Nonlinear Resonant Ultrasound Spectroscopy (NRUS) experiments that rely on repeated sampling of resonance curves are inherently sensitive to measurement protocol due to evolution of material parameters caused by fast and slow dynamic effects. We introduce a model-assisted discrete-time resonance tracking method that maintains a system at its instantaneous resonance condition without the need to acquire full frequency sweeps. Resonance is defined through a prescribed phase relation between excitation and response, and the excitation frequency is iteratively updated using a linearized frequency--phase model. The procedure allows controlled suppression of transient wave buildup using optional feedforward correction with respect to an external control parameter. The method is demonstrated on NRUS and on conditioning--relaxation protocol conducted on a sandstone bar, providing estimates of resonance frequency and damping. Comparison with conventional approaches shows that measurement speed and mode stability significantly influence the inferred nonlinear indicators. The proposed framework is not limited to nonlinear acoustics and can be applied to arbitrary resonant systems with slowly evolving parameters.

Compact stars serve as natural systems where matter exists at densities far beyond those achievable in laboratory experiments. Among them, magnetars are expected to possess interior magnetic fields that may reach values of the order of $10^{17}-10^{18}$ G. These extreme conditions are expected to alter the microscopic and macroscopic properties of dense matter. In this review, we examine how strong magnetic fields affect fermionic matter through mechanisms such as Landau quantization and anomalous magnetic moment interactions. We further discuss the behaviour of magnetized hadronic matter within relativistic mean-field approaches and consider the possible emergence of additional degrees of freedom, including hyperons, $Δ$ resonances, meson condensates and quark matter. The consequences of these effects for neutron-star structure and observational constraints are also briefly outlined.

The FAIR principles have transformed how computational data and workflows are shared in materials research, yet existing repositories can only serve pre-computed entries -- broad coverage is perpetually incomplete and cannot adapt to new questions on demand. To address these challenges, we present OptiMat Alloys, a large language model-powered conversational agent for multi-principal element alloy exploration built on three pillars: a living database that stores every calculation with provenance, low-barrier accessibility through a web interface requiring zero programming expertise, and built-in uncertainty quantification via cross-potential and cross-configuration validation. Coupling foundational machine learning interatomic potentials covering near-all periodic table of elements with natural-language interaction, OptiMat Alloys enables targeted, on-demand computation guided by the user's domain knowledge-extending FAIR from pre-computed repositories to on-demand knowledge generation and making computational alloy screening accessible to any materials scientist.

I show that the clock ambiguity cannot be solved by a purely relational condition like the noninteraction condition, and it is even stronger, extending to evolution laws. The ambiguity is solved by specifying the physical meaning of observables. Page and Wootters (1983) showed how time and dynamics can emerge from entanglement within a stationary quantum system containing a clock. The clock ambiguity problem is that, from a purely relational stance and without fixing a clock-world split, the emergence is ambiguous, resulting in any possible history (Albrecht 1995). I show that the ambiguity is stronger than previously recognized. Under the relational stance, it extends from histories to the evolution laws themselves. The spectrum of any ideal clock uniformizes the spectra of the world's evolution operators, leaving only the dimension of the Hilbert spaces as invariant information. Fixing the clock-world split can solve the ambiguity, but this would block spacetime symmetries. One might want to remove the ambiguity up to a unitary equivalence by imposing noninteraction, as in Marletto and Vedral (2017). But once the clock spectrum uniformizes the world spectrum, unitary equivalence becomes too coarse to distinguish any two possible world dynamics, which is the result proved here. Thus a purely relational condition such as noninteraction is insufficient. Nor can all different decompositions be regarded as equally valid perspectives, since then records would not be correlated with the events they record, and empirical knowledge would be impossible. The resolution is therefore not to embrace the ambiguity, but to recognize what a bare reading of the Page-Wootters structure omits: the physical meaning of the operators.

We propose Annealed Langevin Monte Carlo for Flow ODE Sampling (ALMC-ODE), a method for generating samples from unnormalized target distributions, with a particular emphasis on multimodal densities that are challenging for standard Markov chain Monte Carlo methods. ALMC-ODE is based on a probability-flow ordinary differential equation (ODE) derived from stochastic interpolants, which continuously transports a standard Gaussian reference distribution at $t = 0$ to the target distribution $ρ$ at $t = 1$. The key innovation lies in an annealed Langevin Markov chain that evolves through a sequence of intermediate distributions bridging the reference and the target. The resulting importance-weighted particles, reweighted via a Jarzynski-based scheme, yield a low-variance estimator of the velocity field governing the ODE. On the theoretical side, we establish a Jarzynski-type reweighting identity for general time-inhomogeneous transition kernels, characterize the optimal backward kernel that minimizes the variance of the importance weights, and prove an $\mathcal{O}(1/n)$ mean squared error bound for the resulting velocity-field estimator. Numerical experiments on challenging benchmarks, including Gaussian mixture models and a 64-dimensional Allen--Cahn field system, demonstrate that ALMC-ODE significantly outperforms both direct Monte Carlo ODE approaches and Hamiltonian Monte Carlo when applied to highly multimodal target distributions.

Within many bacterial colonies, persister cells exist as a subpopulation that is tolerant to antibiotics and other stressors, yet not genetically distinct from the rest of the colony. A recent study has proposed epigenetic inheritance as a mechanism that leads to the presence of persister cells. We analyze a nonlocal PDE--ODE model introduced in that study to describe the epigenetic inheritance process and establish its mathematical well-posedness, including existence, uniqueness, and nonnegativity of solutions. We identify a sharp parameter threshold delineating extinction from persistence of the colony: below this threshold the washout equilibrium is globally asymptotically stable, while above it a unique positive equilibrium exists and the population is weakly persistent. Notably, this threshold is independent of the internal community structure.

Recent disruptions at major maritime chokepoints have exposed the structural fragility of liner shipping networks. Existing indicators measure connectivity, but none quantify its structural vulnerability from a supply-side perspective. We propose the Maritime Connectivity Vulnerability Index (MCVI), capturing three dimensions mapped to distinct UNCTAD sources: low overall connectivity (LSCI), weak bilateral integration (LSBCI), and port infrastructure concentration (PLSCI). The index covers 185 economies over 2006-2025 using pooled fractional rank normalization and equal-weight aggregation from publicly available data. SIDS exhibit a mean vulnerability 0.234 points above non-SIDS economies, with the gap widening from 0.232 to 0.249 over two decades. A modest global decline of 4.2% is observed. Port concentration dominates for nearly 40% of economies (72 of 185), establishing infrastructure diversification as a distinct policy priority. Rankings are highly stable across alternative weighting schemes, normalization methods (Spearman rho = 0.97-0.999), and PCA-derived weights; Monte Carlo simulation (1,000 replications) confirms rho > 0.95 in every realization. External validation shows strong negative correlation with the World Bank Logistics Performance Index (rho = -0.61 across seven waves) and positive correlation with ad valorem maritime freight rates (rho = +0.32). Panel regressions reveal a vulnerability paradox whereby small trade-dependent economies are simultaneously the most trade-open and the most vulnerable. Pre-crisis MCVI predicts trade losses during the COVID-19 supply shock (rho = -0.25, p < 0.005), while the contrasting positive correlation during the 2008-2009 demand shock (rho = +0.23, p = 0.01) validates the supply-side specificity of the index.

We investigate discriminability from an operational and contextuality-oriented perspective using a two-copy comparison game based on SWAP-type measurements. The resulting score $D_{\mathrm{op}}$ provides an experimentally accessible notion of distinguishability that does not rely on a minimum-error discrimination task. We first examine whether this discriminability game can directly witness preparation contextuality. Within a preparation-noncontextual ontological model, we derive a direct upper bound on the game score under a SWAP-like comparison rule and a sharp single-copy test, and show that this bound is saturated in the natural qubit realization. Thus, the direct game alone does not provide a contextuality witness in that regime. We then consider a Bell-coupled scenario in which two-copy comparison measurements are applied to Bob's conditional preparations. This yields a state-dependent upper bound on the CHSH value in terms of operational separation parameters, and hence in terms of the distinguishability of the conditional states. Our results establish a quantitative link between operational discriminability and the strength of nonclassical correlations, showing that discriminability can act as an operational resource constraining Bell-type nonclassical correlations.

The bright [C II] 158 micron line is widely used to trace star-forming gas and feedback-driven outflows in high-redshift galaxies. Using the SPICE simulations, we investigate how bursty versus smooth stellar feedback shapes galaxy properties at z > 5 as traced by [C II] emission. All models exhibit a tight correlation between [C II] luminosity (L_[CII]) and star formation rate (SFR), though bursty feedback yields systematically lower L_[CII] at fixed SFR and larger intrinsic scatter. [C II] emission is more extended than rest-frame UV light by factors of ~2-4, consistent with ALMA observations. While outflows are ubiquitous and mass outflow rates scale with L_[CII] (reaching ~10 Msun/yr), the net mass flux remains inflow-dominated in [C II]-bright systems. The emission is dominated by low-velocity (|v_rad| < 200 km/s) cold gas, with fast outflows contributing little, causing [C II]-based kinematics to overestimate cold gas velocities and underestimate fast components by factors of ~2-5. Consequently, inferred mass-loading factors and wind energetics are biased low, and large line widths primarily reflect the gravitational potential rather than outflow speeds. Although [C II] spatial and spectral properties alone do not distinguish feedback models, gas kinematics provides a strong diagnostic: smooth feedback promotes earlier disk settling, yielding higher V/sigma and disk fractions (~48% vs. ~28% for bursty feedback at z = 5). Overall, [C II] robustly traces star formation but is a biased tracer of feedback-driven outflows, highlighting the need for multiwavelength constraints on the multiphase ISM.

This paper is concerned with the global existence and uniqueness of classical solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients in three-dimensional bounded domains or in the whole space $\mathbb{R}^N$ $(N=2,3)$ with non-vacuum far-field density. Specifically, we assume that the shear viscosity coefficient $μ(ρ)=ρ^α$ and the bulk viscosity coefficient $λ(ρ)=(α-1)ρ^α$, which satisfy the BD entropy relation. For arbitrarily large spherically symmetric initial data, we establish the global existence and uniqueness of spherically symmetric classical solutions under the following conditions: for $N=2$, $α\in (0.54369,1)$ and $γ\in (1,\infty)$; for $N=3$ (both bounded domains and the whole space), $α\in (0.67661,1)$ and $γ\in (1,6α-3)$. In the two-dimensional case $\mathbb{R}^2$, the restriction on $α$ can be further relaxed to $α\in (9-6\sqrt{2},1)$ provided that the initial data satisfy additional weighted integrability conditions. Moreover, we show that the solution will not exhibit vacuum in any finite time provided that no vacuum is present initially.

Artificial Intelligence (AI) is reshaping how developers adopt software engineering practices, yet the multi-dimensional nature of developer-AI interaction remains under-explored. Prior studies have primarily examined dimensions observable from developer activities such as "Prompt Crafting" and "Code Editing," overlooking how hidden intentions and emotional dimensions intertwine with concrete actions during AI-assisted programming. To understand this phenomenon, we conducted a mixed-methods study with 76 developers split into AI-assisted and non-AI groups. Each performed programming tasks (Python with API management or Java with SQL). Developers retrospectively labeled their self-reported intentions, tool-supported actions, and emotions from screen recordings, supplemented by surveys and interviews. Our user study resulted in a novel model named S-IASE with four dimensions to describe programming behavior: intention, action, supporting tool, and emotion for a given development state. Our analysis reveals aggregated and sequential behavioral patterns. For example, using AI assistants often makes developers more focused on actively creating code, evaluating, and verifying generated results. AI-assisted participants showed emotionally stable development flow, as opposed to non-AI-assisted participants who experienced more fluctuating emotions. Interviews revealed further nuance: some developers reported impostor-like feelings, expressing guilt or self-doubt about relying on AI. Our work bridges an important gap in understanding the complexities of developer-AI interaction in programming context.

A key challenge in classical machine learning is to mitigate overparameterization by selecting sparse solutions. We translate this concept to the quantum domain, introducing quantum sparsity as a principle based on minimizing quantum information shared across multiple parties. This allows us to address fundamental issues in quantum data processing and convergence issues such as the barren plateau problem in Variational Quantum Algorithm (VQA). We propose a practical implementation of this principle using the topological Entanglement Entropy (TEE) as a cost function regularizer. A non-negative TEE is associated with states with a sparse structure in a suitable basis, while a negative TEE signals untrainable chaos. The regularizer, therefore, guides the optimization along the critical edge of chaos that separates these regimes. We link the TEE to structural complexity by analyzing quantum states encoding functions of tunable smoothness, deriving a quantum Nyquist-Shannon sampling theorem that bounds the resource requirements and error propagation in VQA. Numerically, our TEE regularizer demonstrates significantly improved convergence and precision for complex data encoding and ground-state search tasks. This work establishes quantum sparsity as a design principle for robust and efficient VQAs.

A mixed graph contains (undirected) edges as well as (directed) arcs, thus generalizing undirected and directed graphs. A proper coloring $c$ of a mixed graph $G$ assigns a positive integer to each vertex such that $c(u)\neq c(v)$ for every edge $\{u,v\}$ and $c(u)<c(v)$ for every arc $(u,v)$ of $G$. As in classical coloring, the objective is to minimize the number of colors. Thus, mixed (graph) coloring generalizes classical coloring of undirected graphs and allows for more general applications, such as scheduling with precedence constraints, modeling metabolic pathways, and process management in operating systems; see a survey by Sotskov [Mathematics, 2020]. We initiate the systematic study of the parameterized complexity of mixed coloring. We focus on structural graph parameters that lie between cliquewidth and vertex cover, primarily with respect to the underlying undirected graph. Unlike classical coloring, which is fixed-parameter tractable (FPT) parameterized by treewidth or neighborhood diversity, we show that mixed coloring is W[1]-hard for treewidth and even paraNP-hard for neighborhood diversity. To utilize the directedness of arcs, we introduce and analyze natural generalizations of neighborhood diversity and cliquewidth to mixed graphs, and show that mixed coloring becomes FPT when parameterized by mixed neighborhood diversity. Further, we investigate how these parameters are affected if we add transitive arcs, which do not affect colorings. Finally, we provide tight bounds on the chromatic number of mixed graphs, generalizing known bounds on mixed interval graphs.

We present a numerical-relativity study of comparable-mass boson star-black hole (BS-BH) head-on collisions, focusing on both initial-data construction and gravitational-wave (GW) phenomenology. We show that plain superposition can strongly perturb the BS core, leading to large constraint violations and unphysical radial oscillations. To remedy this problem, we introduce a one-body conformal-factor correction and find that it robustly suppresses these artifacts. Using the improved initial data, we analyze GW emission from equal- and unequal-mass BS-BH binaries and compare with matched BS-BS and BH-BH baselines. For equal masses, the BS-BH radiated energy increases with BS compactness and approaches the BH-BH limit for highly compact stars. For unequal masses, the dominant $(2,0)$ mode often remains close to the BH-BH morphology, whereas the subdominant $(3,0)$ mode provides clear discriminatory power when the BH is the heavier companion. Our results identify higher multipoles as a key observable for distinguishing mixed BS-BH mergers from pure BH binaries.

Mutual TLS (mTLS) provides strong, certificate-based authentication for both clients and servers, yet its adoption for user-facing websites remains rare. This paper presents a longitudinal study of mTLS usability, tracking 46 senior and graduate computer science students who configured client certificates from scratch, used them for routine authentication over a semester-long course, and managed credentials across multiple devices. The results reveal that initial setup is a major bottleneck; while daily use was considered smooth, it did not improve long-term usability perceptions. Most concerningly, only 9% of participants fully understood the security implications of certificate-based authentication. We conclude that in a realistic, tooling-heavy deployment utilizing OpenSSL, a custom CA, and a 3072-bit minimum key requirement, even highly technical students struggled significantly. We argue this provides empirical evidence that today mTLS user experience is fundamentally misaligned with non-PKI specialists, and it is difficult to see a path toward mainstream adoption without substantial platform-level changes.

Let $\mathfrak{F}$ be a non-archimedean local field of residue characteristic $p$ and $G$ be one of the groups $\mathrm{GL}_2(\mathfrak{F})$, $\mathrm{SL}_2(\mathfrak{F})$ or $\mathrm{PGL}_2(\mathfrak{F})$. Let $\mathcal{H}_G$ denote the pro-$p$ Iwahori-Hecke algebra of $G$ over $\overline{\mathbb{F}}_p$. We study the homotopy category $\mathrm{Ho}(\mathcal{H}_G)$ of Hovey's Gorenstein projective model structure on the category of $\mathcal{H}_G$-modules and relate it to the singularity category $\mathrm{Sing}(X_{q,\mathbf{G}})$ of an explicit scheme. When $G=\mathrm{GL}_2(\mathfrak{F})$, this scheme was first introduced by Dotto-Emerton-Gee \cite{DEG22}. We obtain in that case an equivalence $\mathrm{Ho}(\mathcal{H}_{\mathrm{GL}_2})\simeq \mathrm{Sing}(X_{q,\mathrm{GL}_2})$ and recover from this Grosse-Klönne's mod-$p$ Langlands correspondence for Hecke modules \cite{GK20}, building on work of Pépin-Schmidt \cite{PeSch25_2}. We furthermore describe $\mathrm{Ho}(\mathcal{H}_G)$ completely explicitly when $G=\mathrm{SL}_2(\mathfrak{F})$ or $\mathrm{PGL}_2(\mathfrak{F})$, and make additional computations in the $\mathrm{GL}_2$ case.

Prognostic covariate adjustment (PROCOVA) is a two-sample two-stage estimation method used in randomized controlled trials. In the first stage, a prognostic score, defined as the conditional expectation of an outcome given covariates under the control treatment, is estimated using historical data. In the second stage, analysis of covariance with the estimated prognostic score and treatment assignment as explanatory variables is performed, and the average treatment effect is estimated. Although the prognostic score is estimated in this procedure, the variance estimator, which treats the prognostic score as known, has been used. Furthermore, the difference in the asymptotic variance between cases where the prognostic score is known versus where it is estimated has not been previously clarified. In this study, we derived these two asymptotic variances and showed that they are equal. We also constructed two variance estimator: one that treats the prognostic score as known, and another that accounts for its estimation, and compared their performance through simulation studies and data applications. For PROCOVA, since both variance estimators are asymptotically valid, it is generally recommended to use a variance estimator that treats the prognostic score as known, as it is simpler to derive and implement. However, when historical data is small, a variance estimator that explicitly accounts for prognostic score estimation is recommended if conservative inference is preferred.

We present a graded modal type theory, a dependent type theory with grades that can be used to enforce various properties of the code. The theory has $Π$-types, weak and strong $Σ$-types, natural numbers, an empty type, and a universe, and we also extend the theory with weak and strong unit types and graded $Σ$-types. The theory is parameterized by a modality structure, a kind of partially ordered semiring, whose elements (grades) are used to track the usage of variables in terms and types. Different modalities are possible. We focus mainly on quantitative properties, in particular erasure: with the erasure modality one can mark function arguments as erasable. The theory is fully formalized in Agda. The formalization, which uses a syntactic Kripke logical relation at its core and is based on earlier work, establishes major meta-theoretic properties such as subject reduction, consistency, normalization, and decidability of definitional equality. We also prove a substitution theorem for grade assignment, and preservation of grades under reduction. Furthermore we study an extraction function that translates terms to an untyped $λ$-calculus and removes erasable content, in particular function arguments with the "erasable" grade. For a certain class of modalities we prove that extraction is sound, in the sense that programs of natural number type have the same value before and after extraction. Soundness of extraction holds also for open programs, as long as all variables in the context are erasable, the context is consistent, and erased matches are not allowed for weak $Σ$-types.

We propose a log-concavity conjecture for BPS invariants arising in the enumerative geometry of planar curve singularities, identified with the local Euler obstructions of Severi strata in their versal deformations. We further extend this conjecture to ruling polynomials of Legendrian links and to E-polynomials of character varieties. We establish these conjectures for irreducible weighted-homogeneous singularities (torus knots) and for ADE singularities, and prove a multiplicative property for ruling polynomials compatible with log-concavity.

We study the regularity and branching of strictly abnormal minimizing geodesics in sub-Riemannian geometry. We construct examples of real-analytic sub-Riemannian manifolds admitting minimizing geodesics that lose regularity at an interior point of their domain and exhibit branching, thereby resolving longstanding open questions. Moreover, using a lifting procedure, we provide the existence of non-smooth and branching minimizing geodesics also in Carnot groups.

Raman scattering underlies a broad range of spectroscopic and light-generation techniques, yet its conventional description, based on the Raman gain spectrum, accurately describes only long-pulse, steady-state dynamics. We present a time-domain theoretical approach that provides a unified and physically-transparent description of Raman interactions across all temporal regimes. It enables direct visualization of Raman temporal dynamics and accounts for spectrotemporal aspects of Raman phenomena, which cannot be addressed by prior theories. In particular, molecules with strong Raman responses do not produce an efficient soliton self-frequency shift in gas-filled hollow-core fibers. The time-domain analysis exposes temporal and spectral distortions from the Raman response that impact frequency-shifting detrimentally, and identifies how these distortions can be suppressed by reducing the Raman interaction to a perturbation on the electronic response. Experiments that employ gas mixtures with tunable Raman fractions of the nonlinear response demonstrate up to a four-fold increase in quantum efficiency (from 20 to 80%) compared to the pure molecular gas, and unity-efficiency Raman shifting will be possible. The new time-domain framework uncovers phenomena that are inaccessible through the decades-old frequency-domain treatment of Raman scattering, and it applies to Raman interactions in solids, liquids, and gases on various timescales.

Environmental, Social, and Governance (ESG) considerations play a central role in contemporary financial decision-making. In parallel, Large Language Model (LLM) applications in this domain have primarily emphasized well-defined discriminative tasks, such as classification or scoring, which have proven effective for structured analysis and benchmarking. However, this prevailing focus offers limited support for more interactive and generative ESG scenarios, where embedded domain knowledge and contextual understanding are essential. In this work, we propose an ESG-oriented adaptation pipeline for LLMs that integrates ESG principles not only as a target domain, but also as guiding constraints throughout training and evaluation. Building on the Qwen-3-4B architecture, we explore parameter-efficient adaptation strategies using Low-Rank Adaptation (LoRA) and the Instruction-Residual Method (IRM) to produce three ESG-specialized models. We evaluate the proposed models on ESG question answering under both zero-shot and knowledge-augmented settings, using a diverse set of generative, semantic, readability, and environmental impact metrics. Our results show that the ESG-adapted models consistently outperform their original counterparts and competitive baselines such as Llama-3 and Gemma-3. Although limitations remain in tool-based knowledge integration, this work establishes a foundation for ESG-oriented language generation and highlights the importance of responsible, domain-aware LLM adaptation.

Gravitational-wave observations of binary black hole (BH) mergers provide a novel avenue for testing massive-star evolution and the resulting BH mass spectrum. Recent population analyses under the hierarchical-merger hypothesis have offered evidence for the BH mass gap and inferred its lower edge to $\sim 44 - 68$ M$_\odot$. Motivated by these findings, we compute low-metallicity ($Z=10^{-5}$) helium star models with MESA and systematically explore the effect of uncertainties in the $^{12}$C$(α, γ)^{16}$O and $^{16}$O+$^{16}$O reaction rates on the final fate. Varying the $^{12}$C$(α, γ)^{16}$O reaction rate by $-3 σ$ to $+3σ$, we find that the predicted BH mass gap shifts from $\sim104 - 184$ M$_\odot$ to $\sim45 - 135$ M$_\odot$. In contrast, scaling the $^{16}$O+$^{16}$O reaction rate by global factors of 0.1, 1, and 10 has only a modest effect on the lower edge of the BH mass gap (less than 5 M$_\odot$), and shifts the upper edge by more than 10 M$_\odot$. Using the predictions of our models together with the literature estimates for the lower edge of the BH mass gap, we constrain the astrophysical S factor of $^{12}$C$(α, γ)^{16}$O reaction at 300 keV of $S_{300} \simeq$ 137.6 - 263.4 keV barn.

In this work, we propose a neural network-enhanced finite element strategy to compute the minimizer of the Ginzburg-Landau energy based on an unsupervised deep Ritz-type strategy. We treat the parameter $κ$ as a variable input parameter to obtain possible minimizers for a large range of $κ$-values. This allows for two possible strategies: 1) The neural network may be extensively trained to work as a stand-alone solver. 2) Neural network results are used as starting values for a subsequent classical iterative minimization procedure. The latter strategy particularly circumvents the missing reliability of the neural network-based approach. Numerical examples are presented that show the potential of the proposed strategy.

We demonstrate efficient diffraction of intense ultrashort laser pulses using optical-field-ionization-induced plasma-neutral gratings formed by spatially structured ionization of a neutral molecular gas in the interference field of two femtosecond pump pulses. The transient refractive index modulation of the plasma structure persists for at least 10 picoseconds and is used to diffract intense femtosecond signal pulses into the 1st order of diffraction with an average efficiency of up to 35$\%$. Plasma gratings are shown to provide stable diffraction at signal laser intensities greater than $ 10^{14}\text{ W/cm}^2$, exceeding the damage thresholds of conventional solid-state optics by more than two orders of magnitude, continuously for hours at a 10-Hz repetition rate. The experimental diffraction efficiency scales with the grating aperture allowing for a larger millimeter-scale plasma optic, increases with the pump energy and electron density, and reaches a maximum at a specific grating length in agreement with the coupled-mode theory for periodic media. These results demonstrate the scalability, tunability, and high damage threshold of transmissive plasma-based photonic structures, opening new prospects for controlling multi-petawatt laser beams.

We prove a nearly polynomial inverse theorem for the Gowers $U^d$ norm, over finite fields of non-small characteristic, for polynomials of degree $d+1$. The case of degree $d$ was very recently settled by Milićević and Randelović with a fully polynomial bound. We moreover provide a nearly polynomial inverse theorem for homogeneous polynomials of any degree smaller than $2d$. Our methods may be of independent interest, and include a refined notion of polynomial decomposition that captures correlation with polynomials of lower degree than classical notions do, and a new correlation lemma that improves upon similar lemmas in the literature. Additionally, we illustrate the usefulness of the new correlation lemma by using it to give an alternative proof for the aforementioned result of Milićević and Randelović.

The CYGNO experiment employs an optical readout to image particle interactions in a gaseous Time Projection Chamber (TPC), combining cameras and photomultiplier tubes (PMTs) to achieve high spatial resolution and timing information. This approach enables detailed track reconstruction but poses significant challenges for data acquisition, particularly in view of the next experimental phase, CYGNO-04, which will operate multiple cameras simultaneously. In this paper, we present an upgrade of the CYGNO Trigger and Data Acquisition (T-DAQ) system, developed starting from the LIME configuration and validated on the MANGO prototype. The upgrade introduces a continuous imaging acquisition mode, substantially reducing the camera dead time, together with an extended trigger time-tagging scheme that provides a robust global time reference for PMT signals. A synchronous multi-camera DAQ architecture is also implemented and tested, enabling coordinated operation of multiple optical sensors without a master camera. The performance of the upgraded system is validated through dedicated tests, demonstrating stable continuous acquisition, reliable time-tagging, and consistent synchronization across multiple cameras. These results establish a solid and scalable foundation for the CYGNO-04 DAQ and represent a key step toward efficient data acquisition in future large-scale optical TPC detectors.

The shape of the heliosphere, regarded as comet-like since the 1960s, has recently been the subject of intense debate in the last decade. There is disagreement whether the heliospheric tail extends to $\sim$10,000 au in a comet-like shape or if it is short ($\sim$400 au) with a split. Energetic neutral atom (ENA) maps from Cassini/INCA at energies from 5.2 to 13.5 keV revealed a global structure extending from the nose to the heliospheric tail known as the Belt whose origin has remained largely unexplored. Here, we use a state-of-the-art multi-ion magnetohydrodynamic (MHD) model and a novel reconnection simulation to establish that the Belt structure is consistent with a split tail heliosphere but not with a comet-like heliosphere. In a split-tail heliosphere there is a region of low-$β$ (ratio of thermal to magnetic pressure) in the downwind direction close to the heliopause. Direct simulations of this region reveal that magnetic reconnection is strong and drives the energetic particles that produce the >5.2keV ENAs measured by INCA in the low latitude portion of the Belt. Since the comet-like heliosphere does not produce this low-$β$ region and the resultant reconnection-drive mechanism for the >5.2keV ENAs, our results indicate that the INCA observations are inconsistent with a comet-like heliosphere. Further, these simulations and analysis establish for the first time that magnetic reconnection in the complex magnetic fields, expected in astrospheres across the universe, are likely to be a source of energetic particles and radiation.

The subtour relaxation of the traveling salesman problem (TSP) plays a central role in approximation algorithms and polyhedral studies of the TSP. A long-standing conjecture asserts that the integrality gap of the subtour relaxation for the metric TSP is exactly 4/3. In this paper, we extend the exact verification of this conjecture for small numbers of vertices. Using the framework introduced by Benoit and Boyd in 2008, we confirm their results up to n=10. We further show that for n=11 and n=12, the published lists of extreme points of the subtour polytope are incomplete: one extreme point is missing for n=11 and twenty-two extreme points are missing for n=12. We extend the enumeration of the extreme points of the subtour polytope to instances with up to 14 vertices in the general case. Restricted to half-integral vertices, we extend the enumeration of extreme points up to n=17. Our results provide additional support for the 4/3-Conjecture. Our lists of extreme points are available on the public bonndata repository (https://doi.org/10.60507/FK2/JK95PC).

The standard gravitational-baryogenesis operator $λ\,\nabla_μR\,J^μ$, with $λ\equiv ε/M_\ast^{2}$, is usually treated as a spectator interaction that generates an effective chemical potential in a prescribed background. When included in the gravitational action, however, it defines a genuine curvature--matter-coupling variational problem, relevant for the baryon, lepton, and $B\!-\!L$ currents, whether described microscopically by particle-physics operators or macroscopically by a fluid current $J^μ=n_Xu^μ$. Up to a boundary term the interaction is equivalent to $-λR\nabla_μJ^μ$, making its $f(R,{\rm Matter})$ character manifest, but the metric equations remain open unless the metric dependence of $J^μ$ is specified. For an arbitrary local realization $J^μ(Ψ,g)$ we derive the universal part of the field equations and isolate the realization-dependent tensor generated by $δ_g J^μ$. In the vector-density realization the explicit $J^α\nabla_αR$ term cancels, but an algebraic term $-λg_{μν}R\nabla_αJ^α$ survives, so the theory admits only a partial effective-Planck-mass interpretation, $M_{\rm eff}^2=M_{\rm Pl}^2-2λ\nabla_μJ^μ$, and a time-dependent effective gravitational coupling during baryogenesis. Specializing to flat Friedmann-Lemaître-Robertson-Walker (FLRW) with a homogeneous current $J^μ=n_Xu^μ$, we obtain the modified Friedmann and Raychaudhuri equations, the associated continuity relation, and dimensionless diagnostics that quantify when the spectator approximation is controlled. We also discuss the implications for gravitational-baryogenesis studies in modified theories of gravity, providing a consistent General Relativity (GR) baseline for implementations in both standard cosmology and modified-gravity frameworks.