We define the grove polynomials, a set-valued extension of forest polynomials. We show that they are $K$-theoretically dual to the quasisymmetric Schubert cells which pave the quasisymmetric flag variety, in the same way that Grothendieck polynomials are dual to Schubert cells in the complete flag variety. As a consequence, the finite truncations of the multi-fundamental quasisymmetric functions of Lam-Pylyavskyy acquire a geometric interpretation as $K$-theoretic representatives of quasisymmetric Schubert cells.

We introduce a novel software-oriented model of quantum computation motivated by the practical constraints of near-term quantum hardware. In this model, gates are specified by constraints expressed in terms of Pauli observables, with each disjoint layer of gates accompanied by a pairwise or $k$-local quantum state tomography of the device. We prove that the model is equivalent to the coupling-graph-restricted circuit model and hence universal for BQP, with a polynomial overhead: simulating a depth-$D$ circuit on $N$ qubits requires at most $O(D^2 N \log N)$ complexity. The model formalizes an idiom shared by existing work that ranges from quantum imaginary time evolution for the study of quantum systems to the use of quantum computers for procedural generation in games. It therefore provides a natural interface for designing quantum software entirely in terms of physically observable quantities, relevant for the NISQ era and into fault-tolerance.

We present the first complete lattice QCD calculation of the four structure-dependent form factors governing the rare charged kaon decay $K^- \to \ell^- \barν_\ell \ell'^+ \ell'^-$, with fully controlled statistical and systematic uncertainties. Our calculation is based on gauge ensembles generated by the Extended Twisted Mass Collaboration (ETMC) with $N_f = 2+1+1$ flavors of Wilson-clover twisted-mass fermions. Simulations are performed directly at the physical values of the light and strange quark masses, and include an estimate of the quark-disconnected contributions in which the virtual photon couples to sea quarks. All four form factors are determined across the kinematical region probed by experiments. The Spectral Function Reconstruction (SFR) method of Ref. [1] is employed to overcome the analytic continuation problem for dilepton invariant masses above the two-pion threshold. Finite-volume effects are investigated using ensembles with spatial extents $L\simeq [3.8,7.6]~\mathrm{fm}$, while the continuum limit is obtained from three lattice spacings in the range $a\in[0.057, 0.08]~\mathrm{fm}$. Our results for the form factors enable the evaluation of decay rates and differential observables for all four channels, $K^- \to e^- \barν_e e^+ e^-$, $K^- \to e^- \barν_e μ^+ μ^-$, $K^- \to μ^- \barν_μe^+ e^-$, and $K^- \to μ^- \barν_μμ^+ μ^-$, thereby providing first-principles Standard Model predictions against which existing and upcoming measurements can be directly compared. A detailed phenomenological analysis of the decay rates and associated observables is presented in a companion paper [2].

This paper investigates the non-resistive compressible magnetohydrodynamic (MHD) equations in $\mathbb{R}^2$. We establish the global existence and stability of classical solutions for initial data sufficiently close to a constant equilibrium state. A distinguishing feature of our result is that global stability is derived solely from pure $H^s$ energy estimate and intrinsic $L^2$ time-decay mechanism, thereby bypassing the traditional initial data requirement of $L^1$ integrability or negative-order Sobolev norm regularity. To achieve this goal, firstly we introduce some quantities motivated by effective viscous flux, which intrinsically couples density and magnetic field perturbation. Secondly, to overcome the critical time-decay obstacle arising from the absence of negative-index regularity, we develop a novel pseudo-negative-derivative technique. Moreover, we regard the wildest nonlinear term as a whole and abandon obtaining time decay estimate for each item. These approaches enable us to close the higher-order energy estimate entirely within standard Sobolev spaces.

Cosmic rays (CRs) are a ubiquitous non-thermal component of the interstellar medium (ISM). A data-driven three-dimensional (3D) map of their distribution is essential for understanding CR transport and constraining the spatial distribution of their sources. In this work, we reconstructed the 3D spatial distribution of the Galactic cosmic-ray proton (CRp) density. We model the diffuse gamma-ray emission arising from inelastic hadronic interactions between CRps and interstellar gas. Using a map of dust-correlated diffuse gamma-ray emission based on ten years of Fermi-LAT observations together with a three-dimensional gas density model, we infer the spatial CRp distribution through a morphological matching approach. The logarithmic CRp density field is described by a Gaussian process defined on a spherical-times-radial grid, while both the field and its correlation structure are inferred simultaneously using Iterative Charted Refinement. The posterior distribution of the reconstructed 3D CRp density field is approximated using geometric variational inference. The reconstructed CRp density exhibits a smooth but spatially structured distribution with a limited dynamical range across the Galactic disk. We find a moderate enhancement of the CRp density toward the inner Galaxy. The inferred normalization at the Solar position is consistent with local CR measurements by the AMS-02 instrument.

We prove Shokurov's global index conjecture for foliations in dimension at most three. This answers a question of the first author, Meng, and Xie in dimension three. The main result of this paper is partially obtained by generative AI, particularly the Rethlas system.

Let $G$ be a simple connected graph on $n$ vertices, and let $λ_1(G),λ_2(G),\ldots,λ_n(G)$ be the eigenvalues of its adjacency matrix $A(G)$. For $p>0$, define the $p$-energy of $G$ by $\mathcal E_p(G)=\sum_{i=1}^n |λ_i(G)|^p$. We prove that, for every real number $p\ge 2$ and every simple connected graph $G$ on $n$ vertices, $$ \mathcal E_p(G)\ge \mathcal E_p(P_n), $$ where $P_n$ denotes the path on $n$ vertices. Moreover, for each fixed $p>2$, equality holds if and only if $G\cong P_n$. Together with the previously known star-minimality results, this completes the solution of two questions of Nikiforov. The proof combines two different comparison principles. For $2<p<4$, we use a bipartite reduction, a Mellin representation of fractional powers, and a determinant comparison involving matching generating polynomials and tree shifts. For $p\ge4$, we prove a second-order stop-loss comparison for the squared singular values of bipartite graphs. This comparison is established by rank-one spectral-shift estimates, deletion-minimal counterexamples, and a finite certified analysis of the terminal sparse-sun configurations. As applications, we obtain sharp path-minimality results for positive $p$-energies in several cases, and for Laplacian and signless Laplacian power sums and related indices.

The behavior of magnetic field lines in a turbulent plasma is a key property of the medium, with important consequences for plasma dynamics and charged-particle transport. We study the diffusion properties of magnetic field lines in synthetic turbulence featuring different polarization configurations for the magnetic perturbations, as prescribed by the existing magnetohydrodynamic modes (namely, Alfvénic and magnetosonic). These turbulent field realizations are then compared with the isotropic (or, random) polarization case, which is the one typically adopted in the literature. We construct polarized synthetic turbulence simulations and study the properties of field lines through the running diffusion coefficient. Our key findings can be summarized as follow: (i) field line wandering is strongly dependent on polarization configurations, (ii) we unveil that the sub-diffusive phase of field line is highly dependent on the polarization and is well reproduced by theoretical predictions based on Corrsin's hypothesis in the low turbulence level regime, (iii) in particular the scaling of the asymptotic diffusion coefficient in magnetosonic-like polarization is $(δB/B)^4$ at odd with the $(δB/B)^2$ scaling found in the quasi-linear regime for random polarization, (iv) interestingly we note that the subdiffusive phase of field line transport in the magnetosonic-like polarization follows closely the one observed in recent high resolution MHD turbulence simulations, we end giving a word of caution when FL transport is investigated in such simulations.

In this paper, we devise a $\operatorname{prox}$-based semi-smooth Newton method for the non-differentiable TV-minimization problem. To this end, the primal-dual optimality conditions are reformulated as a nonlinear operator equation with Newton-(type-)differentiable structure. We investigate the question of well-posedness of the resulting semi-smooth Newton scheme in the infinite-dimensional setting and identify structural properties of the associated Newton-type derivatives. For a conforming finite element discretization, we prove that the resulting semi-smooth Newton method is globally well-posed and locally super-linearly convergent. The approach extends to a large class of convex minimization problems, coincides with established semi-smooth Newton methods for obstacle problems, satisfies a primal-dual invariance, and, under suitable additional assumptions, is well-posed in the infinite-dimensional setting. Numerical experiments indicate a robust practical performance of the proposed method, including reliable reduction of the discrete primal-dual gap estimator to machine precision, robustness with respect to the choice of proximity parameters, an improved convergence basin compared to a canonical primal semi-smooth Newton method, and effective performance even for quadratically graded meshes using only a mesh-independent initialization criterion.

Weak decays of charged kaons with an additional lepton-antilepton pair, $K^- \to \ell^- \barν_\ell \ell'^{+} \ell'^{-}$ ($K_{\ell2\ell'}$), are suppressed at order $O(G_{F}^{2}α_{\rm em}^{2})$ in the Standard Model (SM) and provide sensitive probes of its flavour structure, as well as independent determinations of the Cabibbo angle $|V_{us}|$. In this Letter we present the SM predictions for all four channels with $\ell,\ell' =e,μ$, based on the first complete lattice QCD calculation of the structure-dependent form factors reported in a companion paper [1]. Using the PDG value [2] $|V_{us}|^{\rm PDG}=0.22431(85)$, we obtain branching fractions with controlled uncertainties and precisions ranging from $2\%$ to $7\%$, depending on the channel. For the three modes with published measurements, our results agree with experiment. For the $K_{\mu2μ}$ mode, for which no published experimental result is available, we compare our prediction with the preliminary NA62 result, finding agreement at the $1.4σ$ level. Conversely, the measured decay rates can be used together with our results to extract $|V_{us}|$ from these modes. A weighted average over the two most precise channels, $K_{\mu2e}$ and $K_{\mu2μ}$, yields $|V_{us}|=0.2283(42)$, corresponding to a $1.8\%$ determination. These results pave the way for using $K_{\ell2\ell'}$ decays as precision probes of the SM.

This article presents dynamic directional lane allocation in urban air mobility (UAM) corridors as a discrete-time mixed-integer linear program (MILP). This formulation activates, deactivates, and reverses lane direction as bi-directional airspace demand evolves. We model demand from disaggregate ground travel data by decomposing each trip into a multi-modal sequence with first-, middle-, and last-mile legs and routing the UAM-served middle-mile segment through a vertiport-side dispatch model. We use the San Francisco Bay Area as a case study by placing a multi-region spanning corridor between Contra Costa county and Silicon Valley. We find that the dynamic policy cuts unused airspace capacity by 5x, increases mean lane utilization from 36-48% to 67% at the same service level relative to baselines, and reduces commuting-population mean travel time by up to 21.6%. These results show that dynamic configuration of airspace capacity alleviates a significant percentage of the under-utilization issue of lane-based UAM airspace design and UAM concept of operations. This dynamic allocation also provides a safe, structural way to increase throughput, making UAM a more viable complement to multimodal door-to-door mobility systems.

In this note, we show various minimality results for a geometric theory of fields $T$: $T$ is stable if and only if it is strongly minimal, $T$ is simple if and only if it has SU-rank 1, and $T$ is rosy if and only if $T$ is surgical. Combining the first equivalence with an earlier result of Hrushovski, we deduce that algebraically bounded stable fields are precisely expansions of algebraically closed fields by constants. We then consider algebraically bounded and o-minimal expansions of fields with generic derivations. We show that if $\mathbb{M}$ is a simple algebraically bounded structure and $Δ$ is a generic tuple of derivations on $\mathbb{M}$, then $(\mathbb{M};Δ)$ is supersimple if and only if the derivations commute. Similarly, if $\mathbb{M}$ is an o-minimal structure and $Δ$ is a generic tuple of $T$-derivations on $\mathbb{M}$, then $(\mathbb{M};Δ)$ is superrosy if and only if the derivations commute. We obtain explicit bounds on ranks using the Kolchin polynomial.

Self-evolving multi-agent systems (MAS) have emerged as a promising route to LLM agents that continually improve from experience, with persistent memory at their foundation. However, existing designs almost exclusively adopt a centralized repository shared across agents, incurring communication and coordination overhead, raising privacy concerns, and collapsing agent diversity. We propose DecentMem, a decentralized memory framework in which each agent maintains its own dual-pool memory -- an exploitation pool of consolidated past trajectories and an exploration pool of LLM-generated candidates for unseen contexts. The two pools are reweighted online based on stage-wise feedback from an LLM-as-a-judge. Theoretically, we prove that this design guarantees global reachability of the solution space and achieves $O(\log T)$ cumulative regret, matching the stochastic bandit lower bound up to constants. In practice, across three MAS frameworks (AutoGen, DyLAN, AgentNet), three Qwen3 backbones (4B/8B/14B), two Gemma4 backbones (E2B/E4B) and five benchmarks spanning math, code, QA, and embodied tasks, DecentMem improves average accuracy by up to 23.8% over the strongest centralized memory baseline and by up to 52.5% over the no-memory baseline, while reducing token usage by up to 49%.

We consider bipartite exact entanglement embezzlement with a catalyst state vector $ψ$ in a Hilbert space $\mathcal{H}$ using unitaries (or more generally, contractions). If $\mathcal{M} \subseteq \mathcal{B}(\mathcal{H})$ is a von Neumann algebra and $U \in M_d \otimes \mathcal{M}$ and $V \in \mathcal{M}' \otimes M_d$ are unitaries (or more generally contractions), then such a protocol is of the form $(U \otimes I_d)(I_d \otimes V)(e_0 \otimes ψ\otimes e_0)=\sum_{i=0}^{d-1} α_i e_i \otimes ψ\otimes e_i$, where each $α_i>0$ and $\sum_{i=0}^{d-1} α_i^2=1$. We show that any such protocol must arise from a unique state on the tensor product $\mathcal{O}_d \otimes \mathcal{O}_d$ of the Cuntz algebra with itself. As a result, we prove that exact entanglement embezzlement is a self-test for a collection of $d$ Cuntz isometries for each party and a unique quasi-free state on the Cuntz algebra $\mathcal{O}_d$ in the sense of \cite{Iz93}. Moreover, we use modular theory to show that the von Neumann algebra generated by the copy of $\mathcal{O}_d$ is the unique separable approximately finite-dimensional Type $\text{III}_λ$ factor for some $0<λ\leq 1$, where $λ$ can be determined by an algebraic condition on the Schmidt coefficients of the state $φ=\sum_{i=0}^{d-1} α_i e_i \otimes e_i$.

For 24 years, it has been an open problem to obtain improved bounds, for the maximal function over a sparse sequence of discrete spherical averages, going beyond the range for the full discrete spherical maximal function. I formulate a conjecture to characterize the boundedness of such maximal functions and state a theorem in support of it.

Fast magnetosonic waves are among the fundamental oscillation modes of astrophysical plasmas. To study their dynamics, we carry out numerical simulations of the wave turbulence kinetic equation, which describes the evolution of the energy spectrum of a set of weakly nonlinear fast magnetosonic waves. This kinetic equation, which involves three-wave interactions, has recently been derived from compressible magnetohydrodynamics in the low-$β$ limit (Galtier 2023). It has an exact stationary solution, the Kolmogorov-Zakharov spectrum, corresponding to a direct energy cascade. Here we perform free decay simulations of the kinetic equation for which we propose a Kolmogorov-type phenomenology to explain the temporal decay laws of energy and integral length scale. In the forced simulations, we show that the cascade is in fact composed of a mixture of a forward cascade for counter-propagating waves, and a backward cascade for co-propagating waves, with the former being stronger than the latter. The Kolmogorov-Zakharov energy spectrum in $k^{-3/2}$ is found in the radial direction with an anisotropy due to the amplitude that depends on the angle relative to the strong mean magnetic field. We give the analytical expression of the Kolmogorov-Zakharov constant, which is numerically verified in the high Reynolds number limit. Our study provides a theoretical explanation for certain observations in the solar wind plasma (Zhao et al. 2022), where a regime of weak turbulence has been identified for fast magnetosonic waves, alongside a critical balance regime for strong Alfvén wave turbulence.

We study the cohomological classification of vector bundles on smooth real affine surfaces and threefolds. We show that, as was observed in joint work in A. Asok and J. Fasel and in a coming joint paper with S. Banerjee and J. Fasel, under suitable cohomological assumptions on the real locus of such varieties, this classification mirrors the one obtained on algebraically closed base fields by Mohan Kumar and Murthy and by Asok and Fasel. Using an argument due to Fasel, we also give an efficient proof of a theorem of Kucharz characterising the triples of algebraic cycles that can be realised as the Chern classes of a rank $3$ bundle on a smooth real affine threefold. We further answer the questions left open by Kucharz; to our knowledge, we give the first instance of a projective module over a smooth affine $\mathbb{R}$-algebra of dimension $3$ with trivial Chern classes which is not stably free.

Optical amplifiers are ubiquitous in science and technology and are the workhorse of modern communications. Currently, virtually all amplifiers rely on atomic resonances, such as rare-earth-doped fibers, or are based on III-V semiconductors. Fueled by emerging applications, there is increased demand for amplifiers that are high-gain, broadband, low-noise, and deliver high output power outside traditional wavelength ranges. Over the past few decades, it has been shown that optical parametric amplifiers (OPAs) can address this challenge. Pioneering works on highly nonlinear optical fibers or bulk crystals have demonstrated their potential, but high pump powers and long fiber length limited their practical use. Recently, a renaissance of OPAs has occurred with the demonstration of photonic integrated circuits, which exhibit higher effective nonlinearity and enable wider bandwidths. Yet they require ultra-low loss, highly precise dispersion engineering, and large chip footprints, limiting OPA performance to date. Here, we overcome these limitations and, using periodically poled thin-film lithium tantalate (PPLT) photonic integrated circuits, we demonstrate continuous-wave optical parametric gain up to 23.5 dB, with a flat-top profile spanning across an 850 nm-wide optical wavelength window, corresponding to 100 THz and covering all communication bands. Moreover, on-chip output signal power as large as 313 mW in the optical O-band is achieved. We further realize all-optical inter-band modulation transfer between the C- and O-bands. Our approach uses cascaded second-order nonlinear processes that provide high effective third-order nonlinearities while preserving the wide material bandgap. These results establish PPLT integrated photonic circuits as a scalable platform for broadband optical amplification and frequency conversion across wavelengths where rare-earth doped amplifiers are absent.

We formulate a quantum master equation for the many-particle density matrix of electrons propagating through a single-mode conductor, combining elastic scattering by disorder with time-resolved projective measurements that monitor the outcome of scattering events. The full counting statistics of transmitted electrons has a binomial distribution function, whose mean ${\cal T}$ and variance ${\cal T}(1-{\cal T})$ determine the conductance and shot noise power, respectively. Monitoring suppresses the phase coherence responsible for one-dimensional localization: The decay with conductor length $L$ of the typical transmission probability crosses over at $L\simeq \ell_ϕ$ from the exponential $e^{-L/ξ}$ (with localization length $ξ$) to the Ohmic $1/L$ decay. Numerical solution of the master equation gives, for weak monitoring, a logarithmic dependence $\ell_ϕ\simeq ξ\ln(v_{\rm F}τ_ϕ/ξ)$ of the coherence length $\ell_ϕ$ on the mean time $τ_ϕ$ between measurements.

In this paper, we introduce and study a new class of rings calling them {\it weakly $ΔU$-rings}, hereafter abbreviated as {\it $WΔU$-rings} for short. A ring $R$ is said to be $WΔU$ if every unit of $R$ can be expressed as $\pm 1 + d$ for some $d \in Δ(R)$, where $Δ(R)$ is the largest Jacobson radical of $R$ that is closed under multiplication by units. Utilizing the known structure of $Δ(R)$, we investigate the relationships between $WΔU$ rings and certain classical concepts such as $ΔU$-rings, $UJ$-rings, $WUJ$-rings, as well as clean and exchange rings. Among the main results, we show that a matrix ring $M_n(R)$ is never $WΔU$ for any $n \ge 2$. We also provide complete characterizations of local, semi-local, semi-simple and semi-regular rings that are $WΔU$. Furthermore, it is shown for exchange rings that the $WΔU$ property is equivalent to being $WUJ$. Furthermore, the behavior of $WΔU$-rings under various ring extensions, including skew polynomial rings, skew power series rings, triangular matrix rings, trivial extensions and group rings, is thoroughly examined. Several examples are given to illustrate that the class of $WΔU$-rings properly contains the class of $ΔU$-rings. Finally, necessary and sufficient conditions for a group ring $RG$ to be $WΔU$ are established too. Resuming all of the presented above, our results expanded those by Karabaçak et al. published in J. Algebra \& Appl. (2021).

Photovoltaic generation plays a central role in the energy transition, yet understanding its adoption dynamics requires robust analytical frameworks that capture both temporal and spatial patterns of decision behavior. This study applies a data-driven decision analytics approach to examine residential self-consumption photovoltaic installations in Catalonia within an innovation diffusion framework. The temporal evolution of adoption is modeled using a logistic growth function, providing evidence that imitation effects are a primary driver of adoption decisions. To extend the analysis, a quantitative methodology is developed to estimate the influence of external factors on adoption behavior, revealing that social perception exerts a stronger impact than regulatory and socioeconomic variables when considered independently. In addition, a spatial analytics component is incorporated to assess territorial heterogeneity, identifying correlations between adoption patterns and demographic and socioeconomic characteristics. The findings contribute to predictive and diagnostic analytics by offering a structured framework to model technology diffusion and inform policy and investment decisions aimed at accelerating sustainable energy adoption.

Machine learning interatomic potentials (MLIPs) enable atomistic simulations with near ab initio accuracy at significantly reduced computational cost, but their broader adoption is often limited by fragmented tooling, limited scalability, and inflexible software design. We present mlip v2, a new generation of the mlip library that advances efficient and scalable molecular simulation through a unified and extensible framework. The new release features a targeted API redesign with improved modularity and control, enabling flexible customization of training, data processing, and simulation workflows. It further integrates a new high-performance backend for equivariant operations, e3j, significantly accelerating model inference and simulations. In addition, the framework introduces a range of entirely new capabilities, including the eSEN architecture with a Mixture-of-Experts formulation for scalable training on large and diverse datasets, improved handling of electrostatics through more physically grounded charge modeling and long-range interaction treatment, and advanced simulation features such as NPT ensembles and nudged elastic band methods. Together, these extensions significantly broaden the scope of MLIP applications, enabling efficient modeling of complex, reactive, and out-of-equilibrium systems, and bridging the gap between ML research and practical molecular simulation applications. The library is available on GitHub and on PyPI under the Apache license 2.0.

We investigate photon-axion conversion in the vicinity of rotating Kerr black holes where strong gravity traps photons on near-circular trajectories, effectively enhancing the path length. We explore the observable signatures of such a conversion near the photon region. The process, driven by ambient magnetic fields, is significantly more efficient around supermassive black holes such as M87*, since the luminosity of photons increases with the mass of the BH. By numerically evaluating photon path lengths (on which the conversion depends), we analyze how key parameters-photon frequency, axion mass, photon-axion coupling, magnetic field strength, plasma density, and black hole spin-affect the conversion probability and the resultant dimming of photon spectral luminosity. We find that the conversion is most efficient at high frequencies (X-rays and gamma rays), while the frequency window associated with efficient conversion widens with an increase in the photon-axion coupling and a decrease in the electron density and the axion mass. The magnitude of dimming of the photon spectral luminosity depends primarily on the magnetic field, the photon-axion coupling and the BH spin. Our study reveals that rotating black holes generally exhibit enhanced dimming compared to static ones. Thus, if future telescopes achieving a resolution $\sim 10^{-5}$ arcsec in the X-ray/gamma-ray band detect a dimming of the photon spectral luminosity, then they can provide interesting constraints on the axion mass and its coupling with photons.

The dynamical systems having both bosonic and fermionic variables play an important role in the theory of supersymmetry. This article addresses the control problems including both bosonic and fermionic variables on Lie supergroup as the configuration space. Here, the control systems are characterized using the normalizer of Lie subsuperalgebra of left-invariant vector fields in the Lie superalgebra of all smooth vector fields of Lie supergroup. Then, the linear control system is studied in detail and its controllability criterion is proposed along with suitable examples.

Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies have mainly focused on the statistics, sampling, forecasting, and attribution of extremes from observable variables. In this paper, we develop a mathematical framework for studying the mechanisms and pathways of extreme events in partially-observed stochastic dynamical systems with hidden variables. By integrating data assimilation with information-theoretic and trajectory-based diagnostics, we infer latent precursor dynamics from observations, quantify their uncertainty, and determine how their influence propagates toward observed extreme events. Conditional Gaussian models provide a tractable analytical setting for deriving closed-form diagnostics, while the framework extends through numerical methods. The analysis proceeds from two complementary perspectives. From a trajectory-wise viewpoint, we compare filtering and smoothing distributions to identify the onset of hidden precursors and quantify temporal influence. From a statistical viewpoint, we construct event-conditioned hidden-state distributions to identify sensitive triggering directions, latent pathways, and multiple classes of extreme-event mechanisms through clustering. Three numerical examples illustrate the methodology. In an intermittent stochastic model, hidden damping dynamics emerge before observed bursts, where discrepancies between the filter and smoother provide an onset diagnostic. In a stochastic model with damping and forcing, separate damping-induced, forcing-driven, and mixed pathways to extremes are identified. In a nonlinear topographic-flow model, distinct mechanisms and pathways for blocking and unblocking patterns associated with observed extreme events are revealed.

Let $P$ be a set of $n$ points in the plane, where each element of $P$ is assigned a weight $ω(p)$, positive or negative. In this paper, we present an algorithm that runs in $O(n^4\log n)$ time and $O(n)$ space to find two possibly overlapping axis-aligned rectangles $A$ and $B$ so as to maximize the total weight of the points contained in the symmetric difference of $A$ and $B$. The same optimization framework can easily be adapted to solve related problems such as to maximize the total weight in the symmetric difference of $k \geq 3$ boxes and/or in the union of $k \geq 2$ boxes.

We present measurements of K-shell x-ray emission following charge exchange of fully ionized argon with various neutral gaseous targets at small collision energies inside an electron beam ion trap. We also resolve the principal quantum number of electron capture in extreme-ultraviolet spectra from initially bare and hydrogen-like oxygen ions held in the same trap. We analyze discrepancies between these as well as previous measurements with theoretical models based on the multichannel Landau-Zener approach.

In this work, we have considered the Laguerre polynomial. This polynomial has been studied in several branches of theoretical physics and applied Mathematics. J. K. Prajapat at.al derived condition so that Laguerre polynomial satisfy convexity, strong starlikeness, close-to-convexity and strongly convexity. In this article, characteristics properties such as exponential subordination have been studied. Moreover Janowski starlikeness and convexity have been investigated for this polynomial. Several examples and corollaries have been mentioned to validates the result.

People are increasingly turning to AI assistance for simple tasks, e.g., arithmetic, spell-check, and answering simple questions. But does AI assistance actually save users time and effort? We investigate people's propensity to use AI for cognitively simple tasks and assess whether their reliance is well-calibrated. Across three pre-registered user studies (N = 2691), we find that people frequently choose to use AI even when doing so is inefficient (i.e. provides no meaningful time or effort savings). We identify systematic miscalibration at two levels: (1) a self-estimate miscalibration where people on average believe that they are using AI less than they actually are, and (2) efficiency-gain illusions where people overestimate how much time and effort savings AI use affords. We also identify a session-level carryover effect where a participant's prior AI use leads to further AI adoption and entrenches their miscalibration about time savings. Our results shed light on the mechanisms and biases underlying people's choice of whether to use AI as well as the risk of an overreliance feedback loop.

Dwarf galaxies in the Local Group offer a way to test dark matter (DM) models against stellar kinematic data. In this work, we study degenerate fermionic DM in two cases: the standard non-interacting Fermi gas, and an interacting degenerate DM fluid described by a phenomenological equation of state motivated by interacting Fermi systems. These interactions modify the compressibility of the DM fluid and, in some regions of parameter space, lead to mechanically unstable branches that must be treated through a Maxwell construction. We solve the corresponding non-relativistic hydrostatic equations consistently and compute the line-of-sight velocity-dispersion profiles using the spherical Jeans equation. We then perform MCMC fits to eight classical Milky Way dwarf spheroidal galaxies. The data favor DM fermion masses in the range $100$--$300\,{\rm eV}$. We find that the interacting and non-interacting equations of state give broadly similar posterior distributions for the fermion mass, central density, and stellar anisotropy. Current data therefore do not strongly prefer an interacting equation of state over the free degenerate Fermi-gas, thereby excluding large deviations from the non-interacting limit.