149,884 research outputs found
Statistical Derivation of Basic Equations of Diffusional Kinetics in Alloys with Application to the Description of Diffusion of Carbon in Austenite
Basic equations of diffusional kinetics in alloys are statistically derived
using the master equation approach. To describe diffusional transformations in
substitution alloys, we derive the "quasi-equilibrium" kinetic equation which
generalizes its earlier versions by taking into account possible "interaction
renormalization" effects. For the interstitial alloys Me-X, we derive the
explicit expression for the diffusivity D of an interstitial atom X which
notably differs from those used in previous phenomenological treatments. This
microscopic expression for D is applied to describe the diffusion of carbon in
austenite basing on some simple models of carbon-carbon interaction. The
results obtained enable us to make certain conclusions about the real form of
these interactions, and about the scale of the "transition state entropy" for
diffusion of carbon in austenite.Comment: 26 pages, 5 postscript figures, LaTe
Collective Field Formulation of the Multispecies Calogero Model and its Duality Symmetries
We study the collective field formulation of a restricted form of the
multispecies Calogero model, in which the three-body interactions are set to
zero. We show that the resulting collective field theory is invariant under
certain duality transformations, which interchange, among other things,
particles and antiparticles, and thus generalize the well-known strong-weak
coupling duality symmetry of the ordinary Calogero model. We identify all these
dualities, which form an Abelian group, and study their consequences. We also
study the ground state and small fluctuations around it in detail, starting
with the two-species model, and then generalizing to an arbitrary number of
species.Comment: latex, 53 pages, no figures;v2-minor changes (a paragraph added
following eq. (61)
SuperSpike: Supervised learning in multi-layer spiking neural networks
A vast majority of computation in the brain is performed by spiking neural
networks. Despite the ubiquity of such spiking, we currently lack an
understanding of how biological spiking neural circuits learn and compute
in-vivo, as well as how we can instantiate such capabilities in artificial
spiking circuits in-silico. Here we revisit the problem of supervised learning
in temporally coding multi-layer spiking neural networks. First, by using a
surrogate gradient approach, we derive SuperSpike, a nonlinear voltage-based
three factor learning rule capable of training multi-layer networks of
deterministic integrate-and-fire neurons to perform nonlinear computations on
spatiotemporal spike patterns. Second, inspired by recent results on feedback
alignment, we compare the performance of our learning rule under different
credit assignment strategies for propagating output errors to hidden units.
Specifically, we test uniform, symmetric and random feedback, finding that
simpler tasks can be solved with any type of feedback, while more complex tasks
require symmetric feedback. In summary, our results open the door to obtaining
a better scientific understanding of learning and computation in spiking neural
networks by advancing our ability to train them to solve nonlinear problems
involving transformations between different spatiotemporal spike-time patterns
Dynamics of Pure Shape, Relativity and the Problem of Time
A new approach to the dynamics of the universe based on work by O Murchadha,
Foster, Anderson and the author is presented. The only kinematics presupposed
is the spatial geometry needed to define configuration spaces in purely
relational terms. A new formulation of the relativity principle based on
Poincare's analysis of the problem of absolute and relative motion (Mach's
principle) is given. The enire dynamics is based on shape and nothing else. It
leads to much stronger predictions than standard Newtonian theory. For the
dynamics of Riemannian 3-geometries on which matter fields also evolve,
implementation of the new relativity principle establishes unexpected links
between special relativity, general relativity and the gauge principle. They
all emerge together as a self-consistent complex from a unified and completely
relational approach to dynamics. A connection between time and scale invariance
is established. In particular, the representation of general relativity as
evolution of the shape of space leads to unique definition of simultaneity.
This opens up the prospect of a solution of the problem of time in quantum
gravity on the basis of a fundamental dynamical principle.Comment: 17 pages. To appear in Decoherence and Entropy in Complex Systems
(Proceedings of the Conference DICE, Piombino 2002, ed. H. -T. Elze, Spring
Lecture Notes in Physics 2003
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