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We present an inference scheme of long timescale, non-exponential kinetics from molecular dynamics simulations accelerated by stochastic resetting. Standard simulations provide valuable insight into chemical processes but are limited to timescales shorter than ∼ 1 μ s. Slower processes require the use of enhanced sampling methods to expedite them and inference schemes to obtain the unbiased kinetics. However, most kinetics inference schemes assume an underlying exponential first-passage time distribution and are inappropriate for other distributions, e.g., with a power-law decay. We propose an inference scheme that is designed for such cases, based on simulations enhanced by stochastic resetting. We show that resetting promotes enhanced sampling of the first-passage time distribution at short timescales but often also provides sufficient information to estimate the long-time asymptotics, which allows the kinetics inference. We apply our method to a model system and a peptide in an explicit solvent, successfully estimating the unbiased mean first-passage time while accelerating the sampling by more than an order of magnitude. [ABSTRACT FROM AUTHOR]

In this paper, the Riemann‐Hilbert (RH) approach for the integrable discrete Hirota equation with bounded boundary conditions is presented. In the direct scattering problem, we study the analyticity, asymptotics, symmetries of the eigenfunctions, and scattering coefficients and analyze the distribution of discrete eigenvalues. In the inverse scattering problem, the RH problem is constructed and solved as well as the reconstruction formula of potential is derived based on asymptotics. Finally, combining the time evolution, we solve the first‐ and second‐order dark soliton solutions on the nonzero background under the reflectionless condition. [ABSTRACT FROM AUTHOR]

The Bradley-Terry model is a common model for analyzing paired comparison data. Under differential private mechanism, there is a lack of asymptotic properties for the parameter estimator of parameters in this model. In this article, we show that the moment estimators of the parameters based on the differential private degree sequence with Laplace noise is uniformly consistent and asymptotically normal. Simulations are provided to illustrate asymptotic results. [ABSTRACT FROM AUTHOR]

This paper deals with compatibility of space‐time kernels with (either) full, spatially dynamical, or space‐time compact support. We deal with the dilemma of statistical accuracy versus computational scalability, which are in a notorious trade‐off. Apparently, models with full support ensure maximal information but are computationally expensive, while compactly supported models achieve computational scalability at the expense of loss of information. Hence, an inspection of whether these models might be compatible is necessary. The criterion we use for such an inspection is based on equivalence of Gaussian measures. We provide sufficient conditions for space‐time compatibility. As a corollary, we deduce implications in terms of maximum likelihood estimation and misspecified kriging prediction under fixed domain asymptotics. Some results of independent interest relate about the space‐time spectrum associated with the classes of kernels proposed in the paper. [ABSTRACT FROM AUTHOR]

ABSTRACT We consider conditions for the decay in time of solutions of nonhomogenous hyperbolic equations. It is proven that solutions of the equations go to 0 in L2$$ {L}^2 $$ at infinity if and only if an equation's right‐hand side uniquely determines the initial conditions in a certain way. We also obtain that a hyperbolic equation has a unique solution that vanishes when t→∞$$ t\to \infty $$. [ABSTRACT FROM AUTHOR]

We consider a gauge-invariant Ginzburg–Landau functional (also known as Abelian Yang–Mills–Higgs model), on Hermitian line bundles over closed Riemannian manifolds of dimension n ≥ 3 . Assuming a logarithmic energy bound in the coupling parameter, we study the asymptotic behaviour of critical points in the London limit. After a convenient choice of the gauge, we show compactness of finite-energy critical points in Sobolev norms. Moreover, thanks to a suitable monotonicity formula, we prove that the energy densities of critical points, rescaled by the logarithm of the coupling parameter, converge to the weight measure of a stationary, rectifiable varifold of codimension 2. [ABSTRACT FROM AUTHOR]

The turbulent boundary layer in a viscous incompressible fluid developing longitudinally past the surface of a thin cone or cylinder at a finite distance from the laminar–turbulent transition zone is studied. The characteristic Reynolds number, determined from the external flow velocity and the length of the body, is assumed to be large, and the thickness of the boundary layer is small and comparable to the radius of the body. The asymptotic method of multiple scales is used to find solutions to the Navier–Stokes equations. Instead of the traditional decomposition of the solution into time-averaged values and their fluctuations, the velocities and pressure are expressed as an asymptotic series consisting of steady and perturbed terms. As a result, the viscous steady flow ('secondary') that arises in the boundary layer as a mandatory component of fast turbulent fluctuations was described. Analytical and numerical solutions for the radial steady velocity are presented, describing the self-induced suction of fluid from the external flow into the boundary layer. Further analytical solutions are obtained for the longitudinal and circumferential velocities, which differ markedly from the laminar regime. The solutions found are somewhat similar to the degenerate (one-dimensional) case of self-sustaining longitudinal thin structures in turbulent shear flows. A qualitative comparison with direct numerical simulations is presented. [ABSTRACT FROM AUTHOR]

In this paper, we present a stochastic algorithm for parameter estimation based on panel quantile regression model. We propose an easy-to-implement estimator based on the proposed algorithm. We profile the quantile-specific fixed effects as functions of the parameters of interest based on the Gaussian mixture representation of the asymmetric Laplace (AL) likelihood and eliminate the fixed effects through a data transformation. Parameters of interest can be estimated via quantile regression. Under a set of sufficient conditions, the proposed estimator is consistent and asymptotically normal when n and T both go to infinity. The proposed estimator is illustrated via both simulations and real data examples. [ABSTRACT FROM AUTHOR]

While the effects of external factors like fluid mechanical forces and scaffold geometry on tissue growth have been extensively studied, the influence of cell behavior—particularly nutrient consumption and depletion within the scaffold—has received less attention. Incorporating such factors into mathematical models allows for a more comprehensive understanding of tissue-engineering processes. This work presents a comprehensive continuum model for cell proliferation within two-dimensional tissue-engineering scaffolds. Through mathematical modeling and asymptotic analysis based on the small aspect ratio of the scaffolds, the study aims to reduce computational burdens and solve mathematical models for tissue growth within porous scaffolds. The model incorporates fluid dynamics of nutrient feed flow, nutrient transport, cell concentration, and tissue growth, considering the evolving scaffold porosity due to cell proliferation, with the crux of the work establishing the ideal pore shape for channels within the tissue-engineering scaffold to obtain the maximum tissue growth. We investigate scaffolds with specific two-dimensional initial porosity profiles, and our results show that scaffolds which are uniformly graded in porosity throughout their depth promote more tissue growth. [ABSTRACT FROM AUTHOR]

Flexibility design has been widely adopted in practice as a competitive strategy to respond effectively to uncertainties. In this article, we analyze the fulfillment flexibility for dual-channel retail networks, in which the firms should fulfill both online demands from retailing platforms and in-store offline demands. In particular, by setting the order of fulfillment, we find that a dual-channel retail network can be equivalently transformed to an online retail network with stochastic inventory and demand. By implementing copositive programming, we obtain an asymptotic robust lower bound for the ratio of expected sales to fully flexible expected sales under a K-chain design. This bound only depends on the partial moment information and support set of demands, rather than the complete demand distribution information. Interestingly, we derive the optimality of a K-chain in symmetric balanced networks and the performance of the K-chain under different distributions is robust. In addition, numerical experiments are conducted to further deliver some insights for practitioners. The uncertainties of in-store demand or inventory will reduce the expected sales while both fulfillment flexibility and safety inventory can be used to enhance the performance of a retail system. Finally, we find that the correlation coefficient between in-store demand and online demand will affect the decision-making significantly. [ABSTRACT FROM AUTHOR]

The asymptotic analysis theory is a powerful mathematical tool employed in the study of complex systems. By exploring the behavior of mathematical models in the limit as certain parameters tend toward infinity or zero, the asymptotic analysis facilitates the extraction of simplified limit-equations, revealing fundamental principles governing the original complex dynamics. We will highlight the versatility of asymptotic methods in handling different scenarios, ranging from fluid mechanics to biological systems and economic mechanisms, with a greater focus on the financial markets models. This short overview aims to convey the broad applicability of the asymptotic analysis theory in advancing our comprehension of complex systems, making it an indispensable tool for researchers and practitioners across different disciplines. In particular, such a theory could be applied to reshape intricate financial models (e.g., stock market volatility models) into more manageable forms, which could be tackled with time-saving numerical implementations. [ABSTRACT FROM AUTHOR]

Abstract.Let {X,Xn,n≥1} be a sequence of independent and identically distributed random variables in a sub-linear expectation (Ω,H,Ê) with a capacity 핍 under Ê. In this article, under some suitable conditions, two general forms of precise asymptotics for maxima of partial sums hold under sub-linear expectation. It can describe the relations among the boundary function, weighted function, convergence rate, and limit value in studies of precise asymptotics. The results extend some precise asymptotics from the traditional probability space to the sub-linear expectation space, and also extend the precise asymptotics from partial sums to maxima of partial sums. [ABSTRACT FROM AUTHOR]

Cointegration analysis was developed for nonstationary linear processes that exhibit stationary relationships between coordinates. Estimation of the cointegration relationships in a multidimensional cointegrated process typically proceeds in two steps. First, the rank is estimated, then the auto‐regression matrix is estimated, conditionally on the estimated rank (reduced rank regression). The asymptotics of the estimator is usually derived under the assumption of knowing the true rank. In this paper, we quantify the asymptotic bias and find the asymptotic distributions of the cointegration estimator in case of misspecified rank. Furthermore, we suggest a new class of weighted reduced rank estimators that allow for more flexibility in settings where rank selection is hard. We show empirically that a proper choice of weights can lead to increased predictive performance when there is rank uncertainty. Finally, we illustrate the estimators on empirical EEG data from a psychological experiment on visual processing. [ABSTRACT FROM AUTHOR]

We study asymptotic profiles for singular solutions to a class of critical strongly coupled fourth order systems on the punctured ball. Assuming a superharmonicity condition, we prove that sufficiently close to the isolated singularity, singular solutions behave like the so-called Emden–Fowler solution to the blow-up limit problem. On the technical level, we use an involved spectral analysis to study the Jacobi fields' growth properties in the kernel of the linearization of our system around a blow-up limit solution, which may be of independent interest. Our main theorem positively answers a question posed by Frank and König (2019) [12] concerning the local behavior of singular solutions close to the isolated singularity for scalar solutions in the punctured ball. It also extends to the case of strongly coupled systems, the celebrated asymptotic classification due to Korevaar et al. (1999) [21]. [ABSTRACT FROM AUTHOR]

We present two new algorithms for solving norm equations over global function fields with at least one infinite place of degree one. The first of these is a substantial improvement of a method due to Gaál and Pohst, while the second approach uses index calculus techniques and is significantly faster asymptotically and in practice. Both algorithms incorporate compact representations of field elements which results in a significant gain in performance compared to the Gaál–Pohst approach. We provide Magma implementations, analyze the complexity of all three algorithms under varying asymptotics on the field parameters, and provide empirical data on their performance. [ABSTRACT FROM AUTHOR]

In the present paper we study the stability problem for a stretched tube conveying fluid with boundary control. The abstract spectral problem concerns operator pencils of the forms Mλ=λ2G+λD+CandPλ=λI−T$$\begin{equation*} \hspace*{6pc}\mathcal {M}{\left(\lambda \right)}=\lambda ^2G+\lambda D+C\quad \text{and}\quad \mathcal {P}{\left(\lambda \right)}=\lambda I-T \end{equation*}$$taking values in different Hilbert product spaces. Thorough analysis is made of the existence, location, multiplicities, and asymptotics of eigenvalues in the complex plane and Riesz basisness of the corresponding eigenfunctions and eigenvectors. Well‐posedness of the closed‐loop system represented by the initial‐value problem for the abstract equation ẋt=Txt$$\begin{equation*} \hspace*{12pc}\dot{{x}}{\left(t\right)}=Tx{\left(t\right)} \end{equation*}$$is established in the framework of C0$C_0$‐semigroups as well as expansions of the solutions in terms of eigenvectors and stability of the closed‐loop system. For the parameters of the problem we give new regions, larger than those in the literature, in which a stretched tube with flow, simply supported at one end, with a boundary controller applied at the other end, can be exponentially stabilised. [ABSTRACT FROM AUTHOR]

We are concerned with a coefficient inverse problem of a multidimensional heat equation. The objective is to reconstruct the sought coefficient from a sequence of observations of the solution taken at a single point. To do so we first obtain an explicit formula for the sought coefficient, and then see how we can approximate it using few observations only. We also show that asymptotics of the solution help reduce the data processing to overcome the curse of dimensionality. This new and direct reconstruction method is fast and gives an alternative to iterative and Newton's type methods. Numerical examples are provided at the end. [ABSTRACT FROM AUTHOR]

In this paper, we study the topological asymptotic expansion of a topology optimisation problem that is constrained by the Poisson equation with the design/shape variable entering through the right hand side. Using an averaged adjoint approach, we give explicit formulas for topological derivatives of arbitrary order for both an L 2 and H 1 tracking-type cost function in both dimension two and three and thereby derive the complete asymptotic expansion. As the asymptotic behaviour of the fundamental solution of the Laplacian differs in dimension two and three, also the derivation of the topological expansion significantly differs in dimension two and three. The complete expansion for the H 1 cost functional directly follows from the analysis of the variation of the state equation. However, the proof of the asymptotics of the L 2 tracking-type cost functional is significantly more involved and, surprisingly, the asymptotic behaviour of the bi-harmonic equation plays a crucial role in our proof. [ABSTRACT FROM AUTHOR]

Abstract.In this article, we establish precise asymptotics for complete integral convergence in the law of iterated logarithm under the sub-linear expectation space. We extend some precise asymptotics for complete integral convergence theorems from the classical probability space to sub-linear expectation space. Further, we extend the precise asymptotics theorem to the maximum of partial sums under the sub-linear expectation space. [ABSTRACT FROM AUTHOR]

The objective of this research is to investigate the initial value problem of a higher-order matrix-type nonlinear Schrödinger (NLS) equation with discrete spectrum as simple and double poles (simple and second-order zeros rank(P(x,t,kn))=3 and second- and third-order zeros under rank(P(x,t,kn))=2) under zero boundary conditions (ZBCs). Specifically, we not only consider the analyticity, symmetries and asymptotics of the Jost function, scattering and reflection coefficients in the process of direct scattering, but also residue conditions, norming constants, RH problem and the reconstruction formula in the process of inverse scattering. There exist some differences between it and the RH method in the study of vector and scalar equations, like the order of each pole of a−1(k) being less than or equal to the order of the zeros of deta(k) (assuming k=kn∈ℂ+ is a second- or third-order zero of deta(k) under rank(P(x,t,kn))=2(⇔rank(a(kn))=0)), etc. [ABSTRACT FROM AUTHOR]

We consider a class of statistical estimation problems in which we are given a random data matrix |${\boldsymbol{X}}\in{\mathbb{R}}^{n\times d}$| (and possibly some labels |${\boldsymbol{y}}\in{\mathbb{R}}^{n}$|⁠) and would like to estimate a coefficient vector |${\boldsymbol{\theta }}\in{\mathbb{R}}^{d}$| (or possibly a constant number of such vectors). Special cases include low-rank matrix estimation and regularized estimation in generalized linear models (e.g. sparse regression). Firstorder methods proceed by iteratively multiplying current estimates by |${\boldsymbol{X}}$| or its transpose. Examples include gradient descent or its accelerated variants. Under the assumption that the data matrix |${\boldsymbol{X}}$| is standard Gaussian, Celentano, Montanari, Wu (2020, Conference on Learning Theory, pp. 1078–1141. PMLR) proved that for any constant number of iterations (matrix vector multiplications), the optimal firstorder algorithm is a specific approximate message passing algorithm (known as 'Bayes AMP'). The error of this estimator can be characterized in the high-dimensional asymptotics |$n,d\to \infty $|⁠ , |$n/d\to \delta $|⁠ , and provides a lower bound to the estimation error of any firstorder algorithm. Here we present a simpler proof of the same result, and generalize it to broader classes of data distributions and of firstorder algorithms, including algorithms with non-separable nonlinearities. Most importantly, the new proof is simpler, does not require to construct an equivalent tree-structured estimation problem, and is therefore susceptible of a broader range of applications. [ABSTRACT FROM AUTHOR]

The stability of the flow induced by a linearly stretched, flat sheet with a temperature gradient between the sheet and the free stream is investigated via a complementary numerical and large Reynolds number lower-branch asymptotic analysis. This analysis involves the derivation of new basic flow solutions which extend the exact analytical solutions of Crane, by coupling the energy and momentum equations with a temperature-dependent viscosity. In the most extreme case considered, the Reynolds number at which instabilities are observed is approximately halved compared to the isothermal case, thereby justifying its consideration as a physically meaningful flow variable of interest with potential implications for industrial extrusion processes. [ABSTRACT FROM AUTHOR]

The present study examines an asymptotic analysis of electroosmotic flow phenomena bounded by the symmetrical wavy channel containing an anisotropic porous material under the variable pressure gradient and zeta potential. The incorporation of anisotropic porous material introduces additional complexities to the flow behavior. Electric potential is regulated by the non-linear Poisson–Boltzmann equation, which is linearized by the Debye–Hückel linearization process, and flow velocity inside the porous channel is governed by the Brinkman equation. The aspect ratio of the channel is considered to be significantly small, i.e., ( δ 2 ≪ 1). Obtaining analytical solutions to these non-linear coupled equations is a formidable challenge. To address this challenge, the equations are tackled by employing an asymptotic series expansion with respect to a small parameter, specifically the ratio of the channel thickness, where δ 2 ≪ 1. The graphical analysis based on the derived expressions for flow quantities—such as fluid velocity, flow rate, flow resistance, wall shear stress, and pressure gradient along the wall—demonstrates the considerable impact of various governing parameters. These parameters, including the Debye–Hückel parameter, anisotropic ratio, slip length, and fluctuation amplitude, play a crucial role in influencing the behavior of these flow characteristics, highlighting their importance in determining the system's overall flow dynamics. The results demonstrate that an increment in the anisotropic ratio corresponds to an enhancement in fluid velocity and augmented flow rate. This relationship stems from the observed phenomenon wherein an enhancement in the anisotropic ratio leads to an augmentation in the permeability along the x-direction, thereby leading to an elevation in velocity and subsequently enhancing the flow rate. The study also examines the impact of flow reversal at the crests of the wavy channel resulting from the anisotropic ratio. The findings from our study have confirmed the axial fluid velocity in a purely pressure-driven flow system, where electroosmotic effects are not present. These results enhance our understanding of how anisotropic permeability affects fluid flow in microfluidic systems, especially when electrokinetic forces are at play. [ABSTRACT FROM AUTHOR]

In this paper, we systematically study the N -solitons and asymptotic analysis of the integrable n -component third–fifth-order Sasa–Satsuma equations. We conduct the spectral analysis on the (n + 2) -order matrix Lax pair to formulate a Riemann–Hilbert (RH) problem, which is used to generate the N -soliton solutions via the determinants. Moreover, we visually represent the interaction dynamics of multi-soliton solutions and analyze their asymptotic behaviors. Finally, we present the higher-order N -soliton solutions by dealing with the RH problem with higher-order zeros. These results will be useful to further analyze the multi-soliton structures and design the related physical experiments. [ABSTRACT FROM AUTHOR]

The aim of the article is to create a method for studying the asymptotics of solutions to second-order differential equations with irregular singularities. The method allows us to prove the convergence of formal series included in the asymptotics of solutions for a wide class of second-order differential equations in the neighborhoods of their irregular singular points, including the point at infinity, which is generally irregular. The article provides a number of applications of the method for studying the asymptotics of solutions to both ordinary differential equations and partial differential equations. [ABSTRACT FROM AUTHOR]

U-statistics are fundamental in modeling statistical measures that involve responses from multiple subjects. They generalize the concept of the empirical mean of a random variable X to include summations over each m-tuple of distinct observations of X. W. Stute introduced conditional U-statistics, extending the Nadaraya–Watson estimates for regression functions. Stute demonstrated their strong pointwise consistency with the conditional expectation r (m) (φ , t) , defined as E [ φ (Y 1 , ... , Y m) | (X 1 , ... , X m) = t ] for t ∈ X m . This paper focuses on estimating functional single index (FSI) conditional U-processes for regular time series data. We propose a novel, automatic, and location-adaptive procedure for estimating these processes based on k-Nearest Neighbor (kNN) principles. Our asymptotic analysis includes data-driven neighbor selection, making the method highly practical. The local nature of the kNN approach improves predictive power compared to traditional kernel estimates. Additionally, we establish new uniform results in bandwidth selection for kernel estimates in FSI conditional U-processes, including almost complete convergence rates and weak convergence under general conditions. These results apply to both bounded and unbounded function classes, satisfying certain moment conditions, and are proven under standard Vapnik–Chervonenkis structural conditions and mild model assumptions. Furthermore, we demonstrate uniform consistency for the nonparametric inverse probability of censoring weighted (I.P.C.W.) estimators of the regression function under random censorship. This result is independently valuable and has potential applications in areas such as set-indexed conditional U-statistics, the Kendall rank correlation coefficient, and discrimination problems. [ABSTRACT FROM AUTHOR]

We formulate an inverse scattering transformation for the focusing Hirota equation with asymmetric boundary conditions, which means that the limit values of the solution at spatial infinities have different amplitudes. For the direct problem, we do not use Riemann surfaces, but instead analyze the branching properties of the scattering problem eigenvalues. The Jost eigenfunctions and scattering coefficients are defined as single-valued functions on the complex plane, and their analyticity properties, symmetries, and asymptotics are obtained, which are helpful in constructing the corresponding Riemann–Hilbert problem. On an open contour, the inverse problem is described by a Riemann–Hilbert problem with double poles. Finally, for comparison purposes, we consider the initial value problem with one-sided nonzero boundary conditions and obtain the formulation of the inverse scattering transform by using Riemann surfaces. [ABSTRACT FROM AUTHOR]

In this paper, we are interested in the mathematical properties of methods based on a fictitious domain approach combined with reduced-order interface coupling conditions, which have been recently introduced to simulate 3D-1D fluid-structure or structure-structure coupled problems. To give insights on the approximation properties of these methods, we investigate them in a simplified setting by considering the Poisson problem in a two-dimensional domain with non-homogeneous Dirichlet boundary conditions on small inclusions. The approximated reduced problem is obtained using a fictitious domain approach combined with a projection on a Fourier finite-dimensional space of the Lagrange multiplier associated to the Dirichlet boundary constraints, obtaining in this way a Poisson problem with defective interface conditions. After analyzing the existence of a solution of the reduced problem, we prove its convergence towards the original full problem, when the size of the holes tends towards zero, with a rate which depends on the number of modes of the finite-dimensional space. In particular, our estimates highlight the fact that to obtain a good convergence on the Lagrange multiplier, one needs to consider more modes than the first Fourier mode (constant mode). This is a key issue when one wants to deal with real coupled problems, such as fluid-structure problems for instance. Next, the numerical discretization of the reduced problem using the finite element method is analyzed in the case where the computational mesh does not fit the small inclusion interface. As is standard for these types of problem, the convergence of the solution is not optimal due to the lack of regularity of the solution. Moreover, convergence exhibits a well-known locking effect when the mesh size and the inclusion size are of the same order of magnitude. This locking effect is more apparent when increasing the number of modes and affects the Lagrange multiplier convergence rate more heavily. To resolve these issues, we propose and analyze a stabilized method and an enriched method for which additional basis functions are added without changing the approximation space of the Lagrange multiplier. Finally, the properties of numerical strategies are illustrated by numerical experiments. [ABSTRACT FROM AUTHOR]

The paper considers a nonstandard risk model with stochastic return and perturbation, in which the price process of the investment portfolio is described as a geometric Lévy process and each main claim may induce a delayed by-claim. When the main claims and by-claims have subexponential distributions, we obtain some asymptotic estimations of the finite-time ruin probability. [ABSTRACT FROM AUTHOR]

For a random partition, one of the most basic questions is: what can one expect about the parts that arise? For example, what is the distribution of the parts of random partitions modulo N$N$? As most partitions contain a 1, and indeed many 1s arise as parts of a random partition, it is natural to expect a skew toward 1(modN)$1\ (\mathrm{mod} \, N)$. This is indeed the case. For instance, Kim, Kim, and Lovejoy recently established "parity biases" showing how often one expects partitions to have more odd than even parts. Here, we generalize their work to give asymptotics for biases (modN)$\ (\mathrm{mod} \, N)$ for partitions into distinct parts. The proofs rely on the Circle Method and give independently useful techniques for analyzing the asymptotics of Nahm‐type q$q$‐hypergeometric series. [ABSTRACT FROM AUTHOR]

The author addresses the question, under which conditions an active jammer will be successful in corrupting a wireless communication link, when both the desired link and the jamming link are subject to multipath signal fading. To this end, a simple closed‐form analytical expression is derived for the resulting block‐error probability (BLEP) under Nakagami‐m$m$ fading with in general unequal fading parameters for the desired and the jamming link. As a by‐product, a novel expression for the corresponding probability of a capacity outage is obtained. An asymptotic analysis and numerical evaluation of the BLEP expression show that in the single‐antenna case the jammer will indeed be successful in corrupting the wireless link, unless there is a rather high signal‐to‐noise ratio (SNR) advantage for the desired link. This even holds true, when signal fading for the jamming link is significantly more severe than for the desired link. Finally, the case of multiple antennas is considered and the benefits of array processing and diversity reception at the desired receiver are explored. It is found that receive array processing can significantly improve the resulting BLEP, provided that the desired link is characterized by favorable fading conditions. On the other hand, diversity reception can significantly improve the BLEP, if the desired link has favorable SNR conditions. [ABSTRACT FROM AUTHOR]

Reconfigurable intelligent surfaces (RISs), which consist of numerous passive reflecting elements, have emerged as a prominent technology to enhance energy and spectral efficiency for future wireless networks. RISs have the capability to intelligently reconfigure the incident wave, reflecting it towards the intended target without requiring energy for signal processing. Consequently, they have become a promising solution to support the demand for high-throughput satellite communication (SatCom) and enhanced coverage for areas inaccessible to terrestrial networks. This paper presents an asymptotic analysis of an RIS-assisted SatCom system. In this system, an unmanned aerial vehicle equipped with an RIS operates as a mobile reflector between a satellite and users. In particular, a passive beamformer is designed with the aim of asymptotically attaining optimal performance, considering the limitations imposed by practical SatCom systems. Moreover, the closed-form expressions for the ergodic achievable rate and outage probability are derived considering the proposed passive beamforming technique. Furthermore, we extend the system model to a multicast system and asymptotically analyze the optimality of the proposed scheme, leveraging the derived asymptotic results in the unicast system. The results of the simulations confirm that our analyses can precisely and analytically assess the performance of the RIS-assisted SatCom system, confirming the asymptotic optimality of the proposed scheme. [ABSTRACT FROM AUTHOR]

In this paper, we derive the effective model describing a thin-domain flow with permeable boundary through which the fluid is injected into the domain. We start with incompressible Stokes system and perform the rigorous asymptotic analysis. Choosing the appropriate scaling for the injection leads to a compressible effective model. In this paper, we derive the effective model describing a thin-domain flow with permeable boundary through which the fluid is injected into the domain. We start with incompressible Stokes system and perform the rigorous asymptotic analysis. Choosing the appropriate scaling for the injection leads to a compressible effective model. [ABSTRACT FROM AUTHOR]

In this article, densities (and their derivatives) of subordinators and inverse subordinators are considered. Under minor restrictions, generally milder than the existing in the literature, employing a useful modification of the saddle point method, we obtain the large asymptotic behaviour of these densities (and their derivatives) for a specific region of space and time and quantify how the ratio between time and space affects the explicit speed of convergence. The asymptotics is governed by an exponential term depending on the Laplace exponent of the subordinator and the region represents the behaviour of the subordinator when it is atypically small (the inverse one is larger than usual). As a result, a route to the derivation of novel general or particular fine estimates for densities with explicit constants in the speed of convergence in the region of the lower envelope/the law of iterated logarithm is available. Furthermore, under mild conditions, we provide a power series representation for densities (and their derivatives) of subordinators and inverse subordinators. This representation is explicit and based on the derivatives of the convolution of the tails of the corresponding Lévy measure, whose smoothness is also investigated. In this context, the methods adopted are based on Laplace inversion and strongly rely on the theory of Bernstein functions extended to the cut complex plane. As a result, smoothness properties of densities (and their derivatives) and their behaviour near zero immediately follow. [ABSTRACT FROM AUTHOR]

In this paper we consider two dimensional quantum system with an infinite waveguide of the width d and a transversally invariant profile. Furthermore, we assume that at a distant ρ there is a perturbation defined by the Kato measure. We show that, under certain conditions, the resolvent of the Hamiltonian has the second sheet pole which reproduces the resonance at z (ρ) with the asymptotics z (ρ) = E β ; n + O ( exp ⁡ (− 2 | E β ; n | ρ) ρ) for ρ large and with the resonant energy E β ; n . Moreover, we show that the imaginary component of z (ρ) satisfies Fermi's golden rule which we explicitly derive. [ABSTRACT FROM AUTHOR]

Reinforcement Learning holds great promise for data-driven decision-making in various social contexts, including healthcare, education, and business. However, classical methods that focus on the mean of the total return may yield misleading results when dealing with heterogeneous populations typically found in large-scale datasets. To address this issue, we introduce the K-Value Heterogeneous Markov Decision Process, a framework designed to handle sequential decision problems with latent population heterogeneity. Within this framework, we propose auto-clustered policy evaluation for estimating the value of a given policy and auto-clustered policy iteration for estimating the optimal policy within a parametric policy class. Our auto-clustered algorithms can automatically identify homogeneous subpopulations while simultaneously estimating the action value function and the optimal policy for each subgroup. We establish convergence rates and construct confidence intervals for the estimators. Simulation results support our theoretical findings, and an empirical study conducted on a real medical dataset confirms the presence of value heterogeneity and validates the advantages of our novel approach. for this article are available online, including a standardized description of the materials available for reproducing the work. [ABSTRACT FROM AUTHOR]

This article develops a unified and computationally efficient method for change-point estimation along the time dimension in a nonstationary spatio-temporal process. By modeling a nonstationary spatio-temporal process as a piecewise stationary spatio-temporal process, we consider simultaneous estimation of the number and locations of change-points, and model parameters in each segment. A composite likelihood-based criterion is developed for change-point and parameter estimation. Under the framework of increasing domain asymptotics, theoretical results including consistency and distribution of the estimators are derived under mild conditions. In contrast to classical results in fixed dimensional time series that the localization error of change-point estimator is O p (1) , exact recovery of true change-points is possible in the spatio-temporal setting. More surprisingly, the consistency of change-point estimation can be achieved without any penalty term in the criterion function. In addition, we further establish consistency of the change-point estimator under the infill asymptotics framework where the time domain is increasing while the spatial sampling domain is fixed. A computationally efficient pruned dynamic programming algorithm is developed for the challenging criterion optimization problem. Extensive simulation studies and an application to the U.S. precipitation data are provided to demonstrate the effectiveness and practicality of the proposed method. for this article are available online. [ABSTRACT FROM AUTHOR]

Huber regression (HR) is a popular flexible alternative to the least squares regression when the error follows a heavy-tailed distribution. We propose a new method called the enveloped Huber regression (EHR) by considering the envelope assumption that there exists some subspace of the predictors that has no association with the response, which is referred to as the immaterial part. More efficient estimation is achieved via the removal of the immaterial part. Different from the envelope least squares (ENV) model whose estimation is based on maximum normal likelihood, the estimation of the EHR model is through Generalized Method of Moments. The asymptotic normality of the EHR estimator is established, and it is shown that EHR is more efficient than HR. Moreover, EHR is more efficient than ENV when the error distribution is heavy-tailed, while maintaining a small efficiency loss when the error distribution is normal. Moreover, our theory also covers the heteroscedastic case in which the error may depend on the covariates. The envelope dimension in EHR is a tuning parameter to be determined by the data in practice. We further propose a novel generalized information criterion (GIC) for dimension selection and establish its consistency. Extensive simulation studies confirm the messages from our theory. EHR is further illustrated on a real dataset. for this article are available online. [ABSTRACT FROM AUTHOR]

In this paper we study the evolution of a small rigid body in a viscous incompressible fluid, in particular we show that a small particle is not accelerated by the fluid in the limit when its size converges to zero under a lower bound on its mass. This result is based on a new a priori estimate on the velocities of the centers of mass of rigid bodies that holds in the case when their masses are also allowed to decrease to zero. [ABSTRACT FROM AUTHOR]

Nested simulation concerns estimating functionals of a conditional expectation via simulation. In this paper, we propose a new method based on kernel ridge regression to exploit the smoothness of the conditional expectation as a function of the multidimensional conditioning variable. Asymptotic analysis shows that the proposed method can effectively alleviate the curse of dimensionality on the convergence rate as the simulation budget increases, provided that the conditional expectation is sufficiently smooth. The smoothness bridges the gap between the cubic root convergence rate (that is, the optimal rate for the standard nested simulation) and the square root convergence rate (that is, the canonical rate for the standard Monte Carlo simulation). We demonstrate the performance of the proposed method via numerical examples from portfolio risk management and input uncertainty quantification. This paper was accepted by Baris Ata, stochastic models and simulation. Funding: The authors acknowledge financial support from the National Natural Science Foundation of China [Grant NSFC 12101149] and the Hong Kong Research Grants Council [Grants GRF 17201520 and GRF 17206821]. Supplemental Material: The e-companion and data files are available at https://doi.org/10.1287/mnsc.2022.00204. [ABSTRACT FROM AUTHOR]

We consider fermionic ground states of the Landau Hamiltonian, H B , in a constant magnetic field of strength B > 0 in R 2 at some fixed Fermi energy μ > 0 , described by the Fermi projection P B : = 1 (H B ≤ μ) . For some fixed bounded domain Λ ⊂ R 2 with boundary set ∂ Λ and an L > 0 we restrict these ground states spatially to the scaled domain L Λ and denote the corresponding localised Fermi projection by P B (L Λ) . Then we study the scaling of the Hilbert-space trace, tr f (P B (L Λ)) , for polynomials f with f (0) = f (1) = 0 of these localised ground states in the joint limit L → ∞ and B → 0 . We obtain to leading order logarithmically enhanced area-laws depending on the size of LB. Roughly speaking, if 1/B tends to infinity faster than L, then we obtain the known enhanced area-law (by the Widom–Sobolev formula) of the form L ln (L) a (f , μ) | ∂ Λ | as L → ∞ for the (two-dimensional) Laplacian with Fermi projection 1 (H 0 ≤ μ) . On the other hand, if L tends to infinity faster than 1/B, then we get an area law with an L ln (μ / B) a (f , μ) | ∂ Λ | asymptotic expansion as B → 0 . The numerical coefficient a (f , μ) in both cases is the same and depends solely on the function f and on μ . The asymptotic result in the latter case is based upon the recent joint work of Leschke, Sobolev and the second named author [7] for fixed B, a proof of the sine-kernel asymptotics on a global scale, and on the enhanced area-law in dimension one by Landau and Widom. In the special but important case of a quadratic function f we are able to cover the full range of parameters B and L. In general, we have a smaller region of parameters (B, L) where we can prove the two-scale asymptotic expansion tr f (P B (L Λ)) as L → ∞ and B → 0 . [ABSTRACT FROM AUTHOR]

The homogenization method is developed for operators with rapidly oscillating coefficients, intended for use in problems of quasiclassical asymptotics and not assuming a periodic structure of coefficient oscillations. Algebras of locally averaged functions are studied, a homogenization theorem for differential operators of general form is proved, and some features of the method are illustrated using the example of the wave equation. [ABSTRACT FROM AUTHOR]

In this paper, we study the eta-invariant of elliptic parameter-dependent boundary-value problems and its main properties. Using Melrose's approach, we define the eta-invariant as a regularization of the winding number of the family. In this case, the regularization of the trace requires obtaining the asymptotics of the trace of compositions of invertible parameter-dependent boundaryvalue problems for large values of the parameter. Obtaining the asymptotics uses the apparatus of pseudodifferential boundary-value problems and is based on the reduction of parameter-dependent boundary-value problems to boundary-value problems with no parameter. [ABSTRACT FROM AUTHOR]

We show a quantitative analysis of the perturbed electric field of a 3D anisotropic conductive rod geometry embedded in homogeneous background, which is an extension of the work in 2D case. The solution to the perturbed problem is presented by layer potential techniques, and dedicated asymptotic analysis is employed for characterization of the density function. The asymptotic result shows that near the high curvature boundary of the rod, the electric field is much strong, compared with other parts adjacent to the rod. [ABSTRACT FROM AUTHOR]

In this paper the existence of intersections for functions of several Brownian motions on the Carnot group is studied. A condition is presented for the existence of such intersections with Probability 1, which is in the form of the asymptotics of a measure on a specific family of small balls. The measure is arbitrary but can be chosen as a surface measure on the manifold related to intersections, and the balls are constructed using the distances related to the processes. Additionally, if the same condition holds in a weaker form, it is shown that there is a Hausdorff measure, such that the value of this Hausdorff measure on the set of intersection points is finite with Probability 1. [ABSTRACT FROM AUTHOR]

Consider an insurance risk model with constant force of interest under the assumption that an immediate claim is accompanied by a random number of delayed claims. In the presence of heavy tails on claim distributions and dependence structures among modelling components, we study the uniform asymptotics for an insurer's ruin-related quantities, where the uniformity holds for all time horizons varying in a relevant interval. [ABSTRACT FROM AUTHOR]

Hyperboloidal slices are spacelike slices that reach future null infinity. Their asymptotic behaviour is different from Cauchy slices, which are traditionally used in numerical relativity simulations. This work uses free evolution of the formally-singular conformally compactified Einstein equations in spherical symmetry. One way to construct gauge conditions suitable for this approach relies on building the gauge source functions from a time-independent background spacetime metric. This background reference metric is set using the height function approach to provide the correct asymptotics of hyperboloidal slices of Minkowski spacetime. The present objective is to study the effect of different choices of height function on hyperboloidal evolutions via the reference metrics used in the gauge conditions. A total of 10 reference metrics for Minkowski are explored, identifying some of their desired features. They include 3 hyperboloidal layer constructions, evolved with the non-linear Einstein equations for the first time. Focus is put on long-term numerical stability of the evolutions, including small initial gauge perturbations. The results will be relevant for future (puncture-type) hyperboloidal evolutions, 3D simulations and the development of coinciding Cauchy and hyperboloidal data, among other applications. [ABSTRACT FROM AUTHOR]

This paper investigates rogue wave patterns in the nonlocal nonlinear Schrödinger (NLS) equation. Initially, employing the Kadomtsev–Petviashvili reduction method, rogue wave solutions of the nonlocal NLS equation, whose τ function is a 2 × 2 block matrix, are simplified. Afterward, utilizing the asymptotic analysis approach, we investigate the rogue wave patterns when two free parameters a 2 m 1 + 1 and b 2 m 2 + 1 are considerably large and fulfill the condition | a 2 m 1 + 1 | 2 / (2 m 1 + 1) = O (| b 2 m 2 + 1 | 1 / (2 m 2 + 1) ) . Our findings reveal that under these conditions, rogue wave solutions of the nonlocal NLS equation exhibit novel patterns, which consist of three regions, which are the outer region, the middle region and the inner region. In the outer and middle regions, only single rogue waves with singularities may occur, and their locations are characterized by roots of two polynomials from the Yablonskii–Vorob'ev polynomial hierarchies. In the inner region, a possible lower order rogue wave may appear, which can be singular or regular, depending on the values of m 1 , m 2 , the sizes of τ function, and certain free parameters. Finally, the numerical results indicate that the predicted outcomes are in close alignment with real rogue waves. [ABSTRACT FROM AUTHOR]