Inverse Compton scattering (ICS) is a unique source of highly monochromatic x-ray and gamma radiation. We investigate theoretically the cumulative effects of repeated head-on interactions between the electron beam and a train of powerful laser pulses inside a linear accelerating structure placed between mirrors of an optical resonator. We find that the longitudinal momentum spread converges exponentially to an equilibrium value due to the competition between quantum excitation (heating) and radiation friction (cooling). The predictions of the developed theory coincide very well with computer simulations. Our work establishes the necessity to account for cumulative transverse beam dynamics in the design and optimization of future stable, high-brightness ICS sources.

This work analyzes an operational route to classical behavior for reduced quantum states using the intrinsic reference basis (IRB). Relative to a fixed physical conjugation, the IRB separates intrinsic populations from a real antisymmetric cohesion sector. A globally bounded cohesion index is defined and its exponential contraction is proved for phase-free dephasing dynamics aligned with the IRB; for general aligned dephasing, the corresponding modulus-based coherence functional contracts at the same computable rates. The results provide distance bounds to the IRB-diagonal description and a logarithmic upper bound on the time required to reach a prescribed experimental tolerance. The IRB projectors constitute state-derived candidate pointer sectors, and they become dynamically stable pointer sectors when the effective dephasing generator is aligned with them and damps the relevant inter-sector coherences. Degenerate population sectors lead naturally to block-classicality and protected intra-block coherence. In a two-level active sector, the cohesion index equals fringe visibility, giving a direct interferometric test of the contraction law. The construction is independent of any spacetime- or unification-emergence hypothesis and is intended as a channel-level complement to environment-induced einselection.

Thin liquid films are ubiquitous across many natural and engineering systems, including films which are laden with surface active molecules, i.e. surfactants. The presence of surfactants may have a destabilising effect on the film owing to their influence on surface tension, the so-called Marangoni effect, which in turn can induce flows in the film. Classical thin-film models for surfactant-laden films lead to paradigmatic gradient dynamics equations governing the film height and surfactant concentration and have been widely studied. However, in all these works, which are based on fluid dynamics or nonequilibrium thermodynamics, the shape of surfactants is neglected, and they have been treated as symmetric point-like particles. In general, this is a drastic oversimplification, as surfactants are amphiphilic with a polar head-tail structure. To account for this effect we use elements from the statistical mechanics of classical fluids, namely density-functional theory (DFT), and its dynamic extension (DDFT). Starting from DDFT and under the long-wave approximation, we derive the pertinent thin-film equations with the surfactants treated as polar uniaxial particles. These are equations which govern the film height, as well as the surfactant concentration and polarisation field. They preserve the gradient dynamics form by appropriately defining the free energy, which contains the usual interfacial contributions, as well as further contributions from the polarisation field. In doing so, we uncover a novel form of a generalised surface tension that is dependent on the surfactant polarisation as well as concentration, and show that it arises in a thermodynamically consistent way.

We investigate the category of ``matricial order operator spaces,'' which generalize operator systems, being equipped with both matricial norms and matricial order. For these objects, we develop duality theory. Taking a cue from the theory of ordered normed spaces, we introduce two important properties describing the interplay between order and norm -- ``normality'' and ``generation,'' and show that they are dual to each other. As examples, we consider operator systems (in particular, C*-algebras), and Schatten spaces. We also describe the minimal and maximal matricial order structures (which, again, turn out to be in duality), and show how Banach lattices can be equipped with such structures.

We denote by $\mathcal{R}_{g;m}$ the moduli space of $m$--pointed Prym curves of genus $g$, that is, tuples $[\widetilde C / C; x_1, \dots, x_m]$ where $[C, x_1, \dots, x_m]$ is an $m$--pointed curve of genus $g$ and $\widetilde C/ C$ is an étale double cover of $C$. In this paper, we address the problem of the non--tautology of the Chow ring of $\mathcal{R}_{g;m}$. The locus which allows us to achieve earlier bounds for the non--tautology of $\mathrm{CH}^\bullet(\mathcal{R}_{g})$ compared to $\mathcal{M}_g$ is the component $\mathcal{R}\mathcal{B}_g^0$ of the locus of bi--elliptic Prym curves. This parametrises covers $[\widetilde C/ C]$ such that, if $C \rightarrow E$ is the bi--elliptic structure, the composition $\widetilde C \rightarrow E$ factors through an elliptic cover of $E$. Our main contribution is thus the non--tautology of the class $[\mathcal{R}\mathcal{B}_8^0] \in \mathrm{CH}^*(\mathcal{R}_8)$. In the course of establishing this theorem, a similar result for the compact moduli spaces $\overline{\mathcal{R}}_{g; 2m}$ for $g + m \geq 8$ is proven.

GaAs-based nanowires hosting active quantum heterostructures provide a promising route toward monolithic integration of single-photon sources on silicon, a key requirement for scalable quantum photonics. However, ultrathin axial quantum-emitter formation is often hindered by facet-dependent growth dynamics and rotational twins, which induce lateral overgrowth and compromise interface abruptness. Here, we develop InGaAs-based quantum emitters by tailoring facet evolution via dilute Sb incorporation, which efficiently suppresses twins and promotes confined axial insertion at the growth-front facet. This approach significantly enhances the probability of obtaining abrupt, few-nanometer-thin quantum dots at the nanowire tip. Single-nanowire optical spectroscopy reveals intense, spatially localized emission from the active region with lifetimes as short as (0.51 $\pm$ 0.02) ns, and second-order photon-correlation measurements consistently exhibit pronounced antibunching with $g^{(2)}(0)<0.4$, confirming single-photon emission. These results establish a strong correlation between twin density and axial heterostructure formation, identifying defect control as a key factor in realizing monolithically integrated nanowire single-photon sources.

Based on the fractional entropy originating from fractional quantum mechanics, the fractional holographic dark energy (FHDE) model has been proposed. In this paper, we consider an interaction between the pressureless matter and FHDE and analyze three different interacting FHDE models. Combining the latest observational data including SNIa, OHD, BAO, and CMB, we estimate the model parameters and find that the interaction forms $Q=\gamma H \rho_{de}$ and $Q=\beta H \rho_{m}+\gamma H \rho_{de}$ show some preference from the observational data. Using phase space analysis, we further find that only interacting FHDE model with $Q=\beta H \rho_{m}+\gamma H \rho_{de}$ can describe the full evolutionary history of the universe. The statefinder diagnostic pair reveals that this model deviates from the $\Lambda$CDM model but converges to the $\Lambda$CDM fixed point and the de Sitter expansion fixed point in the future. Finally, we analyze the evolution of cosmological parameters and demonstrate that this model can drive the late time acceleration of the universe.

Pseudorandom codes (PRCs), introduced by Christ and Gunn (CRYPTO '2024), are error-correcting codes whose codewords are computationally indistinguishable from uniformly random strings, while still being decodable by someone holding the key. They provide a natural primitive for robust and undetectable watermarking, particularly in applications to AI-generated content. Although recent works have obtained strong results for substitution errors, the edit-error setting remains much less understood, especially in the high-rate regime and over small alphabets. We study public-key pseudorandom codes against edit errors. First, we give a new reduction showing that binary zero-bit PRCs robust against a constant fraction of substitution errors can be transformed into binary zero-bit PRCs robust against edit errors. Consequently, under any assumption that yields zero-bit Hamming-robust PRCs, one also obtains zero-bit PRCs for edit channels, albeit only for the weaker class of sublinear polynomial edit channels, namely channels with edit error rate $1/n^{\gamma}$ for any constant $\gamma>0$. In the high-rate regime, we construct public-key PRCs with rate arbitrarily close to $1$ over sufficiently large constant alphabets, and with rate arbitrarily close to $1/2$ over the binary alphabet. Moreover, if we allow the alphabet size to be $\mathrm{poly}(\lambda)$, where $\lambda$ is the security parameter, then our public-key PRCs can attain the Singleton bound for insertion-deletion channels. Taken together, these results yield the first high-rate public-key binary PRC constructions for edit channels, under the same assumption that yields zero-bit Hamming-robust PRCs.

In a previous paper, a process algebra based on ACP (Algebra of Communicating Processes) was proposed in which processes involving data can be handled by means of features originating from imperative programming. In this paper, an extension of that process algebra with probabilistic choice operators is presented that rests on the principle that probabilistic choices are always resolved before choices involved in alternative composition and parallel composition are resolved. This extension is devised, among other things, to be used for modeling and analyzing algorithms that are important in the area of distributed computing. Many canonical problems in that area call for a probabilistic algorithm. In this paper, a probabilistic algorithm for the leader election problem is modeled using the presented process algebra.

In this article, we study the zero-divisor graph of the commutative ring with identity $R= \mathbb{F}_p + u\mathbb{F}_p + v\mathbb{F}_p + uv\mathbb{F}_p,$ where $u^2 = 0, v^2 = 0, uv = vu$ and $p$ is an odd prime. We determine several graph-theoretic properties associated with the zero-divisor graph $\Gamma(R),$ including the clique number, chromatic number, vertex connectivity, edge connectivity, diameter and girth. In addition, we compute certain topological indices of the graph $\Gamma(R).$ Furthermore, we find the eigenvalues, energy and spectral radius of the adjacency matrix, the Laplacian matrix and the Eccentricity matrix of the zero-divisor graph $(\Gamma(R).$

Kunchenko's method of polynomial maximization provides a semiparametric apparatus for parameter estimation under non-Gaussian errors, but its classical power basis relies on finite higher-order integer moments. This paper introduces the Parametrically Adaptive Transition Polynomial (PATP), a signed-parity fractional-power family controlled by a continuous parameter alpha in [0,1]. The quadratic exponent map p_i(alpha) connects the fractal regime p_i(0)=1/i, the degenerate linear point p_i(1/2)=1, and the signed-parity integer-power regime p_i(1)=i. For the degree-S=2 case we derive a closed-form variance-reduction coefficient g_2(alpha) in terms of signed and absolute fractional moments, identify the singular behavior at alpha=1/2, and state the moment and regularity conditions under which the formula is meaningful. The construction should be read as a Form-B PATP analogue within Kunchenko's generalized apparatus, not as an exact recovery of the canonical even-power PMM basis at alpha=1. Numerical illustrations on canonical distributions are used to examine the finite-sample behavior of the signed-parity estimator and to mark the boundary of applicability for extremely heavy-tailed cases such as Cauchy.

We study parameter estimation for univariate stochastic differential equations with locally Lipschitz drift and Hölder continuous multiplicative diffusion, a class commonly arising in several applications. Existing inference methods typically rely on either the Euler-Maruyama discretisation, despite its lack of strong convergence and failure to preserve the state space, or on approximations, e.g. Gaussian approximation or truncation of Hermite's expansions, impacting on their stability and computational efficiency. We introduce the first explicit pseudo-likelihood estimators based on numerical splitting schemes that are both strong mean-square convergent and state space preserving for this class of SDEs. Our approach is based on a novel decomposition of the SDE that exploits reducibility and the Lamperti transform, leading to Lie-Trotter (LT) and Strang splitting schemes yielding explicit pseudo-likelihoods and maximum likelihood estimators based on them. We prove strong mean-square convergence, state space preservation, and improved robustness with respect to the discretisation step compared to Euler-Maruyama-based methods. We further establish consistency and asymptotic normality of the LT estimator. Because the proposed numerical scheme couples drift and diffusion parameters in the pseudo-likelihood, the asymptotic analysis requires new proof techniques. Extensive simulations demonstrate that the proposed estimators outperform existing methods in both accuracy and computational efficiency.

We propose a betweenness centrality measure and algorithms for stochastic networks, where edges can fail and weights vary across realizations, making the most central node random. Our approach models the sequence of reported central nodes as an absorbing Markov chain and measures node importance by the share of pre-absorption time spent at each node. This produces a way to study centrality under uncertainty, which can then be estimated with Monte Carlo simulation. We also analyze robustness when the transition kernel is only approximately known, using row-wise perturbations to assess sensitivity and potential ranking changes. The framework further admits extensions to weighted rewards and restricted candidate sets without altering the Markov chain formulation. Experiments on Erdős-Rényi, Watts-Strogatz, and Les Misérables networks with stochastic edges show that the method identifies a small set of dominant nodes, reveals stable versus sensitive rankings under perturbations, and supports reward-based and structure-constrained variants.

A global packet may simultaneously contain an automorphic representation and a non-automorphic representation. The global $\mathcal S$-group is expected, and known in some cases, to specify the automorphic representations in each global packet. For a covering group of an algebraic torus, it is not obvious from the definition whether the analogue of a global $\mathcal S$-group has finite order. In this paper, we verify this finiteness for a Brylinski-Deligne covering group of a torus.

We view ultrametric spaces as two-sorted structures consisting of a set of points and of a linearly ordered set of distances. We call the appropriate notion of embeddings distance-carrying (dc for short). Those are obtained by combining isometries and linear order embeddings. We show that the class of all finite two-sorted ultrametric spaces with dc-embeddings is Fraïssé, and that the limit is the countable rational Urysohn ultrametric space $\mathbb{U}$. The space $\mathbb{U}$ is dc-universal for all countable ultrametric spaces, and its Cauchy completion $\overline{\mathbb{U}}$ is dc-universal for all separable ultrametric spaces, which is in contrast with the situation of classical ultrametric spaces and isometric embeddings, where no such universal space can exist. We study further properties of $\mathbb{U}$, of its variants, and of its automorphism group, which is richer than its group of isometries. In particular, we provide two types of tree representations of the two-sorted ultrametric spaces, discuss connections to valued fields, and characterize the automorphism group of $\mathbb{U}$ as the semidirect product of a group of order preserving bijections and a group of isometries. Furthermore, we show universality of $\operatorname{Aut}(\mathbb{U})$ and identify its universal minimal flow.

Motivated by recent theoretical and experimental advances, hyperbolic lattices have emerged as a paradigmatic setting in which geometry becomes an active organizing principle of quantum systems. Their negative curvature, exponential volume growth, and non-Abelian translation symmetry make them fundamentally distinct from Euclidean lattices and give rise to rich geometry-dependent physics, but also hinder the direct application of well-established analytical and computational approaches originally developed for physical systems defined on Euclidean lattices. To establish a unified framework for geometry-dependent physics on Euclidean and hyperbolic lattices, we develop \textit{higher-order non-uniform cellular automata} (NUCA) as a local-to-global construction for translationally invariant regular lattices. This construction derives geometry-dependent update rules through a lattice-deforming procedure that embeds hyperbolic lattices into a Euclidean square lattice, thereby encoding hyperbolic geometry while preserving physical locality. It thus provides a systematic route toward quantum and classical physics on hyperbolic lattices. We demonstrate the framework in three applications ranging from quantum many-body physics to non-equilibrium statistical physics. First, on the hyperbolic $\{5,4\}$ lattice, a linear NUCA generates exactly solvable subsystem symmetry-protected topological (SSPT) models and spontaneous subsystem symmetry-breaking models. Second, as a quantum generalization, we construct non-uniform Clifford quantum cellular automata (CQCA) for the hyperbolic cluster state. Third, we formulate a probabilistic NUCA for directed percolation (DP) on the hyperbolic lattice.

This paper considers functional series whose terms are higher-order derivatives of Chebyshev polynomials of the second kind, where the degree of the polynomial is related to the order of the derivative. Analytic summation is used to determine the rational functions to which these series converge. These functions are expressed in terms of Chebyshev polynomials evaluated at a specific argument. Connections are established between derivatives of Chebyshev polynomials of the second kind and special numerical sequences generated by linear recurrence relations. New closed-form formulas are obtained for the sums of the series at various values of the argument. As consequences, combinatorial identities are derived for the Fibonacci, Lucas, and Pell numbers, for sections of the Fibonacci sequence, and for their convolutions. By means of analytic continuation, sums of formally divergent series are obtained, which in special cases correspond to the classical Euler formulas.

We introduce a notion of weak definability of first order structures, show that various classification-theoretic properties are or are not preserved under it, and that the properties which are preserved can also be characterized in terms of it.

Dense, compact circumstellar media (CSM) are required to power strongly interacting supernovae, yet their physical origin remains uncertain. We present a systematic study of binary stellar evolution models computed with MESA, demonstrating that Case C mass transfer, initiated after core helium ignition, can naturally produces the dense, nearby CSM inferred in interacting events. Across a grid of binary models, we find that donors of 10--20 solar masses in binaries with separations of approximately 1000--2700 solar radius undergo late-stage Roche-lobe overflow within ~10^3 yr prior to core collapse, ejecting ~0.01--0.2 solar masses and forming CSM extending to ~10^16--10^18 cm. Our results suggest that the Case C mass transfer may account for ~13% of all core-collapse supernova (CCSN) progenitors, rather than representing a rare channel. A subset of these Case C binaries produces CSM properties that are quantitatively in agreement with those inferred for interacting supernovae such as SN 2014C. In contrast to earlier binary interactions or single-star mass loss, Case C transfer operates at the right time and scale to shape the immediate pre-supernova environment without requiring ad hoc eruptive mechanisms. Our results identify late-stage binary interaction as a robust and physically motivated channel for producing the dense CSM that powers interacting supernovae.

Flavor remains one of the most successful yet least understood structures of the Standard Model. The discovery of the Higgs boson completed the electroweak account of mass generation, but did not explain the origin of fermion families, mass hierarchies, or mixing patterns. In this sense, flavor can be regarded as an empirically successful but conceptually incomplete structure. Neutrinos occupy a particularly sensitive place within this problem: their masses are tiny, their mixing is large, and their mass-generation mechanism may differ from that of charged fermions. In this article, we discuss flavor as an open conceptual problem and argue that DUNE, as a phased program spanning precision oscillation measurements and sensitivity to BSM and dark-sector phenomena, provides a powerful framework for testing the self-consistency and possible limits of the present three-flavor description. In particular, the complementarity between the long-baseline program and the Phase I near-detector complex, together with the DUNE-PRISM strategy for controlling interaction-model systematics and enabling data-driven near-to-far predictions, makes DUNE especially well-suited to search for small, correlated departures from the minimal flavor framework.

Calibration of an honest confidence interval means choosing, for each $\alpha\in(0,1)$, how the corresponding $\alpha$-critical value is converted into a radius yielding coverage probability at least $1-\alpha$. Standard-normal critical-value calibration (SNC) is the default route for many confidence intervals based on nonparametric smoothers in nonparametric econometrics. However, this calibration method creates a structural difficulty: the normalization yielding a limiting distribution also makes a small estimation bias become a non-negligible inferential bias. We take a different calibration route by combining the tail control of empirical Bernstein inequalities with a fixed-length-radius optimization from bias-aware inference. We establish the formal theory in canonical scalar-covariate regression and density settings, with the regression theory ranging from local-polynomial to weighted-average estimators. The resulting empirical Bernstein confidence intervals (EBCIs) are "safe" and "sharp". Safety means that, uniformly over functions with some $S$-th order local smoothness, both one-sided and two-sided intervals attain the nominal coverage level up to a remainder $o(n^{-\frac{2S}{2S+1}})$, or an exponential remainder in bounded or sub-Gaussian settings. Sharpness means that interval widths shrink at the minimax rate $n^{-\frac{S}{2S+1}}$. Moreover, in the small-$\alpha$ regime, the EBCI radius is first-order aligned with the radii of bias-aware fixed-length confidence intervals. Thus, EBCI safely converts correctly specified smoothness into both coverage accuracy and interval-length efficiency. The contribution is not a new bias-control approach, but a new calibration principle for the radius of a confidence interval. The method can be combined with existing ideas such as bias-aware inference (BA) and robust bias correction (RBC), while avoiding the bias inflation induced by SNC.

We study the optical appearance of rotating black holes embedded in dark matter environments using a phenomenological ray tracing framework. Rather than focusing on a single geometry, we compare two effective rotating backgrounds obtained from static dark matter sourced seed metrics: a regular Einasto-type black hole and a cored-NFW black hole. Kerr is used as the reference spacetime. We construct observer-screen images by numerical backward ray tracing and analyse the horizon structure, shadow boundary, lensing bands, transfer maps, and synthetic intensity distributions produced by a common semi-analytic accretion prescription. We also introduce simple image-level diagnostics, an angular-size confrontation with M87* and Sgr A*, and simplified visibility-amplitude diagnostics. These additions are not intended as an EHT fit, but as a controlled way to identify which observables are most affected by the dark matter dressing. For the representative parameters considered here, the Einasto-supported geometry remains very close to Kerr, while the cored-NFW case produces a stronger redistribution of the image, with larger centroid displacement, stronger brightness asymmetry, an outward shift of the characteristic bright-ring scale, and a visible change in the normalized visibility amplitude. The results indicate that rotating dark-matter-dressed backgrounds can produce systematic image-domain and Fourier-domain deviations that are partially degenerate with spin, inclination, and emission modelling. The framework is lightweight and extensible, and provides a first step toward future GRRT and GRMHD studies of rotating black holes in dark matter environments.

The discovery of the gravitational-wave event GW170817 from a binary neutron star merger, together with its multi-wavelength electromagnetic counterparts, marks the beginning of the era of multi-messenger gravitational-wave astronomy. Observations of gravitational-wave signals from compact binary mergers enable an independent measurement of the luminosity distance to the source. This implies that gravitational-wave sources can serve as "standard sirens" to probe the expansion history of the Universe, providing a new approach to constrain cosmological parameters. In this paper, we review the basic principles of using gravitational-wave standard sirens to constrain cosmology. We discuss various methods for determining the source distance and redshift, as well as the capabilities of second- and third-generation ground-based detectors and space-based detectors in constraining cosmological parameters, especially the Hubble constant and dark energy parameters. By examining three types of standard sirens: binary neutron star mergers with electromagnetic counterparts as bright sirens, stellar-mass binary black hole mergers as dark sirens, and the dark lensed sirens, we illustrate the methodology, challenges, and future prospects of the standard siren approach.

We prove that the KSGNS construction can be viewed as an endofunctor on a category whose objects are positive $C^*$-correspondences from a fixed $C^*$-algebra and morphisms are given by intertwiners which account for automorphisms of the fixed $C^*$-algebra. Using this perspective, we provide a functorial perspective for strict positive equivariant $C^*$-correspondences of $C^*$-dynamical systems and show every strict positive equivariant $C^*$-correspondence of $C^*$-dynamical systems unitarily uniquely dilates under the KSGNS construction to an equivariant $C^*$-correspondence of the dynamical systems.

Wildfires are becoming increasingly frequent, with potentially devastating consequences, including loss of life, infrastructure destruction, and severe environmental damage. Low-Earth-orbit satellites equipped with onboard sensors can capture critical information relative to active wildfires and enable near-real-time detection through machine learning algorithms applied to the acquired data. We propose a framework that automates the complete wildfire detection and satellite scheduling pipeline, entitled the WildFire-applicable Intelligent and Responsive Ensemble for Detection and Scheduling (WildFIRE-DS). This paper develops an algorithm to realize the vision of the WildFIRE-DS as a proof of concept, integrating three key components: wildfire detection in satellite imagery, statistical updating that incorporates data from repeated flyovers, and multisatellite scheduling optimization. The algorithm enables wildfire detection using convolutional neural networks with sensor fusion techniques, incorporates subsequent flyover information via Bayesian statistics, and schedules a constellation of satellites using the state-of-the-art Reconfigurable Earth Observation Satellite Scheduling Problem. Simulated experiments conducted using real-world wildfire locations and the orbits of operational Earth observation satellites to demonstrate that this autonomous detection and scheduling approach effectively enhances wildfire monitoring capabilities.

Call-by-need evaluation for the lambda-calculus can be seen as merging the best of call-by-name and call-by-value, namely the wise erasing behaviour of the former and the wise duplicating behaviour of the latter. To better understand how duplication and erasure can be combined, we design a degenerated calculus, dubbed call-by-silly, that is symmetric to call-by-need in that it merges the worst of call-by-name and call-by-value, namely silly duplications by-name and silly erasures by-value. We validate the design of the call-by-silly calculus via rewriting properties and multi types. In particular, we mirror the main theorem about call-by-need -- that is, its operational equivalence with call-by-name -- showing that call-by-silly and call-by-value induce the same contextual equivalence. This fact shows the blindness with respect to efficiency of call-by-value contextual equivalence. We also define a call-by-silly strategy and a call-by-silly abstract machine implementing the strategy. Moreover, we measure the number of steps taken by the strategy via tight multi types. Lastly, we prove that the call-by-silly strategy computes evaluation sequences of maximal length in the calculus.

Electric field-assisted chemistry has attracted much attention in recent years, particularly in the context of oriented external electric fields for controlling molecular structure and reactivity. Such fields have been explored in a wide range of applications, including switching materials, nanoparticles, controllable catalysts, medicines, and clinical therapies. However, the determination of fixed fields in the laboratory frame becomes ineffective for flexible molecules, as conformational changes can significantly alter the relative orientation between the applied field and molecular structure. In this work, we propose two molecular reference frames -- the principal axis frame and the local reference frame -- to define oriented electric fields within the molecular framework. These coordinate systems powerfully eliminate ambiguities in the relative orientation between the applied field and the molecule. Analytic nuclear gradients in the presence of external electric fields are derived and implemented, with an initial application to field-dependent geometry optimizations of cis- and trans-formanilide. Analysis of the resulting field-induced equilibrium structures reveals distinct structural responses, validating the accuracy and robustness of the proposed formalism. The analytic gradient framework enables systematic investigations of molecular properties and reactivity under arbitrarily oriented electric fields, opening new opportunities for computational modeling and rational design in electric field-controlled chemistry.

The presence of stochastic elements in combinatorial optimization problems makes them particularly challenging, as such problems quickly become intractable for classical computers even at relatively small sizes. In this work, we propose a novel quantum-classical hybrid scheme for solving a class of stochastic optimization problems known as chance-constrained knapsack problems, in which item weights follow probability distributions and constraints may be violated within a specified risk tolerance. Our method employs knapsack-specific QAOA-based circuits to generate samples which, when combined with a new self-consistent classical recovery scheme introduced in this work, produce high-quality solutions. Experiments carried out on IBM Heron processors, using circuits with depths up to 177 and comprising 3443 gates acting on as many as 150 qubits, yield solutions that indicate performance comparable to classical optimization schemes. The proposed quantum-classical scheme paves the way to tackling such problems, with the potential to outperform approaches that rely solely on classical computation.

Video temporal grounding (VTG) aims to localize the start and end timestamps of the event described by a given query within an untrimmed video. Despite the strong open-world video understanding and recognition ability of video language large models (Vid-LLMs), outputting precise temporal grounding information remains challenging, since explicit temporal cues are scarce in untrimmed videos, and query-relevant entities are hard to track consistently across the video timeline. In this paper, we present \MarkIt{}, a training-free framework that transforms an input video into a query-conditioned marked video, which empowers Vid-LLMs to generate more reliable temporal localization predictions. The core component of \MarkIt{} is an annotation-free query-to-mask grounding bridge (Q2M-Bridge). Given a natural-language query, it automatically derives a compact set of canonical subject tags through linguistic parsing and normalization, then maps these tags to query-conditioned instance masks using text-conditioned open-vocabulary segmentation. The bridge also embeds lightweight semantic instance markers and a persistent frame index into each frame, effectively transforming long-range temporal reasoning into explicit visual cues for Vid-LLMs. \MarkIt{} adopts an inference-time plug-and-play design, needs no modifications to Vid-LLM weights, and is fully compatible with supervised fine-tuning. Experiments conducted on multiple mainstream moment retrieval and highlight detection benchmarks demonstrate that \MarkIt {} achieves state-of-the-art results, delivering consistent temporal grounding improvements across a wide range of existing models.

The superconducting diode effect (SDE), characterized by a nonreciprocal supercurrent, has attracted significant attention in recent years due to its potential applications. However, most studies have focused on weakly correlated models, leaving the impact of strong electron-electron interactions on the SDE largely unexplored. In this work, we bridge this gap by investigating the SDE in asymmetric band metals with Hatsugai-Kohmoto (HK) interaction, which are exactly solvable due to their locality in Bloch momentum space. Through a combination of low-energy analysis and a numerical self-consistent approach, we demonstrate that HK interaction can enhance the SDE's quality factor. Our findings shed light on the role of strong electron-electron correlations in shaping the SDE.