Understanding Living Systems

Understanding Living Systems presents an integrated approach covering mathematics, physics, computer science, biology and medicine. Modelling approaches to living systems range between a top-down (differential equations) and a bottom-up (agent-based) models. Recently, computational modelling has been proposed as an intermediate level approach. This promising approach needs further improvements in order to deal in particular with the modularity of the representation of complex interactions. For that purpose, the authors present a new framework based on Higher Order Category Theory allowing modelling the physiological, pathological and repaired structure dynamics and evolution of living systems via a Categorification Modelling Approach: dynamics as modifications of structure, and evolution as modifications of dynamics. In the novel approach presented in Understanding Living Systems, the physiological structure is modelled at the level of n-categories (n-categories, n-functors, n-natural transformations, n-adjunctions etc.), the dynamics is modelled at the level of (n+h)-categories, and the evolution is modelled at the level of (n+h+k)categories. The pathological structure is modelled at the level of n-categories (n+n’)-categories, the pathological repaired dynamics is modelled at the level of (n+n’ + h+h’)-categories and the pathological evolution is modelled at the level of (n+n’ + h+ h’ + k+k’)-categories. The repaired structure is modelled at the level of n-categories (n+n’+n”)-categories, the repaired dynamics is modelled at the level of (n+n’+n” + h+h’+h”)-categories and the repaired evolution is modelled at the level of (n+n’+n” + h+h’+h” +  k+k’+k”)categories. This new approach advances the field of computational modeling for biomedical engineers, computer scientists, physicians, and mathematical researchers. Presents the principles and methods of modelling living systems to provide a solid foundation for understanding the fieldDiscusses symmetries and categorical modelling in fields such molecular biology, genetics and epigenetics, homeostatis and immune response, as well as the biomedical engineering applications of the models in these various areasProvides complete coverage of biomedical interaction networks in fields such as Psycho-Neuro-Endocrine-Immune interactions, neurons and brain categorical interactions, as well as natural and enatural interatcions, along with the biomedical engineering applications of the models in these various areas