When designing and evaluating an experiment or observational study, it is useful to have a realistic hypothesis regarding the average treatment effect. We present an approach to conceptualizing this average by first considering a distribution of effects. We demonstrate with examples in medicine, economics, and psychology.

This study investigates the influence of different types of non-pharmaceutical interventions (NPIs) on epidemic progression using SIR compartmental models. We analyze the optimization of two distinct targets: the final epidemic size and the infection peak, particularly how they respond to variations in the initiation time of the NPIs. We derive analytical approximations for the critical points of the infection curve of the standard mean-field SIR model with NPIs, and for the epidemic size, enabling a systematic comparison. The analytical results reveal the existence of six different allowed scenarios for the evolution of the epidemic with a single NPI. Furthermore, by employing degree-based mean-field network models, we distinguish between NPIs that decrease the transmission rate (individual and environmental measures) and those that reduce social contacts (lock down measures). We find that, when assuming equal effects on the reproductive number, the former are more efficient in reducing the final epidemic size. Meanwhile, the effectivities of both types of NPIs differ in reducing primary and secondary peaks. The results for all models consistently confirm that minimizing the infection peak requires earlier implementation of the NPI than minimizing the epidemic size, offering new insights for strategic public health timing.

As Language Models (LMs) advance, Semantic Error Correction (SEC) has emerged as a promising approach for reliable network designs. Yet existing methods prioritize intent over accuracy, falling short of verbatim recovery. Our recent work, Cross-Layer SEC (CL-SEC), addressed this by fusing physical-layer Log-Likelihood Ratios (LLRs) with semantic context, but its real-time feasibility remained unvalidated. This paper demonstrates CL-SEC on a live Software-Defined Radio (SDR) testbed, resolving implementation barriers with: 1) an SDR middleware enabling real-time LLR extraction from FPGA hardware, and 2) a generalized inference interface supporting modern encoder-decoder LMs. Real-world experiments confirm that the cross-layer fusion significantly outperforms either source alone.

Large Language Models (LLMs) have been a promising way for automated vulnerability detection. However, most prior studies have explored the use of LLMs to detect vulnerabilities only within single functions, disregarding those related to interprocedural dependencies. These studies overlook vulnerabilities that arise from data and control flows that span multiple functions. Thus, leveraging the context provided by callers and callees may help identify vulnerabilities. This study empirically investigates the effectiveness of detection, the inference cost, and the quality of explanations of four modern LLMs (Claude Haiku 4.5, GPT-4.1 Mini, GPT-5 Mini, and Gemini 3 Flash) in detecting vulnerabilities related to interprocedural dependencies. To do that, we conducted an empirical study on 509 vulnerabilities from the ReposVul dataset, systematically varying the level of interprocedural context (target function code-only, target function + callers, and target function + callees) and evaluating the four modern LLMs across C, C++, and Python. The results show that Gemini 3 Flash offers the best cost-effectiveness trade-off for C vulnerabilities, achieving F1 >= 0.978 at an estimated cost of $0.50-$0.58 per configuration, and Claude Haiku 4.5 correctly identified and explained the vulnerability in 93.6% of the evaluated cases. Overall, the findings have direct implications for the design of AI-assisted security analysis tools that can generalize across codebases in multiple programming languages.

We establish a two-weight fractional Poincaré-Sobolev sandwich, consisting of a two-weight fractional Poincaré-Sobolev inequality and a two-weight embedding from the first-order Sobolev space to a Triebel-Lizorkin space defined via a difference norm. Our constants are asymptotically sharp as the fractional parameter approaches $1$. Our results are new even in the one-weight case. For each inequality we give explicit quantitative dependence on Muckenhoupt weight characteristics and treat both subcritical and critical regimes, the former via elementary methods and the latter via sparse domination. As one of our main tools, we establish a new sparse domination result for Triebel-Lizorkin difference norms. Our methods unify, simplify and significantly extend various earlier approaches.

Noisy speech separation systems are typically trained on fully-synthetic mixtures, limiting generalization to real-world scenarios. Though training on mixtures of in-domain (thus often noisy) speech is possible, we show that this leads to undesirable optima where mixture noise is retained in the estimates, due to the inseparability of the background noises and the loss function's symmetry. To address this, we propose ring mixing, a batch strategy of using each source in two mixtures, alongside a new Signal-to-Consistency-Error Ratio (SCER) auxiliary loss penalizing inconsistent estimates of the same source from different mixtures, breaking symmetry and incentivizing denoising. On a WHAM!-based benchmark, our method can reduce residual noise by upwards of half, effectively learning to denoise from only noisy recordings. This opens the door to training more generalizable systems using in-the-wild data, which we demonstrate via systems trained using naturally-noisy speech from VoxCeleb.

The Koopman-von Neumann equation describes the evolution of wavefunctions associated with autonomous ordinary differential equations and can be regarded as a quantum physics-inspired formulation of classical mechanics. The main advantage compared to conventional transfer operators such as Koopman and Perron-Frobenius operators is that the Koopman-von Neumann operator is unitary even if the dynamics are non-Hamiltonian. Projecting this operator onto a finite-dimensional subspace allows us to represent it by a unitary matrix, which in turn can be expressed as a quantum circuit. We will exploit relationships between the Koopman-von Neumann framework and classical transfer operators in order to derive numerical methods to approximate the Koopman-von Neumann operator and its eigenvalues and eigenfunctions from data. Furthermore, we will show that the choice of basis functions and domain are crucial to ensure that the operator is well-defined. We will illustrate the results with the aid of guiding examples, including simple undamped and damped oscillators and the Lotka-Volterra model.

The interpretation of the parameters appearing in constitutive models for viscoelastic fluids is essential for analyzing theoretical predictions and understanding the origin of phenomena observed in experiments. In this work, we examine the physical significance of the Deborah ($De$) and Weissenberg ($Wi$) numbers, along with other key parameters commonly used in these models. The central objective is to clarify the extent to which these dimensionless groups effectively characterise the competition between elastic and viscous effects in complex flows. While these parameters are ubiquitous in theoretical and experimental research, their interpretation is often context-dependent and prone to ambiguity. To address this, we analyse two representative scenarios: an analytical solution for unsteady planar flow and a numerical simulation of viscoelastic flow between rotating coaxial cylinders, governed by the Oldroyd-B constitutive equations. Our findings elucidate the distinct roles of these dimensionless numbers, offering guidelines for their rigorous interpretation in both analytical and numerical studies.

As statistical systems, galaxies exhibit a rich interplay between organized structure and stochastic fluctuations across a broad range of spatial scales. This duality motivates the need for quantitative frameworks capable of capturing their morphological complexity. The ordinal patterns framework, along with its associated statistical measures: permutation entropy ($H$), disequilibrium ($D_E$), statistical complexity ($C$), and ordinal network node entropy, has recently emerged as a powerful tool for analyzing such complexity in physical systems. We apply this framework in a multiwavelength, multiscale analysis of the galaxy NGC 628, utilizing observations in the near-ultraviolet, near-infrared, mid-infrared, and millimeter bands. Our results reveal a characteristic spatial scale of approximately 200 parsecs, marking the transition from small-scale structures influenced by star formation and stellar feedback to larger-scale morphology governed by the galaxy's dynamics. Furthermore, we find that the $C$ vs. $H$ trajectories for all wavelengths converge toward a common attractor curve, consistent with the behavior of isotropic Gaussian random fields. This convergence suggests a universal statistical behavior in galactic structure at large scales, despite the differing physical processes traced by each wavelength.

Gibbs states are a natural model of quantum matter at thermal equilibrium. We investigate the role of external fields in shaping the entanglement structure and computational complexity of high-temperature Gibbs states. External fields can induce entanglement in states that are otherwise provably separable, and the crossover scale is $h\asymp β^{-1} \log(1/β)$, where $h$ is an upper bound on any on-site potential and $β$ is the inverse temperature. We introduce a quasi-local Lindbladian that satisfies detailed balance and rapidly mixes to the Gibbs state in $\mathcal{O}(\log(n/ε))$ time, even in the presence of an arbitrary on-site external field. Additionally, we prove that for any $β<1$, there exist local Hamiltonians for which sampling from the computational-basis distribution of the corresponding Gibbs state with a sufficiently large external field is classically hard, under standard complexity-theoretic assumptions. Therefore, high-temperature Gibbs states with external fields are natural physical models that can exhibit entanglement and classical hardness while also admitting efficient quantum Gibbs samplers, making them suitable candidates for quantum advantage via state preparation.

Large language model (LLM) agents increasingly rely on third-party API routers to dispatch tool-calling requests across multiple upstream providers. These routers operate as application-layer proxies with full plaintext access to every in-flight JSON payload, yet no provider enforces cryptographic integrity between client and upstream model. We present the first systematic study of this attack surface. We formalize a threat model for malicious LLM API routers and define two core attack classes, payload injection (AC-1) and secret exfiltration (AC-2), together with two adaptive evasion variants: dependency-targeted injection (AC-1.a) and conditional delivery (AC-1.b). Across 28 paid routers purchased from Taobao, Xianyu, and Shopify-hosted storefronts and 400 free routers collected from public communities, we find 1 paid and 8 free routers actively injecting malicious code, 2 deploying adaptive evasion triggers, 17 touching researcher-owned AWS canary credentials, and 1 draining ETH from a researcher-owned private key. Two poisoning studies further show that ostensibly benign routers can be pulled into the same attack surface: a leaked OpenAI key generates 100M GPT-5.4 tokens and more than seven Codex sessions, while weakly configured decoys yield 2B billed tokens, 99 credentials across 440 Codex sessions, and 401 sessions already running in autonomous YOLO mode. We build Mine, a research proxy that implements all four attack classes against four public agent frameworks, and use it to evaluate three deployable client-side defenses: a fail-closed policy gate, response-side anomaly screening, and append-only transparency logging.

Recent astronomical observations, in particular from the Kepler and TESS missions and their related follow-ups, have revealed an abundance of exoplanets in the size range between Neptune (4 Earth radii) and Earth (1 Earth radii ), as well as a low occurrence rate of planets around twice the radius of Earth (2 Earth radii). This paper uses statistical methods, in particular, the survival function analysis, to address the known exoplanet population observed mainly from the Kepler's primary mission, in order to mathematically elucidate the orbital distributions (expressed in either the orbital period P or the orbital semi-major axis a), for each of the host stars, in both a collective way, and also separately for the planets grouped into various radius bins. We uncover a log-uniform distribution for the majority of planets except the giants. Based on the results of the statistics, we then visit several possible formation scenarios and pathways for planets in different size ranges, in order to explain the results from a theoretical point-of-view.

Real-time control of distribution networks requires accurate information about the system state. In practice, however, such information is difficult to obtain because real-time measurements are available only at a limited number of locations. This paper proposes a novel data-driven power flow (DDPF) framework for balanced radial distribution networks. The proposed algorithm combines the behavioral approach with the DistFlow model and leverages offline historical data to solve power flow problems using only a limited set of real-time measurements. To design DDPF under sparse measurement conditions, we develop a sensor placement problem based on optimal network reductions. This allows us to determine sensor locations subject to a predefined sensor budget and to explicitly account for the radial nature of distribution networks. Unlike approaches that rely on full observability, the proposed framework is designed for practical distribution grids with sparse measurement availability. This enables data-driven power flow for real-time operation while reducing the number of required sensors. On several test cases, the proposed DDPF algorithm could demonstrate accurate voltage magnitude predictions, with a maximum error less than 0.001 p.u., with as little as 25% of total locations equipped with sensors.

We study the atomic Hydrogen (HI) content of galaxies in the core of the Shapley Supercluster (SSC) at <z> ~ 0.048, using observations from the MeerKAT Galaxy Cluster Legacy Survey and optical data from the Shapley Supercluster Survey (ShaSS) project. Our sample comprises 169 galaxies with HI detections in the dynamically active region of Abell 3558 and SC1329-313. Following the literature, we classify galaxies into star-forming main sequence (SFMS), transition (TZ), and red sequence (RS) populations, and examine how the HI content varies across these populations. Galaxies on the SFMS exhibit an average HI gas fraction offset of 0.038 dex from the gas fraction main sequence, while TZ and RS populations show depleted HI fractions of -0.034 and -0.211 dex. HI depletion timescales span from 6 to 170 Gyr (SFMS-TZ-RS) confirming increasingly inefficient star formation with quenching. Scaling relations between HI mass and stellar mass in the SSC are generally consistent with field samples. The most direct signature of the dense environment of the SSC is the marked predominance of TZ galaxies, in contrast to what is observed in the field-dominated sample of xGASS, where the population is mostly composed of SFMS galaxies. Moreover, the SFMS and RS populations have similar size, again in contrast with field populations. These results suggest that galaxies in the SSC are undergoing environmental quenching through starvation or strangulation, rather than rapid gas stripping. Despite detectable HI reservoirs, many galaxies exhibit long depletion times, indicating reduced gas accretion and inefficient star formation.

The phenomenon of electron tunneling has long been central to quantum transport and continues to provide a powerful framework for understanding and controlling electronic processes in solids. When combined with optical excitation, tunneling becomes a particularly rich platform for experiments, because light can drive nonequilibrium carrier populations and open transport pathways that are inaccessible without optical excitation. The emergence of van der Waals (vdW) materials has greatly expanded this opportunity by enabling atomically thin heterostructures with clean interfaces, engineered barriers, and highly tunable band alignment. In this review, we discuss the fundamental mechanisms of photo-assisted transport and the realization of vdW tunnel junctions, and show how they provide electrical access to nonequilibrium dynamics and collective excitations in quantum materials. We further examine emerging functionalities including photodetection, tunneling-driven light emission, sensing, and memory. Finally, we present a forward-looking perspective on new opportunities such as quantum-geometric probes, twist-resolved spectroscopy, moire ferroelectricity, and scalable architectures for computing and sensing.

The first search for the lepton-flavour violating decays $B^+ \to π^+ μ^{\pm} e^{\mp}$ in proton-proton collisions is presented, using data collected by the LHCb experiment between 2011 and 2018, corresponding to an integrated luminosity of 9 fb$^{-1}$. No significant signal is observed and an upper limit on the branching fraction is set at $\mathcal{B}(B^+ \to π^+ μ^{\pm} e^{\mp}) < 1.8 \times 10^{-9}$ at the $90\%$ confidence level, two orders of magnitude more restrictive than the current world average. This is the first constraint on lepton-flavour violating $b \to d$ quark transitions at the LHC and also sets the most stringent upper limits to date on $b \to d μ^{\pm} e^{\mp}$ transitions. Limits on left-handed and scalar scenarios beyond the Standard Model are also reported.

Weak gravitational lensing is one of the primary cosmological probes, providing powerful constraints on the cosmological model. As Stage IV surveys are expected to deliver data of unprecedented precision, accurate modeling of weak gravitational lensing observables across both linear and non-linear scales becomes increasingly important. In this work, we investigate weak lensing in modified gravity (MG) models, extensions of the standard $Λ$CDM cosmology in which gravity deviates from general relativity, generally introducing modifications to the lensing equation. We parametrize these modifications through the common phenomenological function $Σ_\mathrm{mg}$ and apply ray-tracing to the density maps of N-body and hydrodynamical simulations. We model the time dependence of $Σ_\mathrm{mg}$ analytically, while we introduce a phenomenological scale dependence to represent the screening mechanisms by which MG models reduce to general relativity in high-density environments. Starting from the output of the FLAMINGO hydrodynamical simulations, we generate fully ray-traced convergence maps using our modified lensing model. We analyze how the parameters of our prescription affect the weak lensing convergence power spectrum and compare these effects to other known sources of variation, in particular cosmological parameters and baryonic feedback. We find that the modifications to the lensing equation deriving from the MG model produce non-negligible signatures in the convergence power spectrum and that, within extensions of the $Λ$CDM framework, these effects can be larger than those induced by baryonic physics. Our results indicate that modified lensing should become a standard ingredient of the analysis of modified gravity simulations.

Data-driven control has emerged as a powerful paradigm for synthesizing controllers directly from data, bypassing explicit model identification. However, this reliance on data introduces new and largely unexplored vulnerabilities. In this paper, we show that an attacker can systematically poison the data used for control synthesis, causing any linear state-feedback controller synthesized by the planner to destabilize the physical system. Concerningly, we show that the attacker can achieve this objective without knowledge of the system model or the controller synthesis procedure. To this end, we develop a recursive data-poisoning mechanism that generates falsified state trajectories, inducing a precise geometric shift in the apparent system dynamics. More broadly, our results establish that data-driven control pipelines can be deterministically destabilized by model-agnostic attacks operating solely at the data level. Numerical simulations corroborate these findings for both noise-free and noisy data.

We introduce a new method for the determination of the ratio of production fractions $R^{\pm0}=\mathcal B(Υ(4S)\to B^+B^-)/\mathcal B(Υ(4S)\to B^0\bar B^0)$ based on $\bar B\to D^{(*)}\ell\bar ν$ decays. Given the importance of these modes, we perform a comprehensive analysis of the available data, extracting the information on their branching fractions and \Rpmz in parallel and providing their correlations in order to avoid double-use of this information in phenomenological analyses. We obtain the most precise value for $R^{\pm0}$ from a single channel so far, about 2$σ$ from unity. The combination with previously available determinations from other channels yields $R^{\pm0}=1.062(19)$, constituting evidence for isospin violation in $Υ(4S)$ decays. This demonstrates the necessity to take this effect into account in experimental and phenomenological analyses. The results for the $\bar B\to D^{(*)}\ell\bar ν$ branching fractions are up to $1.6σ$ larger compared to averages available in the literature, owing to the removal of overlooked inconsistencies in the treatment of older analyses and correcting for d'Agostini bias where possible, thereby reducing the $V_{cb}$ puzzle.

Achieving device-to-device reproducibility is a critical bottleneck for scalable photonic integrated circuits, as subtle variations in bottom-up epitaxial growth and fabrication severely limit yield. We present a machine learning workflow for III-V multi-quantum well microring lasers that first optimizes growth and geometry parameters via multi-objective Bayesian optimization, then leverages variational autoencoders (VAEs) to attribute residual device-to-device variability to its underlying sources. By explicitly targeting threshold variance alongside absolute performance, we demonstrate 100% lasing yield across all designs. The optimized multi-quantum well microring laser fields achieved a median lasing threshold of $16~μ\mathrm{J}\,\mathrm{cm}^{-2}\,\mathrm{pulse}^{-1}$, a $73\%$ reduction in threshold variance relative to the previously reported best values, and a median emission wavelength of $1333~\mathrm{nm}$, in the telecommunications O-band. Furthermore, to diagnose residual performance dispersion under nominally identical conditions, VAEs were used to isolate the key components of device morphology that impact performance. This analysis successfully decoupled geometric from material disorder, quantitatively linking previously unmeasured morphological variations to population-level threshold fluctuations. This data-driven workflow bridges the gap between fundamental epitaxy and reliable manufacturing, establishing a generalizable blueprint for designing and yield-optimizing complex, non-linear optoelectronic devices.

This work is inspired by a remark of de Gennes about polyelectrolytes, which are charged polymers. A common model for a polymer is a self-avoiding or self-repelling random walk or Brownian motion. For polyelectrolytes, the repelling potential is the Coulomb potential arising from pairs of charged particles. We show that in the continuous case of Brownian motion in three dimensions, the radius of gyration of a polyelectrolyte of length T grows linearly with T, up to logarithmic corrections.

The Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) promises to drastically accelerate the discovery of ultracool dwarfs (UCDs) over the course of its 10-year survey of the Southern Hemisphere. With the official start of LSST imminent, we showcase LSST's capabilities for discovering and characterizing UCDs using early commissioning data (Data Preview 1). The LSST photometric system at this stage remains poorly understood for faint UCDs. Thus, we begin by cross-matching Data Preview 1 against known UCD catalogs. We recover 1 known UCD from the Ultracool Sheet, 17 UCDs from the Dark Energy Survey, and 17 low mass stars from the Gaia Catalog of Nearby Stars. Using these known UCDs alongside recent spectroscopically-confirmed Euclid objects, we select 89 ultracool dwarf candidates in LSST fields, 17 of which are unique to this work. We present our candidates, a photometric temperature estimate, and discuss lessons learned from using early LSST data products. Finally, we turn to the future and predict potential UCD counts in upcoming LSST commissioning data (Data Preview 2), which is expected to be available to the Rubin community in 2026. Using synthetic populations of brown dwarfs, we forecast over 17,000 objects may be discovered and characterized in Data Preview 2. We predict that several hundred known objects and thousands of as-of-yet undiscovered UCDs may be detected in Data Preview 2 fields.

Research on how people experience music emphasizes the importance of exploration and diversity in listening. However, music recommender systems struggle with facilitating exploration. Even when music recommender systems are able to recommend something valuable to users that is outside their typical preferences, it still remains difficult to spark their interest. This paper presents a user study examining the efficacy of immersive and informative introductions in stimulating interest in songs that are beyond one's usual preferences, an experience called Taste-Broadening Serendipity. We uncover two important mechanisms behind the effect of introductions: transportation and cognitive elaboration. Our findings indicate that transportation (i.e., being absorbed into a narrative world) is the strongest predictor of Taste-Broadening Serendipity, while cognitive elaboration (i.e., learning something new about the artist or social context in which the music emerged) has a weaker effect but is easier to stimulate. We propose that song introductions can play an important role in facilitating exploration and increasing diversity of listening on music streaming platforms.

Cold Neptunes and sub-Neptunes are among the most common products of planet formation and likely dominate the angular-momentum budgets in most planetary systems, yet their dynamical impact on planetary architectures remains poorly understood. Using N-body simulations, we investigate the evolution of multi-Neptune systems assembled into resonant chains during the gas-disk phase and later coupled to remnant planetesimal disks. We show that planetesimal disks containing $\simeq 1$-$4\%$ of the planetary mass efficiently disrupt resonant chains and trigger global dynamical instabilities on timescales of $1~\mathrm{Myr}$-$1~\mathrm{Gyr}$, providing a pathway for delayed instability long after gas-disk dispersal, albeit with instability timescales that are highly sensitive to disk mass. The ensuing instability drives large-scale orbital rearrangement and loss of planets through collisions, tidal disruption, and ejections. Notably, in most systems at least one planet is scattered inward to $\sim 0.1~\mathrm{au}$ on $\sim 10$-$100$ Myr timescales (for $\sim 5$-$50\; M_\oplus$ planets) following instability onset, with a substantial fraction undergoing tidal capture or disruption. This tidal capture can provide a natural pathway to hot Neptune formation, while compact inner chains, if present, would be destroyed on $\sim 100~\mathrm{Myr}$ timescales by cold sub-Neptunes, naturally explaining the observed decline in the resonant fraction. We argue that the predictions of our model, which yields mass-segregated planets and corresponding relative abundances of cold, wide-orbit, and free-floating planets, can be tested by ongoing and upcoming microlensing surveys.

A range of charts with different strengths and weaknesses exists to support the visual analysis of univariate distributions, with a limited understanding of which charts best support which tasks and users, and how practitioners use charts. We categorize the available charts for univariate distributions into four groups and present the results of a mixed-methods comparison (n=215) of participants' perception and preferences across boxplots, violinplots, jittered stripplots, and histograms as representatives of their respective categories. The click-to-select approach in our study, combined with data on participants' subjective experiences and preferences, allows to both measure accuracy on benchmark tasks and discuss participants' choices qualitatively. Our analysis reveals differences between charts in task accuracy, common misunderstandings, and preferences across various low-level tasks, and indicates that chart preference and familiarity do not necessarily align with participants' task performance. Interviews with five visualization practitioners further reveal that charts widely preferred by general audiences (such as histograms) or commonly used in scientific domains (such as boxplots) are not inherently the most effective for all tasks.

Fast-ion conductors such as BaSnF4 are of significant interest for next-generation solid-state battery technologies due to their high ionic conductivity and chemical stability. However, the behaviour of these materials under extreme conditions remains poorly understood, despite the relevance of pressure-induced modifications for tuning functional properties. In this study, we combine density functional theory (DFT) calculations with high-pressure experiments to investigate the structural evolution of BaSnF4 up to 40 GPa. DFT predicts two pressure-induced phase transitions: from the ambient-pressure tetragonal P4/nmm phase to a monoclinic P21/m-I structure at 10 GPa, and subsequently to a denser monoclinic P21/m-II phase at 32 GPa. The first transition is experimentally confirmed via angle-dispersive X-ray diffraction, Raman spectroscopy, and electrical resistivity measurements, all performed at ambient temperature. The second transition is supported by distinct changes in high-pressure Raman modes and resistivity behaviour, consistent with a further structural reorganization. These findings not only clarify the high-pressure phase diagram of BaSnF4, but also shed light on the potential for pressure-tuned ionic transport in fluorostannate-based solid electrolytes.

Electromagnetic cascades are initiated by TeV gamma rays propagating through the intergalactic medium (IGM), and they can be used to constrain the weak intergalactic magnetic field (IGMF) in cosmic voids. Primary TeV photons produce electrons and positrons through electromagnetic pair production, which can be deflected out of the line-of-sight to the observer by IGMF. In addition, electron-positron pairs can perturb the IGM, triggering plasma instabilities that can cool down the pairs before they upscatter cosmic background photons to GeV energies via inverse Compton (IC) scattering. We investigate the influence of plasma instabilities on the cascade spectrum by introducing a parameterized model for the instability using a publicly available Monte Carlo framework CRPropa. We use extended-emission observations within the field of view of the observer to constrain the IGMF in the presence of plasma instability cooling. Based on spectral observations of the blazar 1ES 0229+200 from Fermi-LAT, we find the best-fit photon spectrum including the plasma instability and IGMF parameters that reproduces the observational data for different observer field-of-view angles and obtain the IGMF constraint in cosmic voids. We find that plasma instabilities with a characteristic length scale of order $10^{2}~\text{kpc}$ reproduce the observed photon spectrum and imply an IGMF strength of order $10^{-17}~\text{G}$.

Visibility Graph Analysis (VGA) is a key space syntax method for understanding how spatial configuration shapes human movement, but its reliance on all-pairs BFS computation limits practical application to small study areas. We present a system that combines three techniques to scale VGA to city-scale problems: (i) delta-compressed CSR storage using LEB128 varint encoding, which achieves ~4x compression and enables memory-mapped graphs exceeding available RAM; (ii) HyperBall, a probabilistic distance estimator based on HyperLogLog counter propagation, applied here for the first time to visibility graphs, reducing BFS complexity from O(N|E|) to O(D|E|2^p); and (iii) GPU-accelerated CUDA kernels with a fused decode-union kernel that streams the compressed graph via PCIe and performs LEB128 decoding entirely in shared memory. HyperBall's iteration count equals the topological depth limit, so the radius-n analysis that practitioners already use as standard translates directly into proportional speedup -- unlike depthmapX, whose BFS time is invariant to depth setting due to the small diameter of visibility graphs. Using depthmapX's own visibility algorithm (sparkSieve2) to ensure identical edge sets, our tool achieves a 239x end-to-end speedup at 42,705 cells and scales to 236,000 cells (4.8 billion edges) in 137 seconds -- problem sizes far beyond depthmapX's practical limit. At p=10, Visual Mean Depth achieves Pearson r=0.999 with 1.7% median relative error across 20 matched configurations.

Langevin stochastic differential equations provide a dynamical description of pulsar timing noise and gravitational wave background (GWB) signals. They are also central to state space algorithms that have gained traction in pulsar timing array analysis due to their linear computational scaling with the number of observations. In this work, we utilize established methods in diffusion theory to derive analytical solutions (means, covariances, and probability density functions) to Langevin equations relevant to red noise and the GWB signal in pulsars. The solutions give direct physical insight on the dynamics of pulsar timing signals. As a canonical example, we show that the pulsar spin frequency modeled as an Ornstein-Uhlenbeck process is mathematically inconsistent with a stationary GWB signal when the timing residual is the direct observable. The nonstationarity can be partially dealt with by marginalizing over long time deterministic trends in the data. Then, we show that a random process based on an overdamped harmonic oscillator supports both a stationary spin frequency and phase residuals, consistent with a stationary GWB signal. We also turn our attention to a phenomenological model of a neutron star -- a two-component model with spin wandering -- that has been motivated to explain observed timing noise in radio pulsars. We derive analytical expressions for the means, covariances, and cross-covariances of the crust and superfluid rotational states driven by white noise. The associated constant deterministic torques are linked to the quadratic spin-down of pulsars. The solutions reveal the physical origin of nonstationarity in the residual model: the coexistence of damped and diffusive eigenmodes of the system.

We develop methods for constructing and computing conformal invariants of submanifolds, with a particular emphasis on conformal submanifold scalars and conformally invariant integrals of natural submanifold scalars. These methods include a direct construction of the extrinsic ambient space, a construction of global invariants of conformally compact minimal submanifolds of conformally compact Einstein manifolds via renormalized extrinsic curvature integrals, and the introduction of a large class of conformal submanifold scalars that are easily computed at minimal submanifolds of Einstein manifolds. As an application, we derive an explicit Gauss--Bonnet--Chern-type formula relating the renormalized area of a conformally compact $k$-dimensional minimal submanifold of a conformally compact Einstein manifold to its Euler characteristic and the integral of a conformal submanifold scalar of weight $-k$. As another application, we prove a rigidity result for conformally compact minimal submanifolds of conformally compact hyperbolic manifolds.