Results 1  10
of
10
Stochastic neural network model for spontaneous bursting in hippocampal slices
"... A biologically plausible, stochastic, neural network model that exhibits spontaneous transitions between a lowactivity ͑normal͒ state and a highactivity ͑epileptic͒ state is studied by computer simulation. Brief excursions of the network to the highactivity state lead to spontaneous population b ..."
Abstract
 Add to MetaCart
periodic orbits ͑UPOs͒ of systems exhibiting deterministic chaos. Simulations of the effects of the application of chaos control, periodic pacing, and anticontrol to the network model yield results that are qualitatively similar to those obtained in experiments on hippocampal slices. Estimation
Deterministic Chaos and Noise in Three In Vitro Hippocampal Models of Epilepsy
 Ann. Biomed. Eng
, 2001
"... Recent reports have suggested that chaos control techniques may be useful for electrically manipulating epileptiform bursting behavior in neuronal ensembles. Because the dynamics of spontaneous in vitro bursting had not been well determined previously, analysis of this behavior in the rat hippocampu ..."
Abstract
 Add to MetaCart
bicuculline #20 #M# and picrotoxin #250 #M#. The existence of chaos and determinism was assessed using two different analytical techniques: unstable periodic orbit #UPO# analysis and a new technique for estimating Lyapunov exponents. Significance of these results was assessed by comparing the calculations
Shortterm frequencydependent plasticity at recurrent mossy fiber synapses of the epileptic brain
 Journal of Neuroscience
, 2003
"... The recurrent mossy fiber pathway of the dentate gyrus expands dramatically in human temporal lobe epilepsy and in animal models of this disorder, creating monosynaptic connections among granule cells. This novel granule cell network can support reverberating excitation but is difficult to activate ..."
Abstract

Cited by 5 (0 self)
 Add to MetaCart
with lowfrequency stimulation. This study used hippocampal slices from pilocarpinetreated rats to explore the dependence of synaptic transmission in this pathway on stimulus frequency. Minimal electrically evoked EPSCs exhibited a high failure rate (�60%). Stimulus trains delivered at a frequency of �1
Proof Copy 004107abe
 Ann. Biomed. Eng
, 2001
"... Recent reports have suggested that chaos control techniques may be useful for electrically manipulating epileptiform bursting behavior in neuronal ensembles. Because the dynamics of spontaneous in vitro bursting had not been well determined previously, analysis of this behavior in the rat hippocampu ..."
Abstract
 Add to MetaCart
bicuculline #20 #M# and picrotoxin #250 #M#. The existence of chaos and determinism was assessed using two different analytical techniques: unstable periodic orbit #UPO# analysis and a new technique for estimating Lyapunov exponents. Significance of these results was assessed by comparing the calculations
Manipulating Epileptiform Bursting In The Rat Hippocampus Using Chaos Control And Adaptive Techniques
"... Epilepsy is a relatively common disease, afflicting 12% of the population, yet many epileptic patients are not sufficiently helped by current pharmacological therapies. Recent reports have suggested that chaos control techniques may be useful for electrically manipulating epileptiform bursting beha ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
behavior in vitro and could possibly lead to an alternative method for preventing seizures. We implemented chaos control of spontaneous bursting in the rat hippocampal slice using robust control techniques: stable manifold placement (SMP) and an adaptive tracking algorithm designed to overcome
Manipulating Epileptiform Bursting in the Rat Hippocampus Using Chaos Control and Adaptive Techniques
"... Abstract—Epilepsy is a relatively common disease, afflicting 1%–2 % of the population, yet many epileptic patients are not sufficiently helped by current pharmacological therapies. Recent reports have suggested that chaos control techniques may be useful for electrically manipulating epileptiform bu ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
and nonstationarity. Noise might actually be lower in vivo, where regulatory inputs to the hippocampus are still intact. Thus, it may still be feasible to use chaos control algorithms for preventing epileptic seizures. Index Terms—Adaptive, control, epilepsy, chaos, hippocampus, periodic orbit, seizure, synaptic
Abstract Identification of determinism in noisy neuronal systems
, 2002
"... Most neuronal ensembles are nonlinear excitable systems. Thus it is becoming common to apply principles derived from nonlinear dynamics to characterize neuronal systems. One important characterization is whether such systems contain deterministic behavior or are purely stochastic. Unfortunately, man ..."
Abstract
 Add to MetaCart
the presence of fixed points (or unstable periodic orbits) and to assess stationarity. If these are present, it implies that the system contains determinism. We demonstrate the use and possible limitations of these two techniques in two systems: the Hénon map, a classic example of a chaotic system
IDENTIFICATION OF DETERMINISM IN NOISY NEURONAL SYSTEMS Marc W. Slutzky
"... Most neuronal ensembles are nonlinear excitable systems. Thus it is becoming common to apply principles derived from nonlinear dynamics to characterize neuronal systems. One important distinction to be made is whether a system contains deterministic behavior or is purely stochastic. Unfortunately, m ..."
Abstract
 Add to MetaCart
can be used to verify the presence of fixed points (or unstable periodic orbits) in a system. If these are present, it implies that the system contains determinism. We demonstrate the use of these two techniques in two systems: the Hnon map, which is a classic example of a chaotic system
[2], Chapter 6):
, 2003
"... The purpose of this paper is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon the mathematical structures involved, rather than numerical computations. The opening section reviews and clarifies the FriedmannRobertsonWalker models of General Relativist ..."
Abstract
 Add to MetaCart
The purpose of this paper is to review, clarify, and critically analyse modern mathematical cosmology. The emphasis is upon the mathematical structures involved, rather than numerical computations. The opening section reviews and clarifies the FriedmannRobertsonWalker models of General Relativistic Cosmology, while Section 2 deals with the spatially homogeneous models. Particular attention is paid to the topological and geometrical aspects of these models. Section 3 explains how the mathematical formalism can be linked with astronomical observation. Sections 4 and 5 provide a critical analysis of Inflationary Cosmology and Quantum Cosmology, with particular attention to the claims made that these theories can explain the creation of the universe. 1 The FriedmannRobertsonWalker models Let us review and clarify the topological and geometrical aspects of the FriedmannRobertsonWalker (FRW) models of General Relativistic Cosmology. Geometrically, a FRW model is a 4dimensional Lorentzian manifold M which can be expressed as a warped product, (O’Neill [1], Chapter 12; Heller
Abstract Cosmological Black Holes as Models of Cosmological Inhomogeneities
, 2006
"... Since cosmological black holes modify the density and pressure of the surrounding universe, and introduce heat conduction, they produce simple models of cosmological inhomogeneities that can be used to study the eect of inhomogeneities on the universe's expansion. In this thesis, new cosmologi ..."
Abstract
 Add to MetaCart
Since cosmological black holes modify the density and pressure of the surrounding universe, and introduce heat conduction, they produce simple models of cosmological inhomogeneities that can be used to study the eect of inhomogeneities on the universe's expansion. In this thesis, new cosmological black hole solutions are obtained by generalizing the expanding KerrSchild cosmological black holes to obtain the charged case, by performing a KerrSchild transformation of the Einsteinde Sitter universe (instead of a closed universe) to obtain nonexpanding KerrSchild cosmological black holes in asymptotically
at universes, and by performing a conformal transformation on isotropic black hole spacetimes to obtain isotropic cosmological black hole spacetimes. The latter approach is found to produce cosmological black holes with energymomentum tensors that are physical throughout spacetime, unlike previous solutions for cosmological black holes, which violate the energy conditions in some region of spacetime. In addition, it is demonstrated that radiationdominated and matterdominated Einsteinde Sitter universes can be directly matched across a hypersurface of constant time, and this is used to generate the rst solutions for primordial black holes that evolve from being in radiationdominated background universes to matterdominated background universes. Finally, the Weyl curvature, volume expansion, velocity eld, shear, and acceleration are calculated for the cosii mological black holes. Since the nonisotropic black holes introduce shear, according to Raychaudhuri's equation they will tend to decrease the volume expansion of the universe. Unlike several studies that have suggested the relativistic backreaction of inhomogeneities would lead to an accelerating expansion of the universe, it is concluded that shear should be the most likely in
uence of inhomogeneities, so they should most likely decrease the universe's expansion. iii