Let $L(λ)$ be a simple highest weight module of a classical Lie algebra $\mathfrak{g}$ with highest weight $λ-ρ$, where $ρ$ is half the sum of positive roots. Joseph proved that the associated variety of the annihilator ideal of $L(λ)$ (also called the annihilator variety) is the Zariski closure of a nilpotent orbit in $\mathfrak{g}^*$. Recently, Bai--Ma--Wang introduced a partition algorithm to describe this corresponding nilpotent orbit for a given highest weight module $L(λ)$. In this paper, we present a new direct proof of Bai--Ma--Wang's partition algorithm using Sommers duality.

Interval-aware Approximate Nearest Neighbor (ANN) search arises in applications where each object is associated with a numeric value or interval, and queries must satisfy both vector-similarity and interval constraints. Existing methods are typically tailored to a single query semantics, such as interval-filtered ANN search, and therefore require multiple specialized indexes to support diverse workloads, leading to substantial indexing and memory overhead. To address this limitation, we propose the Unified Interval-aware Relative Neighborhood Graph (URNG), a unified graph framework for interval-aware ANN search. URNG preserves the monotonic searchability of relative-neighborhood-graph based ANN indexes while additionally ensuring structural heredity over query-induced subgraphs, enabling a single index to support multiple interval-aware query semantics. Building on this framework, we develop UG, a practical graph index that efficiently approximates URNG through unified interval-aware pruning and iterative repair, together with a query algorithm for interval-aware ANN search. Extensive experiments on 5 datasets show that UG consistently achieves a strong accuracy-efficiency trade-off across diverse interval-aware workloads while maintaining competitive index construction cost and memory usage.

A recent analysis of the centrifugal instability in the case of pressure-supported compressible relativistic rotation, with application to astrophysical jets, yielded a generalisation of the famous Rayleigh criterion for Newtonian flows. According to this criterion, the centrifugal instability is strongly affected by the flow Mach number, and not only in the relativistic fluid dynamics but also in its Newtonian limit. To validate the Newtonian version of this criterion, we performed axisymmetric numerical simulations of non-relativistic transonic rotating flows which are stable according to the original Rayleigh criterion but can be either stable or unstable according to the new one. The results of computer simulations are found to be in perfect agreement with the theory. The hydrodynamic stability of accretion disks is often explained by referring to the original Rayleigh criterion, even if their rotation is highly supersonic. To clarify the matter, we analysed the hydrodynamic stability of flows rotating about central compact object and derived an instability criterion that retains the explicit dependence on the flow Mach number. This criterion turns out to be equivalent to the standard Solberg-Høiland criterion, which does not involve the Mach number. The same applies to the case of pressure-supported rotation, where the role of gravity is played by the centrifugal force.

Let $D \subset \mathbb{R}^d$ ($d \geq 2$) be a bounded connected open set of class $C^m$ with $m \geq 3$. We prove that, for a generic domain $Ω\in \mathcal{O}^m(D)$ in the sense of Baire category for the Micheletti topology, every Dirichlet-Laplacian eigenfunction has nonzero mean, $\int_Ωφ_n \neq 0$ for all $n \geq 1$. This answers a question raised by Steinerberger and Venkatraman. The proof rests on a shape-derivative computation whose degeneracy is identified with an overdetermined elliptic problem of Schiffer type. Rather than resolving this problem, we bypass it through a Baire-category argument based on the meagerness of domains with analytic boundary. As a consequence, we obtain that for a generic domain the Dirichlet heat equation is approximately controllable, and rapidly stabilizable, i.e. stabilizable at any prescribed exponential decay rate, by a single spatially homogeneous scalar control, via the Fattorini-Hautus criterion.

We study Kohn-Sham Density Functional Theory (DFT) models describing the electronic structure of two-dimensional materials placed in a three-dimensional environment, encapsulated between two parallel conducting electrodes. In this geometry, the Dirichlet boundary conditions at the electrodes screen the Coulomb interaction, which becomes effectively short-ranged, of Yukawa type. We prove that some nonlinear Kohn-Sham DFT models are well-posed in this setting, both for periodic materials (such as graphene) and for quasi-periodic materials (such as twisted bilayer graphene and other moiré materials for generic incommensurate twist angles).

In closed quantum systems, local information spreads throughout the entire system and becomes highly complex under unitary evolution. In contrast, when the system is embedded in an environment, system-environment coupling can transfer information from the system into the environment, thereby reducing the rate of complexity growth within the system. This leads to the environment-induced scrambling transition established in previous works. In this work, we identify entropy injection from the environment as a different physical process that instead enhances many-body chaos. Our setup consists of coupling a system that is already in equilibrium with one environment to another environment, which serves as an entropy reservoir and drives the system into a non-equilibrium state. When entropy flows into the system through either heat transfer or particle transfer, the effective Hilbert space explored by the system enlarges, a mechanism that can enhance many-body chaos. We explicitly demonstrate this idea by constructing a solvable complex Brownian SYK model, in which both the relaxation toward the steady state and the steady-state quantum Lyapunov exponent can be computed analytically. Our results provide a controllable mechanism for tuning quantum scrambling through entropy flow in quantum many-body systems coupled to environments.

We propose a minimal, rotation-free model of magnetohydrodynamic (MHD) dynamo action driven by laminar thermal convection in a regular tetrahedral cavity. Unlike canonical planetary-dynamo settings, where flow helicity is supplied by global rotation, the present system generates robust flow helicity purely through the geometric constraints imposed by tetrahedral boundaries. Direct numerical simulations show exponential amplification of a weak seed magnetic field and a nonlinear saturated state in which the magnetic energy exceeds the kinetic energy. The convective flow organizes into a highly symmetric pattern with \(D_4\) dihedral symmetry. The dynamo-generated magnetic field obeys a corresponding signed \(D_4\) symmetry involving antisymmetry under \(π\)-rotations about the two horizontal axes of the tetrahedron. The tetrahedral dynamo provides a conceptually transparent setting for isolating geometry-induced helicity, magnetic-field amplification, and a closed induction cycle in a non-rotating laminar flow.

We establish the correct parameter governing the convergence time of the 3-Majority and 2-Choices dynamics on the complete graph in the synchronous model. Recent work [Shimizu and Shiraga, PODC'25] provides matching upper and lower bounds on the number of rounds to consensus, but only in a weak sense: the bounds are shown to coincide for some initial opinion configuration. In contrast, we obtain tight bounds in a strong sense, with upper and lower bounds matching up to logarithmic factors for every initial configuration. Let $α$ (0) be the initial opinion-frequency vector, and denote by ___$α$ (0) ___ $\infty$ its maximum entry. We show that 3-Majority reaches consensus in $Θ$(min{___$α$ (0) ___ -1 $\infty$ , $\sqrt$ n}) rounds w.h.p., while 2-Choices reaches consensus in $Θ$(___$α$ (0) ___ -1 $\infty$ ) rounds w.h.p. Our results demonstrate that the convergence time of both dynamics is governed not by global parameters such as the number of opinions k or the squared ${\ell}$ 2 norm of the initial opinion distribution, but rather by the ''local'' parameter ___$α$ (0) ___ $\infty$ , the maximum initial opinion density.

Topological charges based on Berry phase play the fundamental role in the topological physics. However, such topological charges remain unexplored in quasicrystals, impeding the systematic understanding of topological states in such quasiperiodic systems. In this work, by deriving all the allowed topological charges according to group representation theory and the corresponding low-energy effective Hamiltonians, we establish a universal framework for Berry-phase-based topological charges in two-dimensional quasicrystals. Taking the $C_{8v}$ quasicrystal as an example, we demonstrate and characterize a higher topological charge of $C=4$, which is inaccessible in conventional periodic systems. Applying our framework to photonic quasicrystals, we uncover that the circling of photon momentum around the charge gives a $C$ times winding of the electromagnetic field distribution pattern. Such observable feature provides a direct experimental method to probe the topological charges. Our work paves the way for exploring topological charges in quasiperiodic matter, and fundamentally bridges periodic and quasiperiodic topological band theories.

In this work, we settle a problem that dates back to the early 2000s. We provide a complete characterization of special matchings of arbitrary Bruhat intervals in Coxeter groups of type $A$ and apply this result to prove a conjecture of Brenti from 2003 concerning the computation of Kazhdan-Lusztig $R$-polynomials via special matchings. This yields new evidence in support of the Combinatorial Invariance Conjecture.

Multispecies spatial data arise in many applications where interactions between different entities are central to system behaviour, including biomedical imaging, geospatial analysis, and species ecology. Despite their importance, relatively few quantitative tools exist to capture such interactions. In this work, we propose magnitude-based features for the analysis of multispecies spatial data. Magnitude is a real-valued invariant of finite metric spaces that can be interpreted as an effective number of points, incorporating both spatial configuration and scale. We develop global and local magnitude feature vectors and demonstrate their utility on synthetic tumour microenvironment data, and in tissue microarray data from human colorectal cancer samples. Locally, the method identifies distinct neighbourhood types and reveals spatial heterogeneity; in the model, this includes radial patterns associated with different qualitative outcomes of the simulations, while in the real-world data it reflects the importance of tertiary lymphoid structure-like interactions between B and T cell populations. Globally, the approach recovers known classifications of long-term simulation outcomes across parameter regimes in synthetic data, and suggests important roles for CD4+ T cells and CD163+ macrophages in distinguishing patients with favourable Crohn's like reactions from unfavourable diffuse immune infiltration. Together, these results suggest that magnitude-based features provide a powerful and flexible tool for the analysis of multispecies spatial data.

Global nonnegative martingale solutions are shown to exist for a stochastic Keller-Segel system with a nonlocal Fisher-KPP source and super-linear multiplicative noise. The result is obtained for nonnegative initial data with no smallness assumption, provided that the nonlocal source term is dominant. The main difficulty stems from the absence of a coercive structure and the super-linear nature of the noise. An additional cut-off with finite L^2 norm in the classical Galerkin method is added to establish a well-posed approximation problem. Moreover, due to the nonlocal Fisher-KPP structure, it is necessary to prove the positivity of the approximating solution in order to obtain uniform estimates. In the compactness arguments, the usual tightness argument in the framework of Hilbert spaces cannot be directly applied to the uniform estimates obtained in this paper. As a result, we develop a more general version of the compactness argument and tightness criterion, presented in the appendix, which will be applied throughout the paper. This allows for the global existence of nonnegative martingale solutions to be derived from Jakubowski's version of the Skorokhod Theorem, along with a thorough discussion of the convergence properties.

Originally motivated by creating first-person computer visualizations within Riemannian manifolds -- the author was led to study deformable-body mechanics, as rigid-body mechanics is not available in a generic Riemannian manifold due to its lack of nontrivial isometry group. Hyperelasticity is a particularly nice sub-category of continuum mechanics in which a deformable, elastic body's behavior is determined by a stored energy density function. This allows problems to be posed variationally, and powerful tools brought to bear on studying and solving them. This article presents numerical simulations of static solutions to a particular class of problems in hyperelastic mechanics in 2-dimensional Riemannian manifolds in which a flat hyperelastic body $B$ is embedded into a region $Ω$ in a nowhere-flat surface $S$ of revolution $z=z\left(r\right)$ such that $\left|K\left(r\right)\right|$ decreases as $r\to\infty$, where $K$ denotes the Gaussian curvature of $S$. For example, the funnel $z=-r^{-1}$ or the paraboloid $z=\frac{1}{2}r^{2}$. Because $B$ is flat, the body can't achieve a zero-stored-energy configuration, and restorative forces arise in the body to move it toward a region of lower stored energy -- meaning, toward a flatter configuration. With the addition of a gravitational potential $U\left(r\right)=z\left(r\right)$ on $S$, forces act on the body to pull it toward $r=0$. If the body has sufficient stiffness and remains within the region $Ω$, then the body has an equilibrium configuration in which the body's deformation-response forces perfectly cancel the gravitational forces. Such a configuration represents a kind of "levitation" phenomenon within this surface. The numerical implementation of this problem will be detailed and the resulting numerical solutions and various consequences discussed.

In this paper, we propose a segment-wise soft robotic antenna (SRA) system, where each soft robotic arm referred to as a tentacle, comprises multiple independently controllable segments with bending, elongation-retraction, and sweeping motions. By adjusting segment motion parameters, the positions of surface-mounted antennas are reconfigured, distinguishing it from conventional reconfigurable antenna (RA) systems. Based on this model, we propose two antenna deployment schemes: the segmented end-antenna configuration (SEAC), where fixed antennas are mounted at the segment ends and reconfigured via segment motions; and the hybrid end-and-intermediate antenna configuration (HEIAC), where RAs are further integrated as intra-segment antennas. In HEIAC, soft-robot segment deformation provides large-scale spatial reconfiguration, while RAs enable fine-grained adjustment. For SEAC, we formulate a sum-rate maximization problem accounting for inter-segment connectivity and the nonlinear mapping from segment deformation parameters to antenna coordinates, and develop a penalty dual decomposition-projected gradient ascent (PDD-PGA) algorithm. For HEIAC, we jointly optimize segment deformation, intra-segment antenna positions, and antenna activation using a block coordinate descent (BCD)-PDD-PGA algorithm with greedy backward antenna selection. Simulation results demonstrate that the proposed schemes substantially outperform fixed-position antenna arrays and conventional RA baselines. In particular, SEAC and HEIAC achieve 37.9% and 32.1% sum-rate gains over conventional 3D reconfigurable arrays, respectively, while SEAC provides up to a 49.3% gain in compact array deployments.

We introduce the Hierarchical Excitatory Process (HEP), a flexible point process model for event-time data observed under repeated external stimuli. The proposed framework models the conditional intensity of a point process as a superposition of excitation effects induced by external stimuli, characterised by kernels with parameters dynamically evolving over time. This hierarchical construction enables modulation of excitation strength across repeated stimuli, providing an interpretable structure. We establish likelihood-based inference for the proposed model and embed HEP within a model-based clustering framework to identify latent groups sharing similar response dynamics. Simulation studies demonstrate the model's ability to recover evolving latent patterns, and an application to spike train recordings from the sea slug Aplysia pedal ganglion illustrates how HEPs are able to characterise stimulus-driven excitability of neurons across repeated stimulation under different experimental conditions.

The stress concentrations caused by inherent roughness of natural and manufactured surfaces often induce plastic deformation at contact interfaces, a challenge compounded by competing influences of the size effect of plastic deformation and self-affine rough surface topography. To address this, we developed a novel methodology based on stochastic theory using compounded Chapman-Kolmogorov equations, for the first time, to solve elastoplastic contact problems involving scale-dependent hardness. Our approach formulates three integral equations describing the evolution of probability density functions of elastic contact pressure, relative plastic contact area, and relative non-contact area across geometrical scales. We thoroughly investigate the effects of scale-dependent hardness on contact pressure distribution, relative elastic and plastic contact areas, and the area-to-load relationship. By adjusting various mechanical and material properties, our model predicts a smooth transition from linear elasticity to elastic-plastic behavior and finally to full plasticity. A key advancement is the derivation of a new topographic yield parameter incorporating a wider range of material and geometrical properties, aiding identification of contact status. Numerical solutions enable highly precise determination of elastic and plastic limits via curve-fitting, and we also provide a new diagram for rapid identification of contact status. This study pioneers a stochastic process framework for applying the compounded Chapman-Kolmogorov equation to rough surface contact analysis, and the integral equations characterizing how interfacial properties evolve with scale could offer valuable insights for other multidisciplinary fields where multiscale roughness is critical, such as earthquakes, electrical contact, and contact electrification.

Recently, constructions of linear complementary pairs (LCPs) of codes and linear complementary dual (LCD) codes on function fields have attracted considerable attention due to the wide range of applications of these codes. Such constructions rely on non-special divisors of degrees $g$ and $g-1$. In this work, we investigate Kummer extensions defined by $y^m = f(x)$ with $f(x)\in\mathbb{F}_q(x)$ and establish an arithmetic characterization of non-special divisors whose support can contain non-totally ramified places. Based on this characterization, we explicitly construct non-special divisors of degree $g-1$ on the GK curve. Moreover, utilizing pure gaps, we explicitly provide several families of effective non-special divisors of degree $g$ on Kummer extensions with the same multiplicities. We then develop a general framework for constructing LCPs of algebraic geometry (AG) codes on Kummer extensions. By virtue of canonical divisors, we show that the security parameters of LCPs of AG codes can be determined within this framework, which also enables the construction of LCD AG codes. Finally, we illustrate our results with representative examples, including LCPs of codes on the GK curve and LCD codes on quotients of the Hermitian curve.

The process of deriving the Desarguesian plane $PG(2,q^2)$ to get the Hall plane is well known, and the problem of when a conic in $PG(2,q^2)$ inherits to an arc in the Hall plane has been solved. In this article we look at the generalisation of replacing an André net of $PG(2,q^t)$, $t\geq 3$ to construct an André plane of order $q^t$. This article looks at the case where $q$ is odd and $t$ is prime, and determines when a conic in $PG(2,q^t)$ inherits to an arc in an André plane. Further, the number of arcs in an André plane that are inherited in this way is enumerated.

We consider the problem of privately releasing a $k$-dimensional vector under updates: Starting with a zero vector, at times $t_1, t_2,\dots$ the vector is updated by adding $x^{(1)}, x^{(2)},\dots$, respectively. For positive integers $T$, $k$ we model the updates as a data set $\{(t_i, x^{(i)})\}_i$, where $t_i \in [T]$ and $x^{(i)} \in B_k$ (the $k$-dimensional unit ball). Two such data sets are said to be neighboring if their symmetric difference has size at most $1$. The continual release consists of the sum $A^{(t)} = \sum_{i \; : \; t_i \leq t} x^{(i)}$ for each time step $t=1,\dots,T$. Classical continual release techniques allow us to release an approximation of $A^{(1)},\dots,A^{(T)}$ with additive noise of magnitude $\text{polylog}(T)$, computed in time $O(kT)$, even in the on-line, adaptive case where data is continually revealed for the current time step. Motivated by private sketching techniques, we consider the setting where only a \emph{subset} of entries in $A^{(t)}$ need to be released at time step $t$. Our new result is that it is possible to sample any desired entry in a given noise vector in \emph{constant time} while reproducing exactly the distribution of the binary tree mechanism with Gaussian noise. The improvement on the known time bound of $O(\log T)$ comes from a new data structure that allows us to sample a new noise value with the correct correlations in constant time using Brownian bridges. We present two data management applications, of independent interest, that use our technique in conjunction with differentially private CountSketches: 1) A dynamic data structure for orthogonal range counting queries with a better privacy/accuracy/space trade-off than previous data structures, and 2) Join size estimation, where in addition we show improved high-probability bounds.

Grover's algorithm achieves a quadratic speedup for unstructured search given a global oracle for the target set. In many applications, however, the target set is specified as the intersection of multiple constraint sets. Constructing a global oracle for the intersection can be costly, whereas the individual constraint oracles are often much simpler to implement. We study a randomized Grover search algorithm that directly uses these constraint oracles. At each iteration, one of the corresponding Grover operators is selected at random. For the two-operator case with uniform sampling, we prove that the success probability approaches one after \[ Θ\left(\frac\pi4\sqrt{\frac{N}{r}}\right) \] iterations, where $r$ is the size of the intersection. Thus, the algorithm achieves the same asymptotic query complexity as standard Grover search but without requiring a global oracle. We then generalize the analysis to arbitrary sampling distributions and an arbitrary number of Grover operators through an auxiliary operator that approximates the expected Grover evolution, while retaining the same asymptotic complexity. We further show that highly biased sampling distributions can still achieve near-unit success probability, enabling cheaper Grover operators to be used more frequently. Finally, we prove asymptotic optimality and support the theoretical results with numerical simulations.

We prove an exact Fourier-dimension formula for scalar dyadic Mandelbrot cascades pushed forward to fixed C^2 Jordan curves with nonvanishing curvature. Let W be in the minimal Kahane-Peyriere regime, let the scalar dyadic cascade live on T = R/Z, and let gamma map T to R^2 be a fixed C^2 Jordan curve with nonvanishing curvature, parametrized at constant speed. For the push-forward measure mu_gamma, we prove that, almost surely on non-extinction, its Fourier dimension is A_loc(W), the usual local exponent obtained by optimizing over q>1 from the moment expression involving E[W^q]. The upper bound follows from the scalar circle local-dimension theorem, bi-Lipschitz transfer to the fixed curve, and a deterministic curved-support obstruction for Fourier dimension. The lower bound follows from a fixed-curve finite-r annular theorem, which gives summable annular Fourier decay under a single finite moment witness. The main analytic input is a deterministic phase-geometry package for fixed nondegenerate C^2 curves: stationary tubes, derivative bands, and phase-bin coefficient estimates replacing the explicit trigonometric structure available on the unit circle.

High-frequency focused acoustic beams are promising for selective trapping of cells in fluids, but the related acoustic absorption may generate large acoustothermal effect which could cause thermal heating on cells or microparticles and bring extra acoustic body force due to the thermal gradient. The theory of the bulk acoustic streaming and acoustic radiation force in a focused-beam for the three-dimensional selective trapping of a cell has been developed [Li and Gong, Phys. Rev. Fluids, 11, 054201 (2026)], however, the acoustothermal effect and its feedback on the acoustic field at high frequency with strong absorption remain weakly understood. To solve this issue, we develop a theoretical and numerical model that couples acoustic propagation, bulk acoustic streaming, and acoustothermal effect in water. The acoustic body force is decomposed into a viscous-attenuation-induced acoustic body force $\mathbf{f}_{\mathrm{E}}$ and a temperature-gradient-induced acoustic body force $\mathbf{f}_{\mathrm{T}}$, while the temperature field is fed back to the frequency-domain acoustic calculation through the temperature-dependent material properties. Taking the single focused beam for example, within the pressure range constrained by the mechanical index, $\mathbf{f}_{\mathrm{T}}$ remains weaker than $\mathbf{f}_{\mathrm{E}}$, whereas streaming-induced convection can markedly reduce the temperature rise when the thermal Peclet number ($Pe_T$) exceeds unity. This work establishes a theoretical basis for predicting and controlling the intercoupling of bulk acoustic streaming and acoustothermal effec of high-frequency focused beams which will be helpful for the design of single-beam acoustical tweezers.

With the widespread adoption of Large Language Models (LLMs) in software engineering (SE) tasks such as code understanding, debugging, and vulnerability detection, their powerful semantic reasoning ability has also introduced new security and privacy risks. LLMs can analyze, reconstruct, or even reverse-engineer source code logic, potentially leading to the leakage of intellectual property. To address this issue, we propose Acoda, a genetic algorithm-based adversarial code obfuscation framework that defends against LLM-based code analysis. Acoda leverages two key mechanisms of LLMs, namely safety alignment and token-based information processing, to design 8 semantics-preserving obfuscation methods. It iteratively optimizes obfuscation strategies through a genetic algorithm to generate adversarial samples that maximize defensive effectiveness. In addition, we propose a quantitative evaluation framework based on LLM responses, which combines an auxiliary LLM and four evaluation metrics to assess how target LLMs analyze obfuscated code comprehensively. Experimental results show that Acoda can effectively induce LLMs to refuse or misinterpret code analysis. On 7 state-of-the-art LLMs, including GPT-4o, DeepSeek, Qwen, Llama, and Gemma, Acoda achieves an attack success rate (ASR) of up to 70%, with strong cross-model transferability and minimal runtime overhead, while ensuring that the semantics of the original code remain unchanged. Overall, this study provides a new perspective for code protection and LLM security defense in the era of LLMs.

We study the full automorphism groups of smooth cubic fourfolds with prescribed symplectic automorphism group. Our starting point is the classification of symplectic automorphism groups by Laza and Zheng. We focus on the non-symplectic index, namely, the index of the symplectic automorphism group in the full automorphism group. We prove general restrictions on this index. We also compute bounds by group-theoretic and lattice-theoretic methods. In several cases, we determine all possible indices. For coinvariant lattices of rank 19, we classify all possible pairs consisting of the symplectic automorphism group and the full automorphism group.

We investigate polarization-selective absorption in a visible-wavelength heterostructure consisting of a ReS$_2$ stripe grating, an $α$-MoO$_3$ spacer, and an Au back-reflector using finite-difference time-domain simulations. For an optimized geometry with a grating period of 500 nm, stripe width of 250 nm, and ReS$_2$ thickness of 80 nm, the structure exhibits near-unity absorption of 99.99\% at 650.5 nm under TE-polarized illumination. The resonant field is concentrated near the outer edges of the ReS$_2$ stripe, while absorption power density is localized in the same region, consistent with a localized edge mode. The absorption response depends strongly on polarization, producing a TE--TM resonance separation of 16.2 nm. Replacing either the biaxial ReS$_2$ layer or the anisotropic $α$-MoO$_3$ spacer with isotropic equivalents substantially modifies the spectral response and reduces the polarization-dependent wavelength separation. In addition, rotating the crystal orientation of the ReS$_2$/$α$-MoO$_3$ stack shifts both the resonance wavelength and peak absorption without changing the device geometry. The results show that the combination of anisotropic resonator and spacer layers provides an effective means of controlling resonant absorption and polarization selectivity in van der Waals photonic structures.

Current-induced spin-orbit torque has emerged as a powerful technique for manipulating magnetization switching of ferromagnet/nonmagnet (FM/NM) based memory cell. By investigating nonequilibrium spin torque effect in a van der Waals heterobilayer, trigonal $\text{Cr}_{3}\text{Te}_{4}/\text{PtTe}_{2}$, the first-principles quantum transport calculations are applied to determine both local spin induction, resulting from Rashba-Edelstein effect in the FM layer, and spin current injection, flowing from the NM to the FM layer. Our work reveals that local spin induction significantly generates the fieldlike torque, which primarily governs the switching current in systems with strong in-plane magnetic anisotropy. Our work emphasizes the importance of optimizing spin Hall effect in the NM layer for perpendicular magnetic anisotropy (PMA)-based magnetization switching and maximizing the Rashba effect in the FM layer for in-plane magnetic anisotropy (IMA)-based switching.

In 'On Denoting' Russell proposed the most influential theory of definite descriptions, expressions of the form 'the F'. Characteristic for Russell's approach is that definite descriptions are not treated as what they appear to be on the surface, i.e. as singular terms. Instead they are eliminated by a contextual definition. Russell formalises definite descriptions in the context of complete sentences of the form 'The F is G'. This requires scope markers to distinguish, e.g., internal from external negation. It was recognised by Burge, and Kalish and Montague, however, that the essential features of Russell's approach may be formalised while respecting the syntactic category to which definite descriptions appear to belong. An alternative, favoured by Neale, follows Russell in that complete sentences 'The F is G' are formalised by a binary quantifier. The undeniable importance of the theory of definite descriptions for logic, mathematics and philosophy demands that it be formalised to meet the standards of modern proof theory. This is the topic of the present paper. We systematise, compare and extend existing approaches. After presenting its essential features, we formalise Russell's theory of definite descriptions in sequent calculus. Three approaches will be considered. The first uses a binary quantifier, whereas the remaining two employ the term-forming iota operator. The first of these employs only the iota operator, the other employs in addition the lambda operator which does duty as a scope marker. All systems satisfy the standards for modern proof theory, in particular cut elimination. The appendix reformulates these systems in natural deduction, which is more convenient for practical purposes.

Multimodal entity linking (MEL) is the task that consists of matching textual and visual mentions of entities in unstructured data to their corresponding entities in a knowledge base (KB). To be effective in large-scale practical settings, MEL systems must meet three objectives: high linking accuracy, computational efficiency, and storage efficiency, i.e., a compact yet efficient index of the KB. In this paper, we highlight that state-of-the-art systems fail to simultaneously satisfy these 3 requirements. To meet this three-fold objective, we propose FAST-MEL, a lightweight encoder-based MEL solution that relies on a novel and compact fixed-size vectorized representation of both the textual and visual information of each entity or mention. It matches the accuracy of the best systems but performs three orders of magnitude faster. It also consumes one order of magnitude less storage than the fastest systems.

Dielectronic recombination (DR) is expected to be the dominant recombination process during the non-local thermodynamic equilibrium (non-LTE) phase of kilonovae, yet reliable DR data remain unavailable for most heavy ions. Current spectral models therefore rely on simplified recombination prescriptions, introducing significant uncertainties into predicted spectra. We present an optimization strategy for open f-shell ions using \texttt{AUTOSTRUCTURE}, targeting uranium ions U II--U IV relevant to kilonova ejecta. As a benchmark case, calculations are performed for Nd III to validate the treatment of the f-shell structure and its impact on DR. The resulting DR rate coefficients are of order $10^{-10}$--$10^{-12}$ cm$^{3}$s$^{-1}$ over temperatures relevant to kilonova plasmas. The optimized rates are intended for implementation in radiative-transfer calculations with \texttt{SUMO} to assess the sensitivity of kilonova spectra to improved recombination physics. The Nd III benchmark demonstrates that refinements to the atomic structure can produce measurable changes in spectral features, motivating similar calculations for actinide ions.

White-light interferometry enables ambiguity-free localization by synthesizing interference envelopes from multiple optical wavelengths, but no analogous capability has been realized for coherent matter waves. Here we report the first experimental demonstration of multi-wavelength atom interferometry, establishing the matter-wave counterpart of white-light interferometry. By exploiting counter-propagating atomic beams as multi-wavelength matter wave sources and synthesizing interference envelopes from their spectral components, we realize inertial measurements based on envelope localization rather than conventional fringe-phase estimation. The resulting multi-scale interferometric response provides ambiguity-free operation, a well-defined rotational scale factor, and reduced sensitivity to initial phase bias. As a proof of principle, we demonstrate simultaneous dual-axis rotation and acceleration sensing and directly resolve the phase ambiguity that fundamentally limits conventional open-loop atom interferometers. We further measure the Earth's rotation with a relative error of 4.3% and a long-term stability of 93 ppm at an averaging time of 15,000 s. Our results establish multi-wavelength atom interferometry as a new paradigm for coherent matter-wave sensing, extending the principles of white-light interferometry to atom optics and opening new opportunities for inertial sensing, geodesy, precision metrology, and inertial navigation.