603 research outputs found

### Generating Coherent Patterns of Activity from Chaotic Neural Networks

SummaryNeural circuits display complex activity patterns both spontaneously and when responding to a stimulus or generating a motor output. How are these two forms of activity related? We develop a procedure called FORCE learning for modifying synaptic strengths either external to or within a model neural network to change chaotic spontaneous activity into a wide variety of desired activity patterns. FORCE learning works even though the networks we train are spontaneously chaotic and we leave feedback loops intact and unclamped during learning. Using this approach, we construct networks that produce a wide variety of complex output patterns, input-output transformations that require memory, multiple outputs that can be switched by control inputs, and motor patterns matching human motion capture data. Our results reproduce data on premovement activity in motor and premotor cortex, and suggest that synaptic plasticity may be a more rapid and powerful modulator of network activity than generally appreciated

### A Massive Non-Abelian Vector Model

The introduction of a Lagrange multiplier field to ensure that the classical
equations of motion are satisfied serves to restrict radiative corrections in a
model to being only one loop. The consequences of this for a massive
non-Abelian vector model are considered.Comment: 8 pages, LaTeX format; further comments added; accepted for
publication at the Canadian Journal of Physic

### Homeostasis and Learning through Spike-Timing Dependent Plasticity

Synaptic plasticity is thought to be the neuronal correlate of learning. Moreover, modification of synapses contributes to the activity-dependent homeostatic maintenance of neurons and neural networks. In this chapter, we review theories of synaptic plasticity and show that both homeostatic control of activity and detection of correlations in the presynaptic input can arise from spike-timing dependent plasticity (STDP). Relations to classical rate-based Hebbian learning are discussed

### A Model Behind the Standard Model

In spite of its many successes, the Standard Model makes many empirical
assumptions in the Higgs and fermion sectors for which a deeper theoretical
basis is sought. Starting from the usual gauge symmetry $u(1) \times su(2)
\times su(3)$ plus the 3 assumptions: (A) scalar fields as vielbeins in
internal symmetry space \cite{framevec}, (B) the ``confinement picture'' of
symmetry breaking \cite{tHooft,Banovici}, (C) generations as ``dual'' to colour
\cite{genmixdsm}, we are led to a scheme which offers: (I) a geometrical
significance to scalar fields, (II) a theoretical criterion on what scalar
fields are to be introduced, (III) a partial explanation of why $su(2)$ appears
broken while $su(3)$ confines, (IV) baryon-lepton number (B - L) conservation,
(V) the standard electroweak structure, (VI) a 3-valued generation index for
leptons and quarks, and (VII) a dynamical system with all the essential
features of an earlier phenomenological model \cite{genmixdsm} which gave a
good description of the known mass and mixing patterns of quarks and leptons
including neutrino oscillations. There are other implications the consistency
of which with experiment, however, has not yet been systematically explored. A
possible outcome is a whole new branch of particle spectroscopy from $su(2)$
confinement, potentially as rich in details as that of hadrons from colour
confinement, which will be accessible to experiment at high energy.Comment: 66 pages, added new material on phenomenology, and some new
reference

### The Sachs-Wolfe Effect: Gauge Independence and a General Expression

In this paper we address two points concerning the Sachs-Wolfe effect: (i)
the gauge independence of the observable temperature anisotropy, and (ii) a
gauge-invariant expression of the effect considering the most general situation
of hydrodynamic perturbations. The first result follows because the gauge
transformation of the temperature fluctuation at the observation event only
contributes to the isotropic temperature change which, in practice, is absorbed
into the definition of the background temperature. Thus, we proceed without
fixing the gauge condition, and express the Sachs-Wolfe effect using the
gauge-invariant variables.Comment: 5 pages, closer to published versio

### Vacuum Bubble in an Inhomogeneous Cosmology

We study the propagation of bubbles of new vacuum in a radially inhomogeneous
Lemaitre-Tolman-Bondi background that includes a cosmological constant. This
exemplifies the classical evolution of a tunneling bubble through a metastable
state with curvature inhomogeneities, and will be relevant in the context of
the Landscape. We demand that the matter profile in the LTB background satisfy
the weak energy condition. For sample profiles that satisfy this restriction,
we find that the evolution of the bubble (in terms of the physically relevant
coordinates intrinsic to the shell) is largely unaffected by the prsence of
local inhomogeneities. Our setup should also be a useful toy model for
capturing the effects of ambient inhomogeneities on an inflating region.Comment: 31 pages, 21(!) figures, v2: minor changes, figures re-sized (might
require zoom on some systems), references adde

### Basic Gravitational Currents and Killing-Yano Forms

It has been shown that for each Killing-Yano (KY)-form accepted by an
$n$-dimensional (pseudo)Riemannian manifold of arbitrary signature, two basic
gravitational currents can be defined. Conservation of the currents are
explicitly proved by showing co-exactness of the one and co-closedness of the
other. Some general geometrical facts implied by these conservation laws are
also elucidated. In particular, the conservation of the one-form currents
implies that the scalar curvature of the manifold is a flow invariant for all
of its Killing vector fields. It also directly follows that, while all KY-forms
and their Hodge duals on a constant curvature manifold are the eigenforms of
the Laplace-Beltrami operator, for an Einstein manifold this is certain only
for KY 1-forms, $(n-1)$-forms and their Hodge duals.Comment: 11 page

### CBR Anisotropy from Primordial Gravitational Waves in Two-Component Inflationary Cosmology

We examine stochastic temperature fluctuations of the cosmic background
radiation (CBR) arising via the Sachs-Wolfe effect from gravitational wave
perturbations produced in the early universe. We consider spatially flat,
perturbed FRW models that begin with an inflationary phase, followed by a mixed
phase containing both radiation and dust. The scale factor during the mixed
phase takes the form $a(\eta)=c_1\eta^2+c_2\eta+c_3$, where $c_i$ are
constants. During the mixed phase the universe smoothly transforms from being
radiation to dust dominated. We find analytic expressions for the graviton mode
function during the mixed phase in terms of spheroidal wave functions. This
mode function is used to find an analytic expression for the multipole moments
$\langle a_l^2\rangle$ of the two-point angular correlation function
$C(\gamma)$ for the CBR anisotropy. The analytic expression for the multipole
moments is written in terms of two integrals, which are evaluated numerically.
The results are compared to multipoles calculated for models that are {\it
completely} dust dominated at last-scattering. We find that the multipoles
$\langle a_l^2\rangle$ of the CBR temperature perturbations for $l>10$ are
significantly larger for a universe that contains both radiation and dust at
last-scattering. We compare our results with recent, similar numerical work and
find good agreement. The spheroidal wave functions may have applications to
other problems of cosmological interest.Comment: 28 pgs + 6 postscript figures, RevTe

### Gravitational Waves in a Spatially Closed deSitter Spacetime

Perturbation of gravitational fields may be decomposed into scalar,vector and
tensor components.In this paper we concern with the evolution of tensor mode
perturbations in a spatially closed deSitter background of RW form. It may be
thought as gravitional waves in a classical description. The chosen background
has the advantage of to be maximally extended and symmetric. The spatially flat
models commonly emerge from inflationary scenarios are not completely
extended.We first derive the general weak field equations.Then the form of the
field equations in two special cases, planar and spherical waves are obtained
and their solutions are presented. We conclued with discussing the significance
of the results and their implications.Comment: 16 pages,no figure

### Perturbative Expansion around the Gaussian Effective Action: The Background Field Method

We develop a systematic method of the perturbative expansion around the
Gaussian effective action based on the background field method. We show, by
applying the method to the quantum mechanical anharmonic oscillator problem,
that even the first non-trivial correction terms greatly improve the Gaussian
approximation.Comment: 16 pages, 3 eps figures, uses RevTeX and epsf. Errors in Table 1 are
corrected and new references are adde

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