The integration of storage and renewable resources fundamentally alters resource-adequacy analysis. Because storage couples decisions across time, it invalidates the traditional reliability models that are based on time-independent capacity demand curves. Moreover, renewables introduce temporally correlated intermittency. To address this, we formulate the capacity procurement problem as a two-stage stochastic program, where the capacity decision is made in the first stage, while the expected unserved energy is evaluated by a second-stage dispatch problem that considers uncertainties such as generator failures via Markov chains, temporally correlated renewable output, and stochastic load. We implement the resulting stochastic capacity procurement (SCP) model on a New England system with 305 generators, including conventional, renewable, and storage units. Using the stochastic decomposition (SD) algorithm, we solve the SCP with up to 20,000 Monte Carlo samples, each representing a six-month trajectory of more than 4,300 hours of uncertainty across all units. We analyze the convergence behavior of SD and show that convergence for the stochastic program happens faster than reliable estimation of the reliability metrics, which require more samples than are used in typical stochastic programs. These results show that chronologically detailed Monte Carlo sampling can be integrated into capacity procurement optimization in a computationally tractable manner, enabling reliability evaluation with controlled statistical accuracy at realistic system scales.

Conventional Boltzmann--Gibbs statistical mechanics successfully describes systems with weak to moderate correlations, where the number of accessible configurations $W(N)$ grows exponentially with the number of degrees of freedom~$N$. However, this framework breaks down for systems with strong correlations or long-range interactions, for which the configuration space exhibits non-exponential growth. While numerous generalized entropies have been proposed to address this limitation, a coherent link to classical thermodynamic laws has remained elusive. Here, we propose group entropies as a unifying framework, defining universality classes of entropies through the asymptotic scaling of $W(N)$, each yielding an extensive entropy. We show that this approach provides the basis for a consistent thermodynamic formulation beyond the Boltzmann--Gibbs paradigm. In particular, by expressing these entropies in terms of thermodynamic state variables and taking the thermodynamic limit, we demonstrate their consistency with classical thermodynamics, in close analogy to the emergence of the Clausius entropy from the Boltzmann--Gibbs formalism. Focusing on the zeroth thermodynamic law, we identify the empirical temperature and, by using Carathéodory's formulation of the second law, we derive the associated absolute temperature. As an application of the thermodynamic framework obtained, we analyze black-hole thermodynamics using the group entropy class corresponding to stretched-exponential behavior of $W(N)$. In particular, we show that a hallmark property of black holes -- their negative specific heat -- emerges naturally within this framework while the entropy remains extensive. This result holds for the stretched-exponential entropies associated with both the Bekenstein--Hawking and Barrow entropy scalings.

The hydrogen envelope is the outermost layer of a DA white dwarf; it makes up the entirety of the stellar photosphere, and yet its typical extent is difficult to model theoretically and remains poorly observationally constrained. As a result, hydrogen envelope mass is a substantial source of systematic uncertainty in physical properties of white dwarf, including overall masses and cooling ages. In this work, we fit a Gaussian mixture model to gravitational redshifts from high-resolution spectroscopy, paired with radius measurements from Gaia BP/RP spectra, to measure the mass-radius relation for a sample of 468 white dwarfs. Our results are in excellent agreement with the predicted mass-radius relations of state-of-the-art evolutionary models, including those from the MESA Isochrones and Stellar Tracks (MIST) library. We find that mass-radius relations such as MIST which assume a thick and mass-dependent hydrogen envelope are preferred by the observed probability density function over models which assume a constant hydrogen envelope mass. Proper treatment of the evolution of white dwarf progenitors is thus important for accurately modeling the mass-radius relation. Our results indicate that gravitational redshift measurements of large samples of white dwarfs in wide binaries are promising probes of the hydrogen envelope masses of DA white dwarfs.

Mathematical modeling plays a vital role in epidemiology, offering insights into the spread and control of infectious diseases. The compartmental models developed by Kermack and McKendrick, particularly the SI (Susceptible-Infected) and SIR (Susceptible-Infected-Recovered) models, form the basis of many epidemic studies. While some simple cases permit analytical solutions, most real-world models require numerical methods such as Euler's method, the fourth-order Runge-Kutta (RK4) method, and Predictor-Corrector (P-C) methods. These methods are typically implemented in scientific computing software like Python, MATLAB, and R. However, the computational efficiency and run-time performance of these software tools in solving epidemiological models have not been comprehensively compared in the literature. This study addresses this gap by solving the SI and SIR models using Euler's method, RK4, and P-C methods in Python, MATLAB, and R. Execution times are recorded for each implementation to evaluate computational efficiency. Additionally, for the SI model, where an exact analytical solution exists, R2 values are computed to assess numerical accuracy. For the SIR model, a high-accuracy reference solution is obtained by solving the system using MATLAB's ODE45 solver, and the SIR solutions computed via the RK4 method in MATLAB are compared against this reference. The results provide a comparative perspective on the accuracy and run-time performance across different software and numerical methods, offering practical guidance for researchers and practitioners in selecting suitable tools for epidemic modeling.

The proliferation of IoT and V2X systems generates unprecedented sensitive data at the network edge, demanding privacy-preserving architectures that enable secure sharing without exposing raw information. Contemporary solutions face a fundamental privacy-efficiency-trust trilemma: achieving strong privacy guarantees, computational efficiency for resource-constrained devices, and decentralized trust simultaneously remains intractable with single-paradigm approaches. This survey systematically analyzes 75 technical papers (2007--2025) through a novel three-dimensional taxonomy classifying architectures into Decentralized Computation, Cryptography-based, and Distributed Ledger approaches. Temporal analysis reveals dramatic acceleration during 2024--2025, with 48% of all papers published in this period -- Decentralized Computation dominates at 44% of contributions and 59% of 2025 publications. Comprehensive Security Threat Mapping and Technology Maturity Assessment demonstrate that mature solutions occupy narrow design regions excelling in one or two dimensions while compromising others, conclusively validating the trilemma hypothesis. We identify emerging hybrid architectures combining complementary paradigms as the essential path forward. Critical challenges including security guarantee composition across layers, multi-layer coordination overhead minimization, and post-quantum security integration must be addressed for practical deployment in next-generation intelligent transportation systems and IoT ecosystems.

The quasi-Monte Carlo method is widely used in computational finance, whose efficiency strongly depends on the smoothness and effective dimension of the integrand. In this work, we investigate the combination of importance sampling and the active subspace method under the quasi-Monte Carlo framework and propose a three-step approach, referred to as the IS-AS-preintegration method, which sequentially applies importance sampling, active subspace, and preintegration. The proposed method is applied to the option pricing and sensitivity analysis problems in finance, and its performance is evaluated through extensive numerical experiments. The results demonstrate that the proposed method is highly competitive compared with existing popular methods. In particular, for out-of-the-money and deep out-of-the-money options, the proposed approach overcomes the limitations of the preintegration via active subspace method and achieves superior variance reduction, while maintaining comparable performance for other moneyness cases.

This paper addresses the estimation of a dynamic interaction network, a network of influence among individuals, under projected visual stimuli to quantify the influences of inter-individual interactions and external stimuli on collective behavior. Building upon our previously proposed network estimation model, which assumes a Boids-type model and employs a sparse regression framework to infer inter-individual influence networks from trajectory data, we extend the formulation by introducing a stimulus term. This enables the model to capture how individuals react to and propagate externally projected visual stimuli within the group. The resulting framework allows simultaneous estimation of inter-individual and stimulus-related interaction strengths. We also introduce entropy-based indices to capture the possible biases of individuals' influence. Our experiments with fish schools under projector-based visual stimuli demonstrate the effectiveness of the proposed indices in quantifying schooling behavior and identifying influential individuals within the group, serving as the basis for real-time, interpretable metrics of collective dynamics.

We provide a unified way to calculate the Gromov norm of the Kähler class of all (compact manifolds uniformized by) bounded symmetric domains. This was done for three classical domains by Domin and Toledo and for the general case by Clerc and Ørsted. Here, the calculation is much simplified by a combination of the ideas in Domin-Toledo and a work of Toledo, with the help of the Polydisc Theorem. The equality is achieved if and only if the triangle is ideal with three vertices on the Shilov boundary.

Hydrogel diffusiophoresis is the deformation of a hydrogel due to a solute gradient that leads to a gradient of pairwise interactions between the solute particles and the hydrogel polymers to trigger osmotic flux. Unlike typical osmosis, it occurs without any interface selectivity of the gel to the solute and can overcome the diffusive swelling without any structural modifications to the gel. We have recently shown this effect for linear deformations of a chemically responsive polyacrylic acid (PAA) hydrogel that releases ions upon arrival of a stimulus (acid), thus internally generating the solute gradient required for diffusiophoresis [Phys. Rev. Lett. 132, 208201 (2024)]. Here we develop a nonlinear poroelastic theory for large diffusiophoretic gel strains in two models: Model I considers deformations of a generic gel when an external solute gradient is imposed. In Model II, the gel generates the solute gradient internally, motivated by the coupled PAA gel, solute (copper), and stimulus (acid) system. In Model II, we investigate the nonlinear deformations for high stimulus concentrations or by changing the solute particle size to boost steric polymer-solute interactions, as well as under a stimulus flow through the gel driven by a pressure drop across the domain. Model I indicates that deformations can be stored while the stimulus gradient persists. Compared to the experimental strain rates in Katke [Phys. Rev. Lett. 132, 208201 (2024)], Model II demonstrates that varying the stimulus concentration can increase the strain rate up to four times, changing the solute particle size up to $\sim 25$ times, and imposed flow up to $\sim 40$ times. Our theory couples nonlinear poroelasticity, polymer-solute interactions, and reaction-transport dynamics to predict large and fast diffusiophoretic gel deformations, which may find applications in hydrogel-based soft robotics and drug delivery.

Irregular errors such as heteroscedasticity and nonnormality remain major challenges in linear modeling. These issues often lead to biased inference and unreliable measures of uncertainty. Classical remedies, such as robust standard errors and weighted least squares, only partially address the problem and may fail when heteroscedasticity interacts with skewness or nonlinear mean structures. To address this, we propose a two-stage cumulative distribution function-based (CDF-based) beta regression framework that models the full conditional distribution of the response. The approach first transforms the outcome using a smoothed empirical CDF and then fits a flexible beta regression, allowing heteroscedasticity and nonnormality to be handled naturally through the mean-precision structure of the beta distribution. Predictions are mapped back to the original scale via the empirical quantile function, which preserves interpretability. A comprehensive Monte Carlo study shows that the proposed method consistently achieves good distributional accuracy and well-calibrated prediction intervals compared with OLS, WLS, and GLS. Application to the concrete compressive strength dataset demonstrates its stability and practical advantages.

Static Application Security Testing (SAST) tools often suffer from high false positive rates, leading to alert fatigue that consumes valuable auditing resources. Recent efforts leveraging Large Language Models (LLMs) as filters offer limited improvements; however, these methods treat LLMs as passive, stateless classifiers, which lack project-wide context and the ability to learn from analyses to discover unknown, similar vulnerabilities. In this paper, we propose vEcho, a novel framework that transforms the LLM from a passive filter into a virtual security expert capable of learning, memory, and reasoning. vEcho equips its core reasoning engine with a robust developer tool suite for deep, context-aware verification. More importantly, we introduce a novel Echoic Vulnerability Propagation (EVP) mechanism. Driven by a Cognitive Memory Module that simulates human learning, EVP enables vEcho to learn from verified vulnerabilities and proactively infer unknown, analogous flaws, achieving a paradigm shift from passive verification to active discovery. Extensive experiments on the CWE-Bench-Java dataset demonstrate vEcho's dual advantages over the state-of-the-art baseline, IRIS. Specifically, vEcho achieves a 65% detection rate, marking a 41.8% relative improvement over IRIS's 45.83%. Crucially, it simultaneously addresses alert fatigue by reducing the false positive rate to 59.78%, a 28.3% relative reduction from IRIS's 84.82%. Furthermore, vEcho proactively identified 37 additional known vulnerabilities beyond the 120 documented in the dataset, and has discovered 51 novel 0-day vulnerabilities in open-source projects.

We present data from the ALMA Central Molecular Zone Exploration Survey (ACES) Large Program, which provides broad spectral-line and 3 mm continuum coverage of the Central Molecular Zone (CMZ) at a spatial resolution of 0.1 pc. The survey delivers homogeneous, wide-field mosaics that enable direct comparisons of the physical and chemical conditions across diverse environments in the Galactic center. In this data release paper, we present the CS(2-1), SO(2_3-1_2), CH3CHO(5_1,4-4_1,3), HC3N(11-10), and H40a lines observed simultaneously within two broad spectral windows. These lines reveal pronounced spatial and chemical variations across the CMZ, tracing distinct components of molecular gas, shock-affected regions, and ionized structures. The high angular resolution and multi-line capability of the ACES dataset make it a powerful resource for future studies of gas dynamics, star formation activity, and the physical connection between the CMZ and Sgr A*.

Given a graph $F$, the expansion $F^{(r)}$ of $F$ is defined as the $r$-uniform hypergraph obtained from $F$ by adding a set of $(r-2)$ distinct new vertices to each edge of $F$. In this paper, we investigate spectral stability results for hypergraphs and their applications.We first establish a spectral stability property: for any $r$-uniform hypergraph containing no copy of the expansion $F^{(r)}$ of a $(k+1)$-chromatic graph $F$, if its $p$-spectral is close to the extremal value, then the hypergraph is structurally close to $T_r(n, k)$, the complete $k$-partite $r$-uniform hypergraph on $n$ vertices where sizes of any two parts differ by at most one.Using this spectral stability result, we determine the unique extremal hypergraph that maximizes the $p$-spectral radius among all $n$-vertex $r$-uniform hypergraphs without $t$ vertex-disjoint copies of the expansion $K_{k+1}^{(r)}$ of $K_{k+1}$. We prove that this extremal hypergraph is isomorphic to $K_{t-1}^{r} \,\vee\, T_r(n-t+1, k)$, the join of the complete $r$-uniform hypergraph $K_{t-1}^{r}$ and $T_r(n-t+1, k)$.As a corollary, we show that $K_{t-1}^{r} \,\vee\, T_r(n-t+1, k)$ is the unique extremal hypergraph for $tK_{k+1}^{(r)}$, which extends a result of Pikhurko [J. Combin. Theory Ser. B, 103 (2013) 220--225] for expanded complete graphs.

This manuscript describes a radiation-hardened current-mode delta-sigma ADC fabricated in a standard 130 nm CMOS technology and qualified for total ionizing doses up to 100 Mrad. The operational signal range achieved with a 100 s integration window exceeds 200 dB. The converter is designed for beam loss monitoring applications in high-energy physics, where it must handle input currents spanning nine decades, from 1 mA down to 1 pA, while providing a fast 10 us response time for machine protection. To meet these conflicting requirements, the architecture exploits the inherent trade-off between resolution and acquisition time provided by delta-sigma conversion: a first-order architecture, sampling at 20 MHz, delivers 11-bit effective resolution within the critical 10 us window for critical currents around 1 mA. Integration times above 10 s enable the sub-picoampere resolution required for precise beam alignment and background monitoring. The chip integrates two independent channels, consumes 25 mW from a 1.2 V supply, and relies on radiation-hardening techniques such as triple-redundant digital logic, custom ESD protections, and manual enclosed layout for critical analog transistors. Post-irradiation measurements up to 100 Mrad show no significant performance degradation, and the uncalibrated integral nonlinearity remains within [+4, -5] LSBs over the 1 mA to 5 uA range. The converter's flexibility and radiation tolerance make it suitable not only for the HL-LHC beam loss monitoring upgrade but also for other precision current measurement applications in harsh environments.

We present an investigation of the full width at half maximum (FWHM, or γ) of absorption features of Type Ia supernova (SNe Ia). We found that, the average value of FWHM can be well predicted with the rest wavelength (λ). The velocity also plays an important role, as objects with a higher velocity tend to have a larger FWHM. Temperature may be the third factor, as we found that, at the same velocity (but different phases), a normal-velocity (NV) object tends to have a larger FWHM than high-velocity (HV) object. Also, 1991T/1999aa-like objects that are believed to have relatively high temperatures show the largest FWHMs if compared at the same velocity. Generally speaking, FWHM evolves very slowly with time and shows no correlation with Δm15, but 1991T/1999aa-like objects are characterized by relatively fast decreasing FWHM. On the other hand, we found that, objects with relatively small FWHMs shows a tighter correlation between absorption depth (A) and Δm15, possibly a sign of higher degree of homogeneity. We also found that A/γ of Si II λ5972 has a strong correlation with Δm15, and more importantly, a relatively slow time evolution, making it a useful luminosity estimator even in the absence of phase information.

Gauge fixing is an essential step in lattice QCD calculations, particularly for studying gauge-dependent observables. Traditional iterative algorithms are computationally expensive and often suffer from critical slowing down and scaling bottlenecks on large lattices. We present a novel machine learning framework for lattice gauge fixing, where Wilson lines are utilized to construct gauge transformation matrices within a convolutional neural network. The model parameters are optimized via backpropagation, and we introduce a hybrid strategy that combines a neural-network-based transformation with subsequent iterative methods. Preliminary tests on SU(3) gauge theory ensembles for Coulomb gauge demonstrate the potential of this approach to improve the efficiency of lattice gauge fixing. Furthermore, we show that the model exhibits lattice size transferability, where parameters optimized on smaller lattices remain effective for larger volumes without additional training. This framework provides a scalable path toward mitigating critical slowing down in high-precision gauge fixing.

Moiré network formation in graphene bilayers breaks stacking symmetry, giving rise to domain walls that host topologically protected one-dimensional states. Here we show that these systems undergo an additional symmetry breaking at the level of the domain-wall network geometry, leading to the spontaneous emergence of chiral network configurations that are not determined by topology alone. Using atomistic structural relaxation and electronic-structure calculations, we show that TDW networks adopt chiral geometries through lattice relaxation. Via developing a comprehensive phase diagram defined by strain and interlayer flexibility, we discover three equilibrium network morphologies: straight, mono-chiral, and dual-chiral. Chiral networks arise from the global minimization of TDW energy under moiré geometric constraints. Tight-binding calculations show that straight networks host junction-centred states, whereas chiral networks shift spectral weight toward asymmetric edge modes. While topologically protected states naturally emerge at AB/BA domain boundaries in moiré bilayers, we demonstrated that the localization of boundary states is network-symmetry dependent. Our results show that symmetry breaking at both the stacking and network levels provides a new way to understand and control low-energy electronic states in moiré bilayers.

Clustering techniques offer a powerful framework for analyzing complex flow dynamics and reducing computational costs in large-scale simulations. In this work, we propose a novel clustering-based approach using Vector Quantization Principal Component Analysis (VQPCA) to identify structural sensitivity zones, namely the regions where the fluid flow is more receptive to changes. To the authors knowledge, this is the first application of VQPCA to a fluid dynamics problem for the identification of flow patterns and dynamically relevant regions. As a fully data-driven technique, it does not rely on adjoint methods; therefore, this approach has the advantage of having low computational cost, since it depends exclusively on data from the direct problem. The VQPCA technique demonstrates its ability to extract dominant flow features by clustering the flow field into regions characterized by their intrinsic dynamics. To assess the validity of this method, it is used to investigate the wake behind a circular cylinder, revealing similarities to previously established structural sensitivity regions. The robustness of the approach is further assessed through validation and calibration in different operating conditions in this flow scenario. As an extension of the analysis, we address the complex dynamics of two planar synthetic jets, where the clustering insights can lead to develop flow control strategies. These results highlight the potential of clustering-based methods as practical and effective tools to analyze and optimize fluid flows.

We prove the following generalization of a well-known result of Duffin and Schaeffer: For any given countable sets $Y \subset\mathbb{R}$ and $Z\subset\mathbb{R}\setminus\operatorname{span}_\mathbb{Q}(\{1\}\cup Y)$, there exist functions $ψ$ such that the set of inhomogeneously $ψ$-approximable numbers has zero measure or full measure, according as the inhomogeneous parameter lies in $Y$ or $Z$. The proof uses an analogue of residue systems where the residues can take arbitrary real values, and it also requires information about the distribution of primes lying in Bohr sets. We extend a theorem of Rogers to the more general real residues setting, and we extend Dirichlet's theorem for prime numbers lying in arithmetic progressions to prime numbers lying in Bohr sets. We also prove that circle rotations equidistribute when sampled along such primes, provided the rotation angle is rationally independent of the Bohr set parameter, generalizing a theorem of Vinogradov. An appendix by Manuel Hauke answers a combinatorial question that is posed in the introduction.

We study when a density-matching Kohn--Sham (KS) description can reproduce a many-body Berry phase in a correlated insulator, despite the fact that geometric phases are functionals of the wave function. Focusing on the one-dimensional SSH--Hubbard chain on a ring as a controlled interacting topological model, we introduce a $U(1)$ twist $θ$ (flux insertion). The many-body ground state along the full twist cycle is computed by the density-matrix renormalization group (DMRG), while the onsite interaction $U$ is tuned from the noninteracting to the strong-coupling regime. At half filling in the inversion-symmetric gapped regime, our DMRG calculations show that the density remains constant within numerical accuracy over the entire $(θ,U)$ range studied. Thus, the density has no dependence on either the flux $θ$ or the interaction strength $U$. Accordingly, the symmetry-preserving density constraint collapses the KS reference to an SSH-type quadratic representative with $U$-independent geometric diagnostics. Nevertheless, the many-body wave function exhibits a nontrivial geometric response: the quantum metric associated with the $θ$-parametrized ground-state manifold depends on $θ$ at intermediate $U$ and is strongly suppressed at large $U$, consistent with the charge fluctuation freezing. Intriguingly, the KS and many-body Berry phases coincide throughout the gapped regime as $U$ is tuned from weak to strong coupling. We show that this agreement is best understood as symmetry-enforced $\mathbb{Z}_2$ sector matching, rather than as evidence that the density encodes the many-body Berry connection.

We verify the local analogue of Jiang's conjecture for the upper bound of the geometric wavefront sets of Arthur type representations of split classical $p$-adic groups with $p\gg 0$, under a certain condition. As a consequence, we also obtain the upper bound conjecture of Kim and the second author, and Hazeltine--Liu--Lo--Shahidi, under the same assumptions. The proof uses Waldspurger's work on the endoscopic transfer supplemented by results of Konno and Varma, as well as the wavefront set computations in the unipotent case by Mason-Brown--Okada and the second author.

Semantic communication (SemCom) redefines wireless communication from reproducing symbols to transmitting task-relevant semantics. However, this AI-native architecture also introduces new vulnerabilities, as semantic failures may arise from adversarial perturbations to models, corrupted training data, desynchronized priors, or misaligned inference even when lower-layer transmission reliability and cryptographic protection remain intact. This survey provides a defense-centered and system-oriented synthesis of security in SemCom via AI defense. We analyze AI-centric threat models by consolidating existing studies and organizing attack surfaces across model-level, channel-realizable, knowledge-based, and networked inference vectors. Building on this foundation, we present a structured taxonomy of defense strategies organized by where semantic integrity can be compromised in SemCom systems despite correct symbol delivery, spanning semantic encoding, wireless transmission, knowledge integrity, and coordination among multiple agents. These categories correspond to distinct security failure modes, including representation fragility, channel-realizable manipulation, semantic prior poisoning or desynchronization, and adversarial propagation through distributed inference. We also examine security utility operating envelopes that capture tradeoffs among semantic fidelity, robustness, latency, and energy under realistic constraints, survey evaluation frameworks and representative applications, and identify open challenges in cross-layer composition and deployment-time certification. Overall, this survey offers a unified system-level perspective that enables readers to understand major threat and defense mechanisms in AI-native SemCom systems and to leverage emerging security techniques in the design and deployment of robust SemCom architectures for next-generation intelligent networks.

Numerical simulations of contaminant dispersion, as after a gas leakage incident on a chemical plant, can provide valuable insights for both emergency response and preparedness. Simulation approaches combine incompressible Navier-Stokes (INS) equations with advection-diffusion (AD) processes to model wind and concentration field. However, the computational cost of such high-fidelity simulations increases rapidly for complex geometries like urban environments, making them unfeasible in time-critical or multi-query "what-if" scenarios. Therefore, this study focuses on the application of model order reduction (MOR) techniques enabling fast yet accurate predictions. To this end, a thorough comparison of intrusive and non-intrusive MOR methods is performed for the computationally more demanding parametric INS problem with varying wind velocities. Based on these insights, a non-intrusive reduced-order model (ROM) is constructed accounting for both wind velocity and direction. The study is conducted on a two-dimensional domain derived from real-world building footprints, preserving key features for analyzing the dispersion of, for instance, denser contaminants. The resulting ROM enables faster than real-time predictions of spatio-temporal contaminant dispersion from an instantaneous source under varying wind conditions. This capability allows assessing wind measurement uncertainties through a Monte Carlo analysis. To demonstrate the practical applicability, an interactive dashboard provides intuitive access to simulation results.

The proportion of edges in a Gaussian graphical model (GGM) characterizes the complexity of its conditional dependence structure. Since edge presence corresponds to a nonzero entry of the precision matrix, estimation of this proportion can be formulated as a large-scale multiple testing problem. We propose an estimator that combines p-values from simultaneous edge-wise tests, conducted under false discovery rate control, with Storey's estimator of the proportion of true null hypotheses. We establish weak dependence conditions on the precision matrix under which the empirical cumulative distribution function of the p-values converges to its population counterpart. These conditions cover high-dimensional regimes, including those arising in genetic association studies. Under such dependence, we characterize the asymptotic bias of the Schweder--Spjøtvoll estimator, showing that it is upward biased and thus slightly underestimates the true edge proportion. Simulation studies across a variety of models confirm accurate recovery of graph complexity.

We prove concentration bounds for random Euclidean combinatorial optimization problems with $p$--costs. For bipartite matching and for the (mono- and bi-partite) traveling salesperson problem in dimension $d\ge 3$, we obtain concentration at the natural energy scale $n^{1-p/d}$ for $1\le p<d^2/2$. Our method combines a Poincaré inequality with a robust geometric mechanism providing uniform bounds on the edges of optimizers. We also formulate a conjectural $p\!\to\!q$ transfer principle for the $p$--optimal matching which, if true, would extend the concentration range to all $p\ge 1$.

The VMAF (video multi-method assessment fusion) metric for image and video coding recently gained more and more popularity as it is supposed to have a high correlation with human perception. This makes training and particularly fine-tuning of machine-learned codecs on this metric interesting. However, VMAF is shown to be attackable in a way that, e.g., unsharpening an image can lead to a gain in VMAF quality while decreasing the quality in human perception. A particular version of VMAF called VMAF NEG has been designed to be more robust against such attacks and therefore it should be more useful for fine-tuning of codecs. In this paper, our contributions are threefold. First, we identify and analyze the still existing vulnerability of VMAF NEG towards attacks, particulary towards the attack that consists in employing VMAF NEG for image codec fine-tuning. Second, to benefit from VMAF NEG's high correlation with human perception, we propose a robust loss including VMAF NEG for fine-tuning either the encoder or the decoder. Third, we support our quantitative objective results by providing perceptive impressions of some image examples.

We study visibility from a fixed point in the presence of a Poisson process of $λ$--geodesic hyperplanes in a $d$-dimensional hyperbolic space. The family of $λ$--geodesic hyperplanes interpolates between totally geodesic hyperplanes and horospheres. Our main result establishes a universality principle for this model: we prove that the fundamental visibility properties are invariant with respect to the parameter $λ\in[0,1]$. Namely, there is a critical intensity $γ_{\mathrm{crit}}>0$ such that the visible region is unbounded with positive probability for $γ< γ_{\mathrm{crit}}$ and almost surely bounded for $γ> γ_{\mathrm{crit}}$. For $d=2$ we establish almost sure boundedness also at criticality. The value for $γ_{\mathrm{crit}}$ is explicit and does not depend on $λ$. In the bounded phase, we show that the mean visible volume is identical with the known formula for $λ=0$. The key integral-geometric step is an explicit computation showing that the measure of $λ$-geodesic hyperplanes hitting a geodesic segment is a linear function of the length of the segment, independent of~$λ$.

In this work, we numerically verify the Jarzynski equality and Crook fluctuation theorem for a Brownian particle diffusing in a heterogeneous thermal bath and hence having a non-Gaussian position distribution. We use the diffusing-diffusivity model to take the account of heterogeneity of the thermal bath where the mobility is considered as a fluctuating quantity. The Brownian particle is confined by a time-dependent harmonic potential. By changing the stiffness coefficient, we perform an isothermal process. We use the stochastic thermodynamics framework to calculate the work. We find that the Jarzynski equality and the Crook fluctuation theorem are convincingly satisfied for a non-Gaussion system. We also find that the work distribution is non-Gaussian for diffusing-diffusivity system even at a larger process time.

We extend the first order dissipative relativistic hydrodynamics model of Bemfica-Disconzi-Noronha- Kovtun (BDNK) in order to include the charge number current in full first order expansion with out-of-equilibrium contribution proportional to the evolution equation of the ideal fluid. We obtain a fully second order system of partial differential equation (PDE) that can be casted in a fully conservative way. We analyze the hyperbolicity of this model coupled to Einstein field equations using a newly developed technique that allows for hyperbolicity studies without explicit first order reduction. Furthermore, we identify a frame choice where our formulation is causal, stable and with positive entropy generation for a wide range of equations of state (EoS). Our analysis shows that the inclusion of an out-of-equilibrium correction to the charge current, plays an important role in guaranteeing the strong hyperbolicity and, therefore, the well-posedness of the system. If such correction is not applied, an extra frame restriction must be added to the present in the literature in order to obtain a strongly hyperbolic system.

We analyse CMB constraints on stable networks of cosmic strings and domain walls using for the first time full Planck 2018 data together with BICEP/Keck 2018 $B$-mode measurements. The defect-induced anisotropies are computed using the Unconnected Segment Model for Nambu-Goto and Abelian-Higgs strings, as well as for stable domain walls, and included in a full Markov Chain Monte Carlo analysis jointly varying all $Λ$CDM parameters, the tensor-to-scalar ratio, and the string/domain wall tension. No statistically significant evidence for defects is found, although we observe a mild preference for non-zero cosmic string tension. Our results improve previous constraints on the defect power spectrum by up to a factor of two. In the particular case of strings, the improvement is driven by the $B$-mode data, and is especially pronounced for Abelian-Higgs strings. We also present forecasts for the Simons Observatory and the LiteBIRD satellite: the former will improve string tension constraints by about a factor of three, while the latter those on the domain wall tension by about a factor of ten. Finally, we assess the impact of Nambu-Goto string loops on CMB anisotropies in light of both current and future observations.