scholarly journals Dynamics and processing in finite self-similar networks

2012 ◽  
Vol 9 (74) ◽  
pp. 2131-2144 ◽  
Author(s):  
Simon DeDeo ◽  
David C. Krakauer
Keyword(s):  
Time Scales ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Multiple Scales ◽  
Social Systems ◽  
Small World ◽  
System Size ◽  
Low Noise ◽  
Trophic Networks ◽  
Self Similar

A common feature of biological networks is the geometrical property of self-similarity. Molecular regulatory networks through to circulatory systems, nervous systems, social systems and ecological trophic networks show self-similar connectivity at multiple scales. We analyse the relationship between topology and signalling in contrasting classes of such topologies. We find that networks differ in their ability to contain or propagate signals between arbitrary nodes in a network depending on whether they possess branching or loop-like features. Networks also differ in how they respond to noise, such that one allows for greater integration at high noise, and this performance is reversed at low noise. Surprisingly, small-world topologies, with diameters logarithmic in system size, have slower dynamical time scales, and may be less integrated (more modular) than networks with longer path lengths. All of these phenomena are essentially mesoscopic, vanishing in the infinite limit but producing strong effects at sizes and time scales relevant to biology.

Algorithmic and Stochastic Representations of Gene Regulatory Networks and Protein-Protein Interactions

2019 ◽  
Vol 19 (6) ◽  
pp. 413-425 ◽  
Author(s):  
Athanasios Alexiou ◽  
Stylianos Chatzichronis ◽  
Asma Perveen ◽  
Abdul Hafeez ◽  
Ghulam Md. Ashraf
Keyword(s):  
Protein Interactions ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Review Paper ◽  
Boolean Networks ◽  
Diagnostic Tools ◽  
Complex Nature ◽  
Cellular Interactions ◽  
Protein Protein Interactions ◽  
Deterministic Models

Background:Latest studies reveal the importance of Protein-Protein interactions on physiologic functions and biological structures. Several stochastic and algorithmic methods have been published until now, for the modeling of the complex nature of the biological systems.Objective:Biological Networks computational modeling is still a challenging task. The formulation of the complex cellular interactions is a research field of great interest. In this review paper, several computational methods for the modeling of GRN and PPI are presented analytically.Methods:Several well-known GRN and PPI models are presented and discussed in this review study such as: Graphs representation, Boolean Networks, Generalized Logical Networks, Bayesian Networks, Relevance Networks, Graphical Gaussian models, Weight Matrices, Reverse Engineering Approach, Evolutionary Algorithms, Forward Modeling Approach, Deterministic models, Static models, Hybrid models, Stochastic models, Petri Nets, BioAmbients calculus and Differential Equations.Results:GRN and PPI methods have been already applied in various clinical processes with potential positive results, establishing promising diagnostic tools.Conclusion:In literature many stochastic algorithms are focused in the simulation, analysis and visualization of the various biological networks and their dynamics interactions, which are referred and described in depth in this review paper.

scholarly journals BioNetLink - An Architecture for Working with Network Data

2014 ◽  
Vol 11 (2) ◽  
pp. 68-79
Author(s):  
Matthias Klapperstück ◽  
Falk Schreiber
Keyword(s):  
Experimental Data ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Large Data ◽  
Biological Data ◽  
Network Data ◽  
Data Sets ◽  
Dynamic Views ◽  
Gene Regulatory ◽  
Multiple Network

Summary The visualization of biological data gained increasing importance in the last years. There is a large number of methods and software tools available that visualize biological data including the combination of measured experimental data and biological networks. With growing size of networks their handling and exploration becomes a challenging task for the user. In addition, scientists also have an interest in not just investigating a single kind of network, but on the combination of different types of networks, such as metabolic, gene regulatory and protein interaction networks. Therefore, fast access, abstract and dynamic views, and intuitive exploratory methods should be provided to search and extract information from the networks. This paper will introduce a conceptual framework for handling and combining multiple network sources that enables abstract viewing and exploration of large data sets including additional experimental data. It will introduce a three-tier structure that links network data to multiple network views, discuss a proof of concept implementation, and shows a specific visualization method for combining metabolic and gene regulatory networks in an example.

scholarly journals Small world in a seismic network: the California case

2008 ◽  
Vol 15 (3) ◽  
pp. 389-395 ◽  
Author(s):  
A. Jiménez ◽  
K. F. Tiampo ◽  
A. M. Posadas
Keyword(s):  
Complex Networks ◽  
Recent Work ◽  
Brain Activity ◽  
Social Systems ◽  
Small World ◽  
Functional Networks ◽  
Topological Properties ◽  
Southern California Region ◽  
Seismic Area ◽  
The Brain

Abstract. Recent work has shown that disparate systems can be described as complex networks i.e. assemblies of nodes and links with nontrivial topological properties. Examples include technological, biological and social systems. Among them, earthquakes have been studied from this perspective. In the present work, we divide the Southern California region into cells of 0.1°, and calculate the correlation of activity between them to create functional networks for that seismic area, in the same way that the brain activity is studied from the complex network perspective. We found that the network shows small world features.

SMALL-WORLD AND SCALE-FREE PROPERTIES OF FRACTAL NETWORKS MODELED ON n-DIMENSIONAL SIERPINSKI PYRAMID

Fractals ◽  
2017 ◽  
Vol 25 (06) ◽  
pp. 1750057 ◽  
Author(s):  
CHENG ZENG ◽  
MENG ZHOU
Keyword(s):  
Small World ◽  
The Self ◽  
Scale Free ◽  
Evolving Networks ◽  
Self Similar

In this paper, we construct evolving networks based on the construction of the [Formula: see text]-dimensional Sierpinski pyramid by the self-similar structure. We show that such networks have scale-free and small-world effects.

The Shortest Path to Network Geometry

2021 ◽  
Author(s):  
M. Ángeles Serrano ◽  
Marián Boguñá
Keyword(s):  
Routing Protocols ◽  
Hyperbolic Plane ◽  
Network Science ◽  
Small World ◽  
The Self ◽  
Geometric Description ◽  
Apparent Lack ◽  
Network Geometry ◽  
Connectivity Patterns ◽  
Self Similar

Real networks comprise from hundreds to millions of interacting elements and permeate all contexts, from technology to biology to society. All of them display non-trivial connectivity patterns, including the small-world phenomenon, making nodes to be separated by a small number of intermediate links. As a consequence, networks present an apparent lack of metric structure and are difficult to map. Yet, many networks have a hidden geometry that enables meaningful maps in the two-dimensional hyperbolic plane. The discovery of such hidden geometry and the understanding of its role have become fundamental questions in network science giving rise to the field of network geometry. This Element reviews fundamental models and methods for the geometric description of real networks with a focus on applications of real network maps, including decentralized routing protocols, geometric community detection, and the self-similar multiscale unfolding of networks by geometric renormalization.

scholarly journals Genes and environments, development and time

2020 ◽  
Vol 117 (38) ◽  
pp. 23235-23241
Author(s):  
W. Thomas Boyce ◽  
Marla B. Sokolowski ◽  
Gene E. Robinson
Keyword(s):  
Regulatory Networks ◽  
Multiple Scales ◽  
Stressful Events ◽  
Critical Periods ◽  
Gene Environment ◽  
And Behavior ◽  
Influence Gene Expression ◽  
Dynamic Interplay ◽  
Epigenetic Processes

A now substantial body of science implicates a dynamic interplay between genetic and environmental variation in the development of individual differences in behavior and health. Such outcomes are affected by molecular, often epigenetic, processes involving gene–environment (G–E) interplay that can influence gene expression. Early environments with exposures to poverty, chronic adversities, and acutely stressful events have been linked to maladaptive development and compromised health and behavior. Genetic differences can impart either enhanced or blunted susceptibility to the effects of such pathogenic environments. However, largely missing from present discourse regarding G–E interplay is the role of time, a “third factor” guiding the emergence of complex developmental endpoints across different scales of time. Trajectories of development increasingly appear best accounted for by a complex, dynamic interchange among the highly linked elements of genes, contexts, and time at multiple scales, including neurobiological (minutes to milliseconds), genomic (hours to minutes), developmental (years and months), and evolutionary (centuries and millennia) time. This special issue of PNAS thus explores time and timing among G–E transactions: The importance of timing and timescales in plasticity and critical periods of brain development; epigenetics and the molecular underpinnings of biologically embedded experience; the encoding of experience across time and biological levels of organization; and gene-regulatory networks in behavior and development and their linkages to neuronal networks. Taken together, the collection of papers offers perspectives on how G–E interplay operates contingently within and against a backdrop of time and timescales.

Measuring Information Propagation and Processing in Biological Systems

2009 ◽  
pp. 190-226
Author(s):  
Juha Kesseli ◽  
Andre S. Ribeiro ◽  
Matti Nykter
Keyword(s):  
Information Processing ◽  
Dynamical Systems ◽  
Biological Networks ◽  
Regulatory Networks ◽  
Dynamical Behavior ◽  
Measurement Data ◽  
Distribution Data ◽  
Information Propagation ◽  
Information Management Systems ◽  
Element Activity

In this chapter the authors study the propagation and processing of information in dynamical systems. Various information management systems can be represented as dynamical systems of interconnected information processing units. Here they focus mostly on genetic regulatory networks that are information processing systems that process and propagate information stored in genome. Boolean networks are used as a dynamical model of regulation, and different ways of parameterizing the dynamical behavior are studied. What are called critical networks are in particular under study, since they have been hypothesized as being the most effective under evolutionary pressure. Critical networks are also present in man-made systems, such as the Internet, and provide a candidate application area for findings on the theory of dynamical networks in this chapter. The authors present approaches of annealed approximation and find that avalanche size distribution data supports criticality of regulatory networks. Based on Shannon information, they then find that a mutual information measure quantifying the coordination of pairwise element activity is maximized at criticality. An approach of algorithmic complexity, the normalized compression distance (NCD), is shown to be applicable to both dynamical and topological features of regulatory networks. NCD can also be seen to enable further utilization of measurement data to estimate information propagation and processing in biological networks.

scholarly journals Predicting N-Strain Coexistence from Co-colonization Interactions: Epidemiology Meets Ecology and the Replicator Equation

2020 ◽  
Vol 82 (11) ◽  
Author(s):  
Sten Madec ◽  
Erida Gjini
Keyword(s):  
Species Interactions ◽  
Community Dynamics ◽  
Secondary Infection ◽  
Social Systems ◽  
System Size ◽  
Replicator Equation ◽  
Efficient Computation ◽  
Volterra Systems ◽  
Infection Processes ◽  
Resistance To Invasion

AbstractMulti-type infection processes are ubiquitous in ecology, epidemiology and social systems, but remain hard to analyze and to understand on a fundamental level. Here, we study a multi-strain susceptible-infected-susceptible model with coinfection. A host already colonized by one strain can become more or less vulnerable to co-colonization by a second strain, as a result of facilitating or competitive interactions between the two. Fitness differences between N strains are mediated through $$N^2$$ N 2 altered susceptibilities to secondary infection that depend on colonizer-cocolonizer identities ($$K_{ij}$$ K ij ). By assuming strain similarity in such pairwise traits, we derive a model reduction for the endemic system using separation of timescales. This ‘quasi-neutrality’ in trait space sets a fast timescale where all strains interact neutrally, and a slow timescale where selective dynamics unfold. We find that these slow dynamics are governed by the replicator equation for N strains. Our framework allows to build the community dynamics bottom-up from only pairwise invasion fitnesses between members. We highlight that mean fitness of the multi-strain network, changes with their individual dynamics, acts equally upon each type, and is a key indicator of system resistance to invasion. By uncovering the link between N-strain epidemiological coexistence and the replicator equation, we show that the ecology of co-colonization relates to Fisher’s fundamental theorem and to Lotka-Volterra systems. Besides efficient computation and complexity reduction for any system size, these results open new perspectives into high-dimensional community ecology, detection of species interactions, and evolution of biodiversity.

scholarly journals ADVANCED DYNAMIC ALGORITHMS FOR THE DECAY OF METASTABLE PHASES IN DISCRETE SPIN MODELS: BRIDGING DISPARATE TIME SCALES

1999 ◽  
Vol 10 (08) ◽  
pp. 1483-1493 ◽  
Author(s):  
M. A. NOVOTNY
Keyword(s):  
Monte Carlo ◽  
Markov Chains ◽  
Transfer Matrix ◽  
Time Scales ◽  
System Size ◽  
Metastable Phases ◽  
Spin Models ◽  
Dynamic Algorithms ◽  
Absorbing Markov Chains

An overview of advanced dynamical algorithms capable of spanning the widely disparate time scales that govern the decay of metastable phases in discrete spin models is presented. The algorithms discussed include constrained transfer-matrix, Monte Carlo with Absorbing Markov Chains (MCAMC), and projective dynamics (PD) methods. The strengths and weaknesses of each of these algorithms are discussed, with particular emphasis on identifying the parameter regimes (system size, temperature, and field) in which each algorithm works best.

scholarly journals Biological network analysis with deep learning

2020 ◽  
Author(s):  
Giulia Muzio ◽  
Leslie O’Bray ◽  
Karsten Borgwardt
Keyword(s):  
Neural Networks ◽  
Deep Learning ◽  
Biological Networks ◽  
Protein Function ◽  
Regulatory Networks ◽  
Biological Network ◽  
Gene Interaction ◽  
Disease Diagnosis ◽  
Interaction Prediction ◽  
Graph Neural Networks

Abstract Recent advancements in experimental high-throughput technologies have expanded the availability and quantity of molecular data in biology. Given the importance of interactions in biological processes, such as the interactions between proteins or the bonds within a chemical compound, this data is often represented in the form of a biological network. The rise of this data has created a need for new computational tools to analyze networks. One major trend in the field is to use deep learning for this goal and, more specifically, to use methods that work with networks, the so-called graph neural networks (GNNs). In this article, we describe biological networks and review the principles and underlying algorithms of GNNs. We then discuss domains in bioinformatics in which graph neural networks are frequently being applied at the moment, such as protein function prediction, protein–protein interaction prediction and in silico drug discovery and development. Finally, we highlight application areas such as gene regulatory networks and disease diagnosis where deep learning is emerging as a new tool to answer classic questions like gene interaction prediction and automatic disease prediction from data.

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