27,223 research outputs found
Small-world MCMC and convergence to multi-modal distributions: From slow mixing to fast mixing
We compare convergence rates of Metropolis--Hastings chains to multi-modal
target distributions when the proposal distributions can be of ``local'' and
``small world'' type. In particular, we show that by adding occasional
long-range jumps to a given local proposal distribution, one can turn a chain
that is ``slowly mixing'' (in the complexity of the problem) into a chain that
is ``rapidly mixing.'' To do this, we obtain spectral gap estimates via a new
state decomposition theorem and apply an isoperimetric inequality for
log-concave probability measures. We discuss potential applicability of our
result to Metropolis-coupled Markov chain Monte Carlo schemes.Comment: Published at http://dx.doi.org/10.1214/105051606000000772 in the
Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute
of Mathematical Statistics (http://www.imstat.org
Two problems related to prescribed curvature measures
Existence of convex body with prescribed generalized curvature measures is
discussed, this result is obtained by making use of Guan-Li-Li's innovative
techniques. In surprise, that methods has also brought us to promote
Ivochkina's estimates for prescribed curvature equation in \cite{I1, I}.Comment: 12 pages, Corrected typo
Ferromagnetic behaviour in the strongly interacting two-component Bose gas
We investigate the low temperature behaviour of the integrable 1D
two-component spinor Bose gas using the thermodynamic Bethe ansatz. We find
that for strong coupling the characteristics of the thermodynamics at low
temperatures are quantitatively affected by the spin ferromagnetic states,
which are described by an effective ferromagnetic Heisenberg chain. The free
energy, specific heat, susceptibility and local pair correlation function are
calculated for various physical regimes in terms of temperature and interaction
strength. These thermodynamic properties reveal spin effects which are
significantly different than those of the spinless Bose gas. The zero-field
susceptibility for finite strong repulsion exceeds that of a free spin
paramagnet. The critical exponents of the specific heat and
the susceptibility are indicative of the ferromagnetic
signature of the two-component spinor Bose gas. Our analytic results are
consistent with general arguments by Eisenberg and Lieb for polarized spinor
bosons.Comment: 15 pages, 6 figures, revised version, references added, minor
correction
Fermionization and fractional statistics in the strongly interacting one-dimensional Bose gas
We discuss recent results on the relation between the strongly interacting
one-dimensional Bose gas and a gas of ideal particles obeying nonmutual
generalized exclusion statistics (GES). The thermodynamic properties considered
include the statistical profiles, the specific heat and local pair
correlations. In the strong coupling limit , the
Tonks-Girardeau gas, the equivalence is with Fermi statistics. The deviation
from Fermi statistics during boson fermionization for finite but large
interaction strength is described by the relation , where is a measure of the GES. This gives a quantitative
description of the fermionization process. In this sense the recent
experimental measurement of local pair correlations in a 1D Bose gas of
Rb atoms also provides a measure of the deviation of the GES parameter
away from the pure Fermi statistics value . Other
thermodynamic properties, such as the distribution profiles and the specific
heat, are also sensitive to the statistics. They also thus provide a way of
exploring fractional statistics in the strongly interacting 1D Bose gas.Comment: 7 pages, 4 figure
Phase Transitions and Pairing Signature in Strongly Attractive Fermi Atomic Gases
We investigate pairing and quantum phase transitions in the one-dimensional
two-component Fermi atomic gas in an external field. The phase diagram,
critical fields, magnetization and local pairing correlation are obtained
analytically via the exact thermodynamic Bethe ansatz solution. At zero
temperature, bound pairs of fermions with opposite spin states form a singlet
ground state when the external field . A completely ferromagnetic
phase without pairing occurs when the external field . In the
region we observe a mixed phase of matter in which paired
and unpaired atoms coexist. The phase diagram is reminiscent of that of type II
superconductors. For temperatures below the degenerate temperature and in the
absence of an external field, the bound pairs of fermions form hard-core bosons
obeying generalized exclusion statistics.Comment: 9 pages, 5 figures, expanded version with additional text, references
and figure
Cumulative Prospect Theory Based Dynamic Pricing for Shared Mobility on Demand Services
Cumulative Prospect Theory (CPT) is a modeling tool widely used in behavioral
economics and cognitive psychology that captures subjective decision making of
individuals under risk or uncertainty. In this paper, we propose a dynamic
pricing strategy for Shared Mobility on Demand Services (SMoDSs) using a
passenger behavioral model based on CPT. This dynamic pricing strategy together
with dynamic routing via a constrained optimization algorithm that we have
developed earlier, provide a complete solution customized for SMoDS of
multi-passenger transportation. The basic principles of CPT and the derivation
of the passenger behavioral model in the SMoDS context are described in detail.
The implications of CPT on dynamic pricing of the SMoDS are delineated using
computational experiments involving passenger preferences. These implications
include interpretation of the classic fourfold pattern of risk attitudes,
strong risk aversion over mixed prospects, and behavioral preferences of self
reference. Overall, it is argued that the use of the CPT framework corresponds
to a crucial building block in designing socio-technical systems by allowing
quantification of subjective decision making under risk or uncertainty that is
perceived to be otherwise qualitative.Comment: 17 pages, 6 figures, and has been accepted for publication at the
58th Annual Conference on Decision and Control, 201
Collective dispersion relations for the 1D interacting two-component Bose and Fermi gases
We investigate the elementary excitations of charge and spin degrees for the
1D interacting two-component Bose and Fermi gases by means of the discrete
Bethe ansatz equations. Analytic results in the limiting cases of strong and
weak interactions are derived, where the Bosons are treated in the repulsive
and the fermions in the strongly attractive regime. We confirm and complement
results obtained previously from the Bethe ansatz equations in the
thermodynamic limit.Comment: 12 pages, 1 figur
- …