We investigate whether the redshift evolution of the fixed-$k$ dimensionless 21 cm power spectrum, $Δ^2_{21}(k, z)$, contains sufficient information to reconstruct reionization histories $x_{\mathrm{HI}}(z)$ with artificial neural networks. Using semi-numerical realizations generated within a restricted three-parameter 21cmFAST model family, we train a compact feed-forward network to learn the inverse mapping from power-spectrum trajectories to the neutral-fraction history over $6 \le z \le 15$. For $k = 0.1$, $0.5$, and $1.0\ h\ \mathrm{Mpc}^{-1}$, representative tests on an independent test set show that the midpoint redshift $z_{50}$ is recovered more accurately than the duration $Δz = z_{75} - z_{25}$: $z_{50}$ is reconstructed with MAE = 0.0046 and RMSE = 0.0100, whereas $Δz$ yields MAE = 0.0302 and RMSE = 0.0378. This result indicates that fixed-$k$ power-spectrum evolution carries stronger information about the timing of reionization than about the detailed width of the transition within the adopted prior. We further test an idealized foreground-free SKA1-Low-like thermal-plus-sample-variance noise model and find that the reconstruction remains stable in the favorable signal-to-noise regime considered here. These results demonstrate that neural networks can serve as prior-dependent inverse mapping for reconstructing reionization histories from 21 cm power-spectrum evolution.

We reveal the existence of a universal upper bound on the magnetoelectric coupling of any bi-isotropic nanoparticle. The bound arises solely from energy conservation, making it independent of the specific material properties of the nanoparticle and illumination conditions. Moreover, the bound does not rely on reciprocity, being identical for reciprocal (chiral) and non-reciprocal (Tellegen) nanoparticles. We further show that the chiral Mie coefficient of spherical particles of arbitrary optical size obeys the same bound across all multipolar scattering channels. Our results introduce a universal metric on the magnetoelectric coupling of bi-isotropic objects, setting identical limits on chiral and Tellegen light-matter interactions at the single particle level.

Skyrmion crystals have been primarily discovered under a magnetic field for materials with non-centrosymmetric interactions. More recent developments have investigated the stability of skyrmion crystals in itinerant magnets without magnetic field. In this study, we find that a type of skyrmion crystal with two topological charges per unit cell and no magnetization at the ferromagnetic point in reciprocal space, SkX-2, is naturally stabilized in an $SO(3)$-symmetric model with short-range interactions realized by the Heisenberg model on the triangular lattice with scalar chirality. We complement our numerical results with a theoretical analysis that quantitatively describes the transition from the ferromagnetic ground state to the SkX-2 and the evolution of the topological charge density. Despite the constraints given by the Mermin-Wagner theorem at finite temperature, the SkX-2 exhibits both a first-order phase transition associated with translation symmetry breaking and a continuous transition to a floating solid, depending on the charge density controlled by the model parameters. Finally, the tetrahedral phase supported by an antiferromagnetic interaction in our model is found to host $\mathbb{Z}_2$-vortices at finite temperature, suggesting the existence of an additional vortex topological transition.

This paper examines how wartime economic controls shaped stock-price formation in Japan from 1930 to 1943. We develop a four-portfolio asset-pricing model in which zaibatsu affiliation affects expected payoffs and the translation of valuations into economic scale through lower financing wedges. We then construct daily capitalization-weighted indices and four benchmark portfolios based on a two-by-two sort by zaibatsu affiliation and military orientation. Using a CAPM-AR(p)-SV event-study framework that allows for serial correlation and stochastic volatility, we show that the model rationalizes capitalization concentration, segmented abnormal returns, delayed cumulative adjustment, regime-risk insulation of zaibatsu portfolios, and zaibatsu-concentrated responses to embedded-rent or group-continuation shocks. The evidence is consistent not with a collapse of semi-strong efficiency, but with institutionally contingent efficiency: stock prices continued to respond to news while capitalizing uneven access to credit, materials, and procurement.

Reasoning has become a defining capability of modern foundation models, yet its development in the audio modality remains limited. Audio poses challenges that are distinct from those of text and vision. It is continuous, temporally dense, and contains linguistic, paralinguistic, and environmental information at multiple time scales. As a result, audio reasoning models must align acoustic signals with the discrete semantic space of large language models, while still preserving fine-grained information needed for reliable inference. Progress is also limited by three major obstacles: the scarcity of genuinely audio-grounded reasoning data, shortcut learning and modality hallucination, and the tension between reasoning depth and real-time latency in spoken interaction. In this paper, we present the first dedicated survey of audio reasoning. We provide a unified formulation that distinguishes direct predictive modeling from reasoning-augmented generation, review the architectural and training foundations of audio reasoning models, and systematically organize recent advances in Audio-to-Text, Audio-to-Speech, Audio-Visual Reasoning and Agentic Audio Reasoning. We further examine emerging paradigms such as Chain-of-Thought prompting, supervised fine-tuning, reinforcement learning, and latency-aware spoken interaction, and discuss evaluation practices, open challenges, and future directions. Our goal is to offer a coherent roadmap for developing robust, efficient, and natively grounded audio reasoning systems.

In many stochastic models, the observables of interest are naturally encoded in double transforms (e.g., Laplace transforms) that couple spatial and temporal variables. Notably, the double transform often provides the only analytically tractable starting point for the study of processes with correlated increments or path constraints. We extend the Tauberian approach for precise large deviations of stochastic processes belonging to the domain of attraction of spectrally positive stable laws, previously developed for single-variable Laplace--Stieltjes transforms [9], to the bivariate setting. This methodology provides a direct route to asymptotic behaviour that is otherwise difficult to characterize using single-transform techniques. As illustrative examples, we derive precise large deviations for random sums with increments correlated to the stopping time and for path-dependent observables of random walks constrained to remain positive.

We present a chip scale planar cavity platform based on an attached split ring resonator (ASRR) integrated with yttrium iron garnet (YIG) structures to achieve strong magnon photon coupling in a compact hybrid system. The ASRR geometry was numerically optimized by tuning inter ring spacing, gap width, substrate thickness, and permittivity, resulting in a quality factor of Q = 190 at 5.48 GHz, enabling strong microwave magnetic field confinement and reduced radiative losses. The optimized cavity was coupled to YIG elements of three geometries: full ring, half ring, and disk. Full electromagnetic simulations show that the full ring geometry exhibits balanced performance with coupling strength 115 MHz and cooperativity 13.10, while the half ring shows a comparable coupling strength of 108 MHz and slightly higher cooperativity 13.50, despite edge induced demagnetizing effects. In contrast, the disk geometry couples at lower bias magnetic fields and achieves the strongest interaction (135 MHz, 25.30), enabled by improved microwave magnetic field overlap. These results demonstrate that geometry, rather than magnetic volume alone, is a key design parameter for tailoring magnon photon coupling, providing a practical framework for lithography compatible, on chip hybrid magnonic and quantum devices.

We investigate the thermodynamic and structural properties of divalent patchy hard rods confined to a one-dimensional channel by modeling the bonding sites as attractive square-well (SW) patches located at the rod tips. The zero-range sticky limit is recovered by letting the well width vanish while keeping the stickiness parameter finite. While Wertheim's first-order thermodynamic perturbation theory (TPT1) becomes exact in this sticky limit, it fails for finite-range site-site interactions. We show that the theory can be made exact in one dimension by replacing the standard law of mass action with an exact relation between the density and the fraction of unbonded sites, together with an exact bonding free-energy contribution. Finite-range SW sites produce a richer structural behavior than sticky sites, including monotonic and oscillatory asymptotic decay of the pair correlation function, separated by the Fisher--Widom line. In the monotonic regime, the correlation length exhibits an absolute maximum defining the Widom line, while in the oscillatory regime it may display a local maximum and minimum, whose locus defines the ``Extrema of the Correlation length under Oscillatory decay'' (ECO) line. These features disappear in the sticky limit, where the system remains entirely in the oscillatory regime. We also show that the high-pressure behavior of the correlation length changes from $ξ\sim p^2$ for finite-range SW sites to $ξ\sim p^3$ in the sticky limit.

Mixed-integer extensions of evolution strategies (ES) that discretize selected coordinates of sampled continuous vectors often impose a lower bound on the standard deviation of integer variables to prevent premature convergence. While these methods show promising empirical results, this handling can slow the convergence of continuous variables, and its impact has lacked a clear theoretical account. In this paper, we provide a convergence analysis of evolution strategies for mixed-integer optimization, inspired by the drift analysis of the (1+1)-ES in the continuous domain. Specifically, we consider two (1+1)-ES variants for mixed-integer domains: (1+1)-LB-ES, which introduces a lower bound on the standard deviation for integer variables, and (1+1)-LUB-ES, which combines both lower and upper bounds to enhance the convergence of the continuous variables. Focusing on the optimization phase after the integer variables have been optimized, we rigorously analyze their convergence behavior on a benchmark function designed for mixed-integer domains. Our results show that (1+1)-LB-ES can suffer from premature convergence when the number of integer variables is large, while (1+1)-LUB-ES achieves linear convergence under suitable parameter settings. These findings provide theoretical insights into the impact of integer handling on convergence performance and guidance for the design of mixed-integer ES.

We find that the effective dimension of the Wasserstein space of energy eigenstates decreases as a quantum system becomes more chaotic. To demonstrate this, we study a quantum coupled harmonic oscillator system using Husimi Q-representations, to which Sinkhorn-regularized optimal transport is applied to construct an embedding geometry via the Gram-spectrum method. We also demonstrate that exponential OTOC growth, referred to here as quantum scrambling even in the absence of chaos, induces a folding structure in the emergent Wasserstein space, which may underlie the chaotic reduction of the Wasserstein dimension. At the separatrix (the scrambling point) of the inverted harmonic oscillator, the Wasserstein distance correctly captures the Lyapunov exponent. Furthermore, we discover that a branching structure in the Wasserstein space signals quantum scar states within the chaotic sea of phase space. Our optimal transport approach thus provides a new diagnostic for quantum chaos, quantum scrambling, quantum scars, and quantum Lyapunov exponents. The observed chaotic dimensional reduction also supports the recent conjecture [arXiv:2604.17649] that the Wasserstein space serves as an emergent holographic space through the manifold hypothesis, since chaoticity is a characteristic signature of black holes in holography.

We present a compact photodiode-based diagnostic array developed to study low-energy neutral beam injection in the LTX-$β$ spherical tokamak. The in-vacuum diagnostic combines filtered soft-x-ray (SXR), narrowband Lyman-$α$, and unfiltered AXUV photodiode rows with partly overlapping, nearly coincident tangential views of the plasma, including the neutral beam path. This geometry provides simultaneous sensitivity to beam-induced SXR emission; neutral-hydrogen line radiation associated with recycling, fast neutrals and fueling; and broadband emission that can include direct neutral impacts from fast-ion charge-exchange losses. Initial measurements from 12-20 keV hydrogen beam operation show beam-synchronous detector responses in all three modalities. The unfiltered AXUV signals exhibit millisecond-scale rise and fall times that are much slower than the detector response, that vary across sightlines, and depend on lithium-conditioning history. Comparison with classical slowing-down time estimates indicates that charge exchange with background neutrals contributes appreciably to the measured decay. The diagnostic can potentially be used to constrain a forward model to estimate the time-resolved balance of beam heating and fueling for small tokamaks.

T Coronae Borealis (T CrB) is a symbiotic recurrent nova (RN) that exhibits both nova eruptions and long-term active phases resembling superoutbursts and normal outbursts. Motivated by proposed connections between these events and the binary orbit, we test whether the onset, maximum, or termination of the active phases is locked to orbital phase. We use long-term optical $B$- and $V$-band light curves from the American Association of Variable Stars Observers (AAVSO) International Database and historical photometry from the literature. We measure the onset, maximum, and termination times of superoutbursts and normal outbursts and convert these times to orbital phase. We test the resulting circular distributions with Kuiper and Watson statistics. We find no statistically significant orbital-phase locking. The maxima and termination are consistent with a uniform phase distribution. The smallest probabilities occur for the normal-outburst onset phases ($p_{\rm MC}=0.083$ for the Kuiper statistic and $p_{\rm MC}=0.079$ for the Watson statistic), but these values do not satisfy either a commonly used $p<0.05$ criterion or a $3σ$ criterion ($p=0.0027$). We therefore treat any apparent onset preference as a non-detection. The four historical nova eruptions likewise do not provide robust evidence for a unique ignition phase once the small sample size, historical date uncertainties, and long-term period changes are considered. The two known secondary eruptions occurred at similar phases, but two events are insufficient to establish an orbital-geometry connection. Overall, the active phases of T CrB appear to be governed primarily by accretion-disk physics rather than by a fixed binary phase.

We study the two-dimensional $q$-state clock model in the presence of an additional $p$-fold symmetry-breaking crystalline field using Monte Carlo simulations. While the pure clock model exhibits Berezinskii--Kosterlitz--Thouless (BKT) transitions for sufficiently large $q$, the effect of competing discrete anisotropies on this topological phase remains nontrivial. We show that even weak crystalline fields qualitatively modify the phase diagram by suppressing the BKT phase and inducing transitions to states with true long-range order. The resulting behavior depends sensitively on the interplay between the intrinsic $\mathbb{Z}_q$ symmetry and the imposed $\mathbb{Z}_p$ anisotropy. In particular, in the six-state clock model for $p=2$ we observe qualitatively different scenarios depending on the sign of the field: a single transition for $h_2>0$ and a two-step ordering process for $h_2<0$ with an intermediate ordered phase. For $p=3$, the system exhibits a direct transition consistent with three-state Potts criticality. These results demonstrate that the phase structure cannot be inferred from symmetry considerations alone, but is governed by the competition between distinct locking mechanisms. Our findings provide a discrete counterpart to the multi-frequency sine-Gordon description of generalized $XY$ models and illustrate how additional anisotropies reshape topological phase transitions in two dimensions.

This paper focuses on the estimation of partially observed branching processes. First, the estimators from a frequentist perspective proposed in the literature are reviewed. The main objective of this paper is to present computational tools based on sequential Monte Carlo methods to perform Bayesian inference for these processes. In particular, the Liu-West particle filter is applied to perform Bayesian estimation of the parameters of interest for an epidemic model fitted by a partially observed branching process. As application, the example given in [8] is revisited and extended.

Multiferroic CFO-BCTSn composite nanofibers were synthesized using a sol-gel electrospinning method. Electron microscopy revealed well-defined fibers with diameters of 120-150 nm. Structural analyses using X-ray diffraction, Raman spectroscopy, and high-resolution transmission electron microscopy confirmed the coexistence of the spinel CFO phase and the perovskite BCTSn phase without detectable secondary phases. Magnetic hysteresis measurements demonstrated the magnetic behavior of the nanofibers, while piezoresponse force microscopy confirmed their piezoelectric properties. Magnetoelectric coupling was evidenced by differences between the magnetic hysteresis loops of electrically poled and unpoled samples. These lead-free composite nanofibers show potential for nanoscale magnetoelectric devices and magnetic field sensing applications.

Although the density functional theory plus Hubbard $U$ correction method (DFT+U) is broadly used to study electronic structure of strongly correlated materials, the extension of this method to electron-phonon $g$ matrices has received limited attention. Here, we implement an algorithm that integrates DFT+U method with the finite-displacement method for the calculations of phonons and electron-phonon $g$ matrices. The Hubbard $U$ corrections are applied not only to electronic and phonon structures, but, more importantly, also to electron-phonon $g$ matrices. We demonstrate our algorithm in two prototypical correlated materials: infinite-layer nickelates LaNiO$_2$ and ruthenium dioxide RuO$_2$. We find that: i) While the Hubbard $U$ corrections weakly increase the electron-phonon interaction of 20% hole-doped LaNiO$_2$, its total electron-phonon coupling remains small and is insufficient to account for the observed superconducting transition temperature of about 10-30 K. Our results contrast with the recent work showing that the full GW corrections yield an elevated electron-phonon coupling of 20% hole-doped LaNiO$_2$ five times larger than its DFT value. We attribute this discrepancy to the differences in the Fermi surface topology between DFT+$U$ and GW methods. ii) The inclusion of Hubbard $U$ corrections eliminates the imaginary phonon modes of RuO$_2$ under strain on the TiO$_2$ substrate and substantially reduces the electron-phonon coupling. Our results alleviate the discrepancy between the reported large theoretical electron-phonon coupling and the low superconducting transition temperature observed experimentally. Our work provides an algorithm that fully includes the Hubbard $U$ corrections on electron-phonon properties of correlated materials, and highlights the importance of Fermi surface shape and correlation effects on phonon spectrum and electron-phonon $g$ matrices.

Domain names are key assets for organisation. They anchor an organisation's online presence and reputation, and serve as linking pin for web services and, e.g., email. Consequently, a malicious takeover of a domain can lead to significant damages. Organisations register domain names through so-called registrars, a type of business that plays a key role in the domain name industry. This implies that registrars play an important part in safeguarding against malicious takeovers of domains. In this paper we empirically study how registrars implement security controls to prevent against such takeovers. We focus on the top 10 most popular registrars for the .nl ccTLD. We present the results of this study in light of a model for the impact of domain takeovers, that analyses the possible consequence of a takeover. We contrast this against the impact of two other well-known threats: ransomware and DDoS attacks. We find that all registrars in our study implement relatively effective security measures, but that they fall short in more advanced security controls, such as the proper implementation of two-factor authentication. We also find that a domain takeover can have significant impact, potentially equalling that of a ransomware attack.

This paper illustrates the design and implementation of a smart home automation system for the conservation of energy and user control with the help of environmental sensors and Raspberry Pi 5. It monitors real-time conditions like motion, temperature, humidity, light and smoke to automatically control the device's behavior and save energy. A prototype single two-room was developed which uses GPIO/I2C interfaces to integrate sensors and actuators. The fan speed and LED brightness was dynamically controlled using PWM. Manual control and real-time monitoring are made possible through a web dashboard that was developed using Flask and graphical displays, and CSV logs of the energy are taken every 30 seconds. It was designed in an iterative model of sprints and the energy savings during testing was more than 46% over an always-on model. The results prove that with the help of these low-cost, modular devices it is possible to improve sustainability and usability in the home as part of the IoT.

This study explores asymptotically flat wormhole solutions in $f(Q,T)=αQ+ βT$ gravity, expanding upon our prior work (arXiv:2602.00527v1) with matter Lagrangian density, $L_m=-P$ . Here, we examine the implications of employing $Lm=-T$ and $L_m=ρ$. The field equations, derived via action variation, share a common general structure but are fundamentally dictated by the parameters $α$ and $β$ through the coefficients $A_i$. Solutions with linear and asymptotically linear equation of state are explored. We conclude that non-exotic asymptotically flat wormhole solutions exist for all considered matter Lagrangian densities. A key outcome is the demonstration that different $L_m$ choices enable the same shape function to be supported by varied fluid configurations, or vice versa, identical fluids to yield different geometries. The energy conditions and physical characteristics of these solutions are shown to be distinct and critically dependent on the selected $L_m$.

Opinion formation models typically represent each individual as a single variable. However, in practice each individual holds interconnected beliefs whose internal organization may influence collective outcomes. To explore this dependence, we study a three-state opinion model on a network of networks in which each agent has an internal belief graph and interacts with other agents through an external social graph. Each belief can take two opposite polarized states or a neutral one and a neutrality parameter tunes the relative conviction of the neutral stance. We incorporate temperature into the model to account for external social agitation and for the tolerance of internal cognitive dissonance. We explore the stationary state and dynamics of the model using analytical approaches and Monte Carlo simulations on a fully connected external social graph, with internal belief topologies given by one-dimensional chains, cliques, and star-like structures, where there is a central core belief to which all other beliefs are connected. We find that the critical temperature at which the polarized consensus destabilizes increases with the addition of more beliefs to star-like agents but saturates in the case of ring- and clique-like internal topologies. We also consider binary mixtures of agents with different internal topologies in equal proportions, showing that the interplay between agents is regime-dependent, with the dominant topology depending on the value of the neutrality parameter.

Most neural video codecs rely on temporal conditioning, which makes them susceptible to error propagation over long sequences. While Transformer-based architectures like the VCT offer a drift-free alternative, they suffer from high computational complexity and inferior RD performance. The recent SWA addresses these shortcomings by reducing complexity and enhancing RD performance, yet it restricts decoding to a strictly sequential raster-scan order, creating a critical bottleneck in decoding latency. To resolve this, we propose P-SWA, utilizing diagonal wavefronts to enable parallel decoding. By embedding a hyperprior and introducing an accumulator to fuse side information and local spatial context, our method increases decoding speed by 36% over the parallel VCT. Simultaneously, it achieves Bjøntegaard Delta-rate savings of up to 10.0% for I-frames and 7.1% for P-frames over the SWA baseline.

Layered chromium tellurides are model systems for studying low-dimensional magnetism in van der Waals materials. We report the synthesis and characterization of K$_{1-x}$CrTe$_2$ single crystals ($x \approx 0.3$), which crystallize in the $Cm$ space group with trigonal prismatic K$^+$ coordination, unlike the octahedral environments of more stoichiometric ACrX$_2$ compounds. Magnetization measurements show a sharp ferromagnetic transition at $T_{\rm C}=117$ K and in-plane magnetic anisotropy, supported by density functional theory. Neutron diffraction reveals ferromagnetic alignment of Cr spins within and between layers. This contrasts with the out-of-plane A-type antiferromagnetism in LiCrTe$_2$ and NaCrTe$_2$, but resembles CrTe$_2$. These differences likely arise from changes in interlayer spacing, Cr oxidation state, or stacking. AC susceptibility and $μ$SR indicate short-range order above $T_{\rm C}$ and dynamic behavior below. Overall, K$_{1-x}$CrTe$_2$ provides a tunable platform for studying spin orientation and dimensionality in two-dimensional magnets.

The domination problem is a well-studied problem in graph theory. In this paper, we study two natural variants: the hop domination problem and the $2$-step domination problem. Let $G$ be a graph with vertex set $V$ and edge set $E$. For a graph $G$, a subset $S \subseteq V(G)$ is called an \emph{hop dominating set} if every vertex not in $S$ lies at distance of exactly $2$ from at least one vertex in $S$. For $v\in V(G)$, let $N(v,2)$ denote the set of vertices in $V(G)$ that are at distance exactly $2$ from $v$. For a graph $G$, a subset $S \subseteq V(G)$ is called an \emph{$2$-step dominating set} if every vertex $v\in V(G)$ lies at a distance of exactly $2$ from at least one vertex in $S$. The \textsc{Hop Domination} (HD) problem and the \textsc{$2$-Step Domination} ($2$SD) problems ask whether a graph contains a hop domination set or a $2$-step domination set of size at most $k$, respectively. We study the computational complexity of these problems, and show that both are NP-complete, even when restricted to $d$-regular graphs for every $d\geq 3$, claw-free graphs and also unit disk graphs.

This paper explores quantum heat engines based on qubit and qutrit working media interacting with thermal environments through generalized amplitude damping (GAD) channels. We investigate how quantum channels can be employed to model heat absorption, dissipation, and work extraction in open quantum thermal machines, and derive the conditions required for positive work extraction. The effects of quantum correlations, emission probability, population redistribution, and system--environment interactions on the thermodynamic performance of the engine are systematically analyzed across different operational regimes. In addition, we examine the ergotropy of qubit and qutrit systems under dissipative dynamics to understand how environmental effects influence the maximum extractable work. Our results demonstrate that multilevel quantum systems exhibit enhanced work extraction capability and improved robustness against decoherence compared to two-level systems, providing further insight into the role of dissipative dynamics and quantum resources in realistic quantum thermodynamic devices.

Predicting Room Impulse Responses (RIRs) remains a challenge due to the high dimensionality of audio signals and the need for perceptual accuracy. This paper introduces a neural network framework that predicts multi-band Energy Decay Curves (EDCs) directly from room geometry and material properties. Unlike standard models, our framework employs a custom composite loss function that optimizes for both energy levels and decay slopes in the log-domain. This ensures the predicted curves adhere to physical decay principles while maintaining high sensitivity to reverberation time and early reflections. Results demonstrate that the model successfully approximates ground-truth acoustics with minimal error in T30 and clarity indices. The approach offers a computationally efficient alternative to traditional simulations, facilitating realistic audio rendering for interactive virtual environments.

We study the superconducting properties of high-quality PdD$_{x}$ films. The resistivity shows a sharp drop at $T$ $\sim$1.7 K, marking the superconducting transition. However, a finite resistivity persists and vanishes at $\sim$0.6 K. The temperature and magnetic-field dependences of the resistivity exhibit multiple anomalies within the superconducting state, revealing distinct superconducting phases. Such anomalies are absent in PdH$_{x}$ films. These results demonstrate a clear qualitative difference between the superconducting phase diagrams of PdD$_{x}$ and PdH$_{x}$, highlighting the role of nuclear-spin isotope effects.

We develop a regularity and compactness theory for stable capillary minimal hypersurfaces in the half-space $\mathbb{H}^{n+1}$ with contact angle $θ\in (0,π)$ and dimension $n \geq 2$. As a consequence, we obtain the generalized Bernstein theorem for embedded complete stable capillary minimal hypersurfaces in $\mathbb{H}^{n+1}$ with Euclidean area growth. The key innovation is an integral curvature estimate: by carefully selecting an appropriate tilt excess function, we are able to eliminate the boundary terms arising in the stability inequality. Building on this, we establish a boundary sheeting theorem by refining the arguments in [SS81]. These results, combined with a refined classification of stable capillary minimal cones, lead to the main regularity and compactness theorems.

Bilevel optimization problems arise in many applications where decisions must account for the optimal response of another system, such as in game-theoretic settings. However, these problems are notoriously challenging, as even linear bilevel programs are strongly NP-hard. In this work, we consider bilevel optimization with a known upper-level objective and an unknown, potentially time-varying lower-level response, accessible only through noisy zeroth-order observations. We propose W-SparQ-BL, a Bayesian optimization framework that models the lower-level mapping using multi-output Gaussian processes and enables efficient optimization under uncertainty. Our approach leverages a sparse, observation-based approximation to control the effect of noise and temporal variability, while requiring only limited access to additional information over time. We establish regularity results linking the lower-level response to standard RKHS assumptions for common kernels, including Matérn and squared exponential. We prove that W-SparQ-BL achieves sublinear dynamic regret in both stationary and time-varying settings. Experiments on representative time-varying game-theoretic problems demonstrate the effectiveness of our approach.

Spiral galaxies, like the Milky Way, transform at some point in time into a rotationally supported system. Using an extant data-set consisting of 319 835 sub-giants from LAMOST with precise ages from the literature, we determine, for the first time the age when the Milky Way disk spins up, i.e. when the mean circular velocity changes from halo-like to disk-like. We find in concordance previous studies that the spin-up takes place for -1.25 < [Fe/H] <- 0.9 and we can date this transition to a mean age of 12.1 +/- 2.8 Gyr (median age 12.4 Gyr). We further study when the disk became rotationally supported, i.e. when the ordered, disky motion dominates over the random motions. We find that this happens for $-1.25<$[Fe/H]$<-1$. The transition is very rapid in age. This gives support to that the spin-up seen in this and other works genuinely traces the motion to a rotationally supported disk, which has not previously been shown. These transitions are traced by the high-alpha stars. while the low-alpha stars do not spin-up but start directly at approximately the circular velocity seen for the Sun today. The low-alpha disk is rotationally supported with no transition period in [Fe/H] or in age.

Let $\mathscr{C}$ be a reduced $0$-Auslander extriangulated category. Motivated by Pan--Zhu silting reduction for such categories, we introduce the notion of (signed) presilting sequences in $\mathscr{C}$ and establish a bijection between (signed) presilting sequences in $\mathscr{C}$ and (signed) $τ$-exceptional sequences over $Λ= \text{End}_{\mathscr{C}}(P)$, where $P$ is a projective generator of $\mathscr{C}$. This correspondence provides a new perspective on the Buan--Marsh bijection between signed $τ$-exceptional sequences and ordered support $τ$-rigid objects. Furthermore, we introduce a new category $\mathfrak{M}(\mathscr{C})$, called the $τ$-cluster morphism category of $\mathscr{C}$, whose objects are certain extension-closed subcategories of $\mathscr{C}$ and whose morphisms are described in terms of signed presilting sequences. As an application, we recover the $τ$-cluster morphism category of $Λ$ from $\mathfrak{M}(\mathscr{C})$.