Deconvolution with the ℓ1 norm

Geophysics ◽  
1979 ◽  
Vol 44 (1) ◽  
pp. 39-52 ◽  
Author(s):  
Howard L. Taylor ◽  
Stephen C. Banks ◽  
John F. McCoy
Keyword(s):  
Linear Programming ◽  
Spike Train ◽  
Initial Approximation ◽  
Spike Trains ◽  
General Linear ◽  
Programming System ◽  
Sample Rate ◽  
Weighting Procedures

Given a wavelet w and a noisy trace t + s * w + n, an approximation ŝ of the spike train s can be obtained using the [Formula: see text] norm. This extraction has the advantage of preserving isolated spikes in s. On some types of data the spike train ŝ can represent s as a sparse series of spikes, which may be sampled at a rate higher than the sample rate of the data trace t. The extracted spike train ŝ may be qualitatively much different than those commonly extracted using the [Formula: see text] norm. The [Formula: see text] norm can also be used to extract a wavelet ŵ from a trace t when a spike train s is known. This wavelet extraction can be constrained to give a smooth wavelet which integrates to zero and goes to zero at the ends. Given a trace t and an initial approximation for either s or w, it is possible to alternately extract spike trains and wavelets to improve the representation of trace t. Although special algorithms have been developed to solve [Formula: see text] problems, all of the calculations can be performed using a general linear programming system. Proper weighting procedures allow these methods to be used on ungained data.

scholarly journals A Biologically Plausible Computational Model for Auditory Object Recognition

2009 ◽  
Vol 101 (1) ◽  
pp. 323-331 ◽  
Author(s):  
Eric Larson ◽  
Cyrus P. Billimoria ◽  
Kamal Sen
Keyword(s):  
Object Recognition ◽  
Spike Train ◽  
Nearest Neighbor ◽  
Primary Auditory Cortex ◽  
Spike Trains ◽  
Coincidence Detection ◽  
Model Based ◽  
Plausible Model ◽  
Field L ◽  
Song Discrimination

Object recognition is a task of fundamental importance for sensory systems. Although this problem has been intensively investigated in the visual system, relatively little is known about the recognition of complex auditory objects. Recent work has shown that spike trains from individual sensory neurons can be used to discriminate between and recognize stimuli. Multiple groups have developed spike similarity or dissimilarity metrics to quantify the differences between spike trains. Using a nearest-neighbor approach the spike similarity metrics can be used to classify the stimuli into groups used to evoke the spike trains. The nearest prototype spike train to the tested spike train can then be used to identify the stimulus. However, how biological circuits might perform such computations remains unclear. Elucidating this question would facilitate the experimental search for such circuits in biological systems, as well as the design of artificial circuits that can perform such computations. Here we present a biologically plausible model for discrimination inspired by a spike distance metric using a network of integrate-and-fire model neurons coupled to a decision network. We then apply this model to the birdsong system in the context of song discrimination and recognition. We show that the model circuit is effective at recognizing individual songs, based on experimental input data from field L, the avian primary auditory cortex analog. We also compare the performance and robustness of this model to two alternative models of song discrimination: a model based on coincidence detection and a model based on firing rate.

Bursts and recurrences of bursts in the spike trains of spontaneously active striate cortex neurons

1985 ◽  
Vol 53 (4) ◽  
pp. 926-939 ◽  
Author(s):  
C. R. Legendy ◽  
M. Salcman
Keyword(s):  
Standard Deviation ◽  
Spike Train ◽  
Striate Cortex ◽  
Quantitative Measure ◽  
Spike Trains ◽  
Spike Rate ◽  
Occurrence Rate ◽  
Implanted Electrodes ◽  
Firing Rates ◽  
The Mean

Simultaneous recordings were made from small collections (2-7) of spontaneously active single units in the striate cortex of unanesthetized cats, by means of chronically implanted electrodes. The recorded spike trains were computer scanned for bursts of spikes, and the bursts were catalogued and studied. The firing rates of the neurons ranged from 0.16 to 32 spikes/s; the mean was 8.9 spikes/s, the standard deviation 7.0 spikes/s. Bursts of spikes were assigned a quantitative measure, termed Poisson surprise (S), defined as the negative logarithm of their probability in a random (Poisson) spike train. Only bursts having S greater than 10, corresponding to an occurrence rate of about 0.01 bursts/1,000 spikes in a random spike train, were considered to be of interest. Bursts having S greater than 10 occurred at a rate of about 5-15 bursts/1,000 spikes, or about 1-5 bursts/min. The rate slightly increased with spike rate; averaging about 2 bursts/min for neurons having 3 spikes/s and about 4.5 bursts/min for neurons having 30 spikes/s. About 21% of the recorded units emitted significantly fewer bursts than the rest (below 1 burst/1,000 spikes). The percentage of these neurons was independent of spike rate. The spike rate during bursts was found to be about 3-6 times the average spike rate; about the same for longer as for shorter bursts. Bursts typically contained 10-50 spikes and lasted 0.5-2.0 s. When the number of spikes in the successively emitted bursts was listed, it was found that in some neurons these numbers were not distributed at random but were clustered around one or more preferred values. In this sense, bursts occasionally "recurred" a few times in a few minutes. The finding suggests that neurons are highly reliable. When bursts of two or more simultaneously recorded neurons were compared, the bursts often appeared to be temporally close, especially between pairs of neurons recorded by the same electrode; but bursts seldom started and ended simultaneously on two channels. Recurring bursts emitted by one neuron were occasionally accompanied by time-locked recurring bursts by other neurons.

scholarly journals A New Multineuron Spike Train Metric

2008 ◽  
Vol 20 (6) ◽  
pp. 1495-1511 ◽  
Author(s):  
Conor Houghton ◽  
Kamal Sen
Keyword(s):  
Spike Train ◽  
Simulated Data ◽  
Spike Trains ◽  
The Other

The Victor-Purpura spike train metric has recently been extended to a family of multineuron metrics and used to analyze spike trains recorded simultaneously from pairs of proximate neurons. The metric is one of the two metrics commonly used for quantifying the distance between two spike trains; the other is the van Rossum metric. Here, we suggest an extension of the van Rossum metric to a multineuron metric. We believe this gives a metric that is both natural and easy to calculate. Both types of multineuron metric are applied to simulated data and are compared.

Intrinsic features contributing to spike train patterning in proprioceptive cuneate neurons

1987 ◽  
Vol 57 (4) ◽  
pp. 962-976 ◽  
Author(s):  
D. J. Surmeier ◽  
A. L. Towe
Keyword(s):  
Computer Simulation ◽  
Spike Train ◽  
Spike Trains ◽  
Antidromic Activation ◽  
Synaptic Potentials ◽  
Class A ◽  
Class B ◽  
Class C ◽  
Discharge Patterns ◽  
Periodic Inputs

The intrinsic processes contributing to the three discharge patterns of proprioceptive cuneate neurons described by Surmeier and Towe were studied experimentally and with computer simulation. Examination of the alterations in excitability produced by antidromic activation suggested that a prolonged inhibition was a concomitant of discharge in proprioceptive cuneate neurons. Computer simulation was performed to test the possible roles of inhibitory hyperpolarizing processes in governing the observed discharge patterns. These simulations used two constant threshold models. The simplest model linearly integrated synaptic potentials until the spike threshold was reached. After the discharge, synaptic potentials that preceded the spike were ignored (i.e., the model was "reset"). The second model was similar to the first except that following a spike two hyperpolarizing processes were activated and preceding events continued to play a role in membrane potential. Simulation of class A spike trains that possessed positive correlations between nearby intervals was successful only with a resetting model. This suggested that class A neurons have fast, no-memory postspike conductance changes, which effectively shunt synaptic charge. Simulation of class B spike trains was possible with the nonresetting model. At least two periodic inputs, which evoked brief, relatively large EPSPs, were required. In addition, a prominent, fast, spike-dependent hyperpolarization and a small-amplitude, slow hyperpolarization were required. Simulation of class C spike trains was also possible with the nonresetting model. Several periodic inputs were required; one input had to evoke a slow suprathreshold EPSP. In contrast to class B simulations, class C spike train simulation required that a large-amplitude, slow hyperpolarization, as well as a brief hyperpolarization, following spike initiation. The results of class B and C simulations suggested that these two groups differed primarily in the amplitude of a slow, hyperpolarizing, postspike conductance. Some role may also be played by the time course of the driving EPSPs.

scholarly journals Correlations Without Synchrony

1999 ◽  
Vol 11 (7) ◽  
pp. 1537-1551 ◽  
Author(s):  
Carlos D. Brody
Keyword(s):  
Spike Train ◽  
Response Latency ◽  
Quantitative Methods ◽  
Neuronal Excitability ◽  
Spike Trains ◽  
Spike Timing ◽  
Previous Article ◽  
Timing Synchronization

Peaks in spike train correlograms are usually taken as indicative of spike timing synchronization between neurons. Strictly speaking, however, a peak merely indicates that the two spike trains were not independent. Two biologically plausible ways of departing from independence that are capable of generating peaks very similar to spike timing peaks are described here: covariations over trials in response latency and covariations over trials in neuronal excitability. Since peaks due to these interactions can be similar to spike timing peaks, interpreting a correlogram may be a problem with ambiguous solutions. What peak shapes do latency or excitability interactions generate? When are they similar to spike timing peaks? When can they be ruled out from having caused an observed correlogram peak? These are the questions addressed here. The previous article in this issue proposes quantitative methods to tell cases apart when latency or excitability covariations cannot be ruled out.

Spike-Timing Precision Underlies the Coding Efficiency of Auditory Receptor Neurons

2006 ◽  
Vol 95 (4) ◽  
pp. 2541-2552 ◽  
Author(s):  
Ariel Rokem ◽  
Sebastian Watzl ◽  
Tim Gollisch ◽  
Martin Stemmler ◽  
Andreas V. M. Herz ◽  
...  
Keyword(s):  
Spike Train ◽  
Spike Trains ◽  
Neural Representation ◽  
Neural Firing ◽  
Specific Stimulus ◽  
Time Jitter ◽  
Information Rates ◽  
Communication Signals ◽  
Receptor Neurons ◽  
Stimulus Features

Sensory systems must translate incoming signals quickly and reliably so that an animal can act successfully in its environment. Even at the level of receptor neurons, however, functional aspects of the sensory encoding process are not yet fully understood. Specifically, this concerns the question how stimulus features and neural response characteristics lead to an efficient transmission of sensory information. To address this issue, we have recorded and analyzed spike trains from grasshopper auditory receptors, while systematically varying the stimulus statistics. The stimulus variations profoundly influenced the efficiency of neural encoding. This influence was largely attributable to the presence of specific stimulus features that triggered remarkably precise spikes whose trial-to-trial timing variability was as low as 0.15 ms—one order of magnitude shorter than typical stimulus time scales. Precise spikes decreased the noise entropy of the spike trains, thereby increasing the rate of information transmission. In contrast, the total spike train entropy, which quantifies the variety of different spike train patterns, hardly changed when stimulus conditions were altered, as long as the neural firing rate remained the same. This finding shows that stimulus distributions that were transmitted with high information rates did not invoke additional response patterns, but instead displayed exceptional temporal precision in their neural representation. The acoustic stimuli that led to the highest information rates and smallest spike-time jitter feature pronounced sound-pressure deflections lasting for 2–3 ms. These upstrokes are reminiscent of salient structures found in natural grasshopper communication signals, suggesting that precise spikes selectively encode particularly important aspects of the natural stimulus environment.

Temporally Irregular Mnemonic Persistent Activity in Prefrontal Neurons of Monkeys During a Delayed Response Task

2003 ◽  
Vol 90 (5) ◽  
pp. 3441-3454 ◽  
Author(s):  
Albert Compte, ◽  
Christos Constantinidis ◽  
Jesper Tegnér ◽  
Sridhar Raghavachari ◽  
Matthew V. Chafee ◽  
...  
Keyword(s):  
Prefrontal Cortex ◽  
Power Spectrum ◽  
Spike Train ◽  
Temporal Structure ◽  
Spike Trains ◽  
Delay Period ◽  
Delayed Response ◽  
Persistent Activity ◽  
Response Task ◽  
Delayed Response Task

An important question in neuroscience is whether and how temporal patterns and fluctuations in neuronal spike trains contribute to information processing in the cortex. We have addressed this issue in the memory-related circuits of the prefrontal cortex by analyzing spike trains from a database of 229 neurons recorded in the dorsolateral prefrontal cortex of 4 macaque monkeys during the performance of an oculomotor delayed-response task. For each task epoch, we have estimated their power spectrum together with interspike interval histograms and autocorrelograms. We find that 1) the properties of most (about 60%) neurons approximated the characteristics of a Poisson process. For about 25% of cells, with characteristics typical of interneurons, the power spectrum showed a trough at low frequencies (<20 Hz) and the autocorrelogram a dip near zero time lag. About 15% of neurons had a peak at <20 Hz in the power spectrum, associated with the burstiness of the spike train; 2) a small but significant task dependency of spike-train temporal structure: delay responses to preferred locations were characterized not only by elevated firing, but also by suppressed power at low (<20 Hz) frequencies; and 3) the variability of interspike intervals is typically higher during the mnemonic delay period than during the fixation period, regardless of the remembered cue. The high irregularity of neural persistent activity during the delay period is likely to be a characteristic signature of recurrent prefrontal network dynamics underlying working memory.

Sign in / Sign up

Export Citation Format

Share Document