Simulation of nonhomogeneous poisson processes by thinning

Lewis, Peter; Shedler, Gerald S.

doi:10.1002/nav.3800260304

Cited by 731 publications

(407 citation statements)

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“…Simulation of the model in Eq. 3.1 was carried out by using a thinning algorithm, assuming an inhomogeneous Poisson process (22,23). We assumed a 150-cm linear track with a rat running at a constant velocity of 25 cm͞sec and simulated the spiking activity of a single place cell (Fig.…”

Section: Discussionmentioning

confidence: 99%

An analysis of neural receptive field plasticity by point process adaptive filtering

Brown

Nguyen

Frank

et al. 2001

Proc. Natl. Acad. Sci. U.S.A.

168

115

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Neural receptive fields are plastic: with experience, neurons in many brain regions change their spiking responses to relevant stimuli. Analysis of receptive field plasticity from experimental measurements is crucial for understanding how neural systems adapt their representations of relevant biological information. Current analysis methods using histogram estimates of spike rate functions in nonoverlapping temporal windows do not track the evolution of receptive field plasticity on a fine time scale. Adaptive signal processing is an established engineering paradigm for estimating time-varying system parameters from experimental measurements. We present an adaptive filter algorithm for tracking neural receptive field plasticity based on point process models of spike train activity. We derive an instantaneous steepest descent algorithm by using as the criterion function the instantaneous log likelihood of a point process spike train model. We apply the point process adaptive filter algorithm in a study of spatial (place) receptive field properties of simulated and actual spike train data from rat CA1 hippocampal neurons. A stability analysis of the algorithm is sketched in the Appendix. The adaptive algorithm can update the place field parameter estimates on a millisecond time scale. It reliably tracked the migration, changes in scale, and changes in maximum firing rate characteristic of hippocampal place fields in a rat running on a linear track. Point process adaptive filtering offers an analytic method for studying the dynamics of neural receptive fields.T he receptive fields of neurons are dynamic; that is, their responses to relevant stimuli change with experience. Experience-dependent change or plasticity has been documented in a number of brain regions (1-5). For example, in the cat visual system, retinal lesions lead to reorganization of cortical topography (3). Peripheral nerve sectioning can alter substantially the receptive fields of neurons in monkey somatosensory and motor cortices (6, 7). Similarly, the directional tuning of neural receptive fields in monkey motor cortex changes as the animal learns to compensate for an externally applied force field while moving a manipulandum (8). In the rat hippocampus, the system we study here, the pyramidal neurons in the CA1 region have spatial receptive fields. As a rat executes a behavioral task, a given CA1 neuron fires only in a restricted region of the experimental environment, termed the cell's spatial or place receptive field (9). Place fields change in a reliable manner as the animal executes its task (5, 10). When the experimental environment is a linear track, these spatial receptive fields on average migrate and skew in the direction opposite the cell's preferred direction of firing relative to the animal's movement and increase in scale and maximum firing rate (5, 10). Because receptive field plasticity is a characteristic of many neural systems, analysis of these dynamics from experimental measurements is crucial for understanding how different br...

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Section: Discussionmentioning

confidence: 99%

An analysis of neural receptive field plasticity by point process adaptive filtering

Brown

Nguyen

Frank

et al. 2001

Proc. Natl. Acad. Sci. U.S.A.

168

115

View full text Add to dashboard Cite

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“…Throughout this section, and again in section 4 when considering simulated networks, we use Lewis's thinning method [20,26] to generate artificial Hawkes process point patterns.…”

Section: Generating Hawkes Process Point Patternsmentioning

confidence: 99%

Point-process models of social network interactions: Parameter estimation and missing data recovery

et al. 2015

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Electronic communications, as well as other categories of interactions within social networks, exhibit bursts of activity localised in time. We adopt a self-exciting Hawkes process model for this behaviour. First we investigate parameter estimation of such processes and find that, in the parameter regime we encounter, the choice of triggering function is not as important as getting the correct parameters once a choice is made. Then we present a relaxed maximum likelihood method for filling in missing data in records of communications in social networks. Our optimisation algorithm adapts a recent curvilinear search method to handle inequality constraints and a nonvanishing derivative. Finally we demonstrate the method using a data set composed of email records from a social network based at the United States Military Academy. The method performs differently on this data and data from simulations, but the performance degrades only slightly as more information is removed. The ability to fill in large blocks of missing social network data has implications for security, surveillance, and privacy.

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“…Step 1: Generate independent exponentials with rate 1, X 1 ,X 2 , ... and an equal number of uniform random numbers can be compared with the procedure suggested in [3]. This latter procedure simulates points in C(r) by first simulating N , the nuber of such points and then uses the fact that, given N , the points are uniformly distributed in C(r) .…”

Section: Simulating Random Permutations With Weightsmentioning

confidence: 99%