Pub Date : 2021-01-01DOI: 10.1016/b978-0-12-819880-3.00003-2
{"title":"Copyright","authors":"","doi":"10.1016/b978-0-12-819880-3.00003-2","DOIUrl":"https://doi.org/10.1016/b978-0-12-819880-3.00003-2","url":null,"abstract":"","PeriodicalId":54732,"journal":{"name":"Networks and Heterogeneous Media","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78581754","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pedro Aceves-Sanchez, Benjamin Aymard, Diane Peurichard, Pol Kennel, Anne Lorsignol, Franck Plouraboué, Louis Casteilla, Pierre Degond
We propose a new model for the emergence of blood capillary networks. We assimilate the tissue and extra cellular matrix as a porous medium, using Darcy's law for describing both blood and interstitial fluid flows. Oxygen obeys a convection-diffusion-reaction equation describing advection by the blood, diffusion and consumption by the tissue. Discrete agents named capillary elements and modelling groups of endothelial cells are created or deleted according to different rules involving the oxygen concentration gradient, the blood velocity, the sheer stress or the capillary element density. Once created, a capillary element locally enhances the hydraulic conductivity matrix, contributing to a local increase of the blood velocity and oxygen flow. No connectivity between the capillary elements is imposed. The coupling between blood, oxygen flow and capillary elements provides a positive feedback mechanism which triggers the emergence of a network of channels of high hydraulic conductivity which we identify as new blood capillaries. We provide two different, biologically relevant geometrical settings and numerically analyze the influence of each of the capillary creation mechanism in detail. All mechanisms seem to concur towards a harmonious network but the most important ones are those involving oxygen gradient and sheer stress. A detailed discussion of this model with respect to the literature and its potential future developments concludes the paper.
{"title":"A new model for the emergence of blood capillary networks","authors":"Pedro Aceves-Sanchez, Benjamin Aymard, Diane Peurichard, Pol Kennel, Anne Lorsignol, Franck Plouraboué, Louis Casteilla, Pierre Degond","doi":"10.3934/nhm.2021001","DOIUrl":"https://doi.org/10.3934/nhm.2021001","url":null,"abstract":"We propose a new model for the emergence of blood capillary networks. We assimilate the tissue and extra cellular matrix as a porous medium, using Darcy's law for describing both blood and interstitial fluid flows. Oxygen obeys a convection-diffusion-reaction equation describing advection by the blood, diffusion and consumption by the tissue. Discrete agents named capillary elements and modelling groups of endothelial cells are created or deleted according to different rules involving the oxygen concentration gradient, the blood velocity, the sheer stress or the capillary element density. Once created, a capillary element locally enhances the hydraulic conductivity matrix, contributing to a local increase of the blood velocity and oxygen flow. No connectivity between the capillary elements is imposed. The coupling between blood, oxygen flow and capillary elements provides a positive feedback mechanism which triggers the emergence of a network of channels of high hydraulic conductivity which we identify as new blood capillaries. We provide two different, biologically relevant geometrical settings and numerically analyze the influence of each of the capillary creation mechanism in detail. All mechanisms seem to concur towards a harmonious network but the most important ones are those involving oxygen gradient and sheer stress. A detailed discussion of this model with respect to the literature and its potential future developments concludes the paper.","PeriodicalId":54732,"journal":{"name":"Networks and Heterogeneous Media","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2020-12-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138528261","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Functional connectivity in human brain can be represented as a network using electroencephalography (EEG) signals. Network representation of EEG time series can be an efficient vehicle to understand the underlying mechanisms of brain function. Brain functional networks whose nodes are brain regions and edges correspond to functional links between them are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which graph theory metrics are sex dependent. To this end, EEGs from 24 healthy female subjects and 21 healthy male subjects were recorded in eyes-closed resting state conditions. The connectivity matrices were extracted using correlation analysis and were further binarized to obtain binary functional networks. Global and local efficiency measures as graph theory metrics were computed for the extracted networks. We found that male brains have significantly greater global efficiency (i.e., global communicability of the network) across all frequency bands for a wide range of cost values in both hemispheres. Furthermore, for a range of cost values, female brains showed significantly greater right-hemispheric local efficiency (i.e., local connectivity) than male brains.
{"title":"EEG-based functional brain networks: hemispheric differences in males and females","authors":"M. Jalili","doi":"10.3934/NHM.2015.10.223","DOIUrl":"https://doi.org/10.3934/NHM.2015.10.223","url":null,"abstract":"Functional connectivity in human brain can be represented as a network using electroencephalography (EEG) signals. Network representation of EEG time series can be an efficient vehicle to understand the underlying mechanisms of brain function. Brain functional networks whose nodes are brain regions and edges correspond to functional links between them are characterized by neurobiologically meaningful graph theory metrics. This study investigates the degree to which graph theory metrics are sex dependent. To this end, EEGs from 24 healthy female subjects and 21 healthy male subjects were recorded in eyes-closed resting state conditions. The connectivity matrices were extracted using correlation analysis and were further binarized to obtain binary functional networks. Global and local efficiency measures as graph theory metrics were computed for the extracted networks. We found that male brains have significantly greater global efficiency (i.e., global communicability of the network) across all frequency bands for a wide range of cost values in both hemispheres. Furthermore, for a range of cost values, female brains showed significantly greater right-hemispheric local efficiency (i.e., local connectivity) than male brains.","PeriodicalId":54732,"journal":{"name":"Networks and Heterogeneous Media","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70227914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
L. Pérez, J. Bragard, H. Mancini, J. Gallas, A. M. Cabanas, O. Suarez, D. Laroze
We report a systematic investigation of the magnetic anisotropy effects observed in the deterministic spin dynamics of a magnetic particle in the presence of a time-dependent magnetic field. The system is modeled by the Landau-Lifshitz-Gilbert equation and the magnetic field consists of two terms, a constant term and a term involving a harmonic time modulation. We consider a general quadratic anisotropic energy with three different preferential axes. The dynamical behavior of the system is represented in Lyapunov phase diagrams, and by calculating bifurcation diagrams, Poincare sections and Fourier spectra. We find an intricate distribution of shrimp-shaped regular island embedded in wide chaotic phases. Anisotropy effects are found to play a key role in defining the symmetries of regular and chaotic stability phases.
{"title":"Effect of anisotropies on the magnetization dynamics","authors":"L. Pérez, J. Bragard, H. Mancini, J. Gallas, A. M. Cabanas, O. Suarez, D. Laroze","doi":"10.3934/NHM.2015.10.209","DOIUrl":"https://doi.org/10.3934/NHM.2015.10.209","url":null,"abstract":"We report a systematic investigation of the magnetic anisotropy effects \u0000observed in the deterministic spin dynamics of a magnetic particle in the \u0000presence of a time-dependent magnetic field. \u0000The system is modeled by the Landau-Lifshitz-Gilbert equation and the \u0000magnetic field consists of two terms, \u0000a constant term and a term involving a harmonic time modulation. \u0000We consider a general quadratic anisotropic energy with three different \u0000preferential axes. \u0000The dynamical behavior of the system is represented in Lyapunov phase diagrams, \u0000and by calculating bifurcation diagrams, Poincare sections and \u0000Fourier spectra. \u0000We find an intricate distribution of shrimp-shaped regular island embedded \u0000in wide chaotic phases. \u0000Anisotropy effects are found to play a key role in defining the symmetries \u0000of regular and chaotic stability phases.","PeriodicalId":54732,"journal":{"name":"Networks and Heterogeneous Media","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2015-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70227811","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
G. Bastin, A. Bayen, C. D'apice, X. Litrico, B. Piccoli
1. Introduction: Management of canal networks at the age of information technology. With the miniaturization of sensors and their decreasing costs, the paradigm of instrumentation of the built infrastructure and the environment has now been underway for several years, leading to numerous successful and sometimes spectacular realizations such as the instrumentation of the Golden Gate with wireless sensors a few years ago. The convergence of communication, control and sensing on numerous platforms including multi-media platforms has enabled engineers to augment physical infrastructure systems with an information layer, capable of realtime monitoring, with particular success in the health monitoring community. This paradigm has reached a level of maturity, revealed by the emergence of numerous technologies usable to monitor the built infrastructure. Supervisory Control And Data Acquisition (SCADA) systems are a perfect example of such infrastructure, which integrate sensing, communication and control. In the context of management of irrigation networks, the impact of this technology on the control of such systems has the potential of significantly improving efficiency of operations. The idea of “closing the loop” in large scale infrastructure systems is not new, in fact in water management systems such as estuarine environments in the US, State authorities have talked about it for now more than a decade, for example in California. In Vietnam, farmers already operate gates on tidal timescales to manage irrigation properly for rice and shrimps. The “last mile” in enabling one to “close the loop” (at least in the case of estuarine environments is the capability of using sensor data in real time to integrate accurate hydrodynamic features of the system which directly intervene in the feedback loop. 2. Contributions. This special issue of Networks and Heterogeneous Media assembles a collection of articles linked with a workshop on“Irrigation channels and related problems” organized in Maiori, Italy, October 2-4, 2008. The workshop involved experts with fields which included sensor hardware manufacturing, estimation and control, hydrodynamic modeling and control and optimization of partial differential equations. The goal of the workshop was to cross-fertilize ideas between these different fields with the irrigation application in mind. This special issue of Networks and Heterogeneous Media includes articles by some of the presenters on their respective topics of expertise. The complete list, in alphabetical order, is the following:
{"title":"Open problems and research perspectives for irrigation channels","authors":"G. Bastin, A. Bayen, C. D'apice, X. Litrico, B. Piccoli","doi":"10.3934/NHM.2009.4.2I","DOIUrl":"https://doi.org/10.3934/NHM.2009.4.2I","url":null,"abstract":"1. Introduction: Management of canal networks at the age of information technology. With the miniaturization of sensors and their decreasing costs, the paradigm of instrumentation of the built infrastructure and the environment has now been underway for several years, leading to numerous successful and sometimes spectacular realizations such as the instrumentation of the Golden Gate with wireless sensors a few years ago. The convergence of communication, control and sensing on numerous platforms including multi-media platforms has enabled engineers to augment physical infrastructure systems with an information layer, capable of realtime monitoring, with particular success in the health monitoring community. This paradigm has reached a level of maturity, revealed by the emergence of numerous technologies usable to monitor the built infrastructure. Supervisory Control And Data Acquisition (SCADA) systems are a perfect example of such infrastructure, which integrate sensing, communication and control. In the context of management of irrigation networks, the impact of this technology on the control of such systems has the potential of significantly improving efficiency of operations. The idea of “closing the loop” in large scale infrastructure systems is not new, in fact in water management systems such as estuarine environments in the US, State authorities have talked about it for now more than a decade, for example in California. In Vietnam, farmers already operate gates on tidal timescales to manage irrigation properly for rice and shrimps. The “last mile” in enabling one to “close the loop” (at least in the case of estuarine environments is the capability of using sensor data in real time to integrate accurate hydrodynamic features of the system which directly intervene in the feedback loop. 2. Contributions. This special issue of Networks and Heterogeneous Media assembles a collection of articles linked with a workshop on“Irrigation channels and related problems” organized in Maiori, Italy, October 2-4, 2008. The workshop involved experts with fields which included sensor hardware manufacturing, estimation and control, hydrodynamic modeling and control and optimization of partial differential equations. The goal of the workshop was to cross-fertilize ideas between these different fields with the irrigation application in mind. This special issue of Networks and Heterogeneous Media includes articles by some of the presenters on their respective topics of expertise. The complete list, in alphabetical order, is the following:","PeriodicalId":54732,"journal":{"name":"Networks and Heterogeneous Media","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2009-07-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70227962","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The launching meeting of Networks and Heterogeneous Media took place on June 21-23 2006 in Maiori (Salerno, Italy). The meeting was sponsored by the American Institute of Mathematical Sciences, the Istituto per le Applicazioni del Calcolo of Roma, and the DIIMA of University of Salerno. For more information please click the "Full Text" above.
{"title":"Special issue from the launching meeting ofnetworks and heterogeneous media","authors":"B. Piccoli","doi":"10.3934/NHM.2006.1.4I","DOIUrl":"https://doi.org/10.3934/NHM.2006.1.4I","url":null,"abstract":"The launching meeting of Networks and Heterogeneous Media took place \u0000on June 21-23 2006 in Maiori (Salerno, Italy). The meeting was \u0000sponsored by the American Institute of Mathematical Sciences, the \u0000Istituto per le Applicazioni del Calcolo of Roma, and the DIIMA of \u0000University of Salerno. \u0000For more information please click the \"Full Text\" above.","PeriodicalId":54732,"journal":{"name":"Networks and Heterogeneous Media","volume":null,"pages":null},"PeriodicalIF":1.0,"publicationDate":"2006-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70227504","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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