The complexity of biochemical intracellular signal transduction networks has led to speculation that the high degree of interconnectivity that exists in these networks transforms them into an information processing network. To test this hypothesis directly, a large scale model was created with the logical mechanism of each node described completely to allow simulation and dynamical analysis. Exposing the network to tens of thousands of random combinations of inputs and analyzing the combined dynamics of multiple outputs revealed a robust system capable of clustering widely varying input combinations into equivalence classes of biologically relevant cellular responses. This capability was nontrivial in that the network performed sharp, nonfuzzy classifications even in the face of added noise, a hallmark of real-world decision-making.information processing ͉ systems biology

Canalizing functions have important applications in physics and biology. For example, they represent a mechanism capable of stabilizing chaotic behavior in Boolean network models of discrete dynamical systems. When comparing the class of canalizing functions to other classes of functions with respect to their evolutionary plausibility as emergent control rules in genetic regulatory systems, it is informative to know the number of canalizing functions with a given number of input variables. This is also important in the context of using the class of canalizing functions as a constraint during the inference of genetic networks from gene expression data. To this end, we derive an exact formula for the number of canalizing Boolean functions of n variables. We also derive a formula for the probability that a random Boolean function is canalizing for any given bias p of taking the value 1. In addition, we consider the number and probability of Boolean functions that are canalizing for exactly k variables. Finally, we provide an algorithm for randomly generating canalizing functions with a given bias p and any number of variables, which is needed for Monte Carlo simulations of Boolean networks

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A computer science aptitude predictor was administered to students enrolled in a first technical course in computer science to determine potential for success. The study revealed significant differences in the scoring between students who withdrew from the course and those students who did not. The causes for the differences all related to the students' mathematical background: high school performance, previous computer science education, and the number of college mathematics courses taken.

Generalized binomial coefficients of the first and second kind are defined in terms of object selection with and without repetition from weighted boxes. The combinatorial definition unifies the binomial coefficients, the Gaussian coefficients, and the Stirling numbers and their recurrence relations under a common interpretation. Combinatorial proofs for some Gaussian coefficient identities are derived and shown to reduce to the ordinary binomial coefficients when q s 1. This approach provides a different perspective on the subset᎐subspace analogy problem. Generating function relations for the generalized binomial coefficients are derived by formal methods. ᮊ