Building Hierarchical Tree Representations Using Homological-Based Tools

2021 ◽  
pp. 120-130
Author(s):  
Fernando Díaz-del-Río ◽  
Pablo Sanchez-Cuevas ◽  
Helena Molina-Abril ◽  
Pedro Real ◽  
María José Moron-Fernández
2016 ◽  
pp. 397-401
Author(s):  
Gonzalo Navarro ◽  
Kunihiko Sadakane
Keyword(s):  

IEEE Access ◽  
2021 ◽  
pp. 1-1
Author(s):  
Md Whaiduzzaman ◽  
Md. Julkar Nayeen Mahi ◽  
Alistair Barros ◽  
Md. Ibrahim Khalil ◽  
Colin Fidge ◽  
...  

2020 ◽  
pp. 1-14
Author(s):  
SHOTA OSADA

Abstract We prove the Bernoulli property for determinantal point processes on $ \mathbb{R}^d $ with translation-invariant kernels. For the determinantal point processes on $ \mathbb{Z}^d $ with translation-invariant kernels, the Bernoulli property was proved by Lyons and Steif [Stationary determinantal processes: phase multiplicity, bernoullicity, and domination. Duke Math. J.120 (2003), 515–575] and Shirai and Takahashi [Random point fields associated with certain Fredholm determinants II: fermion shifts and their ergodic properties. Ann. Probab.31 (2003), 1533–1564]. We prove its continuum version. For this purpose, we also prove the Bernoulli property for the tree representations of the determinantal point processes.


2012 ◽  
Vol 60 (3) ◽  
pp. 495-505
Author(s):  
M. Startek ◽  
S. Lasota ◽  
M. Sykulski ◽  
A. Bułak ◽  
L. Noé ◽  
...  

Abstract In this paper we present two algorithms that may serve as efficient alternatives to the well-known PSI BLAST tool: SeedBLAST and CTX-PSI Blast. Both may benefit from the knowledge about amino acid composition specific to a given protein family: SeedBLAST uses the advisedly designed seed, while CTX-PSI BLAST extends PSI BLAST with the context-specific substitution model. The seeding technique became central in the theory of sequence alignment. There are several efficient tools applying seeds to DNA homology search, but not to protein homology search. In this paper we fill this gap. We advocate the use of multiple subset seeds derived from a hierarchical tree of amino acid residues. Our method computes, by an evolutionary algorithm, seeds that are specifically designed for a given protein family. The seeds are represented by deterministic finite automata (DFAs) and built into the NCBI-BLAST software. This extended tool, named SeedBLAST, is compared to the original BLAST and PSI-BLAST on several protein families. Our results demonstrate a superiority of SeedBLAST in terms of efficiency, especially in the case of twilight zone hits. The contextual substitution model has been proven to increase sensitivity of protein alignment. In this paper we perform a next step in the contextual alignment program. We announce a contextual version of the PSI-BLAST algorithm, an iterative version of the NCBI-BLAST tool. The experimental evaluation has been performed demonstrating a significantly higher sensitivity compared to the ordinary PSI-BLAST algorithm.


Author(s):  
Hong-Sen Yan ◽  
Feng-Ming Ou ◽  
Ming-Feng Tang

An algorithm is presented, based on graph theory, for enumerating all feasible serial and/or parallel combined mechanisms from the given rotary or translational power source and specific kinematic building blocks. Through the labeled out-tree representations for the configurations of combined mechanisms, the enumeration procedure is developed by adapting the algorithm for the enumeration of trees. A rotary power source and four kinematic building blocks: a crank-rocker linkage, a rack-pinion, a double-slider mechanism, and a cam-follower mechanism, are chosen as the combination to illustrate the algorithm. And, two examples are provided to validate the algorithm.


2011 ◽  
Vol 308-310 ◽  
pp. 1582-1585
Author(s):  
Yi Sheng Huang ◽  
Tso Hsien Liao

Statechart has been utilized as a visual formalism for the modeling of complex systems. It illuminates the features on describing properties of causality, concurrency and synchronization. The reachability structure is used to represented dynamic model by a Boolean function. In this paper, we try to describe State invariant method and equation function for hierarchical tree diagram. Finally, we used them to analyze the urban traffic control systems which are modeled by using Statecharts. Their formalism provides a concept of propositional logic for presenting control strategy.


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