48,475 research outputs found
Dynamics underlying Box-office: Movie Competition on Recommender Systems
We introduce a simple model to study movie competition in the recommender
systems. Movies of heterogeneous quality compete against each other through
viewers' reviews and generate interesting dynamics of box-office. By assuming
mean-field interactions between the competing movies, we show that run-away
effect of popularity spreading is triggered by defeating the average review
score, leading to hits in box-office. The average review score thus
characterizes the critical movie quality necessary for transition from
box-office bombs to blockbusters. The major factors affecting the critical
review score are examined. By iterating the mean-field dynamical equations, we
obtain qualitative agreements with simulations and real systems in the
dynamical forms of box-office, revealing the significant role of competition in
understanding box-office dynamics.Comment: 8 pages, 6 figure
Quantum Communication Through a Spin-Ring with Twisted Boundary Conditions
We investigate quantum communication between the sites of a spin-ring with
twisted boundary conditions. Such boundary conditions can be achieved by a flux
through the ring. We find that a non-zero twist can improve communication
through finite odd numbered rings and enable high fidelity multi-party quantum
communication through spin rings (working near perfectly for rings of 5 and 7
spins). We show that in certain cases, the twist results in the complete
blockage of quantum information flow to a certain site of the ring. This effect
can be exploited to interface and entangle a flux qubit and a spin qubit
without embedding the latter in a magnetic field.Comment: four pages two figure
Analysis of hadronic invariant mass spectrum in inclusive charmless semileptonic B decays
We make an analysis of the hadronic invariant mass spectrum in inclusive
charmless semileptonic B meson decays in a QCD-based approach. The decay width
is studied as a function of the invariant mass cut. We examine their
sensitivities to the parameters of the theory. The theoretical uncertainties in
the determination of from the hadronic invariant mass spectrum are
investigated. A strategy for improving the theoretical accuracy in the value of
is described.Comment: 13 pages, 5 Postscript figure
Thermodynamics of lattice QCD with 2 sextet quarks on N_t=8 lattices
We continue our lattice simulations of QCD with 2 flavours of colour-sextet
quarks as a model for conformal or walking technicolor. A 2-loop perturbative
calculation of the -function which describes the evolution of this
theory's running coupling constant predicts that it has a second zero at a
finite coupling. This non-trivial zero would be an infrared stable fixed point,
in which case the theory with massless quarks would be a conformal field
theory. However, if the interaction between quarks and antiquarks becomes
strong enough that a chiral condensate forms before this IR fixed point is
reached, the theory is QCD-like with spontaneously broken chiral symmetry and
confinement. However, the presence of the nearby IR fixed point means that
there is a range of couplings for which the running coupling evolves very
slowly, i.e. it 'walks'. We are simulating the lattice version of this theory
with staggered quarks at finite temperature studying the changes in couplings
at the deconfinement and chiral-symmetry restoring transitions as the temporal
extent () of the lattice, measured in lattice units, is increased. Our
earlier results on lattices with show both transitions move to weaker
couplings as increases consistent with walking behaviour. In this paper
we extend these calculations to . Although both transition again move to
weaker couplings the change in the coupling at the chiral transition from
to is appreciably smaller than that from to .
This indicates that at we are seeing strong coupling effects and that
we will need results from to determine if the chiral-transition
coupling approaches zero as , as needed for the theory
to walk.Comment: 21 pages Latex(Revtex4) source with 4 postscript figures. v2: added 1
reference. V3: version accepted for publication, section 3 restructured and
interpretation clarified. Section 4 future plans for zero temperature
simulations clarifie
Galerkin FEM for fractional order parabolic equations with initial data in
We investigate semi-discrete numerical schemes based on the standard Galerkin
and lumped mass Galerkin finite element methods for an initial-boundary value
problem for homogeneous fractional diffusion problems with non-smooth initial
data. We assume that , is a convex
polygonal (polyhedral) domain. We theoretically justify optimal order error
estimates in - and -norms for initial data in . We confirm our theoretical findings with a number of numerical tests
that include initial data being a Dirac -function supported on a
-dimensional manifold.Comment: 13 pages, 3 figure
Elastic-Net Regularization: Error estimates and Active Set Methods
This paper investigates theoretical properties and efficient numerical
algorithms for the so-called elastic-net regularization originating from
statistics, which enforces simultaneously l^1 and l^2 regularization. The
stability of the minimizer and its consistency are studied, and convergence
rates for both a priori and a posteriori parameter choice rules are
established. Two iterative numerical algorithms of active set type are
proposed, and their convergence properties are discussed. Numerical results are
presented to illustrate the features of the functional and algorithms
Riccati Solutions of Discrete Painlev\'e Equations with Weyl Group Symmetry of Type
We present a special solutions of the discrete Painlev\'e equations
associated with , and -surface. These
solutions can be expressed by solutions of linear difference equations. Here
the -surface discrete Painlev\'e equation is the most generic
difference equation, as all discrete Painlev\'e equations can be obtained by
its degeneration limit. These special solutions exist when the parameters of
the discrete Painlev\'e equation satisfy a particular constraint. We consider
that these special functions belong to the hypergeometric family although they
seems to go beyond the known discrete and -discrete hypergeometric
functions. We also discuss the degeneration scheme of these solutions.Comment: 22 page
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