10,800 research outputs found
Estimating Social Influence Using Latent Space Adjusted Approach in R
Social influence, sometimes referred to as spillover or contagion, have been
extensively studied in various empirical social network research. However,
there are various estimation challenges in identifying social influence
effects, as they are often entangled with other factors, such as homophily in
the selection process, the individual's preference for the same social
settings, etc. Methods currently available either do not solve these problems
or require strong assumptions. Recent works by Xu 2018 and others show that a
latent-space adjusted approach based on the latent space model has potential to
disentangle the influence from other processes, and the simulation evidence
shows the approach performs better than other state-of-the-art approaches in
terms of recovering the true social influence effect when there is an
unobserved trait co-determining influence and selection. In this paper we
illustrate how latent space adjusted approach accounts for bias in the
estimation of the social influence effect, and demonstrate how this approach
can be implemented to estimate various social influence models with an
empirical example in R.Comment: 15 pages, 2 figure
Asymptotics of the entropy production rate for -dimensional Ornstein-Uhlenbeck processes
In the context of non-equilibrium statistical physics, the entropy production
rate is an important concept to describe how far a specific state of a system
is from its equilibrium state. In this paper, we establish a central limit
theorem and a moderate deviation principle for the entropy production rate of
-dimensional Ornstein-Uhlenbeck processes, by the techniques of functional
inequalities such as Poincar\'e inequality and log-Sobolev inequality. As an
application, we obtain a law of iterated logarithm for the entropy production
rate
Entropy and weak solutions in the LBGK model
In this paper, we derive entropy functions whose local equilibria are
suitable to recover the Euler-like equations in the framework of the Lattice
Boltzmann method. Numerical examples are also given, which are consistent with
the above theoretical arguments.Comment: 13pages,2 figure
Divergent bulk photovoltaic effect in Weyl semimetals
Weyl semimetals (WSM) have been discovered in time-reversal symmetric
materials, featuring monopoles of Berry's curvature in momentum space. WSM have
been distinguished between Type-I and II where the velocity tilting of the cone
in the later ensures a finite area Fermi surface. To date it has not been clear
whether the two types results in any qualitatively new phenomena. Here we focus
on the shift-current response (), a second order
optical effect generating photocurrents. Surprisingly we find that up to an
order unity constant, in Type-II WSM, diverging in the low frequency
limit. This is in stark contrast to the vanishing
behavior () in Type-I WSM. In addition,
in both Type-I and Type-II WSM, a nonzero chemical potential relative to
nodes leads to a large peak of shift-current response with a width and a height , the latter
diverging in the low doping limit. We show that the origin of these divergences
is the singular Berry's connections and the Pauli-blocking mechanism. Similar
results hold for the real part of the second harmonic generation, a closely
related nonlinear optical response.Comment: 10 pages, 4 figures, a new appendix is added, which expands the
discussion of second-harmonic generatio
Kinetic Energy-Based Temperature Computation in Non-Equilibrium Molecular Dynamics Simulation
The average kinetic energy is widely used to characterize temperature in
molecular dynamics (MD) simulation. In this letter, the applicability of three
types of average kinetic energy as measures of temperature is investigated,
i.e., the total kinetic energy, kinetic energy without the centroid translation
part, and thermal disturbance kinetic energy. Our MD simulations indicate that
definitions of temperature based on the kinetic energy including rigid
translational or rotational motion may yield unrealistic results. In contrast,
the thermal disturbance kinetic energy has wider applicability to temperature
computation in non-equilibrium molecular dynamics simulation. If small samples
need to be used for local temperature, then a calibration approach is proposed
to eliminate the sample-size dependence of the average disturbance kinetic
energy.Comment: 4 figure
Large deviation principle of occupation measures for Non-linear monotone SPDEs
Using the hyper-exponential recurrence criterion, a large deviation principle
for the occupation measure is derived for a class of non-linear monotone
stochastic partial differential equations. The main results are applied to many
concrete SPDEs such as stochastic -Laplace equation, stochastic porous
medium equation, stochastic fast-diffusion equation, and even stochastic real
Ginzburg-Landau equation driven by -stable noises.Comment: This paper generalizes the idea in our NOT published paper
arXiv:1510.03522. There is a substantial overlap with arXiv:1510.0352
Irreducibility of stochastic real Ginzburg-Landau equation driven by -stable noises and applications
We establish the irreducibility of stochastic real Ginzburg-Landau equation
with -stable noises by a maximal inequality and solving a control
problem. As applications, we prove that the system converges to its equilibrium
measure with exponential rate under a topology stronger than total variation
and obeys the moderate deviation principle by constructing some Lyapunov test
functions.Comment: Bernoulli (accepted). arXiv admin note: text overlap with
arXiv:1410.724
Large deviation principle of occupation measure for stochastic real Ginzburg-Landau equation driven by -stable noises
We establish a large deviation principle for the occupation measure of the
stochastic real Ginzburg-Landau equation driven by -stable noises. The
proof is based on a hyper-exponential recurrence criterion. Our result
indicates a phenomenon that strong dissipation beats heavy tailed noises to
produce a large deviation, it seems to us that this phenomenon has not been
reported in the known literatures.Comment: This paper fills the gap in the paper arXiv:1410.7247 which has been
withdrawn. We complete the proof in arXiv:1410.7247. arXiv admin note: text
overlap with arXiv:1510.0190
The phase structure of black D1/D5 (F/NS5) system in canonical ensemble
In this paper, we explore means which can be used to change qualitatively the
phase structure of charged black systems. For this, we consider a system of
black D1/D5 (or its S-dual F/NS5). We find that the delocalized charged black
D-strings (F-strings) alone share the same phase structure as the charged black
D5 branes (NS5-branes), having no van der Waals-Maxwell liquid-gas type.
However, when the two are combined to form D1/D5 (F/NS5), the resulting phase
diagram has been changed dramatically to a richer one, containing now the above
liquid-gas type. The effect of adding the charged D-strings (F-strings) on the
phase structure can also be effectively described as a slight increase of the
transverse dimensions to the original D5 (NS5). This may be viewed as a
connection between a brane charge and a fraction of spatial dimension at least
in a thermodynamical sense.Comment: 31 pages, 3 Figures, 2 Tables, minor corrections, version published
in JHE
Dyonic Lieb-Shultz-Mattis Theorem and Symmetry Protected Topological Phases in Decorated Dimer Models
We consider 2+1D lattice models of interacting bosons or spins, with both
magnetic flux and fractional spin in the unit cell. We propose and prove a
modified Lieb-Shultz Mattis (LSM) theorem in this setting, which applies even
when the spin in the enlarged magnetic unit cell is integral. There are two
nontrivial outcomes for gapped ground states that preserve all symmetries. In
the first case, one necessarily obtains a symmetry protected topological (SPT)
phase with protected edge states. This allows us to readily construct models of
SPT states by decorating dimer models of Mott insulators to yield SPT phases,
which should be useful in their physical realization. In the second case,
exotic bulk excitations, i.e. topological order, is necessarily present. While
both scenarios require fractional spin in the lattice unit cell, the second
requires that the symmetries protecting the fractional spin is related to that
involved in the magnetic translations. Our discussion encompasses the general
notion of fractional spin (projective symmetry representations) and magnetic
flux (magnetic translations tied to a symmetry generator). The resulting SPTs
display a dyonic character in that they associate charge with symmetry flux,
allowing the flux in the unit cell to screen the projective representation on
the sites. We provide an explicit formula that encapsulates this physics, which
identifies a specific set of allowed SPT phases.Comment: 25 pages, 16 figure
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