186 research outputs found
Techniques of replica symmetry breaking and the storage problem of the McCulloch-Pitts neuron
In this article the framework for Parisi's spontaneous replica symmetry
breaking is reviewed, and subsequently applied to the example of the
statistical mechanical description of the storage properties of a
McCulloch-Pitts neuron. The technical details are reviewed extensively, with
regard to the wide range of systems where the method may be applied. Parisi's
partial differential equation and related differential equations are discussed,
and a Green function technique introduced for the calculation of replica
averages, the key to determining the averages of physical quantities. The
ensuing graph rules involve only tree graphs, as appropriate for a
mean-field-like model. The lowest order Ward-Takahashi identity is recovered
analytically and is shown to lead to the Goldstone modes in continuous replica
symmetry breaking phases. The need for a replica symmetry breaking theory in
the storage problem of the neuron has arisen due to the thermodynamical
instability of formerly given solutions. Variational forms for the neuron's
free energy are derived in terms of the order parameter function x(q), for
different prior distribution of synapses. Analytically in the high temperature
limit and numerically in generic cases various phases are identified, among
them one similar to the Parisi phase in the Sherrington-Kirkpatrick model.
Extensive quantities like the error per pattern change slightly with respect to
the known unstable solutions, but there is a significant difference in the
distribution of non-extensive quantities like the synaptic overlaps and the
pattern storage stability parameter. A simulation result is also reviewed and
compared to the prediction of the theory.Comment: 103 Latex pages (with REVTeX 3.0), including 15 figures (ps, epsi,
eepic), accepted for Physics Report
Permissive Controller Synthesis for Probabilistic Systems
We propose novel controller synthesis techniques for probabilistic systems
modelled using stochastic two-player games: one player acts as a controller,
the second represents its environment, and probability is used to capture
uncertainty arising due to, for example, unreliable sensors or faulty system
components. Our aim is to generate robust controllers that are resilient to
unexpected system changes at runtime, and flexible enough to be adapted if
additional constraints need to be imposed. We develop a permissive controller
synthesis framework, which generates multi-strategies for the controller,
offering a choice of control actions to take at each time step. We formalise
the notion of permissivity using penalties, which are incurred each time a
possible control action is disallowed by a multi-strategy. Permissive
controller synthesis aims to generate a multi-strategy that minimises these
penalties, whilst guaranteeing the satisfaction of a specified system property.
We establish several key results about the optimality of multi-strategies and
the complexity of synthesising them. Then, we develop methods to perform
permissive controller synthesis using mixed integer linear programming and
illustrate their effectiveness on a selection of case studies
Emergence of hyperons in failed supernovae: trigger of the black hole formation
We investigate the emergence of strange baryons in the dynamical collapse of
a non-rotating massive star to a black hole by the neutrino-radiation
hydrodynamical simulations in general relativity. By following the dynamical
formation and collapse of nascent proto-neutron star from the gravitational
collapse of a 40Msun star adopting a new hyperonic EOS table, we show that the
hyperons do not appear at the core bounce but populate quickly at ~0.5-0.7 s
after the bounce to trigger the re-collapse to a black hole. They start to show
up off center owing to high temperatures and later prevail at center when the
central density becomes high enough. The neutrino emission from the accreting
proto-neutron star with the hyperonic EOS stops much earlier than the
corresponding case with a nucleonic EOS while the average energies and
luminosities are quite similar between them. These features of neutrino signal
are a potential probe of the emergence of new degrees of freedom inside the
black hole forming collapse.Comment: 11 pages, 3 figures, accepted for publication in ApJ
Ground State and Quasiparticle Spectrum of a Two Component Bose-Einstein Condensate
We consider a dilute atomic Bose-Einstein condensate with two non-degenerate
internal energy levels. The presence of an external radiation field can result
in new ground states for the condensate which result from the lowering of the
condensate energy due to the interaction energy with the field. In this
approach there are no instabilities in the quasiparticle spectrum as was
previously found by Goldstein and Meystre (Phys. Rev. A \QTR{bf}{55}, 2935
(1997)).Comment: 20 pages, 2 figures RevTex. Submitted to Phys. Rev. A; Revised
versio
Dynamics and Berry phase of two-species Bose-Einstein condensates
In terms of exact solutions of the time-dependent Schrodinger equation for an
effective giant spin modeled from a coupled two-mode Bose-Einstein condensate
(BEC) with adiabatic and cyclic time-varying Raman coupling between two
hyperfine states of the BEC, we obtain analytic time-evolution formulas of the
population imbalance and relative phase between two components with various
initial states, especially the SU(2)coherent state. We find the Berry phase
depending on the number parity of atoms, and particle number dependence of the
collapse revival of population-imbalance oscillation. It is shown that
self-trapping and phase locking can be achieved from initial SU(2) coherent
states with proper parameters.Comment: 18 pages,5 figure
Testing Broken U(1) Symmetry in a Two-Component Atomic Bose-Einstein Condensate
We present a scheme for determining if the quantum state of a small trapped
Bose-Einstein condensate is a state with well defined number of atoms, a Fock
state, or a state with a broken U(1) gauge symmetry, a coherent state. The
proposal is based on the observation of Ramsey fringes. The population
difference observed in a Ramsey fringe experiment will exhibit collapse and
revivals due to the mean-field interactions. The collapse and revival times
depend on the relative strength of the mean-field interactions for the two
components and the initial quantum state of the condensate.Comment: 20 Pages RevTex, 3 Figure
Integrating motion capture in a virtual reality intervention planning platform to study radiation protection measures for the ATLAS inner detector decommissioning
An intervention planning and evaluation platform has been developed to enable dose estimation and personnel training for the ATLAS inner detector decommissioning. The present paper describes the integration of motion capture into the system, including the dose estimation results for the recorded decommissioning steps
Thermodynamic properties of thin films of superfluid 3He-A
The pairing correlations in superfluid He-3 are strongly modified by
quasiparticle scattering off a surface or an interface. We present theoretical
results and predictions for the order parameter, the quasiparticle excitation
spectrum and the free energy for thin films of superfluid He-3. Both specular
and diffuse scattering by a substrate are considered, while the free surface is
assumed to be a perfectly reflecting specular boundary. The results are based
on self-consistent calculations of the order parameter and quasiparticle
excitation spectrum at zero pressure. We obtain new results for the phase
diagram, free energy, entropy and specific heat of thin films of superfluid
He-3.Comment: Replaced with an updated versio
Macroscopic Quantum Fluctuations in the Josephson Dynamics of Two Weakly Linked Bose-Einstein Condensates
We study the quantum corrections to the Gross-Pitaevskii equation for two
weakly linked Bose-Einstein condensates. The goals are: 1) to investigate
dynamical regimes at the borderline between the classical and quantum behaviour
of the bosonic field; 2) to search for new macroscopic quantum coherence
phenomena not observable with other superfluid/superconducting systems. Quantum
fluctuations renormalize the classical Josephson oscillation frequencies. Large
amplitude phase oscillations are modulated, exhibiting collapses and revivals.
We describe a new inter-well oscillation mode, with a vanishing (ensemble
averaged) mean value of the observables, but with oscillating mean square
fluctuations. Increasing the number of condensate atoms, we recover the
classical Gross-Pitaevskii (Josephson) dynamics, without invoking the
symmetry-breaking of the Gauge invariance.Comment: Submitte
Alignment-Free Phylogenetic Reconstruction
14th Annual International Conference, RECOMB 2010, Lisbon, Portugal, April 25-28, 2010. ProceedingsWe introduce the first polynomial-time phylogenetic reconstruction algorithm under a model of sequence evolution allowing insertions and deletions (or indels). Given appropriate assumptions, our algorithm requires sequence lengths growing polynomially in the number of leaf taxa. Our techniques are distance-based and largely bypass the problem of multiple alignment
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