We investigate the power of threshold circuits of small depth. In particular, we give functions that require exponential size unweighted threshold circuits of depth 3 when we restrict the bottom fanin. We also prove t...
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We give a probabilistic algorithm for computing the greatest common divisor (GCD) of two polynomials over an algebraic number field. We can compute the GCD using O(llog5(l)) expected binary operations where l is the s...
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We show that we can compute the Subresultant Polynomial Remainder Sequence over an algebraic number field in 0((n5m3 + n4m5) log2(nDEm)) binary operations, where the generator of the field is given by a monic irreduci...
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This report describes a three-dimensional computer model of the olfactory cortex developed for the study of cortical oscillations and their biological significance. The model was designed with the intention of investi...
This report describes a three-dimensional computer model of the olfactory cortex developed for the study of cortical oscillations and their biological significance. The model was designed with the intention of investigating the relative role of network circuitry and network unit properties, resulting in a model complexity between simple Hopfield nets and detailed realistic simulations. Network connections are essentially the same as in a detailed simulation of the olfactory (piriform) cortex by Wilson and Bower (1989), but the network units are here modeled with continuous output functions and single compartments. It is shown that the present model is capable of reproducing all major results of the more complex model, corresponding to spatiotemporal patterns found in the actual cortex (Freeman 1975). This indicates that action potentials and the geometry of cells are not needed per se for explaining certain cortical activities. In contrast, connections between units, in particular feedforward and feedback inhibitory loops and long-range, excitatory-excitatory connections, are found to be crucial for the dynamical behavior of this system. The model describes intrinsic oscillatory properties of olfactory cortex and reproduces response patterns associated with a continuous random-input signal and with a shock pulse given to the cortex. In the latter case, waves of activity move across the model cortex in a way similar to the detailed simulations by Wilson and Bower, and consistent with corresponding global dynamic behavior of the functioning cortex. For a constant random input, the network is able to oscillate with two separate frequencies simultaneously, purely as a result of its intrinsic network properties. A delicate balance between inhibition and excitation, in terms of connection strength and timing of events, is necessary for coherent frequency and phase of the oscillating neural units. The analytical equations used in this model seem an adequate representation
作者：
Lars LangemyrNumerical Analysis and Computing Science
Royal Institute of Technology S-100 44 Stockholm Sweden and Wilhelm-Schickard-Institut für Informatik Universitat Tübingen Auf dem Sand 13 W-7400 Tübingen Germany
Focus-of-attention is extremely important in human visual perception. If computer vision systems are to perform tasks in a complex, dynamic world they will have to be able to control processing in a way that is analog...
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Focus-of-attention is extremely important in human visual perception. If computer vision systems are to perform tasks in a complex, dynamic world they will have to be able to control processing in a way that is analogous to visual attention in humans. Problems connected to foveation (examination of selected regions of the world at high resolution) are examined. In particular, the problem of finding and classifying junctions from this aspect is considered. It is shown that foveation as simulated by controlled, active zooming in conjunction with scale-space techniques allows for robust detection and classification of junctions.
In this paper we consider initial-boundary value problems for systems with a small parameter epsilon. The problems are mixed hyperbolic-parabolic when epsilon > 0 and hyperbolic when epsilon = 0. Often the solution...
In this paper we consider initial-boundary value problems for systems with a small parameter epsilon. The problems are mixed hyperbolic-parabolic when epsilon > 0 and hyperbolic when epsilon = 0. Often the solution can be expanded asymptotically in epsilon and to first approximation it consists of the solution of the corresponding hyperbolic problem and a boundary layer part. We prove sufficient conditions for the expansion to exist and give estimates of the remainder. We also examine how the boundary conditions should be choosen to avoid 0(1) boundary layers.
An efficient parallel algorithm for the tree-decomposition problem for fixed width w is presented. The algorithm runs in time O(log/sup 3/ n) and uses O(n) processors on a concurrent-read, concurrent-write parallel ra...
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An efficient parallel algorithm for the tree-decomposition problem for fixed width w is presented. The algorithm runs in time O(log/sup 3/ n) and uses O(n) processors on a concurrent-read, concurrent-write parallel random access machine (CRCW PRAM). This result can be used to construct efficient parallel algorithms for three important classes of problems: MS (monadic second-order) properties, linear EMS (extended monadic second-order) extremum problems, and enumeration problems for MS properties, for graphs of tree width at most w. The sequential time complexity of the tree-composition problem for fixed w is improved, and some implications for this improvement are stated.< >
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