We study forecasting of the realized covariation in electricity markets. The realized covariation in this context is a matrix-valued representation of the latent infinite-dimensional covariance operator and a parsimonious matrix-HAR type model is constructed to facilitate estimation. We test the model on one-week ahead forecasts of the weekly realized covariation and find that the inclusion of longer time horizons and renewable generation information adds important predictive power. We also investigate the prediction of risk premia in electricity forward markets and find that our variance forecasts provide substantially improved forecasts of spread risk premia compared to standard methods relying on backward looking volatility.

We prove a conditional Schoen-type Harnack inequality for positive weak solutions of the critical $p$-Laplace equation $$ -Δ_p u=g(u),\qquad 1<p<n, $$ under a global critical Sobolev growth assumption and the monotonicity condition that $s^{-(p^*-1)}g(s)$ is nonincreasing. The result is conditional on two inputs, the classification of bounded positive entire blow-up limits as Aubin--Talenti $p$-bubbles and a preliminary singular-rate upper control on the normalized necks. Under these two hypotheses, solutions in $B_{3R}$ satisfy $$ \Big(\sup_{B_R}u\Big)\Big(\inf_{B_{2R}}u\Big)^{p-1} \le C R^{p-n}. $$ The main point is a Pohozaev-neck argument which upgrades the preliminary singular decay rate $|x|^{-(n-p)/p}$ to the sharp $p$-harmonic fundamental rate $|x|^{-(n-p)/(p-1)}$. The argument replaces the Kelvin-transform and moving-sphere methods available in the conformally invariant semilinear case $p=2$, but unavailable for the general $p$-Laplacian.

Ultrastable lasers play a key role in optical frequency metrology, setting measurement speed and ultimately impacting both stability and accuracy of optical frequency standards. Here we demonstrate laser fractional frequency instability at ${4}\times10^{-17}$ and laser frequency linewidth of $12\,$mHz full width at half maximum, employing a 68 cm long optical reference cavity operating at room temperature. To the best of our knowledge, both frequency instability and linewidth are the lowest ever reported for a room temperature system. This work highlights that state-of-the-art frequency stability and spectral purity are achievable at room temperature, making them accessible to a broader range of users.

Low-Reynolds-number microswimmers have recently attracted much interest for their ubiquity in biology and their applications in biotechnology and medicine. However, a key obstacle for the design and deployment of artificial microswimmers lies in their autonomy: to successfully perform tasks in any real-world scenario, these swimmers need to be able to interact with and adapt to their environment without external control. Here, we train a simple two-dimensional model microswimmer (consisting of three-bead) to learn autonomous swimming strategies via Reinforcement Learning, focusing on neuroevolution techniques to derive controller architectures with minimal complexity. We identify five different, characteristic swimming gaits: three of these gaits lead to directed locomotion with varying grades of efficiency and two gaits result in a rotational, inefficient movement. Remarkably, all of these gaits can be achieved by very simple neural networks (with less than ten nodes and weights), showing that low-Reynolds-number swimming can be achieved efficiently and robustly while requiring only minimal computational power. These results are of particular interest to the experimental design of artificial microswimmers and may have implications for modeling biological microorganisms such as Chlamydomonas reinhardtii.

Uncertainty quantification in neural networks prediction is a main issue for usual applications. Our approach seeks at reducing computation costs by directly evaluating uncertainty using PDE's information on the asymptotic variance, rather than the deep ensemble method which may be seen as a Monte Carlo estimation of the prediction, requiring the training of multiple networks. We thus study the law of the limiting process describing the random fluctuations around the mean-field limit of wide two-layer neural networks trained by stochastic gradient descent in a weak-noise regime. Building on a recent trajectorial central limit theorem, in which this limit is characterized as the weak solution of a linear stochastic evolution equation, we identify its law explicitly. More precisely, we show that it is a centered Gaussian process in the dual of a weighted Sobolev space, and we derive a closed covariance representation for the finite-dimensional distributions obtained by testing it against smooth functions. This covariance is expressed through the solution of a backward transport equation with a nonlocal source term, whose coefficients are driven by the mean-field trajectory. As a consequence, by testing against the activation function at a fixed input, we obtain an expression for the limiting variance of the corresponding network-output fluctuations. We illustrate this result numerically on a one-dimensional regression example.

Understanding the cellular composition of complex tissues, such as tumors, is a key challenge in biology and medicine. A common approach, known as deconvolution, aims to estimate the cellular composition from bulk molecular measurements. With the growing availability of multiple types of molecular data, it is often assumed that combining data sources should improve deconvolution performance. Here, we present HADACA3, a community-driven benchmark designed to evaluate this assumption. We conducted a four-day collaborative competition followed by a large-scale computational benchmark, testing more than 250,000 analysis pipelines across nine datasets with matched DNA methylation (DNAm) and RNA profiles, representing a wide range of biological and experimental conditions. Our framework jointly evaluates the impact of preprocessing, feature selection, modeling, and integration strategies. We find that DNAm alone achieves the highest median performance across datasets, making it the most stable and reliable single-modality approach. However, multi-omics integration strategies can regularly achieve higher top performance in specific datasets and pipeline configurations. Among the tested strategies, late integration based on error-weighted averaging provides a strong and reliable baseline, while non-linear early integration methods, such as optimal transport, show promising results on real biological datasets. Overall, our results show that multi-omics integration does not systematically improve average performance over DNAm alone, but can improve best-case performance in specific settings. This highlights a trade-off between robustness and peak performance, and emphasizes the importance of aligning integration strategies with the statistical properties of the data. All data, code, and evaluation tools are publicly available to support reproducible research and future method development.

The present notes are based on a series of lectures prepared for an introductory eight-class course on the modern framework of the off-shell double copy. The course was held from April 16 to May 4, 2026, at Universidad de Buenos Aires (UBA). These lectures, aimed at PhD and master's students, are self-contained and require only a basic knowledge of classical field theory. The main goal is to review the fundamental concepts of gauge and gravitational theories in order to explore the off-shell frameworks of the single and double copy. In the final part of the course, we explore modern approaches to reinterpreting the single and double copy within T-duality-invariant frameworks.

We consider the inverse medium scattering problem for the Helmholtz equation in two dimensions, i.e., the task to recover a compactly supported penetrable two-dimensional scatterer from full knowledge of the associated far field data or, equivalently, the far field operator. Although this problem is uniquely solvable, it is severely ill-posed and nonlinear. In the regime of weak scattering, the Born approximation yields a linearized relation between the contrast and the far field data, thus overcoming the second difficulty. This linear setting allows to build on recent work on linearized electrical impedance tomography, which relies on triangular Zernike decompositions, to derive an explicit reconstruction formula that expresses the expansion coefficients of the contrast in terms of those of the far field data. By choosing the expansion functions appropriately, the resulting system matrix decouples into separate (infinite) triangular systems for the spatial angular frequencies in the contrast. Consequently, each of these systems can be solved independently by performing forward substitutions. Our numerical experiments indicate that this approach, combined with an adequate regularization method, remains effective even when applied to full nonlinear far field data beyond the Born regime.

Since the initial disclosure of the extraordinary piezoelectric coefficients of Potassium sodium niobate (KNN) in near-equimolar bulk ceramics, its development trajectory has resembled a rollercoaster, with its integration into microelectronics severely lagging due to thermodynamic stability issues and poor planar process compatibility. In this work, we revisit the bulk-derived phase diagram for the specific case of thin films integrated on silicon. By systematically investigating Mn-doped K1-xNaxNbO3 films grown on 8-inch wafers, we demonstrate that the optimal stoichiometry for thin films fundamentally diverges from the bulk equimolar standard. A Na-rich composition (> 70 at.%) is required to overcome substrate-induced constraints, effectively suppressing pyrochlore formation and chemical phase segregation while promoting dense columnar growth with a complete (001) out-of-plane polar orientation. Consequently, Na-rich films deliver outstanding functional properties, reaching remanent polarizations up to 14 uC cm-2, with piezoelectric coefficients of d33f= 79 pm/V and e31f = 10 C/m2. Supported by Density Functional Theory simulations, we correlate this enhancement with improved stability and a strain-driven structural reorientation toward a lower-symmetry monoclinic phase with tilted polarization. By redefining the phase engineering rules for wafer-scale thin films, our results establish a clear route toward KNN integration in microsystems.

A metric graph with a mechanical Hamiltonian on each edge does not, by itself, define a deterministic classical motion through a branching vertex: conservation of energy fixes only the outgoing speed, not the outgoing edge-end. We study the deterministic problem obtained after this missing vertex datum is supplied. On each edge $e$, with coordinate $q\in[0,\ell_e]$, the Hamiltonian is $H_e(q,p)=p^2/2+V_e(q)$, where $V$is continuous on the graph and $C^2$ on every edge. At each vertex we prescribe an energy-preserving Borel isomorphism from incoming to outgoing nonzero boundary covectors. The resulting phase space is the measurable quotient that identifies each incoming boundary covector with its prescribed outgoing one. After excluding the finitely many energy levels $V(v)$, the edgewise Hamilton equations and the vertex laws concatenate to a global one-parameter group of bimeasurable transformations. The group preserves energy and the quotient measure induced by the edgewise Liouville measures $dq\,dp$. The proof uses no smooth symplectic structure on the quotient; the invariance follows from ordinary edgewise Liouville invariance, a uniform no-Zeno estimate on compact regular energy windows, and preservation of the transverse Liouville flux $r\,dr$ by the speedwise vertex permutations. If the vertex laws are compatible with momentum reversal, then the quotient dynamics is reversible. On regular energy surfaces satisfying the usual regular-value condition, the induced time-parametrization measure is invariant as well.

Understanding when and how galaxies quench their star formation is crucial for understanding the dominant physical processes at play. The spectral energy distribution (SED) of galaxies encodes significant information on their past histories: the relative importance of different physical processes influences the observed distribution of SED shapes in the galaxy population. We use a simulation based inference (SBI) approach to directly constrain the distribution of formation times, quenching times and quenching timescales within the massive galaxy population at z >~ 2 from their broad band photometric colour distribution at 1.7<z<2. We demonstrate that a simple distribution of double power-law star formation histories accurately fits the distribution of SED shapes of galaxies with log10(M*/Msol)>10.3. We measure a quenched galaxy fraction of 0.24+/-0.02, with the number density of quenched galaxies rising rapidly 2.5Gyr after the Big Bang (z<~2.6). Galaxies must quench rapidly to achieve the precise bimodal colour distribution: defining the quenching timescale as the time from peak star formation rate (SFR_peak) -> 0.5xSFR_peak, the quenching timescale distribution has a mode at 97_{-25}^{+31}Myr, a median of 182+/-16Myr and a tail to ~700Myr. To achieve full quiescence takes a median time of ~400Myr. Comparing to direct number density measurements of quenched galaxies at z>2 the combination of recent and rapid quenching inferred from the fossil record suggests a substantial rejuvenation and/or merger rate for quenched galaxies observed directly at z>3.5.

This article develops a rigorous Lagrangian formulation of variational calculus for minimal surfaces, using extensively the concept of pullback covariant derivative. It is shown, in particular, using a geometric argument that all tangential variations vanish. First and second normal variations are then derived.

Fixed-ansatz Variational Quantum Eigensolvers (VQE), such as the Unitary Coupled Cluster with Singles and Doubles (UCCSD) framework, frequently suffer from severe initialization paralyzation and zero-gradient traps when evaluated using the non-local Bravyi-Kitaev (BK) fermion-to-qubit mapping. In this work, we systematically demonstrate how the Adaptive Derivative-Assembled Pseudo-Trotter (ADAPT-VQE) framework shatters these structural limitations across three distinct electronic and geometric molecular pillars: Lithium Hydride ($\text{LiH}$), Hydrogen Fluoride ($\text{HF}$), and Water ($\text{H}_2\text{O}$), under heavily stretched or asymmetric multi-reference configurations. While conventional UCCSD-VQE flatlines completely at a zero energy shift ($0.000000$~Ha) due to global phase cancellations inherent to the BK tree structures, our dynamic ADAPT-VQE loop successfully isolates the dominant symmetry-breaking operators using analytical commutator gradients. To bypass the severe $\mathcal{O}(N^3)$ computational bottlenecks of dense matrix exponentiation and Singular Value Decomposition on larger registers, we implement a highly optimized, vector-based Taylor series expansion state-evolution engine. Our numerical results show that the accelerated ADAPT-VQE framework achieves instant, exact Full Configuration Interaction (FCI) convergence within the very first macro-cycle across all three molecular systems, maintaining absolute numerical stability up to a 12-qubit register space. This study establishes a robust, hardware-efficient path for simulating strongly correlated, highly polarized triatomic chemical environments on near-term local architectures.

We investigate the strong identity condition (SIC) for almost-canonically seminormed rings, a class of topological graded rings that includes enveloping algebras of vertex operator algebras. This condition was introduced in the algebro-geometric theory of conformal blocks, where it governs the smoothing of nodal curves. To understand the representation-theoretic meaning of SIC, we develop the representation theory of almost-canonically seminormed rings, including Zhu-type algebras, induced modules, rationality conditions, tensor product compatibility, and an end formula for the mode transition algebra. Our main result characterizes the strong identity condition in terms of orthogonal expansions, projectivity of canonical modules, and Morita-type equivalences induced by Zhu-type algebras. As an application, we show that for vertex operator algebras of CFT type, the smoothing property is equivalent to the Zhu algebra inducing a Morita-type equivalence with the category of admissible modules. Consequently, the strong identity condition identifies the precise representation-theoretic obstruction to extending algebraic smoothing beyond the semisimple setting. We further illustrate the theory through explicit examples, including the Weyl algebra and several irrational vertex operator algebras where the strong identity condition fails.

We develop a concept for the numerical treatment of shape optimization problems based on the combination of phase field and sharp interface methods. On the one hand, phase field methods are very well suited to numerically determine the shape, size and topology of a sought domain, but on the other hand they have problems to sharpen out domains where they e.g. should develop corners. However, this is the strength of a sharp-interface approach developed in our group, which provides shape updates in the Lipschitz topology. This leads to a two-stage process that first determines an optimized shape using the phase field method. The resulting domain is the starting solution for the sharp interface shape optimization method. Both methods are discretized with the finite element method. The starting mesh for the sharp method is constructed from the finite element mesh of the optimal phase field solution using its properly post processed zero-level set. We describe this construction process in detail and investigate the performance of our method on a selection of test problems from the literature and from applications.

We propose a novel search strategy for heavy Majorana neutrinos based on the lepton-number-violating process $μ^{-}p \to jN \to j(\ell^{+}W^{-})$ at future muon-proton ($μp$) colliders equipped with 1 TeV muon beams and 7 TeV proton beams, yielding a center-of-mass energy of approximately 5.3 TeV. For heavy neutrinos with masses in the range $200~\text{GeV} \lesssim m_N \lesssim 1000~\text{GeV}$, this analysis targets the decay chain $N \to \ell^{+}W^{-} \to \ell^{+}jj$, producing a characteristic final state consisting of one charged lepton and three well-resolved jets. For TeV-scale Majorana neutrinos, the $W$ boson is highly boosted, such that its hadronic decay products coalesce into a prominent fat-jet ($J$) signature. We conduct comprehensive signal and background analyses that account for realistic detector effects to assess the search sensitivity. We derive the projected $2σ$ exclusion limits on the neutrino mixing parameter $|V_{\ell N}|^2$ based on two typical integrated luminosity scenarios of $100~\text{fb}^{-1}$ and $1~\text{ab}^{-1}$. The results demonstrate that the proposed search strategy can achieve constraints substantially superior to the existing bounds from the LHC and other high-energy colliders. This study demonstrates that future $μp$ colliders can provide competitive sensitivity for probing heavy Majorana neutrinos over the mass range $200~\text{GeV} \leq m_N \leq 3000~\text{GeV}$.

Large Language Models (LLMs) are increasingly employed as proxies for human behavior in computational social science. However, their tendency to internalize biases from training data raises concerns about their reliability in politically sensitive domains, specifically in regard to their susceptibility to persuasive language. In this work, we examine whether LLMs endorse persuasion-infused messages and whether partisan persona prompting modulates such endorsement. We evaluate six LLMs from different geographic regions on content annotated with persuasion techniques drawn from real-world media sources, measuring the likelihood of endorsement using a five-point Likert scale. The models are prompted as either a neutral social media user or as a user with left- or right-leaning political views. Results show that without political conditioning, LLMs generally do not endorse messages containing persuasion techniques, though model-level differences emerge, and that partisan persona prompting increases polarization of endorsement, particularly for persuasion-infused content. Endorsement further varies by persuasion technique and topic. These findings raise concerns about agentic LLM deployments in politically sensitive environments and complicate their use as reliable simulators of human political cognition.

We present efforts to identify, characterize, and mitigate narrow spectral artifacts in LIGO detector data during the fourth LIGO-Virgo-KAGRA observing run. Narrow spectral artifacts in gravitational-wave detectors are non-astrophysical noise sources that can degrade searches for narrowband persistent gravitational waves. Identifying and, where possible, mitigating these noise sources is one of the core efforts of the LIGO Detector Characterization group. Key software tools have been updated and new tools deployed for the fourth LIGO-Virgo-KAGRA observing run to facilitate investigations and data monitoring. We discuss these tool upgrades, and present several identified narrowband artifacts that have been successfully investigated and mitigated in LIGO data. Regardless of whether artifacts are mitigated or not, narrowband persistent gravitational-wave searches require information on which frequency bands contain non-astrophysical artifacts. Minimizing the number of bands containing non-astrophysical artifacts is essential to maximize the potential for discovery of a new class of gravitational-wave signals.

In this paper, we re-examine the well-known question of why electric charges exist only in quantized portions. In this context, we revisit the motion of a charged particle in a field-free region around a current-carrying solenoid. Solving the corresponding Schrödinger equation leads to a simultaneous quantization condition for the magnetic flux and the electric charge. We also demonstrate the Lorentz invariance of this condition by showing that the magnetic flux behaves like a pseudoscalar under Lorentz transformations.

Understanding the processes behind the evolution of complex networks is a key objective in network science. An effective framework for tackling this challenge is network model selection, which involves finding the model from a set of candidates that best explains a given network. This book is a systematic review of methods for this purpose. Each method is outlined in three parts: its core principle (used to organize methods into four categories), other relevant details including my own observations, and software availability. The book provides a comprehensive overview of the state-of-the-art in network model selection and concludes by exploring future directions. A unified, optimal method could identify the mechanisms that shape real-world networks more precisely than any current approach. This work represents the first step toward developing such an optimal method. It will be a valuable resource for students and researchers in network science.

NVSHMEM is NVIDIA's OpenSHMEM-based PGAS communication library for GPU clusters, enabling GPU-initiated, one-sided communication through symmetric memory. Despite its growing adoption, a system-level understanding of its design and behavior remains scattered across documentation, source code, and application experience. This paper presents a concise study of NVSHMEM's programming model, implementation, and performance characteristics, focusing on symmetric memory, one-sided operations, and device-side collectives. We also examine DeepEP as a case study of NVSHMEM in performance-critical sparse deep learning workloads. Our analysis shows that NVSHMEM pioneered a device-side symmetric-memory programming model that enables fine-grained GPU-driven communication and is important for approaching the hardware performance limit. Overall, this work defines NVSHMEM's role as a systems building block, highlights its design tradeoffs, and identifies opportunities for improving GPU communication runtimes.

Practical requirements such as improving wall-plug efficiency and reducing system footprint have become increasingly important with the introduction of extreme ultraviolet (EUV) lithography into high-volume semiconductor manufacturing. These demands motivate the development of solid-state mid-infrared lasers as alternatives to current CO2 lasers. Systematic exploration of laser-to-EUV conversion efficiency (EUV-CE) over a broad parameter space is essential when altering the drive laser's wavelength, because the EUV-CE depends on the laser parameters in a complex manner. In this work, we performed a large-scale grid search of more than 140,000 parameter combinations for laser-produced tin plasma EUV sources using the radiation-hydrodynamics code STAR-1D, which is validated against EUV source experiments. The systematic wavelength dependence of the optimum pulse width and target size is governed by the requirement to simultaneously achieve the electron temperature and density optimal for EUV emission, maintain efficient laser absorption, and suppress EUV self-absorption. The resulting CE map predicts a global maximum of 5.63% at 5.5 μm. For the practically relevant 2 μm solid-state driver, a maximum CE of 4.64% is obtained, in good agreement with recent experimental results. Multiple operating points are identified over a broad range of pulse parameters, providing guidance for 2 μm-driven EUV source development.

We propose quantum algorithms for preparing thermal states via the simulation of the thermofield double states. The key idea is to leverage double-bracket quantum algorithms to implement imaginary-time evolution on thermofield double states, whose reduced state realizes the Gibbs state. Our method, termed double-bracket thermofield double (DB-TFD), introduces two variants. The first, the vanilla DB-TFD algorithm, directly implements imaginary-time evolution using double-bracket quantum imaginary-time evolution. The second, poly DB-TFD, employs double-bracket quantum signal processing to approximate the imaginary-time evolution operator via a polynomial transformation. We demonstrate that the complexity of the poly DB-TFD algorithm scales exponentially with the inverse temperature in a broad practical regime. This scaling is consistent with existing methods, and numerical simulations support the corresponding theoretical bound. We further demonstrate the utility of DB-TFD in quantum Boltzmann machines for generative modeling, achieving improved performance compared with variational imaginary-time evolution approaches. These results establish DB-TFD as a promising route for thermal state preparation in the near-term and early-fault-tolerant regimes.

Malware research primarily studies the results, the methods, and the impact. Even from an offensive security perspective, what is examined is the method, not the development strategy of the offender. This study investigates the behavioral signatures and coding patterns embedded in the malware source code. By analyzing a large corpus of leaked malware code and comparing it with carefully selected benign open-source software, we apply static application security testing and compute multiple software metrics. Based on cognitive psychology and criminological theories, our work interprets differences in code structure and quality as behavioral indicators, reflecting distinct motivational structures, risk tolerances, and development strategies of malware authors compared to benign software developers. Our findings reveal that malware code is generally smaller, less documented, and exhibits higher cyclomatic complexity per function, with reduced use of abstraction mechanisms such as classes and closures. Vulnerability analysis further reveals that malware exhibits more issues of the types that benign code typically avoids, suggesting a minimal investment in secure development practices. These patterns imply a development style optimized for expedience, operational secrecy, and evasion rather than long-term maintainability. Nonetheless, the code quality metrics indicate that it does not deviate significantly from benign software enough to be distinctive. By framing code metrics as proxies for behavioral signals and strategic choices, we demonstrate how quantitative software analysis can enrich behavioral cybersecurity research, offering new insights into the practices and priorities of malware developers. Our results pave the way for further research in the behavioral profiling of cyber offenders.

The complex radio light curves of tidal disruption events (TDEs) challenge our understanding of the properties of both the outflows and the circumnuclear medium (CNM) surrounding supermassive black holes. In this work, we explore outflow-CNM interactions across a broad parameter space using three-dimensional hydrodynamic simulations, adopting a broken power-law CNM density profile with a transition near the Bondi radius. The outflow-CNM interaction inside Bondi radius produces an early radio flare (\(\lesssim 2\) yr) once the emitting region becomes optically thin. A second radio rebrightening can appear a few years later if the outflow decelerates beyond Bondi radius. We also find that either a very dense inner CNM, which causes rapid deceleration, or a rarefied outer CNM suppresses the late rebrightening that will produces a single early-peaked flare. In contrast, a rarefied CNM inside the Bondi radius suppresses the early flare and yields a single late-peaked event. For the case of very dense CNM at large radii, the interaction will trigger a sharp late-time rise as observed in some TDEs. We further explore the interaction of a relativistic jet with a broken power-law CNM, which can reproduce the characteristic light curves as observed in jetted TDEs without invoking complex jet structure.

An operator $A$ on a complex Hilbert space $\Hh$ is called antilinear if $A(x+y)=Ax+Ay$ and $A(λx)=\ovλ Ax$ for $x,y\in \cD(A)$ and $λ\in \dC$. We investigate some classes of densely defined antilinear unbounded operators, especially antilinear normal operators. We give various characterizations of antilinear normal operators and study a class of such operators in detail. Our main result is a structure theorem for unbounded antilinear normal operators.

The BRUIT-FM Challenge asks participants to reduce ''noise'' on an open dataset of real and synthetic broadband seafloor seismology data. The dataset includes signals from earthquakes, ocean infragravity waves and seafloor currents. It also includes training datasets of synthetic data with solutions. Participants are asked to remove or separate these signals to obtain the best earthquake and seafloor compliance signals. The authors will make a first assessment of the noise reduction, based on noise reduction and ease of use. Participants are invited to a community workshop, in which they will validate the preliminary assessment and collaborate on a community paper describing the results, identifying promising pathways and proposing new directions. The best results will be added to a new version of the dataset, which will persist as a benchmark for future developments.

We investigate physics-informed neural networks (PINNs) for computing the $s$-wave bound states of the hypernucleus $_Λ^{208}$Pb, modeled as a two-body system composed of a $Λ$ hyperon and a $^{207}$Pb core. The interaction is described by a Woods--Saxon potential without spin--orbit coupling. In the PINN formulation, the radial bound-state wave function is represented by an artificial neural network, and the eigenenergies are obtained from the Rayleigh--Ritz variational quotient. Because PINN eigenvalue calculations can depend on the residual-loss formulation and random-seed initialization, two residual losses are compared across four independent random seeds. Their performance is assessed using eigenvalue accuracy, coefficient of variation, signal-to-noise ratio, bias--variance decomposition, and Hermitian spectral-ordering consistency. The normalized residual loss gives the most stable and physically consistent bound-state spectrum for the four seeds considered. With this loss, the computed bound-state energies and root-mean-square radii are in very good agreement with the corresponding theoretical values. The resulting wave functions are used to construct the Jost functions through the Wronskian with incoming and outgoing Riccati--Hankel functions. From these Jost functions, the residue of the partial-wave $S$-matrix at the bound-state pole, the Asymptotic Normalization and the Nuclear Vertex Constants are extracted. These quantities show reasonable agreement with theoretical values, although with larger standard deviations than those obtained for the eigenenergies and radii. The results indicate that the Rayleigh--Ritz formulation combined with a seed-robust normalized residual loss provides a stable PINN framework for bound-state and Jost-function-based calculations in hypernuclear two-body systems.

Real-time systems require the careful handling of timing aspects in their models. For critical applications, this entails the use of time-aware formal methods. Currently, most of these formal methods express their semantics by reduction to timed automata or timed transition systems, and are associated with model-checking-based verification techniques. In this regard, they are intended to be used as a posteriori analysis methods, on systems that have already been developed. In contrast, methods such as Event-B have been designed to build systems incrementally using a correct-by-construction approach, but are not equipped with the ability to express timing aspects and constraints. We propose a non-intrusive, tool-supported embedding of time and clocks in Event-B inspired by the features and semantics of timed automata, that enables the design of complex real-time systems while benefiting from the entire ecosystem and tooling support of the method. Refinement is extended to also take time into account, making it possible to design complex systems gradually in a correct-by-construction manner while integrating timing aspects from the top level. The embedding and associated methodology are illustrated on a case study, showcasing both how timed Event-B models may be derived from timed automata, and also how the extended expressivity of first-order logic and set theory at the core of Event-B enables finer modelling.

High-order thermodynamic nonequilibrium (TNE) in three-dimensional compressible flows reflects the breakdown of low-order kinetic moment closure in strong-gradient regions. Using Chapman-Enskog analysis, we identify the kinetic moment constraints required to describe third-order TNE. The analysis yields the third-order constitutive relations and evolution equations for the viscous stress and heat flux, together with second-order expressions for their associated higher-order fluxes. These constraints enable the construction of a three-dimensional super-Burnett-level discrete Boltzmann model with 91 discrete velocities. The resulting D3V91 model reproduces shock-tube wave structures and resolves high-order TNE contributions that lower-order DBMs do not capture reliably. These results demonstrate that high-order TNE has a multigradient, rather than single-gradient, origin. For the four TNE quantities considered here, odd-order central moments, including the heat flux and the viscous-stress flux , are primarily governed by temperature gradients, whereas even-order central moments, including the viscous stress and the heat-flux-related flux , are dominated by velocity gradients. These leading-gradient dependences are not exclusive; they are substantially modified by density gradients, secondary gradients and transition-layer widths through higher-order derivative terms, gradient products and cross-couplings. When the secondary contributions become comparable to the leading-gradient terms, the nonequilibrium response transitions from a near-linear regime to an approximately exponential regime. This work establishes a super-Burnett-level DBM framework that treats kinetic moment closure and multigradient coupling consistently, providing a basis for resolving and interpreting high-order TNE in three-dimensional compressible flows.