Modular architectures are a promising route toward scalable superconducting quantum processors, but finite fabrication yield and the lack of high quality temporary interconnects impose fundamental limitations on system size. Here, we demonstrate chip-scale liquid-metal interconnects that show promise for plug-and-play superconducting quantum circuits by enabling non-destructive module replacement while maintaining high microwave performance. Using gallium-based liquid metals, we realize high-quality inter-module signal and ground interconnects, comparable in performance to conventional coplanar waveguide resonators. We illustrate consistent device characteristics across three thermal cycles between room temperature and 15 mK, as well as the ability to reform superconducting connections following module replacement. A width-dependent resonance frequency shift reveals a significant kinetic inductance fraction, which we attribute to the presence of $β$-phase tantalum as confirmed by X-ray characterization. Finally, we investigate power-dependent loss mechanisms and observe high-power dissipative nonlinearities qualitatively consistent with a readout-power heating model. These results establish liquid metals as viable chip-scale interconnects for reconfigurable, modular superconducting quantum systems.

We explore the helical quantum two-body problem i.e. two repulsively Coulomb interacting particles confined to move along a helix. The effective potential possesses a tunable number of potential wells superimposed on the repulsive Coulomb interaction that can be varied by changing the ratio of the pitch and radius of the helix. The anharmonicity of these wells depends crucially on this ratio and on the order of the well which can be seen also by analyzing the individual wells energy eigenvalue spacing. Our main focus is the investigation of the quantum dynamics of differently prepared wave packets that scatter from the multi-well potential landscape. We show that there exists a rich pattern forming transient evolution which depends also on the number of bound states of the individual wells. We demonstrate how the multiple wells leave their fingerprints in the dynamics leading, among others, to oscillatory structures on different spatial scales, the formation of beats and pulsed emission from single well localized wave packets due to their intrawell dynamics.

We study the influence of spin--orbit coupling (SOC) on orbital magnetism in $\mathrm{Pb}_{1-x}\mathrm{Sn}_x\mathrm{Te}$, a narrow-gap semiconductor. Using the $π$-matrix method, we calculate material-specific Landau levels and evaluate the magnetization, fully including interband effects. The system exhibits diamagnetism for both $x = 0$ and $x = 0.35$, with the latter showing a stronger response due to its smaller gap. The magnitude of diamagnetism increases monotonically with SOC strength, particularly in strong magnetic fields. To clarify the underlying mechanism, we introduce the free--Zeeman--Dirac (fZD) model and fit its parameters to the calculated Landau levels. The analysis reveals that SOC enhances the Dirac-type interband contribution relative to the Zeeman term, leading to increased diamagnetism. These results demonstrate that SOC can play a key role in orbital magnetism through interband effects.

Rydberg molecule, formed by one or more Rydberg atoms, exhibits remarkable properties, including an exceptionally large spatial extent, rich rovibrational level structures, permanent electric dipole moments, and a pronounced sensitivity to external fields. Based on the underlying binding mechanisms, Rydberg molecules can be divided into three categories, the ground-Rydberg molecule that is bound via a low-energy electron-atom scattering interaction between ground atom and Rydberg electron, the Rydberg-Rydberg molecule that is bound via a long-range electrostatic interaction between Rydberg atoms, and the ion-Rydberg molecule that is bound via single- or multi-polar interactions between Rydberg atom and ion. This review focuses on recent theoretical and experimental advances in diatomic Rydberg molecules, covering their formation and binding mechanisms, potential energy curves, experimental observations, and spectroscopic properties, with the aim of providing a comprehensive overview of the current state and future prospects of this rapidly developing field.

We study a generalization of specialized Simpson's main estimate in the context of cyclic harmonic $G$-bundles induced by split automorphisms. We apply it to the classification of Toda type $G$-harmonic bundles.

We establish gradient estimates of solutions to a class of nonlinear elliptic equations with measure data under Orlicz-type growth conditions. The growth is governed by the structural condition \[ 0<i_a\le t g'(t)/g(t)\le s_a<1. \] We obtain two types of regularity results: pointwise Wolff potential estimates for the gradient of solutions in the singular regime $i_a \in \big(\frac{n-1}{2n-1},1\big)$, and Lipschitz regularity of the solutions in the regime $i_a \in (0,1)$. In the power-type case $g(t)=t^{p-1}$, our results recover the known gradient estimates for the singular $p$-Laplace equation.

This article proposes a multi-phase-field model using the Puck failure theory to predict the failure in fiber-reinforced composites (FRCs) laminates. Specifically, this work proposes a two-dimensional multi-field model in conjunction with a mesh overlay method to compute in-plane damage in the FRCs laminates with various ply orientations. The formulation considers the two independent phase-field variables to trigger fiber and inter-fiber-dominated failure separately, thereby accessing the interrelation between the damage. Furthermore, the model considers two characteristic length scales and two structural tensors to describe the damage modes accurately. Each ply in the laminate is represented using a separate mesh and is combined using the mesh overlay method. Four benchmark examples are utilized to demonstrate the predictive capability of the proposed model. Specifically, coupon tests in tensile and compressive loading, open-hole tension, compact tension, and double-edged notched tension examples are presented along with the comparison with the experimental results from the literature. Furthermore, results regarding cross-ply laminates and isotropic laminates show the model's ability to mimic the experimental results both qualitatively and quantitatively.

Analog joint source-channel coding (JSCC) has demonstrated superior performance for semantic communications through graceful degradation across channel conditions. However, a fundamental hardware-software mismatch prevents deployment on modern digital physical layers (PHYs): analog JSCC generates continuous-valued symbols requiring infinite waveform diversity, while digital PHYs produce a finite set of discrete waveforms and employ non-differentiable operations that break end-to-end gradient flow. Existing solutions either fundamentally limit representation granularity or require impractical white-box PHY access. We introduce D2AJSCC, a novel framework enabling high-fidelity analog JSCC deployment on standard digital PHYs. Our approach exploits orthogonal frequency-division multiplexing's parallel subcarrier structure as a waveform synthesizer: computational PHY inversion determines input bitstreams that orchestrate subcarrier amplitudes and phases to emulate ideal analog waveforms. To enable end-to-end training despite non-differentiable PHY operations, we develop ProxyNet-a differentiable neural surrogate of the communication link that provides uninterrupted gradient flow while preventing JSCC degeneration. Simulation results for image transmission over WiFi PHY demonstrate that our system achieves near-ideal analog JSCC performance with graceful degradation across SNR conditions, while baselines exhibit cliff effects or catastrophic failures. By enabling next-generation semantic transmission on legacy infrastructure without hardware modification, our framework promotes sustainable network evolution and bridges the critical gap between analog JSCC's theoretical promise and practical deployment on ubiquitous digital hardware.

This paper was motivated by the worldwide May 12 initiative that aims to celebrate, encourage, and inspire women in mathematics. It presents in short how the May 12 initiative has arisen, what are some of the events in the first years, in particular the Generalized functions online workshop that started in 2021 in this context (and has continued as an annual event ever since), and a brief overview of some female mathematicians who have significant scientific contributions and who are the first women in some aspects: Maryam Mirzakhani (the first female mathematician who was awarded with the prestigious Fields medal; the May 12 initiative appeared in her honour), Hypatia (considered to be the earliest known female mathematician), Sofia Kovalevskaya (the first woman who has been awarded a doctorate in mathematics and considered to be the first woman who got a full professorship in mathematics in the modern academic sense), Emmy Noether (the first woman who gave a plenary lecture at the International Congress of Mathematicians), Karen Uhlenbeck (the first woman awarded with the prestigious Abel Prize), and Ingrid Daubechies (the first woman who became a full professor in mathematics at Princeton University, the first woman elected for President of the International Mathematical Union, the first woman who received the National Academy of Sciences Award in Mathematics). The paper was an invited contribution for the Akademie Intakt of the Austrian Academy of Sciences. It appeared in Akademie Intakt 2021, English Edition, Austrian Academy of Sciences, Vienna, 2021, 10-13, and it is submitted to arXiv with a permission from the publisher.

Parameter estimation-based observer (PEBO) is a recently developed constructive tool to design state observers for nonlinear systems. It reformulates the state estimation problem as one of online parameter identification, effectively addressing many open estimation challenges in practical applications. The feasibility of a PEBO design relies on two fundamental properties: transformability and identifiability. The former pertains to the existence of an injective solution to a suitable partial differential equation, whereas the latter characterizes the uniqueness of the parameterization induced by the resulting nonlinear regression model. In this paper, we analyze the existence of PEBOs for general nonlinear systems by studying these two properties in detail and by providing sufficient conditions under which they hold.

Positron emission tomography (PET) scans expose patients to radiation, which can be mitigated by reducing the dose, albeit at the cost of diminished quality. This makes low-dose (LD) PET recovery an active research area. Previous studies have focused on standard-dose (SD) PET recovery from LD PET scans and/or multi-modal scans, e.g., PET/CT or PET/MRI, using deep learning. While these studies incorporate multi-modal information through conditioning in a single-task model, such approaches may limit the capacity to extract modality-specific features, potentially leading to early feature dilution. Although recent studies have begun incorporating pathology-rich data, challenges remain in effectively leveraging multi-modality inputs for reconstructing diverse features, particularly in heterogeneous patient populations. To address these limitations, we introduce a multi-modality multi-task diffusion model (M2Diff) that processes MRI and LD PET scans separately to learn modality-specific features and fuse them via hierarchical feature fusion to reconstruct SD PET. This design enables effective integration of complementary structural and functional information, leading to improved reconstruction fidelity. We have validated the effectiveness of our model on both healthy and Alzheimer's disease brain datasets. The M2Diff achieves superior qualitative and quantitative performance on both datasets.

Recent developments in the multipole reformulation of X-ray absorption spectroscopy (XAS) have provided a unified framework to describe magnetic and orbital responses in terms of ferroic multipole order parameters. X-ray magnetic circular dichroism (XMCD) is known to probe spin, orbital, and anisotropic magnetic dipole (AMD) moments. Its applications to altermagnets and noncollinear antiferromagnets have revealed that the XMCD response is often governed by the ferroic states of the AMD in the photo-excited states rather than by conventional magnetic dipoles in the ground states. In this work, we extend the multipole-based analysis to X-ray magnetic linear dichroism (XMLD) and demonstrate that XMLD in altermagnets can be understood as a manifestation of piezomagnetic effects: linear couplings between magnetic dipole and electric quadrupole moments. Using symmetry analysis combined with exact diagonalization calculations of $L_{2,3}$-edge XAS, we systematically investigate representative altermagnets, including $α$-MnTe, MnF$_2$, and CrSb. We show that the ferroic ordering of higher-rank magnetic multipoles, particularly spinful magnetic octupoles, gives rise to characteristic field-odd XMLD signals that directly reflect the underlying piezomagnetic response tensors allowed by magnetic point-group symmetry. Furthermore, we discuss XMCD signals induced by piezomagnetic effects, in which strain generates magnetic dipole moments. Our results establish XMLD and XMCD as element-specific probes of magnetoelastic multipole order in altermagnets and provide a general symmetry-based pathway to identify hidden ferroic multipoles and strain-controllable spin phenomena beyond conventional ferromagnetism.

Phase-space features of a reduced version of the Toda-like Hamiltonian, $\mathcal{H}(x,\,k)$, written in a form constrained by the condition $\partial^2 \mathcal{H} / \partial x \partial k = 0$, with $x$ and $k$ as canonically conjugate variables, are analyzed in terms of Wigner currents. For Wigner currents convoluted with either thermodynamic or Gaussian ensembles, the underlying Hamiltonian dynamics admits analytic corrections due to quantum distortions over the classical phase-space pattern, computed and interpreted through quantifiers of quantumness and stationarity. Notably, while emulating the Lotka-Volterra (LV) dynamics that describe ecological competition systems, the Toda-like classical dynamics allows for analytical solutions with computable periods corresponding to closed phase-space orbits of isotropic prey-predator population distributions. The essential conditions for understanding how classical and quantum evolution can coexist are provided at different scales of quantumness, driven by the associated convoluting ensemble parameter. In the case of Gaussian statistical ensembles, the exact profile of the quantum distortions over classical prey-predator phase-space trajectories is obtained non-perturbatively. Our results indicate that, besides the classical stability admitted by LV models, the Toda-like patterns also exhibit quantum stability. Therefore, this can be regarded as the first step as a predictive theoretical framework towards more robust descriptions of quantum patterns in competitive microscopic biosystems.

Photospheric emission from relativistic gamma-ray burst (GRB) jets is a promising mechanism for producing the Band-like spectra observed in the prompt phase, yet the connections between jet structure, dissipation location, and polarization signatures remain unclear. We investigate time-dependent photospheric radiation transfer in structured relativistic jets by coupling two-dimensional axisymmetric special relativistic hydrodynamic (SRHD) simulations with Monte Carlo photon propagation. Photon escape and subphotospheric dissipation are characterized using the residual line-of-sight optical depth tau_out evaluated along each photon trajectory, allowing a direction-dependent treatment of photon decoupling in structured jets. The radiative transfer includes Klein-Nishina Compton scattering and polarization evolution using the Mueller matrix formalism. We perform a systematic parameter study exploring the effects of viewing angle, electron-positron pair loading (Z_pm), and the optical-depth window of subphotospheric dissipation. The model produces time-resolved spectra, peak-energy evolution E_pk(t), Band parameters, polarization degree Pi(E,t), and last-scattering statistics. We find that jet angular structure and the geometry of the line-of-sight optical depth strongly regulate spectral evolution and polarization signatures. The dissipation depth and pair loading jointly control the stability of E_pk, the formation of high-energy spectral tails, and the energy dependence of polarization. These results provide quantitative predictions for GRB prompt-emission spectra and polarization that can be tested with current and upcoming high-energy polarimeters.

We systematically investigate the field-aligned propagation and collisional absorption of normally incident laser light in a strongly magnetized inhomogeneous plasma. Analytical expressions for electric fields in both vacuum and plasma are derived. Using analytical modelling and particle-in-cell simulations, we establish the cutoff conditions, absorption efficiencies, and scaling laws for the right-hand (R) and left-hand (L) circularly polarized waves. The dependence of collisional absorption coefficient on magnetic field strength, plasma scale length and laser intensity are quantified. In particular, L waves reflect at cutoff density, with absorption strongly enhanced as the magnetic field increases. For the R-waves, the absorption decreases with increasing magnetic field when the normalized electron cyclotron frequency is less than unity. However, when it exceeds unity, the R-waves propagate as whistler modes without a cutoff, allowing penetration into overdense plasma. This enables deep energy deposition inside overdense plasma. These results provide a framework for understanding laser-plasma energy coupling through collisional absorption in strongly magnetized inhomogeneous plasma.

This paper presents a one-dimensional transient drift--diffusion simulator for advanced solar cells, integrating a structure-preserving finite-volume spatial discretization with Scharfetter--Gummel--type fluxes and a high-order, L-stable implicit Runge--Kutta (Radau IIA) temporal integrator. The scheme ensures local charge conservation, handles sharp material interfaces, and achieves second-order spatial and fifth-order temporal convergence. Its accuracy is verified against the classical depletion approximation in $p$--$n$ junction and validated through excellent agreement with the established simulator for an organic photovoltaic device. The framework's extensibility is demonstrated by incorporating exciton kinetics in organic solar cells, capturing multi-timescale dynamics, and by modeling mobile ions in perovskite solar cells, reproducing characteristic $\tmem{J}$--$\tmem{V}$ hysteresis without empirical parameters. This work provides a robust, high-order numerical foundation for simulating coupled charge, exciton, and ion transport in next-generation photovoltaic devices.

Spatial transcriptomics (ST) technologies enable transcriptome-wide gene expression profiling while preserving spatial resolution, offering unprecedented opportunities to uncover complex spatial structures. Due to the ultra-high dimensionality of ST data, identifying spatially variable genes (SVGs) associated with unknown spatial clusters has become a central task in ST data analysis. Here, we develop a distribution-free SVG screening method based on a novel quasi-likelihood ratio statistic, the MM-test, combined with a knockoff procedure to control the false discovery rate (FDR). MM-test leverages auxiliary information, such as spatial distances, about the unknown spatial domains for SVG screening. Notably, in addition to two-dimensional ST datasets, MM-test is well-suited for increasingly common three-dimensional (3D), multi-slice ST datasets. Extensive benchmarking using simulations and 34 real ST datasets demonstrates that MM-test consistently outperforms existing SVG detection methods. In a 3D mouse brain dataset, MM-test accurately delineates fine-scale structures that are challenging for other methods, such as the 3D architecture of the pyramidal layer of the hippocampal cornu ammonis and the dentate gyrus. Theoretical guarantees-including selection consistency, FDR control, and an error bound for post-selection clustering-are also established.

Fluctuations in the growing surfaces of classical systems can exhibit universal scaling behavior, known as Family-Vicsek (FV) scaling. Although this phenomenon was originally discovered in classical stochastic models, recent theoretical studies have demonstrated the presence of FV scaling in quantum many-body systems as well. Here, we observe the universal FV scaling in a one-dimensional Bose gas in an optical lattice. By monitoring the fluctuations of particle number in half of the system, which corresponds to the surface roughness, we extract all scaling exponents and demonstrate that the entire relaxation-from the growth of quantum fluctuations to their saturation-is captured by a single universal scaling function. Our results demonstrate that universal scaling laws of classical surface growth extend to quantum many-body systems, establishing a unified framework for nonequilibrium universality across classical and quantum systems.

Consider a connected graph $G$, and assume that every edge fails independently with probability $q$. The {\em (all-terminal) reliability polynomial} is the probability in $q$ that the spanning connected subgraph of operational edges is connected. In this paper we focus on the real roots of reliability polynomials ({\em reliability roots}). We prove that almost every graph has a nonreal reliability root, and that the reliability polynomials of graphs have roots dense on the interval $[β,0]$ where $β\approx-0.5707202942$.

We show that the Brascamp-Lieb (BL) constant BL(-,p) is a semi-algebraic function on the set of feasible data. Consequently, it is algebraic in the sense that it satisfies a polynomial relation of the form P(V, BL(V,p))=0 for a non-zero polynomial P. In fact, we establish an analogous statement in the more general setting of quiver BL constants associated to representations of bipartite quivers.

Developing AI literacy is increasingly urgent as generative AI reshapes creative practice. Yet most AI literacy frameworks are top-down and expert-driven, overlooking how literacy emerges organically in creative communities. To address this gap, we performed a large-scale analysis of 122k Reddit conversations from 80 creative-oriented subreddits over a three-year period. Our analysis identified four consistent themes in AI literacy-related discussions, and we further traced how discourse shifted alongside major AI events. Surprisingly, creators primarily frame AI literacy around how to use tools effectively, foregrounding practice and task skills, while discussions of AI capabilities and ethics surge only around high-profile events. Our findings suggest that AI literacy is dynamic, practice-driven, and event-responsive rather than static or purely conceptual. This study provides insights for researchers, designers, and policymakers to develop learning resources, community support, and policies that better promote AI literacy in creative communities.

Torons are three-dimensional double-twist solitons in chiral nematic liquid crystals that form localised director configurations protected by topology and bounded by closed defect loops. They behave as particle-like entities while retaining a fully reconfigurable optical response. Here it is shown experimentally that individual torons can be created, steered and parked on demand using tailored alternating-current electric fields in planar cells, enabling deterministic control of both position and trajectory. By tuning the ratio of cell thickness to cholesteric pitch and systematically adjusting waveform parameters, including amplitude, modulation frequency, duty-cycle asymmetry and small DC offsets, robust toron nucleation is achieved and programmable translation is realised along arbitrary in-plane directions with submicrometre placement accuracy. Directional transport is controlled within a defined frequency and temperature window and can be reversed by changing modulation conditions even at zero offset. A dedicated graphical interface enables real-time switching between waveform presets so that torons follow scripted paths and draw user-defined shapes. Quantitative Landau-de Gennes Q-tensor simulations reproduce toron nucleation and the ensuing translational dynamics, supporting an interpretation in which waveform-controlled director reorientation, reorientation-driven flow and rectified polarity-sensitive coupling jointly bias the drift. Finally, three proof-of-concept functions are demonstrated: a software-defined liquid-crystal racetrack memory analogue with optical readout, deterministic path writing for reconfigurable patterning, and toron-mediated pick-and-place transport of microparticles for micromanipulation.

Given a finite set $P\subset\mathbb{R}^2$, the directed Theta-6 graph, denoted $\vecΘ_6(P)$, is a well-studied geometric graph due to its close relationship with the Delaunay triangulation. The $\vecΘ_6(P)$-graph is defined as follows: the plane around each point $u\in P$ is partitioned into $6$ equiangular cones with apex $u$, and in each cone, $u$ is joined to the point whose projection on the bisector of the cone is closest. Equivalently, the $\vecΘ_6(P)$-graph contains an edge from $u$ to $v$ exactly when the interior of $\nabla_u^v$ is disjoint from $P$, where $\nabla_u^v$ is the unique equilateral triangle containing $u$ on a corner, $v$ on the opposite side, and whose sides are parallel to the cone boundaries. It was previously shown that the spanning ratio of the $\vecΘ_6(P)$-graph is between $4$ and $7$ in the worst case (Akitaya, Biniaz, and Bose \emph{Comput. Geom.}, 105-106:101881, 2022). We close this gap by showing a tight spanning ratio of 5. This is the first tight bound proven for the spanning ratio of any $\vecΘ_k(P)$-graph. Our lower bound models a long path by mapping it to a converging series. Our upper bound proof uses techniques novel to the area of spanners. We use linear programming to prove that among several candidate paths, there exists a path satisfying our bound.

We present observations and analysis of two low planet/host mass-ratio ($q$) microlensing planets discovered in high-magnification events. KMT-2025-BLG-0811Lb has $q \sim 4.5 \times 10^{-5}$, and a Bayesian analysis favors a super-Earth/mini-Neptune orbiting an M- or K-dwarf host at a projected separation of $\sim 3$ au. KMT-2025-BLG-0912Lb has $q = 2.6 \times 10^{-4}$ and likely hosts a super-Earth/mini-Neptune around either a low-mass M dwarf or a brown dwarf at $\sim 1$ au. Even with an observing cadence of $Γ> 30~{\rm hr}^{-1}$ during the planetary signal, KMT-2025-BLG-0811 still exhibits the "central-resonant" degeneracy. Reviewing nine such events, we find that the "central-resonant" degeneracy can be divided into two distinct types that occupy separate regions in the plane of $q$ and normalized source radius ($ρ$). Type~I events have similar $q$ but substantially different $ρ$ and are more difficult to resolve from the light curves. For Type~II events, the "resonant" solutions have relatively lower $q$ and larger $ρ$. Our review provides guidance for searching for the alternative solution once one solution has been identified.

The weaponization of LLMs for automated malware generation poses an existential threat to conventional detection paradigms. AI-generated malware exhibits polymorphic, metamorphic, and context-aware evasion capabilities that render signature-based and shallow heuristic defenses obsolete. This paper introduces a novel hybrid analysis framework that synergistically combines \emph{concolic execution} with \emph{LLM-augmented path prioritization} and \emph{deep-learning-based vulnerability classification} to detect zero-day AI-generated malware with provable guarantees. We formalize the detection problem within a first-order temporal logic over program execution traces, define a lattice-theoretic abstraction for path constraint spaces, and prove both the \emph{soundness} and \emph{relative completeness} of our detection algorithm, assuming classifier correctness. The framework introduces three novel algorithms: (i) an LLM-guided concolic exploration strategy that reduces the average number of explored paths by 73.2\% compared to depth-first search while maintaining equivalent malicious-path coverage; (ii) a transformer-based path-constraint classifier trained on symbolic execution traces; and (iii) a feedback loop that iteratively refines the LLM's prioritization policy using reinforcement learning from detection outcomes. We provide a comprehensive implementation built upon \texttt{angr} 9.2, \texttt{Z3} 4.12, Hugging Face Transformers 4.38, and PyTorch 2.2, with configuration details enabling reproducibility. Experimental evaluation on the EMBER, Malimg, SOREL-20M, and a novel AI-Gen-Malware benchmark comprising 2{,}500 LLM-synthesized samples demonstrates that achieves 98.7\% accuracy on conventional malware and 97.5\% accuracy on AI-generated threats, outperforming ClamAV, YARA, MalConv, and EMBER-GBDT baselines by margins of 8.4--52.2 percentage points on AI-generated samples.

Satellite-derived fire observations are the primary input for learning-based wildfire spread prediction, yet they are inherently incomplete due to cloud cover, smoke obscuration, and sensor artifacts. This partial observability introduces a domain gap between the clean data used to train forecasting models and the degraded inputs encountered during deployment, often leading to unreliable predictions. To address this challenge, we formulate wildfire forecasting under partial observability using a two-stage probabilistic framework that decouples observation recovery from spatiotemporal prediction. Stage-I reconstructs plausible fire maps from corrupted observations via conditional inpainting, while Stage-II models wildfire dynamics on the recovered sequences using a spatiotemporal forecasting network. We consider four network architectures for the reconstruction module-a Residual U-Net (MaskUNet), a Conditional VAE (MaskCVAE), a cross-attention Vision Transformer (MaskViT), and a discrete diffusion model (MaskD3PM)-spanning CNN-based, latent-variable, attention-based, and diffusion-based approaches. We evaluate the performance of the two-stage approach on the WildfireSpreadTS (WSTS) dataset under various settings, including pixel-wise and block-wise masking, eight corruption levels (10%-80%), four fire scenarios, and leave-one-year-out cross-validation. Results show that all learning-based recovery models substantially outperform non-learning baselines, with MaskCVAE and MaskUNet achieving the strongest overall performance. Importantly, inserting the reconstruction stage before forecasting significantly mitigates the domain gap, restoring next-day prediction accuracy to near-clean-input levels even under severe information loss.

Statistical analysis of agricultural experiments is based on structured experimental designs such as randomized block, factorial, split-plot, and multi-environment trials. While the theoretical bases of these approaches are sound, their implementation in modern programming frameworks usually involves manual specification of statistical models, choice of error terms, and subjective interpretation of interaction effects. This divide between experimental design and computational implementation opens the door to misleading inference and inconsistent reporting. We introduce AgroDesign, a Python framework that makes experimental design the central specification of statistical analysis. The framework translates specified experimental designs directly into valid linear models, automatically identifies error strata, conducts hypothesis testing and mean separation, checks assumptions of linear models, and provides decision-focused interpretations. The framework integrates fixed-effect ANOVA, hierarchical designs, linear mixed models, and genotype-by-environment stability analysis into a single declarative framework. AgroDesign is validated on canonical designs in agricultural statistics and shows consistency with traditional statistical analysis while strictly enforcing correct interpretation constraints, especially in interaction-dominant and multi-stratum designs. By integrating design semantics into computation, the framework minimizes analyst-driven modeling choices and enhances reproducibility.

A set of orthogonal pure states is an unextendible biseparable basis (UBB), which means that its complementary subspace contains only genuinely entangled states. UBBs thus serve as an effective tool for constructing genuinely entangled subspaces. If every state within such a subspace exhibits distillable entanglement across all bipartitions, it becomes particularly advantageous for applications in quantum information. In this paper, we mainly conduct research on the 4-qudit quantum systems, where the local dimension $d$ is not less than 3. We present an approach for constructing UBB and prove that the UBB established in this way is strongly nonlocal. We build several genuinely entangled subspaces and demonstrate the distillability of the genuinely entangled subspaces across all bipartitions. In addition, we also describe the specific orthonormal basis for some genuinely entangled subspaces. These results will not only contribute to the development of quantum nonlocality theory, but also provide a crucial theoretical foundation for practical quantum information processing tasks.

We study stationary fluctuations at criticality for a one-dimensional reaction--diffusion process combining symmetric simple exclusion dynamics with Glauber-type spin flips. The strength of the Glauber interaction is tuned to the critical regime in which the quadratic term in the effective potential vanishes. Focusing on the stationary distribution, we show that the total magnetization scaled by $n^{3/4}$ exhibits non-Gaussian fluctuations. More precisely, we prove that under the invariant measure the rescaled magnetization converges in distribution to a random variable with density proportional to $\exp\{-2(θy^2 + y^4/2)\}$. In contrast with the previous result, we show that the density field acting on the faster modes, that is, those associated to zero-mean test functions, have much smaller Gaussian fluctuations. It follows from the previous two results that the rescaled density field projects onto the magnetization in the sense that its action on zero-mean test functions vanishes in the limit.

Software engineering (SE) conferences are vital for knowledge exchange and collaboration, yet can also involve significant barriers for researchers in geographically distant regions such as New Zealand. We identify barriers such as high travel costs, misaligned academic calendars, and limited representation, and propose strategies including hybrid participation, cost-conscious venues, and governance reforms. We make recommendations to promote equitable global participation and strengthen the SE research community.