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Advances in Computational and Applied Mathematics
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Advances in Computational and Applied Mathematics

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Engineering Mathematics".

Deadline for manuscript submissions: closed (15 April 2021) | Viewed by 15029

Special Issue Editors

Dr. Francesca Pitolli

E-Mail Website
Guest Editor
Department of Basic and Applied Sciences for Engineering, University of Roma 'La Sapienza', Rome, Italy
Interests: approximation theory; sparse representation; inverse problem; numerical solution of fractional differential problems
Dr. Annalisa Pascarella

E-Mail Website
Guest Editor
Istituto per le Applicazioni del Calcolo (IAC) “M. Picone”, 00185 Roma, Italy
Interests: Inverse Problem; Statistical Inversion Theory; Neuroimaging; Magneto-EncephaloGraphy

Special Issue Information

Dear Colleagues,

The advanced technologies developed these days produce a huge and heterogeneous amount of data acquired by different devices. The main challenge is to extract from the data the significant features that could characterize the phenomena under study. To this end, it is crucial to construct efficient numerical methods which are able to process data with high dimensionality. This can be done by constructing new methods that combine mathematical tools from different fields, such as multiresolution analysis, information theory, Bayesian inference, and machine learning.

This Special Issue is focused on recent advances on numerical and statistical methods for the processing of high-dimensional data for various applications, such as astronomy, neuroscience, video-surveillance, and forensic, to cite a few. The issue collects contributions from scholars in different fields of the mathematics in order to compare different points of view and to give a new insight into the problem. The aim is to make available to the scientific community efficient tools for a wide range of applications.

We invite our colleagues to submit papers related to the construction and validation of numerical and statistical methods to solve applied problems with high dimensional data. 

Prof. Dr. Francesca Pitolli
Dr. Annalisa Pascarella
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • Inverse problem
  • Linear regression
  • Signal processing
  • Information theory
  • Sparse representation

Published Papers (7 papers)

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Research

26 pages, 2189 KiB  
Article
Modeling Epidemic Spread among a Commuting Population Using Transport Schemes
by Daniela Calvetti, Alexander P. Hoover, Johnie Rose and Erkki Somersalo
Mathematics 2021, 9(16), 1861; https://0-doi-org.brum.beds.ac.uk/10.3390/math9161861 - 05 Aug 2021
Cited by 2 | Viewed by 1806
Abstract
Understanding the dynamics of the spread of COVID-19 between connected communities is fundamental in planning appropriate mitigation measures. To that end, we propose and analyze a novel metapopulation network model, particularly suitable for modeling commuter traffic patterns, that takes into account the connectivity [...] Read more.
Understanding the dynamics of the spread of COVID-19 between connected communities is fundamental in planning appropriate mitigation measures. To that end, we propose and analyze a novel metapopulation network model, particularly suitable for modeling commuter traffic patterns, that takes into account the connectivity between a heterogeneous set of communities, each with its own infection dynamics. In the novel metapopulation model that we propose here, transport schemes developed in optimal transport theory provide an efficient and easily implementable way of describing the temporary population redistribution due to traffic, such as the daily commuter traffic between work and residence. Locally, infection dynamics in individual communities are described in terms of a susceptible-exposed-infected-recovered (SEIR) compartment model, modified to account for the specific features of COVID-19, most notably its spread by asymptomatic and presymptomatic infected individuals. The mathematical foundation of our metapopulation network model is akin to a transport scheme between two population distributions, namely the residential distribution and the workplace distribution, whose interface can be inferred from commuter mobility data made available by the US Census Bureau. We use the proposed metapopulation model to test the dynamics of the spread of COVID-19 on two networks, a smaller one comprising 7 counties in the Greater Cleveland area in Ohio, and a larger one consisting of 74 counties in the Pittsburgh–Cleveland–Detroit corridor following the Lake Erie’s American coastline. The model simulations indicate that densely populated regions effectively act as amplifiers of the infection for the surrounding, less densely populated areas, in agreement with the pattern of infections observed in the course of the COVID-19 pandemic. Computed examples show that the model can be used also to test different mitigation strategies, including one based on state-level travel restrictions, another on county level triggered social distancing, as well as a combination of the two. Full article
(This article belongs to the Special Issue Advances in Computational and Applied Mathematics)
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9 pages, 1840 KiB  
Article
A Modified Recursive Regularization Factor Calculation for Sparse RLS Algorithm with l1-Norm
by Junseok Lim, Keunhwa Lee and Seokjin Lee
Mathematics 2021, 9(13), 1580; https://0-doi-org.brum.beds.ac.uk/10.3390/math9131580 - 05 Jul 2021
Cited by 2 | Viewed by 1761
Abstract
In this paper, we propose a new calculation method for the regularization factor in sparse recursive least squares (SRLS) with l1-norm penalty. The proposed regularization factor requires no prior knowledge of the actual system impulse response, and it also reduces computational [...] Read more.
In this paper, we propose a new calculation method for the regularization factor in sparse recursive least squares (SRLS) with l1-norm penalty. The proposed regularization factor requires no prior knowledge of the actual system impulse response, and it also reduces computational complexity by about half. In the simulation, we use Mean Square Deviation (MSD) to evaluate the performance of SRLS, using the proposed regularization factor. The simulation results demonstrate that SRLS using the proposed regularization factor calculation shows a difference of less than 2 dB in MSD from SRLS, using the conventional regularization factor with a true system impulse response. Therefore, it is confirmed that the performance of the proposed method is very similar to that of the existing method, even with half the computational complexity. Full article
(This article belongs to the Special Issue Advances in Computational and Applied Mathematics)
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17 pages, 847 KiB  
Article
Modified Inertial Forward–Backward Algorithm in Banach Spaces and Its Application
by Yanlai Song and Mihai Postolache
Mathematics 2021, 9(12), 1365; https://0-doi-org.brum.beds.ac.uk/10.3390/math9121365 - 12 Jun 2021
Cited by 1 | Viewed by 1423
Abstract
In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a q-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial [...] Read more.
In this paper, we present a new modified inertial forward–backward algorithm for finding a common solution of the quasi-variational inclusion problem and the variational inequality problem in a q-uniformly smooth Banach space. The proposed algorithm is based on descent, splitting and inertial ideas. Under suitable assumptions, we prove that the sequence generated by the iterative algorithm converges strongly to the unique solution of the abovementioned problems. Numerical examples are also given to demonstrate our results. Full article
(This article belongs to the Special Issue Advances in Computational and Applied Mathematics)
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20 pages, 2267 KiB  
Article
Oversampling Errors in Multimodal Medical Imaging Are Due to the Gibbs Effect
by Davide Poggiali, Diego Cecchin, Cristina Campi and Stefano De Marchi
Mathematics 2021, 9(12), 1348; https://0-doi-org.brum.beds.ac.uk/10.3390/math9121348 - 11 Jun 2021
Cited by 6 | Viewed by 2637
Abstract
To analyze multimodal three-dimensional medical images, interpolation is required for resampling which—unavoidably—introduces an interpolation error. In this work we describe the interpolation method used for imaging and neuroimaging and we characterize the Gibbs effect occurring when using such methods. In the experimental section [...] Read more.
To analyze multimodal three-dimensional medical images, interpolation is required for resampling which—unavoidably—introduces an interpolation error. In this work we describe the interpolation method used for imaging and neuroimaging and we characterize the Gibbs effect occurring when using such methods. In the experimental section we consider three segmented three-dimensional images resampled with three different neuroimaging software tools for comparing undersampling and oversampling strategies and to identify where the oversampling error lies. The experimental results indicate that undersampling to the lowest image size is advantageous in terms of mean value per segment errors and that the oversampling error is larger where the gradient is steeper, showing a Gibbs effect. Full article
(This article belongs to the Special Issue Advances in Computational and Applied Mathematics)
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15 pages, 4001 KiB  
Article
On the Stability of Convection in a Non-Newtonian Vertical Fluid Layer in the Presence of Gold Nanoparticles: Drug Agent for Thermotherapy
by Khaled S. Mekheimer, Bangalore M. Shankar, Shaimaa F. Ramadan, Hosahalli E. Mallik and Mohamed S. Mohamed
Mathematics 2021, 9(11), 1302; https://0-doi-org.brum.beds.ac.uk/10.3390/math9111302 - 06 Jun 2021
Cited by 16 | Viewed by 2263
Abstract
We consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due [...] Read more.
We consider the effect of gold nanoparticles on the stability properties of convection in a vertical fluid layer saturated by a Jeffreys fluid. The vertical boundaries are rigid and hold at uniform but different temperatures. Brownian diffusion and thermophoresis effects are considered. Due to numerous applications in the biomedical industry, such a study is essential. The linear stability is investigated through the normal mode disturbances. The resulting stability problem is an eighth-order ordinary differential complex eigenvalue problem that is solved numerically using the Chebyshev collection method. Its solution provides the neutral stability curves, defining the threshold of linear instability, and the critical parameters at the onset of instability are determined for various values of control parameters. The results for Newtonian fluid and second-grade fluid are delineated as particular cases from the present study. It is shown that the Newtonian fluid has a more stabilizing effect than the second-grade and the Jeffreys fluids in the presence of gold nanoparticles and, Jeffreys fluid is the least stable. Full article
(This article belongs to the Special Issue Advances in Computational and Applied Mathematics)
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26 pages, 2083 KiB  
Article
Anomaly Detection in Multichannel Data Using Sparse Representation in RADWT Frames
by Daniela De Canditiis and Italia De Feis
Mathematics 2021, 9(11), 1288; https://0-doi-org.brum.beds.ac.uk/10.3390/math9111288 - 03 Jun 2021
Cited by 2 | Viewed by 2095
Abstract
We introduce a new methodology for anomaly detection (AD) in multichannel fast oscillating signals based on nonparametric penalized regression. Assuming the signals share similar shapes and characteristics, the estimation procedures are based on the use of the Rational-Dilation Wavelet Transform (RADWT), equipped with [...] Read more.
We introduce a new methodology for anomaly detection (AD) in multichannel fast oscillating signals based on nonparametric penalized regression. Assuming the signals share similar shapes and characteristics, the estimation procedures are based on the use of the Rational-Dilation Wavelet Transform (RADWT), equipped with a tunable Q-factor able to provide sparse representations of functions with different oscillations persistence. Under the standard hypothesis of Gaussian additive noise, we model the signals by the RADWT and the anomalies as additive in each signal. Then we perform AD imposing a double penalty on the multiple regression model we obtained, promoting group sparsity both on the regression coefficients and on the anomalies. The first constraint preserves a common structure on the underlying signal components; the second one aims to identify the presence/absence of anomalies. Numerical experiments show the performance of the proposed method in different synthetic scenarios as well as in a real case. Full article
(This article belongs to the Special Issue Advances in Computational and Applied Mathematics)
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20 pages, 962 KiB  
Article
Solving 3-D Gray–Scott Systems with Variable Diffusion Coefficients on Surfaces by Closest Point Method with RBF-FD
by Marzieh Raei, Salvatore Cuomo, Giovanni Colecchia and Gerardo Severino
Mathematics 2021, 9(9), 924; https://0-doi-org.brum.beds.ac.uk/10.3390/math9090924 - 21 Apr 2021
Cited by 1 | Viewed by 1833
Abstract
The Gray–Scott (GS) model is a non-linear system of equations generally adopted to describe reaction–diffusion dynamics. In this paper, we discuss a numerical scheme for solving the GS system. The diffusion coefficients of the model are on surfaces and they depend on space [...] Read more.
The Gray–Scott (GS) model is a non-linear system of equations generally adopted to describe reaction–diffusion dynamics. In this paper, we discuss a numerical scheme for solving the GS system. The diffusion coefficients of the model are on surfaces and they depend on space and time. In this regard, we first adopt an implicit difference stepping method to semi-discretize the model in the time direction. Then, we implement a hybrid advanced meshless method for model discretization. In this way, we solve the GS problem with a radial basis function–finite difference (RBF-FD) algorithm combined with the closest point method (CPM). Moreover, we design a predictor–corrector algorithm to deal with the non-linear terms of this dynamic. In a practical example, we show the spot and stripe patterns with a given initial condition. Finally, we experimentally prove that the presented method provides benefits in terms of accuracy and performance for the GS system’s numerical solution. Full article
(This article belongs to the Special Issue Advances in Computational and Applied Mathematics)
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