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

Variable-free exploration of stochastic models: a gene regulatory network example

Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [13], we assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e, effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [9] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free coarse-grained, computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables.Comment: 26 pages, 9 figure

Measurements, Models, Systems and Design

531 s.

A Survey of Quantum Learning Theory

This paper surveys quantum learning theory: the theoretical aspects of machine learning using quantum computers. We describe the main results known for three models of learning: exact learning from membership queries, and Probably Approximately Correct (PAC) and agnostic learning from classical or quantum examples.Comment: 26 pages LaTeX. v2: many small changes to improve the presentation. This version will appear as Complexity Theory Column in SIGACT News in June 2017. v3: fixed a small ambiguity in the definition of gamma(C) and updated a referenc

Gene Regulatory Networks: Modeling, Intervention and Context

abstract: Biological systems are complex in many dimensions as endless transportation and communication networks all function simultaneously. Our ability to intervene within both healthy and diseased systems is tied directly to our ability to understand and model core functionality. The progress in increasingly accurate and thorough high-throughput measurement technologies has provided a deluge of data from which we may attempt to infer a representation of the true genetic regulatory system. A gene regulatory network model, if accurate enough, may allow us to perform hypothesis testing in the form of computational experiments. Of great importance to modeling accuracy is the acknowledgment of biological contexts within the models -- i.e. recognizing the heterogeneous nature of the true biological system and the data it generates. This marriage of engineering, mathematics and computer science with systems biology creates a cycle of progress between computer simulation and lab experimentation, rapidly translating interventions and treatments for patients from the bench to the bedside. This dissertation will first discuss the landscape for modeling the biological system, explore the identification of targets for intervention in Boolean network models of biological interactions, and explore context specificity both in new graphical depictions of models embodying context-specific genomic regulation and in novel analysis approaches designed to reveal embedded contextual information. Overall, the dissertation will explore a spectrum of biological modeling with a goal towards therapeutic intervention, with both formal and informal notions of biological context, in such a way that will enable future work to have an even greater impact in terms of direct patient benefit on an individualized level.Dissertation/ThesisPh.D. Computer Science 201

A Review of Fault Diagnosing Methods in Power Transmission Systems

Transient stability is important in power systems. Disturbances like faults need to be segregated to restore transient stability. A comprehensive review of fault diagnosing methods in the power transmission system is presented in this paper. Typically, voltage and current samples are deployed for analysis. Three tasks/topics; fault detection, classification, and location are presented separately to convey a more logical and comprehensive understanding of the concepts. Feature extractions, transformations with dimensionality reduction methods are discussed. Fault classification and location techniques largely use artificial intelligence (AI) and signal processing methods. After the discussion of overall methods and concepts, advancements and future aspects are discussed. Generalized strengths and weaknesses of different AI and machine learning-based algorithms are assessed. A comparison of different fault detection, classification, and location methods is also presented considering features, inputs, complexity, system used and results. This paper may serve as a guideline for the researchers to understand different methods and techniques in this field