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A nonlinear dynamics perspective of Wolfram’s new kind of science. Part III: Predicting the unpredictable
 International Journal of Bifurcation and Chaos
, 2004
"... This tutorial provides a nonlinear dynamics perspective to Wolfram’s monumental work on A New Kind of Science. By mapping a Boolean local Rule, ortruth table, ontothepoint attractors of a specially tailored nonlinear dynamical system, we show how some of Wolfram’s empirical observations can be justi ..."
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This tutorial provides a nonlinear dynamics perspective to Wolfram’s monumental work on A New Kind of Science. By mapping a Boolean local Rule, ortruth table, ontothepoint attractors of a specially tailored nonlinear dynamical system, we show how some of Wolfram’s empirical observations can be justified on firm ground. The advantage of this new approach for studying Cellular Automata phenomena is that it is based on concepts from nonlinear dynamics and attractors where many fuzzy concepts introduced by Wolfram via brute force observations can be defined and justified via mathematical analysis. The main result of Part I is the introduction of a fundamental concept called linear separability and a complexity index κ for each local Rule which characterizes the intrinsic geometrical structure of an induced “Boolean cube ” in threedimensional Euclidean space. In particular, Wolfram’s seductive idea of a “threshold of
Polynomial Coefficient Based MultiTone Testing of Analog Circuits
"... Abstract—A method of testing for parametric faults of analog circuits based on a polynomial representaion of faultfree function of the circuit is presented. The response of the circuit under test (CUT) is estimated as a polynomial in the applied input voltage at relevant frequencies apart from DC. ..."
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Abstract—A method of testing for parametric faults of analog circuits based on a polynomial representaion of faultfree function of the circuit is presented. The response of the circuit under test (CUT) is estimated as a polynomial in the applied input voltage at relevant frequencies apart from DC. Classification of CUT is based on a comparison of the estimated polynomial coefficients with those of the fault free circuit. The method needs very little augmentation of circuit to make it testable as only output parameters are used for classification. This procedure is shown to uncover several parametric faults causing smaller than 5 % deviations the nominal values. Fault diagnosis based upon sensitivity of polynomial coefficients at relevant frequencies is also proposed.
Hormonal control of apical membrane Na transport in epithelia. Studies with fluctuation analysis
 Journal of ~al Physiology
, 1983
"... ABSTRACT To study the mechanisms by which antidiuretic hormone and prostaglandins regulate Na transport at the apical membranes of the cells of anuran tissues, studies were done with fluctuation analysis. Epithelia of frog skin (Rana pipiens) were treated with vasopressin alone, or treated with vaso ..."
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ABSTRACT To study the mechanisms by which antidiuretic hormone and prostaglandins regulate Na transport at the apical membranes of the cells of anuran tissues, studies were done with fluctuation analysis. Epithelia of frog skin (Rana pipiens) were treated with vasopressin alone, or treated with vasopressin after inhibition of Na transport by indomethacin. The tissues were bathed symmetrically with a ClHCO 3 Ringer solution and shortcircuited continuously. In this experimental circumstance, the amilorideinduced current noise power density spectra were of the Lorentzian type with little or no I /f noise, provided that "scraped " skins were used for study. Despite large changes of Na transport, especially in epithelia treated with indomethacin and vasopressin, the singlechannel Na current remained essentially unchanged, whereas the density of amilorideinhibitable, electrically conductive Na channels was increased by vasopressin and decreased by indomethacin.
Bounds on Defect Level and Fault Coverage in Linear Analog Circuit Testing Area E System Integration and Test, and VLSI Chip Design and Test
"... Transfer function coefficients (TFC) are widely used to test linear analog circuits for parametric and catastrophic faults. This paper presents closed form expressions for an upper bound on the defect level (DL) and a lower bound on fault coverage (FC) achievable in TFC based test method. The comput ..."
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Transfer function coefficients (TFC) are widely used to test linear analog circuits for parametric and catastrophic faults. This paper presents closed form expressions for an upper bound on the defect level (DL) and a lower bound on fault coverage (FC) achievable in TFC based test method. The computed bounds have been tested and validated on several benchmark circuits. Further, application of these bounds to scalable RC ladder networks reveal a number of interesting characteristics. The approach adopted here is general and can be extended to find bounds of DL and FC of other parametric test methods for linear and nonlinear circuits.
EXPLICIT MATRIX FORMULATION FOR THE ANALYSIS OF SYNTHETIC LINEARLY AND NON LINEARLY LOADED MATERIALS IN FDTD
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, 2001
"... The explosive growth in wireless communications has led to an increased demand for wireless products that are cheaper, smaller, and lower power. Recently there has been an increased interest in using CMOS, a traditional digital and low frequency analog IC technology, to implement RF components such ..."
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The explosive growth in wireless communications has led to an increased demand for wireless products that are cheaper, smaller, and lower power. Recently there has been an increased interest in using CMOS, a traditional digital and low frequency analog IC technology, to implement RF components such as mixers, voltage controlled oscillators (VCOs), and low noise amplifiers (LNAs). Future massmarket RF links, such as BlueTooth, will require the potentially lowcost singlechip solutions that CMOS can provide. In order for such singlechip solutions to be realized, RF circuits must be designed that can operate in the presence of noisy digital circuitry. The voltage controlled oscillator (VCO), an important building block for RF systems, is particularly sensitive when exposed to an electrically noisy environment. In addition, CMOS implementations of VCOs have been hampered by the lack of highquality integrated inductors. This thesis focuses on the design of a fully integrated 2.5 GHz LC CMOS VCO. The circuit is intended as a vehicle for future mixed RF/digital noise characterization. The circuit was implemented in a 0.35 µm single poly, 4 metal, 3.3 V, CMOS process
NONLINEAR SIGNAL PROCESSOR DESIGN: A BUILDING BLOCK APPROACH
"... A new approach for the design of nonlinear systems (signal processors) based on an entirely new and interesting paradigm is presented in this paper. It is similar in spirits to the Neural nets paradigm (learn from existing systems) or the object oriented approach that has now become standard in soft ..."
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A new approach for the design of nonlinear systems (signal processors) based on an entirely new and interesting paradigm is presented in this paper. It is similar in spirits to the Neural nets paradigm (learn from existing systems) or the object oriented approach that has now become standard in software engineering and, in fact, takes it one step further as explained in the paper. This approach, though very simple, makes complex nonlinear systems design much easier. A number of practical applications are possible and we discuss few such applications. Detailed results will be provided at the conference 1.
Synthesis of Generalized Van der Pol Oscillator Systems
"... Abstract: In this paper we present the method for synthesis of generalized Van der Pol oscillator systems using Melnikov function. The oscillations in such systems are regarded as limit cycles in perturbed Hamiltonian systems under polynomial perturbations of arbitrary degree. The method of synthesi ..."
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Abstract: In this paper we present the method for synthesis of generalized Van der Pol oscillator systems using Melnikov function. The oscillations in such systems are regarded as limit cycles in perturbed Hamiltonian systems under polynomial perturbations of arbitrary degree. The method of synthesis is based on appropriate computation of perturbation coefficients, so that the prescribed properties are fulfilled. KeyWords: Van der Pol oscillators, Melnikov function, Limit cycles, Synthesis of oscillator systems