977 research outputs found
Accelerated growth in outgoing links in evolving networks: deterministic vs. stochastic picture
In several real-world networks like the Internet, WWW etc., the number of
links grow in time in a non-linear fashion. We consider growing networks in
which the number of outgoing links is a non-linear function of time but new
links between older nodes are forbidden. The attachments are made using a
preferential attachment scheme. In the deterministic picture, the number of
outgoing links at any time is taken as where is
the number of nodes present at that time. The continuum theory predicts a power
law decay of the degree distribution: , while the degree of the node introduced at time is given by
when the
network is evolved till time . Numerical results show a growth in the degree
distribution for small values at any non-zero . In the stochastic
picture, is a random variable. As long as is time-dependent, e.g.,
when follows a distribution . The behaviour
of changes significantly as is varied: for , the
network has a scale-free distribution belonging to the BA class as predicted by
the mean field theory, for smaller values of it shows different
behaviour. Characteristic features of the clustering coefficients in both
models have also been discussed.Comment: Revised text, references added, to be published in PR
MARKET FAILURE IN MULTIPHASE ELECTRIC POWER DEVELOPMENT FOR AGRICULTURAL IRRIGATION
The adoption of multiphase electric power for electric irrigation has been limited in an area characterized by extremely rapid expansion of irrigated acreage despite production cost advantages. Theoretical and empirical evidence of failure in the existing market for multiphase power development are presented. Alternative development mechanisms are presented and discussed.Resource /Energy Economics and Policy,
Fast Locality-Sensitive Hashing Frameworks for Approximate Near Neighbor Search
The Indyk-Motwani Locality-Sensitive Hashing (LSH) framework (STOC 1998) is a
general technique for constructing a data structure to answer approximate near
neighbor queries by using a distribution over locality-sensitive
hash functions that partition space. For a collection of points, after
preprocessing, the query time is dominated by evaluations
of hash functions from and hash table lookups and
distance computations where is determined by the
locality-sensitivity properties of . It follows from a recent
result by Dahlgaard et al. (FOCS 2017) that the number of locality-sensitive
hash functions can be reduced to , leaving the query time to be
dominated by distance computations and
additional word-RAM operations. We state this result as a general framework and
provide a simpler analysis showing that the number of lookups and distance
computations closely match the Indyk-Motwani framework, making it a viable
replacement in practice. Using ideas from another locality-sensitive hashing
framework by Andoni and Indyk (SODA 2006) we are able to reduce the number of
additional word-RAM operations to .Comment: 15 pages, 3 figure
Giant strongly connected component of directed networks
We describe how to calculate the sizes of all giant connected components of a
directed graph, including the {\em strongly} connected one. Just to the class
of directed networks, in particular, belongs the World Wide Web. The results
are obtained for graphs with statistically uncorrelated vertices and an
arbitrary joint in,out-degree distribution . We show that if
does not factorize, the relative size of the giant strongly
connected component deviates from the product of the relative sizes of the
giant in- and out-components. The calculations of the relative sizes of all the
giant components are demonstrated using the simplest examples. We explain that
the giant strongly connected component may be less resilient to random damage
than the giant weakly connected one.Comment: 4 pages revtex, 4 figure
Degree distributions of growing networks
The in-degree and out-degree distributions of a growing network model are determined. The in-degree is the number of incoming links to a given node (and vice versa for out-degree. The network is built by (i) creation of new nodes which each immediately attach to a pre-existing node, and (ii) creation of new links between pre-existing nodes. This process naturally generates correlated in- and out-degree distributions. When the node and link creation rates are linear functions of node degree, these distributions exhibit distinct power-law forms. By tuning the parameters in these rates to reasonable values, exponents which agree with those of the web graph are obtained
Complexity transitions in global algorithms for sparse linear systems over finite fields
We study the computational complexity of a very basic problem, namely that of
finding solutions to a very large set of random linear equations in a finite
Galois Field modulo q. Using tools from statistical mechanics we are able to
identify phase transitions in the structure of the solution space and to
connect them to changes in performance of a global algorithm, namely Gaussian
elimination. Crossing phase boundaries produces a dramatic increase in memory
and CPU requirements necessary to the algorithms. In turn, this causes the
saturation of the upper bounds for the running time. We illustrate the results
on the specific problem of integer factorization, which is of central interest
for deciphering messages encrypted with the RSA cryptosystem.Comment: 23 pages, 8 figure
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