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Giovanni Naldi

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Evelyn Ersanilli

University of Amsterdam

Mansoura University

Sambalpur University,

Vinicius Garcia

Universidade Federal de Pernambuco

Iman Attarzadeh

Islamic Azad University of Tehran, Central branch

Niculae MIHAITA

The Bucharest Academy of Economic Studies

Antoni Martín i Oliveras

Universitat de Barcelona

Ahmad Salman Khan

University of Lahore, Lahore Pakistan

shahnaz khademizadeh

Shahid Chamran University

Francielle Santos

Universidade Federal Rural de Pernambuco

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Papers by Giovanni Naldi

Computational Modeling of Single Neuron Extracellular Electric Potentials and Network Local Field Potentials using LFPsim

Frontiers in Computational Neuroscience, 2016

Local Field Potentials (LFPs) are population signals generated by complex spatiotemporal interact... more Local Field Potentials (LFPs) are population signals generated by complex spatiotemporal interaction of current sources and dipoles. Mathematical computations of LFPs allow the study of circuit functions and dysfunctions via simulations. This paper introduces LFPsim, a NEURON-based tool for computing population LFP activity and single neuron extracellular potentials. LFPsim was developed to be used on existing cable compartmental neuron and network models. Point source, line source, and RC based filter approximations can be used to compute extracellular activity. As a demonstration of efficient implementation, we showcase LFPs from mathematical models of electrotonically compact cerebellum granule neurons and morphologically complex neurons of the neocortical column. LFPsim reproduced neocortical LFP at 8, 32, and 56 Hz via current injection, in vitro post-synaptic N 2a , N 2b waves and in vivo T-C waves in cerebellum granular layer. LFPsim also includes a simulation of multi-electrode array of LFPs in network populations to aid computational inference between biophysical activity in neural networks and corresponding multi-unit activity resulting in extracellular and evoked LFP signals.

Little Tom Thumb among cells: seeking the cues of life

Mathknow, 2009

For a living being or a cell in a developing body, recognizing its peers and locating food source... more For a living being or a cell in a developing body, recognizing its peers and locating food sources or other targets and moving towards them is of paramount importance. In most cases this is achieved by detecting the presence of chemical substances in the environment and moving towards the areas of their higher concentration, a process known as chemotaxis. Despite its fundamental role for life, this phenomenon is not yet fully understood in all its details and mathematical models are proving very useful in guiding biological research. We address here two examples of chemotaxis occurring in the developing embryo: early formation of the vascular plexus and axon navigation in the wiring of the nervous system.

Axonal Na+Channels Ensure Fast Spike Activation and Back-Propagation in Cerebellar Granule Cells

Journal of Neurophysiology, 2008

In most neurons, Na+channels in the axon are complemented by others localized in the soma and den... more In most neurons, Na+channels in the axon are complemented by others localized in the soma and dendrites to ensure spike back-propagation. However, cerebellar granule cells are neurons with simplified architecture in which the dendrites are short and unbranched and a single thin ascending axon travels toward the molecular layer before bifurcating into parallel fibers. Here we show that in cerebellar granule cells, Na+channels are enriched in the axon, especially in the hillock, but almost absent from soma and dendrites. The impact of this channel distribution on neuronal electroresponsiveness was investigated by multi-compartmental modeling. Numerical simulations indicated that granule cells have a compact electrotonic structure allowing excitatory postsynaptic potentials to diffuse with little attenuation from dendrites to axon. The spike arose almost simultaneously along the whole axonal ascending branch and invaded the hillock the activation of which promoted spike back-propagatio...

Modeling Spike-Train Processing in the Cerebellum Granular Layer and Changes in Plasticity Reveal Single Neuron Effects in Neural Ensembles

Computational Intelligence and Neuroscience, 2012

The cerebellum input stage has been known to perform combinatorial operations on input signals. I... more The cerebellum input stage has been known to perform combinatorial operations on input signals. In this paper, two types of mathematical models were used to reproduce the role of feed-forward inhibition and computation in the granular layer microcircuitry to investigate spike train processing. A simple spiking model and a biophysically-detailed model of the network were used to study signal recoding in the granular layer and to test observations like center-surround organization and time-window hypothesis in addition to effects of induced plasticity. Simulations suggest that simple neuron models may be used to abstract timing phenomenon in large networks, however detailed models were needed to reconstruct population coding via evoked local field potentials (LFP) and for simulating changes in synaptic plasticity. Our results also indicated that spatio-temporal code of the granular network is mainly controlled by the feed-forward inhibition from the Golgi cell synapses. Spike amplitud...

A multi-class logistic regression algorithm to reliably infer network connectivity from cell membrane potentials

Frontiers in Applied Mathematics and Statistics

In neuroscience, the structural connectivity matrix of synaptic weights between neurons is one of... more In neuroscience, the structural connectivity matrix of synaptic weights between neurons is one of the critical factors that determine the overall function of a network of neurons. The mechanisms of signal transduction have been intensively studied at different time and spatial scales and both the cellular and molecular levels. While a better understanding and knowledge of some basic processes of information handling by neurons has been achieved, little is known about the organization and function of complex neuronal networks. Experimental methods are now available to simultaneously monitor the electrical activity of a large number of neurons in real time. The analysis of the data related to the activities of individual neurons can become a very valuable tool for the study of the dynamics and architecture of neural networks. In particular, advances in optical imaging techniques allow us to record up to thousands of neurons nowadays. However, most of the efforts have been focused on c...

A Wavelet-Galerkin Method for Elastoplasticity Problems

. We use biorthogonal B{spline wavelet bases to discretize the dynamic response problem for a str... more . We use biorthogonal B{spline wavelet bases to discretize the dynamic response problem for a straight elasto{plastic rod. In an elastic predictor/plastic corrector method, we use interpolatory wavelets for the stress correction. In several numerical experiments, we show the potential of Wavelet{Galerkin methods for elastoplasticity problems. 1 Introduction The numerical treatement of elastoplasticity problems is still a very challenging eld of active research. Besides classical methods such as Finite Dierences, Finite Elements, Spectral Elements and others, quite recently rst attempts using wavelet bases have been made, [11, 21]. In recent years, signicant progress has been made for using Wavelet{Galerkin methods for the numerical solution of certain operator equations including elliptic partial dierential equations, boundary integral equations and also saddle point problems. In fact, wavelets have been proven to give rise to a diagonal multilevel preconditioner for ellipti...

Modelling and Fast Numerical Methods for Granular Flows

IFIP International Federation for Information Processing

In this work we discuss the development of fast algorithms for the inelastic Boltzmann equation d... more In this work we discuss the development of fast algorithms for the inelastic Boltzmann equation describing the coUisional motion of a granular gas. In such systems the collisions between particles occur in an inelastic way and are characterized by a coefficient of restitution which in the general case depends on the relative velocity of the collision. In the quasi-elastic approximation the granular operator is replaced by the sum of an elastic Boltzmann operator and a nonlinear friction term. Fast numerical methods based on a suitable spectral representation of the approximated model are then presented.

Properties of Cerebellar Granule Cells Dipeptidyl Peptidase-Like Protein 6 Is Required for Normal Electrophysiological

channels ensure fast spike activation and back-propagation in cerebellar granule cells.

A wavelet-like Galerkin method for numerical solution of variational inequalities arising in elastoplasticity

Communications in Numerical Methods in Engineering, 2000

The well-known problem of elasticity that may be written as a variational equation has been recen... more The well-known problem of elasticity that may be written as a variational equation has been recently extended to non-linear elastoplastic behaviours giving rise to a class of variational inequalities of second kind . This paper presents a wavelet Galerkin method for the numerical solution of such a class of problems, extensively studied and solved in the past by means of more traditional approaches. The novelty of the scheme presented herein is represented by the capability of wavelets to locate regions where plasticity is growing without the need of any further indicator. This is useful for adaptive remeshing as well as for gaining insight into internal variable models with applications to dynamic analysis and damage identiÿcation.

Understanding Cerebellum Granular Layer Network Computations through Mathematical Reconstructions of Evoked Local Field Potentials

Annals of neurosciences, 2018

The cerebellar granular layer input stage of cerebellum receives information from tactile and sen... more The cerebellar granular layer input stage of cerebellum receives information from tactile and sensory regions of the body. The somatosensory activity in the cerebellar granular layer corresponds to sensory and tactile input has been observed by recording Local Field Potential (LFP) from the Crus-IIa regions of cerebellum in brain slices and in anesthetized animals. In this paper, a detailed biophysical model of Wistar rat cerebellum granular layer network model and LFP modelling schemas were used to simulate circuit's evoked response. Point Source Approximation and Line Source Approximation were used to reconstruct the network LFP. The LFP mechanism in in vitro was validated in network model and generated the in vivo LFP using the same mechanism. The network simulations distinctly displayed the Trigeminal and Cortical (TC) wave components generated by 2 independent bursts implicating the generation of TC waves by 2 independent granule neuron populations. Induced plasticity was s...

Regularization Techniques for Inverse Problem in DOT Applications

Journal of Physics: Conference Series, 2020

Diffuse optical tomography (DOT) is an emerging diagnostic technique which uses near–infra–red li... more Diffuse optical tomography (DOT) is an emerging diagnostic technique which uses near–infra–red light to investigate the optical coefficients distribution in biological tissues. The surface of the tissue is illuminated by light sources, then the outgoing light is measured by detectors placed at various locations on the surface itself. In order to reconstruct the optical coefficients, a mathematical model of light propagation is employed: such model leads to the minimization of the discrepancy between the detected data and the corresponding theoretical field. Due to severe ill–conditioning, regularization techniques are required: common procedures consider mainly ℓ 1–norm (LASSO) and ℓ 2–norm (Tikhonov) regularization. In the present work we investigate two original approaches in this context: the elastic–net regularization, previously used in machine learning problems, and the Bregman procedure. Numerical experiments are performed on synthetic 2D geometries and data, to evaluate the ...

From dynamics to links: a sparse reconstruction of the topology of a neural network

Communications in Applied and Industrial Mathematics, 2019

One major challenge in neuroscience is the identification of interrelations between signals refle... more One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity and how information processing occurs in the neural circuits. At the cellular and molecular level, mechanisms of signal transduction have been studied intensively and a better knowledge and understanding of some basic processes of information handling by neurons has been achieved. In contrast, little is known about the organization and function of complex neuronal networks. Experimental methods are now available to simultaneously monitor electrical activity of a large number of neurons in real time. Then, the qualitative and quantitative analysis of the spiking activity of individual neurons is a very valuable tool for the study of the dynamics and architecture of the neural networks. Such activity is not due to the sole intrinsic properties of the individual neural cells but it is mostly the consequence of the direct influence of other neurons. The deduction of the...

Theta-Frequency Bursting and Resonance in Cerebellar Granule Cells: Experimental Evidence and Modeling of a Slow K+-Dependent Mechanism

The Journal of Neuroscience, 2001

Neurons process information in a highly nonlinear manner, generating oscillations, bursting, and ... more Neurons process information in a highly nonlinear manner, generating oscillations, bursting, and resonance, enhancing responsiveness at preferential frequencies. It has been proposed that slow repolarizing currents could be responsible for both oscillation/burst termination and for high-pass filtering that causes resonance (Hutcheon and Yarom, 2000). However, different mechanisms, including electrotonic effects (Mainen and Sejinowski, 1996), the expression of resurgent currents (Raman and Bean, 1997), and network feedback, may also be important. In this study we report theta-frequency (3-12 Hz) bursting and resonance in rat cerebellar granule cells and show that these neurons express a previously unidentified slow re-polarizing K ϩ current (I K-slow). Our experimental and modeling results indicate that I K-slow was necessary for both bursting and resonance. A persistent (and potentially a resurgent) Na ϩ current exerted complex amplifying actions on bursting and resonance, whereas electrotonic effects were excluded by the compact structure of the granule cell. Theta-frequency bursting and resonance in granule cells may play an important role in determining synchronization, rhythmicity, and learning in the cerebellum.

Algoritmi, numeri e segreti

Kos, 2005

Runge-Kutta discontinuous Galerkin finite element schemes for nonlinear reaction diffusion equations

Siam Polimi, Jun 28, 2013

The reaction-diffusion equation plays an important role in dissipative dynamical systems for phys... more The reaction-diffusion equation plays an important role in dissipative dynamical systems for physical, chemical and biological phenomena. For example, in chemical physics, to describe concentration and temperature distributions, the heat and mass transfer are modeled by a nonlinear diffusion term, while the rate of heat and mass production are described by a nonlinear reaction term. In population dynamics, where the focus is on the evolution of a population density, diffusion terms correspond to random motions of individuals, and reaction terms describe their reproduction and interaction, as in a predator-prey model. Several authors pointed out that the population diffusion mechanisms are more realistically described by (degenerate) non-linear diffusion models like $\partial_t u-\Delta p(u)=r(u)\qquad \mbox{in}\Omega\times (0,+\infty)$ where $\Omega\subset\mathcal{R}^d,$ with $d=1,2$, is a bounded domain, $u$ is a density and $p(u), r(u)$ are the diffusivity and the reaction functions The previous equation is completed by suitable boundary conditions, usually homogeneous Neumann conditions. If $p(u)\simeq u^\gamma$, with $\gamma>0$, the equation is known as the porous media equation, which is degenerate in the sense that $p^\prime(0) = 0$. The solution can develop interfaces between the regions with zero and nonzero population densities, which represent population fronts. Reaction term is modeled by a generalized Kolmogorov-Fisher term, namely $r(u)=u(1-u^\beta)$. The discretization of this problem is challenging because the numerical scheme has to reproduce shock waves or fronts, and preserve stability and invariance properties. We present a new high-order family of numerical methods based on a discontinuous Galerkin space discretization and Runge-Kutta time stepping. These methods are capable to reproduce in the numerical solution some main properties of the analytical solution, like positivity, and to preserve stability and accuracy.

Reconstructing fMRI BOLD signals arising from cerebellar granule neurons - comparing GLM and balloon models

2015 International Joint Conference on Neural Networks (IJCNN), 2015

Understanding the relationship between fMRI BOLD and underlying neuronal activity has been crucia... more Understanding the relationship between fMRI BOLD and underlying neuronal activity has been crucial to connect circuit behavior to cognitive functions. In this paper, we modeled fMRI BOLD reconstructions with general linear model and balloon modeling using biophysical models of rat cerebellum granular layer and stimuli spike trains of various response times. Linear convolution of the hemodynamic response function with the known spiking information reconstructed activity similar to experimental BOLD-like signals with the limitation of short stimuli trains. Balloon model through Volterra kernels gave seemingly similar results to that of general linear model. Our main goal in this study was to understand the activity role of densely populated clusters through BOLD-like reconstructions given neuronal responses and by varying response times for the whole stimulus duration.

Diffusion effects in the sliding filament model of muscle contraction

ABSTRACT

A Comparison Between Relaxation and Kurganov—Tadmor Schemes

Mathematics in Industry, 2008

Discontinuous Galerkin Approximation of Relaxation Models for Linear and Nonlinear Diffusion Equations

SIAM Journal on Scientific Computing, 2012

In this work we present finite element approximations of relaxed systems for nonlinear diffusion ... more In this work we present finite element approximations of relaxed systems for nonlinear diffusion problems, which can also tackle the cases of degenerate and strongly degenerate diffusion equations. Relaxation schemes take advantage of the replacement of the original partial differential equation (PDE) with a semilinear hyperbolic system of equations, with a stiff source term, tuned by a relaxation parameter ε. When ε → 0 + , the system relaxes onto the original PDE: in this way, a consistent discretization of the relaxation system for vanishing ε yields a consistent discretization of the original PDE. The numerical schemes obtained with this procedure do not require solving implicit nonlinear problems and possess the robustness of upwind discretizations. The proposed approximations are based on a discontinuous Galerkin method in space and on suitable implicitexplicit integration in time. Then, in principle, we can achieve any order of accuracy and obtain stable solutions, even when the diffusion equation becomes degenerate and solution singularities develop. Moreover, when needed, we can easily incorporate slope limiters within our schemes in order to handle spurious oscillatory phenomena. Some preliminary theoretical results are given, along with several numerical tests in one and two space dimensions, both for linear and nonlinear diffusion problems, including a degenerate diffusion equation, that provide numerical evidence of the properties of the presented approach.

Increasing Efficiency Through Optimal RK Time Integration of Diffusion Equations

Hyperbolic Problems: Theory, Numerics, Applications, 2008

The application of Runge-Kutta schemes designed to enjoy a large region of absolute stability can... more The application of Runge-Kutta schemes designed to enjoy a large region of absolute stability can significantly increase the efficiency of numerical methods for PDEs based on a method of lines approach. In this work we investigate the improvement in the efficiency of the time integration of relaxation schemes for degenerate diffusion problems, using SSP Runge-Kutta schemes and computing the maximal CFL coefficients. This technique can be extended to other PDEs, linear and nonlinear, provided the space operator has eigenvalues with a non-zero real part.

Computational Modeling of Single Neuron Extracellular Electric Potentials and Network Local Field Potentials using LFPsim

Frontiers in Computational Neuroscience, 2016

Local Field Potentials (LFPs) are population signals generated by complex spatiotemporal interact... more Local Field Potentials (LFPs) are population signals generated by complex spatiotemporal interaction of current sources and dipoles. Mathematical computations of LFPs allow the study of circuit functions and dysfunctions via simulations. This paper introduces LFPsim, a NEURON-based tool for computing population LFP activity and single neuron extracellular potentials. LFPsim was developed to be used on existing cable compartmental neuron and network models. Point source, line source, and RC based filter approximations can be used to compute extracellular activity. As a demonstration of efficient implementation, we showcase LFPs from mathematical models of electrotonically compact cerebellum granule neurons and morphologically complex neurons of the neocortical column. LFPsim reproduced neocortical LFP at 8, 32, and 56 Hz via current injection, in vitro post-synaptic N 2a , N 2b waves and in vivo T-C waves in cerebellum granular layer. LFPsim also includes a simulation of multi-electrode array of LFPs in network populations to aid computational inference between biophysical activity in neural networks and corresponding multi-unit activity resulting in extracellular and evoked LFP signals.

Little Tom Thumb among cells: seeking the cues of life

Mathknow, 2009

For a living being or a cell in a developing body, recognizing its peers and locating food source... more For a living being or a cell in a developing body, recognizing its peers and locating food sources or other targets and moving towards them is of paramount importance. In most cases this is achieved by detecting the presence of chemical substances in the environment and moving towards the areas of their higher concentration, a process known as chemotaxis. Despite its fundamental role for life, this phenomenon is not yet fully understood in all its details and mathematical models are proving very useful in guiding biological research. We address here two examples of chemotaxis occurring in the developing embryo: early formation of the vascular plexus and axon navigation in the wiring of the nervous system.

Axonal Na+Channels Ensure Fast Spike Activation and Back-Propagation in Cerebellar Granule Cells

Journal of Neurophysiology, 2008

In most neurons, Na+channels in the axon are complemented by others localized in the soma and den... more In most neurons, Na+channels in the axon are complemented by others localized in the soma and dendrites to ensure spike back-propagation. However, cerebellar granule cells are neurons with simplified architecture in which the dendrites are short and unbranched and a single thin ascending axon travels toward the molecular layer before bifurcating into parallel fibers. Here we show that in cerebellar granule cells, Na+channels are enriched in the axon, especially in the hillock, but almost absent from soma and dendrites. The impact of this channel distribution on neuronal electroresponsiveness was investigated by multi-compartmental modeling. Numerical simulations indicated that granule cells have a compact electrotonic structure allowing excitatory postsynaptic potentials to diffuse with little attenuation from dendrites to axon. The spike arose almost simultaneously along the whole axonal ascending branch and invaded the hillock the activation of which promoted spike back-propagatio...

Modeling Spike-Train Processing in the Cerebellum Granular Layer and Changes in Plasticity Reveal Single Neuron Effects in Neural Ensembles

Computational Intelligence and Neuroscience, 2012

The cerebellum input stage has been known to perform combinatorial operations on input signals. I... more The cerebellum input stage has been known to perform combinatorial operations on input signals. In this paper, two types of mathematical models were used to reproduce the role of feed-forward inhibition and computation in the granular layer microcircuitry to investigate spike train processing. A simple spiking model and a biophysically-detailed model of the network were used to study signal recoding in the granular layer and to test observations like center-surround organization and time-window hypothesis in addition to effects of induced plasticity. Simulations suggest that simple neuron models may be used to abstract timing phenomenon in large networks, however detailed models were needed to reconstruct population coding via evoked local field potentials (LFP) and for simulating changes in synaptic plasticity. Our results also indicated that spatio-temporal code of the granular network is mainly controlled by the feed-forward inhibition from the Golgi cell synapses. Spike amplitud...

A multi-class logistic regression algorithm to reliably infer network connectivity from cell membrane potentials

Frontiers in Applied Mathematics and Statistics

In neuroscience, the structural connectivity matrix of synaptic weights between neurons is one of... more In neuroscience, the structural connectivity matrix of synaptic weights between neurons is one of the critical factors that determine the overall function of a network of neurons. The mechanisms of signal transduction have been intensively studied at different time and spatial scales and both the cellular and molecular levels. While a better understanding and knowledge of some basic processes of information handling by neurons has been achieved, little is known about the organization and function of complex neuronal networks. Experimental methods are now available to simultaneously monitor the electrical activity of a large number of neurons in real time. The analysis of the data related to the activities of individual neurons can become a very valuable tool for the study of the dynamics and architecture of neural networks. In particular, advances in optical imaging techniques allow us to record up to thousands of neurons nowadays. However, most of the efforts have been focused on c...

A Wavelet-Galerkin Method for Elastoplasticity Problems

. We use biorthogonal B{spline wavelet bases to discretize the dynamic response problem for a str... more . We use biorthogonal B{spline wavelet bases to discretize the dynamic response problem for a straight elasto{plastic rod. In an elastic predictor/plastic corrector method, we use interpolatory wavelets for the stress correction. In several numerical experiments, we show the potential of Wavelet{Galerkin methods for elastoplasticity problems. 1 Introduction The numerical treatement of elastoplasticity problems is still a very challenging eld of active research. Besides classical methods such as Finite Dierences, Finite Elements, Spectral Elements and others, quite recently rst attempts using wavelet bases have been made, [11, 21]. In recent years, signicant progress has been made for using Wavelet{Galerkin methods for the numerical solution of certain operator equations including elliptic partial dierential equations, boundary integral equations and also saddle point problems. In fact, wavelets have been proven to give rise to a diagonal multilevel preconditioner for ellipti...

Modelling and Fast Numerical Methods for Granular Flows

IFIP International Federation for Information Processing

In this work we discuss the development of fast algorithms for the inelastic Boltzmann equation d... more In this work we discuss the development of fast algorithms for the inelastic Boltzmann equation describing the coUisional motion of a granular gas. In such systems the collisions between particles occur in an inelastic way and are characterized by a coefficient of restitution which in the general case depends on the relative velocity of the collision. In the quasi-elastic approximation the granular operator is replaced by the sum of an elastic Boltzmann operator and a nonlinear friction term. Fast numerical methods based on a suitable spectral representation of the approximated model are then presented.

Properties of Cerebellar Granule Cells Dipeptidyl Peptidase-Like Protein 6 Is Required for Normal Electrophysiological

channels ensure fast spike activation and back-propagation in cerebellar granule cells.

A wavelet-like Galerkin method for numerical solution of variational inequalities arising in elastoplasticity

Communications in Numerical Methods in Engineering, 2000

The well-known problem of elasticity that may be written as a variational equation has been recen... more The well-known problem of elasticity that may be written as a variational equation has been recently extended to non-linear elastoplastic behaviours giving rise to a class of variational inequalities of second kind . This paper presents a wavelet Galerkin method for the numerical solution of such a class of problems, extensively studied and solved in the past by means of more traditional approaches. The novelty of the scheme presented herein is represented by the capability of wavelets to locate regions where plasticity is growing without the need of any further indicator. This is useful for adaptive remeshing as well as for gaining insight into internal variable models with applications to dynamic analysis and damage identiÿcation.

Understanding Cerebellum Granular Layer Network Computations through Mathematical Reconstructions of Evoked Local Field Potentials

Annals of neurosciences, 2018

The cerebellar granular layer input stage of cerebellum receives information from tactile and sen... more The cerebellar granular layer input stage of cerebellum receives information from tactile and sensory regions of the body. The somatosensory activity in the cerebellar granular layer corresponds to sensory and tactile input has been observed by recording Local Field Potential (LFP) from the Crus-IIa regions of cerebellum in brain slices and in anesthetized animals. In this paper, a detailed biophysical model of Wistar rat cerebellum granular layer network model and LFP modelling schemas were used to simulate circuit's evoked response. Point Source Approximation and Line Source Approximation were used to reconstruct the network LFP. The LFP mechanism in in vitro was validated in network model and generated the in vivo LFP using the same mechanism. The network simulations distinctly displayed the Trigeminal and Cortical (TC) wave components generated by 2 independent bursts implicating the generation of TC waves by 2 independent granule neuron populations. Induced plasticity was s...

Regularization Techniques for Inverse Problem in DOT Applications

Journal of Physics: Conference Series, 2020

Diffuse optical tomography (DOT) is an emerging diagnostic technique which uses near–infra–red li... more Diffuse optical tomography (DOT) is an emerging diagnostic technique which uses near–infra–red light to investigate the optical coefficients distribution in biological tissues. The surface of the tissue is illuminated by light sources, then the outgoing light is measured by detectors placed at various locations on the surface itself. In order to reconstruct the optical coefficients, a mathematical model of light propagation is employed: such model leads to the minimization of the discrepancy between the detected data and the corresponding theoretical field. Due to severe ill–conditioning, regularization techniques are required: common procedures consider mainly ℓ 1–norm (LASSO) and ℓ 2–norm (Tikhonov) regularization. In the present work we investigate two original approaches in this context: the elastic–net regularization, previously used in machine learning problems, and the Bregman procedure. Numerical experiments are performed on synthetic 2D geometries and data, to evaluate the ...

From dynamics to links: a sparse reconstruction of the topology of a neural network

Communications in Applied and Industrial Mathematics, 2019

One major challenge in neuroscience is the identification of interrelations between signals refle... more One major challenge in neuroscience is the identification of interrelations between signals reflecting neural activity and how information processing occurs in the neural circuits. At the cellular and molecular level, mechanisms of signal transduction have been studied intensively and a better knowledge and understanding of some basic processes of information handling by neurons has been achieved. In contrast, little is known about the organization and function of complex neuronal networks. Experimental methods are now available to simultaneously monitor electrical activity of a large number of neurons in real time. Then, the qualitative and quantitative analysis of the spiking activity of individual neurons is a very valuable tool for the study of the dynamics and architecture of the neural networks. Such activity is not due to the sole intrinsic properties of the individual neural cells but it is mostly the consequence of the direct influence of other neurons. The deduction of the...

Theta-Frequency Bursting and Resonance in Cerebellar Granule Cells: Experimental Evidence and Modeling of a Slow K+-Dependent Mechanism

The Journal of Neuroscience, 2001

Neurons process information in a highly nonlinear manner, generating oscillations, bursting, and ... more Neurons process information in a highly nonlinear manner, generating oscillations, bursting, and resonance, enhancing responsiveness at preferential frequencies. It has been proposed that slow repolarizing currents could be responsible for both oscillation/burst termination and for high-pass filtering that causes resonance (Hutcheon and Yarom, 2000). However, different mechanisms, including electrotonic effects (Mainen and Sejinowski, 1996), the expression of resurgent currents (Raman and Bean, 1997), and network feedback, may also be important. In this study we report theta-frequency (3-12 Hz) bursting and resonance in rat cerebellar granule cells and show that these neurons express a previously unidentified slow re-polarizing K ϩ current (I K-slow). Our experimental and modeling results indicate that I K-slow was necessary for both bursting and resonance. A persistent (and potentially a resurgent) Na ϩ current exerted complex amplifying actions on bursting and resonance, whereas electrotonic effects were excluded by the compact structure of the granule cell. Theta-frequency bursting and resonance in granule cells may play an important role in determining synchronization, rhythmicity, and learning in the cerebellum.

Algoritmi, numeri e segreti

Kos, 2005

Runge-Kutta discontinuous Galerkin finite element schemes for nonlinear reaction diffusion equations

Siam Polimi, Jun 28, 2013

The reaction-diffusion equation plays an important role in dissipative dynamical systems for phys... more The reaction-diffusion equation plays an important role in dissipative dynamical systems for physical, chemical and biological phenomena. For example, in chemical physics, to describe concentration and temperature distributions, the heat and mass transfer are modeled by a nonlinear diffusion term, while the rate of heat and mass production are described by a nonlinear reaction term. In population dynamics, where the focus is on the evolution of a population density, diffusion terms correspond to random motions of individuals, and reaction terms describe their reproduction and interaction, as in a predator-prey model. Several authors pointed out that the population diffusion mechanisms are more realistically described by (degenerate) non-linear diffusion models like $\partial_t u-\Delta p(u)=r(u)\qquad \mbox{in}\Omega\times (0,+\infty)$ where $\Omega\subset\mathcal{R}^d,$ with $d=1,2$, is a bounded domain, $u$ is a density and $p(u), r(u)$ are the diffusivity and the reaction functions The previous equation is completed by suitable boundary conditions, usually homogeneous Neumann conditions. If $p(u)\simeq u^\gamma$, with $\gamma>0$, the equation is known as the porous media equation, which is degenerate in the sense that $p^\prime(0) = 0$. The solution can develop interfaces between the regions with zero and nonzero population densities, which represent population fronts. Reaction term is modeled by a generalized Kolmogorov-Fisher term, namely $r(u)=u(1-u^\beta)$. The discretization of this problem is challenging because the numerical scheme has to reproduce shock waves or fronts, and preserve stability and invariance properties. We present a new high-order family of numerical methods based on a discontinuous Galerkin space discretization and Runge-Kutta time stepping. These methods are capable to reproduce in the numerical solution some main properties of the analytical solution, like positivity, and to preserve stability and accuracy.

Reconstructing fMRI BOLD signals arising from cerebellar granule neurons - comparing GLM and balloon models

2015 International Joint Conference on Neural Networks (IJCNN), 2015

Understanding the relationship between fMRI BOLD and underlying neuronal activity has been crucia... more Understanding the relationship between fMRI BOLD and underlying neuronal activity has been crucial to connect circuit behavior to cognitive functions. In this paper, we modeled fMRI BOLD reconstructions with general linear model and balloon modeling using biophysical models of rat cerebellum granular layer and stimuli spike trains of various response times. Linear convolution of the hemodynamic response function with the known spiking information reconstructed activity similar to experimental BOLD-like signals with the limitation of short stimuli trains. Balloon model through Volterra kernels gave seemingly similar results to that of general linear model. Our main goal in this study was to understand the activity role of densely populated clusters through BOLD-like reconstructions given neuronal responses and by varying response times for the whole stimulus duration.

Diffusion effects in the sliding filament model of muscle contraction

ABSTRACT

A Comparison Between Relaxation and Kurganov—Tadmor Schemes

Mathematics in Industry, 2008

Discontinuous Galerkin Approximation of Relaxation Models for Linear and Nonlinear Diffusion Equations

SIAM Journal on Scientific Computing, 2012

In this work we present finite element approximations of relaxed systems for nonlinear diffusion ... more In this work we present finite element approximations of relaxed systems for nonlinear diffusion problems, which can also tackle the cases of degenerate and strongly degenerate diffusion equations. Relaxation schemes take advantage of the replacement of the original partial differential equation (PDE) with a semilinear hyperbolic system of equations, with a stiff source term, tuned by a relaxation parameter ε. When ε → 0 + , the system relaxes onto the original PDE: in this way, a consistent discretization of the relaxation system for vanishing ε yields a consistent discretization of the original PDE. The numerical schemes obtained with this procedure do not require solving implicit nonlinear problems and possess the robustness of upwind discretizations. The proposed approximations are based on a discontinuous Galerkin method in space and on suitable implicitexplicit integration in time. Then, in principle, we can achieve any order of accuracy and obtain stable solutions, even when the diffusion equation becomes degenerate and solution singularities develop. Moreover, when needed, we can easily incorporate slope limiters within our schemes in order to handle spurious oscillatory phenomena. Some preliminary theoretical results are given, along with several numerical tests in one and two space dimensions, both for linear and nonlinear diffusion problems, including a degenerate diffusion equation, that provide numerical evidence of the properties of the presented approach.

Increasing Efficiency Through Optimal RK Time Integration of Diffusion Equations

Hyperbolic Problems: Theory, Numerics, Applications, 2008

The application of Runge-Kutta schemes designed to enjoy a large region of absolute stability can... more The application of Runge-Kutta schemes designed to enjoy a large region of absolute stability can significantly increase the efficiency of numerical methods for PDEs based on a method of lines approach. In this work we investigate the improvement in the efficiency of the time integration of relaxation schemes for degenerate diffusion problems, using SSP Runge-Kutta schemes and computing the maximal CFL coefficients. This technique can be extended to other PDEs, linear and nonlinear, provided the space operator has eigenvalues with a non-zero real part.