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49
A CoSynthesis Approach to Embedded System Design Automation
, 1994
"... Embedded systems are targeted for specific applications under constraints on relative timing of their actions. For such systems, use of predesigned reprogrammable components such as microprocessors provides an effective way to reduce system cost by implementing part of the functionality as a progr ..."
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Cited by 21 (5 self)
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Embedded systems are targeted for specific applications under constraints on relative timing of their actions. For such systems, use of predesigned reprogrammable components such as microprocessors provides an effective way to reduce system cost by implementing part of the functionality as a program running on the processor. Dedicated hardware is often necessary to achieve requisite timing performance. Analysis of timing constraints is key to determination of an efficient hardwaresoftware implementation. In this paper, we present a methodology to achieve embedded system realizations as cosynthesis of interacting hardware and software components. This cosynthesis is based on synthesis techniques for digital hardware and software compilation under constraints. We present operationlevel timing constraints and develop the notion of satisfiability of constraints by a given implementation. Constraint analysis is then used to define hardware and software portions of functionality...
Combining Theorem Proving and Symbolic Mathematical Computing
 Integrating Symbolic Mathematical Computation and Arti Intelligence, volume 958 of Lecture Notes in Computer Science
, 1995
"... An intelligent mathematical environment must enable symbolic mathematical computation and sophisticated reasoning techniques on the underlying mathematical laws. This paper disscusses different possible levels of interaction between a symbolic calculator based on algebraic algorithms and a theorem p ..."
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Cited by 13 (1 self)
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An intelligent mathematical environment must enable symbolic mathematical computation and sophisticated reasoning techniques on the underlying mathematical laws. This paper disscusses different possible levels of interaction between a symbolic calculator based on algebraic algorithms and a theorem prover. A high level of interaction requires a common knowledge representation of the mathematical knowledge of the two systems. We describe a model for such a knowledge base mainly consisting of type and algorithm schemata, algebraic algorithms and theorems.
From Honest to Intelligent Plotting
, 1995
"... Adaptive and honest plotting are two techniques to improve the quality of curve and surface visualization packages. Beyond honest plotting, we investigate a number of alternative techniques in order to improve correctness and completeness of 2D and 3D plotting, increase efficiency, and achieve bette ..."
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Cited by 10 (3 self)
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Adaptive and honest plotting are two techniques to improve the quality of curve and surface visualization packages. Beyond honest plotting, we investigate a number of alternative techniques in order to improve correctness and completeness of 2D and 3D plotting, increase efficiency, and achieve better usability. We refer to these techniques as intelligent plotting as most of them transparently take advantage of the numerical and/or symbolic capabilities available from some mathematical engine in order to provide better and faster graphical displays. We implemented these techniques inside two very different packages: the Graphing Calculator and IZIC which we used as testbeds for our experiments. 1 Introduction Most general purpose Computer Algebra (CA) systems include more and more sophisticated 2D and 3D plotting facilities. Axiom, Macsyma, Maple, and Mathematica, for example, all include options to change graphical parameters such as colors, labels, viewpoint, or painting style. In a...
Some Remarks on the Constant in the Strengthened C.B.S. Inequality: Application to h and pHierarchical Finite Element Discretizations of Elasticity Problems
, 1997
"... For a class of twodimensional boundary value problems including diffusion and elasticity problems it is proved that the constants in the corresponding strengthened CauchyBuniakowskiSchwarz (C.B.S.) inequality in the cases of hhierarchical and phierarchical finite element discretizations with t ..."
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Cited by 7 (1 self)
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For a class of twodimensional boundary value problems including diffusion and elasticity problems it is proved that the constants in the corresponding strengthened CauchyBuniakowskiSchwarz (C.B.S.) inequality in the cases of hhierarchical and phierarchical finite element discretizations with triangular meshes differ by the factor 0.75. For plane linear elasticity problems and triangulations with right isosceles triangles formulas are presented that show the dependence of the constant in the C.B.S. inequality on the Poisson's ratio. Furthermore, numerically determined bounds of the constant in the C.B.S. inequality are given for threedimensional elasticity problems discretized by means of tetrahedral elements. Finally, the robustness of iterative solvers for elasticity problems is discussed briefly.
Computers, Reasoning and Mathematical Practice
"... ion in itself is not the goal: for Whitehead [117]"it is the large generalisation, limited by a happy particularity, which is the fruitful conception." As an example consider the theorem in ring theory, which states that if R is a ring, f(x) is a polynomial over R and f(r) = 0 for every e ..."
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Cited by 6 (2 self)
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ion in itself is not the goal: for Whitehead [117]"it is the large generalisation, limited by a happy particularity, which is the fruitful conception." As an example consider the theorem in ring theory, which states that if R is a ring, f(x) is a polynomial over R and f(r) = 0 for every element of r of R then R is commutative. Special cases of this, for example f(x) is x 2 \Gamma x or x 3 \Gamma x, can be given a first order proof in a few lines of symbol manipulation. The usual proof of the general result [20] (which takes a semester's postgraduate course to develop from scratch) is a corollary of other results: we prove that rings satisfying the condition are semisimple artinian, apply a theorem which shows that all such rings are matrix rings over division rings, and eventually obtain the result by showing that all finite division rings are fields, and hence commutative. This displays von Neumann's architectural qualities: it is "deep" in a way in which the symbol manipulati...
Stochastic Effects In A Model Of Nematode Infection In Ruminants
, 1998
"... We illustrate the importance of stochastic eects in population models of biological systems and demonstrate a number of analytic and simulationbased approaches that can usefully be applied to such models. In so doing, we compare the stochastic approach to the more usual deterministic one. The mo ..."
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Cited by 5 (1 self)
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We illustrate the importance of stochastic eects in population models of biological systems and demonstrate a number of analytic and simulationbased approaches that can usefully be applied to such models. In so doing, we compare the stochastic approach to the more usual deterministic one. The model studied represents the gastrointestinal infection of ruminants by nematodes when the hosts maintain a xed density. The incorporation of a feedback mechanism, which accounts for the immune response of the infected animals, results in a highly nonlinear model; similar forms of nonlinearity are a feature of many plausible models in population biology. In the absence of an analytic solution to the full stochastic model we explore a number of approximations and compare them to simulations of the full stochastic process. We explore three modes of behaviour of the system. In the endemic regime the stochastic system uctuates widely around the nonzero xed points of the determinist...
Plotting and Scheming with Wavelets
 Mathematics Magazine
, 1996
"... this article. The Matlab Mfiles we used are available from http://www.spelman.edu/~colm. ..."
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Cited by 5 (0 self)
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this article. The Matlab Mfiles we used are available from http://www.spelman.edu/~colm.
Initial Values for a Class of Exponential Sum Least Squares Fitting Problems
, 1998
"... In an earlier report the authors developed an initial value algorithm for one class of exponential sum least squares fitting problems. As a natural extension of that problem the authors in this paper develop an initial value algorithm for a slightly different model in the class of exponential models ..."
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Cited by 5 (4 self)
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In an earlier report the authors developed an initial value algorithm for one class of exponential sum least squares fitting problems. As a natural extension of that problem the authors in this paper develop an initial value algorithm for a slightly different model in the class of exponential models, f (t) = P p i=1 a i (1 \Gamma exp (\Gammab i t)), which occurs in radiophysics in medicin. A method of generalized interpolation will provide initial values a = [a 1 ; :::; a p ] ; b = [b 1 ; :::; b p ] and these are refined by iterative least squares algorithms. New initial value algorithms are developed. For data equidistant in time, generalized interpolation gives explicit expressions for p 2 and a semiheuristic solution for p 3. For data not equidistant in time, the numerical derivatives are estimated. The derivative is another exponential sum for which the authors earlier have developed an initial value algorithm for arbitrary number of terms and data not equidistant in time...
Initial Values for the Exponential Sum Least Squares Fitting Problem
, 1998
"... Exponential sum models f (t) = P p i=1 a i exp (\Gammab i t) are used frequently: In heat diffusion, diffusion of chemical compounds, time series in medicine, economics and the physical sciences and technology. As the fitting of an exponential sum by e.g. a least squares criterion is difficult, go ..."
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Cited by 5 (4 self)
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Exponential sum models f (t) = P p i=1 a i exp (\Gammab i t) are used frequently: In heat diffusion, diffusion of chemical compounds, time series in medicine, economics and the physical sciences and technology. As the fitting of an exponential sum by e.g. a least squares criterion is difficult, good initial values for the parameters a = [a 1 ; :::; a p ] ; b = [b 1 ; :::; b p ] are needed. Interpolation methods will provide initial values and these are then refined by general least squares algorithms. New initial value algorithms are developed. For data equidistant in time, generalized interpolation gives explicit expressions for p 2, and a numerically solvable onevariable equation for 3 p 4. For p ? 4 we use a heuristic algorithm to get rough initial values. For data not equidistant in time a two point interpolation by a exp (\Gammabt) will generate artificial data points equidistant in time. The least squares refinement is not using the artificial data. Numerical results are p...