The theory which is outlined in this lecture, call it RRC for short, is a departure from traditional approaches to reasoning and computation. A principal advance is an enhanced capability for reasoning and computation...
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ISBN:
(纸本)9783642339400
The theory which is outlined in this lecture, call it RRC for short, is a departure from traditional approaches to reasoning and computation. A principal advance is an enhanced capability for reasoning and computation in an environment of uncertainty, imprecision and partiality of truth. The point of departure in RRC is a basic premise in the real world such environment is the norm rather than exception. A concept which has a position of centrality in RRC is that of a restriction. Informally, a restriction is an answer to the question: What is the value of a variable X? More concretely, a restriction, R(X), on a variable, X, is a limitation on the values which X can take a limitation which is induced by what is known or perceived about X. A restriction is singular if the answer to the question is a singleton;otherwise it is nonsingular. Generally, nonsingularity implies uncertainty. A restriction is precisiated if the limitation is mathematically well defined;otherwise it is unprecisiated. Generally, restrictions which are described in a natural language are unprecisiated.
This study provides a normative theory for how Bayesian causal inference can be implemented in neural circuits. In both cognitive processes such as causal reasoning and perceptual inference such as cue integration, th...
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This study provides a normative theory for how Bayesian causal inference can be implemented in neural circuits. In both cognitive processes such as causal reasoning and perceptual inference such as cue integration, the nervous systems need to choose different models representing the underlying causal structures when making inferences on external stimuli. In multisensory processing, for example, the nervous system has to choose whether to integrate or segregate inputs from different sensory modalities to infer the sensory stimuli, based on whether the inputs are from the same or different sources. Making this choice is a model selection problem requiring the computation of Bayes factor, the ratio of likelihoods between the integration and the segregation models. In this paper, we consider the causal inference in multisensory processing and propose a novel generative model based on neural population code that takes into account both stimulus feature and stimulus reliability in the inference. In the case of circular variables such as heading direction, our normative theory yields an analytical solution for computing the Bayes factor, with a clear geometric interpretation, which can be implemented by simple additive mechanisms with neural population code. Numerical simulation shows that the tunings of the neurons computing Bayes factor are consistent with the "opposite neurons" discovered in dorsal medial superior temporal (MSTd) and the ventral intraparietal (VIP) areas for visual-vestibular processing. This study illuminates a potential neural mechanism for causal inference in the brain.
The most expensive part of the known algorithms in the calculation of primary fundamental invariants (of rings of polynomial invariants of finite linear groups over an arbitrary field) is the computation of the radica...
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The goal of this study is to develop a theoretical basis for lensless coherent imaging in the reflection mode. To describe the wave field produced by a reflective obliquely illuminated object we introduce the tilted o...
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This paper presents a computable model for shape constancy. In this approach, object shape transformation, which caused by depth in 2-D image, can be recovered. And in this paper, we used the visual psychology theory ...
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We proposed new basic theory and methods for quantum computation and neuro-computer based on functional path integral of quantum theory. And then we concretely calculated probability amplitudes for quantum circuit and...
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Core spanners are a class of document spanners that capture the core functionality of IBM’s AQL. FC is a logic on strings built around word equations that when extended with constraints for regular languages can be s...
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This textbook is an introduction to economic networks, intended for students and researchers in the fields of economics and applied mathematics. The textbook emphasizes quantitative modeling, with the main underlying ...
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Summary form only given. The author proposes the following definition of massive parallelism. A computational system is massively parallel if the number of processing elements is so large that it may conveniently be c...
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Summary form only given. The author proposes the following definition of massive parallelism. A computational system is massively parallel if the number of processing elements is so large that it may conveniently be considered a continuous quantity. The author proposes this definition of massive parallelism for a number of reasons. First, skillful behavior seems to require significant neural mass. Second, he is interested in computers, such as optical computers and molecular computers, for which the number of processing elements is effectively continuous. Third, continuous mathematics is generally easier than discrete mathematics. The author develops a theoretical framework for understanding massively parallel analog computers.< >
This chapter reviews some past and recent developments in shape comparison and analysis of curves based on the computation of intrinsic Riemannian metrics on the space of curves modulo shape-preserving transformations...
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