Marco Storace

The Hindmarsh-Rose neuron model: Bifurcation analysis and piecewise-linear approximations

This paper provides a global picture of the bifurcation scenario of the Hindmarsh-Rose model. A combination between simulations and numerical continuations is used to unfold the complex bifurcation structure. The bifurcation analysis is carried out by varying two bifurcation parameters and evidence is given that the structure that is found is universal and appears for all combinations of bifurcation parameters. The information about the organizing principles and bifurcation diagrams are then used to compare the dynamics of the model with that of a piecewise-linear approximation, customized for circuit implementation. A good match between the dynamical behaviors of the models is found. These results can be used both to design a circuit implementation of the Hindmarsh-Rose model mimicking the diversity of neural response and as guidelines to predict the behavior of the model as well as its circuit implementation as a function of parameters.

Ultra-Fast Stabilizing Model Predictive Control via Canonical Piecewise Affine Approximations

This paper investigates the use of canonical piecewise affine (PWA) functions for approximation and fast implementation of linear MPC controllers. The control law is approximated in an optimal way over a regular simplicial partition of a given set of states of interest. The stability properties of the resulting closed-loop system are analyzed by constructing a suitable PWA Lyapunov function. The main advantage of the proposed approach to the implementation of MPC controllers is that the resulting stabilizing approximate MPC controller can be implemented on chip with sampling times in the order of tens of nanoseconds.

Piecewise-linear approximation of nonlinear dynamical systems

The piecewise-linear (PWL) approximation technique developed by Julia/spl acute/n et al. in the past few years is applied to find approximate models of dynamical systems dependent on given numbers of state variables and parameters. Referring to some significant examples, i.e., topological normal forms, it is shown that a PWL dynamical system approximating a given smooth system can preserve its main features. In particular, if the approximation accuracy increases, the equivalence between approximating and approximated systems shifts from qualitative to quantitative. The validity of the proposed approach is eventually tested by use of a severe nonlinear example, i.e., the Rosenzweig-MacArthur system, which describes the population dynamics in a tritrophic food chain model.

Digital architectures realizing piecewise-linear multivariate functions: Two FPGA implementations

Digital architectures for the circuit realization of multivariate piecewise-linear (PWL) functions are reviewed and compared. The output of the circuits is a digital word representing the value of the PWL function at the n-dimensional input. In particular, we propose two architectures with different levels of parallelism/complexity. PWL functions with n = 3 inputs are implemented on an FPGA and experimental results are shown. The accuracy in the representation of PWL functions is tested through three benchmark examples, two concerning three-variate static functions and one concerning a dynamical control system defined by a bi-variate PWL function. Copyright

Accurate and Fast Simulation of Channel Noise in Conductance-Based Model Neurons by Diffusion Approximation

Stochastic channel gating is the major source of intrinsic neuronal noise whose functional consequences at the microcircuit- and network-levels have been only partly explored. A systematic study of this channel noise in large ensembles of biophysically detailed model neurons calls for the availability of fast numerical methods. In fact, exact techniques employ the microscopic simulation of the random opening and closing of individual ion channels, usually based on Markov models, whose computational loads are prohibitive for next generation massive computer models of the brain. In this work, we operatively define a procedure for translating any Markov model describing voltage- or ligand-gated membrane ion-conductances into an effective stochastic version, whose computer simulation is efficient, without compromising accuracy. Our approximation is based on an improved Langevin-like approach, which employs stochastic differential equations and no Montecarlo methods. As opposed to an earlier proposal recently debated in the literature, our approximation reproduces accurately the statistical properties of the exact microscopic simulations, under a variety of conditions, from spontaneous to evoked response features. In addition, our method is not restricted to the Hodgkin-Huxley sodium and potassium currents and is general for a variety of voltage- and ligand-gated ion currents. As a by-product, the analysis of the properties emerging in exact Markov schemes by standard probability calculus enables us for the first time to analytically identify the sources of inaccuracy of the previous proposal, while providing solid ground for its modification and improvement we present here.

A modular supervised algorithm for vessel segmentation in red-free retinal images

In this paper, a supervised algorithm for vessel segmentation in red-free images of the human retina is proposed. The algorithm is modular and made up of two fundamental blocks. The optimal values of two algorithm parameters are found out by maximizing proper measures of performances (MOPs) able to evaluate from a quantitative point of view the results provided by the proposed algorithm. The choice of the MOP allows one to tailor the solution to the specific image features to be emphasized. The performances of the algorithm are compared with those of other methods described in the literature. The simulation results show a good trade-off between quality and processing speed times. For instance, in terms of the maximum average accuracy (MAA), K value, and specificity (SP), the best performance outcomes are 0.9587, 0.8069 and 0.9477, respectively.

Synthesis of nonlinear multiport resistors: a PWL approach

This paper presents a method for the approximate synthesis of nonlinear multiport resistors. According to some fundamental circuit theory results, the general problem of synthesizing a multiport resistor with given constitutive equations corresponds to that of the synthesis of nonlinear controlled sources. Following this idea, in this paper, we focus on the design of nonlinear controlled sources using a piecewise-linear (PWL) approach. The constitutive equations are first approximated by resorting to canonical expressions for continuous PWL functions, and then implemented using a set of elementary building blocks. The proposed method is applied to the synthesis of the nonlinear resistive part of an equivalent circuit of the Hodgkin-Huxley nerve membrane model.

Synthesis of multiport resistors with piecewise-linear characteristics: a mixed-signal architecture

Non-linear multiport resistors are the main ingredients in the synthesis of non-linear circuits. Recently, a particular PWL representation has been proposed as a generic design platform (IEEE Trans. Circuits Syst.-I 2002; 49:1138–1149). In this paper, we present a mixed-signal circuit architecture, based on standard modules, that allows the electronic integration of non-linear multiport resistors using the mentioned PWL structure. The proposed architecture is fully programmable so that the unit can implement any user-defined non-linearity. Moreover, it is modular: an increment in the number of input variables can be accommodated through the addition of an equal number of input modules. Copyright

Circuit implementation of piecewise-affine functions based on a binary search tree

In this paper we introduce a digital architecture implementing piecewise-affine functions defined over domains partitioned into polytopes: the functions are linear affine over each polytope. The polytope containing the input vector is found by exploring a previously constructed binary search tree. Once the polytope is detected, the function is evaluated by addressing an affine map whose coefficients are stored in a memory. The architecture has been implemented on FPGA and experimental results for a benchmark example are shown.

A PWL ladder circuit which exhibits hysteresis

A circuit model for static hysteresis is presented. the circuit has a ladder structure with linear capacitors and piece wise linear resistors. the model behaviour shows all basic characteristics of static hysteresis phenomena. the model is put into relation with others proposed in the literature. an analysis of the model properties and a detailed comparison with the static Preisach model are made.