204 research outputs found
Maximum flow and topological structure of complex networks
The problem of sending the maximum amount of flow between two arbitrary
nodes and of complex networks along links with unit capacity is
studied, which is equivalent to determining the number of link-disjoint paths
between and . The average of over all node pairs with smaller degree
is for large with a constant implying that the statistics of is related to the
degree distribution of the network. The disjoint paths between hub nodes are
found to be distributed among the links belonging to the same edge-biconnected
component, and can be estimated by the number of pairs of edge-biconnected
links incident to the start and terminal node. The relative size of the giant
edge-biconnected component of a network approximates to the coefficient .
The applicability of our results to real world networks is tested for the
Internet at the autonomous system level.Comment: 7 pages, 4 figure
Diagnosis of autosomal dominant polycystic kidney disease in utero and in the young infant.
Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135563/1/jum198765249.pd
On -Simple -Path
An -simple -path is a {path} in the graph of length that passes
through each vertex at most times. The -SIMPLE -PATH problem, given a
graph as input, asks whether there exists an -simple -path in . We
first show that this problem is NP-Complete. We then show that there is a graph
that contains an -simple -path and no simple path of length greater
than . So this, in a sense, motivates this problem especially
when one's goal is to find a short path that visits many vertices in the graph
while bounding the number of visits at each vertex.
We then give a randomized algorithm that runs in time that solves the -SIMPLE -PATH on a graph with
vertices with one-sided error. We also show that a randomized algorithm
with running time with gives a
randomized algorithm with running time \poly(n)\cdot 2^{cn} for the
Hamiltonian path problem in a directed graph - an outstanding open problem. So
in a sense our algorithm is optimal up to an factor
Polynomial algorithms for the Maximal Pairing Problem: efficient phylogenetic targeting on arbitrary trees
Background: The Maximal Pairing Problem (MPP) is the prototype of a class of combinatorial optimization problems that are of considerable interest in bioinformatics: Given an arbitrary phylogenetic tree T and weights ωxy for the paths between any two pairs of leaves (x, y), what is the collection of edge-disjoint paths between pairs of leaves that maximizes the total weight? Special cases of the MPP for binary trees and equal weights have been described previously; algorithms to solve the general MPP are still missing, however. Results: We describe a relatively simple dynamic programming algorithm for the special case of binary trees. We then show that the general case of multifurcating trees can be treated by interleaving solutions to certain auxiliary Maximum Weighted Matching problems with an extension of this dynamic programming approach, resulting in an overall polynomial-time solution of complexity (n^4 log n) w.r.t. the number n of leaves. The source code of a C implementation can be obtained under the GNU Public License from http://www.bioinf.uni-leipzig.de/Software/Targeting. For binary trees, we furthermore discuss several constrained variants of the MPP as well as a partition function approach to the probabilistic version of the MPP. Conclusions: The algorithms introduced here make it possible to solve the MPP also for large trees with high-degree vertices. This has practical relevance in the field of comparative phylogenetics and, for example, in the context of phylogenetic targeting, i.e., data collection with resource limitations.Human Evolutionary Biolog
On the complexity of strongly connected components in directed hypergraphs
We study the complexity of some algorithmic problems on directed hypergraphs
and their strongly connected components (SCCs). The main contribution is an
almost linear time algorithm computing the terminal strongly connected
components (i.e. SCCs which do not reach any components but themselves).
"Almost linear" here means that the complexity of the algorithm is linear in
the size of the hypergraph up to a factor alpha(n), where alpha is the inverse
of Ackermann function, and n is the number of vertices. Our motivation to study
this problem arises from a recent application of directed hypergraphs to
computational tropical geometry.
We also discuss the problem of computing all SCCs. We establish a superlinear
lower bound on the size of the transitive reduction of the reachability
relation in directed hypergraphs, showing that it is combinatorially more
complex than in directed graphs. Besides, we prove a linear time reduction from
the well-studied problem of finding all minimal sets among a given family to
the problem of computing the SCCs. Only subquadratic time algorithms are known
for the former problem. These results strongly suggest that the problem of
computing the SCCs is harder in directed hypergraphs than in directed graphs.Comment: v1: 32 pages, 7 figures; v2: revised version, 34 pages, 7 figure
Ninth and Tenth Order Virial Coefficients for Hard Spheres in D Dimensions
We evaluate the virial coefficients B_k for k<=10 for hard spheres in
dimensions D=2,...,8. Virial coefficients with k even are found to be negative
when D>=5. This provides strong evidence that the leading singularity for the
virial series lies away from the positive real axis when D>=5. Further analysis
provides evidence that negative virial coefficients will be seen for some k>10
for D=4, and there is a distinct possibility that negative virial coefficients
will also eventually occur for D=3.Comment: 33 pages, 12 figure
Polycystin-1 Surface Localization Is Stimulated by Polycystin-2 and Cleavage at the G Protein-coupled Receptor Proteolytic Site
The localization of polycystin (PC)1) to the plasma membrane requires coexpression with PC2 and cleavage at the PC1 G protein-coupled receptor proteolytic site. Neither the PC1 binding capacity of PC2 nor its channel function is required for this effect
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