There has recently been exciting progress in the realm of *probabilistic separation logics*. An important subclass of these -- including PSL, Lilac, Bluebell, and pcOL -- are *general-purpose probabilistic logics* (or GPLs, for short), meaning that they provide primitive Hoare-style assertions about probability distributions on the program state, along with powerful modularity principles like *independence* and *conditioning*. However, none of these logics support reasoning about dynamically allocated memory (i.e., pointers into a heap), let alone the more sophisticated resource algebra-based ghost state of modern separation logics like Iris. We argue that this is due to a fundamental obstacle: since the shape of memory (and identity of memory locations) may differ under different random outcomes, it is unclear how pointer ownership can be harmonized with probabilistic independence and conditioning. Furthermore, none of the existing GPLs have been mechanized in a proof assistant. In this paper, we take a substantial first step towards a marriage of GPLs and modern separation logics like Iris, in the form of **Amaryllis**. Amaryllis is the first GPL to support independence and conditional reasoning while also handling dynamic memory allocation. To overcome the aforementioned obstacle, we propose a new *indexed valuation*-style model of probabilistic assertions, whereby ownership of a standard Iris-style resource (e.g., heaps) can be promoted to ownership at the level of distributions in a generic fashion. We then show how to adapt the central Iris notions of *frame-preserving update*, *authoritative resource algebras*, and the *weakest precondition modality* to be sound for probabilistic reasoning and validate dynamic allocation. Finally, we have mechanized all our results in the Rocq proof assistant and developed an Iris-based proof mode for conducting proofs within Amaryllis.

The Edelstein effect in magnetic systems enables magnetization switching via the coupling between current-induced spin accumulation and intrinsic magnetic order, and is therefore highly promising for next-generation spintronic devices. Realizing and manipulating the Edelstein effect in two-dimensional (2D) magnetic systems is particularly desirable for achieving high-efficiency and multifunctional spintronic applications. In this work, based on first-principles calculations and symmetry analysis, we demonstrate that the Edelstein effect can intrinsically arise in the 2D in-plane ferromagnetic semiconductor 2H-VTe2, with its behavior strongly dependent on the magnetization orientation. For monolayer 2H-VTe2 with D3h crystal symmetry, under an applied current along the +x direction, only the time-reversal-even z component and the time-reversal-odd y(x) component of the spin accumulation are allowed when the magnetization is aligned along +x (+y). For ferromagnetic bilayer 2H-VTe2 in AB or BA stacking, where the crystal symmetry is reduced to C3v, additional spin components emerge with the presence of in-plane magnetization. Specifically, for magnetization along +x (+y), besides dSz_even and dSy_odd (dSz_even and dSx_odd), extra components such as dSy_even and dSz_odd (dSy_even) become allowed. Notably, these additional components can be reversibly switched by changing the stacking configuration from AB to BA via interlayer sliding. Our results not only deepen the understanding of current-induced spin accumulation in 2D magnetic systems from both symmetry and first-principles perspectives, but also identify 2H-MX2 materials as a promising platform for realizing intrinsic and tunable Edelstein effects in high-efficiency spin-orbit torque devices.

The integration of large language models (LLMs) in economic simulations has significantly enhanced agent-based modeling, yet existing frameworks struggle to capture the interplay between short-term optimization and long-term strategic planning. Conventional approaches rely on static data-driven predictions, failing to incorporate adaptive behaviors influenced by economic sentiment, market volatility, and individual goals. To address these limitations, we introduce a novel EconAI framework, incorporating economic sentiment indexing (ESI), memory weighting, and dynamic decision-making mechanisms. By quantifying economic belief, adjusting historical data influence, and linking work-consumption behaviors, EconAI achieves a more human-like decision process, where agents adapt their actions based on both market signals and long-term objectives. It is the first LLM-powered simulation system that can simulate the macro/microeconomic environment and interactions in a unified framework. Empirical evaluations show that EconAI improves stability in economic responses, better replicates real-world employment-consumption cycles, and enhances overall decision robustness. This advancement marks a crucial step towards more realistic, adaptive economic agent simulations.

Monolithic active pixel sensor (MAPS) developments have pushed the detection performance in various directions, especially relative to timing where nanosecond-level precision is now considered. This evolution calls for a simultaneous upgrade of the simulation tools. We have developed a simulation flow that covers steps from the signal creation in the sensitive volume to the output of the pixel digital logic that performs the time-of-arrival and time-over-threshold (ToA/ToT) measurements. This approach adds several new features to the traditional use the of the TCAD - Allpix Squared duo, among which : the integration of the pixel wells from the layout in order to precisely describe the pixel key characteristics such as leakage and punch-through currents and the coupling of Monte Carlo simulations (Allpix Squared) with high precision electrical simulations (SPICE). The first (Allpix Squared) for the precise description of the current induced at the collection electrode and the second (SPICE) to guarantee high precision simulation of the front-end electronics using realistic signal events. Irradiation is also modeled, both from the charge propagation side (charge trapping) and from the front-end response side (high input signal discharge). We have applied this methodology to the MAPS developed in the context of the Belle II vertex detector upgrade. In this contribution, we detail the key features of the exhaustive simulation flow, present the outcome of the comparison with the TJ-Monopix2 measurements and discuss the interest of the methodology for the development of modern MAPS.

We study the fully generalized Grover's algorithm to find the optimal phase changes for each step of the iteration to maximize gain in probability of observation of the target, and when phase matching is required. We find that classical Grover's algorithm and phase matching remains to be optimal till the target probability gets close 1. However, as the probability of observation approaches 1, the optimal phase changes differ from $π$ and no longer observe phase matching. We provide the optimization statement to find the optimal phase changes given the current amplitude vector and the size of the set. To analyze this formula, we approach it from a numerical and analytical perspective, with the analytical perspective focusing on special cases that simplify the optimization and allow for general statements about its behavior. Finally, we provide an example of a 5 qubit system and show that for the final iteration the optimal phase changes differ from traditional Grover's algorithm and do not observe phase matching, but lead to an increase in the probability of the target.

Costly cooperation and costly signaling are both difficult to reconcile with simple fitness maximization, yet both are common in biological and social systems. We study a model in which agents emit costly signals and condition their actions on the signals they observe. Across the Prisoner's Dilemma (PD), Snowdrift (SD), and Stag Hunt (SH) games, we ask when this coevolutionary process can sustain cooperation and how it changes across well-mixed populations, spatial lattices, and fluctuating strategic environments. The simulations show that signals are selected less by their raw production costs than by the cooperative responses they currently elicit. In well-mixed populations, the mechanism sustains partial cooperation in PD and SD and drives near-complete cooperation in SH. On lattices, cooperation is strengthened further by local assortment. A reduced mean-field analysis explains why average population feedback is already sufficient in SD and SH, but not in the PD. To account for the PD dynamics, the reduced theory must include transient correlations associated with rare signals, inheritance, or spatial clustering. Our results therefore delineate a class of settings in which costly signals persist because they transiently organize cooperative responses and thereby reshape the effective strategic environment.

We study the asymptotic response time tail in the M/G/n multi-server queue with heavy-tailed (regularly varying) job sizes, a setting representative of modern computing workloads. For single-server systems, tail optimization is well understood: under heavy-tailed job sizes, policies such as SRPT that strictly prioritize short jobs are strongly tail optimal, and giving any priority to large jobs is harmful. For multi-server systems, the question has been almost entirely open. This paper gives the first strongly tail-optimal scheduling policies for the M/G/n queue with heavy-tailed job sizes. Our central finding is that the multi-server case is intrinsically different from the single-server case: giving a small amount of ``sympathy'' to large jobs is essential for strong tail optimality. We establish strong (or arbitrarily close to strong) tail optimality across the full stability region, both with and without knowledge of job sizes.

Enhancing quantum illumination with highly entangled probes remains an active area of research. In this context, non-Gaussian operations provide an effective route for engineering probe states that can surpass the standard two-mode squeezed state (TMSS). In this work, we investigate a specific nonlocal non-Gaussian operation protocol and show that the engineered state using this protocol outperforms previously considered local non-Gaussian scenarios, engineered based on photon catalysis, addition, and subtraction under realistic conditions, including photon loss. Furthermore, by employing a $50{:}50$ beam splitter with photon-number difference detection, we demonstrate a significant enhancement in the signal-to-noise ratio (SNR) for target detection relative to the TMSS. Thus, our protocol exhibits improved performance, highlighting a resource-efficient and experimentally feasible probe for enhanced quantum illumination.

This paper develops a macroscopic, activity-based model of urban active mobility using nonintrusive sensor data. It introduces attendance functions to describe spatio-temporal travel patterns between activities and formulates the disaggregation of aggregated counts as a statistical inference problem. Counts are modeled as Poisson variables, and unknown subpopulation sizes are estimated via maximum likelihood, with theoretical guarantees and an efficient EM algorithm for computation. Grounded in a microscopic stochastic model, the framework offers a scalable and privacy-preserving approach to analyzing urban soft mobility dynamics.

A key science target of the Large Interferometer Space Antenna (LISA) is to carry out multi-messenger observations of massive black hole binaries, observing the merger simultaneously in gravitational waves and with electromagnetic observatories. Identifying that a merger is happening and providing an updating estimate of the sky location in the hours, days and weeks before the merger is critical to enable electromagnetic observations of the merger event. In this work we demonstrate and compare two methods for premerger identification of massive black hole binaries; a zero-latency filter approach and, for the first time, an approach using an ``inpainting'' technique. We apply these methods to the LISA Data Challenge dataset 2a--Sangria-HM--and demonstrate the successful recovery of the 14 signals in the dataset that we expected to be identifiable at least half a day before merger. We show that the inpainting method can identify premerger signals even when gaps are present in the data, demonstrating the recovery of a signal even when 3 day-long data gaps are added to the 14 days preceding merger. Finally, we explore the challenge of overlapping signals, using a region of overlapping signals in the Sangria-HM dataset, all of which merge within a 10-day window, and show how removing signals that have been confidently identified from the data allows us to identify quieter signals in the same period.

While interior point methods have been the centerpiece of nonlinear programming tools used in science and engineering, their reliance on linear solvers that can tackle sparse symmetric indefinite and highly ill-conditioned problems made it difficult to implement them effectively on hardware accelerators. At this time, there are few sparse linear solvers that can be used in this context. Here, we present a novel formulation of an interior point method implemented in our HiOp library, which is designed to be able to run entirely on hardware accelerators. This formulation avoids dependence on sparse solvers altogether, which is achieved by compressing the underlying sparse linear problem into a dense one of manageable size. We demonstrate feasibility of this approach and provide a baseline for future interior point method implementations on hardware accelerators. Our investigation is motivated by problems arising in optimal power flow analysis in power systems engineering and our approach is tailored to the broad class of problems arising in that important domain. We also demonstrate utility of modern programming models based on performance portability libraries, namely, Umpire and RAJA. We discuss trade-offs between performance, portability and development cost in the solution space for this non-linear optimization problem. As a result of this research, we demonstrate for the first time that interior point methods for sparse problems can be efficiently realized on modern computing systems where more than 90% of processing power is in GPUs.

Let $\grad$, $\curl$, and $\dv$ be the graph-theoretic analogues of the gradient, curl, and divergence operators from multivariate calculus. The graph Laplacian $-\dv \grad$ gives rise to the celebrated Laplacian matrix, while the matrix representation of the graph Helmholtzian $\grad \grad^* + \curl^* \curl$ is called the Helmholtzian matrix. In this paper, we present a new graph-theoretic proof that the Helmholtzian matrix indeed represents the graph Helmholtzian. We then investigate the spectral properties of this matrix. Our main results are as follows: (i) a classification of graphs having exactly two distinct Helmholtzian eigenvalues; (ii) the nullity of the Helmholtzian matrix; and (iii) a combinatorial interpretation of the coefficients of the Helmholtzian polynomial. Furthermore, we determine the Helmholtzian spectrum for certain graph products and characterize Helmholtzian integral graphs, as well as derive bounds for the smallest Helmholtzian eigenvalue. Meanwhile, we pose some open problems for future research.

We consider perturbations in the isotropic and homogeneous cosmological model with the spatially flat Friedmann-Lemaitre-Robertson-Walker metric in the framework of the theory of gravity with non-minimal derivative coupling. The Lagrangian of the theory contains the coupling term $ηG^{μν}\nabla_μϕ\nabla_νϕ$ and represents the particular example of a general Horndeski Lagrangian, which results in second-order field equations. It is known that the non-minimal derivative coupling crucially changes scenarios of the Universe evolution on early times. In particular, the $η$-term is dominating on early times and leads to a primary quasi-de Sitter (inflationary) stage which needs no fine-tuned potential. On late times the influence of non-minimal derivative coupling on the Universe evolution completely disappears, and this naturally leads to the transition to the standard cosmological evolution (post-inflationary stage). We have derived a complete set of equations which describe an evolution of scalar, vector and tensor modes of perturbations. All modes are analyzed analytically in two asymptotic cases, and then we construct exact numerical solutions which describe an entire evolution of the modes. We show that all modes, including vector ones, are amplified in the quasi-de Sitter (inflationary) stage, and such the behavior is cardinally distinct from that in Friedmann cosmology.

Quasi-periodic fast propagating (QFP) wave trains observed in the solar corona after some energetic events (solar flares, coronal mass ejections, jets) open possibilities for diagnostics of spatial and temporal scales of the impulsive energy release processes, that are absent in the standard model of a solar flare. Besides, the dynamics of the wave trains and their characteristic spatial and temporal signatures allow to localize the initial energy release volume magenta and to perform fine diagnostics of the transverse structures of plasma inhomogeneities in the solar corona. However, the small number of such events registered significantly limits their promising diagnostic potential. The aim of this paper is to perform an automatic search for fast wave trains in radio data. We apply classifying neural network/machine learning methods. Dynamic radio spectra obtained by HiRAS radio spectrographs within the 20 MHz -- 2.5 GHz frequency band during 2011 were used. We consider 50 global coronal EUV waves as marker events for more a targeted search in HiRAS data. Our automatic detector revealed 50 independent QFP-candidates events with the temporal signatures similar to that of the fast wave trains, with 13 candidates connected with the global waves.

We establish the first existence and uniqueness result for mild solutions of abstract stochastic evolution equations driven by arbitrary cylindrical Lévy processes in Hilbert spaces. The coefficients are assumed to satisfy global Lipschitz conditions, and no moment assumptions are imposed on the driving noise. The principal difficulty arises from the fact that cylindrical Lévy processes exist solely in a generalised sense and typically admit no semimartingale or Lévy-Itô decomposition, which precludes the use of classical existence methods. To overcome these obstacles, we develop a pathwise adaptive Euler-Peano approximation scheme based on noise-dependent stopping times and a fixed-point formulation of the mild solution operator. The resulting approach avoids stochastic calculus techniques relying on semimartingale decompositions and provides a robust and flexible framework for treating multiplicative cylindrical Lévy noise in infinite-dimensional systems.

The unit Euclidean distance degree and the generic Euclidean distance degree are two well-studied invariants of projective varieties. These quantities measure the algebraic complexity of nearest-point problems on a variety, and in many examples arising in optimization, engineering, statistics, and data science, there is a significant gap between them. We refer to this difference as the defect of the Euclidean distance (ED) degree. In this paper, we provide a constructible enhancement and a topological formula for the defect of the ED degree of an arbitrary complex projective variety, extending our previous results from the smooth setting. Since the generic Euclidean distance degree is typically more tractable, our approach offers a new method for computing ED degrees in broad generality.

Hybrid superconductor-semiconductor nanostructures are a central component for research spanning condensed matter physics and quantum information processing. Continued progress relies critically on the ability to characterize, control, and optimize several intrinsic material properties including spin-orbit coupling, band offsets, and disorder in a device-relevant stack that necessarily couples the electronic states of a superconducting metal film and a semiconductor. Here we report a new method to extract fundamental material parameters utilizing simple Shubnikov-de Haas (SdH) oscillation measurements in heterostructures in which metallic electronic states are coupled to a two-dimensional electron gas (2DEG) residing in an InAs quantum well beneath an aluminum thin film. Proper analysis of the full magnetoresistance data facilitates extraction of the quantum well carrier density, spin-orbit coupling strength, and both transport and quantum scattering times. Most importantly, the extracted scattering times in the 2DEG are impacted by the metal-semiconductor coupling strength allowing us to quickly gain information on proximity-induced superconducting gap without any fabrication or mK measurements. The wealth of information that is accessed with these simple measurements positions this methodology as an important tool for hybrid materials optimization.

We introduce the Dreaming $L$-directional Associative Memory (DLAM), a multi-layer Hebbian architecture in which off-line dreaming and supervised heteroassociative coupling coexist within a single energy function, placing our approach within the framework of energy-based models (EBMs). The replica-symmetric free energy, derived via the Guerra interpolation scheme, yields self-consistency equations governing the order parameters across the control-parameter space. The effective local field decomposes into signal, intra-layer dreaming noise, and inter-layer noise. Dreaming improves retrieval by differentially attenuating high-eigenvalue interference modes of the empirical correlation matrix, suppressing inter-pattern crosstalk while preserving the signal. Dreaming and inter-layer coupling prove synergistic, opening retrieval regions unreachable by either mechanism alone, as confirmed by Monte Carlo simulations for $L=3$. Their interplay is most pronounced on pattern disentanglement: given a mixture state as input, the network splits the constituent patterns one-per-layer, recovering each modality-specific pattern from a common cue that simultaneously blends noisy evidence from all sensory channels. Phase diagrams are planar projections of the hyperspace $(α,β,ρ,t)$-where $α$ is the storage load, $β$ the fast-noise inverse temperature, $ρ$ the dataset entropy, and $t$ the sleeping time. In the $(ρ,t)$-plane, the diagrams reveal a data-computation trade-off: off-line consolidation substitutes for additional training data, extending to heteroassociative architectures a phenomenon previously established for autoassociative networks. Enriching the standard Hopfield model with heteroassociativity and dreaming gives rise to EBMs capable of complex tasks beyond classical pattern recognition, contributing to a modern theory of neural information processing.

Underwater images suffer from wavelength-dependent light absorption and scattering, which reduces visual quality. This phenomenon could limit the operational reliability of autonomous underwater vehicles, marine surveys, and offshore inspection systems. Purely classical methods often achieve suboptimal performance in real-world datasets, while purely data-driven methods lack physical interpretability. In this letter, we propose UDehaze-iT, a deep network for underwater image enhancement that estimates scene depth implicitly and derives per-channel transmission through the Beer-Lambert law with learnable attenuation coefficients. We estimate atmospheric light as a semi-classical per-channel scalar, and a zero-initialized residual refiner corrects remaining artefacts after dehazing. To effectively train our method, we apply a composite loss function consisting of five key terms: a L1 loss, a multi-scale patchwise DCT loss, a forward model reconstruction loss, and two regularization terms. With ~0.9M parameters, UDehaze-iT achieves competitive performance on UIEB and UFO-120 datasets.

GW170817 remains the only binary neutron star merger detected through multimessenger emission. Its afterglow has been monitored for nearly a decade, offering an unprecedented opportunity to probe the properties of the outflow. The shallow decay of the very late-time afterglow challenges the prediction of a collimated structured jet. Motivated by recent general-relativistic magnetohydrodynamic simulations, we propose that the GW170817 afterglow is powered by a wobbling jet that drags a ring on the sky. This structure predicts a post-break decay rate shallower than that of a collimated jet, as observers will see a progressively longer emitting arc after the break. A misaligned ring-shaped jet can therefore self-consistently explain the multimessenger data without invoking any extra component. Through a Bayesian analysis of the multimessenger data, we find a ring-shaped jet is favored over a collimated jet at a significance level of 4.8$σ$. Our results imply a wobbling angle of $\sim 27^\circ$. Such a large angle points to a significant disk tilt, potentially arising from disk-infalling gas interaction or asymmetric angular momentum ejection. Similar shallow decays have also been found in other GRB afterglows, raising the possibility that wobbling jets are common among GRBs.

In this work, we present a combination of a multigrid approach and the phi-FEM immersed boundary finite element method to reduce its computational cost while preserving its accuracy. To further reduce the numerical cost of the approach, we also propose the combination of the previous technique with some neural network methods. We illustrate the efficiency of these two approaches with numerical test cases in 2D and 3D.

Large language model agents increasingly rely on skill libraries for multi-step tasks, yet these libraries can accumulate persistent defects as skills are added, reused, patched, and linked to changing dependencies. We call this failure mode skill technical debt: library-level defects that may not break a single skill locally but can harm future retrieval, composition, and execution. Existing skill-based agents mainly focus on task-time retrieval, planning, and repair, while library-time maintenance remains underexplored. We propose SkillOps, a method-agnostic plug-in framework for maintaining skill libraries. SkillOps represents each skill as a typed Skill Contract (P, O, A, V, F), organizes skills with a Hierarchical Skill Ecosystem Graph, and diagnoses library health across utility, compatibility, risk, and validation dimensions. Given a raw skill library, SkillOps produces a maintained library that can be used by existing retrieval or planning agents without changing their internal code. On ALFWorld, SkillOps achieves 79.5 percent task success as a standalone agent, outperforming the strongest baseline by 8.8 percentage points with no additional task-time large language model calls. As a plug-in layer, it improves retrieval-heavy baselines by 0.68 to 2.90 percentage points. The current rule-based maintenance implementation uses nearly zero library-time large language model calls or tokens, showing that skill-library maintenance can be added as a low-overhead architectural layer.

We consider sums of the form $$F_χ(α,β;θ) := \sum_{αp<n\leβp}χ(n)e(nθ),$$ where $χ$ is a non-principal Dirichlet character modulo a prime number $p$. We prove that $$ \sqrt p \log \log p \ll \max_{0 \le θ< 1}{\left|F_χ(α,β;θ)\right|} \ll \sqrt{p}\log p, $$ generalizing an old result of Montgomery as well as a recent result of Iggidr in two aspects: we allow general non-principal characters $χ$, and we consider incomplete mixed character sums.

In a recent series of papers we developed a first-principle and gauge invariant approach to black hole perturbation theory valid to any order. We included back reaction effects to tackle the situation of evaporating black holes and obtained an explicit expression for the dynamics of the reduced phase space to second order. The physics of evaporating black holes is in particular encoded by apparent horizons, an observer dependent generalisation of the event horizon. We determine the shape of the apparent horizon to second order in the perturbations. The area of the apparent horizon is an interesting observable which is expected to decrease in the quantum theory due to Hawking evaporation. We show how the full four dimensional metric can be reconstructed in terms of the reduced phase space variables. In the quantum theory, taking expectation values of this metric, we obtain an effective classical metric, whose causal structure can then be visualised in a quantum corrected Penrose diagram. We conclude with an outlook into the quantisation procedure in the reduced phase space formalism and the implications on the area of the apparent horizon.

We demonstrate that the near-field thermal radiation between subwavelength SiC nanowires with square cross sections is dominated by multiple corner and edge resonances rather than the single surface-phonon-polariton channel of planar surfaces. Fluctuational electrodynamics simulations reveal that these resonances lie within the SiC Reststrahlen band, redshift for thinner nanowires, and yield a four-fold enhancement of thermal conductance. This maximum enhancement occurs when the separation gap nearly matches the nanowire thickness, balancing dimensional confinement and interwire coupling. These findings establish square nanowires as a versatile platform for geometrycontrolled near-field heat transfer in nanoscale heat management and energy conversion.

In statistics permutations typically arise in the context of rank plots for two-dimensional data. Such plots can also be interpreted as discrete copulas. In discrete mathematics, typically in the context of the description of large (non-random) objects, two-dimensional copulas appear as limits of permutations and are then known as permutons if the topology refers to the convergence of pattern frequencies. We obtain a functional central limit theorem for such pattern frequencies in the context of two-dimensional random samples. The result serves as the basis for nonparametric goodness-of-fit tests, for two-sample tests, and for tests of symmetry. This includes a suitable variant of the bootstrap for obtaining critical values. Pattern-based procedures are also of interest in a parametric context. We consider two examples, the Farlie-Gumbel-Morgenstern class and a family of delay copulas. We discuss implementation aspects of the resulting procedures and we provide a simulation study that supplements the theoretical results in the nonparametric case.

Optical spin-orbit interactions (SOI) link photonic spin to momentum, offering a route toward on-chip polarization control and beam steering. Nevertheless, achieving sufficient optical SOI and nonlinearities on sub-micrometer scales - a prerequisite for dense photonic integration - remains an outstanding challenge. Here, we show that highly birefringent van der Waals (vdW) waveguides provide an ideal, chip-compatible platform to address this limitation. We focus on the ferroelectric semiconductor NbOI2, which exhibits record optical nonlinearities and dielectric anisotropy. Using femtosecond optical microscopy, we image light propagation and harmonic conversion beyond the total internal reflection barrier over tens of micrometers in NbOI2 slab waveguides. We report giant optical spin-splitting through the optical spin Hall effect, which facilitates spatial separation of optical spin currents on sub-micrometer scales, in quantitative agreement with a microscopic light-matter interaction model. We further leverage optical spin-momentum locking to realize polarization-controlled waveguide steering. We generalize these observations across various vdW waveguides and empirically confirm a scaling law linking dielectric anisotropy to geometric spin-splitting. Our results establish highly anisotropic vdW waveguides as an ideal platform for densely integrated opto-spintronic technologies.

We provide a Lax-Oleinik-type representation formula for solutions to nonautonomous Hamilton-Jacobi equations posed on networks with a rather general geometry. The networks may possess countably many arcs and allow for the presence of loops. We consider Hamiltonians that are convex and superlinear in the momentum variable, and satisfy a Lipschitz-type condition in the time variable. The representation formula is constructed via an overall Lagrangian that accounts for both the arc-specific dynamics and vertex-based constraints, called flux limiters, which ensure the well-posedness of the problem. We prove that the corresponding action functional admits Lipschitz continuous minimizers without needing to rule out the Zeno phenomenon. Furthermore, we demonstrate that the formula yields the unique solution to the problem even when the flux limiters exceed standard upper bounds.

Fluctuation formulas for elastic and viscoelastic moduli allow their computation from equilibrium molecular dynamics simulations, avoiding explicit nonequilibrium deformation protocols. While such expressions are well established for the quasi-static moduli, and also the linear dynamic moduli, no fluctuation formula exists for the nonlinear time-dependent moduli that govern anharmonic viscoelastic response under finite time-dependent strains. In this work we derive transient-time correlation function expressions for both the linear and the nonlinear dynamic moduli, starting from the DOLLS/SLLOD equations of motion for irrotational motion. The resulting formulas involve equilibrium time correlations of the stress tensor and Born-kinetic terms, and they recover the known quasi-static and linear dynamic results in the appropriate limits.

According to the $B$-mesogenesis framework, the baryon asymmetry of the Universe and dark matter can be simultaneously generated through CP-violating $B$-meson oscillations. In this mechanism, $B$-mesons decay into a Standard Model baryon and a dark-sector antibaryon, denoted by $ψ_{DS}$. Within this scenario, we investigate the allowed mass window for $ψ_{DS}$ using Light Cone Sum Rules (LCSR) for $B_d\rightarrowΛ\, ψ_{DS}$ decay. To include non-perturbative effects, we employ contributions up to twist-6 of the $Λ$ distribution amplitudes in the operator product expansion (OPE). We derive the branching fraction as a function of dark antibaryon mass and, by comparing with the experimental limits by the BaBar and Belle collaborations, determine the mass ranges of $ψ_{DS}$ consistent with the $B$-mesogenesis mechanism.