323 research outputs found
Partitioned Sampling of Public Opinions Based on Their Social Dynamics
Public opinion polling is usually done by random sampling from the entire
population, treating individual opinions as independent. In the real world,
individuals' opinions are often correlated, e.g., among friends in a social
network. In this paper, we explore the idea of partitioned sampling, which
partitions individuals with high opinion similarities into groups and then
samples every group separately to obtain an accurate estimate of the population
opinion. We rigorously formulate the above idea as an optimization problem. We
then show that the simple partitions which contain only one sample in each
group are always better, and reduce finding the optimal simple partition to a
well-studied Min-r-Partition problem. We adapt an approximation algorithm and a
heuristic algorithm to solve the optimization problem. Moreover, to obtain
opinion similarity efficiently, we adapt a well-known opinion evolution model
to characterize social interactions, and provide an exact computation of
opinion similarities based on the model. We use both synthetic and real-world
datasets to demonstrate that the partitioned sampling method results in
significant improvement in sampling quality and it is robust when some opinion
similarities are inaccurate or even missing
A convergent method for linear half-space kinetic equations
We give a unified proof for the well-posedness of a class of linear
half-space equations with general incoming data and construct a Galerkin method
to numerically resolve this type of equations in a systematic way. Our main
strategy in both analysis and numerics includes three steps: adding damping
terms to the original half-space equation, using an inf-sup argument and
even-odd decomposition to establish the well-posedness of the damped equation,
and then recovering solutions to the original half-space equation. The proposed
numerical methods for the damped equation is shown to be quasi-optimal and the
numerical error of approximations to the original equation is controlled by
that of the damped equation. This efficient solution to the half-space problem
is useful for kinetic-fluid coupling simulations
Alternative Route to Strong Interaction: Narrow Feshbach Resonance
We show that a narrow resonance produces strong interaction effects far
beyond its width on the side of the resonance where the bound state has not
been formed. This is due to a resonance structure of its phase shift, which
shifts the phase of a large number of scattering states by before the
bound state emerges. As a result, the magnitude of the interaction energy when
approaching the resonance on the "upper" and "lower" branch from different side
of the resonance is highly asymmetric, unlike their counter part in wide
resonances. Measurements of these effects are experimentally feasible.Comment: 4 pages, 5 figure
Outbreaks of coinfections: the critical role of cooperativity
Modeling epidemic dynamics plays an important role in studying how diseases
spread, predicting their future course, and designing strategies to control
them. In this letter, we introduce a model of SIR
(susceptible-infected-removed) type which explicitly incorporates the effect of
{\it cooperative coinfection}. More precisely, each individual can get infected
by two different diseases, and an individual already infected with one disease
has an increased probability to get infected by the other. Depending on the
amount of this increase, we observe different threshold scenarios. Apart from
the standard continuous phase transition for single disease outbreaks, we
observe continuous transitions where both diseases must coexist, but also
discontinuous transitions are observed, where a finite fraction of the
population is already affected by both diseases at the threshold. All our
results are obtained in a mean field model using rate equations, but we argue
that they should hold also in more general frameworks.Comment: 5 pages, including 5 figure
Bose Gases Near Unitarity
We study the properties of strongly interacting Bose gases at the density and
temperature regime when the three-body recombination rate is substantially
reduced. In this regime, one can have a Bose gas with all particles in
scattering states (i.e. the "upper branch") with little loss even at unitarity
over the duration of the experiment. We show that because of bosonic
enhancement, pair formation is shifted to the atomic side of the original
resonance (where scattering length ), opposite to the fermionic case. In
a trap, a repulsive Bose gas remains mechanically stable when brought across
resonance to the atomic side until it reaches a critical scattering length
. For , the density consists of a core of
upper branch bosons surrounded by an outer layer of equilibrium phase. The
conditions of low three-body recombination requires that the particle number
in a harmonic trap with frequency , where
is a constant.Comment: 4 pages, 4 figure
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