19 research outputs found
Phase Transition in the Aldous-Shields Model of Growing Trees
We study analytically the late time statistics of the number of particles in
a growing tree model introduced by Aldous and Shields. In this model, a cluster
grows in continuous time on a binary Cayley tree, starting from the root, by
absorbing new particles at the empty perimeter sites at a rate proportional to
c^{-l} where c is a positive parameter and l is the distance of the perimeter
site from the root. For c=1, this model corresponds to random binary search
trees and for c=2 it corresponds to digital search trees in computer science.
By introducing a backward Fokker-Planck approach, we calculate the mean and the
variance of the number of particles at large times and show that the variance
undergoes a `phase transition' at a critical value c=sqrt{2}. While for
c>sqrt{2} the variance is proportional to the mean and the distribution is
normal, for c<sqrt{2} the variance is anomalously large and the distribution is
non-Gaussian due to the appearance of extreme fluctuations. The model is
generalized to one where growth occurs on a tree with branches and, in this
more general case, we show that the critical point occurs at c=sqrt{m}.Comment: Latex 17 pages, 6 figure
Continuum Cascade Model of Directed Random Graphs: Traveling Wave Analysis
We study a class of directed random graphs. In these graphs, the interval
[0,x] is the vertex set, and from each y\in [0,x], directed links are drawn to
points in the interval (y,x] which are chosen uniformly with density one. We
analyze the length of the longest directed path starting from the origin. In
the large x limit, we employ traveling wave techniques to extract the
asymptotic behavior of this quantity. We also study the size of a cascade tree
composed of vertices which can be reached via directed paths starting at the
origin.Comment: 12 pages, 2 figures; figure adde
Front propagation into unstable states
This paper is an introductory review of the problem of front propagation into
unstable states. Our presentation is centered around the concept of the
asymptotic linear spreading velocity v*, the asymptotic rate with which
initially localized perturbations spread into an unstable state according to
the linear dynamical equations obtained by linearizing the fully nonlinear
equations about the unstable state. This allows us to give a precise definition
of pulled fronts, nonlinear fronts whose asymptotic propagation speed equals
v*, and pushed fronts, nonlinear fronts whose asymptotic speed v^dagger is
larger than v*. In addition, this approach allows us to clarify many aspects of
the front selection problem, the question whether for a given dynamical
equation the front is pulled or pushed. It also is the basis for the universal
expressions for the power law rate of approach of the transient velocity v(t)
of a pulled front as it converges toward its asymptotic value v*. Almost half
of the paper is devoted to reviewing many experimental and theoretical examples
of front propagation into unstable states from this unified perspective. The
paper also includes short sections on the derivation of the universal power law
relaxation behavior of v(t), on the absence of a moving boundary approximation
for pulled fronts, on the relation between so-called global modes and front
propagation, and on stochastic fronts.Comment: final version with some added references; a single pdf file of the
published version is available at http://www.lorentz.leidenuniv.nl/~saarloo
2008 GREAT Day Program
SUNY Geneseo’s Second Annual GREAT Day.https://knightscholar.geneseo.edu/program-2007/1002/thumbnail.jp
Intelligent Sensor Networks
In the last decade, wireless or wired sensor networks have attracted much attention. However, most designs target general sensor network issues including protocol stack (routing, MAC, etc.) and security issues. This book focuses on the close integration of sensing, networking, and smart signal processing via machine learning. Based on their world-class research, the authors present the fundamentals of intelligent sensor networks. They cover sensing and sampling, distributed signal processing, and intelligent signal learning. In addition, they present cutting-edge research results from leading experts
Recent Developments in Smart Healthcare
Medicine is undergoing a sector-wide transformation thanks to the advances in computing and networking technologies. Healthcare is changing from reactive and hospital-centered to preventive and personalized, from disease focused to well-being centered. In essence, the healthcare systems, as well as fundamental medicine research, are becoming smarter. We anticipate significant improvements in areas ranging from molecular genomics and proteomics to decision support for healthcare professionals through big data analytics, to support behavior changes through technology-enabled self-management, and social and motivational support. Furthermore, with smart technologies, healthcare delivery could also be made more efficient, higher quality, and lower cost. In this special issue, we received a total 45 submissions and accepted 19 outstanding papers that roughly span across several interesting topics on smart healthcare, including public health, health information technology (Health IT), and smart medicine