Stefan Mihalas

Spiking neuron models are used in a multitude of tasks ranging from understanding neural behavior at its most basic level to neuroprosthetics. Parameter estimation of a single neuron model, such that the model's output matches that of a biological neuron is an extremely important task. Hand tuning of parameters to obtain such behaviors is a difficult and time consuming process. This is further complicated when the neuron is instantiated in silicon (an attractive medium in which to implement these models) as fabrication imperfections make the task of parameter configuration more complex. In this paper we show two methods to automate the configuration of a silicon (hardware) neuron's parameters. First, we show how a Maximum Likelihood method can be applied to a leaky integrate and fire silicon neuron with spike induced currents to fit the neuron's output to desired spike times. We then show how a distance based method which approximates the negative log likelihood of the lognormal distribution can also be used to tune the neuron's parameters. We conclude that the distance based method is better suited for parameter configuration of silicon neurons due to its superior optimization speed.

One approach to conveying tactile feedback from sensorized neural prostheses is to characterize the neural signals that would normally be produced in an intact limb and reproduce them through electrical stimulation of the residual peripheral nerves. Toward this end, we have developed an integrate-and-fire model that predicts with millisecond accuracy the timing of responses of the mechanoreceptive afferents that innervate the glabrous skin of the hand. Individual afferents produce highly repeatable and stereotyped responses to a given stimulus. However, responses differ considerably across afferents, even across afferents of a given type. In the present study, we wish to assess the extent to which this within-type variability shapes the signal conveyed by the hand to the brain. Specifically, we wish to determine the extent to which a single canonical model can be used to mimic the responses of a population of afferents during a set of activities of daily living. We find that the spiking responses simulated using the canonical model does not match, in their fine temporal structure, those simulated using individually fit models. However, population firing rates simulated using a canonical model match those simulated using individual models. Our results suggest that afferent heterogeneity is important if the read-out of the response of afferent populations is sensitive to the precise temporal structure of the population response. To the extent that precise spike timing (at a resolution of milliseconds) is not essential, a canonical model can be used to simulate the responses of populations of afferents.

An accurate calculation of the first passage time probability density (FPTPD) is essential for computing the likelihood of solutions of the stochastic leaky integrate-and-fire model. The previously proposed numerical calculation of the FPTPD based on the integral equation method discretizes the probability current of the voltage crossing the threshold. While the method is accurate for high noise levels, we show that it results in large numerical errors for small noise. The problem is solved by analytically computing, in each time bin, the mean probability current. Efficiency is further improved by identifying and ignoring time bins with negligible mean probability current.

Spiking neurons and spiking neural circuits are finding uses in a multitude of tasks such as robotic locomotion control, neuroprosthetics, visual sensory processing, and audition. The desired neural output is achieved through the use of complex neuron models, or by combining multiple simple neurons into a network. In either case, a means for configuring the neuron or neural circuit is required. Manual manipulation of parameters is both time consuming and non-intuitive due to the nonlinear relationship between parameters and the neuron's output. The complexity rises even further as the neurons are networked and the systems often become mathematically intractable. In large circuits, the desired behavior and timing of action potential trains may be known but the timing of the individual action potentials is unknown and unimportant, whereas in single neuron systems the timing of individual action potentials is critical. In this paper, we automate the process of finding parameters. To configure a single neuron we derive a maximum likelihood method for configuring a neuron model, specifically the Mihalas-Niebur Neuron. Similarly, to configure neural circuits, we show how we use genetic algorithms (GAs) to configure parameters for a network of simple integrate and fire with adaptation neurons. The GA approach is demonstrated both in software simulation and hardware implementation on a reconfigurable custom very large scale integration chip.

Most natural scenes are too complex to be perceived instantaneously in their entirety. Observers therefore have to select parts of them and process these parts sequentially. We study how this selection and prioritization process is performed by humans at two different levels. One is the overt attention mechanism of saccadic eye movements in a free-viewing paradigm. The second is a conscious decision process in which we asked observers which points in a scene they considered the most interesting. We find in a very large participant population (more than one thousand) that observers largely agree on which points they consider interesting. Their selections are also correlated with the eye movement pattern of different subjects. Both are correlated with predictions of a purely bottom–up saliency map model. Thus, bottom–up saliency influences cognitive processes as far removed from the sensory periphery as in the conscious choice of what an observer considers interesting.

For simulations of neural networks, there is a trade-off between the size of the network that can be simulated and the complexity of the model used for individual neurons. In this study, we describe a generalization of the leaky integrate-and-fire model that produces a wide variety of spiking behaviors while still being analytically solvable between firings. For different parameter values, the model produces spiking or bursting, tonic, phasic or adapting responses, depolarizing or hyperpolarizing after potentials and so forth. The model consists of a diagonalizable set of linear differential equations describing the time evolution of membrane potential, a variable threshold, and an arbitrary number of firing-induced currents. Each of these variables is modified by an update rule when the potential reaches threshold. The variables used are intuitive and have biological significance. The model's rich behavior does not come from the differential equations, which are linear, but rather from complex update rules. This single-neuron model can be implemented using algorithms similar to the standard integrate-and-fire model. It is a natural match with event-driven algorithms for which the firing times are obtained as a solution of a polynomial equation.

We tested the binding-by-synchrony hypothesis which proposes that object representations are formed by synchronizing spike activity between neurons that code features of the same object. We studied responses of 32 pairs of neurons recorded with microelectrodes 3 mm apart in the visual cortex of macaques performing a fixation task. Upon mapping the receptive fields of the neurons, a quadrilateral was generated so that two of its sides were centered in the receptive fields at the optimal orientations. This one-figure condition was compared with a two-figure condition in which the neurons were stimulated by two separate figures, keeping the local edges in the receptive fields identical. For each neuron, we also determined its border ownership selectivity (H. Zhou, H. S. Friedman, & R. von der Heydt, 2000). We examined both synchronization and correlation at nonzero time lag. After correcting for effects of the firing rate, we found that synchrony did not depend on the binding condition. However, finding synchrony in a pair of neurons was correlated with finding border-ownership selectivity in both members of the pair. This suggests that the synchrony reflected the connectivity in the network that generates border ownership assignment. Thus, we have not found evidence to support the binding-by-synchrony hypothesis.