Logic Based Pattern Recognition - Ontology Content (2)

Logic based Pattern Recognition extends the well known similarity models, where the distance measure is the base instrument for recognition. Initial part (1) of current publication in iTECH-06 reduces the logic based recognition models to the reduced disjunctive normal forms of partially defined Boolean functions. This step appears as a way to alternative pattern recognition instruments through combining metric and logic hypotheses and features, leading to studies of logic forms, hypotheses, hierarchies of hypotheses and effective algorithmic solutions. Current part (2) provides probabilistic conclusions on effective recognition by logic means in a model environment of binary attributes.

Logic Based Pattern Recognition - Ontology Content (1)

* The research is supported partly by INTAS: 04-77-7173 project, http://www.intas.be

The Knowledge: Its Presentation and Role in Recognition Systems

The concept of knowledge is the central one used when solving the various problems of data mining and pattern recognition in finite spaces of Boolean or multi-valued attributes. A special form of knowledge representation, called implicative regularities, is proposed for applying in two powerful tools of modern logic: the inductive inference and the deductive inference. The first one is used for extracting the knowledge from the data. The second is applied when the knowledge is used for calculation of the goal attribute values. A set of efficient algorithms was developed for that, dealing with Boolean functions and finite predicates represented by logical vectors and matrices.

Using SAT for Combinational Implementation Checking

The problem of checking whether a system of incompletely specified Boolean functions is implemented by the given combinational circuit is considered. The task is reduced to testing out if two given logical descriptions are equivalent on the domain of one of them having functional indeterminacy. We present a novel SAT-based verification method that is used for testing whether the given circuit satisfies all the conditions represented by the system of incompletely specified Boolean functions.

Generating More Boundary Elements of Subset Projections

Composition problem is considered for partition constrained vertex subsets of n dimensional unit cube E^n . Generating numerical characteristics of E^n subsets partitions is considered by means of the same characteristics in 1 − n dimensional unit cube, and construction of corresponding subsets is given for a special particular case. Using pairs of lower layer characteristic vectors for E^(1-n) more characteristic vectors for E^n are composed which are boundary from one side, and which take part in practical recognition of validness of a given candidate vector of partitions.

Generating Effective Test Suites for Model Transformations Using Classifying Terms

Generating sample models for testing a model transformation is no easy task. This paper explores the use of classifying terms and stratified sampling for developing richer test cases for model transformations. Classifying terms are used to define the equivalence classes that characterize the relevant subgroups for the test cases. From each equivalence class of object models, several representative models are chosen depending on the required sample size. We compare our results with test suites developed using random sampling, and conclude that by using an ordered and stratified approach the coverage and effectiveness of the test suite can be significantly improved.

equivalence of almost bent and almost perfect nonlinear functions and their generalizations

Vectorial Boolean function, almost bent, almost perfect nonlinear, affine equivalence, CCZ-equivalence

Finding the Relationship between a Search Algorithm and a Class of Functions on Discrete Space by Exhaustive Search

* The work is supported by RFBR, grant 04-01-00858-a.

Congestive heart failure. Correlation between functional class and systolic and diastolic functions assessed by Doppler echocardiography

OBJECTIVE: To evaluate the influence of systolic or diastolic dysfunction, or both on congestive heart failure functional class. METHODS: Thirty-six consecutive patients with a clinical diagnosis of congestive heart failure with sinus rhythm, who were seen between September and November of 1998 answered an adapted questionnaire about tolerance to physical activity for the determination of NYHA functional class. The patients were studied with transthoracic Doppler echocardiography. Two groups were compared: group 1 (19 patients in functional classes I and II) and group 2 (17 patients in functional classes III and IV). RESULTS: The average ejection fraction was significantly higher in group 1 (44.84%±8.04% vs. 32.59%±11.48% with p=0.0007). The mean ratio of the initial/final maximum diastolic filling velocity (E/A) of the left ventricle was significantly smaller in group 1 (1.07±0.72 vs. 1.98±1.49 with p=0.03). The average maximum systolic pulmonary venous velocity (S) was significantly higher in group 1 (53.53cm/s ± 12.02cm/s vs. 43.41cm/s ± 13.55cm/s with p=0.02). The mean ratio of maximum systolic/diastolic pulmonary venous velocity was significantly higher in group 1 (1.52±0.48 vs. 1.08±0.48 with p=0.01). A predominance of pseudo-normal and restrictive diastolic patterns existed in group 2 (58.83% in group 2 vs. 21.06% in group 1 with p=0.03). CONCLUSION: Both the systolic dysfunction index and the patterns of diastolic dysfunction evaluated by Doppler echocardiography worsened with the evolution of congestive heart failure.

Some remarks on the class of continuous (Semi-) strictcly quasiconvex functions

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Superatomic Boolean algebras constructed from strongly unbounded functions

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Additive functions in boolean models of gene regulatory network modules.

Gene-on-gene regulations are key components of every living organism. Dynamical abstract models of genetic regulatory networks help explain the genome's evolvability and robustness. These properties can be attributed to the structural topology of the graph formed by genes, as vertices, and regulatory interactions, as edges. Moreover, the actual gene interaction of each gene is believed to play a key role in the stability of the structure. With advances in biology, some effort was deployed to develop update functions in Boolean models that include recent knowledge. We combine real-life gene interaction networks with novel update functions in a Boolean model. We use two sub-networks of biological organisms, the yeast cell-cycle and the mouse embryonic stem cell, as topological support for our system. On these structures, we substitute the original random update functions by a novel threshold-based dynamic function in which the promoting and repressing effect of each interaction is considered. We use a third real-life regulatory network, along with its inferred Boolean update functions to validate the proposed update function. Results of this validation hint to increased biological plausibility of the threshold-based function. To investigate the dynamical behavior of this new model, we visualized the phase transition between order and chaos into the critical regime using Derrida plots. We complement the qualitative nature of Derrida plots with an alternative measure, the criticality distance, that also allows to discriminate between regimes in a quantitative way. Simulation on both real-life genetic regulatory networks show that there exists a set of parameters that allows the systems to operate in the critical region. This new model includes experimentally derived biological information and recent discoveries, which makes it potentially useful to guide experimental research. The update function confers additional realism to the model, while reducing the complexity and solution space, thus making it easier to investigate.

U-curve: A branch-and-bound optimization algorithm for U-shaped cost functions on Boolean lattices applied to the feature selection problem

This paper presents the formulation of a combinatorial optimization problem with the following characteristics: (i) the search space is the power set of a finite set structured as a Boolean lattice; (ii) the cost function forms a U-shaped curve when applied to any lattice chain. This formulation applies for feature selection in the context of pattern recognition. The known approaches for this problem are branch-and-bound algorithms and heuristics that explore partially the search space. Branch-and-bound algorithms are equivalent to the full search, while heuristics are not. This paper presents a branch-and-bound algorithm that differs from the others known by exploring the lattice structure and the U-shaped chain curves of the search space. The main contribution of this paper is the architecture of this algorithm that is based on the representation and exploration of the search space by new lattice properties proven here. Several experiments, with well known public data, indicate the superiority of the proposed method to the sequential floating forward selection (SFFS), which is a popular heuristic that gives good results in very short computational time. In all experiments, the proposed method got better or equal results in similar or even smaller computational time. (C) 2009 Elsevier Ltd. All rights reserved.