Papers by Christoph Borgers
The IMA Volumes in Mathematics and its Applications, 1999
Institute for Mathematics and its Applications IMA The Institute for Mathematics and its Applicat... more Institute for Mathematics and its Applications IMA The Institute for Mathematics and its Applications was established by a grant from the National Science Foundation to the University of Minnesota in 1982. The IMA seeks to encourage the development and study of fresh mathematical concepts and questions of concern to the other sciences by bringing together mathematicians and scientists from diverse fields in an atmosphere that will stimulate discussion and collaboration. The IMA Volumes are intended to involve the broader scientific community in this process.
The Transversely Integrated Scalar Flux of a Narrowly Focused Particle Beam
SIAM Journal on Applied Mathematics, 1995
Page 1. SIAM J. APPL. MATH. ? 1995 Society for Industrial and Applied Mathematics Vol. 55, No. 1,... more Page 1. SIAM J. APPL. MATH. ? 1995 Society for Industrial and Applied Mathematics Vol. 55, No. 1, pp. 1-22, February 1995 001 THE TRANSVERSELY INTEGRATED SCALAR FLUX OF A NARROWLY FOCUSED PARTICLE BEAM* ...
Proceedings of the National Academy of Sciences, 2008
Simultaneous presentation of multiple stimuli can reduce the firing rates of neurons in extrastri... more Simultaneous presentation of multiple stimuli can reduce the firing rates of neurons in extrastriate visual cortex below the rate elicited by a single preferred stimulus. We describe computational results suggesting how this remarkable effect may arise from strong excitatory drive to a substantial local population of fast-spiking inhibitory interneurons, which can lead to a loss of coherence in that population and thereby raise the effectiveness of inhibition. We propose that in attentional states fast-spiking interneurons may be subject to a bath of inhibition resulting from cholinergic activation of a second class of inhibitory interneurons, restoring conditions needed for gamma rhythmicity. Oscillations and coherence are emergent features, not assumptions, in our model. The gamma oscillations in turn support stimulus competition. The mechanism is a form of “oscillatory selection,” in which neural interactions change phase relationships that regulate firing rates, and attention sh...
Proceedings of the National Academy of Sciences, 2005
We describe a simple computational model, based on generic features of cortical local circuits, t... more We describe a simple computational model, based on generic features of cortical local circuits, that links cholinergic neuromodulation, gamma rhythmicity, and attentional selection. We propose that cholinergic modulation, by reducing adaptation currents in principal cells, induces a transition from asynchronous spontaneous activity to a “background” gamma rhythm (resembling the persistent gamma rhythms evoked in vitro by cholinergic agonists) in which individual principal cells participate infrequently and irregularly. We suggest that such rhythms accompany states of preparatory attention or vigilance and report simulations demonstrating that their presence can amplify stimulus-specific responses and enhance stimulus competition within a local circuit.
Proceedings of the National Academy of Sciences, 2013
Significance Metabotropic GABA B receptors control synaptic transmission and excitability in neur... more Significance Metabotropic GABA B receptors control synaptic transmission and excitability in neuronal circuits of the brain. Although effects of these receptors are predominantly inhibitory at both cellular and network levels, application of the agonist baclofen can promote excitability and induce seizures in patients and animal models of epilepsy. Here we demonstrate that proepileptic effects of baclofen are concentration dependent and result from disinhibition. Although at high doses, baclofen reduces network excitability due to its combined pre- and postsynaptic inhibitory effects in pyramidal cells, at low doses, it leads to an enhanced presynaptic suppression of the synaptic output of a specific set of inhibitory neurons. This disinhibitory effect promotes high-frequency oscillations and the emergence of pathological discharges in the epileptic hippocampal network.
Journal of Computational Physics, 1992
Consider a linear transport problem, and let the mean free path and the absorption cross section ... more Consider a linear transport problem, and let the mean free path and the absorption cross section be of size E. It is well known that one obtains a diffusion problem as E tends to zero. We discretize the transport problem on a fixed mesh, independent of E, consider again the limit e-+0, and ask whether one obtains an accurate discretization of the continuous diffusion problem. The answer is known to be affirmative for the linear discontinuous Galerkin finite element discretization in one space dimension. In this paper, we ask whether the same result holds in two space dimensions. We consider a linear discontinuous discretization based on rectangular meshes. Our main result is that the asymptotic limit of this discrete problem is nof a discretization of the asymptotic limit of the continuous problem and thus that the discretization will be inaccurate in the asymptotic regime under consideration. We also propose a modified scheme which has the correct asymptotic behavior for spatially periodic problems, although not always for problems with boundaries. We present numerical results confirming our formal asymptotic analysis.
Probing mechanisms of gamma rhythmogenesis with cell type-specific optical neural control
Frontiers in Systems Neuroscience, 2009
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Papers by Christoph Borgers