Controllability and accessibility analysis of nonlinear biosystems

Background: We address the problem of determining the controllability and accessibility of nonlinear biosystems. We consider models described by affine-in-inputs ordinary differential equations, which are adequate for a wide array of biological processes. Roughly speaking, the controllability of a dynamical system determines the possibility of steering it from an initial state to any point in its neighbourhood; accessibility is a weaker form of controllability. Methods: While the methodology for analysing the controllability of linear systems is well established, its generalization to the nonlinear case has proven elusive. Thus, a number of related but different properties – including different versions of accessibility, reachability or weak local controllability – have been defined to approach its study, and several partial results exist in lieu of a general test. Here, leveraging the applicable results from differential geometric control theory, we source sufficient conditions to assess nonlinear controllability, as well as a necessary and sufficient condition for accessibility. Results: We develop an algorithmic procedure to evaluate these conditions efficiently, and we provide its open source implementation. Using this software tool, we analyse the accessibility and controllability of a number of models of biomedical interest. While some of them are fully controllable, we find others that are not, as is the case of some models of EGF and NF����B signalling networks. Conclusions: The contributions in this paper facilitate the accessibility and controllability analysis of nonlinear models, not only in biomedicine but also in other areas in which they have been rarely performed to date.Agencia Estatal de Investigación | Ref. PID2020-113992RA-I00Agencia Estatal de Investigación | Ref. RYC-2019-027537-IXunta de Galicia | Ref. ED431F 2021/00

Control of Tipping Points in Stochastic Mutualistic Complex Networks

ACKNOWLEDGMENTS YM was partically supported by the University of Aberdeen Elphinstone Fellowship.Peer reviewedPostprintPublisher PD

The impact of aging on human brain network target controllability

Understanding how few distributed areas can steer large-scale brain activity is a fundamental question that has practical implications, which range from inducing specific patterns of behavior to counteracting disease. Recent endeavors based on network controllability provided fresh insights into the potential ability of single regions to influence whole brain dynamics through the underlying structural connectome. However, controlling the entire brain activity is often unfeasible and might not always be necessary. The question whether single areas can control specific target subsystems remains crucial, albeit still poorly explored. Furthermore, the structure of the brain network exhibits progressive changes across the lifespan, but little is known about the possible consequences in the controllability properties. To address these questions, we adopted a novel target controllability approach that quantifies the centrality of brain nodes in controlling specific target anatomo-functional systems. We then studied such target control centrality in human connectomes obtained from healthy individuals aged from 5 to 85. Main results showed that the sensorimotor system has a high influencing capacity, but it is difficult for other areas to influence it. Furthermore, we reported that target control centrality varies with age and that temporal-parietal regions, whose cortical thinning is crucial in dementia-related diseases, exhibit lower values in older people. By simulating targeted attacks, such as those 19 occurring in focal stroke, we showed that the ipsilesional hemisphere is the most affected one regardless of the damaged area. Notably, such degradation in target control centrality was more evident in younger people, thus supporting early-vulnerability hypotheses after stroke

Networks, Dynamics and Explanation

This paper explores some issues having to do with the use of networks in scientific explanations. It focuses on the very common case in which what is of interest is the spread of some process (a disease, a neural signal etc.) along a network. In such cases, the use of a network in explanation requires the specification of a dynamics governing this process in addition to and independent of the network structure. Such a dynamics will incorporate causal information. This is one of several reasons why it is a mistake to think of network explanations, at least in typical applications, as entirely non-causal. In addition the independence of the network structure and the dynamics of the process occuring on it provides the key to the "directional" features of such explanations. Other topics discussed include the circumstances in which use of networks is most likely to be fruitful and the difference between networks in the form of undirected graphs and the use of directed graphs to represent causal relationships

Approximately Reachable Directions for Piecewise Linear Switched Systems

This paper deals with some reachability issues for piecewise linear switched systems with time-dependent coefficients and multiplicative noise. Namely, it aims at characterizing data that are almost reachable at some fixed time T > 0 (belong to the closure of the reachable set in a suitable L 2-sense). From a mathematical point of view, this provides the missing link between approximate controllability towards 0 and approximate controllability towards given targets. The methods rely on linear-quadratic control and Riccati equations. The main novelty is that we consider an LQ problem with controlled backward stochastic dynamics and, since the coefficients are not deterministic (unlike some of the cited references), neither is the backward stochastic Riccati equation. Existence and uniqueness of the solution of such equations rely on structure arguments (inspired by [7]). Besides solvability, Riccati representation of the resulting control problem is provided as is the synthesis of optimal (non-Markovian) control. Several examples are discussed

Network resilience

Many systems on our planet are known to shift abruptly and irreversibly from one state to another when they are forced across a "tipping point," such as mass extinctions in ecological networks, cascading failures in infrastructure systems, and social convention changes in human and animal networks. Such a regime shift demonstrates a system's resilience that characterizes the ability of a system to adjust its activity to retain its basic functionality in the face of internal disturbances or external environmental changes. In the past 50 years, attention was almost exclusively given to low dimensional systems and calibration of their resilience functions and indicators of early warning signals without considerations for the interactions between the components. Only in recent years, taking advantages of the network theory and lavish real data sets, network scientists have directed their interest to the real-world complex networked multidimensional systems and their resilience function and early warning indicators. This report is devoted to a comprehensive review of resilience function and regime shift of complex systems in different domains, such as ecology, biology, social systems and infrastructure. We cover the related research about empirical observations, experimental studies, mathematical modeling, and theoretical analysis. We also discuss some ambiguous definitions, such as robustness, resilience, and stability.Comment: Review chapter