Results 1  10
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48
Reduction of the HodgkinHuxley Equations to a SingleVariable Threshold Model
 NEURAL COMPUTATION
, 1997
"... It is generally believed that a neuron is a threshold element which fires when some variable u reaches a threshold. Here we pursue the question of whether this picture can be justified and study the fourdimensional neuron model of Hodgkin and Huxley as a concrete example. The model is approximat ..."
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Cited by 67 (22 self)
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It is generally believed that a neuron is a threshold element which fires when some variable u reaches a threshold. Here we pursue the question of whether this picture can be justified and study the fourdimensional neuron model of Hodgkin and Huxley as a concrete example. The model is approximated by a response kernel expansion in terms of a single variable, the membrane voltage. The firstorder term is linear in the input and has the typical form of an elementary postsynaptic potential. Higherorder kernels take care of nonlinear interactions between input spikes. In contrast to the standard Volterra expansion the kernels depend on the firing time of the most recent output spike. In particular, a zeroorder kernel which describes the shape of the spike and the typical afterpotential is included. Our model neuron fires, if the membrane voltage, given by the truncated response kernel expansion crosses a threshold. The threshold model is tested on a spike train generated by t...
Stability and Instability of Fluid Models for ReEntrant Lines
, 1996
"... Reentrant lines can be used to model complex manufacturing systems such as wafer fabrication facilities. As the first step to the optimal or nearoptimal scheduling of such lines, we investigate their stability. In light of a recent theorem of Dai (1995) which states that a scheduling policy is sta ..."
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Cited by 36 (11 self)
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Reentrant lines can be used to model complex manufacturing systems such as wafer fabrication facilities. As the first step to the optimal or nearoptimal scheduling of such lines, we investigate their stability. In light of a recent theorem of Dai (1995) which states that a scheduling policy is stable if the corresponding fluid model is stable, we study the stability and instability of fluid models. To do this we utilize piecewise linear Lyapunov functions. We establish stability of FirstBufferFirstServed (FBFS) and LastBufferFirstServed (LBFS) disciplines in all reentrant lines, and of all workconserving disciplines in any three buffer reentrant lines. For the four buffer network of Lu and Kumar we characterize the stability region of the Lu and Kumar policy, and show that it is also the global stability region for this network. We also study stability and instability of Kellytype networks. In particular, we show that not all workconserving policies are stable for such netw...
P.D.: Landau Hamiltonians with random potentials: localization and the density of states
 Commun. Math. Phys
, 1996
"... We prove the existence of localized states at the edges of the bands for the twodimensional Landau Hamiltonian with a random potential, of arbitrary disorder, provided that the magnetic field is sufficiently large. The corresponding eigenfunctions decay exponentially with the magnetic field and dis ..."
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Cited by 30 (9 self)
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We prove the existence of localized states at the edges of the bands for the twodimensional Landau Hamiltonian with a random potential, of arbitrary disorder, provided that the magnetic field is sufficiently large. The corresponding eigenfunctions decay exponentially with the magnetic field and distance. We also prove that the integrated density of states is Lipschitz continuous away from the Landau energies. The proof relies on a Wegner estimate for the finitearea magnetic Hamiltonians with random potentials and exponential decay estimates for the finitearea Green’s functions. The proof of the decay estimates for the Green’s functions uses fundamental results from twodimensional bond percolation theory. KeyWords: Landau Hamiltonians, random operators, localization. Number of figures: 4
Solving Large Nonsymmetric Sparse Linear Systems Using MCSPARSE
 PARALLEL COMPUTING
, 1996
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The parallel solution of nonsymmetric sparse linear systems using the H* reordering and an . . .
, 1994
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A Conservative Formulation For Plasticity
 Adv. Appl. Math
, 1992
"... . In this paper we propose a fully conservative form for the continuum equations governing ratedependent and rateindependent plastic flow in metals. The conservation laws are valid for discontinuous as well as smooth solutions. In the ratedependent case, the evolution equations are in divergence f ..."
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Cited by 11 (5 self)
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. In this paper we propose a fully conservative form for the continuum equations governing ratedependent and rateindependent plastic flow in metals. The conservation laws are valid for discontinuous as well as smooth solutions. In the ratedependent case, the evolution equations are in divergence form, with the plastic strain being passively convected and augmented by source terms. In the rateindependent case, the conservation laws involve a Lagrange multiplier that is determined by a set of constraints; we show that Riemann problems for this system admit scaleinvariant solutions. 1. Introduction In a previous paper [24], we formulated the equations for elasticity in the Eulerian picture as conservation laws. The motivation for this work was that the Eulerian framework is useful in numerical computations of largedeformation flows. Furthermore, the most effective numerical methods, such as secondorder Godunov schemes and the front tracking method, rely on an understanding of the s...
MCSPARSE: A parallel sparse unsymmetric linear system solver
, 1991
"... In this paper, an unsymmetric sparse linear system solver based on the exploita tion of multilevel parallelism is proposed. One of the main issues addressed is the application of tearing techniques to enhance large grain parallelism in a manner that maintains reasonable stability. This is accomp ..."
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Cited by 8 (3 self)
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In this paper, an unsymmetric sparse linear system solver based on the exploita tion of multilevel parallelism is proposed. One of the main issues addressed is the application of tearing techniques to enhance large grain parallelism in a manner that maintains reasonable stability. This is accomplished by a combination of a novel reordering technique (H*) and pivoting strategy. The large grain parallelism exposed by the reordering is combined with medium (various parallel row updates strategies) and fine grain (vectorization) parallelism to allow adaptation to a wide range of multipro cessor architectures. Experimental results are presented which show the effectiveness of the reordering, as well as the stability and efficiency of the solver.
Layer Reassignment for Antenna Effect Minimization in 3Layer Channel Routing
 Proc. of the 1996 IEEE International Symposium on Defect and Fault Tolerance in VLSI Systems
, 1996
"... As semiconductor technology enters the deep submicron era, reliability has become a major challenge in the design and manufacturing of next generation VLSI circuits. In this paper we focus on one reliability issue  the antenna effect in the context of 3layer channel routing. We first present an an ..."
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Cited by 6 (2 self)
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As semiconductor technology enters the deep submicron era, reliability has become a major challenge in the design and manufacturing of next generation VLSI circuits. In this paper we focus on one reliability issue  the antenna effect in the context of 3layer channel routing. We first present an antenna effect model in 3layer channel routing and, based on this, an antenna effect cost function is proposed. A layer reassignment approach is adopted to minimize this cost function and we show that the layer reassignment problem can be formulated as a network bipartitioning problem. Experimental results show that the antenna effect can be reduced considerably by applying the proposed technique. Compared with previous work, one advantage of our approach is that no extra channel area is required for antenna effect minimization. We show that layer reassignment technique can be used in yieldrelated critical area minimization in 3layer channel routing as well. The tradeoff between these two ...