intensive editing, caption refinement, and supplementary asset integration are delegated to specialized junior and senior-level AI agents. By systematizing tasks from script annotation to final asset exportation, Sima 1.0 significantly reduces the production workload, empowering a single creator to efficiently sustain a rigorous weekly publishing schedule.

Let X be the locally symmetric space associated to a reductive $\mathbb Q$-group G and an arithmetic subgroup $Γ$. An L-module M is a combinatorial model of a constructible complex of sheaves on $\widehat X$, the reductive Borel-Serre compactification of X whose strata $X_P$ are indexed by $Γ$-conjugacy classes of parabolic $\mathbb Q$-subgroups P of G. We show that any L-module M is "mixed" in the sense it is an iterated mapping cone of maps to or from shifted weighted cohomology L-modules on strata $X_P$ of $\widehat X$ with coefficients in V, an irreducible regular $L_P$-module. These weighted cohomology "building blocks" are indexed (up to multiplicity) by V in the weak micro-support of M which is a computable local invariant. As an application we prove that the intersection cohomology of $\widehat X$ is isomorphic to the weighted cohomology of $\widehat X$, at least excluding $\mathbb Q$-types D, E, and F.

We study identification in structural vector autoregressions (SVARs) in which the endogenous variables enter nonlinearly on the left-hand side of the model, a feature we term endogenous nonlinearity, to distinguish it from the more familiar case in which nonlinearity arises only through exogenous or predetermined variables. This class of models accommodates asymmetric impact multipliers, endogenous regime switching, and occasionally binding constraints. We show that, under weak regularity conditions, the model parameters and structural shocks are (nonparametrically) identified up to an orthogonal transformation, exactly as in a linear SVAR. Our results have the powerful implication that most existing identification schemes for linear SVARs extend directly to our nonlinear setting, with the number of restrictions required to achieve exact identification remaining unchanged. We specialise our results to piecewise affine SVARs, which provide a convenient framework for the modelling of endogenous regime switching, and their smooth transition counterparts. We illustrate our methodology with an application to the nonlinear Phillips curve, providing a test for the presence of nonlinearity that is robust to the choice of identifying assumptions, and finding significant evidence for state-dependent inflation dynamics.

We investigate the critical behavior of momentum-space entanglement entropy at dynamical quantum phase transitions (DQPTs) in translationally invariant two-band insulators and superconductors. By analyzing the Su-Schrieffer-Heeger model, the quantum XY chain, and the Haldane model, we establish that the geometric DQPT condition $\hat{\textbf{d}}_{\textbf{k}}^{i} \cdot \hat{\textbf{d}}_{\textbf{k}}^{f} = 0$ manifests as exact degeneracy $p_{\textbf{k}^{*}}=1/2$ in the entanglement spectrum defined with respect to the post-quench eigenbasis, yielding a maximal momentum-space entropy of $\ln 2$. In one dimension, critical momenta appear as isolated points, whereas in two dimensions they form continuous one-dimensional manifolds, reflecting the dimensional dependence of the underlying critical structure. Importantly, alternative bipartitions such as the sublattice basis produce qualitatively different behavior: the entropy becomes explicitly time-dependent and attains a minimum at DQPT critical times, underscoring the essential role of basis selection. Our results establish that momentum-space entanglement entropy, when evaluated in the appropriate eigenbasis, provides a robust, time-independent diagnostic of DQPTs and offers a unified geometric perspective linking entanglement, topology, and non-equilibrium criticality.

Linearized deformations of the thick-walled (low-amplitude) (1+1)-dimensional Q-ball may be decomposed into relativistic modes, which are roughly plane waves, and also long-wavelength corotating and counterrotating Floquet modes. Each mode oscillates at a pair of mirror frequencies which average to the Q-ball frequency. The corotating modes are those of a breather or oscillon plus a very loosely bound mode. The counterrotating modes are described by an irrational-level Pöschl-Teller potential, with two discrete modes which mix with their unbound mirrors, unbinding them and turning them into Feshbach-type quasinormal modes. Expanding to leading order in the Q-ball amplitude, we present all of these modes in closed form, except for the bound mode which does not exist at leading order.

We study a random partial covering model on the $(d-1)$-dimensional unit sphere, where $N$ spherical caps are placed independently and uniformly at random, each covering a surface fraction of $1/N$. This model provides a continuous geometric analogue of the classical balls-into-bins problem. We establish a Central Limit Theorem for the volume of the resulting random partial covering, showing that its fluctuations are asymptotically Gaussian. Moreover, we obtain a quantitative bound on the rate of convergence in the Kolmogorov distance. Our results hold both in fixed dimension and in a high-dimensional regime where the dimension grows at most logarithmically with $N$.

We study the hydrodynamic limit of the Chern--Simons--Higgs system, a relativistic gauge field model involving the Chern--Simons interaction. We introduce a single scaling parameter capturing both the non-relativistic (infinite speed of light) and semi-classical (vanishing Planck constant) regimes. This unified scaling allows us to justify the simultaneous non-relativistic and semi-classical limit, while retaining the nontrivial influence of the Chern--Simons gauge structure. Using a modulated energy method, we establish quantitative convergence rates toward the corresponding compressible Euler--Chern--Simons system as the scaling parameter tends to zero.

We develop a Fredholm alternative for a fractional elliptic operator~$\mathcal{L}$ of mixed order built on the notion of fractional gradient. This operator constitutes the nonlocal extension of the classical second order elliptic operators with measurable coefficients treated by Neil Trudinger in~\cite{trudinger}. We build~$\mathcal{L}$ by weighing the order~$s$ of the fractional gradient over a measure (which can be either continuous, or discrete, or of mixed type). The coefficients of~$\mathcal{L}$ may also depend on~$s$, giving this operator a possibly non-homogeneous structure with variable exponent. These coefficients can also be either unbounded, or discontinuous, or both. A suitable functional analytic framework is introduced and investigated and our main results strongly rely on some custom analysis of appropriate functional spaces.

Understanding how large complex networks achieve synchronization is a problem of fundamental interest, and is typically studied in the asymptotic steady-state regime. In contrast, this study investigates how higher-order interactions affect the time required to reach steady-state synchronization in a complex dynamical system. To this end, an analytical expression for the first synchronization time is derived using the Ott-Antonsen ansatz on a Kuramoto oscillator network with higher-order interactions. Subsequent numerics reveal that increasing coupling strengths accelerates the transition to synchronization, whereas increasing the interaction order produces non-monotonic behavior. In particular, the inclusion of triadic interactions accelerates synchronization, whereas further incorporating higher-order interactions progressively delays convergence to the steady state, in some regimes even falling below the pairwise case.

Electronic health records (EHR) store hundreds of demographic and laboratory variables from large patient populations. Traditional statistical methods have limited capacity in processing mixed-type data (continuous, ordinal) and capturing non-linear relationships in large multivariate data when oversimplified assumptions are made about the distribution (e.g., Gaussian) of disparate variables in EHR data. This paper addresses the limitations mentioned above by repurposing the vine copula method, which is primarily used to synthesize a multivariate distribution from many bivariate cumulative distribution functions (copulas). Vine copulas produce tree structures that represent bivariate conditional dependencies at varying hierarchical levels, decomposing a multivariate distribution. The tree structure is used to rank variables by conditional dependence and to identify a subset of central variables with local dependence, thus simplifying probabilistic mining of high-dimensional EHR data. The proposed application of vine copulas is used to identify conditional dependence between co-morbid conditions and is validated for characterizing different cohorts of EHR patients. The contribution of this paper is a novel approach to probabilistic mining and exploration of healthcare data that provides data-driven explanations, visualization, and variable selection to prognosticate a healthcare outcome. The source code is shared publicly.

Efficiently simulating many-body quantum systems with Coulomb interactions is a fundamental question in quantum physics, quantum chemistry, and quantum computing, yet it presents unique challenges: the Hamiltonian is an unbounded operator (both kinetic and potential parts are unbounded); its Hilbert space dimension grows exponentially with particle number; and the Coulomb potential is singular, long-ranged, non-smooth, and unbounded, violating the regularity assumptions of many prior state-of-the-art many-body simulation analyses. In this work, we establish rigorous error bounds for Trotter formulas applied to many-body quantum systems with Coulomb interactions. Our first main result shows that for general initial conditions in the domain of the Hamiltonian, second-order Trotter achieves a sharp $1/4$ convergence rate with explicit polynomial dependence of the error prefactor on the particle number. The polynomial dependence on system size suggests that the algorithm remains quantumly efficient, even without introducing any regularization of the Coulomb singularity. Notably, although the result under general conditions constitutes a worst-case bound, this rate has been observed in prior work for the hydrogen ground state, demonstrating its relevance to physically and practically important initial conditions. Our second main result identifies a set of physically meaningful conditions on the initial state under which the convergence rate improves to first and second order. For hydrogenic systems, these conditions are connected to excited states with sufficiently high angular momentum. Our theoretical findings are consistent with prior numerical observations.

The next nearby core-collapse supernova (SN) promises to yield a treasure of scientific information through multi-messenger astronomy. Early observations of the shock breakout (SBO) emissions are especially critical to understand the SN explosive mechanism as well as the properties of the progenitor star. Neutrino observatories are able to provide an early alert of a SN before the arrival of the SBO radiation. Super-Kamiokande (SK) has the unique capability to independently reconstruct an accurate SN pointing direction as part of its real-time monitoring system, ``SNWATCH.'' Recent upgrades to SK by adding gadolinium (Gd) to the detection volume have been accompanied by efforts to improve the speed and accuracy of SN direction reconstruction. A new, novel HEALPix-based approach (``HP-Fitter'') can calculate the SN direction from the reconstructed burst event directions in less than one second. As well, the previous maximum-likelihood direction fitter (``ML-Fitter'') was upgraded by incorporating event information from Gd neutron-capture as well as using the HP-Fitter for the initial fit parameters and from code refactoring and optimization. The improved ML-Fitter has better angular resolution but direction reconstruction time is $\mathcal{O}$(sec). Together with improvements in burst detection and event reconstruction times, SNWATCH is now able to generate an SN alert with pointing information in about 90 seconds. These upgrades have been implemented at SK and integrated into a new automated system to provide GCN notices.

The manipulation and sorting of chiral nanoparticles are of fundamental importance in multidisciplinary fields ranging from biochemistry to nanophotonics. In this study, we propose a novel and controllable chirality sorting mechanism for continuous particle separation using focused topological optical quasiparticles. Specifically, we investigate the sorting dynamics driven by tight-focused optical skyrmions and bimerons consisting of tailored spatial modes. By highly focusing free-space topological structure light fields, we generate intricate non-paraxial focal fields with tailored intensity and topological polarization textures. The sorting dynamics are systematically evaluated under the dipole approximation for fused silica nanoparticles. Our analytical calculation demonstrate that optical forces exert opposite directional pushes on particles of opposite chiralities, enabling highly efficient spatial separation. Notably, we demonstrate that this sorting process is controllable; by tuning the topological charges, the sorting distance can be flexibly tailored and expanded. The dynamic sorting process in customized topological structures introduces a promising new paradigm for tunable, wide-range chirality sorting of micro- and nano-particles.