scholarly journals Hexagonal arrays for fault-tolerant matrix multiplication

Filomat ◽  
2015 ◽  
Vol 29 (9) ◽  
pp. 1969-1981
Author(s):  
Emina Milovanovic ◽  
Igor Milovanovic ◽  
Mile Stojcev
Keyword(s):  
Fault Tolerant ◽  
Matrix Multiplication ◽  
Software Tool ◽  
Optimal Number ◽  
Graph Representation ◽  
Matrix Multiplication Algorithm ◽  
Projection Direction ◽  
The Matrix ◽  
The Given ◽  
Hexagonal Arrays

This paper describes mathematical procedure for designing hexagonal systolic arrays that implement fault-tolerant matrix multiplication. Fault-tolerance is achieved by introducing redundancy at algorithm level by defining three equivalent algorithms with disjoint index spaces. The essence of the proposed method is based on mapping data dependency graph that corresponds to the matrix multiplication algorithm, by an appropriate epimorphism, into a graph with desired properties. Since there is a 1:1 correspondence between the algorithm and it?s graph representation, all transformations performed on the graph directly affect the algorithm. Chosen epimorphism depends on the projection direction vector ?? = [?1 ?2 ?3]T and enables obtaining hexagonal arrays with optimal number of processing elements (PEs) for the given matrix dimensions, which realizes fault-tolerant matrix multiplication for the shortest possible time for that number of PEs. The proposed procedure is formally described by explicit formulas and can be used as a software tool for automatic synthesis of fault-tolerant arrays.

scholarly journals EHreact: Extended Hasse Diagrams for the Extraction and Scoring of Enzymatic Reaction Templates

2021 ◽  
Author(s):  
Esther Heid ◽  
Samuel Goldman ◽  
Karthik Sankaranarayanan ◽  
Connor W. Coley ◽  
Christoph Flamm ◽  
...  
Keyword(s):  
Expert Knowledge ◽  
Enzymatic Reaction ◽  
Software Tool ◽  
Optimal Number ◽  
Data Driven ◽  
Enzymatic Reactions ◽  
Hasse Diagrams ◽  
Large Databases ◽  
Rule Sets ◽  
The Given

Data-driven computer-aided synthesis planning utilizing organic or biocatalyzed reactions from large databases has gained increasing interest in the last decade, sparking the development of numerous tools to extract, apply and score general reaction templates. The generation of reaction rules for enzymatic reactions is especially challenging, since substrate promiscuity varies between enzymes, causing the optimal levels of rule specificity and optimal number of included atoms to differ between enzymes. This complicates an automated extraction from databases and has promoted the creation of manually curated reaction rule sets. Here we present EHreact, a purely data-driven open-source software tool to extract and score reaction rules from sets of reactions known to be catalyzed by an enzyme at appropriate levels of specificity without expert knowledge. EHreact extracts and groups reaction rules into tree-like structures, Hasse diagrams, based on common substructures in the imaginary transition structures. Each diagram can be utilized to output a single or a set of reaction rules, as well as calculate the probability of a new substrate to be processed by the given enzyme by inferring information about the reactive site of the enzyme from the known reactions and their grouping in the template tree. EHreact heuristically predicts the activity of a given enzyme on a new substrate, outperforming current approaches in accuracy and functionality.

scholarly journals EHreact: Extended Hasse Diagrams for the Extraction and Scoring of Enzymatic Reaction Templates

2021 ◽  
Author(s):  
Esther Heid ◽  
Samuel Goldman ◽  
Karthik Sankaranarayanan ◽  
Connor W. Coley ◽  
Christoph Flamm ◽  
...  
Keyword(s):  
Expert Knowledge ◽  
Enzymatic Reaction ◽  
Software Tool ◽  
Optimal Number ◽  
Data Driven ◽  
Enzymatic Reactions ◽  
Hasse Diagrams ◽  
Large Databases ◽  
Rule Sets ◽  
The Given

Data-driven computer-aided synthesis planning utilizing organic or biocatalyzed reactions from large databases has gained increasing interest in the last decade, sparking the development of numerous tools to extract, apply and score general reaction templates. The generation of reaction rules for enzymatic reactions is especially challenging, since substrate promiscuity varies between enzymes, causing the optimal levels of rule specificity and optimal number of included atoms to differ between enzymes. This complicates an automated extraction from databases and has promoted the creation of manually curated reaction rule sets. Here we present EHreact, a purely data-driven open-source software tool to extract and score reaction rules from sets of reactions known to be catalyzed by an enzyme at appropriate levels of specificity without expert knowledge. EHreact extracts and groups reaction rules into tree-like structures, Hasse diagrams, based on common substructures in the imaginary transition structures. Each diagram can be utilized to output a single or a set of reaction rules, as well as calculate the probability of a new substrate to be processed by the given enzyme by inferring information about the reactive site of the enzyme from the known reactions and their grouping in the template tree. EHreact heuristically predicts the activity of a given enzyme on a new substrate, outperforming current approaches in accuracy and functionality.

An Implementation of the Matrix Multiplication Algorithm SUMMA in mpF

2005 ◽  
pp. 420-432 ◽  
Author(s):  
Alexey Kalinov ◽  
Ilya Ledovskikh ◽  
Mikhail Posypkin ◽  
Zakhar Levchenko ◽  
Vladimir Chizhov
Keyword(s):  
Matrix Multiplication ◽  
Matrix Multiplication Algorithm ◽  
Multiplication Algorithm ◽  
The Matrix

scholarly journals Mapping matrix multiplication algorithm onto fault-tolerant systolic array

2004 ◽  
Vol 48 (1-2) ◽  
pp. 275-289 ◽  
Author(s):  
N.M. Stojanović ◽  
E.I. Milovanović ◽  
I. Stojmenović ◽  
T.. Milovanović ◽  
T.I. Tokić
Keyword(s):  
Systolic Array ◽  
Fault Tolerant ◽  
Matrix Multiplication ◽  
Matrix Multiplication Algorithm ◽  
Multiplication Algorithm

scholarly journals EHreact: Extended Hasse Diagrams for the Extraction and Scoring of Enzymatic Reaction Templates

2021 ◽  
Author(s):  
Esther Heid ◽  
Samuel Goldman ◽  
Karthik Sankaranarayanan ◽  
Connor W. Coley ◽  
Christoph Flamm ◽  
...  
Keyword(s):  
Expert Knowledge ◽  
Enzymatic Reaction ◽  
Software Tool ◽  
Optimal Number ◽  
Data Driven ◽  
Enzymatic Reactions ◽  
Hasse Diagrams ◽  
Large Databases ◽  
Rule Sets ◽  
The Given

Data-driven computer-aided synthesis planning utilizing organic or biocatalyzed reactions from large databases has gained increasing interest in the last decade, sparking the development of numerous tools to extract, apply and score general reaction templates. The generation of reaction rules for enzymatic reactions is especially challenging, since substrate promiscuity varies between enzymes, causing the optimal levels of rule specificity and optimal number of included atoms to differ between enzymes. This complicates an automated extraction from databases and has promoted the creation of manually curated reaction rule sets. Here we present EHreact, a purely data-driven open-source software tool to extract and score reaction rules from sets of reactions known to be catalyzed by an enzyme at appropriate levels of specificity without expert knowledge. EHreact extracts and groups reaction rules into tree-like structures, Hasse diagrams, based on common substructures in the imaginary transition structures. Each diagram can be utilized to output a single or a set of reaction rules, as well as calculate the probability of a new substrate to be processed by the given enzyme by inferring information about the reactive site of the enzyme from the known reactions and their grouping in the template tree. EHreact heuristically predicts the activity of a given enzyme on a new substrate, outperforming current approaches in accuracy and functionality.

The Convex Polytopes and Homogeneous Coordinate Rings of Bivariate Polynomials

2019 ◽  
Vol 16 (2) ◽  
pp. 1
Author(s):  
Shamsatun Nahar Ahmad ◽  
Nor’Aini Aris ◽  
Azlina Jumadi
Keyword(s):  
Convex Polytopes ◽  
Polynomial Systems ◽  
Matrix Formulation ◽  
Bivariate Polynomials ◽  
Homogeneous Coordinates ◽  
The Matrix ◽  
Projective Vector ◽  
Coordinate Rings ◽  
Resultant Matrix ◽  
The Given

Concepts from algebraic geometry such as cones and fans are related to toric varieties and can be applied to determine the convex polytopes and homogeneous coordinate rings of multivariate polynomial systems. The homogeneous coordinates of a system in its projective vector space can be associated with the entries of the resultant matrix of the system under consideration. This paper presents some conditions for the homogeneous coordinates of a certain system of bivariate polynomials through the construction and implementation of the Sylvester-Bèzout hybrid resultant matrix formulation. This basis of the implementation of the Bèzout block applies a combinatorial approach on a set of linear inequalities, named 5-rule. The inequalities involved the set of exponent vectors of the monomials of the system and the entries of the matrix are determined from the coefficients of facets variable known as brackets. The approach can determine the homogeneous coordinates of the given system and the entries of the Bèzout block. Conditions for determining the homogeneous coordinates are also given and proven.

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