Harmonic Analysis of Boolean Networks: Determinative Power and Perturbations

Consider a large Boolean network with a feed forward structure. Given a probability distribution on the inputs, can one find, possibly small, collections of input nodes that determine the states of most other nodes in the network? To answer this question, a notion that quantifies the determinative power of an input over the states of the nodes in the network is needed. We argue that the mutual information (MI) between a given subset of the inputs X = {X_1, ..., X_n} of some node i and its associated function f_i(X) quantifies the determinative power of this set of inputs over node i. We compare the determinative power of a set of inputs to the sensitivity to perturbations to these inputs, and find that, maybe surprisingly, an input that has large sensitivity to perturbations does not necessarily have large determinative power. However, for unate functions, which play an important role in genetic regulatory networks, we find a direct relation between MI and sensitivity to perturbations. As an application of our results, we analyze the large-scale regulatory network of Escherichia coli. We identify the most determinative nodes and show that a small subset of those reduces the overall uncertainty of the network state significantly. Furthermore, the network is found to be tolerant to perturbations of its inputs

Mobility enhancement of solution-processed Poly(3-Hexylthiophene) based organic transistor using zinc oxide nanostructures

This work reports the mobility enhancement of p-type organic transistors formed using Poly(3-Hexylthiophene) (P3HT) using the dispersion of ZnO (zinc oxide) nanostructures. The ZnO nanostructures considered here are nanorods that were fabricated via a simple one-step aqueous-based chemical approach. Organic Thin Film Transistors (OTFTs) based on these nanocomposites show a mobility enhancement of more than 60% for the P3HT/ZnO nanorod composite compared to its pristine state polymer devices. The results presented here show a great promise for the mobility enhancement of p-type solution processed OFETs and applications. (C) 2011 Elsevier Ltd. All rights reserved

Large Deviations And The Thermodynamic Formalism: A New Proof Of The Equivalence of Ensembles

: equivalence of ensembles holds at the level of measures whenever it holds at the level of thermodynamic functions. The problem of the equivalence of ensembles is not confined to statistical mechanics; it can be found in other areas of applied probability theory -- in information theory, for example. Here the problem is to prove that a sequence of conditioned measures is a Lecture delivered by J.T. Lewis equivalent, in an appropriate sense, to a sequence of "tilted" measures. Our choice of setting is sufficiently general to cover such applications. Probabilistic methods have been used for at least fifty years to prove results about the equivalence of ensembles: Khinchin (1943) used a local central limit theorem to prove it for a classical ideal (non--interacting) gas; Dobrushin and Tirozzi (1977) proved it for lattice gas models for which they were able to establish a local central limit theorem -- a restriction which ruled--out model

Estimation of sensitivity and specificity of site-specific diagnostic tests

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/66191/1/j.1600-0765.1990.tb00903.x.pd