2,934 research outputs found
A Moving Bump in a Continuous Manifold: A Comprehensive Study of the Tracking Dynamics of Continuous Attractor Neural Networks
Understanding how the dynamics of a neural network is shaped by the network
structure, and consequently how the network structure facilitates the functions
implemented by the neural system, is at the core of using mathematical models
to elucidate brain functions. This study investigates the tracking dynamics of
continuous attractor neural networks (CANNs). Due to the translational
invariance of neuronal recurrent interactions, CANNs can hold a continuous
family of stationary states. They form a continuous manifold in which the
neural system is neutrally stable. We systematically explore how this property
facilitates the tracking performance of a CANN, which is believed to have clear
correspondence with brain functions. By using the wave functions of the quantum
harmonic oscillator as the basis, we demonstrate how the dynamics of a CANN is
decomposed into different motion modes, corresponding to distortions in the
amplitude, position, width or skewness of the network state. We then develop a
perturbative approach that utilizes the dominating movement of the network's
stationary states in the state space. This method allows us to approximate the
network dynamics up to an arbitrary accuracy depending on the order of
perturbation used. We quantify the distortions of a Gaussian bump during
tracking, and study their effects on the tracking performance. Results are
obtained on the maximum speed for a moving stimulus to be trackable and the
reaction time for the network to catch up with an abrupt change in the
stimulus.Comment: 43 pages, 10 figure
Minimizing Unsatisfaction in Colourful Neighbourhoods
Colouring sparse graphs under various restrictions is a theoretical problem
of significant practical relevance. Here we consider the problem of maximizing
the number of different colours available at the nodes and their
neighbourhoods, given a predetermined number of colours. In the analytical
framework of a tree approximation, carried out at both zero and finite
temperatures, solutions obtained by population dynamics give rise to estimates
of the threshold connectivity for the incomplete to complete transition, which
are consistent with those of existing algorithms. The nature of the transition
as well as the validity of the tree approximation are investigated.Comment: 28 pages, 12 figures, substantially revised with additional
explanatio
Dissociation cross sections of ground-state and excited charmonia with light mesons in the quark model
We present numerical results for the dissociation cross sections of
ground-state, orbitally- and radially-excited charmonia in collisions with
light mesons. Our results are derived using the nonrelativistic quark model, so
all parameters are determined by fits to the experimental meson spectrum.
Examples of dissociation into both exclusive and inclusive final states are
considered. The dissociation cross sections of several C=(+) charmonia may be
of considerable importance for the study of heavy ion collisions, since these
states are expected to be produced more copiously than the J/psi. The relative
importance of the productions of ground-state and orbitally-excited charmed
mesons in a pion-charmonium collision is demonstrated through the -dependent charmonium dissociation cross sections.Comment: 9 pages, 8 figure
Dynamical and Stationary Properties of On-line Learning from Finite Training Sets
The dynamical and stationary properties of on-line learning from finite
training sets are analysed using the cavity method. For large input dimensions,
we derive equations for the macroscopic parameters, namely, the student-teacher
correlation, the student-student autocorrelation and the learning force
uctuation. This enables us to provide analytical solutions to Adaline learning
as a benchmark. Theoretical predictions of training errors in transient and
stationary states are obtained by a Monte Carlo sampling procedure.
Generalization and training errors are found to agree with simulations. The
physical origin of the critical learning rate is presented. Comparison with
batch learning is discussed throughout the paper.Comment: 30 pages, 4 figure
Supersymmetry Breaking in the Early Universe
Supersymmetry breaking in the early universe induces scalar soft potentials
with curvature of order the Hubble constant. This has a dramatic effect on the
coherent production of scalar fields along flat directions. For the moduli
problem it generically gives a concrete realization of the problem by
determining the field value subsequent to inflation. However it might suggest a
solution if the minimum of the induced potential coincides with the true
minimum. The induced Hubble scale mass also has important implications for the
Affleck-Dine mechanism of baryogenesis. This mechanism requires large squark or
slepton expectation values to develop along flat directions in the early
universe. This is generally not the case if the induced mass squared is
positive, but does occur if it is negative. The resulting baryon to entropy
ratio depends mainly on the dimension of the nonrenormalizable operator in the
superpotential which stabilizes the flat direction, and the reheat temperature
after inflation. Unlike the original scenario, it is possible to obtain an
acceptable baryon asymmetry without subsequent entropy releases.Comment: 11 pages, requires phyzz
Next nearest neighbour Ising models on random graphs
This paper develops results for the next nearest neighbour Ising model on
random graphs. Besides being an essential ingredient in classic models for
frustrated systems, second neighbour interactions interactions arise naturally
in several applications such as the colour diversity problem and graphical
games. We demonstrate ensembles of random graphs, including regular
connectivity graphs, that have a periodic variation of free energy, with either
the ratio of nearest to next nearest couplings, or the mean number of nearest
neighbours. When the coupling ratio is integer paramagnetic phases can be found
at zero temperature. This is shown to be related to the locked or unlocked
nature of the interactions. For anti-ferromagnetic couplings, spin glass phases
are demonstrated at low temperature. The interaction structure is formulated as
a factor graph, the solution on a tree is developed. The replica symmetric and
energetic one-step replica symmetry breaking solution is developed using the
cavity method. We calculate within these frameworks the phase diagram and
demonstrate the existence of dynamical transitions at zero temperature for
cases of anti-ferromagnetic coupling on regular and inhomogeneous random
graphs.Comment: 55 pages, 15 figures, version 2 with minor revisions, to be published
J. Stat. Mec
Statistical mechanics of image restoration and error-correcting codes
We develop a statistical-mechanical formulation for image restoration and
error-correcting codes. These problems are shown to be equivalent to the Ising
spin glass with ferromagnetic bias under random external fields. We prove that
the quality of restoration/decoding is maximized at a specific set of parameter
values determined by the source and channel properties. For image restoration
in mean-field system a line of optimal performance is shown to exist in the
parameter space. These results are illustrated by solving exactly the
infinite-range model. The solutions enable us to determine how precisely one
should estimate unknown parameters. Monte Carlo simulations are carried out to
see how far the conclusions from the infinite-range model are applicable to the
more realistic two-dimensional case in image restoration.Comment: 20 pages, 9 figures, ReVTe
Unique and shared signaling pathways cooperate to regulate the differentiation of human CD4(+) T cells into distinct effector subsets
Improving Signal and Photobleaching Characteristics of Temporal Focusing Microscopy with the Increase in Pulse Repetition Rate
Wide-field temporal focused (WF-TeFo) two-photon microscopy allows for the simultaneous imaging of a large planar area, with a potential order of magnitude enhancement in the speed of volumetric imaging. To date, low repetition rate laser sources with over half a millijoule per pulse have been required in order to provide the high peak power densities for effective two-photon excitation over the large area. However, this configuration suffers from reduced signal intensity due to the low repetition rate, saturation effects due to increased excitation fluences, as well as faster photobleaching of the fluorescence probe. In contrast, with the recent advent of high repetition rate, high pulse energy laser systems could potentially provide the advantages of high repetition rate systems that are seen in traditional two-photon microscopes, while minimizing the negatives of high fluences in WF-TeFo setups to date. Here, we use a 100 microjoule/high repetition rate (50-100 kHz) laser system to investigate the performance of a WF-TeFo two-photon microscope. While using micro-beads as a sample, we demonstrate a proportionate increase in signal intensity with repetition rate, at no added cost in photobleaching. By decreasing pulse intensity, via a corresponding increase in repetition rate to maintain fluorescence signal intensity, we find that the photobleaching rate is reduced by ~98.4%. We then image live C. elegans at a high repetition rate for 25 min. as a proof-of-principle. Lastly, we identify the steady state temperature increase as the limiting process in further increasing the repetition rate, and we estimate that repetition rate in the range between 0.5 and 5 MHz is ideal for live imaging with a simple theoretical model. With new generation low-cost fiber laser systems offering high pulse energy/high repetition rates in what is essentially a turn-key solution, we anticipate increased adoption of this microscopy technique by the neuroscience community
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