Abstract Graphs are a basic tool in modern data representation. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological constructions can be used to gain information otherwise concealed by the low-dimensional nature of graphs. We do this by extending previous work in homological persistence, and proposing novel graph-theoretical constructions. Beyond cliques, we use independent sets, neighborhoods, enclaveless sets and a Ramsey-inspired extended persistence.
{"title":"Topological graph persistence","authors":"Mattia G. Bergomi, M. Ferri, Lorenzo Zuffi","doi":"10.2478/caim-2020-0005","DOIUrl":"https://doi.org/10.2478/caim-2020-0005","url":null,"abstract":"Abstract Graphs are a basic tool in modern data representation. The richness of the topological information contained in a graph goes far beyond its mere interpretation as a one-dimensional simplicial complex. We show how topological constructions can be used to gain information otherwise concealed by the low-dimensional nature of graphs. We do this by extending previous work in homological persistence, and proposing novel graph-theoretical constructions. Beyond cliques, we use independent sets, neighborhoods, enclaveless sets and a Ramsey-inspired extended persistence.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"11 1","pages":"72 - 87"},"PeriodicalIF":1.3,"publicationDate":"2017-07-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41419164","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 address a Boundary Integral Equation (BIE) approach for the analysis of gas dissipation in near-vacuum for Micro Electro Mechanical Systems (MEMS). Inspired by an analogy with the radiosity equation in computer graphics, we discuss an efficient way to compute the visible domain of integration. Moreover, we tackle the issue of near singular integrals by developing a set of analytical formulas for planar polyhedral domains. Finally a validation with experimental results taken from the literature is presented.
{"title":"Integral equations for free-molecule ow in MEMS: recent advancements","authors":"P. Fedeli, A. Frangi","doi":"10.1515/caim-2017-0004","DOIUrl":"https://doi.org/10.1515/caim-2017-0004","url":null,"abstract":"Abstract We address a Boundary Integral Equation (BIE) approach for the analysis of gas dissipation in near-vacuum for Micro Electro Mechanical Systems (MEMS). Inspired by an analogy with the radiosity equation in computer graphics, we discuss an efficient way to compute the visible domain of integration. Moreover, we tackle the issue of near singular integrals by developing a set of analytical formulas for planar polyhedral domains. Finally a validation with experimental results taken from the literature is presented.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"8 1","pages":"67 - 80"},"PeriodicalIF":1.3,"publicationDate":"2017-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44724819","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 Biological systems are typically formed by different cell phenotypes, characterized by specific biological properties and behaviors. In particular, cells are able to undergo phenotypic transitions (i.e., activation or differentiation) upon internal or external stimuli. In order to take these phenomena into account, we here propose a modelling framework in which cell ensembles can be described collectively (i.e., through a distributed mass density) or individually (i.e., as a group of pointwise/concentrated particles) according to their biological determinants. A set of suitable rules involving the introduction of a cell shape function then defines a coherent procedure to model cell activation mechanisms, which imply a switch between the two mathematical representations. The theoretical environment describing cell transition is then enriched by including cell migratory dynamics and duplication/apoptotic processes, as well as the kinetics of selected diffusing chemicals inuencing the system evolution. Remarkably, our approach provides consistency of the same modeling framework across all types of cell representation, as it is suitable to cope with the often ambiguous translation of individual cell arguments (i.e., cell dimensions and interaction radii) into collective cell descriptions. Biologically relevant numerical realizations are also presented: in particular, they deal with phenotypic transitions within cell colonies and with the growth of a tumor spheroid. These phenomena constitute biological systems particularly suitable to assess the advantages of the proposed model and to analyze the role on cell dynamics both of relevant parameters and of the specific form given to the cell shape function.
{"title":"A coherent modeling procedure to describe cell activation in biological systems","authors":"M. Scianna, A. Colombi","doi":"10.1515/caim-2017-0001","DOIUrl":"https://doi.org/10.1515/caim-2017-0001","url":null,"abstract":"Abstract Biological systems are typically formed by different cell phenotypes, characterized by specific biological properties and behaviors. In particular, cells are able to undergo phenotypic transitions (i.e., activation or differentiation) upon internal or external stimuli. In order to take these phenomena into account, we here propose a modelling framework in which cell ensembles can be described collectively (i.e., through a distributed mass density) or individually (i.e., as a group of pointwise/concentrated particles) according to their biological determinants. A set of suitable rules involving the introduction of a cell shape function then defines a coherent procedure to model cell activation mechanisms, which imply a switch between the two mathematical representations. The theoretical environment describing cell transition is then enriched by including cell migratory dynamics and duplication/apoptotic processes, as well as the kinetics of selected diffusing chemicals inuencing the system evolution. Remarkably, our approach provides consistency of the same modeling framework across all types of cell representation, as it is suitable to cope with the often ambiguous translation of individual cell arguments (i.e., cell dimensions and interaction radii) into collective cell descriptions. Biologically relevant numerical realizations are also presented: in particular, they deal with phenotypic transitions within cell colonies and with the growth of a tumor spheroid. These phenomena constitute biological systems particularly suitable to assess the advantages of the proposed model and to analyze the role on cell dynamics both of relevant parameters and of the specific form given to the cell shape function.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"8 1","pages":"1 - 22"},"PeriodicalIF":1.3,"publicationDate":"2017-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48065958","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 study the chemical reaction of inhibition, determine the appropriate parameter ε for the application of Tihonov's Theorem, compute explicitly the equations of the center manifold of the system and find sufficient conditions to guarantee that in the phase space the curves which relate the behavior of the complexes to the substrates by means of the tQSSA are asymptotically equivalent to the center manifold of the system. Some numerical results are discussed.
{"title":"Tihonov theory and center manifolds for inhibitory mechanisms in enzyme kinetics","authors":"A. M. Bersani, A. Borri, A. Milanesi, P. Vellucci","doi":"10.1515/caim-2017-0005","DOIUrl":"https://doi.org/10.1515/caim-2017-0005","url":null,"abstract":"Abstract In this paper we study the chemical reaction of inhibition, determine the appropriate parameter ε for the application of Tihonov's Theorem, compute explicitly the equations of the center manifold of the system and find sufficient conditions to guarantee that in the phase space the curves which relate the behavior of the complexes to the substrates by means of the tQSSA are asymptotically equivalent to the center manifold of the system. Some numerical results are discussed.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"8 1","pages":"102 - 81"},"PeriodicalIF":1.3,"publicationDate":"2017-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/caim-2017-0005","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42423768","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 a kinetic BGK-model for a rarefied polyatomic gas, based on a molecular structure of discrete internal energy levels, an asymptotic Chapman-Enskog procedure is developed in the asymptotic continuum limit in order to derive consistent fluid-dynamic equations for macroscopic fields at Navier-Stokes level. In this way, the model allows to treat the gas as a mixture of mono-atomic species. Explicit expressions are given not only for dynamical pressure, but also for shear stress, diffusion velocities, and heat flux. The analysis is shown to deal properly also with a mixture of reactive gases, endowed for simplicity with translational degrees of freedom only, in which frame analogous results can be achieved.
{"title":"Hydrodynamic limits of kinetic equations for polyatomic and reactive gases","authors":"M. Bisi, G. Spiga","doi":"10.1515/caim-2017-0002","DOIUrl":"https://doi.org/10.1515/caim-2017-0002","url":null,"abstract":"Abstract Starting from a kinetic BGK-model for a rarefied polyatomic gas, based on a molecular structure of discrete internal energy levels, an asymptotic Chapman-Enskog procedure is developed in the asymptotic continuum limit in order to derive consistent fluid-dynamic equations for macroscopic fields at Navier-Stokes level. In this way, the model allows to treat the gas as a mixture of mono-atomic species. Explicit expressions are given not only for dynamical pressure, but also for shear stress, diffusion velocities, and heat flux. The analysis is shown to deal properly also with a mixture of reactive gases, endowed for simplicity with translational degrees of freedom only, in which frame analogous results can be achieved.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"8 1","pages":"23 - 42"},"PeriodicalIF":1.3,"publicationDate":"2017-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/caim-2017-0002","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48818866","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 Time-dependent problems modeled by hyperbolic partial differential equations can be reformulated in terms of boundary integral equations and solved via the boundary element method. In this context, the analysis of damping phenomena that occur in many physics and engineering problems is a novelty. Starting from a recently developed energetic space-time weak formulation for 1D damped wave propagation problems rewritten in terms of boundary integral equations, we develop here an extension of the so-called energetic boundary element method for the 2D case. Several numerical benchmarks, whose numerical results confirm accuracy and stability of the proposed technique, already proved for the numerical treatment of undamped wave propagation problems in several dimensions and for the 1D damped case, are illustrated and discussed.
{"title":"Energetic BEM for the numerical analysis of 2D Dirichlet damped wave propagation exterior problems","authors":"A. Aimi, M. Diligenti, C. Guardasoni","doi":"10.1515/caim-2017-0006","DOIUrl":"https://doi.org/10.1515/caim-2017-0006","url":null,"abstract":"Abstract Time-dependent problems modeled by hyperbolic partial differential equations can be reformulated in terms of boundary integral equations and solved via the boundary element method. In this context, the analysis of damping phenomena that occur in many physics and engineering problems is a novelty. Starting from a recently developed energetic space-time weak formulation for 1D damped wave propagation problems rewritten in terms of boundary integral equations, we develop here an extension of the so-called energetic boundary element method for the 2D case. Several numerical benchmarks, whose numerical results confirm accuracy and stability of the proposed technique, already proved for the numerical treatment of undamped wave propagation problems in several dimensions and for the 1D damped case, are illustrated and discussed.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"8 1","pages":"103 - 127"},"PeriodicalIF":1.3,"publicationDate":"2017-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/caim-2017-0006","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44963751","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 present, in a framework of 1D-membrane Micro-Electro-Mechanical- Systems (MEMS) theory, a formalization of the problem of existence and uniqueness of a solution related to the membrane deformation u for electrostatic actuation in the steady- state case. In particular, we propose a new model in which the electric field magnitude E is proportional to the curvature of the membrane and, for it, we obtain results of existence by Schauder-Tychono's fixed point application and subsequently we establish conditions of uniqueness. Finally, some numerical tests have been carried out to further support the analytical results.
{"title":"Electrostatic field in terms of geometric curvature in membrane MEMS devices","authors":"P. di Barba, L. Fattorusso, M. Versaci","doi":"10.1515/caim-2017-0009","DOIUrl":"https://doi.org/10.1515/caim-2017-0009","url":null,"abstract":"Abstract In this paper we present, in a framework of 1D-membrane Micro-Electro-Mechanical- Systems (MEMS) theory, a formalization of the problem of existence and uniqueness of a solution related to the membrane deformation u for electrostatic actuation in the steady- state case. In particular, we propose a new model in which the electric field magnitude E is proportional to the curvature of the membrane and, for it, we obtain results of existence by Schauder-Tychono's fixed point application and subsequently we establish conditions of uniqueness. Finally, some numerical tests have been carried out to further support the analytical results.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"8 1","pages":"165 - 184"},"PeriodicalIF":1.3,"publicationDate":"2017-03-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43743388","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 consider the Godunov numerical method to the phase-transition trafic model, proposed in [1], by Colombo, Marcellini, and Rascle. Numerical tests are shown to prove the validity of the method. Moreover we highlight the differences between such model and the one proposed in [2], by Blandin, Work, Goatin, Piccoli, and Bayen.
{"title":"The Godunov method for a 2-phase model","authors":"M. Garavello, F. Marcellini","doi":"10.1515/caim-2017-0008","DOIUrl":"https://doi.org/10.1515/caim-2017-0008","url":null,"abstract":"Abstract We consider the Godunov numerical method to the phase-transition trafic model, proposed in [1], by Colombo, Marcellini, and Rascle. Numerical tests are shown to prove the validity of the method. Moreover we highlight the differences between such model and the one proposed in [2], by Blandin, Work, Goatin, Piccoli, and Bayen.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"8 1","pages":"149 - 164"},"PeriodicalIF":1.3,"publicationDate":"2017-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42137306","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 present a comparison of the forecasting performances of three Dynamic Factor Models on a large monthly data panel of macroeconomic and financial time series for the UE economy. The first model relies on static principal-component and was introduced by Stock and Watson (2002a, b). The second is based on generalized principal components and it was introduced by Forni, Hallin, Lippi and Reichlin (2000, 2005). The last model has been recently proposed by Forni, Hallin, Lippi and Zaffaroni (2015, 2016). The data panel is split into two parts: the calibration sample, from February 1986 to December 2000, is used to select the most performing specification for each class of models in a in- sample environment, and the proper sample, from January 2001 to November 2015, is used to compare the performances of the selected models in an out-of-sample environment. The metholodogical approach is analogous to Forni, Giovannelli, Lippi and Soccorsi (2016), but also the size of the rolling window is empirically estimated in the calibration process to achieve more robustness. We find that, on the proper sample, the last model is the most performing for the Inflation. However, mixed evidencies appear over the proper sample for the Industrial Production.
{"title":"A forecasting performance comparison of dynamic factor models based on static and dynamic methods","authors":"F. Marra","doi":"10.2139/ssrn.2912916","DOIUrl":"https://doi.org/10.2139/ssrn.2912916","url":null,"abstract":"Abstract We present a comparison of the forecasting performances of three Dynamic Factor Models on a large monthly data panel of macroeconomic and financial time series for the UE economy. The first model relies on static principal-component and was introduced by Stock and Watson (2002a, b). The second is based on generalized principal components and it was introduced by Forni, Hallin, Lippi and Reichlin (2000, 2005). The last model has been recently proposed by Forni, Hallin, Lippi and Zaffaroni (2015, 2016). The data panel is split into two parts: the calibration sample, from February 1986 to December 2000, is used to select the most performing specification for each class of models in a in- sample environment, and the proper sample, from January 2001 to November 2015, is used to compare the performances of the selected models in an out-of-sample environment. The metholodogical approach is analogous to Forni, Giovannelli, Lippi and Soccorsi (2016), but also the size of the rolling window is empirically estimated in the calibration process to achieve more robustness. We find that, on the proper sample, the last model is the most performing for the Inflation. However, mixed evidencies appear over the proper sample for the Industrial Production.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"8 1","pages":"43 - 66"},"PeriodicalIF":1.3,"publicationDate":"2017-02-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43725047","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}
G. Stabile, Saddam Hijazi, A. Mola, S. Lorenzi, G. Rozza
Abstract Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible ow around a circular cylinder is presented in this work. The ROM is built performing a Galerkin projection of the governing equations onto a lower dimensional space. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pres- sure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) the projection of the Governing equations (momentum equation and Poisson equation for pressure) performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework. The accuracy of the reduced order model is assessed against full order results.
{"title":"POD-Galerkin reduced order methods for CFD using Finite Volume Discretisation: vortex shedding around a circular cylinder","authors":"G. Stabile, Saddam Hijazi, A. Mola, S. Lorenzi, G. Rozza","doi":"10.1515/caim-2017-0011","DOIUrl":"https://doi.org/10.1515/caim-2017-0011","url":null,"abstract":"Abstract Vortex shedding around circular cylinders is a well known and studied phenomenon that appears in many engineering fields. A Reduced Order Model (ROM) of the incompressible ow around a circular cylinder is presented in this work. The ROM is built performing a Galerkin projection of the governing equations onto a lower dimensional space. The reduced basis space is generated using a Proper Orthogonal Decomposition (POD) approach. In particular the focus is into (i) the correct reproduction of the pres- sure field, that in case of the vortex shedding phenomenon, is of primary importance for the calculation of the drag and lift coefficients; (ii) the projection of the Governing equations (momentum equation and Poisson equation for pressure) performed onto different reduced basis space for velocity and pressure, respectively; (iii) all the relevant modifications necessary to adapt standard finite element POD-Galerkin methods to a finite volume framework. The accuracy of the reduced order model is assessed against full order results.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"8 1","pages":"210 - 236"},"PeriodicalIF":1.3,"publicationDate":"2017-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1515/caim-2017-0011","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45946388","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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