Results 1  10
of
14
Computing with Truly Asynchronous Threshold Logic Networks
 THEORETICAL COMPUTER SCIENCE
, 1995
"... We present simulation mechanisms by which any network of threshold logic units with either symmetric or asymmetric interunit connections (i.e., a symmetric or asymmetric "Hopfield net") can be simulated on a network of the same type, but without any a priori constraints on the order of updates of th ..."
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Cited by 19 (7 self)
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We present simulation mechanisms by which any network of threshold logic units with either symmetric or asymmetric interunit connections (i.e., a symmetric or asymmetric "Hopfield net") can be simulated on a network of the same type, but without any a priori constraints on the order of updates of the units. Together with earlier constructions, the results show that the truly asynchronous network model is computationally equivalent to the seemingly more powerful models with either ordered sequential or fully parallel updates.
The Computational Power of Discrete Hopfield Nets with Hidden Units
 Neural Computation
, 1996
"... We prove that polynomial size discrete Hopfield networks with hidden units compute exactly the class of Boolean functions PSPACE/poly, i.e., the same functions as are computed by polynomial spacebounded nonuniform Turing machines. As a corollary to the construction, we observe also that networks wi ..."
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Cited by 11 (6 self)
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We prove that polynomial size discrete Hopfield networks with hidden units compute exactly the class of Boolean functions PSPACE/poly, i.e., the same functions as are computed by polynomial spacebounded nonuniform Turing machines. As a corollary to the construction, we observe also that networks with polynomially bounded interconnection weights compute exactly the class of functions P/poly, i.e., the class computed by polynomial timebounded nonuniform Turing machines.
Modeling and Simulation of Large Biological, Information and SocioTechnical Systems: An Interaction Based Approach
 Interactive Computation: The New
, 2005
"... Summary We describe an interaction based approach for computer modeling and simulation of large integrated biological, information, social and technical (BIST) systems 1 Examples of such systems are urban regional transportation systems, the national electrical power markets and grids, gene regulato ..."
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Cited by 11 (8 self)
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Summary We describe an interaction based approach for computer modeling and simulation of large integrated biological, information, social and technical (BIST) systems 1 Examples of such systems are urban regional transportation systems, the national electrical power markets and grids, gene regulatory networks, the worldwide Internet, infectious diseases, vaccine design and deployment, theater war, etc. These systems are composed of large numbers of interacting human, physical, informational and technological components. These components adapt and learn, exhibit perception, interpretation, reasoning, deception, cooperation and noncooperation, and have economic motives as well as the usual physical properties of interaction. The theoretical foundation of our approach consists of two parts: (i) mathematics of complex interdependent dynamic networks, and (ii) mathematical and computational theory of a class of finite discrete dynamical systems called Sequential Dynamical Systems (SDSs). We then consider engineering principles based on such a theory. As with the theoretical foundation, they consist of two basic parts: (i) Efficient data manipulation, including synthesis, integration, storage and regeneration and (ii) high performance computing oriented system design, development and implementation. The engineering methods allow us to specify, design, and analyze simulations of extremely large systems and implement them on massively parallel architectures. As an illustration of our approach, an interaction based computer modeling and simulation framework to study very large interdependent societal infrastructures is described. 1
Pattern Discovery from Biosequences
, 2002
"... In this thesis we have developed novel methods for analyzing biological data, the primary sequences of the DNA and proteins, the microarray based gene expression data, and other functional genomics data. The main contribution is the development of the pattern discovery algorithm SPEXS, accompanied b ..."
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Cited by 9 (1 self)
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In this thesis we have developed novel methods for analyzing biological data, the primary sequences of the DNA and proteins, the microarray based gene expression data, and other functional genomics data. The main contribution is the development of the pattern discovery algorithm SPEXS, accompanied by several practical applications for analyzing real biological problems. For performing these biological studies that integrate different types of biological data we have developed a comprehensive webbased biological data analysis environment Expression Profiler (http://ep.ebi.ac.uk/)...
Science and Engineering of Large Scale SocioTechnical Simulations
 Proceedings of the 1st International Conference on Grand Challenges in Simulations, held as part of the Western Simulation Conference
, 2002
"... Computer simulation is a computational approach whereby global system properties are produced as dynamics by direct computation of interactions among representations of local system elements. A mathematical theory of simulation consists of an account of the formal properties of sequential evaluation ..."
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Cited by 3 (2 self)
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Computer simulation is a computational approach whereby global system properties are produced as dynamics by direct computation of interactions among representations of local system elements. A mathematical theory of simulation consists of an account of the formal properties of sequential evaluation and composition of interdependent local mappings. When certain local mappings and their interdependencies can be related to particular real world objects and interdependencies, it is common to compute the interactions to derive a symbolic model of the global system made up of the corresponding interdependent objects. The formal mathematical and computational account of the simulation provides a particular kind of theoretical explanation of the global system properties and, therefore, insight into how to engineer a complex system to exhibit those properties. This paper considers the mathematical foundations and engineering principles necessary for building large scale simulations of sociotechnical systems. Examples of such systems are urban regional transportation systems, the national electrical power markets and grid, the worldwide Internet, vaccine design and deployment, theater war, etc. These systems are composed of large numbers of interacting human, physical and technological components. Some components adapt and learn, exhibit perception, interpretation, reasoning, deception, cooperation and noncooperation, and economic motives as well as the usual physical properties of interaction. The systems themselves are large and the behavior of sociotechnical systems is tremendously complex.
Theory of Neuromata
, 1998
"... A finite automaton  the socalled neuromaton, realized by a finite discrete recurrent neural network, working in parallel computation mode, is considered. Both the size of neuromata (i.e., the number of neurons) and their descriptional complexity (i.e., the number of bits in the neuromaton repres ..."
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Cited by 3 (2 self)
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A finite automaton  the socalled neuromaton, realized by a finite discrete recurrent neural network, working in parallel computation mode, is considered. Both the size of neuromata (i.e., the number of neurons) and their descriptional complexity (i.e., the number of bits in the neuromaton representation) are studied. It is proved that a constant time delay of the neuromaton output does not play a role within a polynomial descriptional complexity. It is shown that any regular language given by a regular expression of length n is recognized by a neuromaton with \Theta(n) neurons. Further, it is proved that this network size is, in the worst case, optimal. On the other hand, generally there is not an equivalent polynomial length regular expression for a given neuromaton. Then, two specialized constructions of neural acceptors of the optimal descriptional complexity \Theta(n) for a single nbit string recognition are described. They both require O(n 1 2 ) neurons and either O(n) con...
EnergyBased Computation with Symmetric Hopfield Nets
"... We propose a unifying approach to the analysis of computational aspects of symmetric Hopfield nets which is based on the concept of "energy source". Within this framework we present different results concerning the computational power of various Hopfield model classes. It is shown that polynomial ..."
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Cited by 2 (0 self)
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We propose a unifying approach to the analysis of computational aspects of symmetric Hopfield nets which is based on the concept of "energy source". Within this framework we present different results concerning the computational power of various Hopfield model classes. It is shown that polynomialtime computations by nondeterministic Turing machines can be reduced to the process of minimizing the energy in Hopfield nets (the MIN ENERGY problem). Furthermore, external and internal sources of energy are distinguished. The external sources include e.g. energizing inputs from socalled Hopfield languages, and also certain external oscillators that prove finite analog Hopfield nets to be computationally Turing universal. On the other hand, the internal source of energy can be implemented by a symmetric clock subnetwork producing an exponential number of oscillations which are used to energize the simulation of convergent asymmetric networks by Hopfield nets. This shows that infinite families of polynomialsize Hopfield nets compute the complexity class PSPACE/poly. A special attention is paid to generalizing these results for analog states and continuous time to point out alternative sources of efficient computation. 1
Computational Complexity of Some Enumeration Problems About Uniformly Sparse Boolean Network Automata
 ELECTRONIC COLLOQUIUM ON COMPUTATIONAL COMPLEXITY, REPORT NO. 159 (2006)
, 2006
"... We study the computational complexity of counting the fixed point configurations (FPs), the predecessor configurations and the ancestor configurations in certain classes of graph or network automata viewed as discrete dynamical systems. Some early results of this investigation are presented in two r ..."
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Cited by 2 (0 self)
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We study the computational complexity of counting the fixed point configurations (FPs), the predecessor configurations and the ancestor configurations in certain classes of graph or network automata viewed as discrete dynamical systems. Some early results of this investigation are presented in two recent ECCC reports [39, 40]. In particular, it is proven in [40] that both exact and approximate counting of FPs in the two closely related classes of Boolean network automata, called Sequential and Synchronous Dynamical Systems (SDSs and SyDSs, respectively), are computationally intractable problems when each node is required to update according to a monotone Boolean function. In the present paper, we further strengthen those results by showing that the intractability of exact enumeration of FPs of a monotone Boolean SDS or SyDS still holds even when (i) the monotone update rules are restricted to linear threshold functions, and (ii) the underlying graph is uniformly sparse. By uniform sparseness we mean that every node in the graph has its degree bounded by for a small value of constant. In particular, we prove that exactly enumerating FPs in such SDSs and SyDSs remains #Pcomplete even when no node degree exceeds. Among other consequences, we show that this result also implies intractability of determining the exact memory capacity of discrete Hopfield networks with uniformly sparse and nonnegative integer weight matrices.
Advanced Document Description, a Sequential Approach
, 2005
"... To be able to perform efficient document processing, information systems need to use simple models of documents that can be treated in a smaller number of operations. This problem of document representation is not trivial. For decades, researchers have tried to combine relevant document representati ..."
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Cited by 1 (1 self)
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To be able to perform efficient document processing, information systems need to use simple models of documents that can be treated in a smaller number of operations. This problem of document representation is not trivial. For decades, researchers have tried to combine relevant document representations with efficient processing. Documents are commonly represented by vectors in which each dimension corresponds to a word of the document. This approach is termed “bag of words”, as it entirely ignores the relative positions of words. One natural improvement over this representation is the extraction and use of cohesive word sequences. In this dissertation, we consider the problem of the extraction, selection and exploitation of word sequences, with a particular focus on the applicability of our work to domainindependent document collections written in any language.
Some Afterthoughts on Hopfield Networks
, 1999
"... The present paper investigates four relatively independent issues, each in one section, which complete our knowledge regarding the computational aspects of popular Hopfield nets [9]. In Section 2, the computational equivalence of convergent asymmetric and Hopfield nets is shown with respect to t ..."
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The present paper investigates four relatively independent issues, each in one section, which complete our knowledge regarding the computational aspects of popular Hopfield nets [9]. In Section 2, the computational equivalence of convergent asymmetric and Hopfield nets is shown with respect to the network size. In Section 3, the convergence time of Hopfield nets is analyzed in terms of bit representations. In Section 4, a polynomial time approximate algorithm for the minimum energy problem is shown. In Section 5, the Turing universality of analog Hopfield nets is studied.