We consider the enumeration of plane trees (rooted ordered trees) whose vertices are colored according to a specific coloring rule that prescribes which possible pairs of colors can occur as the colors of a parent vertex and its child. This general construction covers many different examples that have been studied in the literature. Some general necessary and sufficient conditions for two different coloring rules to result in the same counting sequence are established. We also provide exhaustive lists of counting sequences arising from coloring rules with two or three colors, and we find formulas and closed form expressions for many of these sequences. The famous Fibonacci, Catalan, Narayana, and Schröder sequences appear in several cases. Some of these coloring rules are extended to families of coloring rules with arbitrarily many colors.

We study quantitative unique continuation at infinity for Dirac equations with bounded matrix-valued potentials. For the massless Dirac operator $\mathcal{D}_n$ in $\mathbb{R}^n$, we establish a Landis-type estimate showing that the vanishing order of any nontrivial bounded solution of $( \mathcal{D}_n + \mathbb{V} ) φ= 0$ satisfies a lower bound of order $\exp(-κR^{2} (\log R)^{2})$ as $|x|=R\to \infty$; the quadratic growth in the exponent is sharp, in view of previous known results. Our proof follows a Bourgain--Kenig type approach based on a Carleman inequality for Dirac operators which relies on a local Hölder regularity result, which we also prove. In two dimension, we obtain improved quantitative estimates under symmetry assumptions on the potential $\mathbb{V}$ and for real-valued solutions. Finally, we also derive qualitative Landis-type results for Dirac equations with decaying potentials, including critical decay rates.

We present a workflow and associated toolkit to automate the creation of graphical user interfaces (GUI) for executables run from command line interfaces (CLI). The workflow consists of three phases, namely (Step 1) the plugin design, (Step 2) the formal (platform independent) specification of the GUI, and (Step 3) the plugin code generation for the targeted platforms. Our architecture is aligned with the Model--View--Presenter (MVP) pattern: steps one and two build the Model and View descriptions, while step three implements the Presenter layer that binds inputs, invokes the CLI, and updates outputs. Once Step one has been (manually) completed, steps two and three are fully automated. The decoupled MVP design and platform-specific generator modules enable reuse of logic, portability across ecosystems, and significant reductions in engineering effort for complex interactive applications. We primarily use our workflow to generate GUI in structural bioinformatics for CLI executables from the Structural Bioinformatics Library (SBL), targeting three platforms, namely VMD, Pymol and Web servers. The workflow can be used as a guideline, while its implementation available in the package Plugin_manager from the SBL, see https://sbl.inria.fr/doc/Plugin_manager-user-manual.html.

We prove that assuming $\mathfrak{b}=\mathfrak{d}$, in the class of hereditarily Lindelöf spaces, each productively Scheepers space is productively Hurewicz. The above statement remains true in the class of all general topological spaces assuming that $\mathfrak{d}=\aleph_1$. To this end we use combinatorial methods and the Menger covering property parametrized by ultrafilters. We also show that if near coherence of filters holds, then the Scheepers property is equivalent to a Menger property parametrized by any ultrafilter.

We explore the onset of spontaneous strong-to-weak symmetry breaking (SW-SSB) under U(1)-symmetric (i.e., charge-conserving) open-system dynamics. We define this phenomenon for quantum states and classical probability distributions, and explore it in three complementary models, one of which exhibits nontrivial quantum coherence at short times. Our main conclusions are as follows. In one dimension, the strong symmetry is not spontaneously broken at any finite time; however, correlators probing strong-to-weak symmetry breaking develop order on length scales that grow linearly in time, parametrically faster than charge diffusion. We provide numerical evidence for this scaling in multiple distinct probes of SW-SSB, and derive it from a field-theory analysis. Moreover, we relate this scaling to the problem of inferring the charge inside a subregion by measuring its surroundings, and construct explicit decoding protocols that illustrate its origin. In two dimensions, field theory and numerical simulations support a finite-time Berezinskii-Kosterlitz-Thouless-like SW-SSB transition. Within continuum hydrodynamics, by contrast, SW-SSB happens at infinitesimal time in two or more dimensions. The SW-SSB transition time can thus be interpreted as marking the emergence of a continuum hydrodynamic description, or (more precisely) the timescale beyond which non-hydrodynamic information such as discrete particle worldlines can no longer be inferred. We support this picture by analyzing a model in which we exploit SW-SSB to derive a classical stochastic hydrodynamic description from the underlying quantum dynamics.

Nonlinear optical (NLO) materials are essential for many photonic, telecommunication, and laser technologies, yet discovering better NLO molecules is computationally challenging due to the vast chemical space and competing objectives. We compare evolutionary algorithms for molecular design, targeting four objectives: maximizing the ratio of first-to-second hyperpolarizability $(β/γ)$, optimizing HOMO-LUMO gap and linear polarizability to target ranges, and minimizing energy per atom. We encode molecules as SMILES strings and evaluate their properties using quantum-chemical calculations. We compare NSGA-II, MAP-Elites, MOME, a single-objective $(μ+λ)$ evolutionary algorithm, and simulated annealing. Quality diversity methods maintain archives across a measure space defined by atom and bond count, enabling the discovery of structurally diverse molecules. Our results demonstrate that NSGA-II consistently earns high scores in every objective, leading to high-quality molecules, but MOME does a better job exploring a wide range of possibilities, resulting in higher global hypervolume and MOQD scores. However, each method has strengths and weaknesses, and produced many promising molecules.

We revisit the diffusive instability in dusty disks that arises when the dust mass diffusivity and/or viscosity decreases sufficiently steeply with increasing dust density. Our updated model includes an incompressible, viscous gas that responds azimuthally and couples to the dust through drag. We show that the basic criterion for diffusion-slope-driven instability remains approximately $β_\mathrm{diff}\lesssim -2$ for small dust stopping times, with gas feedback providing only modest quantitative changes for parameters motivated by streaming-instability turbulence. We perform nonlinear numerical calculations and confirm linear growth and mode selection toward the fastest-growing wavenumber. However, for power-law closures $D\proptoΣ^{β_\mathrm{diff}}$ with $β_\mathrm{diff}<0$, the nonlinear evolution does not saturate. Instead, steepening gradients amplify the nonlinear dust-pressure term and drive finite-time collapse into increasingly sharp spikes. Motivated by the absence of multidimensional saturation channels in our 1D framework, we test a simple piecewise closure in which the negative diffusion slope operates only over a finite density interval. This modification eliminates blowup and produces peak densities controlled by the imposed saturation scale. Our results support diffusive instabilities as a linear organizing mechanism in dusty turbulence, while highlighting that realistic nonlinear saturation requires additional physics beyond the present closure.

Network datasets appear across a wide range of scientific fields, including biology, physics, and the social sciences. To enable data-driven discoveries from these networks, statistical inference techniques like estimation and hypothesis testing are crucial. However, the size of modern networks often exceeds the storage and computational capacities of existing methods, making timely, statistically rigorous inference difficult. In this work, we introduce a subsampling-based approach aimed at reducing the computational burden associated with estimation and two-sample hypothesis testing. Our strategy involves selecting a small random subset of nodes from the network, conducting inference on the resulting subgraph, and then using interpolation based on the observed connections between the subsample and the rest of the nodes to estimate the entire graph. We develop the methodology under the generalized random dot product graph framework, which affords broad applicability and permits rigorous analysis. Within this setting, we establish consistency guarantees and corroborate the practical effectiveness of the approach through comprehensive simulation studies.

We apply covariate adjustment to the Wincoxon two sample statistic and Wincoxon-Mann-Whitney test in comparing two treatments. The covariate adjustment through calibration not only improves efficiency in estimation/inference but also widens the application scope of the Wilcoxon two sample statistic and Wincoxon-Mann-Whitney test to situations where covariate-adaptive randomization is used. We motivate how to adjust covariates to reduce variance, establish the asymptotic distribution of adjusted Wincoxon two sample statistic, and provide explicitly the guaranteed efficiency gain. The asymptotic distribution of adjusted Wincoxon two sample statistic is invariant to all commonly used covariate-adaptive randomization schemes so that a unified formula can be used in inference regardless of which covariate-adaptive randomization is applied.

In this paper, we propose a projection-free power-limiting droop control for grid-connected power electronics and an associated constrained flow problem. In contrast to projection-based power-limiting droop control, the novel projection-free power-limiting droop control results in networked dynamics that are semi-globally exponentially stable with respect to the set of optimizers of the constrained flow problem. Under a change to edge coordinates, the overall networked dynamics arising from projection-free power-limiting droop control coincide with the projection-free primal-dual dynamics associated with an augmented Lagrangian of the constrained flow problem. Leveraging this result, we (i) provide a bound on the convergence rate of the projection-free networked dynamics, (ii) propose a tuning method for controller parameters to improve the bound on the convergence rate, and (iii) analyze the relationship of the bound on the convergence rate and connectivity of the network. Finally, the analytical results are illustrated using an Electromagnetic transient (EMT) simulation.

Federated cross-domain recommendation (Federated CDR) aims to collaboratively learn personalized recommendation models across heterogeneous domains while preserving data privacy. Recently, large language model (LLM)-based recommendation models have demonstrated impressive performance by leveraging LLMs' strong reasoning capabilities and broad knowledge. However, adopting LLM-based recommendation models in Federated CDR scenarios introduces new challenges. First, there exists a risk of overfitting with domain-specific local adapters. The magnitudes of locally optimized parameter updates often vary across domains, causing biased aggregation and overfitting toward domain-specific distributions. Second, unlike traditional recommendation models (e.g., collaborative filtering, bipartite graph-based methods) that learn explicit and comparable user/item representations, LLMs encode knowledge implicitly through autoregressive text generation training. This poses additional challenges for effectively measuring the cross-domain similarities under heterogeneity. To address these challenges, we propose an LLM-based framework for federated cross-domain recommendation, FeDecider. Specifically, FeDecider tackles the challenge of scale-specific noise by disentangling each client's low-rank updates and sharing only their directional components. To handle the need for flexible and effective integration, each client further learns personalized weights that achieve the data-aware integration of updates from other domains. Extensive experiments across diverse datasets validate the effectiveness of our proposed FeDecider.

Waveguide quantum electrodynamics platforms have emerged as promising candidates for exploring and implementing non-Markovian quantum phenomena. In this work, we investigate the formation and dynamics of superpositions of bound states in a cavity array waveguide coupled to two spatially separated quantum emitters. By tuning the system parameters, we show that spontaneous emission can drive the system into non-local equilibrium states in which both photonic and emitter populations exhibit persistent oscillations. These states arise from the coexistence of bound states embedded in the energy continuum and bound states outside it, leading to hybrid oscillatory modes. We analytically derive the conditions required for the emergence of these states, numerically simulate their formation through spontaneous emission, and predict their long-time behaviour. Our results demonstrate that such bound-state superpositions enable the generation of emitter-emitter interaction through free evolution, while supporting oscillatory breathing modes of the photon density between the emitters.

Cardiovascular outcome trials commonly face competing risks when non-CV death prevents observation of major adverse cardiovascular events (MACE). While Cox proportional hazards models treat competing events as independent censoring, Fine-Gray subdistribution hazard models explicitly handle competing risks, targeting different estimands. This simulation study using bivariate copula models systematically varies competing event rates (0.5%-5% annually), treatment effects on competing events (50% reduction to 50% increase), and correlation structures to compare these approaches. At competing event rates typical of CV outcome trials (~1% annually), Cox and Fine-Gray produce nearly identical hazard ratio estimates regardless of correlation strength or treatment effect direction. Substantial divergence occurs only with high competing rates and directionally discordant treatment effects, though neither estimator provides unbiased estimates of true marginal hazard ratios under these conditions. In typical CV trial settings with low competing event rates, Cox models remain appropriate for primary analysis due to superior interpretability. Pre-specified Cox models should not be abandoned for competing risk methods. Importantly, Fine-Gray models do not constitute proper sensitivity analyses to Cox models per ICH E9(R1), as they target different estimands rather than testing assumptions. As supplementary analysis, cumulative incidence using Aalen-Johansen estimator can provide transparency about competing risk impact. Under high competing-risk scenarios, alternative approaches such as inverse probability of censoring weighting, multiple imputation, or inclusion of all-cause mortality in primary endpoints warrant consideration.

Mid-infrared observations of planet-forming disks reveal a wide diversity in molecular spectra. Carbon and oxygen abundances play a central role in setting the chemical environment of the inner disk and the spectral appearance. We aim to systematically explore how variations in elemental carbon and oxygen abundances affect the mid-infrared spectra of planet-forming disks, and to identify robust mid-infrared molecular diagnostics of C/H, O/H, and the C/O ratio. Using the thermochemical disk code ProDiMo and the line radiative transfer code FLiTs, we construct a grid of 25 models with varying carbon and oxygen abundances, covering a broad range of C/O ratios. We analyze the resulting mid-infrared molecular emission, including species such as $\rm H_2O$, $\rm CO$, $\rm CO_2$, $\rm C_2H_2$, $\rm OH$. We find that the mid-infrared molecular spectra are highly sensitive not only to the C/O ratio, but also to the absolute abundances of carbon and oxygen. Despite the same disk structure and C/O ratios, molecular fluxes (e.g., $\rm C_2H_2$, $\rm CO_2$) vary by more than an order of magnitude. This variation stems from the differences in excitation conditions and emitting regions caused by the elemental abundances of oxygen and carbon. We identify diagnostic molecular flux ratios - such as $\rm CO_2$/$\rm H_2O$ and $\rm H_2O$/$\rm C_2H_2$ - that can serve as tracers of C/H and O/H respectively. By combining these diagnostics, we demonstrate a method to infer the underlying C/O ratio. Our model grid provides a framework for interpreting mid-infrared molecular emission from disks, allowing estimates of elemental abundances if the disk properties and structure are known. Comparisons with recent JWST observations suggest that a variety in C and O abundances is seen in a sample of T Tauri disks, possibly shaped by disk transport processes and the presence of gaps.

In this paper we present the first application of the MiNLO method to the calculation of QED NLO corrections to the production of a neutral vector boson in Drell-Yan processes. We consider only the case of initial-state radiation, when the Z boson decays into neutrinos. We illustrate the abelianization procedure of the MiNLO formulae and discuss the impact that it has on the differential cross section. We then propose a variant of the MiNLO formulae in order to circumvent some of the problems that arise when dealing with QED emissions. Since this is a case study, we use ad-hoc parton distribution functions and a larger value of the electromagnetic coupling constant, in order to emphasize potential discrepancies with respect to the expected behavior of the MiNLO formulae. We quantify the uncertainties connected with the proposed method, also for a the physical value of the electromagnetic coupling. The study presented here is a necessary first step towards incorporating full electroweak effects into the MiNNLOPS framework.

Imagine a student -- let's call him `E', and make him a "he" -- that is enrolled in Calculus 2, and who believes that to pass in maths courses he only needs to memorize methods and apply them quickly and without errors. Let's imagine that `E' is an `E'xtreme case of "bad foundations" and that he knows how to solve $x+2=5$ by doing $x=5-2=3$, but he doesn't know how to substitute the $x$ in $x+2=5$ by 3, and the only way that he knows of "testing the solution" is to apply the same method again and check that he got the same result. When we are teaching Calculus to classes that have many students that are extreme cases of bad foundations we need new strategies and tools; for example, we can't pretend that "taking a particular case" is an obvious operation anymore -- instead we need ways to make these operations easy to visualize. This article shows a way to do that using Maxima.

Current architectures for neutral-atom arrays utilize devices such as acousto-optic deflectors (AODs) and spatial light modulators (SLMs) to multiplex a single classical control line into N qubit control lines. Dynamic control is speed-limited by the response time of AODs, and geometrically constrained to respect a product structure, limiting motion to row-by-row or column-by-column moves. We propose an optical rastering device that can produce any 2D pattern, not limited to grids, at 1 MHz refresh rates. We demonstrate a design with a resolution of 40 x 40 that can be further scaled up to 100 x 100 to match existing and future neutral atom devices. The ability to simultaneously transport atomic qubits in arbitrary directions will enhance qubit connectivity, enable more efficient circuits, and may have broader applications ranging from LiDAR to fluorescence microscopy.

In this study, we propose an implementation methodology of real-time few-shot learning on tiny FPGA SoCs such as the PYNQ-Z1 board with arbitrary fixed-point bit-widths. Tensil-based conventional design environments limited hardware implementations to fixed-point bit-widths of 16 or 32 bits. To address this, we adopt the FINN framework, enabling implementations with arbitrary bit-widths. Several customizations and minor adjustments are made, including: 1.Optimization of Transpose nodes to resolve data format mismatches, 2.Addition of handling for converting the final reduce mean operation to Global Average Pooling (GAP). These adjustments allow us to reduce the bit-width while maintaining the same accuracy as the conventional realization, and achieve approximately twice the throughput in evaluations using CIFAR-10 dataset.

The rates at which individuals memorize and forget environmental information strongly influence their movement paths and long-term space use. To understand how these cognitive time scales shape population-level patterns, we propose and analyze a nonlocal population model with a cognitive map. The population density moves by a Fokker--Planck type diffusion driven by a cognitive map that stores a habitat quality information nonlocally. The map is updated through local presence with learning and forgetting rates, and we consider both truncated and normalized perception kernels. We first study the movement-only system without growth. We show that finite perceptual range generates spatial heterogeneity in the cognitive map even in nearly homogeneous habitats, and we prove a lingering phenomenon on unimodal landscapes: for the fixed high learning rate, the peak density near the best location is maximized at an intermediate forgetting rate. We then couple cognitive diffusion to logistic growth. We establish local well-posedness and persistence by proving instability of the extinction equilibrium and the existence of a positive steady state, with uniqueness under an explicit condition on the motility function. Numerical simulations show that lingering persists under logistic growth and reveal a trade-off between the lingering and total population size, since near the strongest-lingering regime the total mass can fall below the total resource, in contrast to classical random diffusive--logistic models.

We study the design of single-facility service systems operating under multiple recurring regimes with service-level constraints on response times. Regime-dependent arrival and service rates induce hyperexponential response-time distributions, and the design problem selects regime-specific capacities to balance cost, congestion, fairness, and reliability. We propose a mixed-integer exponential conic optimization framework integrating SLA chance constraints, conflict-graph design restrictions, and CVaR-based tail-risk control. Although NP-hard, the problem admits an efficient decomposition scheme and tractable special cases. Computational experiments and a large-scale urban case study show substantial improvements over the current system, quantifying explicit trade-offs between efficiency, congestion control, fairness, and robustness. The framework provides a practical tool for congestion-aware and tail-control service system design.

Given a homotopy Lie algebra (i.e. an $L_\infty$-algebra) $\mathfrak{g}$, we show concretely how the Lada-Markl $\mathfrak{g}$-modules (i.e. representations) assemble into a symmetric monoidal dg-category. Considering the homotopy 2-category of that dg-category, we construct infinitesimal 2-braidings from 2-shifted Poisson structures then show that such infinitesimal 2-braidings are coherent in Cirio and Faria Martins' sense. We then explicitly determine the differential of the Chevalley-Eilenberg algebra associated with a finite-dimensional homotopy Lie algebra and construct the symmetric monoidal dg-equivalence between the category of representations and the category of semi-free dg-modules over the Chevalley-Eilenberg algebra.

We implement the Lights Out problem on a 2D grid and on Mobius ladder graphs and evaluate the performance of Grover's search on real quantum hardware. We use two instances using 9 and 16 qubits, and implement them on publicly available quantum hardware by IBM and IQM. Our experiments show improvements in IBM hardware between the Heron r1 and Heron r2 generations, highlighting progress in IBM hardware during the 2023-2024 period. The Lights Out circuits produced output distributions close to uniform on IQM devices. To diagnose device limitations, we additionally ran a small Grover SAT baseline, finding that IQM Garnet performs more reliably than other tested IQM devices. We also observed that QPUs of the same manufacturing revision can differ significantly in performance (a newer device is not guaranteed to be better), and that calibration has a significant impact on the performance of quantum devices, so the choice of device strongly depends on calibration quality.

Social VR platforms serve as an emergent venue for live performance, enabling co-presence and real-time interaction among distributed performers and audiences within shared virtual environments. Live performances, such as comedy, rely on subtle social cues between performers and audiences, which are missing in VR. However, it remains unclear how comedians utilize avatar-mediated cues in social VR. We conducted semi-structured interviews and observations with 23 virtual comedians on VRChat. Results revealed that virtual comedians transformed their limited nonverbal expressiveness into performative opportunities through intentional control and exaggeration. Additionally, a distinctive culture emerged around context-appropriate emoji reactions from audiences, while challenges such as audio latency and moderation against trolling were highlighted. Our findings advance understanding of how performers creatively adapt to expressive constraints in avatar-mediated settings. We further demonstrate how challenges in performer-audience interaction and moderation provide design insights for systems enhancing feedback visibility and sustain community norms without restricting creative expression.

Checkpoint/Restart (C/R) saves the running state of the programs periodically, which consumes considerable system resources. We observe that not every piece of data is involved in the computation in typical HPC applications; such unused data should be excluded from checkpointing for better storage/compute efficiency. To find out, we propose a systematic approach that leverages automatic differentiation (AD) to scrutinize every element within variables (e.g., arrays) for checkpointing allowing us to identify critical/uncritical elements and eliminate uncritical elements from checkpointing. Specifically, we inspect every single element within a variable for checkpointing with an AD tool to determine whether the element has an impact on the application output or not. We empirically validate our approach with eight benchmarks from the NAS Parallel Benchmark (NPB) suite. We successfully visualize critical/uncritical elements/regions within a variable with respect to its impact (yes or no) on the application output. We find patterns/distributions of critical/uncritical elements/regions quite interesting and follow the physical formulation/logic of the algorithm.The evaluation on NPB benchmarks shows that our approach saves storage for checkpointing by up to 20%.

Long baseline optical and infrared interferometric arrays achieve high angular resolution and enable detailed astrophysical measurements. Interferometers have enabled observations of stars at various stages of evolution, as well as studies of binary stars, circumstellar disks, and active galactic nuclei. The CHARA Array is a long-baseline interferometric array at the Mount Wilson Observatory, USA. At the core of CHARA operations are the delay lines, which equalize the optical path length for all telescopes as the Earth rotates and compensate for optical path variations induced by atmospheric turbulence. We report recent upgrades and performance of the CHARA Array optical delay lines for high-precision interferometric observations. The legacy system had been operational for over two decades, and it was increasingly difficult to acquire replacement parts. Beginning in mid-2021, the control system underwent a major upgrade, replacing the aging VME-based architecture with a modern hybrid FPGA and Linux-based system; this modernization continued through the end of 2024. We describe hardware/software changes, the servo architecture, and lab/on-sky performance. The upgraded system achieves residual delay line cart tracking errors of $\sim12$~nm, the same level as the legacy system, and a control bandwidth of 100-130~Hz, allowing fringe tracking across the R, H, and K bands. Initial commissioning revealed key issues such as metrology time-tick jitter and vibration-induced visibility loss, which were diagnosed and resolved. We note ongoing and future efforts to extend baselines up to 1~km and support advanced observing modes such as dual-field interferometry and nulling. This paper is a reference for current and future use of the CHARA Array and for next-generation instrument design.

This work develops a unified framework for inferring, representing, and statistically characterizing an anisotropic strength surface directly from molecular dynamics data. Large-scale tensile loading simulations are used to generate failure data across all principal stress ratios and loading orientations, facilitated by a data-driven mapping between imposed strain-rate tensors and resulting stresses. The orientation-dependent strength surface is then represented using a constrained parametric formulation in which the surface parameters vary smoothly with loading angle through a low-dimensional functional encoding. To deploy the framework, we specifically consider the case of monocrystalline graphene, which is a prototypical two-dimensional material that has been extensively characterized, both experimentally and computationally, in the literature. For defective graphene, multiple random realizations of vacancy defect distributions are used to construct a stochastic ensemble of angular strength surfaces. Because each anisotropic strength surface requires substantial atomistic sampling to construct, the resulting ensemble is inherently limited in size, motivating the use of compact encoding, dimensionality reduction, and probabilistic modeling to characterize strength variability. Dimensionality reduction via Principal Component Analysis reveals a condensed latent representation of the fitted, encoded surfaces, where a Gaussian mixture model is employed to capture defect-induced variability, including rare outlier behaviors arising from clustered vacancy defects. Sampling from this probabilistic model enables the generation of new, physically admissible strength surfaces and the construction of confidence intervals in both parameter space and stress space. (Abstract shortened to meet arXiv limits.)

Understanding the dynamic nature of brain connectivity is critical for elucidating neural processing, behavior, and brain disorders. Traditional approaches such as sliding-window correlation (SWC) characterize time-varying undirected associations but do not resolve directional interactions, limiting inference about time-resolved information flow in brain networks. We introduce sliding-window prediction correlation (SWpC), which embeds a directional linear time-invariant (LTI) model within each sliding window to estimate time-varying directed functional connectivity (FC). SWpC yields two complementary descriptors of directed interactions: a strength measure (prediction correlation) and a duration measure (window-wise duration of information transfer). Using concurrent local field potential (LFP) and fMRI BOLD recordings from rat somatosensory cortices, we demonstrate stable directionality estimates in both LFP band-limited power and BOLD. Using Human Connectome Project (HCP) motor task fMRI, SWpC detects significant task-evoked changes in directed FC strength and duration and shows higher sensitivity than SWC for identifying task-evoked connectivity differences. Finally, in post-concussion vestibular dysfunction (PCVD), SWpC reveals reproducible vestibular-multisensory brain-state shifts and improves healthy-control vs subacute patient (HC-ST) discrimination using state-derived features. Together, these results show that SWpC provides biologically interpretable, time-resolved directed connectivity patterns across multimodal validation and clinical application settings, supporting both basic and translational neuroscience.

We present a biologically inspired quantum neural network that encodes neuronal populations as fully connected qubits governed by the Lipkin-Meshkov-Glick (LMG) quantum Hamiltonian and stabilized by a synaptic-efficacy feedback implementing activity-dependent homeostatic control. The framework links collective quantum many-body modes and attractor structure to population homeostasis and rhythmogenesis, outlining scalable computational primitives -- stable set points, controllable oscillations, and size-dependent robustness -- that position LMG-based architectures as promising blueprints for bio-inspired quantum brains on future quantum hardware.

After all these years and all these other shared memory programming frameworks, OpenMP is still the most popular one. However, its greater levels of non-deterministic execution makes debugging and testing more challenging. The ability to record and deterministically replay the program execution is key to address this challenge. However, scalably replaying OpenMP programs is still an unresolved problem. In this paper, we propose two novel techniques that use Distributed Clock (DC) and Distributed Epoch (DE) recording schemes to eliminate excessive thread synchronization for OpenMP record and replay. Our evaluation on representative HPC applications with ReOMP, which we used to realize DC and DE recording, shows that our approach is 2-5x more efficient than traditional approaches that synchronize on every shared-memory access. Furthermore, we demonstrate that our approach can be easily combined with MPI-level replay tools to replay non-trivial MPI+OpenMP applications. We achieve this by integrating \toolname into ReMPI, an existing scalable MPI record-and-replay tool, with only a small MPI-scale-independent runtime overhead.

Chatterjee (2016) proved, as an application of his general framework relating superconcentration and chaos, that after the entries of an $n \times n$ matrix drawn from the Gaussian unitary ensemble undergo an entrywise Ornstein-Uhlenbeck (OU) process for time greater than $n^{-1/3}$, the top eigenvector of the matrix becomes almost completely decorrelated from its initial position. More recently, Bordenave, Lugosi, and Zhivotovskiy (2020) showed that the same happens under a discrete resampling model, once more than $n^{5/3}$ randomly chosen entries of a Wigner random matrix are resampled. We generalize these results in several directions: (1) we analyze the decorrelation of any eigenvector under continuous and discrete resampling dynamics, (2) we analyze the discrete resampling process for generalized Wigner matrices with inhomogeneous variance profiles, (3) we analyze a combination of continuous and discrete resampling where an OU process is repeatedly run for a certain time on randomly chosen entries, and (4) we analyze a dependent version of resampling where entries grouped into "blocks" of arbitrary shapes are resampled together. In each case, we show that a given eigenvector decorrelates provided that enough entries have been resampled or that the associated dynamics have been run for a long enough time. Our proofs take a different approach from prior work, relying more directly on the characterization of eigenvectors as derivatives of eigenvalues and reducing the problem of establishing eigenvector noise sensitivity to variants of standard and robust properties of random matrices such as bounds on eigenvalue spacings and eigenvector delocalization.