3,967 research outputs found
On the equivalence between standard and sequentially ordered hidden Markov models
Chopin (2007) introduced a sequentially ordered hidden Markov model, for
which states are ordered according to their order of appearance, and claimed
that such a model is a re-parametrisation of a standard Markov model. This note
gives a formal proof that this equivalence holds in Bayesian terms, as both
formulations generate equivalent posterior distributions, but does not hold in
Frequentist terms, as both formulations generate incompatible likelihood
functions. Perhaps surprisingly, this shows that Bayesian re-parametrisation
and Frequentist re-parametrisation are not identical concepts
Higher-order splitting algorithms for solving the nonlinear Schr\"odinger equation and their instabilities
Since the kinetic and the potential energy term of the real time nonlinear
Schr\"odinger equation can each be solved exactly, the entire equation can be
solved to any order via splitting algorithms. We verified the fourth-order
convergence of some well known algorithms by solving the Gross-Pitaevskii
equation numerically. All such splitting algorithms suffer from a latent
numerical instability even when the total energy is very well conserved. A
detail error analysis reveals that the noise, or elementary excitations of the
nonlinear Schr\"odinger, obeys the Bogoliubov spectrum and the instability is
due to the exponential growth of high wave number noises caused by the
splitting process. For a continuum wave function, this instability is
unavoidable no matter how small the time step. For a discrete wave function,
the instability can be avoided only for \dt k_{max}^2{<\atop\sim}2 \pi, where
.Comment: 10 pages, 8 figures, submitted to Phys. Rev.
Dimension-adaptive bounds on compressive FLD Classification
Efficient dimensionality reduction by random projections (RP) gains popularity, hence the learning guarantees achievable in RP spaces are of great interest. In finite dimensional setting, it has been shown for the compressive Fisher Linear Discriminant (FLD) classifier that forgood generalisation the required target dimension grows only as the log of the number of classes and is not adversely affected by the number of projected data points. However these bounds depend on the dimensionality d of the original data space. In this paper we give further guarantees that remove d from the bounds under certain conditions of regularity on the data density structure. In particular, if the data density does not fill the ambient space then the error of compressive FLD is independent of the ambient dimension and depends only on a notion of âintrinsic dimension'
A note on the moduli-induced gravitino problem
The cosmological moduli problem has been recently reconsidered. Papers [1,2]
show that even heavy moduli (m_\phi > 10^5 GeV) can be a problem for cosmology
if a branching ratio of the modulus into gravitini is large. In this paper, we
discuss the tachyonic decay of moduli into the Standard Model's degrees of
freedom, e.g. Higgs particles, as a resolution to the moduli-induced gravitino
problem. Rough estimates on model dependent parameters set a lower bound on the
allowed moduli at around 10^8 ~ 10^9 GeV.Comment: 6 pages, references added, identical to the published versio
Hooke's law correlation in two-electron systems
We study the properties of the Hooke's law correlation energy (\Ec),
defined as the correlation energy when two electrons interact {\em via} a
harmonic potential in a -dimensional space. More precisely, we investigate
the ground state properties of two model systems: the Moshinsky atom (in
which the electrons move in a quadratic potential) and the spherium model (in
which they move on the surface of a sphere). A comparison with their Coulombic
counterparts is made, which highlights the main differences of the \Ec in
both the weakly and strongly correlated limits. Moreover, we show that the
Schr\"odinger equation of the spherium model is exactly solvable for two values
of the dimension (), and that the exact wave function is
based on Mathieu functions.Comment: 7 pages, 5 figure
Public Authorities as Defendants: Using Bayesian Networks to determine the Likelihood of Success for Negligence claims in the wake of Oakden
Several countries are currently investigating issues of neglect, poor quality care and abuse in the aged care sector. In most cases it is the State who license and monitor aged care providers, which frequently introduces a serious conflict of interest because the State also operate many of the facilities where our most vulnerable peoples are cared for. Where issues are raised with the standard of care being provided, the State are seen by many as a deep-pockets defendant and become the target of high-value lawsuits. This paper draws on cases and circumstances from one jurisdiction based on the English legal tradition, Australia, and proposes a Bayesian solution capable of determining probability for success for citizen plaintiffs who bring negligence claims against a public authority defendant. Use of a Bayesian network trained on case audit data shows that even when the plaintiff case meets all requirements for a successful negligence litigation, success is not often assured. Only in around one-fifth of these cases does the plaintiff succeed against a public authority as defendant
One-loop effective potential in M4 x T2 with and without 't Hooft flux
We review the basic notions of compactification in the presence of a
background flux. In extra-dimentional models with more than five dimensions,
Scherk and Schwarz boundary conditions have to satisfy 't Hooft consistency
conditions. Different vacuum configurations can be obtained, depending whether
trivial or non-trivial 't Hooft flux is considered. The presence of the
"magnetic" background flux provide, in addition, a mechanism for producing
four-dimensional chiral fermions. Particularizing to the six-dimensional case,
we calculate the one-loop effective potential for a U(N) gauge theory on M4 x
T2. We firstly review the well known results of the trivial 't Hooft flux case,
where one-loop contributions produce the usual Hosotani dynamical symmetry
breaking. Finally we applied our result for describing, for the first time, the
one-loop contributions in the non-trivial 't Hooft flux case
Quantum corrections from a path integral over reparametrizations
We study the path integral over reparametrizations that has been proposed as
an ansatz for the Wilson loops in the large- QCD and reproduces the area law
in the classical limit of large loops. We show that a semiclassical expansion
for a rectangular loop captures the L\"uscher term associated with
dimensions and propose a modification of the ansatz which reproduces the
L\"uscher term in other dimensions, which is observed in lattice QCD. We repeat
the calculation for an outstretched ellipse advocating the emergence of an
analog of the L\"uscher term and verify this result by a direct computation of
the determinant of the Laplace operator and the conformal anomaly
Ultracold atoms confined in an optical lattice plus parabolic potential: a closed-form approach
We discuss interacting and non-interacting one dimensional atomic systems
trapped in an optical lattice plus a parabolic potential. We show that, in the
tight-binding approximation, the non-interacting problem is exactly solvable in
terms of Mathieu functions. We use the analytic solutions to study the
collective oscillations of ideal bosonic and fermionic ensembles induced by
small displacements of the parabolic potential. We treat the interacting boson
problem by numerical diagonalization of the Bose-Hubbard Hamiltonian. From
analysis of the dependence upon lattice depth of the low-energy excitation
spectrum of the interacting system, we consider the problems of
"fermionization" of a Bose gas, and the superfluid-Mott insulator transition.
The spectrum of the noninteracting system turns out to provide a useful guide
to understanding the collective oscillations of the interacting system,
throughout a large and experimentally relevant parameter regime.Comment: 19 pages, 15 figures Minor modification were done and new references
were adde
Faraday waves in binary non-miscible Bose-Einstein condensates
We show by extensive numerical simulations and analytical variational
calculations that elongated binary non-miscible Bose-Einstein condensates
subject to periodic modulations of the radial confinement exhibit a Faraday
instability similar to that seen in one-component condensates. Considering the
hyperfine states of Rb condensates, we show that there are two
experimentally relevant stationary state configurations: the one in which the
components form a dark-bright symbiotic pair (the ground state of the system),
and the one in which the components are segregated (first excited state). For
each of these two configurations, we show numerically that far from resonances
the Faraday waves excited in the two components are of similar periods, emerge
simultaneously, and do not impact the dynamics of the bulk of the condensate.
We derive analytically the period of the Faraday waves using a variational
treatment of the coupled Gross-Pitaevskii equations combined with a
Mathieu-type analysis for the selection mechanism of the excited waves.
Finally, we show that for a modulation frequency close to twice that of the
radial trapping, the emergent surface waves fade out in favor of a forceful
collective mode that turns the two condensate components miscible.Comment: 13 pages, 10 figure
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