46,613 research outputs found
Quadratically-Regularized Optimal Transport on Graphs
Optimal transportation provides a means of lifting distances between points
on a geometric domain to distances between signals over the domain, expressed
as probability distributions. On a graph, transportation problems can be used
to express challenging tasks involving matching supply to demand with minimal
shipment expense; in discrete language, these become minimum-cost network flow
problems. Regularization typically is needed to ensure uniqueness for the
linear ground distance case and to improve optimization convergence;
state-of-the-art techniques employ entropic regularization on the
transportation matrix. In this paper, we explore a quadratic alternative to
entropic regularization for transport over a graph. We theoretically analyze
the behavior of quadratically-regularized graph transport, characterizing how
regularization affects the structure of flows in the regime of small but
nonzero regularization. We further exploit elegant second-order structure in
the dual of this problem to derive an easily-implemented Newton-type
optimization algorithm.Comment: 27 page
A survey on Human Mobility and its applications
Human Mobility has attracted attentions from different fields of studies such
as epidemic modeling, traffic engineering, traffic prediction and urban
planning. In this survey we review major characteristics of human mobility
studies including from trajectory-based studies to studies using graph and
network theory. In trajectory-based studies statistical measures such as jump
length distribution and radius of gyration are analyzed in order to investigate
how people move in their daily life, and if it is possible to model this
individual movements and make prediction based on them. Using graph in mobility
studies, helps to investigate the dynamic behavior of the system, such as
diffusion and flow in the network and makes it easier to estimate how much one
part of the network influences another by using metrics like centrality
measures. We aim to study population flow in transportation networks using
mobility data to derive models and patterns, and to develop new applications in
predicting phenomena such as congestion. Human Mobility studies with the new
generation of mobility data provided by cellular phone networks, arise new
challenges such as data storing, data representation, data analysis and
computation complexity. A comparative review of different data types used in
current tools and applications of Human Mobility studies leads us to new
approaches for dealing with mentioned challenges
Efficient Behavior of Small-World Networks
We introduce the concept of efficiency of a network, measuring how
efficiently it exchanges information. By using this simple measure small-world
networks are seen as systems that are both globally and locally efficient. This
allows to give a clear physical meaning to the concept of small-world, and also
to perform a precise quantitative a nalysis of both weighted and unweighted
networks. We study neural networks and man-made communication and
transportation systems and we show that the underlying general principle of
their construction is in fact a small-world principle of high efficiency.Comment: 1 figure, 2 tables. Revised version. Accepted for publication in
Phys. Rev. Let
- …