1,442 research outputs found
The Complexity of Routing with Few Collisions
We study the computational complexity of routing multiple objects through a
network in such a way that only few collisions occur: Given a graph with
two distinct terminal vertices and two positive integers and , the
question is whether one can connect the terminals by at least routes (e.g.
paths) such that at most edges are time-wise shared among them. We study
three types of routes: traverse each vertex at most once (paths), each edge at
most once (trails), or no such restrictions (walks). We prove that for paths
and trails the problem is NP-complete on undirected and directed graphs even if
is constant or the maximum vertex degree in the input graph is constant.
For walks, however, it is solvable in polynomial time on undirected graphs for
arbitrary and on directed graphs if is constant. We additionally study
for all route types a variant of the problem where the maximum length of a
route is restricted by some given upper bound. We prove that this
length-restricted variant has the same complexity classification with respect
to paths and trails, but for walks it becomes NP-complete on undirected graphs
Risk-Averse Matchings over Uncertain Graph Databases
A large number of applications such as querying sensor networks, and
analyzing protein-protein interaction (PPI) networks, rely on mining uncertain
graph and hypergraph databases. In this work we study the following problem:
given an uncertain, weighted (hyper)graph, how can we efficiently find a
(hyper)matching with high expected reward, and low risk?
This problem naturally arises in the context of several important
applications, such as online dating, kidney exchanges, and team formation. We
introduce a novel formulation for finding matchings with maximum expected
reward and bounded risk under a general model of uncertain weighted
(hyper)graphs that we introduce in this work. Our model generalizes
probabilistic models used in prior work, and captures both continuous and
discrete probability distributions, thus allowing to handle privacy related
applications that inject appropriately distributed noise to (hyper)edge
weights. Given that our optimization problem is NP-hard, we turn our attention
to designing efficient approximation algorithms. For the case of uncertain
weighted graphs, we provide a -approximation algorithm, and a
-approximation algorithm with near optimal run time. For the case
of uncertain weighted hypergraphs, we provide a
-approximation algorithm, where is the rank of the
hypergraph (i.e., any hyperedge includes at most nodes), that runs in
almost (modulo log factors) linear time.
We complement our theoretical results by testing our approximation algorithms
on a wide variety of synthetic experiments, where we observe in a controlled
setting interesting findings on the trade-off between reward, and risk. We also
provide an application of our formulation for providing recommendations of
teams that are likely to collaborate, and have high impact.Comment: 25 page
Flow through a circular tube with a permeable Navier slip boundary
For Newtonian fluid flow in a right circular tube, with a linear Navier slip boundary, we show that a second flow field arises which is different to conventional Poiseuille flow in the sense that the corresponding pressure is quadratic in its dependence on the length along the tube, rather than a linear dependence which applies for conventional Poiseuille flow. However, assuming that the quadratic pressure is determined, say from known experimental data, then the new solution only exists for a precisely prescribed permeability along the boundary. While this cannot occur for conventional pipe flow, for fluid flow through carbon nanotubes embedded in a porous matrix, it may well be an entirely realistic possibility, and could well explain some of the high flow rates which have been reported in the literature. Alternatively, if the radial boundary flow is prescribed, then the new flow field exists only for a given quadratic pressure. Our primary purpose here is to demonstrate the existence of a new pipe flow field for a permeable Navier slip boundary and to present a numerical solution and two approximate analytical solutions. The maximum flow rate possible for the new solution is precisely twice that for the conventional Poiseuille flow, which occurs for constant inward directed flow across the boundary
Grouping of tooth surfaces by susceptibility to caries: a study in 5–16 year-old children
BACKGROUND: The decline in caries has slowed and this may be indicative of variation in the susceptibility of differing teeth to caries. This study tests the hypothesis that in children, there are groups of tooth sites that exhibit differences in caries susceptibility. METHODS: Probit analysis of caries data collected from a 4-year longitudinal study of 20,000 schoolchildren aged between 5 and 16 years in 10 differing locations in the United States. RESULTS: The development of dental caries within the mouth followed a fixed hierarchy indicating that tooth surfaces show variation in caries susceptibility. Certain teeth and tooth sites have similar susceptibilities and can be grouped, the sizes of the groups vary. The most susceptible group consists of six tooth surfaces: the buccal pits and occlusal fissured surfaces of the first molar teeth. The second group consisted of 12 sites on the second molar and premolar teeth. The group formed by the least susceptible sites included the largest number of tooth surfaces and consists of the majority of the lower anterior teeth and canines. CONCLUSION: Variation in the caries susceptibility of tooth surfaces exists. Surfaces can be grouped according to caries susceptibility. An effect that reduces the cariogenic challenge of one of the sites within a group is likely to affect all the other sites within the particular group
The New Legal Pluralism
Scholars studying interactions among multiple communities have often used the term legal pluralism to describe the inevitable intermingling of normative systems that results from these interactions. In recent years, a new application of pluralist insights has emerged in the international and transnational realm. This review aims to survey and help define this emerging field of global legal pluralism. I begin by briefly describing sites for pluralism research, both old and new. Then I discuss how pluralism has come to be seen as an attractive analytical framework for those interested in studying law on the world stage. Finally, I identify advantages of a pluralist approach and respond to criticisms, and I suggest ways in which pluralism can help both in reframing old conceptual debates and in generating useful normative insights for designing procedural mechanisms, institutions, and discursive practices for managing hybrid legal/cultural spaces
The approximability of the String Barcoding problem
The String Barcoding (SBC) problem, introduced by Rash and Gusfield (RECOMB, 2002), consists in finding a minimum set of substrings that can be used to distinguish between all members of a set of given strings. In a computational biology context, the given strings represent a set of known viruses, while the substrings can be used as probes for an hybridization experiment via microarray. Eventually, one aims at the classification of new strings (unknown viruses) through the result of the hybridization experiment. In this paper we show that SBC is as hard to approximate as Set Cover. Furthermore, we show that the constrained version of SBC (with probes of bounded length) is also hard to approximate. These negative results are tight
Information transmission in oscillatory neural activity
Periodic neural activity not locked to the stimulus or to motor responses is
usually ignored. Here, we present new tools for modeling and quantifying the
information transmission based on periodic neural activity that occurs with
quasi-random phase relative to the stimulus. We propose a model to reproduce
characteristic features of oscillatory spike trains, such as histograms of
inter-spike intervals and phase locking of spikes to an oscillatory influence.
The proposed model is based on an inhomogeneous Gamma process governed by a
density function that is a product of the usual stimulus-dependent rate and a
quasi-periodic function. Further, we present an analysis method generalizing
the direct method (Rieke et al, 1999; Brenner et al, 2000) to assess the
information content in such data. We demonstrate these tools on recordings from
relay cells in the lateral geniculate nucleus of the cat.Comment: 18 pages, 8 figures, to appear in Biological Cybernetic
The use of virtual reality as a potential restorative environment in school during recess
Peer reviewe
Mechanical Strength of 17 134 Model Proteins and Cysteine Slipknots
A new theoretical survey of proteins' resistance to constant speed stretching
is performed for a set of 17 134 proteins as described by a structure-based
model. The proteins selected have no gaps in their structure determination and
consist of no more than 250 amino acids. Our previous studies have dealt with
7510 proteins of no more than 150 amino acids. The proteins are ranked
according to the strength of the resistance. Most of the predicted top-strength
proteins have not yet been studied experimentally. Architectures and folds
which are likely to yield large forces are identified. New types of potent
force clamps are discovered. They involve disulphide bridges and, in
particular, cysteine slipknots. An effective energy parameter of the model is
estimated by comparing the theoretical data on characteristic forces to the
corresponding experimental values combined with an extrapolation of the
theoretical data to the experimental pulling speeds. These studies provide
guidance for future experiments on single molecule manipulation and should lead
to selection of proteins for applications. A new class of proteins, involving
cystein slipknots, is identified as one that is expected to lead to the
strongest force clamps known. This class is characterized through molecular
dynamics simulations.Comment: 40 pages, 13 PostScript figure
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