1,211,836 research outputs found
Moduli spaces of hyperbolic 3-manifolds and dynamics on character varieties
The space AH(M) of marked hyperbolic 3-manifold homotopy equivalent to a
compact 3-manifold with boundary M sits inside the PSL_2(C)-character variety
X(M) of \pi_1(M). We study the dynamics of the action of Out(\pi_1(M)) on both
AH(M) and X(M). The nature of the dynamics reflects the topology of M.
The quotient AI(M)=AH(M)/Out(\pi_1(M)) may naturally be thought of as the
moduli space of unmarked hyperbolic 3-manifolds homotopy equivalent to M and
its topology reflects the dynamics of the action
Modeling Concept Combinations in a Quantum-theoretic Framework
We present modeling for conceptual combinations which uses the mathematical
formalism of quantum theory. Our model faithfully describes a large amount of
experimental data collected by different scholars on concept conjunctions and
disjunctions. Furthermore, our approach sheds a new light on long standing
drawbacks connected with vagueness, or fuzziness, of concepts, and puts forward
a completely novel possible solution to the 'combination problem' in concept
theory. Additionally, we introduce an explanation for the occurrence of quantum
structures in the mechanisms and dynamics of concepts and, more generally, in
cognitive and decision processes, according to which human thought is a well
structured superposition of a 'logical thought' and a 'conceptual thought', and
the latter usually prevails over the former, at variance with some widespread
beliefsComment: 5 pages. arXiv admin note: substantial text overlap with
arXiv:1311.605
A Quantum-Conceptual Explanation of Violations of Expected Utility in Economics
The expected utility hypothesis is one of the building blocks of classical
economic theory and founded on Savage's Sure-Thing Principle. It has been put
forward, e.g. by situations such as the Allais and Ellsberg paradoxes, that
real-life situations can violate Savage's Sure-Thing Principle and hence also
expected utility. We analyze how this violation is connected to the presence of
the 'disjunction effect' of decision theory and use our earlier study of this
effect in concept theory to put forward an explanation of the violation of
Savage's Sure-Thing Principle, namely the presence of 'quantum conceptual
thought' next to 'classical logical thought' within a double layer structure of
human thought during the decision process. Quantum conceptual thought can be
modeled mathematically by the quantum mechanical formalism, which we illustrate
by modeling the Hawaii problem situation, a well-known example of the
disjunction effect, and we show how the dynamics in the Hawaii problem
situation is generated by the whole conceptual landscape surrounding the
decision situation.Comment: 9 pages, no figure
An Efficient and Accurate Car-Parrinello-like Approach to Born-Oppenheimer Molecular Dynamics
We present a new method which combines Car-Parrinello and Born-Oppenheimer
molecular dynamics in order to accelerate density functional theory based
ab-initio simulations. Depending on the system a gain in efficiency of one to
two orders of magnitude has been observed, which allows ab-initio molecular
dynamics of much larger time and length scales than previously thought
feasible. It will be demonstrated that the dynamics is correctly reproduced and
that high accuracy can be maintained throughout for systems ranging from
insulators to semiconductors and even to metals in condensed phases. This
development considerably extends the scope of ab-initio simulations.Comment: 4 pages, 3 figures; Accepted by Phys. Rev. Lett. for publicatio
Inhibition causes ceaseless dynamics in networks of excitable nodes
The collective dynamics of a network of excitable nodes changes dramatically
when inhibitory nodes are introduced. We consider inhibitory nodes which may be
activated just like excitatory nodes but, upon activating, decrease the
probability of activation of network neighbors. We show that, although the
direct effect of inhibitory nodes is to decrease activity, the collective
dynamics becomes self-sustaining. We explain this counterintuitive result by
defining and analyzing a "branching function" which may be thought of as an
activity-dependent branching ratio. The shape of the branching function implies
that for a range of global coupling parameters dynamics are self-sustaining.
Within the self-sustaining region of parameter space lies a critical line along
which dynamics take the form of avalanches with universal scaling of size and
duration, embedded in ceaseless timeseries of activity. Our analyses, confirmed
by numerical simulation, suggest that inhibition may play a counterintuitive
role in excitable networks.Comment: 11 pages, 6 figure
Ab-Initio Molecular Dynamics
Computer simulation methods, such as Monte Carlo or Molecular Dynamics, are
very powerful computational techniques that provide detailed and essentially
exact information on classical many-body problems. With the advent of ab-initio
molecular dynamics, where the forces are computed on-the-fly by accurate
electronic structure calculations, the scope of either method has been greatly
extended. This new approach, which unifies Newton's and Schr\"odinger's
equations, allows for complex simulations without relying on any adjustable
parameter. This review is intended to outline the basic principles as well as a
survey of the field. Beginning with the derivation of Born-Oppenheimer
molecular dynamics, the Car-Parrinello method and the recently devised
efficient and accurate Car-Parrinello-like approach to Born-Oppenheimer
molecular dynamics, which unifies best of both schemes are discussed. The
predictive power of this novel second-generation Car-Parrinello approach is
demonstrated by a series of applications ranging from liquid metals, to
semiconductors and water. This development allows for ab-initio molecular
dynamics simulations on much larger length and time scales than previously
thought feasible.Comment: 13 pages, 3 figure
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