Understanding quantum mechanics matters because it is the engine that powers the universe. Supported by a comprehensive Glossary, this is an ideal introduction to the mathematics that underpins the engine of quantum mechanics.
An engaging introduction to the science of vision that offers a coherent account of vision based on general information processing principles In this accessible and engaging introduction to modern vision science, James Stone uses visual illusions to explore how the brain sees the world. Understanding vision, Stone argues, is not simply a question of knowing which neurons respond to particular visual features, but also requires a computational theory of vision. Stone draws together results from David Marr's computational framework, Barlow's efficient coding hypothesis, Bayesian inference, Shannon's information theory, and signal processing to construct a coherent account of vision that explains not only how the brain is fooled by particular visual illusions, but also why any biological or computer vision system should also be fooled by these illusions. This short text includes chapters on the eye and its evolution, how and why visual neurons from different species encode the retinal image in the same way, how information theory explains color aftereffects, how different visual cues provide depth information, how the imperfect visual information received by the eye and brain can be rescued by Bayesian inference, how different brain regions process visual information, and the bizarre perceptual consequences that result from damage to these brain regions. The tutorial style emphasizes key conceptual insights, rather than mathematical details, making the book accessible to the nonscientist and suitable for undergraduate or postgraduate study.
A fundamental problem in neural network research, as well as in many other disciplines, is finding a suitable representation of multivariate data, i.e. random vectors. For reasons of computational and conceptual simplicity, the representation is often sought as a linear transformation of the original data. In other words, each component of the representation is a linear combination of the original variables. Well-known linear transformation methods include principal component analysis, factor analysis, and projection pursuit. Independent component analysis (ICA) is a recently developed method in which the goal is to find a linear representation of nongaussian data so that the components are statistically independent, or as independent as possible. Such a representation seems to capture the essential structure of the data in many applications, including feature extraction and signal separation.
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