Fuzzy Logic is a multi-valued logic model based on fuzzy set theory, which may be considered as an extension of Boolean Logic. One of the fields of this theory is the Compensatory Fuzzy Logic, based on the removal of some axioms in order to achieve a sensitive and idempotent multi-valued system. This system is based on a quadruple of continuous operators: conjunction, disjunction, order and negation. In this work we present a new model of Compensatory Fuzzy Logic based on a different set of operators, conjunction and disjunction, than the ones used in the original definition, and then prove that this new model satisfies the required axioms. As an example, we present an application to decision-making, comparing the results against the ones based on the original model.

A more complete understanding of the alterations in cellular regulatory and control mechanisms that occur in the various forms of cancer has been one of the central targets of the genomic and proteomic methods that allow surveys of the abundance and/or state of cellular macromolecules. This preference is driven both by the intractability of cancer to generic therapies, assumed to be due to the highly varied molecular etiologies observed in cancer, and by the opportunity to discern and dissect the regulatory and control interactions presented by the highly diverse assortment of perturbations of regulation and control that arise in cancer. Exploiting the opportunities for inference on the regulatory and control connections offered by these revealing system perturbations is fraught with the practical problems that arise from the way biological systems operate. Two classes of regulatory action in biological systems are particularly inimical to inference, convergent regulation, where a variety of regulatory actions result in a common set of control responses (crosstalk), and divergent regulation, where a single regulatory action produces entirely different sets of control responses, depending on cellular context (conditioning). We have constructed a coarse mathematical model of the propagation of regulatory influence in such distributed, context-sensitive regulatory networks that allows a quantitative estimation of the amount of crosstalk and conditioning associated with a candidate regulatory gene taken from a set of genes that have been profiled over a series of samples where the candidate's activity varies.

MOTIVATION: The technology to genotype single nucleotide polymorphisms (SNPs) at extremely high densities provides for hypothesis-free genome-wide scans for common polymorphisms associated with complex disease. However, we find that some errors introduced by commonly employed genotyping algorithms may lead to inflation of false associations between markers and phenotype. RESULTS: We have developed a novel SNP genotype calling program, SNiPer-High Density (SNiPer-HD), for highly accurate genotype calling across hundreds of thousands of SNPs. The program employs an expectation-maximization (EM) algorithm with parameters based on a training sample set. The algorithm choice allows for highly accurate genotyping for most SNPs. Also, we introduce a quality control metric for each assayed SNP, such that poor-behaving SNPs can be filtered using a metric correlating to genotype class separation in the calling algorithm. SNiPer-HD is superior to the standard dynamic modeling algorithm and is complementary and non-redundant to other algorithms, such as BRLMM. Implementing multiple algorithms together may provide highly accurate genotyping calls, without inflation of false positives due to systematically miss-called SNPs. A reliable and accurate set of SNP genotypes for increasingly dense panels will eliminate some false association signals and false negative signals, allowing for rapid identification of disease susceptibility loci for complex traits. AVAILABILITY: SNiPer-HD is available at TGen's website: http://www.tgen.org/neurogenomics/data.

Many researchers are investigating the possibility of utilizing global gene expression profile data as a platform to infer gene regulatory networks. However, heavy computational burden and measurement noises render these efforts difficult and approaches based on quantized levels are vigorously investigated as an alternative. Methods based on quantized values require a procedure to convert continuous expression values into discrete ones. Although there have been algorithms to quantize values into multiple discrete states, these algorithms assumed strict state mixtures (SSM,) so that all expression profiles were divided into pre-specified number of states. We propose two novel quantization algorithms (QAs), model-based quantization algorithm and model-free quantization algorithm that generalize SSM algorithms in two major aspects. First, our QAs assume the maximum number of expression states (Es) be arbitrary. Second, expression profiles can exhibit any combinations of Espossible states. In this paper, we compare the performances between SSM algorithms and QAs using simulation studies as well as applications to actual data and show that quantizing gene expression data using adaptive algorithms is an effective way to reduce data complexity without sacrificing much of essential information

MOTIVATION: Given a large set of potential features, such as the set of all gene-expression values from a microarray, it is necessary to find a small subset with which to classify. The task of finding an optimal feature set of a given size is inherently combinatoric because to assure optimality all feature sets of a given size must be checked. Thus, numerous suboptimal feature-selection algorithms have been proposed. There are strong impediments to evaluate feature-selection algorithms using real data when data are limited, a common situation in genetic classification. The difficulty is compound. First, there are no class-conditional distributions from which to draw data points, only a single small labeled sample. Second, there are no test data with which to estimate the feature-set errors, and one must depend on a training-data-based error estimator. Finally, there is no optimal feature set with which to compare the feature sets found by the algorithms. RESULTS: This paper describes a genetic test bed for the evaluation of feature-selection algorithms. It begins with a large biological feature-label dataset that is used as an empirical distribution and, using massively parallel computation, finds the top feature sets of various sizes based on a given sample size and classification rule. The user can draw random samples from the data, apply a proposed algorithm, and evaluate the proficiency of the proposed algorithm via three different measures (code provided). A key feature of the test bed is that, once a dataset is input, a single command creates the entire test bed relative to the dataset. The particular dataset used for the first version of the test bed comes from a microarray-based classification study that analyzes a large number of microarrays, prepared with RNA from breast tumor samples from each of 295 patients. AVAILABILITY: The software and supplementary material are available at http://public.tgen.org/tgen-cb/support/testbed/ CONTACT: [email protected].

MOTIVATION: A major problem of pattern classification is estimation of the Bayes error when only small samples are available. One way to estimate the Bayes error is to design a classifier based on some classification rule applied to sample data, estimate the error of the designed classifier, and then use this estimate as an estimate of the Bayes error. Relative to the Bayes error, the expected error of the designed classifier is biased high, and this bias can be severe with small samples. RESULTS: This paper provides a correction for the bias by subtracting a term derived from the representation of the estimation error. It does so for Boolean classifiers, these being defined on binary features. Although the general theory applies to any Boolean classifier, a model is introduced to reduce the number of parameters. A key point is that the expected correction is conservative. Properties of the corrected estimate are studied via simulation. The correction applies to binary predictors because they are mathematically identical to Boolean classifiers. In this context the correction is adapted to the coefficient of determination, which has been used to measure nonlinear multivariate relations between genes and design genetic regulatory networks. An application using gene-expression data from a microarray experiment is provided on the website http://gspsnap.tamu.edu/smallsample/ (user:'smallsample', password:'smallsample)').