9,419 research outputs found
Criticality of the Exponential Rate of Decay for the Largest Nearest Neighbor Link in Random Geometric Graph
Let n points be placed independently in d-dimensional space according to the
densities Let be the longest edge length for the nearest neighbor graph on
these points. We show that converges weakly to
the Gumbel distribution where We also show that the
strong law result, % \lim_{n \to \infty}
\frac{(\lambda^{-1}\log(n))^{1-1/\alpha}d_n}{\sqrt{\log \log n}} \to
\frac{d}{\alpha \lambda}, a.s. % Thus, the exponential rate of decay i.e.
is critical, in the sense that for where
as a.s. as Comment: Communicated to 'Stochastic Processes and Their Applications'. Sep.
11, 2006: replaced paper uploaded on Apr. 27, 2006 by a corrected version;
errors/corrections found by the authors themselve
Nonuniform random geometric graphs with location-dependent radii
We propose a distribution-free approach to the study of random geometric
graphs. The distribution of vertices follows a Poisson point process with
intensity function , where , and is a
probability density function on . A vertex located at
connects via directed edges to other vertices that are within a cut-off
distance . We prove strong law results for (i) the critical cut-off
function so that almost surely, the graph does not contain any node with
out-degree zero for sufficiently large and (ii) the maximum and minimum
vertex degrees. We also provide a characterization of the cut-off function for
which the number of nodes with out-degree zero converges in distribution to a
Poisson random variable. We illustrate this result for a class of densities
with compact support that have at most polynomial rates of decay to zero.
Finally, we state a sufficient condition for an enhanced version of the above
graph to be almost surely connected eventually.Comment: Published in at http://dx.doi.org/10.1214/11-AAP823 the Annals of
Applied Probability (http://www.imstat.org/aap/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Achieving Non-Zero Information Velocity in Wireless Networks
In wireless networks, where each node transmits independently of other nodes
in the network (the ALOHA protocol), the expected delay experienced by a packet
until it is successfully received at any other node is known to be infinite for
signal-to-interference-plus-noise-ratio (SINR) model with node locations
distributed according to a Poisson point process. Consequently, the information
velocity, defined as the limit of the ratio of the distance to the destination
and the time taken for a packet to successfully reach the destination over
multiple hops, is zero, as the distance tends to infinity. A nearest neighbor
distance based power control policy is proposed to show that the expected delay
required for a packet to be successfully received at the nearest neighbor can
be made finite. Moreover, the information velocity is also shown to be non-zero
with the proposed power control policy. The condition under which these results
hold does not depend on the intensity of the underlying Poisson point process.Comment: to appear in Annals of Applied Probabilit
Bulk Majorana mass terms and Dirac neutrinos in Randall Sundrum Model
We present a novel scheme where Dirac neutrinos are realized even if lepton
number violating Majorana mass terms are present. The setup is the
Randall-Sundrum framework with bulk right handed neutrinos. Bulk mass terms of
both Majorana and Dirac type are considered. It is shown that massless zero
mode solutions exist when the bulk Dirac mass term is set to zero. In this
limit, it is found that the effective 4D small neutrino mass is primarily of
Dirac nature with the Majorana type contributions being negligible.
Interestingly, this scenario is very similar to the one known with flat extra
dimensions. Neutrino phenomenology is discussed by fitting both charged lepton
masses and neutrino masses simultaneously. A single Higgs localised on the IR
brane is highly constrained as unnaturally large Yukawa couplings are required
to fit charged lepton masses. A simple extension with two Higgs doublets is
presented which facilitates a proper fit for the lepton masses.Comment: 13 Pages, Few clarifications included and added references. Figure
removed. Published in PR
Multi-learner based recursive supervised training
In this paper, we propose the Multi-Learner Based Recursive Supervised Training (MLRT) algorithm which uses the existing framework of recursive task decomposition, by training the entire dataset, picking out the best learnt patterns, and then repeating the process with the remaining patterns. Instead of having a single learner to classify all datasets during each recursion, an appropriate learner is chosen from a set of three learners, based on the subset of data being trained, thereby avoiding the time overhead associated with the genetic algorithm learner utilized in previous approaches. In this way MLRT seeks to identify the inherent characteristics of the dataset, and utilize it to train the data accurately and efficiently. We observed that empirically, MLRT performs considerably well as compared to RPHP and other systems on benchmark data with 11% improvement in accuracy on the SPAM dataset and comparable performances on the VOWEL and the TWO-SPIRAL problems. In addition, for most datasets, the time taken by MLRT is considerably lower than the other systems with comparable accuracy. Two heuristic versions, MLRT-2 and MLRT-3 are also introduced to improve the efficiency in the system, and to make it more scalable for future updates. The performance in these versions is similar to the original MLRT system
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