scholarly journals Convex skeletons of complex networks

2018 ◽  
Vol 15 (145) ◽  
pp. 20180422 ◽  
Author(s):  
Lovro Šubelj
Keyword(s):  
Protein Interactions ◽  
Spanning Tree ◽  
Autonomous Systems ◽  
Shortest Paths ◽  
Induced Subgraph ◽  
Social Collaboration ◽  
Computer Scientists ◽  
High Betweenness ◽  
Network Backbone ◽  
Definition Of

A convex network can be defined as a network such that every connected induced subgraph includes all the shortest paths between its nodes. A fully convex network would therefore be a collection of cliques stitched together in a tree. In this paper, we study the largest high-convexity part of empirical networks obtained by removing the least number of edges, which we call a convex skeleton. A convex skeleton is a generalization of a network spanning tree in which each edge can be replaced by a clique of arbitrary size. We present different approaches for extracting convex skeletons and apply them to social collaboration and protein interactions networks, autonomous systems graphs and food webs. We show that the extracted convex skeletons retain the degree distribution, clustering, connectivity, distances, node position and also community structure, while making the shortest paths between the nodes largely unique. Moreover, in the Slovenian computer scientists coauthorship network, a convex skeleton retains the strongest ties between the authors, differently from a spanning tree or high-betweenness backbone and high-salience skeleton. A convex skeleton thus represents a simple definition of a network backbone with applications in coauthorship and other social collaboration networks.

scholarly journals Local modal participation analysis of nonlinear systems using Poincaré linearization

2019 ◽  
Vol 99 (1) ◽  
pp. 803-811 ◽  
Author(s):  
Boumediene Hamzi ◽  
Eyad H. Abed
Keyword(s):  
Nonlinear Systems ◽  
Autonomous Systems ◽  
Analytical Formula ◽  
Linear Case ◽  
Local Mode ◽  
Initial Condition ◽  
Initial State ◽  
State Participation ◽  
Symmetry Assumption ◽  
Definition Of

AbstractThe paper studies an extension to nonlinear systems of a recently proposed approach to the definition of modal participation factors. A definition is given for local mode-in-state participation factors for smooth nonlinear autonomous systems. While the definition is general, the resulting measures depend on the assumed uncertainty law governing the system initial condition, as in the linear case. The work follows Hashlamoun et al. (IEEE Trans Autom Control 54(7):1439–1449 2009) in taking a mathematical expectation (or set-theoretic average) of a modal contribution measure over an uncertain set of system initial state. Poincaré linearization is used to replace the nonlinear system with a locally equivalent linear system. It is found that under a symmetry assumption on the distribution of the initial state, the tractable calculation and analytical formula for mode-in-state participation factors found for the linear case persists to the nonlinear setting. This paper is dedicated to the memory of Professor Ali H. Nayfeh.

scholarly journals Betweenness centrality for temporal multiplexes

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Silvia Zaoli ◽  
Piero Mazzarisi ◽  
Fabrizio Lillo
Keyword(s):  
Information Flow ◽  
Real World ◽  
Betweenness Centrality ◽  
Temporal Structure ◽  
Shortest Paths ◽  
Single Layer ◽  
Distance Metric ◽  
Definition Of

AbstractBetweenness centrality quantifies the importance of a vertex for the information flow in a network. The standard betweenness centrality applies to static single-layer networks, but many real world networks are both dynamic and made of several layers. We propose a definition of betweenness centrality for temporal multiplexes. This definition accounts for the topological and temporal structure and for the duration of paths in the determination of the shortest paths. We propose an algorithm to compute the new metric using a mapping to a static graph. We apply the metric to a dataset of $$\sim 20$$ ∼ 20 k European flights and compare the results with those obtained with static or single-layer metrics. The differences in the airports rankings highlight the importance of considering the temporal multiplex structure and an appropriate distance metric.

Gene insulation. Part II: natural strategies in vertebrates

2010 ◽  
Vol 88 (6) ◽  
pp. 885-898 ◽  
Author(s):  
Michèle Amouyal
Keyword(s):  
Gene Expression ◽  
Dna Methylation ◽  
Protein Interactions ◽  
Dna Looping ◽  
Chromatin Domain ◽  
Trna Genes ◽  
Binding Factor ◽  
Genomic Environment ◽  
Nuclear Structures ◽  
Definition Of

The way a gene is insulated from its genomic environment in vertebrates is not basically different from what is observed in yeast and Drosophila (preceding article in this issue). If the formation of a looped chromatin domain, whether generated by attachment to the nuclear matrix or not, has become a classic way to confine an enhancer to a specific genomic domain and to coordinate, sequentially or simultaneously, gene expression in a given program, its role has been extended to new networks of genes or regulators within the same gene. A wider definition of the bases of the chromatin loops (nonchromosomal nuclear structures or genomic interacting elements) is also available. However, whereas insulation in Drosophila is due to a variety of proteins, in vertebrates insulators are still practically limited to CTCF (the CCCTC-binding factor), which appears in all cases to be the linchpin of an architecture that structures the assembly of DNA–protein interactions for gene regulation. As in yeast and Drosophila, the economy of means is the rule and the same unexpected diversion of known transcription elements (active or poised RNA polymerases, TFIIIC elements out of tRNA genes, permanent histone replacement) is observed, with variants peculiar to CTCF. Thus, besides structuring DNA looping, CTCF is a barrier to DNA methylation or interferes with all sorts of transcription processes, such as that generating heterochromatin.

scholarly journals Convexity in complex networks

2018 ◽  
Vol 6 (2) ◽  
pp. 176-203 ◽  
Author(s):  
TILEN MARC ◽  
LOVRO ŠUBELJ
Keyword(s):  
Complex Networks ◽  
Geodesic Distance ◽  
Connected Subgraph ◽  
Geodesic Path ◽  
Connected Subset ◽  
Social Collaboration ◽  
Graph Properties ◽  
Definition Of ◽  
Locally Convex ◽  
Convex Core

AbstractMetric graph properties lie in the heart of the analysis of complex networks, while in this paper we study their convexity through mathematical definition of a convex subgraph. A subgraph is convex if every geodesic path between the nodes of the subgraph lies entirely within the subgraph. According to our perception of convexity, convex network is such in which every connected subset of nodes induces a convex subgraph. We show that convexity is an inherent property of many networks that is not present in a random graph. Most convex are spatial infrastructure networks and social collaboration graphs due to their tree-like or clique-like structure, whereas the food web is the only network studied that is truly non-convex. Core–periphery networks are regionally convex as they can be divided into a non-convex core surrounded by a convex periphery. Random graphs, however, are only locally convex meaning that any connected subgraph of size smaller than the average geodesic distance between the nodes is almost certainly convex. We present different measures of network convexity and discuss its applications in the study of networks.

Molecular Biology of Protein-Protein Interactions for Computer Scientists

2009 ◽  
pp. 1-13 ◽  
Author(s):  
Christian Schönbach
Keyword(s):  
Molecular Biology ◽  
Protein Interactions ◽  
Wnt Signaling Pathway ◽  
Protein Protein Interactions ◽  
Protein Protein Interaction ◽  
Ppi Networks ◽  
Detection Technology ◽  
Challenges And Opportunities ◽  
Computer Scientists ◽  
Assay Methods

Advances in protein-protein interaction (PPI) detection technology and computational analysis methods have produced numerous PPI networks, whose completeness appears to depend on the extent of data derived from different PPI assay methods and the complexity of the studied organism. Despite the partial nature of human PPI networks, computational data integration and analyses helped to elucidate new interactions and disease pathways. The success of computational analyses considerably depends on PPI data understanding. Exploration of the data and verification of their quality requires basic knowledge of the molecular biology of PPIs and familiarity with the assay methods used to detect PPIs. Both topics are reviewed in this chapter. After introducing various types of PPIs the principles of selected PPI assays are explained and their limitations discussed. Case studies of the Wnt signaling pathway and splice regulation demonstrate some of the challenges and opportunities that arise from assaying and analyzing PPIs. The chapter is concluded with an extrapolation to human systems biology that offers a glimpse into the future of PPI networks.

scholarly journals The HUPO Proteomics Standards Initiative Meeting: Towards Common Standards for Exchanging Proteomics Data

2003 ◽  
Vol 4 (1) ◽  
pp. 16-19 ◽  
Author(s):  
Sandra Orchard ◽  
Paul Kersey ◽  
Henning Hermjakob ◽  
Rolf Apweiler
Keyword(s):  
Data Storage ◽  
Mass Spectroscopy ◽  
Protein Interactions ◽  
Data Exchange ◽  
Data Representation ◽  
Protein Protein Interactions ◽  
Proteomics Data ◽  
Inaugural Meeting ◽  
Minimum Requirements ◽  
Definition Of

The Proteomics Standards Initiative (PSI) aims to define community standards for data representation in proteomics and to facilitate data comparison, exchange and verification. Initially the fields of protein–protein interactions (PPI) and mass spectroscopy have been targeted and the inaugural meeting of the PSI addressed the questions of data storage and exchange in both of these areas. The PPI group rapidly reached consensus as to the minimum requirements for a data exchange model; an XML draft is now being produced. The mass spectroscopy group have achieved major advances in the definition of a required data model and working groups are currently taking these discussions further. A further meeting is planned in January 2003 to advance both these projects.

scholarly journals KHOVANOV HOMOLOGY FOR VIRTUAL KNOTS WITH ARBITRARY COEFFICIENTS

2007 ◽  
Vol 16 (03) ◽  
pp. 345-377 ◽  
Author(s):  
VASSILY OLEGOVICH MANTUROV
Keyword(s):  
Spanning Tree ◽  
Classical Case ◽  
Homology Theory ◽  
Homotopy Equivalent ◽  
Khovanov Homology ◽  
Virtual Knots ◽  
Definition Of

In the present paper, we construct Khovanov homology theory with arbitrary coefficients for arbitrary virtual knots. We give a definition of the complex, which is homotopy equivalent to the initial Khovanov complex in the classical case; our definition works in the virtual case as well. The method used in this work allows us to construct a Khovanov homology theory for "twisted virtual knots" in the sense of Bourgoin and Viro [4, 27] (in particular, for knots in RP3). We also generalize some results of the Khovanov homology for virtual knots with arbitrary atoms (Wehrli and Kofman–Champanerkar spanning tree, minimality problems, Frobenius extensions) and orientable ones (Rasmussen's invariant).

Uncertain Distribution-Minimum Spanning Tree Problem

2016 ◽  
Vol 24 (04) ◽  
pp. 537-560 ◽  
Author(s):  
Jian Zhou ◽  
Xiajie Yi ◽  
Ke Wang ◽  
Jing Liu
Keyword(s):  
Risk Management ◽  
Value At Risk ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Graph Transformation ◽  
Numerical Examples ◽  
Uncertain Variables ◽  
Minimum Spanning Tree Problem ◽  
Definition Of ◽  
Uncertain Distribution

This paper studies the minimum spanning tree problem on a graph with uncertain edge weights, which are formulated as uncertain variables. The concept of ideal uncertain minimum spanning tree (ideal UMST) is initiated by extending the definition of the uncertain [Formula: see text]-minimum spanning tree to reect the overall properties of the α-minimum spanning tree weights at any confidence level [Formula: see text]. On the basis of this new concept, the definition of uncertain distribution-minimum spanning tree is proposed in three ways. Particularly, by considering the tail value at risk from the perspective of risk management, the notion of uncertain [Formula: see text]-distribution-minimum spanning tree ([Formula: see text]-distribution-UMST) is suggested. It is shown that the [Formula: see text]-distribution-UMST is just the uncertain expected minimum spanning tree when [Formula: see text] = 0. For any [Formula: see text], this problem can be effectively solved via the proposed deterministic graph transformation-based approach with the aid of the [Formula: see text]-distribution-path optimality condition. Furthermore, the proposed definitions and solutions are illustrated by some numerical examples.

Power Networks Coordinated Planning Based on Improved Steiner Minimum Spanning Tree Theory

2012 ◽  
Vol 433-440 ◽  
pp. 1903-1909
Author(s):  
Han Lin Liu ◽  
Jin Liang Jiang ◽  
Yong Jun Zhang
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Distribution Network ◽  
Weight Coefficient ◽  
Power Networks ◽  
Basic Properties ◽  
Definition Of ◽  
Load Weight ◽  
Better Than

110kV substation’s location and supply area is the crux of the coordination planning for main and distribution network. In this paper, an approach to the coordinated planning of the main grid and distribution network is proposed, which is based on improved weighted Steiner minimum spanning tree theory. This paper will analysis the basic properties of substation firstly, make the definition of Load Weight Coefficient, then use a bound circle to delineate the optimization area. At last, make Load Weight Coefficient as weight, use improved weighted Steiner minimum spanning tree theory to determine the final location of substation. Actual examples show that, in favor of coordinated planning, this method result is obviously better than traditional model’s.

scholarly journals Grundy Domination of Forests and the Strong Product Conjecture

10.37236/9507 ◽  
2021 ◽  
Vol 28 (2) ◽  
Author(s):  
Kayla Bell ◽  
Keith Driscoll ◽  
Elliot Krop ◽  
Kimber Wolff
Keyword(s):  
Connected Graph ◽  
Spanning Tree ◽  
Dominating Set ◽  
Domination Number ◽  
Induced Subgraph ◽  
Strong Product ◽  
Toroidal Graphs ◽  
Maximum Sequence

A maximum sequence $S$ of vertices in a graph $G$, so that every vertex in $S$ has a neighbor which is independent, or is itself independent, from all previous vertices in $S$, is called a Grundy dominating sequence. The Grundy domination number, $\gamma_{gr}(G)$, is the length of $S$. We show that for any forest $F$, $\gamma_{gr}(F)=|V(T)|-|\mathcal{P}|$ where $\mathcal{P}$ is a minimum partition of the non-isolate vertices of $F$ into caterpillars in which if two caterpillars of $\mathcal{P}$ have an edge between them in $F$, then such an edge must be incident to a non-leaf vertex in at least one of the caterpillars. We use this result to show the strong product conjecture of B. Brešar, Cs. Bujtás, T. Gologranc, S. Klavžar, G. Košmrlj, B.~Patkós, Zs. Tuza, and M. Vizer, Dominating sequences in grid-like and toroidal graphs, Electron. J. Combin. 23(4): P4.34 (2016), for all forests. Namely, we show that for any forest $G$ and graph $H$, $\gamma_{gr}(G \boxtimes H) = \gamma_{gr}(G) \gamma_{gr}(H)$. We also show that every connected graph $G$ has a spanning tree $T$ so that $\gamma_{gr}(G)\le \gamma_{gr}(T)$ and that every non-complete connected graph contains a Grundy dominating set $S$ so that the induced subgraph of $S$ contains no isolated vertices. 

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