4,455 research outputs found
Boolean Models of Genomic Regulatory Networks: Reduction Mappings, Inference, and External Control
Computational modeling of genomic regulation has become an important focus of systems biology and genomic signal processing for the past several years. It holds the promise to uncover both the structure and dynamical properties of the complex gene, protein or metabolic networks responsible for the cell functioning in various contexts and regimes. This, in turn, will lead to the development of optimal intervention strategies for prevention and control of disease. At the same time, constructing such computational models faces several challenges. High complexity is one of the major impediments for the practical applications of the models. Thus, reducing the size/complexity of a model becomes a critical issue in problems such as model selection, construction of tractable subnetwork models, and control of its dynamical behavior. We focus on the reduction problem in the context of two specific models of genomic regulation: Boolean networks with perturbation (BNP) and probabilistic Boolean networks (PBN). We also compare and draw a parallel between the reduction problem and two other important problems of computational modeling of genomic networks: the problem of network inference and the problem of designing external control policies for intervention/altering the dynamics of the model
Modeling Financial Time Series with Artificial Neural Networks
Financial time series convey the decisions and actions of a population of human actors over time. Econometric and regressive models have been developed in the past decades for analyzing these time series. More recently, biologically inspired artificial neural network models have been shown to overcome some of the main challenges of traditional techniques by better exploiting the non-linear, non-stationary, and oscillatory nature of noisy, chaotic human interactions. This review paper explores the options, benefits, and weaknesses of the various forms of artificial neural networks as compared with regression techniques in the field of financial time series analysis.CELEST, a National Science Foundation Science of Learning Center (SBE-0354378); SyNAPSE program of the Defense Advanced Research Project Agency (HR001109-03-0001
Gaussian width bounds with applications to arithmetic progressions in random settings
Motivated by problems on random differences in Szemer\'{e}di's theorem and on
large deviations for arithmetic progressions in random sets, we prove upper
bounds on the Gaussian width of point sets that are formed by the image of the
-dimensional Boolean hypercube under a mapping
, where each coordinate is a constant-degree
multilinear polynomial with 0-1 coefficients. We show the following
applications of our bounds. Let be the random
subset of containing each element independently with
probability .
A set is -intersective if
any dense subset of contains a proper -term
arithmetic progression with common difference in . Our main result implies
that is -intersective with probability provided for . This gives a polynomial improvement for all
of a previous bound due to Frantzikinakis, Lesigne and Wierdl, and
reproves more directly the same improvement shown recently by the authors and
Dvir.
Let be the number of -term arithmetic progressions in
and consider the large deviation rate
. We give quadratic
improvements of the best-known range of for which a highly precise estimate
of due to Bhattacharya, Ganguly, Shao and Zhao is valid for
all odd .
We also discuss connections with error correcting codes (locally decodable
codes) and the Banach-space notion of type for injective tensor products of
-spaces.Comment: 18 pages, some typos fixe
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