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The ability of spiking neurons to synchronize their activity in a network depends on the response behavior of these neurons as quantified by the phase response curve (PRC) and on coupling properties. The PRC characterizes the effects of transient inputs on spike timing and can be measured experimentally. Here we use the adaptive exponential… (More)

Mathematical studies of drug induced geometric visual hallucinations include three components: a model (or class of models) that abstracts the structure of the primary visual cortex V1; a mathematical procedure for finding geometric patterns as solutions to the cortical models; and a method for interpreting these patterns as visual hallucinations.… (More)

- Krešimir Josić, José Manuel López, William Ott, LieJune Shiau, Matthew R. Bennett
- PLoS Computational Biology
- 2011

The creation of protein from DNA is a dynamic process consisting of numerous reactions, such as transcription, translation and protein folding. Each of these reactions is further comprised of hundreds or thousands of sub-steps that must be completed before a protein is fully mature. Consequently, the time it takes to create a single protein depends on the… (More)

The vestibular system in almost all vertebrates, and in particular in humans, controls balance by employing a set of six semicircular canals, three in each inner ear, to detect angular accelerations of the head in three mutually orthogonal coordinate planes. Signals from the canals are transmitted to eight (groups of) neck motoneurons, which activate the… (More)

—In a previous article [1], the authors discussed the time-discretization of those relations modeling a class of dynamical systems with friction. The main goal of this article is to address similar problems using a more sophisticated friction model giving a better description of the system behavior when the velocities are close to zero. These investigations… (More)

We study the spike statistics of an adaptive exponential integrate-and-fire neuron stimulated by white Gaussian current noise. We derive analytical approximations for the coefficient of variation and the serial correlation coefficient of the interspike interval assuming that the neuron operates in the mean-driven tonic firing regime and that the stochastic… (More)

- LieJune Shiau, Carlo Laing
- BMC Neuroscience
- 2013

Although variability is a ubiquitous characteristic of the nervous system, under appropriate conditions neurons can generate precisely timed action potentials. Thus considerable attention has been given to the study of a neuron's output in relation to its stimulus. Frequency selectivity of mode locking exhibits in clinical studies of human cardiorespiratory… (More)

Synchronized oscillating activity in cortical circuits is a prevalent phenomenon and considered to be fundamental to cognitive function, selective attention and consciousness. In the present study we describe how spike-frequency adaptation (SFA) affects the synchronization properties of coupled neurons driven to repetitive firing, in dependence of axonal… (More)

This work illustrates an application of vector spaces to data transmission theory. We show how Hamming code error detection and error correction are done through the tool of various theories in vector space. It is hoped that this article will explain the importance of abstract mathematics, such as vector space and basis, in the application of data… (More)

In a previous article (ref. [1]) the authors discussed the application of operator-splitting methods to the time-discretization of those mathematical relations describing the behavior of elasto-dynamical systems with friction, focusing on one-degree of freedom models. The main goal of the present article is to generalize the methodology discussed in ref.… (More)