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A survey on continuous time computations
 New Computational Paradigms
"... Abstract. We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing resu ..."
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Abstract. We provide an overview of theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature. 1
Comparative Analysis of Hypercomputational Systems
, 2006
"... In the 1930s, Turing suggested his abstract model for a practical computer, hypothetically visualizing the digital programmable computer long before it was actually invented. His model formed the foundation for every computer made today. The past few years have seen a change in ideas where philosoph ..."
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Cited by 1 (1 self)
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In the 1930s, Turing suggested his abstract model for a practical computer, hypothetically visualizing the digital programmable computer long before it was actually invented. His model formed the foundation for every computer made today. The past few years have seen a change in ideas where philosophers and scientists are suggesting models of hypothetical computing devices which can outperform the Turing machine, performing some calculations the latter is unable to. The ChurchTuring Thesis, which the Turing machine model embodies, has raised discussions on whether it could be possible to solve undecidable problems which Turing’s model is unable to. Models which could solve these problems, have gone further to claim abilities relating to quantum computing, relativity theory, even the modeling of natural biological laws themselves. These so called ‘hypermachines’ use hypercomputational abilities to make the impossible possible. Various models belonging to different disciplines of physics, mathematics and philosophy, have been suggested for these theories. My (primarily researchoriented) project is based on the study and review of these different hypercomputational models and attempts to compare the different models in terms of computational power. The project focuses on the ability to compare these models of different disciplines on similar grounds and
unknown title
, 2002
"... On the universality of the probability distribution of the product B −1 X of random matrices ..."
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On the universality of the probability distribution of the product B −1 X of random matrices
unknown title
, 2004
"... On the universality of the probability distribution of the product B −1 X of random matrices ..."
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On the universality of the probability distribution of the product B −1 X of random matrices
www.elsevier.com/locate/physd Analogsymbolic memory that tracks via reconsolidation
, 2008
"... A fundamental part of a computational system is its memory, which is used to store and retrieve data. Classical computer memories rely on the static approach and are very different from human memories. Neural network memories are based on autoassociative attractor dynamics and thus provide a high l ..."
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A fundamental part of a computational system is its memory, which is used to store and retrieve data. Classical computer memories rely on the static approach and are very different from human memories. Neural network memories are based on autoassociative attractor dynamics and thus provide a high level of pattern completion. However, they are not used in general computation since there are practically no algorithms to load an arbitrary landscape of attractors into them. In this sense neural network memory models cannot communicate well with symbolic and prior knowledge. We propose the design of a new memory based on localist attractor dynamics with reconsolidation called Reconsolidation Attractor Network (RAN). RAN combines symbolic and subsymbolic features in a very attractive way: it is based on attractors; enables pattern classification under missing data; and demonstrates dynamic reconsolidation, which is very useful for tracking changing concepts. The perception RAN enables is somewhat reminiscent of human perception due to its context sensitivity. Furthermore, it enables an immediate and clear interface with symbolic memories, including loading of attractors by means of trivial wiring, updating attractors, and retrieving them faster without waiting for full convergence. It also scales to any number of concepts. This provides a useful counterpoint to more conventional memory systems, such as random access memory and autoassociative neural networks.
A Survey on Continuous Time Computations (Chapter of the book “New Computational Paradigms”, To appear, Springer)
"... Abstract. We provide an overview of computation theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, sum ..."
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Abstract. We provide an overview of computation theories of continuous time computation. These theories allow us to understand both the hardness of questions related to continuous time dynamical systems and the computational power of continuous time analog models. We survey the existing models, summarizing results, and point to relevant references in the literature. 1