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Appl Math Comput 2020 May 8;372. Epub 2020 Jan 8.

Aerospace Engineering, Texas A&M University, College Station, TX 77843-3141, USA.

This work focuses on the definition and study of the -dimensional -vector, an algorithm devised to perform orthogonal range searching in static databases with multiple dimensions. The methodology first finds the order in which to search the dimensions, and then, performs the search using a modified projection method. In order to determine the dimension order, the algorithm uses the -vector, a range searching technique for one dimension that identifies the number of elements contained in the searching range. Read More

Appl Math Comput 2019 Nov 19;361:87-97. Epub 2019 Jun 19.

Complex Systems Research Center, Shanxi University, Taiyuan 030006, Shanxi, People's Republic of China.

Traditional infectious diseases models on metapopulation networks focus on direct transportations (e.g., direct flights), ignoring the effect of indirect transportations. Read More

Appl Math Comput 2019 Oct 14;359:512-524. Epub 2019 May 14.

School of Mechanical Engineering, Northwestern Polytechnical University, Xi'an 710072, China.

Numerous efforts have been devoted to investigating the network activities and dynamics of isolated networks. Nevertheless, in practice, most complex networks might be interconnected with each other (due to the existence of common components) and exhibit layered properties while the connections on different layers represent various relationships. These types of networks are characterized as multiplex networks. Read More

Appl Math Comput 2018 Sep 10;332:437-448. Epub 2018 Apr 10.

Complex Systems Research Center, Shanxi University, Taiyuan 030006, PR China.

The interaction between disease and disease information on complex networks has facilitated an interdisciplinary research area. When a disease begins to spread in the population, the corresponding information would also be transmitted among individuals, which in turn influence the spreading pattern of the disease. In this paper, firstly, we analyze the propagation of two representative diseases ( and ) in the real-world population and their corresponding information on Internet, suggesting the high correlation of the two-type dynamical processes. Read More

Appl Math Comput 2017 May 26;300:70-78. Epub 2016 Dec 26.

Biomedical Imaging Center, Department of Biomedical Engineering, Rensselaer Polytechnic Institute, Troy, New York 12180, U.S.A.

The radiative transfer equation (RTE) arises in a wide variety of applications, in particular, in biomedical imaging applications associated with the propagation of light through the biological tissue. However, highly forward-peaked scattering feature in a biological medium makes it very challenging to numerically solve the RTE problem accurately. One idea to overcome the difficulty associated with the highly forward-peaked scattering is through the use of a delta-Eddington phase function. Read More

Appl Math Comput 2016 Jun 22;283:339-354. Epub 2016 Mar 22.

College of Science, Air Force Engineering University, Xi'an 710051, PR China.

In reality, the outbreak of emerging infectious diseases including SARS, A/H1N1 and Ebola are accompanied by the common cold and flu. The selective treatment measure for mitigating and controlling the emerging infectious diseases should be implemented due to limited medical resources. However, how to determine the threshold infected cases and when to implement the selective treatment tactics are crucial for disease control. Read More

Appl Math Comput 2015 Oct;268:717-727

PTC Inc., 41 West Otterman Street, Greensburg, PA 15601, USA.

The problem of recovering the ruin probability in the classical risk model based on the scaled Laplace transform inversion is studied. It is shown how to overcome the problem of evaluating the ruin probability at large values of an initial surplus process. Comparisons of proposed approximations with the ones based on the Laplace transform inversions using a fixed Talbot algorithm as well as on the ones using the Trefethen-Weideman-Schmelzer and maximum entropy methods are presented via a simulation study. Read More

Appl Math Comput 2016 Jan;272(Pt 1):148-158

Department CISE, University of Florida, USA.

Geometrically continuous ( ) constructions naturally yield families of finite elements for isogeometric analysis (IGA) that are also for non-tensor-product layout. This paper describes and analyzes one such concrete geometrically generalized IGA element (short: gIGA element) that generalizes bi-quadratic splines to quad meshes with irregularities. The new gIGA element is based on a recently-developed surface construction that recommends itself by its a B-spline-like control net, low (least) polynomial degree, good shape properties and reproduction of quadratics at irregular (extraordinary) points. Read More

Appl Math Comput 2015 Apr;256:37-51

Institute of Nonlinear Science and Engineering Computing, Sichuan University of Science and Engineering, Zigong, Sichuan 643000, PR China.

Let [Formula: see text] be the open unit disk, [Formula: see text] an analytic self-map of [Formula: see text] and [Formula: see text] an analytic function on [Formula: see text]. Let be the differentiation operator and [Formula: see text] the weighted composition operator. The boundedness and compactness of the product-type operator [Formula: see text] from the weighted Bergman-Orlicz space to the Bers type space, weighted Bloch space and weighted Zygmund space on [Formula: see text] are characterized. Read More

Appl Math Comput 2013 Nov;224:205-215

Department of Mathematical Science, Montclair State University, Montclair, NJ 07043, United States.

Protein misfolding and concomitant aggregation towards amyloid formation is the underlying biochemical commonality among a wide range of human pathologies. Amyloid formation involves the conversion of proteins from their native monomeric states (intrinsically disordered or globular) to well-organized, fibrillar aggregates in a nucleation-dependent manner. Understanding the mechanism of aggregation is important not only to gain better insight into amyloid pathology but also to simulate and predict molecular pathways. Read More

Appl Math Comput 2014 Mar;231:357-376

Department of Mathematics, University of Southern California Los Angeles, CA 90089.

We develop a blind deconvolution scheme for input-output systems described by distributed parameter systems with boundary input and output. An abstract functional analytic theory based on results for the linear quadratic control of infinite dimensional systems with unbounded input and output operators is presented. The blind deconvolution problem is then reformulated as a series of constrained linear and nonlinear optimization problems involving infinite dimensional dynamical systems. Read More

Appl Math Comput 2014 Mar 23;230:473-483. Epub 2014 Jan 23.

Department of Mathematics, Wilfrid Laurier University, Waterloo, Ontario, Canada.

A general compartmental model of disease transmission is studied. The generality comes from the fact that new infections may enter any of the infectious classes and that there is an ordering of the infectious classes so that individuals can be permitted (or not) to pass from one class to the next. The model includes staged progression, differential infectivity, and combinations of the two as special cases. Read More

Appl Math Comput 2014 Feb 17;229:480-498. Epub 2014 Jan 17.

Mathematics Discipline, Faculty of Engineering and Industrial Sciences, Swinburne University of Technology, Hawthorn, Victoria 3122, Australia.

This paper deals with the numerical study of population model based on the epidemics of Severe Acute Respiratory Syndrome (). (susceptible, exposed, infected, diagnosed, recovered) model of epidemic is considered with net in flow of individuals into a region. Transmission of disease is analyzed by solving the system of differential equations using numerical methods with different initial population distributions. Read More

Appl Math Comput 2014 Jan 12;226:83-100. Epub 2013 Nov 12.

Department of Applied Mathematics, University of Calcutta, Kolkata, West Bengal, India.

Choice of interaction function is one of the most important parts for modelling a food chain. Many models have been proposed as a diseased-prey predator model with Holling type-I or type-II or type-III interactions, but there is no model with general Holling type interactions. In this paper, we study a diseased prey-predator model with general Holling type interactions. Read More

Appl Math Comput 2013 Sep 2;221:786-801. Epub 2013 Aug 2.

College of Computer Science, Chongqing University, Chongqing 400044, China.

In this paper, by considering pathogen evolution and human interventions behaviors with vaccines or drugs, we build up a novel SEIRW model with the vaccination to the newborn children. The stability of the SEIRW model with time-varying perturbation to predict the evolution tendency of the disease is analyzed. Furthermore, we introduce a time-varying delay into the susceptible and infective stages in the model and give some global exponential stability criteria for the time-varying delay system. Read More

Appl Math Comput 2013 Apr;219(16):8730-8737

Biostatistics and Epidemiology Branch, Health Effects Laboratory Division, National Institute for Occupational Safety and Health, Morgantown, WV 26505, USA.

The problem of recovering a cumulative distribution function of a positive random variable via the scaled Laplace transform inversion is studied. The uniform upper bound of proposed approximation is derived. The approximation of a compound Poisson distribution as well as the estimation of a distribution function of the summands given the sample from a compound Poisson distribution are investigated. Read More

Appl Math Comput 2012 Sep;219(1):45-53

Institut für Computersprachen, Vienna University of Technology, Austria.

Axiomatization of Physics (and science in general) has many drawbacks that are correctly criticized by opposing philosophical views of science. This paper shows that, by giving formal proofs a more prominent role in the formalization, many of the drawbacks can be solved and many of the opposing views are naturally conciliated. Moreover, this approach allows, by means of proof theory, to open new conceptual bridges between the disciplines of Physics and Computer Science. Read More

Appl Math Comput 2011 Nov;218(6):2693-2710

Computational Science Center, University of Vienna, Nordbergstraße 15, Vienna, Austria.

Although the residual method, or constrained regularization, is frequently used in applications, a detailed study of its properties is still missing. This sharply contrasts the progress of the theory of Tikhonov regularization, where a series of new results for regularization in Banach spaces has been published in the recent years. The present paper intends to bridge the gap between the existing theories as far as possible. Read More

Appl Math Comput 2012 Feb;218(12):6841-6850

Department of Biomedical Engineering, Carnegie Mellon University, Pittsburgh, PA, 15213 USA.

High gradient magnetic field separators have been widely used in a variety of biological applications. Recently, the use of magnetic separators to remove malaria-infected red blood cells (pRBCs) from blood circulation in patients with severe malaria has been proposed in a dialysis-like treatment. The capture efficiency of this process depends on many interrelated design variables and constraints such as magnetic pole array pitch, chamber height, and flow rate. Read More

Appl Math Comput 2011 Nov 3;218(5):1941-1961. Epub 2011 Aug 3.

Department of Mathematics, University of Manitoba, Winnipeg, Manitoba, Canada R3T 2N2.

Recent studies suggest that, for disease transmission models with latent and infectious periods, the use of gamma distribution assumption seems to provide a better fit for the associated epidemiological data in comparison to the use of exponential distribution assumption. The objective of this study is to carry out a rigorous mathematical analysis of a communicable disease transmission model with quarantine (of latent cases) and isolation (of symptomatic cases), in which the waiting periods in the infected classes are assumed to have gamma distributions. Rigorous analysis of the model reveals that it has a globally-asymptotically stable disease-free equilibrium whenever its associated reproduction number is less than unity. Read More

Appl Math Comput 2008 Mar;196(2):724-743

University of Southern California, Department of Mathematics, Kaprielian Hall, Room 108, 3620 Vermont Avenue, Los Angeles, CA 90089-2532.

Biosensor measurement of transdermal alcohol oncentration in perspiration exhibits significant variance from subject to subject and device to device. Short duration data collected in a controlled clinical setting is used to calibrate a forward model for ethanol transport from the blood to the sensor. The calibrated model is then used to invert transdermal signals collected in the field (short or long duration) to obtain an estimate for breath measured blood alcohol concentration. Read More

Appl Math Comput 2007 Mar 15;186(1):193-202. Epub 2006 Sep 15.

Department of Applied Mathematics, E.P.S. de Zamora, Universidad de Salamanca, Avda. Requejo 33, 49022-Zamora, Spain.

The main goal of this work is to introduce a theoretical model, based on cellular automata, to simulate epidemic spreading. Specifically, it divides the population into three classes: susceptible, infected and recovered, and the state of each cell stands for the portion of these classes of individuals in the cell at every step of time. The effect of population vaccination is also considered. Read More

Appl Math Comput 2005 Mar 16;162(2):909-924. Epub 2004 Mar 16.

Department of Mathematics and Statistics, York University, Toronto, Ont., Canada M3J 1P3.

We propose a compartmental model BloComp(2,7) that mimics the SARS control strategies implemented by the Chinese government after the middle of April 2003: the division of the whole population into two parallel blocks corresponding to the so-called free environment and the isolated environment and the partition of these blocks further into the compartments of susceptible, exposed, infective, possible, diagnosed, removed and the health care workers. We introduce a novel approach to calculate the transfer rate from the free environment to the isolated environment, and we incorporate into the model the fact that many individuals were misdiagnosed as SARS suspected and hence were mistakenly put in the isolated environment due to lack of fast and effective SARS diagnostic tests. We develop some methods for the parameter identification using the daily reported data from the Ministry of Health of China. Read More