316 research outputs found
Information Spreading in Stationary Markovian Evolving Graphs
Markovian evolving graphs are dynamic-graph models where the links among a
fixed set of nodes change during time according to an arbitrary Markovian rule.
They are extremely general and they can well describe important dynamic-network
scenarios.
We study the speed of information spreading in the "stationary phase" by
analyzing the completion time of the "flooding mechanism". We prove a general
theorem that establishes an upper bound on flooding time in any stationary
Markovian evolving graph in terms of its node-expansion properties.
We apply our theorem in two natural and relevant cases of such dynamic
graphs. "Geometric Markovian evolving graphs" where the Markovian behaviour is
yielded by "n" mobile radio stations, with fixed transmission radius, that
perform independent random walks over a square region of the plane.
"Edge-Markovian evolving graphs" where the probability of existence of any edge
at time "t" depends on the existence (or not) of the same edge at time "t-1".
In both cases, the obtained upper bounds hold "with high probability" and
they are nearly tight. In fact, they turn out to be tight for a large range of
the values of the input parameters. As for geometric Markovian evolving graphs,
our result represents the first analytical upper bound for flooding time on a
class of concrete mobile networks.Comment: 16 page
Revisiting a result of Ko
In this paper we analyze Ko's Theorem 3.4 in \cite{Ko87}.
We extend point b) of Ko's Theorem by showing that
\poneh(\upcoup)=\upcoup. As a corollary, we get the equality
\ph(\upcoup) = \poneh(\upcoup), which is, to our knowledge, a
unique result of type \poneh({\cal C})=\ph({\cal C}), for a class
that would not be equal to \DP.
With regard to point a) of Ko's Theorem, we observe that it also holds for the
classes \upk{k} and for \fewp.
In spite of this, we prove that point b) of Theorem 3.4 fails for such
classes in a relativized world. This is obtained by showing the
relativized separation of \upcoupk{2} from \poneh(\npconp).
Finally, we suggest a natural line of research arising from these facts
Revisiting a result of Ko
In this paper we analyze Ko's Theorem 3.4 in \cite{Ko87}.
We extend point b) of Ko's Theorem by showing that
\poneh(\upcoup)=\upcoup. As a corollary, we get the equality
\ph(\upcoup) = \poneh(\upcoup), which is, to our knowledge, a
unique result of type \poneh({\cal C})=\ph({\cal C}), for a class
that would not be equal to \DP.
With regard to point a) of Ko's Theorem, we observe that it also holds for the
classes \upk{k} and for \fewp.
In spite of this, we prove that point b) of Theorem 3.4 fails for such
classes in a relativized world. This is obtained by showing the
relativized separation of \upcoupk{2} from \poneh(\npconp).
Finally, we suggest a natural line of research arising from these facts
Simple Dynamics for Plurality Consensus
We study a \emph{Plurality-Consensus} process in which each of anonymous
agents of a communication network initially supports an opinion (a color chosen
from a finite set ). Then, in every (synchronous) round, each agent can
revise his color according to the opinions currently held by a random sample of
his neighbors. It is assumed that the initial color configuration exhibits a
sufficiently large \emph{bias} towards a fixed plurality color, that is,
the number of nodes supporting the plurality color exceeds the number of nodes
supporting any other color by additional nodes. The goal is having the
process to converge to the \emph{stable} configuration in which all nodes
support the initial plurality. We consider a basic model in which the network
is a clique and the update rule (called here the \emph{3-majority dynamics}) of
the process is the following: each agent looks at the colors of three random
neighbors and then applies the majority rule (breaking ties uniformly).
We prove that the process converges in time with high probability, provided that .
We then prove that our upper bound above is tight as long as . This fact implies an exponential time-gap between the
plurality-consensus process and the \emph{median} process studied by Doerr et
al. in [ACM SPAA'11].
A natural question is whether looking at more (than three) random neighbors
can significantly speed up the process. We provide a negative answer to this
question: In particular, we show that samples of polylogarithmic size can speed
up the process by a polylogarithmic factor only.Comment: Preprint of journal versio
Application of PRISMA satellite hyperspectral imagery for man-made materials classification in urban areas: a case study in Tuscany Region (Italy)
The coherent dynamics of photoexcited green fluorescent proteins
The coherent dynamics of vibronic wave packets in the green fluorescent
protein is reported. At room temperature the non-stationary dynamics following
impulsive photoexcitation displays an oscillating optical transmissivity
pattern with components at 67 fs (497 cm-1) and 59 fs (593 cm-1). Our results
are complemented by ab initio calculations of the vibrational spectrum of the
chromophore. This analysis shows the interplay between the dynamics of the
aminoacidic structure and the electronic excitation in the primary optical
events of green fluorescent proteins.Comment: accepted for publication in Physical Review Letter
Minimum-energy broadcast in random-grid ad-hoc networks: approximation and distributed algorithms
The Min Energy broadcast problem consists in assigning transmission ranges to
the nodes of an ad-hoc network in order to guarantee a directed spanning tree
from a given source node and, at the same time, to minimize the energy
consumption (i.e. the energy cost) yielded by the range assignment. Min energy
broadcast is known to be NP-hard.
We consider random-grid networks where nodes are chosen independently at
random from the points of a square grid in the
plane. The probability of the existence of a node at a given point of the grid
does depend on that point, that is, the probability distribution can be
non-uniform.
By using information-theoretic arguments, we prove a lower bound
on the energy cost of any feasible solution for
this problem. Then, we provide an efficient solution of energy cost not larger
than .
Finally, we present a fully-distributed protocol that constructs a broadcast
range assignment of energy cost not larger than ,thus still yielding
constant approximation. The energy load is well balanced and, at the same time,
the work complexity (i.e. the energy due to all message transmissions of the
protocol) is asymptotically optimal. The completion time of the protocol is
only an factor slower than the optimum. The approximation quality
of our distributed solution is also experimentally evaluated.
All bounds hold with probability at least .Comment: 13 pages, 3 figures, 1 tabl
Flooding Time in Opportunistic Networks under Power Law and Exponential Inter-Contact Times
Performance bounds for opportunistic networks have been derived in a number
of recent papers for several key quantities, such as the expected delivery time
of a unicast message, or the flooding time (a measure of how fast information
spreads). However, to the best of our knowledge, none of the existing results
is derived under a mobility model which is able to reproduce the power
law+exponential tail dichotomy of the pairwise node inter-contact time
distribution which has been observed in traces of several real opportunistic
networks.
The contributions of this paper are two-fold: first, we present a simple
pairwise contact model -- called the Home-MEG model -- for opportunistic
networks based on the observation made in previous work that pairs of nodes in
the network tend to meet in very few, selected locations (home locations); this
contact model is shown to be able to faithfully reproduce the power
law+exponential tail dichotomy of inter-contact time. Second, we use the
Home-MEG model to analyze flooding time in opportunistic networks, presenting
asymptotic bounds on flooding time that assume different initial conditions for
the existence of opportunistic links.
Finally, our bounds provide some analytical evidences that the speed of
information spreading in opportunistic networks can be much faster than that
predicted by simple geometric mobility models
ARDS secondary to descending necrotizing mediastinitis treated by long-term extracorporeal respiratory support
- …