scholarly journals Linear Prediction of Non-Overlapping Codons in a Genome Sequence

2019 ◽  
Vol 8 (3) ◽  
pp. 7176-7186
Keyword(s):  
Computer Science ◽  
Genetic Code ◽  
Genome Sequence ◽  
Linear Prediction ◽  
Theoretical Computer Science ◽  
Genome Sequences ◽  
Theoretical Computer ◽  
Novel Approach ◽  
A Genome

The concept of ‘non-overlapping n-ary codons’ is proposed in this paper as a novel approach to the study of genome sequences in the framework of theoretical computer science. Given a genome sequence of length N, one can have (N/n) non-overlapping n-ary codons with 0 or 1 or up to n-1 unused nucleotides left out in the sequence. Unused nucleotides are not considered in the scheme of genetic code

scholarly journals Linear Prediction of Overlapping Codons in a Genome Sequence

2020 ◽  
Vol 9 (4) ◽  
pp. 1177-1182
Keyword(s):  
Computer Science ◽  
Genetic Code ◽  
Genome Sequence ◽  
Linear Prediction ◽  
Theoretical Computer Science ◽  
Genome Sequences ◽  
Theoretical Computer ◽  
Novel Approach ◽  
A Genome

The concept of overlapping n-ary codons was proposed in this paper as a novel approach to the study of genome sequences in the framework of theoretical computer science. Given a genome sequence of length N, one can have (N/n) non-overlapping n-ary codons with 0 or 1 or up to n-1 unused nucleotides left out in the sequence. Unused nucleotides are not considered in the scheme of genetic code. Alternatively, one can have (N-n+1) overlapping n-ary codons with no unused nucleotide left out in the sequence.

scholarly journals The simplex geometry of graphs

2019 ◽  
Vol 7 (4) ◽  
pp. 469-490 ◽  
Author(s):  
Karel Devriendt ◽  
Piet Van Mieghem
Keyword(s):  
Graph Theory ◽  
Computer Science ◽  
Network Science ◽  
Theoretical Computer Science ◽  
Probabilistic Methods ◽  
Discrete Mathematics ◽  
Theoretical Computer ◽  
Novel Approach ◽  
Object Of Study ◽  
Scientific Fields

AbstractGraphs are a central object of study in various scientific fields, such as discrete mathematics, theoretical computer science and network science. These graphs are typically studied using combinatorial, algebraic or probabilistic methods, each of which highlights the properties of graphs in a unique way. Here, we discuss a novel approach to study graphs: the simplex geometry (a simplex is a generalized triangle). This perspective, proposed by Miroslav Fiedler, introduces techniques from (simplex) geometry into the field of graph theory and conversely, via an exact correspondence. We introduce this graph-simplex correspondence, identify a number of basic connections between graph characteristics and simplex properties, and suggest some applications as example.

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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