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Cancers remain the lead cause of disease-related, pediatric death in North America. The emerging field of complex systems has redefined cancer networks as a computational system with intractable algorithmic complexity. Herein, a tumor and…
The representation of complex systems as networks is inappropriate for the study of certain problems. We show several examples of social, biological, ecological and technological systems where the use of complex networks gives very limited…
In recent years, deep neural network is introduced in recommender systems to solve the collaborative filtering problem, which has achieved immense success on computer vision, speech recognition and natural language processing. On one hand,…
Complex diseases can be modeled as damage to intracellular networks that results in abnormal cell behaviors. Network-based dynamic models such as Boolean models have been employed to model a variety of biological systems including those…
The problem of controlling complex networks is of interest to disciplines ranging from biology to swarm robotics. However, controllability can be too strict a condition, failing to capture a range of desirable behaviors. Herdability, which…
Biological systems, from a cell to the human brain, are inherently complex. A powerful representation of such systems, described by an intricate web of relationships across multiple scales, is provided by complex networks. Recently, several…
Real complex systems are not rigidly structured; no clear rules or blueprints exist for their construction. Yet, amidst their apparent randomness, complex structural properties universally emerge. We propose that an important class of…
Complex systems and their underlying convoluted networks are ubiquitous, all we need is an eye for them. They pose problems of organized complexity which cannot be approached with a reductionist method. Complexity science and its emergent…
A coupled cell network is a model for many situations such as food webs in ecosystems, cellular metabolism, economical networks... It consists in a directed graph $G$, each node (or cell) representing an agent of the network and each…
Genomic alterations lead to cancer complexity and form a major hurdle for a comprehensive understanding of the molecular mechanisms underlying oncogenesis. In this review, we describe the recent advances in studying cancer-associated genes…
Binary-state models are those in which the constituent elements can only appear in two possible configurations. These models are fundamental in the mathematical treatment of a number of phenomena such as spin interactions in magnetism,…
Understanding the origins of complexity is a fundamental challenge with implications for biological and technological systems. Network theory emerges as a powerful tool to model complex systems. Networks are an intuitive framework to…
Systems composed of distinct complex networks are present in many real-world environments, from society to ecological systems. In the present paper, we propose a network model obtained as a consequence of interactions between two species…
Complex networks describe a wide range of systems in nature and society. Frequently cited examples include Internet, WWW, a network of chemicals linked by chemical reactions, social relationship networks, citation networks, etc. The…
We give a constructive method for realizing an arbitrary directed graph (with no one-cycles) as a heteroclinic or an excitable dynamic network in the phase space of a system of coupled cells of two types. In each case, the system is…
A complex network is a condensed representation of the relational topological framework of a complex system. A main reason for the existence of such networks is the transmission of items through the entities of these complex systems. Here,…
Recent progress in applying complex network theory to problems in quantum information has resulted in a beneficial crossover. Complex network methods have successfully been applied to transport and entanglement models while information…
A common trait of complex systems is that they can be represented by means of a network of interacting parts. It is, in fact, the network organisation (more than the parts) what largely conditions most higher-level properties, which are not…
Modern biological tools have made it possible to unequivocally demonstrate the deep relationship among species in terms of genes and basic molecular mechanisms. In addition, results from genetic, physical and physiological approaches…
Networked structures arise in a wide array of different contexts such as technological and transportation infrastructures, social phenomena, and biological systems. These highly interconnected systems have recently been the focus of a great…