69,468 research outputs found
Evolving nature of human contact networks with its impact on epidemic processes
Human contact networks are constituted by a multitude of individuals and
pairwise contacts among them. However, the dynamic nature, which generates the
evolution of human contact networks, of contact patterns is not known yet.
Here, we analyse three empirical datasets and identify two crucial mechanisms
of the evolution of temporal human contact networks, i.e. the activity state
transition laws for an individual to be socially active, and the contact
establishment mechanism that active individuals adopt. We consider both of the
two mechanisms to propose a temporal network model, named the memory driven
(MD) model, of human contact networks. Then we study the susceptible-infected
(SI) spreading processes on empirical human contact networks and four
corresponding temporal network models, and compare the full prevalence time of
SI processes with various infection rates on the networks. The full prevalence
time of SI processes in the MD model is the same as that in real-world human
contact networks. Moreover, we find that the individual activity state
transition promotes the spreading process, while, the contact establishment of
active individuals suppress the prevalence. Apart from this, we observe that
even a small percentage of individuals to explore new social ties is able to
induce an explosive spreading on networks. The proposed temporal network
framework could help the further study of dynamic processes in temporal human
contact networks, and offer new insights to predict and control the diffusion
processes on networks
Sync in Complex Dynamical Networks: Stability, Evolution, Control, and Application
In the past few years, the discoveries of small-world and scale-free
properties of many natural and artificial complex networks have stimulated
significant advances in better understanding the relationship between the
topology and the collective dynamics of complex networks. This paper reports
recent progresses in the literature of synchronization of complex dynamical
networks including stability criteria, network synchronizability and uniform
synchronous criticality in different topologies, and the connection between
control and synchronization of complex networks as well. The economic-cycle
synchronous phenomenon in the World Trade Web, a scale-free type of social
economic networks, is used to illustrate an application of the network
synchronization mechanism.Comment: 23 pages, 13 figure
-entropy, super Perelman Ricci flows and -Ricci solitons
In this paper, we prove the characterization of the -super
Perelman Ricci flows by various functional inequalities and gradient estimate
for the heat semigroup generated by the Witten Laplacian on manifolds equipped
with time dependent metrics and potentials. As a byproduct, we derive the
Hamilton type dimension free Harnack inequality on manifolds with -super Perelman Ricci flows. Based on a new second order differential
inequality on the Boltzmann-Shannon entropy for the heat equation of the Witten
Laplacian, we introduce a new -entropy quantity and prove its monotonicity
for the heat equation of the Witten Laplacian on complete Riemannian manifolds
with the -condition and on compact manifolds with -super Perelman Ricci flows. Our results characterize the -Ricci solitons and the -Perelman Ricci flows. We also
prove a second order differential entropy inequality on -super Ricci
flows, which can be used to characterize the -Ricci solitons and the
-Ricci flows. Finally, we give a probabilistic interpretation of the
-entropy for the heat equation of the Witten Laplacian on manifolds with the
-condition.Comment: We remove Section 5 from the previous version and add two new results
in Section 5. arXiv admin note: text overlap with arXiv:1412.703
-entropy formulas and Langevin deformation of flows on Wasserstein space over Riemannian manifolds
We introduce Perelman's -entropy and prove the -entropy formula along
geodesic flow on the Wasserstein space over compact
Riemannian manifolds equipped with Otto's infinite dimensional Riemannian
metric. As a corollary, we recapture Lott and Villani's result on the
displacement convexity of on over
Riemannian manifolds with Bakry-Emery's curvature-dimension -condition. To better understand the similarity between the -entropy
formula for the geodesic flow on the Wasserstein space and the -entropy
formula for the heat equation of the Witten Laplacian on the underlying
manifolds, we introduce the Langevin deformation of flows on the Wasserstein
space, which interpolates the geodesic flow and the gradient flow of the
Boltzmann-Shannon entropy on the Wasserstein space over Riemannian manifolds,
and can be regarded as the potential flow of the compressible Euler equation
with damping on manifolds. We prove the local and global existence, uniqueness
and regularity of the potential flow on compact Riemannian manifolds, and prove
an analogue of the Perelman type -entropy formula along the Langevin
deformation of flows on the Wasserstein space on compact Riemannian manifolds.
We also prove a rigidity theorem for the -entropy for the geodesic flow and
provide the rigidity models for the -entropy for the Langevin deformation of
flows on the Wasserstein space over complete Riemannian manifolds with the
-condition. Finally, we prove the -entropy inequalities along the
geodesic flow, gradient flow and the Langevin deformation of flows on the
Wasserstein space over compact Riemannian manifolds with Erbar-Kuwada-Sturm's
entropic curvature-dimension -condition
Hamilton differential Harnack inequality and -entropy for Witten Laplacian on Riemannian manifolds
In this paper, we prove the Hamilton differential Harnack inequality for
positive solutions to the heat equation of the Witten Laplacian on complete
Riemannian manifolds with the -condition, where
and are two constants. Moreover, we introduce the -entropy and
prove the -entropy formula for the fundamental solution of the Witten
Laplacian on complete Riemannian manifolds with the -condition and
on compact manifolds equipped with -super Ricci flows.Comment: To appear in Journal of Functional Analysis. This paper is an
improved version of a part of our previous preprint [14] (arxiv:1412.7034,
version1 (22 December 2014) and version 2 (7 February 2016)
Dynamical transitions in a modulated Landau-Zener model with finite driving fields
We investigate a special time-dependent quantum model which assumes the
Landau-Zener driving form but with an overall modulation of the intensity of
the pulsing field. We demonstrate that the dynamics of the system, including
the two-level case as well as its multi-level extension, is exactly solvable
analytically. Differing from the original Landau-Zener model, the nonadiabatic
effect of the evolution in the present driving process does not destroy the
desired population transfer. As the sweep protocol employs only the finite
driving fields which tend to zero asymptotically, the cutoff error due to the
truncation of the driving pulse to the finite time interval turns out to be
negligibly small. Furthermore, we investigate the noise effect on the driving
protocol due to the dissipation of the surrounding environment. The losses of
the fidelity in the protocol caused by both the phase damping process and the
random spin flip noise are estimated by solving numerically the corresponding
master equations within the Markovian regime.Comment: 6 pages, 4 figure
Harnack inequalities and -entropy formula for Witten Laplacian on Riemannian manifolds with -super Perelman Ricci flow
In this paper, we prove logarithmic Sobolev inequalities and derive the
Hamilton Harnack inequality for the heat semigroup of the Witten Laplacian on
complete Riemannian manifolds equipped with -super Perelman Ricci flow. We
establish the -entropy formula for the heat equation of the Witten Laplacian
and prove a rigidity theorem on complete Riemannian manifolds satisfying the
condition, and extend the -entropy formula to time dependent
Witten Laplacian on compact Riemannian manifolds with -super Perelman
Ricci flow, where and are two constants.
Finally, we prove the Li-Yau and the Li-Yau-Hamilton Harnack inequalities for
positive solutions to the heat equation associated to the
time dependent Witten Laplacian on compact or complete manifolds equipped with
variants of the -super Ricci flow.Comment: Theorem 1.1 in the first version has been improved. In the case of
time dependent metrics and potentials, an error in the proof of Theorem 1.5
(i.e., Theorem 2.2), Theorem 2.3 and Theorem 2.4 in the first version has
been corrected. See Section 4 and Section
The Impact of Information Dissemination on Vaccination in Multiplex Networks
The impact of information dissemination on epidemic control is essentially
subject to individual behaviors. Unlike information-driven behaviors,
vaccination is determined by many cost-related factors, whose correlation with
the information dissemination should be better understood. To this end, we
propose an evolutionary vaccination game model in multiplex networks by
integrating an information-epidemic spreading process into the vaccination
dynamics, and explore how information dissemination influences vaccination. The
spreading process is described by a two-layer coupled
susceptible-alert-infected-susceptible (SAIS) model, where the strength
coefficient between two layers is defined to characterize the tendency and
intensity of information dissemination. We find that information dissemination
can increase the epidemic threshold, however, more information transmission
cannot promote vaccination. Specifically, increasing information dissemination
even leads to a decline of the vaccination equilibrium and raises the final
infection density. Moreover, we study the impact of strength coefficient and
individual sensitivity on social cost, and unveil the role of information
dissemination in controlling the epidemic with numerical simulations
-entropy formulas on super Ricci flows and Langevin deformation on Wasserstein space over Riemannian manifolds
In this survey paper, we give an overview of our recent works on the study of
the -entropy for the heat equation associated with the Witten Laplacian on
super-Ricci flows and the Langevin deformation on Wasserstein space over
Riemannian manifolds. Inspired by Perelman's seminal work on the entropy
formula for the Ricci flow, we prove the -entropy formula for the heat
equation associated with the Witten Laplacian on -dimensional complete
Riemannian manifolds with the -condition, and the -entropy formula
for the heat equation associated with the time dependent Witten Laplacian on
-dimensional compact manifolds equipped with a -super Ricci flow,
where and . Furthermore, we prove an
analogue of the -entropy formula for the geodesic flow on the Wasserstein
space over Riemannian manifolds. Our result recaptures an important result due
to Lott and Villani on the displacement convexity of the Boltzmann-Shannon
entropy on Riemannian manifolds with non-negative Ricci curvature. To better
understand the similarity between above two -entropy formulas, we introduce
the Langevin deformation of geometric flows on the cotangent bundle over the
Wasserstein space and prove an extension of the -entropy formula for the
Langevin deformation. Finally, we make a discussion on the -entropy for the
Ricci flow from the point of view of statistical mechanics and probability
theory.Comment: Survey paper. Submitted to Science China Mathematics. arXiv admin
note: text overlap with arXiv:1604.02596, arXiv:1706.0704
Revisiting numerical real-space renormalization group for quantum lattice systems
Although substantial progress has been achieved in solving quantum impurity
problems, the numerical renormalization group (NRG) method generally performs
poorly when applied to quantum lattice systems in a real-space blocking form.
The approach was thought to be unpromising for most lattice systems owing to
its flaw in dealing with the boundaries of the block. Here the discovery of
intrinsic prescriptions to cure interblock interactions is reported which
clears up the boundary obstacle and is expected to reopen the application of
NRG to quantum lattice systems. While the resulting RG transformation turns out
to be strict in the thermodynamic limit, benchmark tests of the algorithm on a
one-dimensional Heisenberg antiferromagnet and a two-dimensional tight-binding
model demonstrate its numerical efficiency in resolving low-energy spectra for
the lattice systems.Comment: 5 pages, 1 figure, 2 tables, minor revision
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