The shortest wire.
Ontology highlight
ABSTRACT:
SUBMITTER: Miller AF
PROVIDER: S-EPMC2396719 | biostudies-literature | 2008 May
REPOSITORIES: biostudies-literature
Publications
The shortest wire.
Proceedings of the National Academy of Sciences of the United States of America 20080501 21
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Project description:Dynamic processes on networks, be it information transfer in the Internet, contagious spreading in a social network, or neural signaling, take place along shortest or nearly shortest paths. Computing shortest paths is a straightforward task when the network of interest is fully known, and there are a plethora of computational algorithms for this purpose. Unfortunately, our maps of most large networks are substantially incomplete due to either the highly dynamic nature of networks, or high cost of network measurements, or both, rendering traditional path finding methods inefficient. We find that shortest paths in large real networks, such as the network of protein-protein interactions and the Internet at the autonomous system level, are not random but are organized according to latent-geometric rules. If nodes of these networks are mapped to points in latent hyperbolic spaces, shortest paths in them align along geodesic curves connecting endpoint nodes. We find that this alignment is sufficiently strong to allow for the identification of shortest path nodes even in the case of substantially incomplete networks, where numbers of missing links exceed those of observable links. We demonstrate the utility of latent-geometric path finding in problems of cellular pathway reconstruction and communication security.
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Project description:The shortest path problem is one of the most fundamental networks optimization problems. Nowadays, individuals interact in extraordinarily numerous ways through their offline and online life (e.g., co-authorship, co-workership, or retweet relation in Twitter). These interactions have two key features. First, they have a heterogeneous nature, and second, they have different strengths that are weighted based on their degree of intimacy, trustworthiness, service exchange or influence among individuals. These networks are known as multiplex networks. To our knowledge, none of the previous shortest path definitions on social interactions have properly reflected these features. In this work, we introduce a new distance measure in multiplex networks based on the concept of Pareto efficiency taking both heterogeneity and weighted nature of relations into account. We then model the problem of finding the whole set of paths as a form of multiple objective decision making and propose an exact algorithm for that. The method is evaluated on five real-world datasets to test the impact of considering weights and multiplexity in the resulting shortest paths. As an application to find the most influential nodes, we redefine the concept of betweenness centrality based on the proposed shortest paths and evaluate it on a real-world dataset from two-layer trade relation among countries between years 2000 and 2015.
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Project description:We numerically show that the statistical properties of the shortest path on critical percolation clusters are consistent with the ones predicted for Schramm-Loewner evolution (SLE) curves for κ = 1.04 ± 0.02. The shortest path results from a global optimization process. To identify it, one needs to explore an entire area. Establishing a relation with SLE permits to generate curves statistically equivalent to the shortest path from a Brownian motion. We numerically analyze the winding angle, the left passage probability, and the driving function of the shortest path and compare them to the distributions predicted for SLE curves with the same fractal dimension. The consistency with SLE opens the possibility of using a solid theoretical framework to describe the shortest path and it raises relevant questions regarding conformal invariance and domain Markov properties, which we also discuss.
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Project description:Motivation:We introduce a formulation for the general task of finding diverse shortest paths between two end-points. Our approach is not linked to a specific biological problem and can be applied to a large variety of images thanks to its generic implementation as a user-friendly ImageJ/Fiji plugin. It relies on the introduction of additional layers in a Viterbi path graph, which requires slight modifications to the standard Viterbi algorithm rules. This layered graph construction allows for the specification of various constraints imposing diversity between solutions. Results:The software allows obtaining a collection of diverse shortest paths under some user-defined constraints through a convenient and user-friendly interface. It can be used alone or be integrated into larger image analysis pipelines. Availability and implementation:http://bigwww.epfl.ch/algorithms/diversepathsj. Contact:michael.unser@epfl.ch or fred.hamprecht@iwr.uni-heidelberg.de. Supplementary information:Supplementary data are available at Bioinformatics online.
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Project description:BackgroundGraph-based modularity analysis has emerged as an important tool to study the functional organization of biological networks. However, few methods are available to study state-dependent changes in network modularity using biological activity data. We develop a weighting scheme, based on metabolic flux data, to adjust the interaction distances in a reaction-centric graph model of a metabolic network. The weighting scheme was combined with a hierarchical module assignment algorithm featuring the preservation of metabolic cycles to examine the effects of cellular differentiation and enzyme inhibitions on the functional organization of adipocyte metabolism.ResultsOur analysis found that the differences between various metabolic states primarily involved the assignment of two specific reactions in fatty acid synthesis and glycerogenesis. Our analysis also identified cyclical interactions between reactions that are robust with respect to metabolic state, suggesting possible co-regulation. Comparisons based on cyclical interaction distances between reaction pairs suggest that the modular organization of adipocyte metabolism is stable with respect to the inhibition of an enzyme, whereas a major physiological change such as cellular differentiation leads to a more substantial reorganization.ConclusionTaken together, our results support the notion that network modularity is influenced by both the connectivity of the network's components as well as the relative engagements of the connections.
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Project description:BackgroundSequence comparison by alignment is a fundamental tool of molecular biology. In this paper we show how a number of sequence comparison tasks, including the detection of unique genomic regions, can be accomplished efficiently without an alignment step. Our procedure for nucleotide sequence comparison is based on shortest unique substrings. These are substrings which occur only once within the sequence or set of sequences analysed and which cannot be further reduced in length without losing the property of uniqueness. Such substrings can be detected using generalized suffix trees.ResultsWe find that the shortest unique substrings in Caenorhabditis elegans, human and mouse are no longer than 11 bp in the autosomes of these organisms. In mouse and human these unique substrings are significantly clustered in upstream regions of known genes. Moreover, the probability of finding such short unique substrings in the genomes of human or mouse by chance is extremely small. We derive an analytical expression for the null distribution of shortest unique substrings, given the GC-content of the query sequences. Furthermore, we apply our method to rapidly detect unique genomic regions in the genome of Staphylococcus aureus strain MSSA476 compared to four other staphylococcal genomes.ConclusionWe combine a method to rapidly search for shortest unique substrings in DNA sequences and a derivation of their null distribution. We show that unique regions in an arbitrary sample of genomes can be efficiently detected with this method. The corresponding programs shustring (SHortest Unique subSTRING) and shulen are written in C and available at http://adenine.biz.fh-weihenstephan.de/shustring/.
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