ALGORITHMIC COMBINATORICS ON PARTIAL WORDS

2012 ◽  
Vol 23 (06) ◽  
pp. 1189-1206 ◽  
Author(s):  
F. BLANCHET-SADRI
Keyword(s):  
Molecular Biology ◽  
Data Compression ◽  
Pattern Avoidance ◽  
Finite Alphabet ◽  
Open Problems ◽  
The Past ◽  
Partial Word ◽  
De Bruijn ◽  
Subword Complexity ◽  
Partial Words

Algorithmic combinatorics on partial words, or sequences of symbols over a finite alphabet that may have some do-not-know symbols or holes, has been developing in the past few years. Applications can be found, for instance, in molecular biology for the sequencing and analysis of DNA, in bio-inspired computing where partial words have been considered for identifying good encodings for DNA computations, and in data compression. In this paper, we focus on two areas of algorithmic combinatorics on partial words, namely, pattern avoidance and subword complexity. We discuss recent contributions as well as a number of open problems. In relation to pattern avoidance, we classify all binary patterns with respect to partial word avoidability, we classify all unary patterns with respect to hole sparsity, and we discuss avoiding abelian powers in partial words. In relation to subword complexity, we generate and count minimal Sturmian partial words, we construct de Bruijn partial words, and we construct partial words with subword complexities not achievable by full words (those without holes).

scholarly journals Counting Bordered Partial Words by Critical Positions

10.37236/625 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Emily Allen ◽  
F. Blanchet-Sadri ◽  
Cameron Byrum ◽  
Mihai Cucuringu ◽  
Robert Mercaş
Keyword(s):  
Combinatorial Property ◽  
Finite Alphabet ◽  
Theoretical Problem ◽  
Fixed Size ◽  
Fixed Length ◽  
Word Sequence ◽  
Partial Word ◽  
Recursive Formulas ◽  
Partial Words

A partial word, sequence over a finite alphabet that may have some undefined positions or holes, is bordered if one of its proper prefixes is compatible with one of its suffixes. The number theoretical problem of enumerating all bordered full words (the ones without holes) of a fixed length $n$ over an alphabet of a fixed size $k$ is well known. It turns out that all borders of a full word are simple, and so every bordered full word has a unique minimal border no longer than half its length. Counting bordered partial words having $h$ holes with the parameters $k, n$ is made extremely more difficult by the failure of that combinatorial property since there is now the possibility of a minimal border that is nonsimple. Here, we give recursive formulas based on our approach of the so-called simple and nonsimple critical positions.

scholarly journals WORD COMPLEXITY AND REPETITIONS IN WORDS

2004 ◽  
Vol 15 (01) ◽  
pp. 41-55 ◽  
Author(s):  
LUCIAN ILIE ◽  
SHENG YU ◽  
KAIZHONG ZHANG
Keyword(s):  
Data Compression ◽  
Fast Algorithms ◽  
Complexity Measure ◽  
Combinatorics On Words ◽  
Complexity Measures ◽  
Infinite Words ◽  
Infinite Word ◽  
De Bruijn ◽  
Subword Complexity

With ideas from data compression and combinatorics on words, we introduce a complexity measure for words, called repetition complexity, which quantifies the amount of repetition in a word. The repetition complexity of w, R (w), is defined as the smallest amount of space needed to store w when reduced by repeatedly applying the following procedure: n consecutive occurrences uu…u of the same subword u of w are stored as (u,n). The repetition complexity has interesting relations with well-known complexity measures, such as subword complexity, SUB , and Lempel-Ziv complexity, LZ . We have always R (w)≥ LZ (w) and could even be that the former is linear while the latter is only logarithmic; e.g., this happens for prefixes of certain infinite words obtained by iterated morphisms. An infinite word α being ultimately periodic is equivalent to: (i) [Formula: see text], (ii) [Formula: see text], and (iii) [Formula: see text]. De Bruijn words, well known for their high subword complexity, are shown to have almost highest repetition complexity; the precise complexity remains open. R (w) can be computed in time [Formula: see text] and it is open, and probably very difficult, to find fast algorithms.

CYCLIC PARTIAL WORDS

2020 ◽  
Vol 9 (11) ◽  
pp. 9219-9230
Author(s):  
R.K. Kumari ◽  
R. Arulprakasam ◽  
R. Perumal ◽  
V.R. Dare
Keyword(s):  
Dna Sequencing ◽  
Partial Word ◽  
Partial Words ◽  
Cyclic Words

Partial words are linear words with holes. Cyclic words are derived from linear words by linking its first letter after the last one. Both partial words and cyclic words have wide applications in DNA sequencing. In this paper we introduce cyclic partial words and discuss their periodicity and certain properties. We also establish representation of a cyclic partial word using trees.

Hierarchical Reinforcement Learning

2021 ◽  
Vol 54 (5) ◽  
pp. 1-35
Author(s):  
Shubham Pateria ◽  
Budhitama Subagdja ◽  
Ah-hwee Tan ◽  
Chai Quek
Keyword(s):  
Reinforcement Learning ◽  
Future Research ◽  
Comprehensive Overview ◽  
Open Problems ◽  
Practical Applications ◽  
Hierarchical Reinforcement Learning ◽  
The Past ◽  
Agent Learning ◽  
Multi Agent ◽  
Supplementary Material

Hierarchical Reinforcement Learning (HRL) enables autonomous decomposition of challenging long-horizon decision-making tasks into simpler subtasks. During the past years, the landscape of HRL research has grown profoundly, resulting in copious approaches. A comprehensive overview of this vast landscape is necessary to study HRL in an organized manner. We provide a survey of the diverse HRL approaches concerning the challenges of learning hierarchical policies, subtask discovery, transfer learning, and multi-agent learning using HRL. The survey is presented according to a novel taxonomy of the approaches. Based on the survey, a set of important open problems is proposed to motivate the future research in HRL. Furthermore, we outline a few suitable task domains for evaluating the HRL approaches and a few interesting examples of the practical applications of HRL in the Supplementary Material.

Some open problems in computational molecular biology

1999 ◽  
Vol 30 (3) ◽  
pp. 43-49 ◽  
Author(s):  
Tao Jiang ◽  
Paul Kearney ◽  
Ming Li
Keyword(s):  
Molecular Biology ◽  
Open Problems ◽  
Computational Molecular Biology

scholarly journals Trends and Developments in Bioinformatics in 2010: Prospects and Perspectives

2011 ◽  
Vol 20 (01) ◽  
pp. 146-155
Author(s):  
A. V. Alekseyenko ◽  
Y. Aphinyanaphongs ◽  
S. Brown ◽  
D. Fenyo ◽  
L. Fu ◽  
...  
Keyword(s):  
Best Practices ◽  
Open Problems ◽  
The Past ◽  
New Methods ◽  
Methods Development ◽  
Long Term Trends ◽  
To Come ◽  
Generation Sequencing

SummaryTo survey major developments and trends in the field of Bioinformatics in 2010 and their relationships to those of previous years, with emphasis on long-term trends, on best practices, on quality of the science of informatics, and on quality of science as a function of informatics.A critical review of articles in the literature of Bioinformatics over the past year.Our main results suggest that Bioinformatics continues to be a major catalyst for progress in Biology and Translational Medicine, as a consequence of new assaying technologies, most predominantly Next Generation Sequencing, which are changing the landscape of modern biological and medical research. These assays critically depend on bioinformatics and have led to quick growth of corresponding informatics methods development. Clinical-grade molecular signatures are proliferating at a rapid rate. However, a highly publicized incident at a prominent university showed that deficiencies in informatics methods can lead to catastrophic consequences for important scientific projects. Developing evidence-driven protocols and best practices is greatly needed given how serious are the implications for the quality of translational and basic science.Several exciting new methods have appeared over the past 18 months, that open new roads for progress in bioinformatics methods and their impact in biomedicine. At the same time, the range of open problems of great significance is extensive, ensuring the vitality of the field for many years to come.

scholarly journals Modelling reaction kinetics inside cells

2008 ◽  
Vol 45 ◽  
pp. 41-56 ◽  
Author(s):  
Ramon Grima ◽  
Santiago Schnell
Keyword(s):  
Molecular Biology ◽  
Reaction Kinetics ◽  
Single Molecule ◽  
Predictive Accuracy ◽  
Reaction Pathway ◽  
Imaging Techniques ◽  
Deterministic Models ◽  
Non Invasive ◽  
The Past ◽  
Fundamental Length

In the past decade, advances in molecular biology such as the development of non-invasive single molecule imaging techniques have given us a window into the intricate biochemical activities that occur inside cells. In this chapter we review four distinct theoretical and simulation frameworks: (i) non-spatial and deterministic, (ii) spatial and deterministic, (iii) non-spatial and stochastic and (iv) spatial and stochastic. Each framework can be suited to modelling and interpreting intracellular reaction kinetics. By estimating the fundamental length scales, one can roughly determine which models are best suited for the particular reaction pathway under study. We discuss differences in prediction between the four modelling methodologies. In particular we show that taking into account noise and space does not simply add quantitative predictive accuracy but may also lead to qualitatively different physiological predictions, unaccounted for by classical deterministic models.

Iteration Theory: Dynamical Systems and Functional Equations

2003 ◽  
Vol 13 (07) ◽  
pp. 1627-1647 ◽  
Author(s):  
F. Balibrea ◽  
L. Reich ◽  
J. Smítal
Keyword(s):  
Dynamical Systems ◽  
Functional Equations ◽  
Discrete Dynamical Systems ◽  
Iteration Theory ◽  
Open Problems ◽  
Research Directions ◽  
The Past ◽  
New Research

The aim of this paper is to give an account of some problems considered in the past years in the setting of Discrete Dynamical Systems and Iterative Functional Equations, some new research directions and also state some open problems.

VITAMIN B6 DEPENDENCY SYNDROMES: THEIR LARGER SIGNIFICANCE

PEDIATRICS ◽  
1966 ◽  
Vol 37 (4) ◽  
pp. 553-555
Author(s):  
CHARLES R. SCRIVER
Keyword(s):  
Molecular Biology ◽  
Primary Structure ◽  
Vitamin B6 ◽  
Molecular Biologist ◽  
The Past ◽  
Remarkable Advance

DURING the past decade, the molecular biologist has shown us how mutation in the informational code of the gene is eventually translated into an alteration, either in the primary structure of a protein catalyst or in the rate of synthesis of the catalyst. In either case, the function of the catalyst is impaired and the phenotype of the organism is changed. Another, albeit less remarkable, advance in knowledge during the past decade both enhances our view of molecular biology and directly benefits the care of our patients. In 1954 two papers appeared in this journal describing a new cause of convulsions in infancy.

Open Problems in Pattern Avoidance

1993 ◽  
Vol 100 (8) ◽  
pp. 790-793 ◽  
Author(s):  
James Currie
Keyword(s):  
Pattern Avoidance ◽  
Open Problems
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