Bio-medical Ontologies Maintenance and Change Management

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190 I.R. Godínez et al. On the other hand, the work of Lukashin et al. [17] is one of the earliest researches done in promoters localization in DNA sequences by using artificial neural networks. The process therein mentioned uses a small subset (around 10%), taken randomly from the whole set of sequences of promoters, in order to train the network. The learning capacity is tested by presenting the whole set of sequences, obtaining an effectiveness of 94% to 99%. With respect to gene localization, quantitative analysis of similarity between tRNA gene sequences have been done, mainly for the search of evolutive relationships. New sequences have been introduced to this neural network and these are known as tRNA genes [18]. Another example related to promoters localization is a multi-layer feedforward neural network whose architecture is trained in order to predict whether a nucleotide sequence is a bacterial promoter sequence or not [19]. 2.2 Alpha-Beta Associative Memories Basic concepts about associative memories were established three decades ago in [4], [5], [21], nonetheless here we use the concepts, results and notation introduced in the Yáñez-Márquez’s Ph.D. Thesis [22]. An associative memory M is a system that relates input patterns and outputs patterns, during the operation, as follows: x → M → y with x and y the input and output pattern vectors, respectively. Each input vector forms an association with a corresponding output vector. For k integer and positive, the corresponding association will be denoted as: � x k ,y k� . Associative memory M is represented by a matrix whose ij-th component is mij. MemoryM is generated from an apriorifinite set of known associations, known as the fundamental set of associations. Ifμ is an index, the fundamental set is represented as: { (x μ ,y μ ) | μ =1, 2,...,p } with p the cardinality of the set. The patterns that form the fundamental set are called fundamental patterns. If it holds that x μ = y μ , ∀μ ∈{1, 2,...,p }, M is autoassociative, otherwise it is heteroassociative; in this latter case it is possible to establish that ∃μ ∈{1, 2,...,p} for which x μ �= y μ . A distorted version of a pattern x k to be recalled will be denoted as ˜x k . If when feeding a distorted version of x ϖ with ϖ = {1, 2,...,p} to an associative memory M, it happens that the output corresponds exactly to the associated pattern y ϖ , we say that recall is correct. Among the variety of associative memory models described in the scientific literature, there are two models that, because of their relevance, it is important to emphasize: morphological associative memories which were introduced by Ritter et al. [6], and alpha-beta associative memories, which were introduced in [22]-[24]. Because of their excellent characteristics, which allow them to be superior in many aspects to other models for associative
Classifying Patterns in Bioinformatics Databases 191 memories [6], morphological associative memories served as starter point for the creation and development of the alpha-beta associative memories. 2.2.1 The α and β Operators Theheartofthemathematicaltoolsused in the alpha-beta model, are two binary operators designed specifically for these memories. These operators are defined in [22] as follows: First, we define the sets A = {0, 1} and B = {0, 1, 2}, then the operators α and β are defined in tabular form: Table 1. Definition of the Alpha and Beta operators α : A × A → B β : B × A → A xy α(x, y) xy β(x, y) 00 1 00 0 01 0 01 0 10 2 10 0 11 1 11 1 20 1 21 1 The sets A and B,theα and β operators, along with the usual ∧ (minimum) and ∨ (maximum) operators, form the algebraic system (A, B, α, β, ∧, ∨)which is the mathematical basis for the alpha-beta associative memories. The ij-th entry of the matrix y ⊠x t is:[y ⊠ x t ] ij = α (yi,xj). If we consider the fundamental set of patterns: {(xμ ,yμ ) |μ =1, 2,...,p} then, the ij-th entry of the matrix yμ ⊠ (xμ ) t � is: yμ ⊠ (xμ ) t� ij = α � y μ i ,xμ � j 2.2.2 The Learning and Recalling Phases Given that there are two kinds of alpha-beta associative memories, ∨ and ∧, if we consider that each of these kinds is able to operate in two different modes, heteroassociative and autoassociative, we have four different available choices. Due to expediency, we will only discuss here the alpha-beta autoassociative memories of kind ∨. Then, the input and output patterns have the same dimension n, and the memory is a square matrix V =[vij] n×n .Also,the fundamental set takes the form {(x μ ,x μ ) |μ =1, 2,...,p}. LEARNING PHASE For each μ =1, 2,...,p , and from each couple (x μ ,x μ ) build the matrix � x μ ⊠ (x μ ) t� . Then apply the binary ∨ operator to the matrices obtained n×n to get V as follows: V = p � � xμ ⊠ (xμ ) t� . μ=1
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Amandeep S. Sidhu and Tharam S. Dil
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Amandeep S. Sidhu and Tharam S. Dil
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Preface The molecular biology commu
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Preface VII biomedical systems, and
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X Contents Mining Clinical, Immunol
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2 A.S. Sidhu, M. Bellgard, and T.S.
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Towards Bioinformatics Resourceomes
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2 The New Waves Towards Bioinformat
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2.4 Semantic Web Towards Bioinforma
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A Summary of Genomic Databases: Ove
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Appendix A Summary of Genomic Datab
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Protein Data Integration Problem Am
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Protein Data Integration Problem 57
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Fig. 3. Class Hierarchy of Protein
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72 L. Stanescu, D. Dan Burdescu, an
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Substructure Analysis of Metabolic
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entry compound relation subtype com
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Running Time 4500 4000 3500 3000 25
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6 Conclusion Substructure Analysis
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Completing the Total Wellbeing Puzz
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296 M. Fernandez, M. Villasana, and
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Genetic Algorithm in Ab Initio Prot
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Author Index Apiletti, Daniele 169
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