Abstract MagnetoEncephaloGraphy (MEG) devices are helmet–shaped arrays of sensors that measure the tiny magnetic fields produced by neural currents. As they operate at low temperature, they are typically immersed in liquid helium. However, during the cooling process the sensor position and shape can change, with respect to nominal values, due to thermal stress. This implies that an accurate sensor calibration is required before a MEG device is utilized in either neuroscientific research or clinical workflow. Here we describe a calibration scheme developed for the optimal use of a MEG system recently realized at the “Istituto di Cibernetica e Biofisica” of the Italian CNR. To achieve the calibration goal a dedicated magnetic source is used (calibration device) and the geometric parameters of the sensors are determined through an optimisation procedure, based on the Nelder-Mead algorithm, which maximises the correlation coefficient between the predicted and the recorded magnetic field. Then the sensitivity of the sensors is analytically estimated. The developed calibration procedure is validated with synthetic data mimicking a real scenario.
{"title":"A simplex method for the calibration of a MEG device","authors":"V. Vivaldi, Sara Sommariva, A. Sorrentino","doi":"10.2478/caim-2019-0005","DOIUrl":"https://doi.org/10.2478/caim-2019-0005","url":null,"abstract":"Abstract MagnetoEncephaloGraphy (MEG) devices are helmet–shaped arrays of sensors that measure the tiny magnetic fields produced by neural currents. As they operate at low temperature, they are typically immersed in liquid helium. However, during the cooling process the sensor position and shape can change, with respect to nominal values, due to thermal stress. This implies that an accurate sensor calibration is required before a MEG device is utilized in either neuroscientific research or clinical workflow. Here we describe a calibration scheme developed for the optimal use of a MEG system recently realized at the “Istituto di Cibernetica e Biofisica” of the Italian CNR. To achieve the calibration goal a dedicated magnetic source is used (calibration device) and the geometric parameters of the sensors are determined through an optimisation procedure, based on the Nelder-Mead algorithm, which maximises the correlation coefficient between the predicted and the recorded magnetic field. Then the sensitivity of the sensors is analytically estimated. The developed calibration procedure is validated with synthetic data mimicking a real scenario.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"10 1","pages":"35 - 46"},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69187300","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 Charge transport in graphene is crucial for the design of a new generation of nanoscale electron devices. A reasonable model is represented by the semiclassical Boltzmann equations for electrons in the valence and conduction bands. As shown by Romano et al. (J. Comput. Phys., 2015), the discontinuous Galerkin methods are a viable way to tackle the problem of the numerical integration of these equations, even if efficient DSMC with a proper inclusion of the Pauli principle have been also devised. One of the advantages of the solutions obtained with deterministic approach is of course the absence of statistical noise. This fact is crucial for an accurate estimation of the low field mobility as proved by Majorana et al. (J. Math. Industry, 2016) in the case of a unipolar charge transport in a suspended graphene sheet under a constant electric field. The mobility expressions are essential for the drift-diffusion equations which constitute the most adopted models for charge transport in CAD. Here the analysis by Majorana et al. (J. Math. Industry, 2016) is improved in two ways: by including the charge transport both in the valence and conduction bands; by taking into account the presence of an oxide as substrate for the graphene sheet. New models of mobility are obtained and, in particular, relevant improvements of the low field mobility are achieved.
石墨烯中的电荷输运对于新一代纳米级电子器件的设计至关重要。一个合理的模型是用价带和导带电子的半经典玻尔兹曼方程表示的。如Romano et al. (J. Comput.)理论物理。， 2015)，不连续伽辽金方法是解决这些方程数值积分问题的可行方法，即使还设计了适当包含泡利原理的有效DSMC。用确定性方法得到的解的优点之一当然是没有统计噪声。这一事实对于马约拉纳等人证明的低磁场迁移率的准确估计至关重要。工业，2016)在恒定电场下悬浮石墨烯片中单极电荷传输的情况下。漂移-扩散方程是CAD中最常用的电荷输运模型，迁移率表达式对于漂移-扩散方程是必不可少的。这里是马约拉纳等人的分析。Industry, 2016)通过两种方式得到改进:包括价带和导带中的电荷输运;通过考虑氧化物作为石墨烯片的衬底的存在。获得了新的迁移率模型，特别是对低场迁移率进行了相应的改进。
{"title":"Improved mobility models for charge transport in graphene","authors":"G. Nastasi, V. Romano","doi":"10.1515/caim-2019-0011","DOIUrl":"https://doi.org/10.1515/caim-2019-0011","url":null,"abstract":"Abstract Charge transport in graphene is crucial for the design of a new generation of nanoscale electron devices. A reasonable model is represented by the semiclassical Boltzmann equations for electrons in the valence and conduction bands. As shown by Romano et al. (J. Comput. Phys., 2015), the discontinuous Galerkin methods are a viable way to tackle the problem of the numerical integration of these equations, even if efficient DSMC with a proper inclusion of the Pauli principle have been also devised. One of the advantages of the solutions obtained with deterministic approach is of course the absence of statistical noise. This fact is crucial for an accurate estimation of the low field mobility as proved by Majorana et al. (J. Math. Industry, 2016) in the case of a unipolar charge transport in a suspended graphene sheet under a constant electric field. The mobility expressions are essential for the drift-diffusion equations which constitute the most adopted models for charge transport in CAD. Here the analysis by Majorana et al. (J. Math. Industry, 2016) is improved in two ways: by including the charge transport both in the valence and conduction bands; by taking into account the presence of an oxide as substrate for the graphene sheet. New models of mobility are obtained and, in particular, relevant improvements of the low field mobility are achieved.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"10 1","pages":"41 - 52"},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48186825","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 Wigner transport equation can be solved stochastically by Monte Carlo techniques based on the theory of piecewise deterministic Markov processes. A new stochastic algorithm, without time discretization error, has been implemented and studied in the case of the quantum transport through a rectangular potential barrier.
{"title":"Wigner Monte Carlo simulation without discretization error of the tunneling rectangular barrier","authors":"O. Muscato, V. Di Stefano","doi":"10.2478/caim-2019-0009","DOIUrl":"https://doi.org/10.2478/caim-2019-0009","url":null,"abstract":"Abstract The Wigner transport equation can be solved stochastically by Monte Carlo techniques based on the theory of piecewise deterministic Markov processes. A new stochastic algorithm, without time discretization error, has been implemented and studied in the case of the quantum transport through a rectangular potential barrier.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"10 1","pages":"20 - 30"},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48436131","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}
A. M. Bersani, A. Borri, A. Milanesi, G. Tomassetti, P. Vellucci
Abstract In this paper we study the model of the chemical reaction of fully competitive inhibition and determine the appropriate parameter ∊ (related to the chemical constants of the model), for the application of singular perturbation techniques. We determine the inner and the outer solutions up to the first perturbation order and the uniform expansions. Some numerical results are discussed.
{"title":"A study case for the analysis of asymptotic expansions beyond the tQSSA for inhibitory mechanisms in enzyme kinetics.","authors":"A. M. Bersani, A. Borri, A. Milanesi, G. Tomassetti, P. Vellucci","doi":"10.1515/caim-2019-0019","DOIUrl":"https://doi.org/10.1515/caim-2019-0019","url":null,"abstract":"Abstract In this paper we study the model of the chemical reaction of fully competitive inhibition and determine the appropriate parameter ∊ (related to the chemical constants of the model), for the application of singular perturbation techniques. We determine the inner and the outer solutions up to the first perturbation order and the uniform expansions. Some numerical results are discussed.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"10 1","pages":"162 - 181"},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45579640","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 prove the existence and uniqueness for a degenerate pseudo-parabolic problem with memory. This kind of problem arises in the study of the homogenization of some differential systems involving the Laplace-Beltrami operator and describes the effective behaviour of the electrical conduction in some composite materials.
{"title":"A degenerate pseudo-parabolic equation with memory","authors":"M. Amar, D. Andreucci, R. Gianni, C. Timofte","doi":"10.2478/caim-2019-0013","DOIUrl":"https://doi.org/10.2478/caim-2019-0013","url":null,"abstract":"Abstract We prove the existence and uniqueness for a degenerate pseudo-parabolic problem with memory. This kind of problem arises in the study of the homogenization of some differential systems involving the Laplace-Beltrami operator and describes the effective behaviour of the electrical conduction in some composite materials.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"10 1","pages":"71 - 77"},"PeriodicalIF":1.3,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"69187311","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 This paper deals with subsampled spectral gradient methods for minimizing finite sums. Subsample function and gradient approximations are employed in order to reduce the overall computational cost of the classical spectral gradient methods. The global convergence is enforced by a nonmonotone line search procedure. Global convergence is proved provided that functions and gradients are approximated with increasing accuracy. R-linear convergence and worst-case iteration complexity is investigated in case of strongly convex objective function. Numerical results on well known binary classification problems are given to show the effectiveness of this framework and analyze the effect of different spectral coefficient approximations arising from the variable sample nature of this procedure.
{"title":"Subsampled Nonmonotone Spectral Gradient Methods","authors":"S. Bellavia, N. K. Jerinkić, Greta Malaspina","doi":"10.2478/caim-2020-0002","DOIUrl":"https://doi.org/10.2478/caim-2020-0002","url":null,"abstract":"Abstract This paper deals with subsampled spectral gradient methods for minimizing finite sums. Subsample function and gradient approximations are employed in order to reduce the overall computational cost of the classical spectral gradient methods. The global convergence is enforced by a nonmonotone line search procedure. Global convergence is proved provided that functions and gradients are approximated with increasing accuracy. R-linear convergence and worst-case iteration complexity is investigated in case of strongly convex objective function. Numerical results on well known binary classification problems are given to show the effectiveness of this framework and analyze the effect of different spectral coefficient approximations arising from the variable sample nature of this procedure.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"11 1","pages":"19 - 34"},"PeriodicalIF":1.3,"publicationDate":"2018-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46944317","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 classical Boltzmann equation describes well temporal behaviour of a rarefied perfect gas. Modified kinetic equations have been proposed for studying the dynamics of different type of gases. An important example is the transport equation, which describes the charged particles flow, in the semi-classical regime, in electronic devices. In order to reduce the difficulties in solving the Boltzmann equation, simple expressions of a collision operator have been proposed to replace the standard Boltzmann integral term. These new equations are called kinetic models. The most popular and widely used kinetic model is the Bhatnagar-Gross-Krook (BGK) model. In this work we propose and analyse a BGK model for charge transport in graphene.
{"title":"A BGK model for charge transport in graphene","authors":"A. Majorana","doi":"10.1515/caim-2019-0018","DOIUrl":"https://doi.org/10.1515/caim-2019-0018","url":null,"abstract":"Abstract The classical Boltzmann equation describes well temporal behaviour of a rarefied perfect gas. Modified kinetic equations have been proposed for studying the dynamics of different type of gases. An important example is the transport equation, which describes the charged particles flow, in the semi-classical regime, in electronic devices. In order to reduce the difficulties in solving the Boltzmann equation, simple expressions of a collision operator have been proposed to replace the standard Boltzmann integral term. These new equations are called kinetic models. The most popular and widely used kinetic model is the Bhatnagar-Gross-Krook (BGK) model. In this work we propose and analyse a BGK model for charge transport in graphene.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"10 1","pages":"153 - 161"},"PeriodicalIF":1.3,"publicationDate":"2018-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43006494","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 the present paper we propose two mathematical models describing, respectively at the microscopic level and at the mesoscopic level, a system of interacting tumor cells and cells of the immune system. The microscopic model is in terms of a Markov chain defined by the generator, the mesoscopic model is developed in the framework of the kinetic theory of active particles. The main result is to prove the transition from the microscopic to mesoscopic level of description.
{"title":"A Continuous–Time Markov Chain Modeling Cancer–Immune System Interactions","authors":"D. Burini, E. Angelis, M. Lachowicz","doi":"10.2478/caim-2018-0018","DOIUrl":"https://doi.org/10.2478/caim-2018-0018","url":null,"abstract":"Abstract In the present paper we propose two mathematical models describing, respectively at the microscopic level and at the mesoscopic level, a system of interacting tumor cells and cells of the immune system. The microscopic model is in terms of a Markov chain defined by the generator, the mesoscopic model is developed in the framework of the kinetic theory of active particles. The main result is to prove the transition from the microscopic to mesoscopic level of description.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"9 1","pages":"106 - 118"},"PeriodicalIF":1.3,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42140748","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 honeybee swarming process is steered by few scout individuals, which are the unique informed on the location of the target destination. Theoretical and experimental results suggest that bee coordinated flight arises from visual signals. However, how the information is passed within the population is still debated. Moreover, it has been observed that honeybees are highly sensitive to conflicting directional information. In fact, swarms exposed to fast-moving bees headed in the wrong direction show clear signs of disrupted guidance. In this respect, we here present a discrete mathematical model to investigate different hypotheses on the behaviour both of informed and uninformed bees. In this perspective, numerical realizations, specifically designed to mimic selected experiments, reveal that only one combination of the considered assumptions is able to reproduce the empirical outcomes, resulting thereby the most reliable mechanism underlying the swarm dynamics according to the proposed approach. Specifically, this study suggests that (i) leaders indicate the right flight direction by repeatedly streaking at high speed pointing towards the target and then slowly coming back to the trailing edge of the bee cloud; and (ii) uninformed bees, in turn, gather the route information by adapting their movement to all the bees sufficiently close to their position.
{"title":"A particle model reproducing the effect of a conflicting flight information on the honeybee swarm guidance","authors":"Sara Bernardi, A. Colombi","doi":"10.2478/caim-2018-0021","DOIUrl":"https://doi.org/10.2478/caim-2018-0021","url":null,"abstract":"Abstract The honeybee swarming process is steered by few scout individuals, which are the unique informed on the location of the target destination. Theoretical and experimental results suggest that bee coordinated flight arises from visual signals. However, how the information is passed within the population is still debated. Moreover, it has been observed that honeybees are highly sensitive to conflicting directional information. In fact, swarms exposed to fast-moving bees headed in the wrong direction show clear signs of disrupted guidance. In this respect, we here present a discrete mathematical model to investigate different hypotheses on the behaviour both of informed and uninformed bees. In this perspective, numerical realizations, specifically designed to mimic selected experiments, reveal that only one combination of the considered assumptions is able to reproduce the empirical outcomes, resulting thereby the most reliable mechanism underlying the swarm dynamics according to the proposed approach. Specifically, this study suggests that (i) leaders indicate the right flight direction by repeatedly streaking at high speed pointing towards the target and then slowly coming back to the trailing edge of the bee cloud; and (ii) uninformed bees, in turn, gather the route information by adapting their movement to all the bees sufficiently close to their position.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"9 1","pages":"159 - 173"},"PeriodicalIF":1.3,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45813230","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 motion of a spherical bubble rising in a gravitational field in presence of a traveling pressure step wave is investigated. Equations of motion for the bubble radius and center of mass are deduced and several sample cases are analysed by means of their numerical integration. The crucial role played by the traveling speed of the wave front and by the intensity of the pressure step are discussed. A first comparison with the axisymmetric dynamics is discussed.
{"title":"Dynamics of a spherical bubble rising in gravity, subject to traveling pressure disturbance","authors":"G. Riccardi, Enrico De Bernardis","doi":"10.2478/caim-2018-0020","DOIUrl":"https://doi.org/10.2478/caim-2018-0020","url":null,"abstract":"Abstract The motion of a spherical bubble rising in a gravitational field in presence of a traveling pressure step wave is investigated. Equations of motion for the bubble radius and center of mass are deduced and several sample cases are analysed by means of their numerical integration. The crucial role played by the traveling speed of the wave front and by the intensity of the pressure step are discussed. A first comparison with the axisymmetric dynamics is discussed.","PeriodicalId":37903,"journal":{"name":"Communications in Applied and Industrial Mathematics","volume":"9 1","pages":"149 - 158"},"PeriodicalIF":1.3,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45517804","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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