scholarly journals A Multilayer Structure Facilitates the Production of Antifragile Systems in Boolean Network Models

Complexity ◽  
2019 ◽  
Vol 2019 ◽  
pp. 1-11 ◽  
Author(s):  
Hyobin Kim ◽  
Omar K. Pineda ◽  
Carlos Gershenson
Keyword(s):  
Complex Systems ◽  
Real World ◽  
Multilayer Structure ◽  
Boolean Network ◽  
Single Layer ◽  
Network Models ◽  
Boolean Networks ◽  
Multilayer Structures ◽  
Multilayer Networks ◽  
Engineered Systems

Antifragility is a property from which systems are able to resist stress and furthermore benefit from it. Even though antifragile dynamics is found in various real-world complex systems where multiple subsystems interact with each other, the attribute has not been quantitatively explored yet in those complex systems which can be regarded as multilayer networks. Here we study how the multilayer structure affects the antifragility of the whole system. By comparing single-layer and multilayer Boolean networks based on our recently proposed antifragility measure, we found that the multilayer structure facilitated the production of antifragile systems. Our measure and findings will be useful for various applications such as exploring properties of biological systems with multilayer structures and creating more antifragile engineered systems.

scholarly journals Deriving a Boolean dynamics to reveal macrophage activation with in vitro temporal cytokine expression profiles

2019 ◽  
Vol 20 (1) ◽  
Author(s):  
Ricardo Ramirez ◽  
Allen Michael Herrera ◽  
Joshua Ramirez ◽  
Chunjiang Qian ◽  
David W. Melton ◽  
...  
Keyword(s):  
Boolean Network ◽  
Macrophage Activation ◽  
Expression Profiles ◽  
Network Models ◽  
Cytokine Expression ◽  
Boolean Networks ◽  
Experimental Results ◽  
Activated Macrophages ◽  
Activation Patterns

Abstract Background Macrophages show versatile functions in innate immunity, infectious diseases, and progression of cancers and cardiovascular diseases. These versatile functions of macrophages are conducted by different macrophage phenotypes classified as classically activated macrophages and alternatively activated macrophages due to different stimuli in the complex in vivo cytokine environment. Dissecting the regulation of macrophage activations will have a significant impact on disease progression and therapeutic strategy. Mathematical modeling of macrophage activation can improve the understanding of this biological process through quantitative analysis and provide guidance to facilitate future experimental design. However, few results have been reported for a complete model of macrophage activation patterns. Results We globally searched and reviewed literature for macrophage activation from PubMed databases and screened the published experimental results. Temporal in vitro macrophage cytokine expression profiles from published results were selected to establish Boolean network models for macrophage activation patterns in response to three different stimuli. A combination of modeling methods including clustering, binarization, linear programming (LP), Boolean function determination, and semi-tensor product was applied to establish Boolean networks to quantify three macrophage activation patterns. The structure of the networks was confirmed based on protein-protein-interaction databases, pathway databases, and published experimental results. Computational predictions of the network evolution were compared against real experimental results to validate the effectiveness of the Boolean network models. Conclusion Three macrophage activation core evolution maps were established based on the Boolean networks using Matlab. Cytokine signatures of macrophage activation patterns were identified, providing a possible determination of macrophage activations using extracellular cytokine measurements.

Complex Systems as Multilayer Networks

2018 ◽  
Author(s):  
Ginestra Bianconi
Keyword(s):  
Complex Systems ◽  
Information Gain ◽  
Single Layer ◽  
Multilayer Networks ◽  
Research Activity ◽  
Multilayer Network ◽  
New Development ◽  
The Rich ◽  
And Function

Chapter 1 constitutes Part I of the book: ‘Single and Multilayer Networks’. This chapter introduces multilayer networks as an important new development of Network Science that allows a more comprehensive understanding of Complex Systems. It identifies the main motivations driving the research activity in this field of multilayer networks and emphasizes the benefits of taking a multilayer network perpective to characterize network data. The main advantages of a multilayer network approach with respect to the more traditional single layer characterization of complex networks are broadly discussed, focusing on the information gain resulting from the analysis of multilayer networks, the non-reducibility of a multilayer network to a large single network and the rich interplay between structure and function in multilayer networks.

scholarly journals On the Number of Driver Nodes for Controlling a Boolean Network to Attractors

2018 ◽  
Author(s):  
Wenpin Hou ◽  
Peiying Ruan ◽  
Wai-Ki Ching ◽  
Tatsuya Akutsu
Keyword(s):  
Biological Networks ◽  
Boolean Network ◽  
Network Models ◽  
Boolean Networks ◽  
Reasonable Assumption ◽  
Control Problems ◽  
Expected Number ◽  
Linear Complex ◽  
Simulation Results ◽  
Control Complex

AbstractIt is known that many driver nodes are required to control complex biological networks. Previous studies imply that O(N) driver nodes are required in both linear complex network and Boolean network models with N nodes if an arbitrary state is specified as the target. In this paper, we mathematically prove under a reasonable assumption that the expected number of driver nodes is only O(log2N + log2M) for controlling Boolean networks if the targets are restricted to attractors, where M is the number of attractors. Since it is expected that M is not very large in many practical networks, this is a significant improvement. This result is based on discovery of novel relationships between control problems on Boolean networks and the coupon collector’s problem, a well-known concept in combinatorics. We also provide lower bounds of the number of driver nodes as well as simulation results using artificial and realistic network data, which support our theoretical findings.

scholarly journals Multilayer Networks in a Nutshell

2019 ◽  
Vol 10 (1) ◽  
pp. 45-62 ◽  
Author(s):  
Alberto Aleta ◽  
Yamir Moreno
Keyword(s):  
Complex Systems ◽  
General Framework ◽  
Network Science ◽  
Single Layer ◽  
Emergent Behavior ◽  
Technological Systems ◽  
Multilayer Networks ◽  
Dynamical Processes ◽  
Multilayer Systems ◽  
The Past

Complex systems are characterized by many interacting units that give rise to emergent behavior. A particularly advantageous way to study these systems is through the analysis of the networks that encode the interactions among the system constituents. During the past two decades, network science has provided many insights in natural, social, biological, and technological systems. However, real systems are often interconnected, with many interdependencies that are not properly captured by single-layer networks. To account for this source of complexity, a more general framework, in which different networks evolve or interact with each other, is needed. These are known as multilayer networks. Here, we provide an overview of the basic methodology used to describe multilayer systems as well as of some representative dynamical processes that take place on top of them. We round off the review with a summary of several applications in diverse fields of science.

scholarly journals Application of Multilayer Network Models in Bioinformatics

2021 ◽  
Vol 12 ◽  
Author(s):  
Yuanyuan Lv ◽  
Shan Huang ◽  
Tianjiao Zhang ◽  
Bo Gao
Keyword(s):  
Evaluation Method ◽  
Brain Research ◽  
Single Layer ◽  
Network Models ◽  
Assessment Method ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Biological Studies ◽  
Quality Assessment Method ◽  
Object Of Study

Multilayer networks provide an efficient tool for studying complex systems, and with current, dramatic development of bioinformatics tools and accumulation of data, researchers have applied network concepts to all aspects of research problems in the field of biology. Addressing the combination of multilayer networks and bioinformatics, through summarizing the applications of multilayer network models in bioinformatics, this review classifies applications and presents a summary of the latest results. Among them, we classify the applications of multilayer networks according to the object of study. Furthermore, because of the systemic nature of biology, we classify the subjects into several hierarchical categories, such as cells, tissues, organs, and groups, according to the hierarchical nature of biological composition. On the basis of the complexity of biological systems, we selected brain research for a detailed explanation. We describe the application of multilayer networks and chronological networks in brain research to demonstrate the primary ideas associated with the application of multilayer networks in biological studies. Finally, we mention a quality assessment method focusing on multilayer and single-layer networks as an evaluation method emphasizing network studies.

SIMPLIFYING BOOLEAN NETWORKS

2005 ◽  
Vol 08 (04) ◽  
pp. 365-381 ◽  
Author(s):  
KURT A. RICHARDSON
Keyword(s):  
Complex Systems ◽  
Random Sample ◽  
Random Sampling ◽  
Boolean Network ◽  
Sampling Rate ◽  
Network Size ◽  
Boolean Networks ◽  
Sample Method ◽  
Random Sampling Approach ◽  
Sampling Approach

This paper explores the compressibility of complex systems by considering the simplification of Boolean networks. A method, which is similar to that reported by Bastolla and Parisi,4,5 is considered that is based on the removal of frozen nodes, or stable variables, and network "leaves," i.e. those nodes with outdegree = 0. The method uses a random sampling approach to identify the minimum set of frozen nodes. This set contains the nodes that are frozen in all attractor schemes. Although the method can over-estimate the size of the minimum set of frozen nodes, it is found that the chances of finding this minimum set are considerably greater than finding the full attractor set using the same sampling rate. Given that the number of attractors not found for a particular Boolean network increases with the network size, for any given sampling rate, such a method provides an opportunity to either fully enumerate the attractor set for a particular network, or improve the accuracy of the random sampling approach. Indeed, the paper also shows that when it comes to the counting of attractors in an ensemble of Boolean networks, enhancing the random sample method with the simplification method presented results in a significant improvement in accuracy.

scholarly journals The Influence of Canalization on the Robustness of Boolean Networks

2016 ◽  
Author(s):  
C. Kadelka ◽  
J. Kuipers ◽  
R. Laubenbacher
Keyword(s):  
Boolean Functions ◽  
Boolean Network ◽  
Network Models ◽  
Discrete Dynamical Systems ◽  
Boolean Networks ◽  
Molecular Networks ◽  
Weighted Sum ◽  
Computationally Efficient ◽  
Computational Tools ◽  
The Impact

AbstractTime- and state-discrete dynamical systems are frequently used to model molecular networks. This paper provides a collection of mathematical and computational tools for the study of robustness in Boolean network models. The focus is on networks governed by k-canalizing functions, a recently introduced class of Boolean functions that contains the well-studied class of nested canalizing functions. The activities and sensitivity of a function quantify the impact of input changes on the function output. This paper generalizes the latter concept to c-sensitivity and provides formulas for the activities and c-sensitivity of general k-canalizing functions as well as canalizing functions with more precisely defined structure. A popular measure for the robustness of a network, the Derrida value, can be expressed as a weighted sum of the c-sensitivities of the governing canalizing functions, and can also be calculated for a stochastic extension of Boolean networks. These findings provide a computationally efficient way to obtain Derrida values of Boolean networks, deterministic or stochastic, that does not involve simulation.

Link prediction for multilayer networks using interlayer structural information

2021 ◽  
Author(s):  
Fengqin Tang ◽  
Chunning Wang ◽  
Yuanyuan Wang ◽  
Jinxia Su
Keyword(s):  
Complex Systems ◽  
Real World ◽  
Link Prediction ◽  
Prediction Accuracy ◽  
Structural Information ◽  
Multilayer Networks ◽  
Multilayer Network ◽  
Type Form ◽  
Target Layer

A multilayer network is a useful representation for real-world complex systems in which multiple types of connections are formed between entities. Connections of the same type form a specific layer of the network. We propose a novel framework for predicting links in a target layer of a multilayer network by taking into account the interlayer structural information. The method depends on the intuitive assumption that two node pairs in the target layer tend to have similar connection patterns if these pairs of nodes are similar. Further, the prediction accuracy will be improved in the target layer if the structural information of the copies of the node pairs in relevant layers is employed. We demonstrate the effectiveness of the proposed method experimentally by applying it to both simulated and real-world multilayer networks.

Networks

2018 ◽  
Author(s):  
Stefan Thurner ◽  
Rudolf Hanel ◽  
Peter Klimekl
Keyword(s):  
Complex Systems ◽  
Complex Networks ◽  
Phase Diagrams ◽  
Community Detection ◽  
Network Science ◽  
Small World ◽  
Small World Networks ◽  
Multilayer Networks ◽  
Basic Vocabulary

Understanding the interactions between the components of a system is key to understanding it. In complex systems, interactions are usually not uniform, not isotropic and not homogeneous: each interaction can be specific between elements.Networks are a tool for keeping track of who is interacting with whom, at what strength, when, and in what way. Networks are essential for understanding of the co-evolution and phase diagrams of complex systems. Here we provide a self-contained introduction to the field of network science. We introduce ways of representing and handle networks mathematically and introduce the basic vocabulary and definitions. The notions of random- and complex networks are reviewed as well as the notions of small world networks, simple preferentially grown networks, community detection, and generalized multilayer networks.

Controllability of Boolean networks with intermittent disturbances

2020 ◽  
Vol 34 (28) ◽  
pp. 2050309
Author(s):  
Tao You ◽  
Hailun Zhang ◽  
Mingyu Yang ◽  
Xiao Wang ◽  
Yangming Guo
Keyword(s):  
Gene Expression ◽  
Boolean Network ◽  
Boolean Networks ◽  
Genetic Mutations ◽  
Intermittent Control ◽  
Mathematical Tool ◽  
Pulse Control ◽  
Expression Of Genes ◽  
Complicated Process ◽  
Living Being

In biological systems, gene expression is an important subject. In order to clarify the specific process of gene expression, mathematical tools are needed to simulate the process. The Boolean network (BN) is a good mathematical tool. In this paper, we study a Boolean network with intermittent perturbations. This is of great significance for studying genetic mutations in bioengineering. The expression of genes in the internal system of a living being is a very complicated process, and it is clear that the process is trans-ageal for humans. Through the intermittent control and pulse control of the BN, we can obtain the trajectory of gene expression better and faster, which will provide a very important theoretical basis for our next research.

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