scholarly journals FUTURE FOR SCIENTIFIC COMPUTING USING PYTHON

2020 ◽  
Vol 2 (1) ◽  
pp. 30-41
Author(s):  
Rakesh Kumar
Keyword(s):  
Computer Simulation ◽  
Mathematical Models ◽  
High Performance ◽  
Scientific Computing ◽  
Theoretical Computer Science ◽  
Computational Science ◽  
Theoretical Computer ◽  
Analysis Techniques ◽  
Scientific Disciplines ◽  
Computing Approach

Computational science (scientific computing or scientific computation) is concerned with constructing mathematical models as well as quantitative analysis techniques and using computers to analyze as well as solve scientific problems. In practical use, it is basically the application of computer simulation as well as other forms of computation from numerical analysis and theoretical computer science to problems in different scientific disciplines. The scientific computing approach is to gain understanding, basically through the analysis of mathematical models implemented on computers. Python is frequently used for highperformance scientific applications and widely used in academia as well as scientific projects because it is easy to write and performs well. Due to its high performance nature, scientific computing in Python often utilizes external libraries like NumPy, SciPy and Matplotlib etc.

scholarly journals Numerical algorithms for high-performance computational science

2020 ◽  
Vol 378 (2166) ◽  
pp. 20190066 ◽  
Author(s):  
Jack Dongarra ◽  
Laura Grigori ◽  
Nicholas J. Higham
Keyword(s):  
High Performance ◽  
Numerical Algorithms ◽  
Computational Science ◽  
Floating Point ◽  
Important Criterion ◽  
Data Movement ◽  
Floating Point Arithmetic ◽  
High Performance Computers ◽  
Point Arithmetic ◽  
Speed And Accuracy

A number of features of today’s high-performance computers make it challenging to exploit these machines fully for computational science. These include increasing core counts but stagnant clock frequencies; the high cost of data movement; use of accelerators (GPUs, FPGAs, coprocessors), making architectures increasingly heterogeneous; and multi- ple precisions of floating-point arithmetic, including half-precision. Moreover, as well as maximizing speed and accuracy, minimizing energy consumption is an important criterion. New generations of algorithms are needed to tackle these challenges. We discuss some approaches that we can take to develop numerical algorithms for high-performance computational science, with a view to exploiting the next generation of supercomputers. This article is part of a discussion meeting issue ‘Numerical algorithms for high-performance computational science’.

scholarly journals From the Quasi-Total Strong Differential to Quasi-Total Italian Domination in Graphs

Symmetry ◽  
2021 ◽  
Vol 13 (6) ◽  
pp. 1036
Author(s):  
Abel Cabrera Martínez ◽  
Alejandro Estrada-Moreno ◽  
Juan Alberto Rodríguez-Velázquez
Keyword(s):  
Vertex Cover ◽  
Domination Number ◽  
Theoretical Computer Science ◽  
Discrete Mathematics ◽  
Special Issue ◽  
Total Domination Number ◽  
Theoretical Computer ◽  
Graph Parameters ◽  
Semitotal Domination ◽  
Domination In Graphs

This paper is devoted to the study of the quasi-total strong differential of a graph, and it is a contribution to the Special Issue “Theoretical computer science and discrete mathematics” of Symmetry. Given a vertex x∈V(G) of a graph G, the neighbourhood of x is denoted by N(x). The neighbourhood of a set X⊆V(G) is defined to be N(X)=⋃x∈XN(x), while the external neighbourhood of X is defined to be Ne(X)=N(X)∖X. Now, for every set X⊆V(G) and every vertex x∈X, the external private neighbourhood of x with respect to X is defined as the set Pe(x,X)={y∈V(G)∖X:N(y)∩X={x}}. Let Xw={x∈X:Pe(x,X)≠⌀}. The strong differential of X is defined to be ∂s(X)=|Ne(X)|−|Xw|, while the quasi-total strong differential of G is defined to be ∂s*(G)=max{∂s(X):X⊆V(G)andXw⊆N(X)}. We show that the quasi-total strong differential is closely related to several graph parameters, including the domination number, the total domination number, the 2-domination number, the vertex cover number, the semitotal domination number, the strong differential, and the quasi-total Italian domination number. As a consequence of the study, we show that the problem of finding the quasi-total strong differential of a graph is NP-hard.

scholarly journals Optimization Over the Boolean Hypercube Via Sums of Nonnegative Circuit Polynomials

2021 ◽  
Author(s):  
Mareike Dressler ◽  
Adam Kurpisz ◽  
Timo de Wolff
Keyword(s):  
Computer Science ◽  
Affine Transformation ◽  
Optimization Problems ◽  
Polynomial Optimization ◽  
Theoretical Computer Science ◽  
Sums Of Squares ◽  
Theoretical Computer ◽  
Complexity Bounds ◽  
Polynomial Optimization Problems ◽  
Transformation Of Variables

AbstractVarious key problems from theoretical computer science can be expressed as polynomial optimization problems over the boolean hypercube. One particularly successful way to prove complexity bounds for these types of problems is based on sums of squares (SOS) as nonnegativity certificates. In this article, we initiate optimization problems over the boolean hypercube via a recent, alternative certificate called sums of nonnegative circuit polynomials (SONC). We show that key results for SOS-based certificates remain valid: First, for polynomials, which are nonnegative over the n-variate boolean hypercube with constraints of degree d there exists a SONC certificate of degree at most $$n+d$$ n + d . Second, if there exists a degree d SONC certificate for nonnegativity of a polynomial over the boolean hypercube, then there also exists a short degree d SONC certificate that includes at most $$n^{O(d)}$$ n O ( d ) nonnegative circuit polynomials. Moreover, we prove that, in opposite to SOS, the SONC cone is not closed under taking affine transformation of variables and that for SONC there does not exist an equivalent to Putinar’s Positivstellensatz for SOS. We discuss these results from both the algebraic and the optimization perspective.

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