902 research outputs found
Two dimensional QCD is a one dimensional Kazakov-Migdal model
We calculate the partition functions of QCD in two dimensions on a cylinder
and on a torus in the gauge by integrating explicitly
over the non zero modes of the Fourier expansion in the periodic time variable.
The result is a one dimensional Kazakov-Migdal matrix model with eigenvalues on
a circle rather than on a line. We prove that our result coincides with the
standard expansion in representations of the gauge group. This involves a non
trivial modular transformation from an expansion in exponentials of to
one in exponentials of . Finally we argue that the states of the
or partition function can be interpreted as a gas of N free fermions,
and the grand canonical partition function of such ensemble is given explicitly
as an infinite product.Comment: DFTT 15/93, 17 pages, Latex (Besides minor changes and comments added
we note that for U(N) odd and even N have to be treated separately
Finite Temperature Lattice QCD in the Large N Limit
Our aim is to give a self-contained review of recent advances in the analytic
description of the deconfinement transition and determination of the
deconfinement temperature in lattice QCD at large N. We also include some new
results, as for instance in the comparison of the analytic results with
Montecarlo simulations. We first review the general set-up of finite
temperature lattice gauge theories, using asymmetric lattices, and develop a
consistent perturbative expansion in the coupling of the space-like
plaquettes. We study in detail the effective models for the Polyakov loop
obtained, in the zeroth order approximation in , both from the Wilson
action (symmetric lattice) and from the heat kernel action (completely
asymmetric lattice). The distinctive feature of the heat kernel model is its
relation with two-dimensional QCD on a cylinder; the Wilson model, on the other
hand, can be exactly reduced to a twisted one-plaquette model via a procedure
of the Eguchi-Kawai type. In the weak coupling regime both models can be
related to exactly solvable Kazakov-Migdal matrix models. The instability of
the weak coupling solution is due in both cases to a condensation of
instantons; in the heat kernel case, it is directly related to the
Douglas-Kazakov transition of QCD2. A detailed analysis of these results
provides rather accurate predictions of the deconfinement temperature. In spite
of the zeroth order approximation they are in good agreement with the
Montecarlo simulations in 2+1 dimensions, while in 3+1 dimensions they only
agree with the Montecarlo results away from the continuum limit.Comment: 66 pages, plain Latex, figures included by eps
Analysis of slow (theta) oscillations as a potential temporal reference frame for information coding in sensory cortices
While sensory neurons carry behaviorally relevant information in responses that often extend over hundreds of milliseconds, the key units of neural information likely consist of much shorter and temporally precise spike patterns. The mechanisms and temporal reference frames by which sensory networks partition responses into these shorter units of information remain unknown. One hypothesis holds that slow oscillations provide a network-intrinsic reference to temporally partitioned spike trains without exploiting the millisecond-precise alignment of spikes to sensory stimuli. We tested this hypothesis on neural responses recorded in visual and auditory cortices of macaque monkeys in response to natural stimuli. Comparing different schemes for response partitioning revealed that theta band oscillations provide a temporal reference that permits extracting significantly more information than can be obtained from spike counts, and sometimes almost as much information as obtained by partitioning spike trains using precisely stimulus-locked time bins. We further tested the robustness of these partitioning schemes to temporal uncertainty in the decoding process and to noise in the sensory input. This revealed that partitioning using an oscillatory reference provides greater robustness than partitioning using precisely stimulus-locked time bins. Overall, these results provide a computational proof of concept for the hypothesis that slow rhythmic network activity may serve as internal reference frame for information coding in sensory cortices and they foster the notion that slow oscillations serve as key elements for the computations underlying perception
A theoretical model of neuronal population coding of stimuli with both continuous and discrete dimensions
In a recent study the initial rise of the mutual information between the
firing rates of N neurons and a set of p discrete stimuli has been analytically
evaluated, under the assumption that neurons fire independently of one another
to each stimulus and that each conditional distribution of firing rates is
gaussian. Yet real stimuli or behavioural correlates are high-dimensional, with
both discrete and continuously varying features.Moreover, the gaussian
approximation implies negative firing rates, which is biologically implausible.
Here, we generalize the analysis to the case where the stimulus or behavioural
correlate has both a discrete and a continuous dimension. In the case of large
noise we evaluate the mutual information up to the quadratic approximation as a
function of population size. Then we consider a more realistic distribution of
firing rates, truncated at zero, and we prove that the resulting correction,
with respect to the gaussian firing rates, can be expressed simply as a
renormalization of the noise parameter. Finally, we demonstrate the effect of
averaging the distribution across the discrete dimension, evaluating the mutual
information only with respect to the continuously varying correlate.Comment: 20 pages, 10 figure
Effective actions for finite temperature Lattice Gauge Theories
We consider a lattice gauge theory at finite temperature in (+1)
dimensions with the Wilson action and different couplings and
for timelike and spacelike plaquettes. By using the character
expansion and Schwinger-Dyson type equations we construct, order by order in
, an effective action for the Polyakov loops which is exact to all
orders in . As an example we construct the first non-trivial order in
for the (3+1) dimensional SU(2) model and use this effective action
to extract the deconfinement temperature of the model.Comment: Talk presented at LATTICE96(finite temperature
Reading spike timing without a clock: intrinsic decoding of spike trains
The precise timing of action potentials of sensory neurons relative to the time of stimulus presentation carries substantial sensory information that is lost or degraded when these responses are summed over longer time windows. However, it is unclear whether and how downstream networks can access information in precise time-varying neural responses. Here, we review approaches to test the hypothesis that the activity of neural populations provides the temporal reference frames needed to decode temporal spike patterns. These approaches are based on comparing the single-trial stimulus discriminability obtained from neural codes defined with respect to network-intrinsic reference frames to the discriminability obtained from codes defined relative to the experimenter's computer clock. Application of this formalism to auditory, visual and somatosensory data shows that information carried by millisecond-scale spike times can be decoded robustly even with little or no independent external knowledge of stimulus time. In cortex, key components of such intrinsic temporal reference frames include dedicated neural populations that signal stimulus onset with reliable and precise latencies, and low-frequency oscillations that can serve as reference for partitioning extended neuronal responses into informative spike patterns
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