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- All Subjects: Threshold logic
- Creators: Kim, Seungchan
- Creators: Stufken, John
Description
Threshold logic has been studied by at least two independent group of researchers. One group of researchers studied threshold logic with the intention of building threshold logic circuits. The earliest research to this end was done in the 1960's. The major work at that time focused on studying mathematical properties of threshold logic as no efficient circuit implementations of threshold logic were available. Recently many post-CMOS (Complimentary Metal Oxide Semiconductor) technologies that implement threshold logic have been proposed along with efficient CMOS implementations. This has renewed the effort to develop efficient threshold logic design automation techniques. This work contributes to this ongoing effort. Another group studying threshold logic did so, because the building block of neural networks - the Perceptron, is identical to the threshold element implementing a threshold function. Neural networks are used for various purposes as data classifiers. This work contributes tangentially to this field by proposing new methods and techniques to study and analyze functions implemented by a Perceptron After completion of the Human Genome Project, it has become evident that most biological phenomenon is not caused by the action of single genes, but due to the complex interaction involving a system of genes. In recent times, the `systems approach' for the study of gene systems is gaining popularity. Many different theories from mathematics and computer science has been used for this purpose. Among the systems approaches, the Boolean logic gene model has emerged as the current most popular discrete gene model. This work proposes a new gene model based on threshold logic functions (which are a subset of Boolean logic functions). The biological relevance and utility of this model is argued illustrated by using it to model different in-vivo as well as in-silico gene systems.
ContributorsLinge Gowda, Tejaswi (Author) / Vrudhula, Sarma (Thesis advisor) / Shrivastava, Aviral (Committee member) / Chatha, Karamvir (Committee member) / Kim, Seungchan (Committee member) / Arizona State University (Publisher)
Created2012
Description
Threshold regression is used to model regime switching dynamics where the effects of the explanatory variables in predicting the response variable depend on whether a certain threshold has been crossed. When regime-switching dynamics are present, new estimation problems arise related to estimating the value of the threshold. Conventional methods utilize an iterative search procedure, seeking to minimize the sum of squares criterion. However, when unnecessary variables are included in the model or certain variables drop out of the model depending on the regime, this method may have high variability. This paper proposes Lasso-type methods as an alternative to ordinary least squares. By incorporating an L_{1} penalty term, Lasso methods perform variable selection, thus potentially reducing some of the variance in estimating the threshold parameter. This paper discusses the results of a study in which two different underlying model structures were simulated. The first is a regression model with correlated predictors, whereas the second is a self-exciting threshold autoregressive model. Finally the proposed Lasso-type methods are compared to conventional methods in an application to urban traffic data.
ContributorsVan Schaijik, Maria (Author) / Kamarianakis, Yiannis (Committee member) / Reiser, Mark R. (Committee member) / Stufken, John (Committee member) / Arizona State University (Publisher)
Created2015