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Cancers are complex adaptive diseases regulated by the nonlinear feedback systems between genetic instabilities, environmental signals, cellular protein flows, and gene regulatory networks. Understanding the cybernetics of cancer requires…
We study the effect of learning dynamics on network topology. A network of discrete dynamical systems is considered for this purpose and the coupling strengths are made to evolve according to a temporal learning rule that is based on the…
The response to a knockout of a node is a characteristic feature of a networked dynamical system. Knockout resilience in the dynamics of the remaining nodes is a sign of robustness. Here we study the effect of knockouts for binary state…
We formulate general rules for a coarse-graining of the dynamics, which we term `symbolic dynamics', of feedback networks with monotone interactions, such as most biological modules. Networks which are more complex than simple cyclic…
In this review we discuss different mathematical models of gene regulatory networks as relevant to the onset and development of cancer. After discussion of alternative modelling approaches, we use a paradigmatic two-gene network to focus on…
The response of complex networks to perturbations is of utmost importance in areas as diverse as ecosystem management, emergency response, and cell reprogramming. A fundamental property of networks is that the perturbation of one node can…
We develop a general method to explore how the function performed by a biological network can constrain both its structural and dynamical network properties. This approach is orthogonal to prior studies which examine the functional…
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains to be an outstanding problem. We develop an experimentally feasible control framework for nonlinear…
Recent genomic and bioinformatic advances have motivated the development of numerous random network models purporting to describe graphs of biological, technological, and sociological origin. The success of a model has been evaluated by how…
Evolving network models under a dynamic growth rule which comprises the addition and deletion of nodes are investigated. By adding a node with a probability $P_a$ or deleting a node with the probability $P_d=1-P_a$ at each time step, where…
Structural and dynamical fingerprints of evolutionary optimization in biological networks are still unclear. We here analyze the dynamics of genetic regulatory networks responsible for the regulation of cell cycle and cell differentiation…
This thesis is a compendium of research which brings together ideas from the fields of Complex Networks and Computational Neuroscience to address two questions regarding neural systems: 1) How the activity of neurons, via synaptic changes,…
Tumour heterogeneity is increasingly recognized as a major obstacle to therapeutic success across neuro-oncology. Gliomas are characterised by distinct combinations of genetic and epigenetic alterations, resulting in complex interactions…
The principles underlying protein folding remains one of Nature's puzzles with important practical consequences for Life. An approach that has gathered momentum since the late 1990's, looks at protein hetero-polymers and their folding…
We present the mechanism of interaction of Wnt network module, which is responsible for periodic sometogenesis, with p53 regulatory network, which is one of the main regulators of various cellular functions, and switching of various…
Boolean networks are popular tools for the exploration of qualitative dynamical properties of biological systems. Several dynamical interpretations have been proposed based on the same logical structure that captures the interactions…
Recent progress in experimental techniques has enabled us to quantitatively study stochastic and flexible behavior of biological systems. For example, gene regulatory networks perform stochastic information processing and their…
Attractor dynamics are a fundamental computational motif in neural circuits, supporting diverse cognitive functions through stable, self-sustaining patterns of neural activity. In these lecture notes, we review four key examples that…
Genetic regulatory networks with adaptive responses are widely studied in biology. Usually, models consisting only of a few nodes have been considered. They present one input receptor for activation and one output node where the adaptive…
The relation between network structure and dynamics is determinant for the behavior of complex systems in numerous domains. An important long-standing problem concerns the properties of the networks that optimize the dynamics with respect…