2,715 research outputs found
Tight Lower Bounds on the Contact Distance Distribution in Poisson Hole Process
In this letter, we derive new lower bounds on the cumulative distribution
function (CDF) of the contact distance in the Poisson Hole Process (PHP) for
two cases: (i) reference point is selected uniformly at random from
independently of the PHP, and (ii) reference point is located at
the center of a hole selected uniformly at random from the PHP. While one can
derive upper bounds on the CDF of contact distance by simply ignoring the
effect of holes, deriving lower bounds is known to be relatively more
challenging. As a part of our proof, we introduce a tractable way of bounding
the effect of all the holes in a PHP, which can be used to study other
properties of a PHP as well.Comment: To appear in IEEE Wireless Communications Letter
Coexistence of RF-powered IoT and a Primary Wireless Network with Secrecy Guard Zones
This paper studies the secrecy performance of a wireless network (primary
network) overlaid with an ambient RF energy harvesting IoT network (secondary
network). The nodes in the secondary network are assumed to be solely powered
by ambient RF energy harvested from the transmissions of the primary network.
We assume that the secondary nodes can eavesdrop on the primary transmissions
due to which the primary network uses secrecy guard zones. The primary
transmitter goes silent if any secondary receiver is detected within its guard
zone. Using tools from stochastic geometry, we derive the probability of
successful connection of the primary network as well as the probability of
secure communication. Two conditions must be jointly satisfied in order to
ensure successful connection: (i) the SINR at the primary receiver is above a
predefined threshold, and (ii) the primary transmitter is not silent. In order
to ensure secure communication, the SINR value at each of the secondary nodes
should be less than a predefined threshold. Clearly, when more secondary nodes
are deployed, more primary transmitters will remain silent for a given guard
zone radius, thus impacting the amount of energy harvested by the secondary
network. Our results concretely show the existence of an optimal deployment
density for the secondary network that maximizes the density of nodes that are
able to harvest sufficient amount of energy. Furthermore, we show the
dependence of this optimal deployment density on the guard zone radius of the
primary network. In addition, we show that the optimal guard zone radius
selected by the primary network is a function of the deployment density of the
secondary network. This interesting coupling between the two networks is
studied using tools from game theory. Overall, this work is one of the few
concrete works that symbiotically merge tools from stochastic geometry and game
theory
Merging stellar-mass binary black holes
The LIGO and Virgo detectors have recently directly observed gravitational
waves from several mergers of pairs of stellar-mass black holes, as well as
from one merging pair of neutron stars. These observations raise the hope that
compact object mergers could be used as a probe of stellar and binary
evolution, and perhaps of stellar dynamics. This colloquium-style article
summarizes the existing observations, describes theoretical predictions for
formation channels of merging stellar-mass black-hole binaries along with their
rates and observable properties, and presents some of the prospects for
gravitational-wave astronomy.Comment: Colloquium-style article solicited by Reviews of Modern Physics;
comments appreciate
Connectivity in ad-hoc and hybrid networks
We consider a large-scale wireless network, but with a low density of nodes per unit area. Interferences are then less critical, contrary to connectivity. This paper studies the latter property for both a purely ad-hoc network and a hybrid network, where fixed base stations can be reached in multiple hops. We assume here that power constraints are modeled by a maximal distance above which two nodes are not (directly) connected. We find that the introduction of a sparse network of base stations does significantly help in increasing the connectivity, but only when the node density is much larger in one dimension than in the other. We explain the results by percolation theory. We obtain analytical expressions of the probability of connectivity in the 1-dim. case. We also show that at a low spatial density of nodes, bottlenecks are unavoidable. Results obtained on actual population data confirm our findings
Testing goodness of fit for point processes via topological data analysis
We introduce tests for the goodness of fit of point patterns via methods from
topological data analysis. More precisely, the persistent Betti numbers give
rise to a bivariate functional summary statistic for observed point patterns
that is asymptotically Gaussian in large observation windows. We analyze the
power of tests derived from this statistic on simulated point patterns and
compare its performance with global envelope tests. Finally, we apply the tests
to a point pattern from an application context in neuroscience. As the main
methodological contribution, we derive sufficient conditions for a functional
central limit theorem on bounded persistent Betti numbers of point processes
with exponential decay of correlations.Comment: 34 pages, 8 figure
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