The TOPAS symbolic computation system

2011 ◽  
Vol 26 (S1) ◽  
pp. S22-S25 ◽  
Author(s):  
A. A. Coelho ◽  
J. Evans ◽  
I. Evans ◽  
A. Kern ◽  
S. Parsons
Keyword(s):  
Developmental Stage ◽  
Rietveld Refinement ◽  
Symbolic Computation ◽  
Computer Algebra ◽  
Symbolic System ◽  
Symbolic Form ◽  
Functional Changes ◽  
Low Level ◽  
Run Time

Computer algebra removes much of the drudgery from mathematics; it allows users to formulate models by using the language of mathematics and to have those models evaluated with little effort. This symbolic form of representation is often thought of as being separate to dedicated computational programs such as Rietveld refinement. These dedicated programs are often written in low level languages; they are relatively inflexible in what they do and modifying them to change functionality in a small manner is often a major programming task. This paper describes a symbolic system that is integrated into the dedicated Rietveld refinement program called TOPAS. The symbolic component allows large functional changes to be made at run time and with a relatively small amount of effort. In addition, the system as a whole reduces the programming complexity at the developmental stage.

scholarly journals A ONE LINE FACTORING ALGORITHM

2012 ◽  
Vol 92 (1) ◽  
pp. 61-69 ◽  
Author(s):  
WILLIAM B. HART
Keyword(s):  
Computer Algebra ◽  
Time Complexity ◽  
Run Time ◽  
Factoring Algorithm

AbstractWe describe a variant of Fermat’s factoring algorithm which is competitive with SQUFOF in practice but has heuristic run time complexity O(n1/3) as a general factoring algorithm. We also describe a sparse class of integers for which the algorithm is particularly effective. We provide speed comparisons between an optimised implementation of the algorithm described and the tuned assortment of factoring algorithms in the Pari/GP computer algebra package.

scholarly journals Partial Evaluation for Constraint-Based Program Analyses

1999 ◽  
Vol 6 (45) ◽  
Author(s):  
Torben Amtoft
Keyword(s):  
Code Generation ◽  
Partial Evaluation ◽  
Control Flow ◽  
Time Code ◽  
Low Level ◽  
Constraint Graph ◽  
Speed Up ◽  
Run Time

We report on a case study in the application of partial evaluation, initiated<br />by the desire to speed up a constraint-based algorithm for control-flow<br /> analysis. We designed and implemented a dedicated partial evaluator,<br />able to specialize the analysis wrt. a given constraint graph and thus <br />remove the interpretive overhead, and measured it with Feeley's Scheme<br />benchmarks. Even though the gain turned out to be rather limited, our<br />investigation yielded valuable feed back in that it provided a better understanding<br />of the analysis, leading us to (re)invent an incremental version.<br />We believe this phenomenon to be a quite frequent spinoff from using <br />partial evaluation, since the removal of interpretive overhead makes the flow<br />of control more explicit and hence pinpoints sources of inefficiency. <br /> Finally, we observed that partial evaluation in our case yields such regular,<br />low-level specialized programs that it begs for run-time code generation.

Symbolic Computation of Quantities Associated With Time-Periodic Dynamical Systems

2015 ◽  
Author(s):  
W. Grant Kirkland ◽  
S. C. Sinha
Keyword(s):  
Control System ◽  
Dynamical Systems ◽  
System Design ◽  
Symbolic Computation ◽  
Picard Iteration ◽  
Control System Design ◽  
Symbolic Form ◽  
Varying Coefficients ◽  
And Control ◽  
Time Periodic

Many dynamical systems can be modeled by a set of linear/nonlinear ordinary differential equations with periodic time-varying coefficients. The state transition matrix Φ(t,α) associated with the linear part of the equation can be expressed in terms of the periodic Lyapunov-Floquét transformation matrix Q(t,α) and a time-invariant matrix R(α). Computation of Q(t,α) and R(α) in a symbolic form as a function of system parameters α is of paramount importance in stability, bifurcation analysis, and control system design. In the past, a methodology has been presented for computing Φ(t,α) in a symbolic form, however Q(t,α) and R(α) have never been calculated in a symbolic form. Since Q(t,α) and R(α) were available only in numerical forms, general results for parameter unfolding and control system design could not be obtained in the entire parameter space. In this work a technique for symbolic computation of Q(t,α), and R(α) matrices is presented. First, Φ(t,α) is computed symbolically using the shifted Chebyshev polynomials and Picard iteration method as suggested in the literature. Then R(α) is computed using the Gaussian quadrature integral formula. Finally Q(t,α) is computed using the matrix exponential summation method. Using Mathematica, this approach has successfully been applied to the well-known Mathieu equation and a four dimensional time-periodic system in order to demonstrate the applications of the proposed method to linear as well as nonlinear problems.

scholarly journals A Bio-Inspired Integration Method for Object Semantic Representation

2016 ◽  
Vol 6 (3) ◽  
pp. 137-154 ◽  
Author(s):  
Hui Wei
Keyword(s):  
Semantic Representation ◽  
Physiological Mechanism ◽  
Semantic Gap ◽  
Symbolic Form ◽  
Low Level ◽  
Classical Receptive Field ◽  
The One ◽  
Definition Of ◽  
High Level ◽  
Almost All

Abstract We have two motivations. Firstly, semantic gap is a tough problem puzzling almost all sub-fields of Artificial Intelligence. We think semantic gap is the conflict between the abstractness of high-level symbolic definition and the details, diversities of low-level stimulus. Secondly, in object recognition, a pre-defined prototype of object is crucial and indispensable for bi-directional perception processing. On the one hand this prototype was learned from perceptional experience, and on the other hand it should be able to guide future downward processing. Human can do this very well, so physiological mechanism is simulated here. We utilize a mechanism of classical and non-classical receptive field (nCRF) to design a hierarchical model and form a multi-layer prototype of an object. This also is a realistic definition of concept, and a representation of denoting semantic. We regard this model as the most fundamental infrastructure that can ground semantics. Here a AND-OR tree is constructed to record prototypes of a concept, in which either raw data at low-level or symbol at high-level is feasible, and explicit production rules are also available. For the sake of pixel processing, knowledge should be represented in a data form; for the sake of scene reasoning, knowledge should be represented in a symbolic form. The physiological mechanism happens to be the bridge that can join them together seamlessly. This provides a possibility for finding a solution to semantic gap problem, and prevents discontinuity in low-order structures.

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