The Experts below are selected from a list of 3063 Experts worldwide ranked by ideXlab platform
Dimitra D Dionysiou - One of the best experts on this subject based on the ideXlab platform.
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introduction of hypermatrix and Operator Notation into a discrete mathematics simulation model of malignant tumour response to therapeutic schemes in vivo some Operator properties
2009Co-Authors: Georgios S Stamatakos, Dimitra D DionysiouAbstract:The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code). However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete Operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete Operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the Operators’ commutativity and outline the “summarize and jump” strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete Operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83–02, thus strengthening the reliability of the model developed.
Georgios S Stamatakos - One of the best experts on this subject based on the ideXlab platform.
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introduction of hypermatrix and Operator Notation into a discrete mathematics simulation model of malignant tumour response to therapeutic schemes in vivo some Operator properties
2009Co-Authors: Georgios S Stamatakos, Dimitra D DionysiouAbstract:The tremendous rate of accumulation of experimental and clinical knowledge pertaining to cancer dictates the development of a theoretical framework for the meaningful integration of such knowledge at all levels of biocomplexity. In this context our research group has developed and partly validated a number of spatiotemporal simulation models of in vivo tumour growth and in particular tumour response to several therapeutic schemes. Most of the modeling modules have been based on discrete mathematics and therefore have been formulated in terms of rather complex algorithms (e.g. in pseudocode and actual computer code). However, such lengthy algorithmic descriptions, although sufficient from the mathematical point of view, may render it difficult for an interested reader to readily identify the sequence of the very basic simulation operations that lie at the heart of the entire model. In order to both alleviate this problem and at the same time provide a bridge to symbolic mathematics, we propose the introduction of the notion of hypermatrix in conjunction with that of a discrete Operator into the already developed models. Using a radiotherapy response simulation example we demonstrate how the entire model can be considered as the sequential application of a number of discrete Operators to a hypermatrix corresponding to the dynamics of the anatomic area of interest. Subsequently, we investigate the Operators’ commutativity and outline the “summarize and jump” strategy aiming at efficiently and realistically address multilevel biological problems such as cancer. In order to clarify the actual effect of the composite discrete Operator we present further simulation results which are in agreement with the outcome of the clinical study RTOG 83–02, thus strengthening the reliability of the model developed.
Francisco Javier Delgado Cepeda - One of the best experts on this subject based on the ideXlab platform.
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QUANTUM: A Wolfram Mathematica add-on for Dirac Bra-Ket Notation, Non-Commutative Algebra, and Simulation of Quantum Computing Circuits
2016Co-Authors: Francisco Javier Delgado CepedaAbstract:This paper introduces QUANTUM, a free library of commands of Wolfram Mathematica that can be used to perform calculations directly in Dirac braket and Operator Notation. Its development started several years ago, in order to study quantum random walks. Later, many other features were included, like Operator and commutator algebra, simulation and graphing of quantum computing circuits, generation and solution of Heisenberg equations of motion, among others. To the best of our knowledge, QUANTUM remains a unique tool in its use of Dirac Notation, because it is used both in the input and output of the calculations. This work depicts its usage and features in Quantum Computing and Quantum Hamilton Dynamics. © Published under licence by IOP Publishing Ltd
Mehmet Pakdemirli - One of the best experts on this subject based on the ideXlab platform.
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vibrations of continuous systems with a general Operator Notation suitable for perturbative calculations
2001Co-Authors: Mehmet PakdemirliAbstract:The Operator Notation previously developed to analyze vibrations of continuous systems has been further generalized to model a system with an arbitrary number of coupled differential equations. Linear parts of the equations are expressed with an arbitrary linear differential and/or integral Operators, and non-linear parts are expressed with arbitrary quadratic and cubic Operators. Equations of motion are solved in their general form using the method of multiple scales, a perturbation technique. The case of primary resonances of the external excitation and one-to-one internal resonances between the natural frequencies of the equations is considered. The algorithm developed is applied to a non-linear cable vibration problem having small sag-to-span ratios.
Peter Benner - One of the best experts on this subject based on the ideXlab platform.
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a non conforming composite quadrilateral finite element pair for feedback stabilization of the stokes equations
2014Co-Authors: Peter Benner, Jens Saak, Friedhelm Schieweck, Piotr Skrzypacz, Heiko K WeicheltAbstract:In this contribution, we show a method for the boundary feedback stabilization of the Stokes problem around a stationary trajectory. We derive a formal low-rank algorithm for solving the stabilization problem in Operator Notation. The appearing ope rator equations are formulated in terms of stationary partial differential equations (PDEs ) instead of using their finite dimensional representations in terms of matrices. A Galerkin meth od, satisfying the divergence constraint pointwise locally is especially appealing since it r epresents appro- priately the action of the Helmholtz projection. The main advantages of the composite technique are the efficient assemb ly of element matrices, the reduction of computational costs using static condensation, a nd the diagonal mass matrix. The non-conforming character of the composite element guarantees a better sparsity pattern, compared to conforming elements, due to the lower number of couplings between basis functions corresponding to neighboring cells. We also achieve the pointwise mass conservation on sub-triangles of each element.