A. Aimi, L. Desiderio, M. Diligenti, C. Guardasoni
Abstract Starting from a recently developed energetic space-time weak formulation of the Boundary Integral Equations related to scalar wave propagation problems, in this paper we focus for the first time on the 2D elastodynamic extension of the above wave propagation analysis. In particular, we consider elastodynamic scattering problems by open arcs, with vanishing initial and Dirichlet boundary conditions and we assess the efficiency and accuracy of the proposed method, on the basis of numerical results obtained for benchmark problems having available analytical solution.
{"title":"Application of Energetic BEM to 2D Elastodynamic Soft Scattering Problems","authors":"A. Aimi, L. Desiderio, M. Diligenti, C. Guardasoni","doi":"10.1515/caim-2019-0020","DOIUrl":"https://doi.org/10.1515/caim-2019-0020","url":null,"abstract":"Abstract Starting from a recently developed energetic space-time weak formulation of the Boundary Integral Equations related to scalar wave propagation problems, in this paper we focus for the first time on the 2D elastodynamic extension of the above wave propagation analysis. In particular, we consider elastodynamic scattering problems by open arcs, with vanishing initial and Dirichlet boundary conditions and we assess the efficiency and accuracy of the proposed method, on the basis of numerical results obtained for benchmark problems having available analytical solution.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44189619","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Chebyshev polynomials are traditionally applied to the approximation theory where are used in polynomial interpolation and also in the study of di erential equations, in particular in some special cases of Sturm-Liouville di erential equation. Many of the operational techniques presented, by using suitable integral transforms, via a symbolic approach to the Laplace transform, allow us to introduce polynomials recognized belonging to the families of Chebyshev of multi-dimensional type. The non-standard approach come out from the theory of multi-index Hermite polynomials, in particular by using the concepts and the related formalism of translation operators.
{"title":"Multi-Dimensional Chebyshev Polynomials: A Non-Conventional Approach","authors":"C. Cesarano","doi":"10.1515/caim-2019-0008","DOIUrl":"https://doi.org/10.1515/caim-2019-0008","url":null,"abstract":"Abstract Chebyshev polynomials are traditionally applied to the approximation theory where are used in polynomial interpolation and also in the study of di erential equations, in particular in some special cases of Sturm-Liouville di erential equation. Many of the operational techniques presented, by using suitable integral transforms, via a symbolic approach to the Laplace transform, allow us to introduce polynomials recognized belonging to the families of Chebyshev of multi-dimensional type. The non-standard approach come out from the theory of multi-index Hermite polynomials, in particular by using the concepts and the related formalism of translation operators.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47649143","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Starting from the heat equation, we discuss some fractional generalizations of various forms. We propose a method useful for analytic or numerical solutions. By using Hermite polynomials of higher and fractional order, we present some operational techniques to find general solutions of extended form to d'Alembert and Fourier equations. We also show that the solutions of the generalized equations discussed here can be expressed in terms of Hermite-based functions.
{"title":"Generalized special functions in the description of fractional diffusive equations","authors":"C. Cesarano","doi":"10.1515/caim-2019-0010","DOIUrl":"https://doi.org/10.1515/caim-2019-0010","url":null,"abstract":"Abstract Starting from the heat equation, we discuss some fractional generalizations of various forms. We propose a method useful for analytic or numerical solutions. By using Hermite polynomials of higher and fractional order, we present some operational techniques to find general solutions of extended form to d'Alembert and Fourier equations. We also show that the solutions of the generalized equations discussed here can be expressed in terms of Hermite-based functions.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42304422","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper we propose a new algorithm to optimize the parameters of a compartmental problem describing tumor hypoxia. The method is based on a multivariate Newton approach, with Tikhonov regularization, and can be easily applied to data with diverse statistical distributions. Here we simulate [18F]−fluoromisonidazole Positron Emission Tomography dynamic data of hypoxia of a neck tumor and describe the tracer flow inside tumor with a two-compartments compartmental model. We perform optimization on the parameters of the model via the proposed Multivariate Regularized Newton method and validate it against results obtained with a standard Levenberg-Marquardt approach. The proposed algorithm returns parameters that are closer to the ground truth while preserving the statistical distribution of the data.
{"title":"Multivariate Regularized Newton and Levenberg-Marquardt methods: a comparison on synthetic data of tumor hypoxia in a kinetic framework","authors":"Sara Garbarino, G. Caviglia","doi":"10.2478/caim-2019-0006","DOIUrl":"https://doi.org/10.2478/caim-2019-0006","url":null,"abstract":"Abstract In this paper we propose a new algorithm to optimize the parameters of a compartmental problem describing tumor hypoxia. The method is based on a multivariate Newton approach, with Tikhonov regularization, and can be easily applied to data with diverse statistical distributions. Here we simulate [18F]−fluoromisonidazole Positron Emission Tomography dynamic data of hypoxia of a neck tumor and describe the tracer flow inside tumor with a two-compartments compartmental model. We perform optimization on the parameters of the model via the proposed Multivariate Regularized Newton method and validate it against results obtained with a standard Levenberg-Marquardt approach. The proposed algorithm returns parameters that are closer to the ground truth while preserving the statistical distribution of the data.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48608953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Particle Swarm Optimization is an evolutionary optimization algorithm, largely studied during the years: analysis of convergence, determination of the optimal coefficients, hybridization of the original algorithm and also the determination of the best relationship structure between the swarm elements (topology) have been investigated largely. Unfortunately, all these studies have been produced separately, and the same coefficients, derived for the original topology of the algorithm, have been always applied. The intent of this paper is to identify the best set of coefficients for different topological structures. A large suite of objective functions are considered and the best compromise coefficients are identified for each topology. Results are finally compared on the base of a practical ship design application.
{"title":"Effect of parameter selection on different topological structures for Particle Swarm Optimization algorithm","authors":"D. Peri","doi":"10.2478/caim-2019-0021","DOIUrl":"https://doi.org/10.2478/caim-2019-0021","url":null,"abstract":"Abstract Particle Swarm Optimization is an evolutionary optimization algorithm, largely studied during the years: analysis of convergence, determination of the optimal coefficients, hybridization of the original algorithm and also the determination of the best relationship structure between the swarm elements (topology) have been investigated largely. Unfortunately, all these studies have been produced separately, and the same coefficients, derived for the original topology of the algorithm, have been always applied. The intent of this paper is to identify the best set of coefficients for different topological structures. A large suite of objective functions are considered and the best compromise coefficients are identified for each topology. Results are finally compared on the base of a practical ship design application.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42361525","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The invasive capability is fundamental in determining the malignancy of a solid tumor. In particular, tumor invasion fronts are characterized by different morphologies, which result both from cell-based processes (such as cell elasticity, adhesive properties and motility) and from subcellular molecular dynamics (such as growth factor internalization, ECM protein digestion and MMP secretion). Of particular relevance is the development of tumors with unstable fingered morphologies: they are in fact more aggressive and hard to be treated than smoother ones as, even if their invasive depth is limited, they are difficult to be surgically removed. The phenomenon of malignant fingering has been reproduced with several mathematical approaches. In this respect, we here present a qualitative comparison between the results obtained by an individual cell-based model (an extended version of the cellular Potts model) and by a measure-based theoretic method. In particular, we show that in both cases a fundamental role in finger extension is played by intercellular adhesive forces and taxis-like migration.
{"title":"Extension of tumor fingers: A comparison between an individual-cell based model and a measure theoretic approach","authors":"M. Scianna, A. Colombi","doi":"10.2478/caim-2019-0007","DOIUrl":"https://doi.org/10.2478/caim-2019-0007","url":null,"abstract":"Abstract The invasive capability is fundamental in determining the malignancy of a solid tumor. In particular, tumor invasion fronts are characterized by different morphologies, which result both from cell-based processes (such as cell elasticity, adhesive properties and motility) and from subcellular molecular dynamics (such as growth factor internalization, ECM protein digestion and MMP secretion). Of particular relevance is the development of tumors with unstable fingered morphologies: they are in fact more aggressive and hard to be treated than smoother ones as, even if their invasive depth is limited, they are difficult to be surgically removed. The phenomenon of malignant fingering has been reproduced with several mathematical approaches. In this respect, we here present a qualitative comparison between the results obtained by an individual cell-based model (an extended version of the cellular Potts model) and by a measure-based theoretic method. In particular, we show that in both cases a fundamental role in finger extension is played by intercellular adhesive forces and taxis-like migration.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41851501","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract A New graph distance concept introduced for certain coding techniques helped in their design and analysis as in the case of distance-preserving mappings and spectral shaping codes. A graph theoretic construction, mapping binary sequences to permutation sequences and inspired from the k-cube graph has reached the upper bound on the sum of the distances for certain values of the length of the permutation sequence. The new introduced distance concept in the k-cube graph helped better understanding and analyzing for the first time the concept of distance-reducing mappings. A combination of distance and the index-permutation graph concepts helped uncover and verify certain properties of spectral null codes, which were previously difficult to analyze.
{"title":"New Distance Concept and Graph Theory Approach for Certain Coding Techniques Design and Analysis","authors":"K. Ouahada, H. C. Ferreira","doi":"10.1515/caim-2019-0012","DOIUrl":"https://doi.org/10.1515/caim-2019-0012","url":null,"abstract":"Abstract A New graph distance concept introduced for certain coding techniques helped in their design and analysis as in the case of distance-preserving mappings and spectral shaping codes. A graph theoretic construction, mapping binary sequences to permutation sequences and inspired from the k-cube graph has reached the upper bound on the sum of the distances for certain values of the length of the permutation sequence. The new introduced distance concept in the k-cube graph helped better understanding and analyzing for the first time the concept of distance-reducing mappings. A combination of distance and the index-permutation graph concepts helped uncover and verify certain properties of spectral null codes, which were previously difficult to analyze.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49663613","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract We summarize features and results on the problem of the existence of Ground States for the Nonlinear Schrödinger Equation on doubly-periodic metric graphs. We extend the results known for the two–dimensional square grid graph to the honeycomb, made of infinitely-many identical hexagons. Specifically, we show how the coexistence between one–dimensional and two–dimensional scales in the graph structure leads to the emergence of threshold phenomena known as dimensional crossover.
{"title":"Quantum graphs and dimensional crossover: the honeycomb","authors":"R. Adami, Simone Dovetta, Alice Ruighi","doi":"10.2478/caim-2019-0016","DOIUrl":"https://doi.org/10.2478/caim-2019-0016","url":null,"abstract":"Abstract We summarize features and results on the problem of the existence of Ground States for the Nonlinear Schrödinger Equation on doubly-periodic metric graphs. We extend the results known for the two–dimensional square grid graph to the honeycomb, made of infinitely-many identical hexagons. Specifically, we show how the coexistence between one–dimensional and two–dimensional scales in the graph structure leads to the emergence of threshold phenomena known as dimensional crossover.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47472599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Rheumatoid arthritis is an autoimmune disease of unknown etiology that manifests as a persistent inflammatory synovitis and eventually destroys the joints. The immune system recognizes synovial cells as not self and consequently causes lymphocyte and antibody proliferation that is promoted by the pro-inflammatory cytokines, the most significant being tumor necrosis factor TNF-α. In the treatment of rheumatoid arthritis either monoclonal antibodies or soluble receptors are used to neutralize the TNF-α bioactivity, such as sTNFR2, Etanercept and Infliximab. In [M. Jit et al. Rheumatology 2005;44:323-331] a mathematical model that represents the TNF-α dynamics in the inflamed synovial joint within which locally produced TNF-α can bind to cell-surface receptors was proposed. It consists of four coupled ordinary differential equations, that were integrated numerically assuming a range of estimates of the key parameters. In this paper we complement the previous work by determining the general solution of those equations for specific conditions on the parameters. Then we characterize the behavior of TNF-α in the presence of different inhibitors and also evaluate the inhibitors effectiveness in the treatment of rheumatoid arthritis.
{"title":"Solution of a mathematical model for the treatment of rheumatoid arthritis","authors":"L. Matteucci, M. Nucci","doi":"10.2478/caim-2019-0003","DOIUrl":"https://doi.org/10.2478/caim-2019-0003","url":null,"abstract":"Abstract Rheumatoid arthritis is an autoimmune disease of unknown etiology that manifests as a persistent inflammatory synovitis and eventually destroys the joints. The immune system recognizes synovial cells as not self and consequently causes lymphocyte and antibody proliferation that is promoted by the pro-inflammatory cytokines, the most significant being tumor necrosis factor TNF-α. In the treatment of rheumatoid arthritis either monoclonal antibodies or soluble receptors are used to neutralize the TNF-α bioactivity, such as sTNFR2, Etanercept and Infliximab. In [M. Jit et al. Rheumatology 2005;44:323-331] a mathematical model that represents the TNF-α dynamics in the inflamed synovial joint within which locally produced TNF-α can bind to cell-surface receptors was proposed. It consists of four coupled ordinary differential equations, that were integrated numerically assuming a range of estimates of the key parameters. In this paper we complement the previous work by determining the general solution of those equations for specific conditions on the parameters. Then we characterize the behavior of TNF-α in the presence of different inhibitors and also evaluate the inhibitors effectiveness in the treatment of rheumatoid arthritis.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69187736","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Power-line channel is considered to be a very hostile channel compared to other channels in view of the different types of noise that could exist. Therefore, the choice of the error correcting code and the modulation scheme can play a big role in combating the noise in such a channel. M -FSK modulation has shown its robustness for such a type of channel. Two frequency mappings techniques are presented in this paper. In the first technique, M orthogonal frequencies are arranged in sequences based on the value and the position of permutation symbols, while in the second technique, the frequencies are rearranged based on the sign changes of the Walsh-Hadamard transform (WHT). The obtained M-FSK modulation is combined to codes based on Viterbi decoding algorithms since Viterbi decoder is considered to be the maximum-likelihood decoding algorithm for convolutional codes and codes with state machine representation. A mathematical approach and implementation of frequency mappings is introduced to investigate the performance of the new designed communication system in the presence of permanent frequency disturbances, also known as narrow-band interference (NBI), such as those encountered in power line communications (PLC) channel.
{"title":"Mathematical Approach and Implementation of Frequency Mapping Techniques in Power-Line Communications Channel","authors":"T. Lukusa, K. Ouahada, H. C. Ferreira","doi":"10.2478/caim-2019-0015","DOIUrl":"https://doi.org/10.2478/caim-2019-0015","url":null,"abstract":"Abstract Power-line channel is considered to be a very hostile channel compared to other channels in view of the different types of noise that could exist. Therefore, the choice of the error correcting code and the modulation scheme can play a big role in combating the noise in such a channel. M -FSK modulation has shown its robustness for such a type of channel. Two frequency mappings techniques are presented in this paper. In the first technique, M orthogonal frequencies are arranged in sequences based on the value and the position of permutation symbols, while in the second technique, the frequencies are rearranged based on the sign changes of the Walsh-Hadamard transform (WHT). The obtained M-FSK modulation is combined to codes based on Viterbi decoding algorithms since Viterbi decoder is considered to be the maximum-likelihood decoding algorithm for convolutional codes and codes with state machine representation. A mathematical approach and implementation of frequency mappings is introduced to investigate the performance of the new designed communication system in the presence of permanent frequency disturbances, also known as narrow-band interference (NBI), such as those encountered in power line communications (PLC) channel.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":null,"pages":null},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48813914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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