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This work is devoted to the study of rates of convergence of the empirical measures \\mu_{n} = \\frac {1}{n} \\sum_{k=1}^n \\delta_{X_k}, n \\geq 1, over a sample (X_{k})_{k \\geq 1} of independent identically distributed real-valued random variables towards the common distribution \\mu in Kantorovich transport distances W_p. The focus is on finite range bounds on the expected Kantorovich distances \\mathbb{E}(W_{p}(\\mu_{n},\\mu )) or \\big [ \\mathbb{E}(W_{p}^p(\\mu_{n},\\mu )) \\big ]^1/p in terms of moments and analytic conditions on the measure \\mu and its distribution function. The study describes a variety of rates, from the standard one \\frac {1}{\\sqrt n} to slower rates, and both lower and upper-bounds on \\mathbb{E}(W_{p}(\\mu_{n},\\mu )) for fixed n in various instances. Order statistics, reduction to uniform samples and analysis of beta distributions, inverse distribution functions, log-concavity are main tools in the investigation. Two detailed appendices collect classical and some new facts on inverse distribution functions and beta distributions and their densities necessary to the investigation.

This volume contains the proceedings of the AMS Special Session on Celebrating M. M. Rao's Many Mathematical Contributions as he Turns 90 Years Old, held from November 9-10, 2019, at the University of California, Riverside, California.The articles show the effectiveness of abstract analysis for solving fundamental problems of stochastic theory, specifically the use of functional analytic methods for elucidating stochastic processes and their applications. The volume also includes a biography of M. M. Rao and the list of his publications.

In this paper, time changes of the Brownian motions on generalized Sierpinski carpets including

We analyze a class of nonlinear partial differential equations (PDEs) defined on

This volume contains the proceedings of the CRM Workshops on Probabilistic Methods in Spectral Geometry and PDE, held from August 22-26, 2016 and Probabilistic Methods in Topology, held from November 14-18, 2016 at the Centre de Recherches Mathématiques, Université de Montréal, Montréal, Quebec, Canada. Probabilistic methods have played an increasingly important role in many areas of mathematics, from the study of random groups and random simplicial complexes in topology, to the theory of random Schrödinger operators in mathematical physics. The workshop on Probabilistic Methods in Spectral Geometry and PDE brought together some of the leading researchers in quantum chaos, semi-classical theory, ergodic theory and dynamical systems, partial differential equations, probability, random matrix theory, mathematical physics, conformal field theory, and random graph theory. Its emphasis was on the use of ideas and methods from probability in different areas, such as quantum chaos (study of spectra and eigenstates of chaotic systems at high energy); geometry of random metrics and related problems in quantum gravity; solutions of partial differential equations with random initial conditions. The workshop Probabilistic Methods in Topology brought together researchers working on random simplicial complexes and geometry of spaces of triangulations (with connections to manifold learning); topological statistics, and geometric probability; theory of random groups and their properties; random knots; and other problems. This volume covers recent developments in several active research areas at the interface of Probability, Semiclassical Analysis, Mathematical Physics, Theory of Automorphic Forms and Graph Theory.

International students form an important element of most universities’ internationalisation strategies, especially for research and the recruitment of high calibre PhD students (PGRs). Despite the numerous studies of PGRs’ post-arrival experiences, there is a major dearth of research into their pre-arrival, application experiences. Given the worldwide competition for high calibre PGRs, along with impact posed by the Covid-19 pandemic and by Brexit for the UK, it is vital for universities to ensure that factors clearly under their control, such as the information on their websites and the way they communicate, are as informative and helpful as possible. In this article, we draw on social media data to examine the challenges and uncertainties that Korean PGR applicants experienced in navigating the process of applying to UK universities. The paper compares their confusions with information available on university websites and recommends a series of points that higher education institutions should check for. It also reveals and discusses issues associated with communication. While the data has been collected from Korean social media websites, we argue that our paper has broader relevance for the following reasons. First, the same fundamental intercultural issues—different educational systems and different background knowledge—apply to PGR applicants from other countries and so their queries are likely to be similar or comparable. Second, the insights gained from social media websites to facilitate the application process and thereby enhance recruitment can usefully be applied to other countries and levels of study, in a way that has rarely been done to date.

The normal matrix model with algebraic potential has gained a lot of attention recently, partially in virtue of its connection to several other topics as quadrature domains, inverse potential problems and the Laplacian growth. In this present paper we consider the normal matrix model with cubic plus linear potential. In order to regularize the model, we follow Elbau & Felder and introduce a cut-off. In the large size limit, the eigenvalues of the model accumulate uniformly within a certain domain We also study in detail the mother body problem associated to To construct the mother body measure, we define a quadratic differential Following previous works of Bleher & Kuijlaars and Kuijlaars & López, we consider multiple orthogonal polynomials associated with the normal matrix model. Applying the Deift-Zhou nonlinear steepest descent method to the associated Riemann-Hilbert problem, we obtain strong asymptotic formulas for these polynomials. Due to the presence of the linear term in the potential, there are no rotational symmetries in the model. This makes the construction of the associated

This study aimed to study the association between organizational attractiveness, intrinsic motivation, perceived novelty, trust in the process, and the intention to apply, engage, and finish an artificial intelligence recruitment and selection process. It was also tested whether having already had the experience of having been involved in a recruitment and selection process using artificial intelligence moderated these relationships. The sample for this study consisted of 299 participants. The results indicate that organizational attractiveness and perceived novelty are positively and significantly associated with applying to, getting involved in, and completing the recruitment and selection process using artificial intelligence for participants aged between 45 and 54. For participants aged between 35 and 44, trust in the process significantly affects their intention to apply to, get involved in, and complete the recruitment and selection process using artificial intelligence. Intrinsic motivation did not prove to be a significant predictor of the intention to apply to, get involved in, and complete the recruitment and selection process using artificial intelligence.

Hybrid ion exchange (IX) and biological processes have been developed for various water and wastewater treatment applications. These hybrid systems integrate multiple physical, chemical, biological, hydrodynamics, and substrate transport processes to improve the treatment efficiencies and system stability. The mathematical description of the individual process has been well established previously; however, there is a lack of a holistic review and guidelines to develop hybrid models for different treatment systems. In this paper, we summarize the applications of hybrid IX and biological systems, critically review the representative individual process models, and propose the framework to integrate these models for the hybrid process. Additionally, we provide a comprehensive review of the equilibrium, kinetic, and thermodynamic models for the IX process and the key biological process models, along with their applied scenarios. Advanced data-driven modelling and its combination with mechanistic models are also discussed to overcome the drawbacks in conventional modeling approach. We highlight emerging techniques that would lead to higher fidelity models. This review provides a comprehensive guideline for the model development of hybrid systems and presents future research directions to build robust systems.

We provide the spectral expansion in a weighted Hilbert space of a substantial class of invariant non-self-adjoint and non-local Markov operators which appear in limit theorems for positive-valued Markov processes. We show that this class is in bijection with a subset of negative definite functions and we name it the class of generalized Laguerre semigroups. Our approach, which goes beyond the framework of perturbation theory, is based on an in-depth and original analysis of an intertwining relation that we establish between this class and a self-adjoint Markov semigroup, whose spectral expansion is expressed in terms of the classical Laguerre polynomials. As a by-product, we derive smoothness properties for the solution to the associated Cauchy problem as well as for the heat kernel. Our methodology also reveals a variety of possible decays, including the hypocoercivity type phenomena, for the speed of convergence to equilibrium for this class and enables us to provide an interpretation of these in terms of the rate of growth of the weighted Hilbert space norms of the spectral projections. Depending on the analytic properties of the aforementioned negative definite functions, we are led to implement several strategies, which require new developments in a variety of contexts, to derive precise upper bounds for these norms.