4,601 research outputs found
Path integrals and wavepacket evolution for damped mechanical systems
Damped mechanical systems with various forms of damping are quantized using
the path integral formalism. In particular, we obtain the path integral kernel
for the linearly damped harmonic oscillator and a particle in a uniform
gravitational field with linearly or quadratically damped motion. In each case,
we study the evolution of Gaussian wavepackets and discuss the characteristic
features that help us distinguish between different types of damping. For
quadratic damping, we show that the action and equation of motion of such a
system has a connection with the zero dimensional version of a currently
popular scalar field theory. Furthermore we demonstrate that the equation of
motion (for quadratic damping) can be identified as a geodesic equation in a
fictitious two-dimensional space.Comment: 15 pages, 6 figure
Bayesian Networks for Max-linear Models
We study Bayesian networks based on max-linear structural equations as
introduced in Gissibl and Kl\"uppelberg [16] and provide a summary of their
independence properties. In particular we emphasize that distributions for such
networks are generally not faithful to the independence model determined by
their associated directed acyclic graph. In addition, we consider some of the
basic issues of estimation and discuss generalized maximum likelihood
estimation of the coefficients, using the concept of a generalized likelihood
ratio for non-dominated families as introduced by Kiefer and Wolfowitz [21].
Finally we argue that the structure of a minimal network asymptotically can be
identified completely from observational data.Comment: 18 page
Heat Conduction Process on Community Networks as a Recommendation Model
Using heat conduction mechanism on a social network we develop a systematic
method to predict missing values as recommendations. This method can treat very
large matrices that are typical of internet communities. In particular, with an
innovative, exact formulation that accommodates arbitrary boundary condition,
our method is easy to use in real applications. The performance is assessed by
comparing with traditional recommendation methods using real data.Comment: 4 pages, 2 figure
Detecting a conditional extrme value model
In classical extreme value theory probabilities of extreme events are
estimated assuming all the components of a random vector to be in a domain of
attraction of an extreme value distribution. In contrast, the conditional
extreme value model assumes a domain of attraction condition on a
sub-collection of the components of a multivariate random vector. This model
has been studied in
\cite{heffernan:tawn:2004,heffernan:resnick:2007,das:resnick:2008a}.
In this paper we propose three statistics which act as tools to detect this
model in a bivariate set-up. In addition, the proposed statistics also help to
distinguish between two forms of the limit measure that is obtained in the
model.Comment: 21 pages, 4 figure
Learning Users’ Interests in a Market-Based Recommender System
Recommender systems are widely used to cope with the problem of information overload and, consequently, many recommendation methods have been developed. However, no one technique is best for all users in all situations. To combat this, we have previously developed a market-based recommender system that allows multiple agents (each representing a different recommendation method or system) to compete with one another to present their best recommendations to the user. Our marketplace thus coordinates multiple recommender agents and ensures only the best recommendations are presented. To do this effectively, however, each agent needs to learn the users’ interests and adapt its recommending behaviour accordingly. To this end, in this paper, we develop a reinforcement learning and Boltzmann exploration strategy that the recommender agents can use for these tasks. We then demonstrate that this strategy helps the agents to effectively obtain information about the users’ interests which, in turn, speeds up the market convergence and enables the system to rapidly highlight the best recommendations
The cubic period-distance relation for the Kater reversible pendulum
We describe the correct cubic relation between the mass configuration of a
Kater reversible pendulum and its period of oscillation. From an analysis of
its solutions we conclude that there could be as many as three distinct mass
configurations for which the periods of small oscillations about the two pivots
of the pendulum have the same value. We also discuss a real compound Kater
pendulum that realizes this property.Comment: 25 pages 4figure
Incompressible flow in porous media with fractional diffusion
In this paper we study the heat transfer with a general fractional diffusion
term of an incompressible fluid in a porous medium governed by Darcy's law. We
show formation of singularities with infinite energy and for finite energy we
obtain existence and uniqueness results of strong solutions for the
sub-critical and critical cases. We prove global existence of weak solutions
for different cases. Moreover, we obtain the decay of the solution in ,
for any , and the asymptotic behavior is shown. Finally, we prove the
existence of an attractor in a weak sense and, for the sub-critical dissipative
case with , we obtain the existence of the global attractor
for the solutions in the space for any
Depinning of kinks in a Josephson-junction ratchet array
We have measured the depinning of trapped kinks in a ratchet potential using
a fabricated circular array of Josephson junctions. Our ratchet system consists
of a parallel array of junctions with alternating cell inductances and
junctions areas. We have compared this ratchet array with other circular
arrays. We find experimentally and numerically that the depinning current
depends on the direction of the applied current in our ratchet ring. We also
find other properties of the depinning current versus applied field, such as a
long period and a lack of reflection symmetry, which we can explain
analytically.Comment: to be published in PR
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