Graphs and matroids weighted in a bounded incline algebra.
Ontology highlight
ABSTRACT:
SUBMITTER: Lu LX
PROVIDER: S-EPMC4122196 | biostudies-other | 2014
REPOSITORIES: biostudies-other
Similar Datasets
Project description:Community detection is a fundamental procedure in the analysis of network data. Despite decades of research, there is still no consensus on the definition of a community. To analytically test the realness of a candidate community in weighted networks, we present a general formulation from a significance testing perspective. In this new formulation, the edge-weight is modeled as a censored observation due to the noisy characteristics of real networks. In particular, the edge-weights of missing links are incorporated as well, which are specified to be zeros based on the assumption that they are truncated or unobserved. Thereafter, the community significance assessment issue is formulated as a two-sample test problem on censored data. More precisely, the Logrank test is employed to conduct the significance testing on two sets of augmented edge-weights: internal weight set and external weight set. The presented approach is evaluated on both weighted networks and un-weighted networks. The experimental results show that our method can outperform prior widely used evaluation metrics on the task of individual community validation.
| S-EPMC8514603 | biostudies-literature
Project description:The dynamics of diffusion-like processes on temporal networks are influenced by correlations in the times of contacts. This influence is particularly strong for processes where the spreading agent has a limited lifetime at nodes: disease spreading (recovery time), diffusion of rumors (lifetime of information), and passenger routing (maximum acceptable time between transfers). We introduce weighted event graphs as a powerful and fast framework for studying connectivity determined by time-respecting paths where the allowed waiting times between contacts have an upper limit. We study percolation on the weighted event graphs and in the underlying temporal networks, with simulated and real-world networks. We show that this type of temporal-network percolation is analogous to directed percolation, and that it can be characterized by multiple order parameters.
| S-EPMC6098025 | biostudies-literature
Project description:There is an acute need for better tools to extract knowledge from the growing flood of sequence data. For example, thousands of complete genomes have been sequenced, and their metabolic networks inferred. Such data should enable a better understanding of evolution. However, most existing network analysis methods are based on pair-wise comparisons, and these do not scale to thousands of genomes. Here we propose the use of weighted graphs as a data structure to enable large-scale phylogenetic analysis of networks. We have developed three types of weighted graph for enzymes: taxonomic (these summarize phylogenetic importance), isoenzymatic (these summarize enzymatic variety/redundancy), and sequence-similarity (these summarize sequence conservation); and we applied these types of weighted graph to survey prokaryotic metabolism. To demonstrate the utility of this approach we have compared and contrasted the large-scale evolution of metabolism in Archaea and Eubacteria. Our results provide evidence for limits to the contingency of evolution.
| S-EPMC3949676 | biostudies-literature
Project description:We propose a novel method to test the existence of community structure in undirected, real-valued, edge-weighted graphs. The method is based on the asymptotic behavior of extreme eigenvalues of a real symmetric edge-weight matrix. We provide a theoretical foundation for this method and report on its performance using synthetic and real data, suggesting that this new method outperforms other state-of-the-art methods.
| S-EPMC5860707 | biostudies-literature
Project description:Relational algebra (RA) comprises a basis of important operations, sufficient to power state-of-the-art reasoning engines for Datalog and related logic-programming languages. Parallel RA implementations can thus play a significant role in extracting parallelism inherent in a wide variety of analytic problems. In general, bottom-up logical inference can be implemented as fixed-point iteration over RA kernels; relations dynamically accumulate new tuples of information according to a set of rules until no new tuples can be discovered from previously inferred tuples and relevant rules (RA kernels). While this strategy has been quite successful in single-node contexts, it poses unique challenges when distributed over many-node, networked clusters—especially regarding how the work-load is balanced across available compute resources. In this paper, we identify two fundamental kinds of load imbalance and present a strategy to address each. We investigate both spatial load imbalance—imbalance across each relation (across compute nodes)—and temporal load imbalance–imbalance in tuples produced across fixed-point iterations. For spatial balancing, we implement refinement and consolidation procedures. For temporal balancing, we implement a technique that permits the residual workload from a busy iteration to roll over to a new iteration. In sum, these techniques permit fully dynamic load-balancing of relational algebra that is robust to changes across time.
| S-EPMC7295339 | biostudies-literature
Project description:The Kaplan–Meier product-limit estimator is a simple and powerful tool in time to event analysis. An extension exists for populations stratified into cohorts where a population survival curve is generated by weighted averaging of cohort-level survival curves. For making population-level comparisons using this statistic, we analyse the statistics of the area between two such weighted survival curves. We derive the large sample behaviour of this statistic based on an empirical process of product-limit estimators. This estimator was used by an interdisciplinary National Institutes of Health–Social Security Administration team in the identification of medical conditions to prioritize for adjudication in disability benefits processing.
| S-EPMC6281901 | biostudies-other
Project description:MotivationBeyond identifying genetic variants, we introduce a set of Boolean relations, which allows for a comprehensive classification of the relations of every pair of variants by taking all minimal alignments into account. We present an efficient algorithm to compute these relations, including a novel way of efficiently computing all minimal alignments within the best theoretical complexity bounds.ResultsWe show that these relations are common, and many non-trivial, for variants of the CFTR gene in dbSNP. Ultimately, we present an approach for the storing and indexing of variants in the context of a database that enables efficient querying for all these relations.Availability and implementationA Python implementation is available at https://github.com/mutalyzer/algebra/tree/v0.2.0 as well as an interface at https://mutalyzer.nl/algebra.
| S-EPMC9879725 | biostudies-literature
Project description:Superenhancers are crucial structural genomic elements determining cell fate, and they are also involved in the determination of several diseases, such as cancer or neurodegeneration. Although there are pipelines which use independent pieces of software to predict the presence of superenhancers from genome-wide chromatin marks or DNA-interaction protein binding sites, there is not yet an integrated software tool that processes automatically algebra combinations of raw data sequencing into a comprehensive final annotated report of predicted superenhancers.We have developed NaviSE, a user-friendly streamlined tool which performs a fully-automated parallel processing of genome-wide epigenomics data from sequencing files into a final report, built with a comprehensive set of annotated files that are navigated through a graphic user interface dynamically generated by NaviSE. NaviSE also implements an 'epigenomics signal algebra' that allows the combination of multiple activation and repression epigenomics signals. NaviSE provides an interactive chromosomal landscaping of the locations of superenhancers, which can be navigated to obtain annotated information about superenhancer signal profile, associated genes, gene ontology enrichment analysis, motifs of transcription factor binding sites enriched in superenhancers, graphs of the metrics evaluating the superenhancers quality, protein-protein interaction networks and enriched metabolic pathways among other features. We have parallelised the most time-consuming tasks achieving a reduction up to 30% for a 15 CPUs machine. We have optimized the default parameters of NaviSE to facilitate its use. NaviSE allows different entry levels of data processing, from sra-fastq files to bed files; and unifies the processing of multiple replicates. NaviSE outperforms the more time-consuming processes required in a non-integrated pipeline. Alongside its high performance, NaviSE is able to provide biological insights, predicting cell type specific markers, such as SOX2 and ZIC3 in embryonic stem cells, CDK5R1 and REST in neurons and CD86 and TLR2 in monocytes.NaviSE is a user-friendly streamlined solution for superenhancer analysis, annotation and navigation, requiring only basic computer and next generation sequencing knowledge. NaviSE binaries and documentation are available at: https://sourceforge.net/projects/navise-superenhancer/ .
| S-EPMC5461685 | biostudies-literature
Project description:BackgroundRobert Rosen's Metabolism-Replacement, or (M,R), system can be represented as a compact network structure with a single source and three products derived from that source in three consecutive reactions. (M,R) has been claimed to be non-reducible to its components and algorithmically non-computable, in the sense of not being evaluable as a function by a Turing machine. If (M,R)-like structures are present in real biological networks, this suggests that many biological networks will be non-computable, with implications for those branches of systems biology that rely on in silico modelling for predictive purposes.ResultsWe instantiate (M,R) using the process algebra Bio-PEPA, and discuss the extent to which our model represents a true realization of (M,R). We observe that under some starting conditions and parameter values, stable states can be achieved. Although formal demonstration of algorithmic computability remains elusive for (M,R), we discuss the extent to which our Bio-PEPA representation of (M,R) allows us to sidestep Rosen's fundamental objections to computational systems biology.ConclusionsWe argue that the behaviour of (M,R) in Bio-PEPA shows life-like properties.
| S-EPMC3879122 | biostudies-literature
Project description:Road networks are a classical stage for applications in network science and graph theory. Meanwhile, many combinatorial problems that arise in road networks are computationally intractable. Thus, an attractive way of tackling them is through efficient heuristics with provable performance guarantees, better known as approximation algorithms. This motivates the intersection of algorithm design with the aforementioned fields. Specifically, identifying measures that characterize graphs and exploiting them in the design of algorithms may yield practical heuristics with rigorous mathematical justification. Herein, we propose a new graph measure, namely the asymmetry factor ΔG of a directed graph G, with immediate algorithmic results via a symmetrization procedure and the black box use of approximation algorithms for symmetric graphs. Crucially, we analyze the asymmetry factors of the road networks from a diverse set of twelve cities, providing empirical evidence that road networks exhibit low bounded asymmetry and thereby justifying the practical use of algorithms for symmetric graphs.
| S-EPMC6697698 | biostudies-literature