Topic
Symbolic method
About: Symbolic method is a research topic. Over the lifetime, 180 publications have been published within this topic receiving 2495 citations.
Papers published on a yearly basis
Papers
TL;DR: In this paper, a general unified approach for arranging quantum operators of optical fields into ordered products (normal ordering, antinormal ordering, Weyl ordering) by fashioning Dirac's symbolic method and representation theory is presented.
Abstract: We present a general unified approach for arranging quantum operators of optical fields into ordered products (normal ordering, antinormal ordering, Weyl ordering (or symmetric ordering)) by fashioning Dirac's symbolic method and representation theory. We propose the technique of integration within an ordered product (IWOP) of operators to realize our goal. The IWOP makes Dirac's representation theory and the symbolic method more transparent and consequently more easily understood. The beauty of Dirac's symbolic method is further revealed. Various applications of the IWOP technique, such as in developing the entangled state representation theory, nonlinear coherent state theory, Wigner function theory, etc, are presented.
336 citations
TL;DR: In this article, a symbolic method for organizing the representation theory of one-dimensional superalgebras is presented, which relies on special objects, which are called adinkra symbols, which supply tangible geometric forms to the still emerging mathematical basis underlying supersymmetry.
Abstract: We present a symbolic method for organizing the representation theory of one-dimensional superalgebras. This relies on special objects, which we have called adinkra symbols, which supply tangible geometric forms to the still-emerging mathematical basis underlying supersymmetry.
202 citations
TL;DR: A simple and systematic method is described for calculating the integral of a polynomial function over an arbitrary nonconvex polyhedron and the practical accuracy of the result is within the accuracy of floating-point arithmetic.
Abstract: A simple and systematic method is described for calculating the integral of a polynomial function over an arbitrary nonconvex polyhedron. First a general formula is presented for direct evaluation of the integral of a polynomial over a 3-D simplex. An integral over a polyhedron can then be easily calculated by using the central projection method and decomposing a polyhedron symmetrically into a set of simplices and accumulating the results from each simplex based on this formula. This method adopts a systematic and automatic decomposition. It is analytically exact, but the practical accuracy of the result is within the accuracy of floating-point arithmetic. Furthermore, the time complexity of this method is linearly proportional to the number of vertices of a polyhedron.
125 citations
TL;DR: This work proposes a specific algorithm, called "false flipped symbols," for establishing the presence of temporal irreversibility without the need for generating surrogate data.
Abstract: We describe a symbolic approach for measuring temporal "irreversibility" in time-series measurements. Temporal irreversibility is important because it excludes Gaussian linear dynamics and static transformations of such dynamics from the set of possible generating processes. A symbolic method for measuring temporal irreversibility is attractive because it is computationally efficient, robust to noise, and simplifies statistical analysis of confidence limits. We propose a specific algorithm, called "false flipped symbols," for establishing the presence of temporal irreversibility without the need for generating surrogate data. Besides characterizing experimental data, our results are relevant to the question of selecting alternative models. We illustrate our points with numerical model output and experimental measurements.
124 citations
1 Jan 2003
TL;DR: This work describes a technique for fully automatic parametric WCET analysis, which is based on known mathematical methods: an abstract interpretation to calculate parametric constraints on program flow, a symbolic method to count integer points in polyhedra, and a symbolic ILP technique to solve the subsequent IPET calculation of WCET bound.
Abstract: Worst-Case Execution Time (WCET) analysis means to compute a safe upper bound to the execution time of a piece of code. Parametric WCET analysis yields symbolic upper bounds: expressions that may contain parameters. These parameters may represent, for instance, values of input parameters to the program, or maximal iteration counts for loops. We describe a technique for fully automatic parametric WCET analysis, which is based on known mathematical methods: an abstract interpretation to calculate parametric constraints on program flow, a symbolic method to count integer points in polyhedra, and a symbolic ILP technique to solve the subsequent IPET calculation of WCET bound. The technique is capable of handling unstructured code, and it can find upper bounds to loop iteration counts automatically.
109 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 5 |
| 2020 | 7 |
| 2019 | 8 |
| 2018 | 3 |
| 2017 | 6 |
| 2016 | 5 |