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**1 - 6**of**6**### Efficient Nonlinear Mapping Using The Multi-Layer Perceptron

, 1994

"... In this thesis, the mapping capability of the Gabor polynomial is reviewed and the nonlinear mapping capability of Multi-layer perceptron(MLP) is discussed in terms of the number of parameters used to represent them. It is shown that the pattern storage capability of multi-variate polynomial is m ..."

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In this thesis, the mapping capability of the Gabor polynomial is reviewed and the nonlinear mapping capability of Multi-layer perceptron(MLP) is discussed in terms of the number of parameters used to represent them. It is shown that the pattern storage capability of multi-variate polynomial is much higher than the commonly used lower bound on multilayer perceptron pattern storage. It is also shown that multi-layer perceptron networks having second and third degree polynomial activations can be constructed which implement Gabor polynomials and therefore have the same high pattern storage capability. The polynomial networks are mapped to a conventional sigmoidal MLP resulting in highly efficient network. It is shown clearly that albeit techniques like output weight optimization and con...

### BOLTZMANN'S «NACHWIRKUNG » AND HEREDITARY MECHANICS

"... The origins of modern viscoelasticity theories (and, more generally, of “hereditary ” systems theories) are usually traced back to the work of Ludwig Boltzmann and Vito Volterra. This indication poses a first task to the historian: going beyond a generic reference in order to analyze Boltzmann' ..."

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The origins of modern viscoelasticity theories (and, more generally, of “hereditary ” systems theories) are usually traced back to the work of Ludwig Boltzmann and Vito Volterra. This indication poses a first task to the historian: going beyond a generic reference in order to analyze Boltzmann's and Volterra's contributions and to place them within the scientific context of their times. However, as one faces this study many problems arise, so forcing to extend the analysis to a much more complex framework than a mere description. Historiography on “hereditary ” theories is extremely poor, being limited to some papers written by Volterra. In his first writings on these topics, 1 Volterra appropriately mentioned other contributions preceding his own work which was considered by him, at least in part, as a development

### The Frequency Domain Behavioral Modeling and Simulation of Nonlinear Analog Circuits and Systems

, 1993

"... LUNSFORD II, PHILIP J. The Frequency Domain Behavioral Modeling and Simulation of Nonlinear Analog Circuits and Systems. (Under the direction of Michael B. Steer.) A new technique for the frequency-domain behavioral modeling and simulation of nonautonomous nonlinear analog subsystems is presented. ..."

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LUNSFORD II, PHILIP J. The Frequency Domain Behavioral Modeling and Simulation of Nonlinear Analog Circuits and Systems. (Under the direction of Michael B. Steer.) A new technique for the frequency-domain behavioral modeling and simulation of nonautonomous nonlinear analog subsystems is presented. This technique extracts values of the Volterra nonlinear transfer functions and stores these values in binary files. Using these files, the modeled substem can be simulated for an arbitrary periodic input expressed as a finite sum of sines and cosines. Furthermore, the extraction can be based on any circuit simulator that is capable of steady state simulation. Thus a large system can be divided into smaller subsystems, each of which is characterized by circuit level simulations or lab measurements. The total system can then be simulated using the subsystem characterization stored as tables in binary files.

### 856 PROCEEDINGS OF THE IRE From Circuit Theory to

"... Summary-The past two decades have witnessed profound changes in the composition, functions and the level of complexity of electrical as well as electronic systems which are employed in modem technology. As a result, classical RLC network theory, which was the mainstay of electrical engineering at a ..."

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Summary-The past two decades have witnessed profound changes in the composition, functions and the level of complexity of electrical as well as electronic systems which are employed in modem technology. As a result, classical RLC network theory, which was the mainstay of electrical engineering at a time when RLC networks were the bread and butter of the electrical engineer, has been and is being increasingly relegated to the status of a specialized branch of a much broader discipline-system theory-which is concerned with systems of all types regardless of their physical identity and purpose. This paper presents a brief survey of the evolution of system theory, together with an exposition of some of its main concepts, techniques and problems. The discussion is centered on the notion of state and emphasizes the role played by state-space techniques. The paper concludes with a brief statement of some of the key problems of system theory. I.

### 1LOCAL/GLOBAL IN MATHEMATICS AND PAINTING1

"... Twentieth century mathematicians have succesfully mastered a method or way of looking that combines local and global tools, and which has lead, for example, to the resolution of long standing open problems such as Fermat´s Last Theorem2 and the Conjecture of Taniyama, Shimura and Weil. In parts 1 an ..."

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Twentieth century mathematicians have succesfully mastered a method or way of looking that combines local and global tools, and which has lead, for example, to the resolution of long standing open problems such as Fermat´s Last Theorem2 and the Conjecture of Taniyama, Shimura and Weil. In parts 1 and 2 we will give a brief description of this way of looking, which we will then use, in part 3 as well as in the appendix, to analyse three concrete paintings of Pablo Picasso. When Michele Emmer invited me to participate in the second volume of “The Visual Mind”, I was already deeply inmersed in an on-going process that has been moving quite different people-most of us mathematicians, painters, musicians and architects-, for a long time. This process has lead us to analyze, in conversations and reflections as well as in concrete pieces of work, what we have been calling “transmission of knowledge”, in its many facets, starting from its personal, intellectual and professional impact on us and our work. As part of this process, in the spring of 1997 Laura Tedeschini-Lalli invited me to participate with a short cycle of conferences in the mathematics course she was then teaching at the School of Architecture, University Roma 3. During the mini-course, whose material can be

### Characterization, Modeling, and Control of the Nonlinear Ac- tuation Response of Ionic Polymer Transducers

, 2005

"... Ionic polymer transducers are a class of electroactive polymer materials that exhibit coupling between the electrical, chemical, and mechanical domains. With the ability for use as both sensors and actuators, these compliant, light weight, low voltage materials have the potential to benefit diverse ..."

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Ionic polymer transducers are a class of electroactive polymer materials that exhibit coupling between the electrical, chemical, and mechanical domains. With the ability for use as both sensors and actuators, these compliant, light weight, low voltage materials have the potential to benefit diverse application areas. Since the transduction properties of these materials were recently discovered, full understanding of their dynamic characteristics has not yet been achieved. This research has the goal of better understanding the actuation response of ionic polymers. A specific emphasis has been placed on investigating the observed nonlinear behavior because the existing proposed models do not account for these characteristics. Employing the Volterra representation, harmonic ratio analysis, and multisine excitations, characterization results for cantilever samples showed that the nonlinearity is dynamic and input-dependent, dominant at low frequencies, and that its influence varies depending on the solvent. It was determined that lower viscosity solvents trigger the nonlinear mechanisms at higher frequencies. Additionally, the primary components of the harmonic distortion appear to result from quadratic and cubic nonlinearities.