The sum-rank metric provides a unifying framework that generalizes both the celebrated Hamming and rank metrics, and has found applications in areas such as network coding, distributed storage, and space-time coding. A central problem is to determine the maximum size of a code with prescribed minimum distance. In this paper, we derive new sharp upper bounds on the size of a sum-rank-metric code using spectral and optimization techniques, including a semidefinite programming (SDP) bound that can outperform the best existing bounds based on computational experiments. Furthermore, we compare the Delsarte linear programming (LP) bound and a recent eigenvalue LP bound, and show equivalences between them, with particular emphasis on extremal regimes of the sum-rank metric. Finally, we show how to use the several SDP, LP and eigenvalue bounds to prove non-existence results for certain optimal and perfect sum-rank metric codes. Our results suggest that the combination of spectral and optimization methods effectively captures the hybrid nature of the sum-rank metric, providing new techniques that overcome the limitations of classical coding-theoretic approaches.

The toughness of a graph $G$, denoted by $τ(G)$, is defined by $τ(G)=$min $\{\frac{|S|}{c(G-S)}:S\subseteq V(G)$ and $c(G-S)\geq2\}$. A graph $G$ is said to be $τ$-tough if $τ(G)\geq τ$. Let $k\geq2$ be an integer. A tree $T$ is called a $k$-tree if $d_{T}(v)\leq k$ for each $v\in V(T)$, that is, the maximum degree of a $k$-tree is at most $k$. A $k$-tree $T$ is a spanning $k$-tree if $T$ is a spanning subgraph of a connected graph $G$. In 1989, Win [Graphs Combin. 5 (1989) 201--205] proved that if $τ(G)\geq\frac{1}{k-2}$, where $k\geq3$, then $G$ contains a spanning $k$-tree. Liu, Fan and Shu [Discrete Math. 348 (2025) 114593] provided a tight sufficient condition based on the spectral condition for connected $\frac{1}{k}$-tough and $\frac{1}{k-1}$-tough graphs to contain a spanning $k$-tree, where $k\geq3$ is an integer. A natural and interesting problem arises: Can the value of $τ$ be refined? When $\frac{1}{k-2}>τ\geq\frac{1}{k-1}$, we initially establish a lower bound on the size to ensure that a connected $\frac{t}{t(k-2)+1}$-tough graph $G$ contains a spanning $k$-tree, where $k\geq3$ and $t\geq1$ are integers. Meanwhile, we provide two sufficient conditions in terms of spectral radius and signless Laplacian spectral radius for a connected $\frac{t}{t(k-2)+1}$-tough graph $G$ to contain a spanning $k$-tree, where $k\geq3$ and $t\geq1$ are integers. When $t=1$, we obtain the result $η=1$ from Liu, Fan and Shu.

Linear mixed models are widely used to analyze non-independent data, but inference for fixed effects can be unreliable under misspecification of the random-effects distribution, inaccurate Fisher information estimation, or convergence failures, leading to a lack of control over false positives. These difficulties are amplified in multivariate settings, where within-cluster and between-response dependence must be modeled jointly. We propose a testing procedure for fixed effects in multivariate linear mixed models that avoids Fisher information estimation and does not require correct specification of the random-effects distribution by combining score statistics with clusterwise sign-flipping transformations. Our method accommodates both forms of dependence and yields asymptotically valid inference under weak distributional assumptions on the data-generating process.

Archival XMM and ROSAT X-ray data are used to investigate the structure of the Abell 548 - Abell 3367 region. Based on previous optical studies, this is a region likely to be rich in structure though studies are in disagreement regarding the connection between Abell 3367 and Abell 548. We use the available archival X-ray data together with kinematic data of counterpart galaxies to address this question and to determine the structure in this region. The region is particularly rich in X-ray structure elongated along a SW-NE axis consisting of numerous extended X-ray sources. In general, the structure consists of many galaxy groups and clusters which appear segregated in X-ray luminosity with the least luminous $\sim$ 30% toward the outer region of the clusters, possibly tracing a filament. We find evidence to suggest a supercluster of 3 clusters at redshifts: $\sim$ 0.04, 0.045, and 0.06. Some of the X-ray sources coincident with Abell 3367 have counterpart galaxy redshifts consistent with Abell 548 and others are significantly higher. This supports that Abell 548 and Abell 3667, form a supercluser and the higher redshift X-ray source is a background object. They are part of a larger structure consisting of a previously identified cluster at redshift 0.04, and two groups at redshift $\sim$ 0.06. In addition, there is a filamentary structure at z $\sim$ 0.103. The ubiquity of groups in the large scale structure suggests that they provide an environment where galaxies are in close proximity and evolution via interaction can proceed well before the galaxies make their way into the dense central region of a cluster.

This paper investigates the heat equation on a bounded domain with a Robin boundary condition, where the reactivity parameter (or killing rate) is modeled as a continuous-time Markov chain. We analyze the system under two stochastic frameworks using a functional analytic approach. First, we examine the annealed case, which accounts for the joint stochasticity of the diffusion and the switching mechanism. We describe the solution via a strongly continuous contraction semigroup on a product space. We identify its infinitesimal generator, which incorporates the state-dependent Robin conditions into its domain, and provide a corresponding Feynman-Kac formula. Second, we study the quenched setting for fixed realizations of the switching paths. We characterize the solution through a non-autonomous evolution family (propagator) and derive a Feynman-Kac-type representation involving the boundary local time of a reflected Brownian motion. We prove an averaging principle in the fast-switching limit, showing that the system converges to a deterministic Robin problem. These results are applied to a biophysical model of stochastically gated receptors on cell membranes.

The volume of scientific manuscripts is growing faster than the capacity to evaluate them, yet the institutions that govern peer review have remained largely unchanged. The result is a widening mismatch: reviewer scarcity, noisier assessments, and declining confidence in editorial decisions. Every scientist wants better reviews, but review quality depends on the total burden, which no single author can shift. To isolate this tension, we provide a game-theoretic thought experiment: a voluntary lottery in which authors accept a chance of random pre-review rejection, reducing reviewer burden and improving the quality of surviving evaluations. We show that a Nash equilibrium emerges in which authors voluntarily enter the lottery. Scientists who care about the literature they read, not just the papers they publish, will opt in, raising the quality of published science for all.

Capturing ultrafast transient phenomena conventionally requires streak cameras or computational imaging based on compressed sensing, which lead to complex and costly systems. In this Letter, we demonstrate, to the best of our knowledge, the first fully passive single-shot ultrafast imaging architecture assembled entirely from off-the-shelf, low-cost components. A commercial microlens array combined with a stack of standard microscope cover glasses maps temporal information into multiple spatial channels, and a consumer-grade CMOS image sensor records all delayed replicas within a single camera exposure. The proposed system has a total hardware cost below US\$500 and captures the evolution of a picosecond laser pulse with a temporal sampling interval of 1.46~ps, an effective frame rate of 685~Gfps, and a sequence depth of ten frames. The temporal fidelity of the system is verified by recovering the expected Gaussian pulse profile, and the spatial resolution is characterized through a point-source measurement with a point spread function of 1.86 and 1.62 pixels full width at half maximum along the horizontal and vertical directions, respectively. The proposed architecture presents an alternative approach to single-shot ultrafast imaging with a simple, low-cost, computation-free, and fully passive design.

We derive a class of inner-extremal regular black hole solutions characterized by a degenerate inner horizon. These geometries arise as polymerized vacuum configurations inspired by loop quantum gravity and constitute effective quantum-gravity solutions that admit a Birkhoff-type theorem, rendering them unique within the considered framework. We show that such inner-extremal horizon configurations exist only for a finely tuned value of the mass determined by the parameters of the theory. Building on this construction, together with the corresponding non-degenerate regular black hole solutions, we perform a generic analysis of the mass inflation phenomenon in four-dimensional spacetimes using a colliding null-shell setup near the inner horizon. We identify the conditions under which mass inflation becomes significant and examine how the presence of a minimal length scale affects this behavior, with particular emphasis on the case where such a scale is motivated by loop quantum gravity. Finally, we comment on the stability of these configurations under the null-shell perturbations considered in our analysis.

We investigate the behavior of discrete interface growth models belonging to the Edwards--Wilkinson (EW) and Kardar--Parisi--Zhang (KPZ) universality classes, when defined on a complete graph, a topology commonly used to probe the infinite-dimensional limit of statistical mechanical systems. Our aim is to assess to what extent discrete lattice models reproduce the behavior of their corresponding continuum equations in this highly connected setting. After assessing the trivial behavior shown by some well known cases (like random deposition with surface relaxation or the etching model), we focus on two paradigmatic models associated with the KPZ universality class, the Restricted Solid-on-Solid (RSOS) and Ballistic Deposition (BD) models, and assess non-trivial behavior through several observables including the roughness, height fluctuations, power spectra, and two-time autocorrelation functions. Still, despite similarities with continuum equations, important differences arise in the fluctuations and long-time dynamics. In both discrete models the rescaled height fluctuations display a pronounced left tail, indicating the presence of lagging nodes. While the RSOS model exhibits a saturation roughness that decreases with system size, similarly to the EW and KPZ equations, the BD model exhibits a saturation roughness that increases with system size and an additional ultrafast growth regime, placing it outside the KPZ universality class on a complete graph.

Integrating theoretical neuroscience, decision theory, and probabilistic inference offers a promising route to understanding human cognition, yet concrete methodological bridges between agentic AI models and behavioral data analysis remain formally underdeveloped. We advance this synthesis under the framework of agentic behavioral modeling (ABM), which treats artificial agents as latent, generative hypotheses about cognitive mechanisms and evaluates them by their statistical adequacy in explaining human behavior. After outlining its conceptual foundations, we apply the framework to two minimal laboratory paradigms: a binary perceptual contrast-discrimination task and a symmetric two-armed bandit learning task. We formalize each task-agent-data system as a joint probability model, derive explicit conditional log-likelihoods for behavioral inference, validate different model variants using model and parameter recovery simulations, and evaluate them in light of empirical data. Using these minimal examples, we provide an agent-centric interpretation of the psychometric function, derive optimal policies for both tasks, and show the equivalence between Rescorla-Wagner learning and Bayesian inference in symmetric bandits. More broadly, this work may serve as a conceptual and practical foundation for applying ABM to cognitive behavioral science.

Angular is one of the most widely adopted frameworks for developing large-scale, dynamic web applications. As projects increase in scope and complexity, developers face growing challenges in managing architecture and maintaining clean, modular code. These challenges often lead to design flaws, commonly referred to as code smells. While React-specific smells have been cataloged in prior studies, limited knowledge exists regarding Angular-specific smells and how they manifest. This study investigates Angular code smells through a grey literature review, consolidating community knowledge and technical discussions. From the collected sources, 11 distinct Angular code smells were identified, 6 of which also occur in React-based systems, suggesting that some issues are cross-framework. Each smell was analyzed, exemplified, and grouped according to its technical characteristics. Based on the resulting catalog, we implemented an automated static analysis tool to detect Angular code smells. The tool was empirically evaluated using a manually validated dataset, and its effectiveness was assessed through standard information retrieval metrics. The evaluation results indicate high detection performance across all smells, achieving accuracy values above 0.88 and F1-scores ranging from 0.89 to 1.00. The findings reveal recurring issues such as component overloading, duplicated logic, and inefficient template bindings, reinforcing the relevance of systematic detection support. This study presents the first catalog of Angular-specific code smells derived from grey literature and demonstrates the feasibility and effectiveness of automated detection, providing a solid foundation for future empirical studies and tool development aimed at improving front-end code quality.

We construct valuatively independent bases for the space of sections of an ample line bundle on a log Calabi--Yau pair over a discretely valued field and the space of regular functions on an affine CY pair with maximal boundary. While the bases are not in general unique, they induce canonical functions on the respective skeletons and are expected to agree with tropicalizations of theta functions when they exist. The proof uses techniques from the study of higher rank degenerations in K-stability.

Galaxy physical properties are influenced by their environments, but the processes responsible for mass and environmental quenching and structural transformations remain debated. Galaxy clusters are ideal laboratories for investigating galaxy formation and evolution, offering a full range of galaxy properties and environments. Observations of large-scale structures, particularly filaments in cluster outskirts ($r \sim5r_{200}$), are currently constrained to the low-redshift Universe. To explore galaxy evolution at intermediate redshifts, deep photometric data, ideally combined with spectroscopic redshifts, are essential. Abell S1063 cluster ($z$ = 0.346) is observed within the Galaxy Assembly as a function of the Mass and Environment program with the VLT Survey Telescope (VST-GAME) combined VISTA Public Survey program Galaxy Cluster At Vircam. We investigate galaxy evolution across a wide range of stellar masses and environments. We release a multiwavelength photometric catalog with photometric redshifts for 64394 sources in $1x1 deg^2$. The analysis of overdensity regions provides insights for future studies on galaxy properties in cluster outskirts. The dataset is obtained through deep ($r<$24.65 mag) and wide optical ($u$, $g$, $r$, $i$, VST) and near-infrared ($Y$, $J$, $K_s$, VISTA) observations. The photometric catalog includes all detected sources, excluding nearby or overlapping objects, saturated stars, and image artifacts. The multiwavelength catalog enabled photometric redshift estimates and identification of cluster members. The density field allowed comparison of galaxy properties, colors, and masses across environments. We detect a very dense structure near the cluster center, and with such a large field of view, we find another dense region to the north-west, in the opposite direction to the cluster elongation. Filaments connecting the regions are also visible.

Standard random-effects meta-analysis relies heavily on the assumption that the underlying true effects are normally distributed. In the social sciences, where evidence synthesis increasingly involves large, highly heterogeneous datasets, this assumption is often restrictive and unjustified. Misspecification of the random-effects distribution prevents the detection of asymmetry or multimodality, potentially leading to erroneous conclusions regarding the prevalence of adverse effects or the existence of specific subgroups. This paper introduces a Penalized Gaussian Mixture (PGM) framework designed to recover the entire probability density function of true effects without enforcing a rigid parametric shape. The method adapts to different non-normal scenarios, including skewed and multimodal distributions, while reducing to the normal case when supported by the data. A simulation study demonstrates that in large, highly heterogeneous meta-analyses, PGM yields substantially more accurate estimates of tail probabilities and the density function than standard methods when normality is violated, without substantially compromising efficiency under normality. An empirical application to environmental education data illustrates the practical utility of the method. The proposed framework provides researchers with a robust tool to move beyond simple summary statistics and characterize the complex nature of the true effect distribution in the real world.

Stoquasticity, originating in sign-problem-free physical systems, gives rise to $\sf StoqMA$, introduced by Bravyi, Bessen, and Terhal (2006), a quantum-inspired intermediate class between $\sf MA$ and $\sf AM$. Unentanglement similarly gives rise to ${\sf QMA}(2)$, introduced by Kobayashi, Matsumoto, and Yamakami (CJTCS 2009), which generalizes $\sf QMA$ to two unentangled proofs and still has only the trivial $\sf NEXP$ upper bound. In this work, we initiate a systematic study of the power of unentanglement without destructive interference via ${\sf StoqMA}(2)$, the class of unentangled stoquastic Merlin-Arthur proof systems. Although $\sf StoqMA$ is semi-quantum and may collapse to $\sf MA$, ${\sf StoqMA}(2)$ turns out to be surprisingly powerful. We establish the following results: - ${\sf NP} \subseteq {\sf StoqMA}(2)$ with $\widetilde{O}(\sqrt{n})$-qubit proofs and completeness error $2^{-{\rm polylog}(n)}$. Conversely, ${\sf StoqMA}(2) \subseteq {\sf EXP}$ via the Sum-of-Squares algorithm of Barak, Kelner, and Steurer (STOC 2014); with our lower bound, our refined analysis yields the optimality of this algorithm under ETH. - ${\sf StoqMA}(2)_1 \subseteq {\sf PSPACE}$, and the containment holds with completeness error $2^{-2^{{\rm poly}(n)}}$. - ${\sf PreciseStoqMA}(2)$, a variant of ${\sf StoqMA}(2)$ with exponentially small promise gap, cannot achieve perfect completeness unless ${\sf EXP}={\sf NEXP}$. In contrast, ${\sf PreciseStoqMA}$ achieves perfect completeness, since ${\sf PSPACE} \subseteq {\sf PreciseStoqMA}_1$. - When the completeness error is negligible, ${\sf StoqMA}(k) = {\sf StoqMA}(2)$ for $k\geq 2$. Our lower bounds are obtained by stoquastizing the short-proof ${\sf QMA}(2)$ protocols via distribution testing techniques. Our upper bounds for the nearly perfect completeness case are proved via our new rectangular closure testing framework.

Degenerate spinor Bose gases with repulsive density-density interaction and anti-ferromagnetic spin-spin coupling in one spatial dimension are shown to be described by a quantum integrable matrix extension of the nonlinear Schrödinger model, whose fundamental fields are described by an $m\,\times\,n$ matrix of bosonic field operators. The eigenstates of this model are constructed for arbitrarily sized matrix field operators by means of algebraic Bethe-ansatz techniques, and the corresponding Bethe equations governing the spectra of conserved quantities are derived. The approach thus generalizes previously chosen techniques to account for arbitrary spin multiplets and their spin-spin interaction. Focusing on the specific case of the $2\times2$ model, which is shown to correspond to a spin-$1$ Bose gas, a set of integral equations is derived, which describe its equilibrium thermodynamic properties. From these, the ground state phase diagram is computed both, numerically and analytically in the parameter plane spanned by the chemical potential and an external magnetic field. Furthermore, the existence of paired bound states is shown to modify the Pauli exclusion principle for interacting bosons in one dimension. In particular, it is found that no two quasiparticle rapidities can coincide, provided that the Lieb parameter satisfies $γ>4/3$.

Star-forming galaxies (SFGs) are a subclass of $γ$-ray emitters and a correlation between their $γ$-ray luminosity ($L_{\rm γ}$) and the total infrared (IR) luminosity ($L_{\rm IR}$) has been established based on the Fermi Large Area Telescope (LAT) data. NGC 2403 and NGC 3424 have been reported as outliers in the $L_{\rm γ}$-$L_{\rm IR}$ correlation with light curves showing significant variability, which contrasts with the temporally stable $γ$-ray emission in other SFGs, originating primarily from cosmic rays interacting with interstellar medium. In this study, we reanalyze the $γ$-ray emission in the directions of NGC 2403 and NGC 3424 using more than 16.5 yr Fermi-LAT data. NGC 3424 is found to be spatially coincident with the detected $γ$-ray source, while NGC 2403 is significantly offset from the nearest $γ$-ray source, suggesting an implausible association. We confirm the previously reported variability of both $γ$-ray sources and the significant deviation from the $L_{\rm γ}$-$L_{\rm IR}$ correlation when assuming an association of both $γ$-ray sources with the two galaxies. Our findings lend further support to the interpretation that their $γ$-ray emission is driven primarily by alternative radiative processes-rather than by star formation activity-such as the ejecta of the Type IIP supernova SN 2004dj in NGC 2403 interacting with a surrounding high-density shell and an obscured active galactic nucleus in NGC 3424.

We measured unusual critical currents as functions of temperature in the zero field and as functions of a magnetic field perpendicular to the substrate surface at a given temperature close to the critical temperature in thin-film long quasi-one-dimensional superconducting aluminum two-width structures consisting of narrow and wide wires with different critical temperatures. It is found that the experimental critical switching current as a function of the field at a given temperature, determined by the appearance of a dc voltage on a short section of the structure, is nonlocal (dependent on electron transport in the area containing the junction line between the narrow and wide wires). When current flows through the narrow and wide wires of the structure, the switching currents, experimental and calculated within the framework of the Ginzburg-Landau theory, differ radically from each other. A nonzero switching current exists in high fields greater than the maximum critical magnetic field in a quasi-one-dimensional superconducting wire. In the aluminum two-width structures studied here, the unusual measured switching current challenges description by known theories.

We present a systematic derivation of regular black hole solutions - and their horizonless counterparts - that achieve regularization via an anti-de Sitter core. These geometries emerge as polymerized vacuum solutions inspired by loop quantum gravity, constituting effective quantum gravity configurations that admit a Birkhoff-type theorem and are uniquely determined by their mass. Using an auxiliary relational dust clock, together with the absence of gravitational waves in spherical symmetry, we exploit the structural ultralocality of the system to decompose the dynamics into independent shell degrees of freedom. The dust field acts as a reference clock for deparameterization and does not source the vacuum geometries considered here. These assumptions tightly constrain the Lemaitre-Tolman-Bondi shell Hamiltonian to a factorized form and the static vacuum metric function to a universal expression. We examine the possibility of a bounce and analyze how its presence is encoded, or missed, in finite-order effective truncations of the full model. The procedure for deriving the explicit physical Hamiltonian is described for a generic case before specializing to a specific model of interest. Finally, we construct a four-dimensional covariant completion of the spatially covariant Lagrangian, showing that it belongs to the class of generalized extended mimetic gravity models.

The potential to utilize metal-organic frameworks as a replacement for rare earth materials as well as in technological applications has prompted increased interested in this material class. The simulation of organic materials, including metal-organic frameworks (MOFs), represents a computational challenge due to an increased average number of atoms in the unit cell. Compounding this challenge, modern materials databases are generally limited to inorganic structures due to their utility in modern technologies such as batteries and integrated circuits. Machine-learning tools appear ideally suited to study these systems. However, organic materials are generally underrepresented in the training sets of foundational models. In this work we leverage the the Organic Materials Database (OMDB) to create a training dataset comprised of more than 15,000 single-point first-principles computations for finetuning machine learned interatomic potentials. Specifically, we fine tune CHGNet and implement a site substitution workflow to identify novel, highly magnetic, MOFs from structural prototypes within the QMOF database.

User simulators are increasingly central to interactive information retrieval, yet the community lacks standardized evaluation tools. Simulators serve two objectives, behavioral realism (matching real user behavior) and tester reliability (producing valid system rankings), and these are often conflated despite being distinct and sometimes conflicting. We present SimEval-IR, an open-source toolkit and benchmark suite that makes this distinction measurable. SimEval-IR provides: (1) a canonical session schema unifying session search and conversational interactions, with validated dataset adapters and explicit loss accounting; (2) three executable benchmarks covering behavioral realism, tester reliability with RATE-style estimation, and an analysis linking the two; and (3) baseline results across four real datasets in two languages and four simulator families. Our key finding: the classifier-discriminator ''human-likeness'' check, the dominant realism test in the literature, has essentially no pooled predictive power for system-ranking validity ($r{=}{+}0.09$, $n{=}48$), while marginal click-depth distance and Fréchet distance over session embeddings give a much stronger signal ($|r|{=}0.43$ and $0.40$, $p{\leq}0.005$). SimEval-IR is released with all configurations and scripts to reproduce the reported analysis.

In this paper, we present a new approach to obtain so-called damping estimates for self-similar solutions to general hyperbolic relaxation systems applying the method of characteristics. Such damping estimates are an important part of the stability theory of shock profiles, where they enable the closure of nonlinear stability arguments. We extend the damping estimates obtained in Mascia and Zumbrun (2005) from the $L^2$-case to the $L^\infty$-case and, at the same time, generalize the $L^2$-estimates to the non-symmetric setting. Our estimates open the door to a general stability theory of shock profiles of hyperbolic relaxation systems under nonlocalised perturbations in one space dimension.

Discontinuous shear thickening (DST) in dense suspensions leads to flow instabilities that limit processing in many systems. While high-power ultrasound has been reported to reduce the apparent viscosity of such materials, the origin of this effect remains unclear. Here, we investigate dense adhesive cornstarch suspensions, where shear thickening arises from fragile, load-bearing force networks embedded in heterogeneous density-wave structures. Using a rheo-ultrasound setup, we show that ultrasound does not directly reduce viscosity but instead shifts the shear-thickening transition toward higher shear rates. This is evidenced by the collapse of stress probability distributions onto master curves, revealing a continuous evolution toward more fluid-like states without a sharp threshold. We interpret these results through a separation of time scales, in which the suspension behaves as an effectively immobile porous medium subjected to high-frequency interstitial flows. Fluidization then arises from a combination of boundary slip, bulk destabilization of force networks by drag-force fluctuations, and localized acoustic streaming. Beyond these mechanisms, we propose that ultrasound modifies the stability of force networks by introducing fluctuating hydrodynamic forces at the pore scale. As a result, larger stresses or shear rates are required to sustain jammed states, leading to a continuous renormalization of the DST transition. These findings provide a consistent physical picture of acoustic fluidization in adhesive suspensions and establish ultrasound as a powerful tool to control discontinuous shear thickening in confined flows.

The cohomological rigidity problem for toric orbifolds asks when an integral cohomology isomorphism implies a homotopy equivalence. In this paper we reformulate the cohomological rigidity problem in the context of $4$-dimensional toric orbifolds by introducing what we call proper isomorphisms, a variant of a concept studied by J.H.C. Whitehead. We prove that each proper isomorphism class of $4$-dimensional toric orbifolds contains at most two distinct homotopy types, and that the two classifications agree in certain special circumstances.

The mixed alkali or mixed mobile ion effect in glasses manifests itself by strong nonlinear variations of ionic transport properties upon mixing of different types of mobile ions. We develop a theory for this effect based on thermally activated hopping transport in disordered site energy landscapes that consistently incorporates the statistical-mechanical and kinetic aspects of a mobile ion mixture. This includes a consideration of the joint probability density of site energy states, generalized Fermi distributions for mean site occupations, and cross-terms in the current response described by nondiagonal Onsager coefficients. The theory shows that a mixed alkali effect can arise even when the two ion species share identical site energy distributions. It suffices that sites have distinct energies when occupied by ions of different type. Taking into account that a mismatch energy is needed for ions of one type to occupy sites adapted to the other type, the mixed alkali effect becomes stronger. Spatial correlations between site energies are needed for the mobility of the majority ion to decrease stronger than exponential upon replacement by the minority ion. The theory agrees well with kinetic Monte Carlo simulations. Application to mixed alkali phosphate glasses yields good agreement with measured conductivity activation energies.

We present D-Rex, a person-specific framework for photorealistic, relightable, expressive, and animatable full-body human avatars with free-viewpoint rendering. Existing methods for relightable full-body avatars rely on explicit 3D intrinsic decomposition with analytic reflectance models, which require accurate geometry registration and careful optimization to capture realistic light transport effects. This tight coupling of relighting with avatar modeling has hindered expressiveness: to our knowledge, no existing method demonstrates strong facial animation alongside relighting, limiting applicability in telepresence, gaming, and virtual production. We propose to decouple relighting entirely from avatar modeling by treating it as an image-space post-process: a learned translation from flat-lit, albedo-like renderings to a target HDR illumination. To this end, we leverage the strong generative prior of a pre-trained video diffusion relighting model, fine-tuned via LoRA on paired flat-lit and relit frames captured in a light stage. The flat-lit driving frames are produced by an independent expressive full-body avatar framework trained under white-light conditions, requiring no modification to support relighting, making D-Rex directly applicable to any white-light avatar system. We demonstrate that D-Rex enables view- and temporally consistent relighting while faithfully preserving expressive motion and fine-grained facial detail, outperforming physically-based relightable avatar baselines. Project page is https://vcai.mpi-inf.mpg.de/projects/DRex/

We investigate the systematics of the maximum Electron-decay energy E as a function of the mass number A along isotopic chains with a fixed proton number across Z<47. By making use of the available curated nuclear data, we find that, for each fixed Z, the decay energy can be described to excellent accuracy by a linear dependence on A, provided that even-A and odd-A isotopes are treated separately. This yields two straight-line trends for each element, which are characterized by the slope and intercept parameters that can be systematically tabulated across the studied range. The corresponding fits are remarkably accurate, where the coefficients of determination are typically almost unity. Such an element-by-element empirical regularity does not appear to have been previously tabulated in a compact systematic form in the nuclear physics literature. We hence provide a simple and compact parameterization of Electron-decay energetics along isotopic chains with respect to our stated scope, whereby the approach at hand may prove useful for the analysis of decay-energy evolution, behavioral classification, and preliminary estimates of Electron-decay properties. The broader theoretical motivation that initially led us to search for such a regularity is discussed only after the confirmation of our results through experimental data is established.

The Etzion-Silberstein conjecture asserts that, for any finite field $\mathbb F$, Ferrers diagram $\mathcal D$, and integer $d$, there exists a linear matrix code supported on $\mathcal D$ with minimum rank distance $d$ that attains a natural upper bound on its dimension. Codes achieving this bound are called maximum Ferrers diagram (MFD) codes. While the conjecture has been established for several classes of diagrams (including rectangular, monotone, and MDS-constructible cases), it remains open in general. In this paper, we study the reducibility of Ferrers diagrams. For a fixed distance $d$, a diagram $\mathcal D$ is said to reduce to $\mathcal D'$ if an MFD code for $(\mathcal D,d)$ can be obtained from one for $(\mathcal D',d)$ via shortening or inclusion. Diagrams that are not reducible are called irreducible. We show that the conjecture holds for all diagrams if and only if it holds for irreducible ones, thereby reducing the problem to this fundamental class. Our main result provides a complete characterization of irreducible diagrams: for each $d$, they correspond exactly to the integer points of a polytope $\mathfrak{P}_d \subset \mathbb{R}^{2d-3}$. We prove that these polytopes are integral, enabling the use of Ehrhart-theoretic tools to study their structure. Finally, we formulate a new conjecture on puncturing and inclusion of maximum rank distance codes, and show that it arises as a special case of the Etzion-Silberstein conjecture.

In this work, we investigate a classical cosmological test - the dependence of galaxy surface brightness on redshift z (the Tolman test). We analyzed 6 860 galaxies with reliably determined spectroscopic redshifts from the ASTRODEEP-JWST photometric catalogue. We find that (a) the mean surface brightness of galaxies indeed decreases with increasing distance, and (b) the observed trend shows a significant departure from the prediction of the standard cosmological model, which expects the mean surface brightness to decline as ~ (1 + z)^-4.

High-order harmonic generation (HHG) in solids - the frequency up-conversion of an optical signal - is governed by symmetries. At terahertz (THz) frequencies, HHG is a key technology to access high frequency spectral windows that are usually difficult to cover using conventional solid state laser technologies. This effect has been recently exploited in graphene where HHG has been demonstrated, albeit only at odd multiples of the driving frequency owing to its inherent centro-symmetry. In topological insulators (TIs), the combination of spin-orbit interaction and time-reversal symmetry create an insulating bulk state with an inverted band order, inseparably connected with conducting surface states. TIs have been predicted to support unconventional high harmonic generation from the bulk and topological surface, which are usually difficult to be distinguished. However, no experimental results have been provided, so far. Here, we exploit the strong optical field amplification provided by an array of single or double split ring resonators, with embedded Bi2Se3 or (InxBi(1-x))2Se3/ Bi2Se3 van der Waals heterostructures, to achieve up-conversion in the 6.4 (even) - 9.7 (odd) THz frequency range. This results from bulk centro-symmetry (odd states) and symmetry breaking in the topological surface states (odd and even).