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Approximation of probability density functions via location-scale finite mixtures in Lebesgue spaces

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arXiv 2020年

作者： Nguyen, Trung Tin Chamroukhi, Faicel Nguyen, Hien D. McLachlan, Geoffrey J. Normandie Univ Unicaen Cnrs Lmno Caen14000 France School of Engineering and Mathematical Sciences Department of Mathematics and Statistics La Trobe University MelbourneVIC Australia School of Mathematics and Physics University of Queensland St. Lucia Brisbane Australia

The class of location-scale finite mixtures is of enduring interest both from applied and theoretical perspectives of probability and statistics. We establish and prove the following results: to an arbitrary degree of accuracy, (a) location-scale mixtures of a continuous probability density function (PDF) can approximate any continuous PDF, uniformly, on a compact set;and (b) for any finite p ≥ 1, location-scale mixtures of an essentially bounded PDF can approximate any PDF in Lp, in the *** Codes 62E17 (Primary), 41A30 (Secondary) Copyright © 2020, The Authors. All rights reserved.

关键词： Probability density function

The Elliptical Ornstein-Uhlenbeck Process

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arXiv 2020年

作者： Sykulski, Adam M. Olhede, Sofia C. Sykulska-Lawrence, Hanna M. Department of Mathematics and Statistics Lancaster University United Kingdom École Polytechnique Fédérale de Lausanne Switzerland Department of Aeronautical and Astronautical Engineering University of Southampton United Kingdom

We introduce the elliptical Ornstein-Uhlenbeck (OU) process, which is a generalisation of the well-known univariate OU process to bivariate time series. This process maps out elliptical stochastic oscillations over time in the complex plane, which are observed in many applications of coupled bivariate time series. The appeal of the model is that elliptical oscillations are generated using one simple first order stochastic differential equation (SDE), whereas alternative models require more complicated vectorised or higher order SDE representations. The second useful feature is that parameter estimation can be performed semi-parametrically in the frequency domain using the Whittle Likelihood. We determine properties of the model including the conditions for stationarity, and the geometrical structure of the elliptical oscillations. We demonstrate the utility of the model by measuring periodic and elliptical properties of Earth's polar motion. © 2020, CC BY.

关键词： Differential equations

The Most Probable Transition Paths of Stochastic Dynamical Systems: A Sufficient and Necessary Characterization

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arXiv 2021年

作者： Huang, Yuanfei Huang, Qiao Duan, Jinqiao School of Mathematics and Statistics Center for Mathematical Sciences Hubei Key Laboratory of Engineering Modeling and Scientific Computing Huazhong University of Science and Technology Wuhan430074 China Department of Statistics and Data Science National University of Singapore 6 Science Drive 2 Singapore117546 Singapore School of Data Science City University of Hong Kong Kowloon Hong Kong Department of Mathematics Faculty of Sciences University of Lisbon Campo Grande Edifício C6 LisboaPT-1749-016 Portugal Division of Mathematical Sciences School of Physical and Mathematical Sciences Nanyang Technological University 21 Nanyang Link Singapore637371 Singapore The Dongguan Key Laboratory for Data Science and Intelligent Medicine Department of Mathematics Department of Physics Great Bay University Guangdong Dongguan523000 China

The most probable transition paths of a stochastic dynamical system are the global minimizers of the Onsager–Machlup action functional and can be described by a necessary but not sufficient condition, the Euler–Lagrange equation (a second-order differential equation with initial-terminal conditions) from a variational principle. This work is devoted to showing a sufficient and necessary characterization for the most probable transition paths of stochastic dynamical systems with Brownian noise. We prove that, under appropriate conditions, the most probable transition paths are completely determined by a first-order ordinary differential equation. The equivalence is established by showing that the Onsager–Machlup action functional of the original system can be derived from the corresponding Markovian bridge process. For linear stochastic systems and the nonlinear Hongler’s model, the first-order differential equations determining the most probable transition paths are shown analytically to imply the Euler–Lagrange equations of the Onsager–Machlup functional. For general nonlinear systems, the determining first-order differential equations can be approximated, in a short time or for the small noise case. Some numerical experiments are presented to illustrate our results. Copyright © 2021, The Authors. All rights reserved.

关键词： Dynamical systems

Corrigendum to “Techno-economic model to appraise the use of cattle manure in biodigesters in the generation of electrical energy and biofertilizer” [Biomass Bioenergy 150 (2021) 1–11]

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Biomass and Bioenergy 2023年 179卷

作者： Simone Andreia Guares José Donizetti de Lima Gilson Adamczuk Oliveira Industrial and Systems Engineering Graduate Program (PPGEPS) UTFPR Pato Branco Parana Brazil Department of Mathematics Federal Technological University of Parana (UTFPR) Pato Branco Parana Brazil Department of Mechanical Engineering Federal Technological University of Parana (UTFPR) Pato Branco Parana Brazil

Metropolis-Hastings with averaged acceptance ratios

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arXiv 2020年

作者： Andrieu, Christophe Yıldırım, Sinan Doucet, Arnaud Chopin, Nicolas School of Mathematics University of Bristol United Kingdom Department of Statistics University of Oxford United Kingdom Faculty of Engineering and Natural Sciences Sabancı University Turkey ENSAE France

Markov chain Monte Carlo (MCMC) methods to sample from a probability distribution π defined on a space (Θ, T ) consist of the simulation of realisations of Markov chains {θn, n ≥ 1} of invariant distribution π and such that the distribution of θi converges to π as i → ∞. In practice one is typically interested in the computation of expectations of functions, say f, with respect to π and it is also required that averages M−1∑Mn=1 f(θn) converge to the expectation of interest. The iterative nature of MCMC makes it difficult to develop generic methods to take advantage of parallel computing environments when interested in reducing time to convergence. While numerous approaches have been proposed to reduce the variance of ergodic averages, including averaging over independent realisations of {θn, n ≥ 1} simulated on several computers, techniques to reduce the "burn-in" of MCMC are scarce. In this paper we explore a simple and generic approach to improve convergence to equilibrium of existing algorithms which rely on the Metropolis-Hastings (MH) update, the main building block of MCMC. The main idea is to use averages of the acceptance ratio w.r.t. multiple realisations of random variables involved, while preserving π as invariant distribution. The methodology requires limited change to existing code, is naturally suited to parallel computing and is shown on our examples to provide substantial performance improvements both in terms of convergence to equilibrium and variance of ergodic averages. In some scenarios gains are observed even on a serial machine. Copyright © 2020, The Authors. All rights reserved.

关键词： Monte Carlo methods

Entropy and relative entropy from information-theoretic principles

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arXiv 2020年

作者： Gour, Gilad Tomamichel, Marco The Department of Mathematics and Statistics Institute for Quantum Science and Technology University of Calgary Alberta Canada The Department of Electrical and Computer Engineering The Centre for Quantum Technologies National University of Singapore Singapore Singapore

We introduce an axiomatic approach to entropies and relative entropies that relies only on minimal information-theoretic axioms, namely monotonicity under mixing and data-processing as well as additivity for product distributions. We find that these axioms induce sufficient structure to establish continuity in the interior of the probability simplex and meaningful upper and lower bounds, e.g., we find that every relative entropy satisfying these axioms must lie between the Rényi divergences of order 0 and ∞. We further show simple conditions for positive definiteness of such relative entropies and a characterisation in terms of a variant of relative trumping. Our main result is a one-to-one correspondence between entropies and relative entropies. Copyright © 2020, The Authors. All rights reserved.

关键词： Entropy

Fluorescence correlation spectroscopy for the measurement and prediction of drug release from degradable hydrogels 42

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Fluorescence correlation spectroscopy for the measurement an...

42nd Society for Biomaterials Annual Meeting and Exposition 2019: The Pinnacle of Biomaterials Innovation and Excellence

作者： Sheth, Saahil Barnard, Emily Rathinam, Muruhan Zustiak, Silviya P. Department of Biomedical Engineering Saint Louis University St. LouisMO United States Department of Mathematics and Statistics University of Maryland Baltimore County BaltimoreMD United States

ISBN: (纸本)9781510883901

Statement of Purpose: Hydrogels, and degradable hydrogels in particular, are at the forefront of an ever-growing drug delivery technology industry, estimated to reach a market size of over $90 billion by 2025. As a drug delivery system, hydrogels have been used in a variety of applications including osteoarthritis, diabetes, and even cancer therapy. A significant advantage of using hydrogels in this capacity is the ability to modify the hydrogel for a specific application. Hydrogels can be tailored by altering several properties such as functionality, mesh size, or degradation rate. Currently, it is difficult to predict drug release profiles from degradable hydrogels due to changes within the hydrogel structure during degradation. In this study, we aim to develop a simple analytical approach based on Fickian diffusion models for predicting drug release profiles from a degradable hydrogel. We used three model proteins of varying molecular weights (MW): lysozyme (14 kDa), bovine serum albumin (BSA;66 kDa), and immunoglobulin G (IgG;150 kDa). We used fluorescence correlation spectroscopy (FCS), a single-molecule detection technique, to determine protein diffusivity over time as a function of hydrogel degradation. We also tracked changes in geometry of the hydrogel over the same period. Using the diffusivity and geometry data, we applied a predictive algorithm to model the protein release profiles from degradable hydrogels. Finally, we validated the model using conventional bulk release experiments. © 2019 Omnipress - All rights reserved.

关键词： Hydrogels

Long-time asymptotics of non-degenerate non-linear diffusion equations

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arXiv 2020年

作者： Christov, Ivan C. Ibraguimov, Akif Islam, Rahnuma School of Mechanical Engineering Purdue University West LafayetteIN47907 United States Department of Mathematics & Statistics Texas Tech University LubbockTX79409 United States

We study the long-time asymptotics of prototypical non-linear diffusion equations. Specifically, we consider the case of a non-degenerate diffusivity function that is a (non-negative) polynomial of the dependent variable of the problem. We motivate these types of equations using Einstein's random walk paradigm, leading to a partial differential equation in non-divergence form. On the other hand, using conservation principles leads to a partial differential equation in divergence form. A transformation is derived to handle both cases. Then, a maximum principle (on both an unbounded and a bounded domain) is proved, in order to obtain bounds above and below for the time-evolution of the solution to the non-linear diffusion problem. Specifically, these bounds are based on the fundamental solution of the linear problem (the so-called Aranson's Green function). Having thus sandwiched the long-time asymptotics of solutions to the non-linear problems between two fundamental solutions of the linear problem, we prove that, unlike the case of degenerate diffusion, a non-degenerate diffusion equation's solution converges onto the linear diffusion solution at long times. Select numerical examples support the mathematical theorems and illustrate the convergence process. Our results have implications on how to interpret asymptotic scalings of potentially anomalous diffusion processes (such as in the flow of particulate materials) that have been discussed in the applied physics literature. Copyright © 2020, The Authors. All rights reserved.

关键词： Partial differential equations

Biomass waste as an alternative source of carbon and silicon-based absorbents for CO2 capturing application

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Chemosphere 2023年 343卷

作者： Suresh, R. Gnanasekaran, Lalitha Rajendran, Saravanan Jalil, A.A. Soto-Moscoso, Matias Khoo, Kuan Shiong Ma, Zengling Halimatul Munawaroh, Heli Siti Show, Pau Loke Departamento de Ingeniería Mecánica Facultad de Ingeniería Universidad de Tarapacá Avda. General Velásquez 1775 Arica Chile University Centre for Research & Development Department of Mechanical Engineering Chandigarh University Punjab Mohali140413 India Department of Chemical Engineering Lebanese American University Byblos Lebanon Centre of Hydrogen Energy Institute of Future Energy Johor UTM Johor Bahru81310 Malaysia Faculty of Chemical and Energy Engineering Universiti Teknologi Malaysia Johor UTM Johor Bahru81310 Malaysia Universidad Autónoma de Chile Chile Department of Chemical Engineering and Materials Science Yuan Ze University Taoyuan Taiwan Centre for Herbal Pharmacology and Environmental Sustainability Chettinad Hospital and Research Institute Chettinad Academy of Research and Education Tamil Nadu Kelambakkam603103 India Zhejiang Provincial Key Laboratory for Subtropical Water Environment and Marine Biological Resources Protection Wenzhou University Wenzhou325035 China Study Program of Chemistry Faculty of Mathematics and Science Education Universitas Pendidikan Indonesia Jalan Dr. Setiabudhi 229 Bandung40154 Indonesia Department of Chemical Engineering Khalifa University P.O. Box 127788 Abu Dhabi United Arab Emirates Department of Chemical and Environmental Engineering Faculty of Science and Engineering University of Nottingham Malaysia Jalan Broga Selangor Darul Ehsan Semenyih Malaysia

The production of low-cost solid adsorbents for carbon dioxide (CO2) capture has gained massive consideration. Biomass wastes are preferred as precursors for synthesis of CO2 solid adsorbents, due to their high CO2 adsorption efficiency, and ease of scalable low-cost production. This review particularly focuses on waste biomass-derived adsorbents with their CO2 adsorption performances. Specifically, studies related to carbon (biochar and activated carbon) and silicon (silicates and geopolymers)-based adsorbents were summarized. The impact of experimental parameters including nature of biomass, synthesis route, carbonization temperature and type of activation methods on the CO2 adsorption capacities of biomass-derived pure carbon and silicon-based adsorbents were evaluated. The development of various enhancement strategies on biomass-derived adsorbents for CO2 capture and their responsible factors that impact adsorbent's CO2 capture proficiency were also reviewed. The possible CO2 adsorption mechanisms on the adsorbent's surface were highlighted. The challenges and research gaps identified in this research area have also been emphasized, which will help as further research prospects. © 2023 Elsevier Ltd

关键词： Carbon dioxide