For the double of a quiver, the works of Ginzburg, Bocklandt-Le Bruyn and Schedler show that its closed paths, called the necklaces, have a natural Lie bialgebra structure. Schedler also constructed,in [Int. Math. Res. Notices, 2005 (12), 725-760], a Hopf algebra that quantizes this Lie bialgebra. In this paper, we pursue one more step in this direction by constructing its biquantization, in the sense of Turaev [Ann. Sci. École Norm. Sup. (4) 24 (1991), no. 6, 635-704].

Cloud rendering is widely used in gaming and XR to overcome limited client-side GPU resources and to support heterogeneous devices. Existing systems typically deliver the rendered scene as a 2D video stream, which tightly couples the transmitted content to the server-rendered viewpoint and limits latency compensation to image-space reprojection or warping. In this paper, we investigate an alternative approach based on streaming a live 3D Gaussian Splatting (3DGS) scene representation instead of only rendered video. We present a Unity-based prototype in which a server constructs and continuously optimizes a 3DGS model from real-time rendered reference views, while streaming the evolving representation to remote clients using full model snapshots and incremental updates supporting relighting and rigid object dynamics. The clients reconstruct the streamed Gaussian model locally and render their current viewpoint from the received representation. This approach aims to improve viewpoint flexibility for latency compensation and to better amortize server-side scene modeling across multiple users than per-user rendering and video streaming. We describe the system design, evaluate it, and compare it with conventional image warping.

We show that the error-gated Hebbian rule for PCA (EGHR-PCA), a three-factor learning rule equivalent to Oja's subspace rule under Gaussian inputs, can be systematically derived from Oja's subspace rule using frame theory. The global third factor in EGHR-PCA arises exactly as a frame coefficient when the learning rule is expanded with respect to a natural frame on the space of symmetric matrices. This provides a principled, non-heuristic derivation of a biologically plausible learning rule from its mathematically canonical counterpart.

We investigate the stable and retract rationality of multinorm one tori associated to finite {é}tale algebras. Our results are organized according to the greatest common divisor $d$ of the degrees of the factors. We show that these tori are stably rational for $d=1$, and obtain a criterion for retract rationality that can be attributed to our previous results. For $d>1$, we provide sufficient conditions for the failure of retract rationality. We further generalize results of Endo--Miyata (1975) and Endo (2011) by giving an equivalent condition for multinorm one tori to be stably rational under the assumption that they split over Galois extensions with Galois groups in which all Sylow subgroups are cyclic. A similar result also holds when they split over dihedral Galois extensions.

We provide a new existence result for weak solutions to the one-dimensional Euler equations with a maximal density constraint, corresponding to a unilateral constraint on the density. Such models arise in the description of congestion phenomena in compressible flows. Our approach is based on a microscopic approximation by a system of N solid particles of identical radius r, with 2r = 1/N . The particles move freely until collision, after which perfectly inelastic interactions are imposed, so that colliding particles stick together. At this level, the non-overlapping condition is encoded through Signorini-type constraints from contact mechanics. Passing to the limit as N $\rightarrow$ +$\infty$, we rigorously establish the connection between these microscopic Signorini conditions and the macroscopic unilateral constraint on the density, together with the associated sign condition on the congestion pressure. The analysis is carried out in a Lagrangian framework, which is natural at the microscopic level and relies at the macroscopic level on the monotone rearrangement associated with the density. A key ingredient of our result is a monotonicity property of the congested region, which allows us to reduce the dynamics to a first-order evolution in time.

Recently, high-temperature superconductivity has been established in bilayer La3Ni2O7, which exhibits a density-wave (DW) transition at ~ 150 K under ambient pressure. The DW order is believed to be linked to superconductivity, as it is suppressed upon the emergence of superconductivity at high pressures. Here, we explore the ultrafast dynamics of high-energy electronic excitations from 10 K to room temperature under ambient pressure using time-resolved optical spectroscopy. Two high-energy electronic excitations at ~1.8 and ~ 2.4 eV, arising from distinct interband transitions, are identified. They exhibit different DW gaps of approximately 54 and 67 meV, respectively, along with relaxation dynamics that can be well described by the Rothwarf-Taylor model. In addition, we observe four coherent Raman-active phonon modes that exhibit distinct coupling with different electronic excitations. The phonon softening with increasing temperature can be well described between ~100 K and room temperature by a semi-quantitative model, which includes thermal expansion and anharmonic phonon-phonon coupling. At cryogenic temperatures, deviations from the measured temperature-dependent phonon frequencies and the model fits suggest an additional contribution from electron-phonon coupling. Our study provides direct evidence of the complex gap structure and phonon dynamics in this material, offering critical insights into the DW mechanism and many-body effects.

Protein-protein interactions (PPIs) between a virus and its host govern infection, replication, and pathogenesis. While high-throughput mapping has identified thousands of virus-host associations, much of the virus-host interactome remains uncharacterized due to the labor-intensive nature of experimental screens, the inherent difficulty in capturing transient interactions, and the limited sequence homology across divergent viral families. Here, we introduce ViraHinter, a dual-modal deep learning framework for the precise prediction of virus-host interactions and large-scale inference of interaction landscapes. ViraHinter couples a structure-generation branch with a sequence-representation branch, integrating structure-informed pair representations with ESM-derived embeddings to learn generalizable interaction rules across unseen viruses. We benchmark ViraHinter on pathogenic coronaviruses and influenza A viruses and show that it consistently outperforms RoseTTAFold2-PPI, AlphaFold 3 and RoseTTAFold2-Lite in prioritizing high-confidence candidates even under severe class imbalance and across diverse interface regimes. Notably, it successfully identifies novel functionally relevant host factors and recapitulates the structural plasticity of the complex interfaces. By intersecting predictions across multiple influenza subtypes, ViraHinter reveals 33 shared host factors, offering a roadmap for broad-spectrum antiviral discovery. ViraHinter therefore serves as a robust computational approach for studying virus-host interactions, enabling systematic screening of host factors for all known human-infecting viruses, providing new insights into the shared mechanisms of viral pathogenesis, and accelerating the discovery of novel therapeutic targets and the development of broad-spectrum antivirals.

We argue that the topological structure of Abelian gauge theories, such as Maxwell electrodynamics, in the background of a Euclidean Schwarzschild black hole manifests itself through an asymmetry in Hawking radiation. In particular, the topology of the black hole manifold, characterised by a non-contractible 2-sphere and Euler characteristic $χ= 2$, admits non-trivial gauge-field configurations. These take the form of 2-form field strengths that are closed but not exact. From a topological perspective, such configurations are classified by the second cohomology group, which is isomorphic to $\mathbb{Z} \oplus \mathbb{Z}$, and are labelled by integer electric ($n$) and magnetic ($m$) charges, $(n,m)$. Self-dual ($n = m$) and anti-self-dual ($n = -m$) dyonic configurations carry vanishing Euclidean energy and are fully compatible with the Euclidean Schwarzschild geometry. More general dyonic configurations, by contrast, are interpreted as off-shell Euclidean field configurations. Nevertheless, both classes contribute to the thermal equilibrium vacuum and to finite-temperature correlation functions in the corresponding Lorentzian framework. Furthermore, because of the non-trivial topology, the electromagnetic $θ_{\rm EM}$-term contributes to the physical observables. In particular, it sources $CP$-asymmetric Hawking radiation, observable as an imbalance between left- and right-polarised photons in the emission spectrum. We briefly discuss some implications of this phenomenon.

This paper develops matrix-multiplication-based iterative refinement for diagonalizable non-Hermitian eigendecompositions. The main theory concerns simple eigenvalues and distinguishes two input regimes. In the right-only regime, where only approximate right eigenvectors and eigenvalues are available, a first-order derivation selects the update and the resulting post-update residual identity is exact, yielding a quadratic residual bound. In the left-right regime, where approximate left and right eigenvectors are both available, the computable driving matrix is an exact perturbation of the inverse-based one and the biorthogonality correction satisfies an exact Newton--Schulz-type error identity. Under a small biorthogonality error, these relations yield a local second-order estimate for the resulting $W$-method. Clustered eigenvalues are handled separately by a stabilization extension based on clusterwise re-diagonalization and suppression of intracluster corrections, whose effect is verified on controlled matrices with ill-conditioned cluster bases. The method is intended as post-processing for an already accurate eigendecomposition. The attraction region is not analyzed, and no complete theory is given for the clustered case.

In this paper, we consider the Schrödinger operators on $ \ell^{2}(\N) $, defined for all $ x\in\mathbb{T} $ by \begin{equation} (H(x)u)_n = u_{n+1} + u_{n-1} + λf(2^{n} x) u_n, \quad \text{for } n \geq 0,\notag \end{equation} with the Dirichlet boundary condition $ u_{-1}=0 $. Building on Zhang's recent breakthrough work [Comm.Math.Phys.405:231(2024)] that resolved Damanik's open problem [Proc.Sympos. Pure Math.76,Amer.Math.Soc.(2007)] on the uniform positivity of the Lyapunov exponent, for the potential $ f \in C^{1}(0,1)$ with $ \|f\|_{C^{1}(0,1)} < C $ and $ \inf_{x \in (0,1)} |f^{\prime}(x)| > c>0 $, we obtain the large deviation estimate and prove that for a.e. $ x \in \mathbb{T} $ and sufficiently large $ λ> λ_{0} $, the operators $ H(x) $ display Anderson localization. Furthermore, if the potentials also have zero mean, our analysis reveals that the doubling map models can exhibit localization behavior for both small and large coupling constants $ λ$.

Along the bacterial chromosome, regions called rrn operons contain genes that are transcribed into ribosomal RNA. These operons are among the most transcriptionally active sites in the genome. It has been observed in E. coli that RNA polymerase (RNAP), while binding to these genetic loci along the chromosome during transcription, forms dense clusters, leading to spatial colocalization of the operons within the cell. Recent experimental evidence suggests that liquid-liquid phase separation contributes to the formation of RNAP clusters, with the antitermination factor NusA playing a key role. We present a simulation model to investigate the mechanisms underlying the formation of these biomolecular condensates. We propose that mutual attraction between NusA proteins, which exhibit a miscibility gap at higher concentrations, drives condensate formation via a polymer-assisted condensation pathway, and we demonstrate how these condensates promote the colocalization of rrn operons. Our results reconcile seemingly disparate experimental observations of chromosomal organization reported in fluorescence-based imaging and Hi-C experiments.

We present a method to measure electric-charge transport in high-energy nuclear collisions using a beam-energy scan of isobaric systems. Comparing collisions of nuclei with identical mass number but different atomic number allows the charge difference ($ΔQ$) to be extracted with a double-ratio technique that suppresses most experimental systematic uncertainties. By varying the beam energy, the rapidity gap ($Δy$) over which electric charge is transported can be systematically scanned. Simulations of Ru+Ru and Zr+Zr collisions at $\sqrt{s_{\rm NN}}$=19.6-200GeV with UrQMD and PYTHIA Angantyr show that midrapidity $ΔQ$ decreases exponentially with increasing $Δy$, with the slope parameter exhibiting strong model dependence. Comparisons with the baryon number transport reveal distinct patterns. In both UrQMD and PYTHIA Angantyr (with and without final-state baryon junctions), where baryon number is carried solely by valence quarks, the rapidity slope for baryon transport is larger than that for electric-charge transport. In contrast, scenarios that include baryon junctions in the initial state are expected to produce the opposite trend. This demonstrates that an isobar beam-energy scan provides a sensitive probe of electric-charge transport and offers new constraints on the microscopic mechanisms governing conserved-charge redistribution in QCD matter.

Chirality in superconductor-ferromagnet hybrids strongly influences phenomena such as the observable signatures of long-range triplet superconductivity, but its microscopic origin in nominally centrosymmetric ferromagnets is still unclear. Here, we combine structural characterization, polarization-analyzed grazing-incidence small-angle neutron scattering (PA-GISANS), first-principles calculations, and deep-learning-assisted multiscale modeling to study FePd and Nb/FePd heterostructures. Experimentally, we observe partial L1$_0$ order, atomic intermixing, anti-phase boundaries, and a depth-dependent defect gradient across the FePd layer, together with a finite net magnetic chirality at room temperature. The GISANS asymmetry indicates that the main chiral contribution lies in-plane, with an additional out-of-plane component associated with depth-dependent magnetic inhomogeneity. Theoretically, we show that chemical disorder in FePd, especially when combined with a compositional gradient, produces finite Dzyaloshinskii-Moriya interactions and stabilizes chiral finite-$\mathbf{q}$ magnetic modulations with mixed Bloch-Néel character. In the mesoscopic model, the resulting in-plane modulation length approaches the experimentally observed range. These results identify disorder and compositional gradients as intrinsic microscopic sources of net chirality in FePd-based films, showing that the observed chirality does not arise only from interface effects.

The early dark energy resolution of Hubble tension seems to be suggesting a scale-invariant Harrison-Zeldovich spectrum of primordial scalar perturbation, i.e. $n_s=1$ ($|n_s-1|\sim {\cal O}(0.001)$) for $H_0\sim 73$km/s/Mpc. In this work, we propose a possibility to acquire $n_s=1$ in single field slow-roll models of inflation. In our consideration, the potential of inflaton during inflation still preserve the shape of well-known single field inflation models in deep slow-roll region, but inflation ends suddenly due to a large step of inflaton potential. In particular, we investigate the implication of our scheme for chaotic inflation and Starobinski inflation, and show how they can be compatible with the observation for $n_s=1$.

Let $(X,\mathbf{q},μ)$ be an ultra-RD-space with upper dimension $n\in(0,\infty)$; i.e., it is a quasi-ultrametric space of homogeneous type whose measure $μ$ satisfies an additional reverse doubling property. Let $\mathrm{ind\,}(X,\mathbf{q})\in(0,\infty]$ denote its lower smoothness index, as introduced by Mitrea et al. In this monograph, the authors first construct a new approximation of the identity on quasi-ultrametric spaces of homogeneous type, achieving a maximal degree of smoothness $0<\varepsilon\preceq\mathrm{ind\,}(X,\mathbf{q})$. This fundamental tool is then used to derive sharp homogeneous (as well as inhomogeneous) continuous/discrete Calderón reproducing formulae on ultra-RD-spaces. As applications, the authors establish Littlewood--Paley function characterizations for both Hardy spaces and Triebel--Lizorkin spaces on ultra-RD-spaces. The authors further introduce Hardy--Lorentz spaces $H^{p,q}_\ast(X)$ via the grand maximal function, with the sharp range $p\in(\frac{n}{n+\mathrm{ind\,}(X,\mathbf{q})},\infty)$ and $q\in(0,\infty]$, and provide their real-variable characterizations using radial/non-tangential maximal functions, (finite) atoms, molecules, and various Littlewood--Paley functions. Based on these characterizations, the authors prove a duality theorem between Hardy--Lorentz spaces and Campanato--Lorentz spaces, establish a real interpolation theorem for Hardy--Lorentz spaces, and derive boundedness results for Calderón--Zygmund operators on them. It should be emphasized that many of the main results in this monograph are indeed established in the more general setting of quasi-ultrametric spaces of homogeneous type.

Radar-based convective precipitation nowcasting suffers from rapid performance degradation beyond 30 minutes due to missing thermodynamic variables. Existing deep learning models also face blurring effects, training instability, and limited interpretability. To address this, we propose MAG-Net, a Physics-Aware Multi-modal Attention-guided Generator Network. It integrates radar dynamics with selected geostationary satellite channels (IR 10.8, WV 7.1, BTD) to incorporate thermodynamic and microphysical precursors. MAG-Net features a Dual-Stream Encoder for heterogeneous modalities and a Symmetric Dual-Head Decoder optimizing reflectivity regression and event probability via an uncertainty-weighted multi-task strategy. Furthermore, an inference-time Gradient-Preserving Fusion (GPF) strategy combines probabilistic constraints with regression details for better high-frequency texture retention. Experiments on a large-scale dataset (2018-2023) over southeastern China show MAG-Net outperforms deterministic (e.g., CPrecNet) and generative (e.g., DGMR) baselines. Specifically, it improves CSI40 by 0.083 (0.172 to 0.255) over CPrecNet, enhancing intense convective echo detection. Finally, Integrated Gradients (IG) analysis reveals the model's reliance on satellite inputs increases with forecast lead time and convective intensity, confirming that satellite data captures critical precursors for severe weather prediction.

Multi-Vector Similarity Search is essential for fine-grained semantic retrieval in many real-world applications, offering richer representations than traditional single-vector paradigms. Due to the lack of native multi-vector index, existing methods rely on a filter-and-refine framework built upon single-vector indexes. By treating token vectors within each multi-vector object in isolation and ignoring their correlations, these methods face an inherent dilemma: aggressive filtering sacrifices recall, while conservative filtering incurs prohibitive computational cost during refinement. To address this limitation, we propose MV-HNSW, the first native hierarchical graph index designed for multi-vector data. MV-HNSW introduces a novel edge-weight function that satisfies essential properties (symmetry, cardinality robustness, and query consistency) for graph-based indexing, an accelerated multi-vector similarity computation algorithm, and an augmented search strategy that dynamically discovers topologically disconnected yet relevant candidates. Extensive experiments on seven real-world datasets show that MV-HNSW achieves state-of-the-art search performance, maintaining over 90% recall while reducing search latency by up to 14.0$\times$ compared to existing methods.

Investigating the properties of the first stars in the universe is essential, yet it remains an open question. One way to explore these stars is by examining their effects on the surrounding gas during the epoch of reionization. In this study, we investigate whether the 21-cm global signal can constrain the typical mass and star formation efficiency of first-generation stars. We perform semi-numerical simulations that include the escape fraction of ionizing photons, which depends on stellar and halo masses, as well as the heating structure surrounding a halo that hosts the first star, determined by radiation hydrodynamics (RHD) simulations. By applying Fisher analysis, while accounting for foreground emissions, we demonstrate that future observations with instruments such as the Radio Experiment for the Analysis of Cosmic Hydrogen (REACH) could provide meaningful constraints on these properties.

In this paper we prove that every homeomorphism of a compact metric space admitting an invariant probability measure with full support can be approximated in the $C^0$-Gromov--Hausdorff topology by homeomorphisms with zero topological entropy. The argument relies on the ergodic decomposition theorem and on the existence of points with dense positive orbit in the supports of suitable ergodic components. As a consequence, topological entropy is not stable under $C^0$-Gromov--Hausdorff perturbations within this class. We also show that if, in addition, the homeomorphism is topologically $GH$-stable, then its periodic points are dense in the ambient space. Finally, by combining this framework with a previous result on transitive and topologically $GH$-stable homeomorphisms, we deduce that every dynamics in this class admits an invariant measure with full support and therefore falls within the scope of the general approximation theorem by zero-entropy systems.

Superconducting qubits are compelling platforms for charge-parity detection and, due to their theoretical sensitivity on the meV energy scale, hold promise for rare event searches. In this work, we realize high-fidelity mapping of charge-parity states onto qubit states using an offset-charge-tunable transmon qubit and efficiently characterize the fidelity of the charge-parity detection via randomized benchmarking. Specifically, a gate control line is applied to control offset charge, allowing us to achieve the single-qubit gate fidelity up to 99.96%. We combine a net-zero-based pulse on the gate line with a spin-echo-based sequence to realize charge-parity mapping, achieving a fidelity of 99.37%. Then, we demonstrate continuous monitoring of the charge-parity state with over 93.4% fidelity at a 4-μs sampling interval. Finally, an error analysis of charge-parity detection is performed, and it is found that qubit readout is currently the largest source of error. We believe this work lays the foundation for future exploration of ultra-low energy particles.

This paper investigates strategic interactions within a three party deception security game involving a defender, an insider, and external attackers. We propose a robust deception mechanism where the leader manipulates game parameters perceived by followers to enhance defense performance when followers operate under misperceived and uncertain observation. Specifically, we propose a unified three party leader follower game framework and introduce the concepts of Deception Stackelberg equilibria (DSE) and Hyper Nash equilibria (HNE), which generalize classical two-player Stackelberg and deception games. We develop necessary and sufficient conditions for the consistency between DSE and HNE, ensuring that the defender's utility remains invariant when the hierarchical structure degenerates into a simultaneous-move scenario. Moreover, we propose a scalable hypergradient-based algorithm with established convergence guarantees for seeking DSE, efficiently addressing the computational challenges posed by non-smooth and set-valued best-response mappings. Finally, we apply theoretical analysis to practical scenarios in secure wireless communication and defense against insider-assisted false data injection attacks.

We propose a novel numerical approach to compute the Pareto front in multivariate polynomial multi-objective optimization problems. When the objective functions and (equality) constraints are multivariate polynomials, the Pareto front, which describes the efficient points of the multiple (often conflicting) objective functions, can be interpreted as a subset of a positive-dimensional algebraic variety. By combining the objective functions with weights and considering the weights as additional decision variables, we can eliminate all variables except the objective values and obtain one (or multiple) polynomial equation(s) that describes the Pareto front. Unlike sampling-based methods that approximate the Pareto front point-wise, our elimination-based approach yields an explicit algebraic relation between the objective values, representing the Pareto front as a geometric object in the objective space without requiring a predetermined number of sample points. Besides numerical examples illustrating the elimination-based approach, we use elimination on a challenging application that originates from system identification, in which we analyze the trade-off between misfit and latency terms when determining the optimal model parameters from measured data.

Ferroelectric nematic phases are a new class of polar fluids in which spontaneous polarization is directly coupled to the orientational order, providing unique opportunities for creating self-organized materils with spatially modulated electric polarization and nonlinear optical response. Here we report the spontaneous emergence of polarization modulated textures in a chiral ferroelectric nematic material close to the transition to the chiral twist-bend ferroelectric nematic phase. By systematically varying cell thickness and surface anchoring conditions, we map the formation of these modulated states, revealing stripe, square and hexagonal morphologies determined via confinement conditions. These structures are directly translated into periodic modulation of the nonlinear optical response, as evidenced by second-harmonic generation imaging. Comparison with an elasticity based theoretical framework and numerical free energy minimization shows that the instability originates from the softening of the bend elastic constant in the chiral nematic phase as the system approaches the lower-temperature heliconical polar phase. The resulting elastic frustration, combined with confinement, drives the formation of spatially periodic director distortions, highlighting ferroelectric nematic fluids as a promising platform for self-assembled nonlinear optical materials.

To date, the best methods for estimating the growth of mean values of arithmetic functions rely on the Vorono\"ı summation formula. By noticing a general pattern in the proof of his summation formula, Vorono\"ı postulated that analogous summation formulas for $\sum a(n)f(n)$ can be obtained with ``nice" test functions $f(n)$, provided $a(n)$ is an ``arithmetic function". These arithmetic functions $a(n)$ are called so because they are expected to appear as coefficients of some $L$-functions satisfying certain properties. It has been well-known that the functional equation for a general $L$-function can be used to derive a Vorono\"ı-type summation identity for that $L$-function. In this article, we show that such a Vorono\"ı-type summation identity in fact endows the $L$-function with some structural properties, yielding in particular the functional equation. We do this by considering Dirichlet series satisfying functional equations involving multiple Gamma factors and show that a given arithmetic function appears as a coefficient of such a Dirichlet series if and only if it satisfies the aforementioned summation formulas.

We introduce a family of scale-invariant entropy statistics derived from logarithmically aggregated distance distributions of point processes, with prime numbers serving as a motivating example. The construction associates to each finite configuration a scalar quantity encoding structural features of relative spacing while remaining insensitive to absolute scale. This work is intended as a methodological contribution rather than a source of new raw results.

Distance Comparison Operations (DCOs), which decide whether the distance between a data vector and a query is within a threshold, are a critical performance bottleneck in vector similarity search. Recent DCO methods that avoid full-dimensional distance computations promise significant speedups, but their readiness for production vector database systems remains an open question. To address this, we conduct a comprehensive benchmark of 8 DCO algorithms across 10 datasets (with up to 100M vectors and 12,288 dimensions) and diverse hardware configurations (CPUs with/without SIMD, and GPUs). Our study reveals that these methods are not silver bullets: their efficiency is highly sensitive to data dimensionality, degrades under out-of-distribution queries, and is unstable across hardware. Yet, our evaluation also demonstrates often-overlooked merits: they can accelerate index construction and data updates. Despite these benefits, their unstable performance, which can be slower than a full-dimensional scan, leads us to conclude that recent algorithmic advancements in DCO are not yet ready for production deployment.

This Letter studies the optimization of a wireless communications system empowered by a periodically time-modulated reconfigurable intelligent surface, coined time-Floquet RIS (TF-RIS), in the presence of mutual coupling (MC) among the RIS elements. In contrast to a conventional RIS whose elements may be reconfigured between signaling intervals, a TF-RIS periodically modulates its elements within a signaling interval, thereby inducing frequency conversion. Periodic time modulation is particularly attractive for harmonic backscatter communications to avoid self-jamming. Based on time-Floquet multiport network theory, we formulate an MC-aware optimization problem for binary-amplitude-shift-keying (BASK) harmonic backscatter communications with practical 1-bit-programmable TF-RIS elements. We propose a general discrete-optimization algorithm and evaluate its performance based on realistic model parameters. We systematically examine the performance dependence on the time resolution of the periodic modulation and the number of retained harmonics. Benchmarking against an MC-unaware approach reveals the importance of MC awareness for the more challenging optimization problem of simultaneous desired-harmonic-channel-gain maximization and undesired-harmonic-channel-gain minimization.

Differential diagnosis of mental disorders remains a fundamental challenge in real-world clinical practice, where multiple conditions often exhibit overlapping symptoms. However, most existing public datasets are developed under single-disorder settings and rely on limited data elicitation paradigms, restricting their ability to capture disorder-specific patterns. In this work, we investigate differential mental disorder detection through psychology-inspired multimodal stimuli, designed to elicit diverse emotional, cognitive, and behavioral responses grounded in findings from experimental psychology. Based on this paradigm, we collect a large-scale multimodal mental health dataset (MMH) covering depression, anxiety, and schizophrenia, with all diagnostic labels clinically verified by licensed psychiatrists. To effectively model the heterogeneous signals induced by diverse elicitation tasks, we further propose a paradigm-aware multimodal framework that leverages inter-disorder differences prior knowledge as prompt-guided semantic descriptions to capture task-specific affective and interaction contexts for multimodal representation learning in the new differential mental disorder detection task. Extensive experiments show that our framework consistently outperforms existing baselines, underscoring the value of psychology-inspired stimulus design for differential mental disorder detection.

We propose a novel non-compact, positivity-preserving scheme for linear non-divergence form elliptic equations. Based on the Feynman--Kac formula, the solution is represented as a conditional expectation associated with a diffusion process.Instead of using compact Markov chain approximations, we construct a wide-stencil scheme by approximating the expectation with carefully designed transition probabilities, ensuring both consistency and positivity preservation. The method is effective for anisotropic diffusion problems with mixed derivatives, where classical schemes typically fail unless the covariance matrix is diagonally dominant. A key feature of the proposed framework is its robust treatment of boundary conditions. For Dirichlet boundaries, we introduce a quadtree-based non-uniform stopping-time strategy, achieving $O(h)$ accuracy. For Neumann boundaries, a discrete specular reflection mechanism is employed, yielding $O(h^{1/2})$ convergence. Periodic boundaries are handled through modular wrapping, also achieving $O(h)$ accuracy. The resulting schemes are unconditionally stable and positivity-preserving due to their probabilistic structure. Numerical experiments confirm the theoretical convergence rates under all boundary conditions considered.

As part of the graph minor project, Robertson and Seymour showed in 1990 that the class of graphs that can be embedded in a given surface can be characterized by a finite set of minimal excluded minors. However, their proof, because existential, provides no explicit information about these excluded minors. In 1993, Seymour established the first upper bound on the order of such minimal excluded minors. Very recently, Houdaigoui and Kawarabayashi improved this result by deriving a quasi-polynomial upper bound. Despite this progress, the gap between this bound and the known linear lower bound $Ω(g)$ (where $g$ denotes the genus) remains substantial. In particular, they conjectured that a polynomial upper bound should hold. In this paper, we confirm this conjecture by showing that the order of the minimal excluded minors for a surface of genus $g$ is $O(g^{8+\varepsilon})$ for every $\varepsilon >0$. This result significantly narrows the gap between the known lower and upper bounds, bringing the asymptotic behavior much closer to the conjectured optimum. Our approach introduces a new forbidden structure of minimal excluded minors. Let $G$ be a minimal excluded minor for a surface of Euler genus $g$. Houdaigoui and Kawarabayashi showed that $G$ contains $O(\log g)$ pairwise disjoint cycles that are contractible and nested in some embedding of $G$. We strengthen this result by proving a separator-based variant: for any contractible subgraph $H \subseteq G$ with a separator of size $s$ (with $H$ completely contained in one side), the subgraph $H$ contains $O(\log s)$ disjoint cycles that are contractible and nested in some embedding of $G$. This allows us to replace a genus-dependent bound with a separator-dependent one, which is the main new ingredient in deriving our polynomial bound.