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89
Fluctuating synaptic conductances recreate in vivolike activity in neocortical neurons
 Neuroscience
, 2001
"... AbstractöTo investigate the basis of the £uctuating activity present in neocortical neurons in vivo, we have combined computational models with wholecell recordings using the dynamicclamp technique. A simpli¢ed `pointconductance' model was used to represent the currents generated by thousands of ..."
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Cited by 49 (22 self)
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AbstractöTo investigate the basis of the £uctuating activity present in neocortical neurons in vivo, we have combined computational models with wholecell recordings using the dynamicclamp technique. A simpli¢ed `pointconductance' model was used to represent the currents generated by thousands of stochastically releasing synapses. Synaptic activity was represented by two independent fast glutamatergic and GABAergic conductances described by stochastic randomwalk processes. An advantage of this approach is that all the model parameters can be determined from voltageclamp experiments. We show that the pointconductance model captures the amplitude and spectral characteristics of the synaptic conductances during background activity. To determine if it can recreate in vivolike activity, we injected this pointconductance model into a singlecompartment model, or in rat prefrontal cortical neurons in vitro using dynamic clamp. This procedure successfully recreated several properties of neurons intracellularly recorded in vivo, such as a depolarized membrane potential, the presence of highamplitude membrane potential £uctuations, a lowinput resistance and irregular spontaneous ¢ring activity. In addition, the pointconductance model could simulate the enhancement of responsiveness due to background activity. We conclude that many of the characteristics of cortical neurons in vivo can be explained by fast glutamatergic and
Characterization of Subthreshold Voltage Fluctuations in Neuronal Membranes
, 2003
"... Synaptic noise due to intense network activity can have a significant impact on the electrophysiological properties of individual neurons. This is the case for the cerebral cortex, where ongoing activity leads to strong barrages of synaptic inputs, which act as the main source of synaptic noise affe ..."
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Cited by 28 (13 self)
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Synaptic noise due to intense network activity can have a significant impact on the electrophysiological properties of individual neurons. This is the case for the cerebral cortex, where ongoing activity leads to strong barrages of synaptic inputs, which act as the main source of synaptic noise affecting on neuronal dynamics. Here, we characterize the subthreshold behavior of neuronal models in which synaptic noise is represented by either additive or multiplicative noise, described by OrnsteinUhlenbeck processes. We derive and solve the FokkerPlanck equation for this system, which describes the time evolution of the probability density function for the membrane potential. We obtain an analytic expression for the membrane potential distribution at steady state and compare this expression with the subthreshold activity obtained in HodgkinHuxleytype models with stochastic synaptic inputs. The differences between multiplicative and additive noise models suggest that multiplicative noise is adequate to describe the highconductance states similar to in vivo conditions. Because the steadystate membrane potential distribution is easily obtained experimentally, this approach provides a possible method to estimate the mean and variance of synaptic conductances in real neurons.
Modeling channel popularity dynamics in a large IPTV system
 In ACM Sigmetrics
, 2009
"... Understanding the channel popularity or content popularity is an important step in the workload characterization for modern information distribution systems (e.g., World Wide Web, peertopeer filesharing systems, videoondemand systems). In this paper, we focus on analyzing the channel popularity ..."
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Cited by 20 (3 self)
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Understanding the channel popularity or content popularity is an important step in the workload characterization for modern information distribution systems (e.g., World Wide Web, peertopeer filesharing systems, videoondemand systems). In this paper, we focus on analyzing the channel popularity in the context of Internet Protocol Television (IPTV). In particular, we aim at capturing two important aspects of channel popularity – the distribution and temporal dynamics of the channel popularity. We conduct indepth analysis on channel popularity on a large collection of user channel access data from a nationwide commercial IPTV network. Based on the findings in our analysis, we choose a stochastic model that finds good matches in all attributes of interest with respect to the channel popularity. Furthermore, we propose a method to identify subsets of user population with inherently different channel interest. By tracking the change of population mixtures among different user classes, we extend our model to a multiclass population model, which enables us to capture the moderate diurnal popularity patterns exhibited in some channels. We also validate our channel popularity model using real user channel access data from commercial IPTV network.
IntegrateandFire Neurons Driven by Correlated Stochastic Input
, 2002
"... Neurons are sensitive to correlations among synaptic inputs. However, analytical models that explicitly include correlations are hard to solve analytically, so their influence on a neuron’s response has been difficult to ascertain. To gain some intuition on this problem, we studied the firing times ..."
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Cited by 17 (4 self)
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Neurons are sensitive to correlations among synaptic inputs. However, analytical models that explicitly include correlations are hard to solve analytically, so their influence on a neuron’s response has been difficult to ascertain. To gain some intuition on this problem, we studied the firing times of two simple integrateandfire model neurons driven by a correlated binary variable that represents the total input current. Analytic expressions were obtained for the average firing rate and coefficient of variation (a measure of spiketrain variability) as functions of the mean, variance, and correlation time of the stochastic input. The results of computer simulations were in excellent agreement with these expressions. In these models, an increase in correlation time in general produces an increase in both the average firing rate and the variability of the output spike trains. However, the magnitude of the changes depends differentially on the relative values of the input mean and variance: the increase in firing rate is higher when the variance is large relative to the mean, whereas the increase in variability is higher when the variance is relatively small. In addition, the firing rate always tends to a finite limit value as the correlation time increases toward infinity, whereas the coefficient of variation typically diverges. These results suggest that temporal correlations may play a major role in determining the variability as well as the intensity of neuronal spike trains.
The betaJacobi matrix model, the CS decomposition, and generalized singular value problems
 Foundations of Computational Mathematics
, 2007
"... Abstract. We provide a solution to the βJacobi matrix model problem posed by Dumitriu and the first author. The random matrix distribution introduced here, called a matrix model, is related to the model of Killip and Nenciu, but the development is quite different. We start by introducing a new matr ..."
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Cited by 14 (3 self)
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Abstract. We provide a solution to the βJacobi matrix model problem posed by Dumitriu and the first author. The random matrix distribution introduced here, called a matrix model, is related to the model of Killip and Nenciu, but the development is quite different. We start by introducing a new matrix decomposition and an algorithm for computing this decomposition. Then we run the algorithm on a Haardistributed random matrix to produce the βJacobi matrix model. The Jacobi ensemble on R n, parameterized by β> 0, a> −1, and b> −1, is the probability distribution whose density is proportional to Q β 2 i λ (a+1)−1
On a Model for Quantum Friction I  Fermi's Golden Rule and Dynamics at Zero Temperature
, 1994
"... . We investigate the dynamics of a quantum particle in a confining potential linearly coupled to a bosonic field at temperature zero. For a massive field we show, by employing complex deformation techniques, that the Markoviansemigroup which approximates the particle dynamics on the time scale ø = ..."
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Cited by 13 (0 self)
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. We investigate the dynamics of a quantum particle in a confining potential linearly coupled to a bosonic field at temperature zero. For a massive field we show, by employing complex deformation techniques, that the Markoviansemigroup which approximates the particle dynamics on the time scale ø = 2 t ( strength of the coupling) is determined by the resonances of the full energy operator. We also show that Markovianmaster equation technique leads to the right prediction for the lifetime of resonances. We discuss the dissipation of the particle into its ground state both in the time mean and on the above time scale. 1. Introduction Friction, as a notion in classical physics, has been set on solid mathematical grounds by the theory of OrnsteinUhlenbeck processes. The dynamics of a particle experiencing frictional forces is governed by the Langevin equation, a second order nonlinear stochastic differential equation in the time variable. This equation has been widely investigated ...
Ergodic Properties of Classical Dissipative Systems I
 I. Acta Math
, 1998
"... We consider a class of models in which a Hamiltonian system A, with a finite number of degrees of freedom, is brought into contact with an infinite heat reservoir B. We develop the formalism required to describe these models near thermal equilibrium. Using a combination of abstract spectral techniqu ..."
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Cited by 12 (1 self)
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We consider a class of models in which a Hamiltonian system A, with a finite number of degrees of freedom, is brought into contact with an infinite heat reservoir B. We develop the formalism required to describe these models near thermal equilibrium. Using a combination of abstract spectral techniques and harmonic analysis we investigate the singular spectrum of the Liouvillean L of the coupled system A + B. We provide a natural set of conditions which ensure that the spectrum of L is purely absolutely continuous except for a simple eigenvalue at zero. It then follows from the spectral theory of dynamical systems (Koopmanism) that the system A + B is strongly mixing. From a probabilistic point of view, we study a new class of random processes on finite dimensional manifolds: nonMarkovian OrnsteinUhlenbeck processes. The paths of such a process are solutions of a random integrodifferential equation with Gaussian noise which is a natural generalization of the well known Langevin equ...
Robust strategies for managing rangelands with multiple stable attractors
 Journal of Environmental Economics and Management
, 2004
"... Savanna rangelands are characterized by dynamic interactions between grass, shrubs, fire and livestock driven by highly variable rainfall. When the livestock are grazers (only or preferentially eating grass) the desirable state of the system is dominated by grass, with scattered trees and shrubs. Ho ..."
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Cited by 8 (1 self)
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Savanna rangelands are characterized by dynamic interactions between grass, shrubs, fire and livestock driven by highly variable rainfall. When the livestock are grazers (only or preferentially eating grass) the desirable state of the system is dominated by grass, with scattered trees and shrubs. However, the system can have multiple stable attractors and a perturbation such as a drought can cause it to move from such a desired configuration into one that is dominated by shrubs with very little grass. In this paper, using the rangelands of New SouthWales in Australia as an example, we provide a methodology to find robust management strategies in the context of this complex ecological system driven by stochastic rainfall events. The control variables are sheep density and the degree of fire suppression. By comparing the optimal solution where it is assumed the manager has perfect knowledge and foresight of rainfall conditions with one where the rainfall variability is ignored, we found that rainfall variability and the related uncertainty lead to a reduction of the possible expected returns from grazing activity by 33%. Using a genetic algorithm, we develop robust management strategies for highly variable rainfall that more than doubles expected returns compared to those obtained under variable rainfall using an optimal solution based on average rainfall (i.e., where the manager ignores rainfall variability).
When is an Integrateandfire Neuron like a Poisson Neuron?
 In
, 1996
"... In the Poisson neuron model, the output is a ratemodulated Poisson process (Snyder and Miller, 1991); the time varying rate parameter r(t) is an instantaneous function G[:] of the stimulus, r(t) = G[s(t)]. In a Poisson neuron, then, r(t) gives the instantaneous firing ratethe instantaneous pro ..."
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Cited by 7 (0 self)
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In the Poisson neuron model, the output is a ratemodulated Poisson process (Snyder and Miller, 1991); the time varying rate parameter r(t) is an instantaneous function G[:] of the stimulus, r(t) = G[s(t)]. In a Poisson neuron, then, r(t) gives the instantaneous firing ratethe instantaneous probability of firing at any instant tand the output is a stochastic function of the input. In part because of its great simplicity, this model is widely used (usually with the addition of a refractory period), especially in in vivo single unit electrophysiological studies, where s(t) is usually taken to be the value of some sensory stimulus. In the integrateandfire neuron model, by contrast, the output is a filtered and thresholded function of the input: the input is passed through a lowpass filter (determined by the membrane time constant ø ) and integrated until the membrane potential v(t) reaches threshold `, at which point v(t) is reset to its initial value. By contrast with the Po...
Maximal inequalities for the OrnsteinUhlenbeck process
, 1998
"... Let V = (Vt)t 0 be the OrnsteinUhlenbeck velocity process solving ..."
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Cited by 6 (2 self)
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Let V = (Vt)t 0 be the OrnsteinUhlenbeck velocity process solving