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56
The Global Structure of Traveling Waves in Spatially Discrete Dynamical Systems
 J. Dynam. Differential Equations
, 1997
"... We obtain existence of traveling wave solutions for a class of spatially discrete systems, namely lattice differential equations. Uniqueness of the wave speed c, and uniqueness of the solution with c 6= 0, are also shown. More generally, the global structure of the set of all traveling wave solution ..."
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Cited by 34 (5 self)
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We obtain existence of traveling wave solutions for a class of spatially discrete systems, namely lattice differential equations. Uniqueness of the wave speed c, and uniqueness of the solution with c 6= 0, are also shown. More generally, the global structure of the set of all traveling wave solutions is shown to be a smooth manifold where c 6= 0. Convergence results for solutions are obtained at the singular perturbation limit c ! 0. 1 Introduction We are interested in lattice differential equations, namely infinite systems of ordinary differential equations indexed by points on a spatial lattice, such as the Ddimensional integer lattice Z D . Our focus in this paper is the global structure of the set of traveling wave solutions for such systems. This entails results on existence and uniqueness, and on continuous (or smooth) dependence of traveling waves and their speeds on parameters, as well as some delicate convergence results in the singular perturbation case c ! 0 of the wav...
AER Image Filtering Architecture for VisionProcessing Systems
 IEEE Trans. Circuits Syst. I, Fundam. Theory Appl
, 1999
"... A VLSI architecture is proposed for the realization of realtime twodimensional (2D) image filtering in an addressevent representation (AER) vision system. The architecture is capable of implementing any convolutional kernel F (x; y) as long as it is decomposable into xaxis and yaxis components ..."
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Cited by 23 (7 self)
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A VLSI architecture is proposed for the realization of realtime twodimensional (2D) image filtering in an addressevent representation (AER) vision system. The architecture is capable of implementing any convolutional kernel F (x; y) as long as it is decomposable into xaxis and yaxis components, i.e., F (x; y)=H(x)V (y), for some rotated coordinate system fx; yg and if this product can be approximated safely by a signed minimum operation. The proposed architecture is intended to be used in a complete vision system, known as the boundary contour system and feature contour system (BCSFCS) vision model, proposed by Grossberg and collaborators. The present paper proposes the architecture, provides a circuit implementation using MOS transistors operated in weak inversion, and shows behavioral simulation results at the system level operation and some electrical simulations. Index TermsAnalog integrated circuits, communication systems, convolution circuits, Gabor filters, image anal...
Pattern Formation and Spatial Chaos in Spatially Discrete Evolution Equations
, 1995
"... We consider an array of scalar nonlinear dynamical systems u = \Gammaf (u), arranged on the sites of a spatial lattice, for example on the integer lattice ZZ 2 in the plane IR 2 . We impose a coupling between nearest neighbors, and also between nextnearest neighbors, in the form of discrete La ..."
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Cited by 20 (9 self)
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We consider an array of scalar nonlinear dynamical systems u = \Gammaf (u), arranged on the sites of a spatial lattice, for example on the integer lattice ZZ 2 in the plane IR 2 . We impose a coupling between nearest neighbors, and also between nextnearest neighbors, in the form of discrete Laplacians with + and \Thetashaped stencils. These couplings can be of any strength, and of either sign (positive or negative), and the resulting infinite systems of ODE's need not be near a PDE continuum limit. We study stable equilibria for such systems, from the point of view of pattern formation and spatial chaos, where these terms mean that the spatial entropy of the set of stable equilibria is zero, respectively, positive. In particular, for an idealized class of nonlinearities f corresponding to a "double obstacle" at u = \Sigma1 with f(u) = flu in between, it is natural to consider "mosaic solutions," namely equilibria which assume only the values u i;j 2 f\Gamma1; 0; 1g at each (i; ...
Pattern Formation and Spatial Chaos in Lattice Dynamical Systems: II
"... We survey a class of continuoustime lattice dynamical systems, with an idealized nonlinear. We introduce a class of equilibria called mosaic solutions, which are composed of the elements 1, \Gamma1, and 0, placed at each lattice point. A stability criterion for such solutions is given. The spatial ..."
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Cited by 18 (6 self)
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We survey a class of continuoustime lattice dynamical systems, with an idealized nonlinear. We introduce a class of equilibria called mosaic solutions, which are composed of the elements 1, \Gamma1, and 0, placed at each lattice point. A stability criterion for such solutions is given. The spatial entropy h of the set of all such stable solutions is defined, and we study how this quantity varies with parameters. Systems are qualitatively distinguished according to whether h = 0 (termed pattern formatio), or h ? 0 (termed spatial chaos). Numerical techniques for calculating h are described. 1. Mosaic Solutions As described in the companion paper [4], we study the phenomenon of pattern formation and spatial chaos in lattice dynamical systems. In order for us to see these phenomena globally, we consider a special class of equilibrium solutions, called mosaic solutions, introduced in [5], and studied there and in [6]. We work here with the system (1:1) u i;j = \Gammafi + \Delta + ...
Spatial Patterns, Spatial Chaos, And Traveling Waves In Lattice Differential Equations
 in: Stochastic and Spatial Structures of Dynamical Systems, eds. S.J. van Strien and S.M. Verduyn Lunel, NorthHolland
, 1996
"... We survey recent results in the theory of lattice differential equations. Such equations yield continuoustime, usually infinitedimensional, dynamical systems, which possess a discrete spatial structure modeled on a lattice. The systems we consider, generally over a higherdimensional lattice such ..."
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Cited by 10 (6 self)
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We survey recent results in the theory of lattice differential equations. Such equations yield continuoustime, usually infinitedimensional, dynamical systems, which possess a discrete spatial structure modeled on a lattice. The systems we consider, generally over a higherdimensional lattice such as ZZ D ` IR D , are the simplest nontrivial ones which incorporate both local nonlinear dynamics and short range interactions. Of particular interest are stable equilibria, and the regular patterns, or lack thereof, that are displayed. Traveling wave solutions in such systems are also discussed. 1 Introduction By a lattice differential equation or LDE we mean a system of ordinary differential equations, often of infinite order, in which the state vector u = fu j g j2 is coordinatized by a set , the lattice, which possesses some underlying spatial structure. Typical choices of ` IR D are the Ddimensional integer lattices ZZ D , the hexagonal lattice in the plane, and the crystall...
A CMOS generalpurpose sampleddata analogue microprocessor
 ISCAS 2000
, 2000
"... This paper presents a generalpurpose sampleddata analogue processing element that essentially functions as an analogue microprocessor (AµP). The AµP executes software programs, in a way akin to a digital microprocessor, while nevertheless operating on analogue sampled data values. This enables the ..."
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Cited by 10 (2 self)
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This paper presents a generalpurpose sampleddata analogue processing element that essentially functions as an analogue microprocessor (AµP). The AµP executes software programs, in a way akin to a digital microprocessor, while nevertheless operating on analogue sampled data values. This enables the design of mixedmode systems which retain the speed/area/power advantages of the analogue signal processing paradigm while being fully programmable, generalpurpose systems. A proofofconcept integrated circuit has been implemented in 0.8 µm CMOS technology, using switchedcurrent techniques. Experimental results and examples of the application of the AµPs in image processing are presented. 1.
Learning a simple recurrent neural state space model to behave like Chua's double scroll
, 1995
"... In this short paper we present a simple discrete time autonomous neural state space model (recurrent network) that behaves like Chua's double scroll. The model is identified using Narendra's dynamic backpropagation procedure. Learning is done in `packets' of increasing time horizon. Keywords. Do ..."
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Cited by 10 (4 self)
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In this short paper we present a simple discrete time autonomous neural state space model (recurrent network) that behaves like Chua's double scroll. The model is identified using Narendra's dynamic backpropagation procedure. Learning is done in `packets' of increasing time horizon. Keywords. Double scroll, recurrent network, neural state space model, dynamic backpropagation, sensitivity model, local optimization. 1 Introduction The last ten years Chua's circuit has become a paradigm for studying chaos [11]. This simple electrical circuit is able to produce complex behaviour and to bifurcate from order to chaos [5]. Moreover Chua's circuits have been used recently as cells within cellular neural networks instead of classical neurons, leading to phenomena such as e.g. spiral waves [4][13][14]. On the other hand cellular and generalized cellular neural networks are in itself also able to produce double scroll or ndouble scroll like behaviour respectively [1][9][15][17]. The latter...
Szatmári: “The New Framework of Applications  The Aladdin System
 J. of Circuits, Systems, and Computers (JCSC), Vol
, 2003
"... The first CNN technologybased, high performance industrial visual computer called Aladdin is reported. The revolutionary device is the world premier of the ACE4k Cellular Visual Microprocessor (CVM) chip powering an industrial visual computer. One of the most important features of the Aladdin syste ..."
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Cited by 3 (0 self)
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The first CNN technologybased, high performance industrial visual computer called Aladdin is reported. The revolutionary device is the world premier of the ACE4k Cellular Visual Microprocessor (CVM) chip powering an industrial visual computer. One of the most important features of the Aladdin system is the image processing library. The library reduces algorithm development time, provides efficient codes, error free operation in binary, and accurate operation in grayscale nodes. Moreover the library provides an easy way to use the Aladdin system for those who are not familiar with the CNN technology. Keywords: CNN technology; vision system; Cellular Visual Microprocessor. 1.
Motion Segmentation and Tracking with Edge Relaxation and Optimization using Fully Parallel Methods in the Cellular Nonlinear Network Architecture
, 2001
"... In this paper we outline a fully parallel and locally connected computation model for the segmentation of motion events in video sequences based on spatial and motion information. Extraction of motion information from video series is very time consuming. Most of the computing effort is devoted to th ..."
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Cited by 3 (0 self)
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In this paper we outline a fully parallel and locally connected computation model for the segmentation of motion events in video sequences based on spatial and motion information. Extraction of motion information from video series is very time consuming. Most of the computing effort is devoted to the estimation of motion vector fields, defining objects and determining the exact boundaries of these objects. The split and merge segmentation of different small areas, those obtained by oversegmentation, needs an optimization process. In our proposed algorithm the process starts from an oversegmented image, then the segments are merged by applying the information coming from the spatial and temporal auxiliary data: motion fields and motion history, calculated from consecutive image frames. This grouping process is defined through a similarity measure of neighboring segments, which is based on intensity, speed and the timedepth of motionhistory. There is also a feedback for checking the merging process, by this feedback we can accept or refuse the cancellation of a segmentborder. Our parallel approach is independent of the number of segments and objects, since instead of graph representation of these components, image features are defined on the pixel level. We use simple VLSI implementable functions like arithmetic and logical operators, local memory transfers and convolution. These elementary instructions are used to build up the basic routines such as motion displacement field detection, disocclusion removal, anisotropic diffusion, grouping by stochastic optimization. This relaxationbased motion segmentation can be a basic step of the effective coding of image series and other automatic motion tracking systems. The proposed system is ready to be implemented in a Cellular Nonl...
CNN Based SpatioTemporal Nonlinear Filtering and Endocardial Boundary Detection in Echocardiography
 Proc. ECCTD97
, 1997
"... : In this paper, a CNN based spatiotemporal approach is introduced for finding the endocardial (inner) boundary of the left ventricle from a sequence of echocardiographic images. The discussed analogic 1 CNN algorithm combines optimal nonlinear filtering and constrained wave propagation in ord ..."
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Cited by 3 (1 self)
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: In this paper, a CNN based spatiotemporal approach is introduced for finding the endocardial (inner) boundary of the left ventricle from a sequence of echocardiographic images. The discussed analogic 1 CNN algorithm combines optimal nonlinear filtering and constrained wave propagation in order to estimate the continuous contour of a moving object in a medium where the edges are illdefined. In the preprocessing phase, nonlinear filtering is employed to remove the coherent speckle noise that corrupts the images. It is verified that an optimal filtering strategy should estimate the mode of the local intensity histogram. Three different approximations of the mode filter were implemented, derived from robust statistics 2 and geometrydriven diffusion 3 , that give an output consistent with the maximum likelihood estimate of the noisy sequence. The kernel of the left ventricle is located and the boundary is found using a fuzzyadaptive technique that embodies constrained w...