Constructing compact causal mathematical models for complex dynamics

From microbial communities, human physiology to social and biological/neural networks, complex interdependent systems display multi-scale spatio-temporal patterns that are frequently classified as non-linear, non-Gaussian, non-ergodic, and/or fractal. Distinguishing between the sources of nonlineari...

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Bibliographic Details
Published in:2017 ACM IEEE 8th International Conference on Cyber Physical Systems (ICCPS) pp. 97 - 107
Main Authors: Xue, Yuankun, Bogdan, Paul
Format: Conference Proceeding
Language:English
Published: New York, NY, USA ACM 18.04.2017
Series:ACM Other Conferences
Subjects:
Biological system modeling
Causal inference
Complex dynamics
Complex systems
Computational modeling
Computer systems organization > Embedded and cyber-physical systems
Computing methodologies > Modeling and simulation > Model development and analysis > Modeling methodologies
Fractal dynamics
Fractals
Mathematical model
Mathematics of computing > Information theory
Mathematics of computing > Probability and statistics > Multivariate statistics
Mathematics of computing > Probability and statistics > Probabilistic inference problems
Mathematics of computing > Probability and statistics > Stochastic processes
Non-linearity
Nonlinear dynamical systems
Spatio-temporal coupling
Theory of computation > Theory and algorithms for application domains > Machine learning theory > Models of learning
Time series analysis
causal inference
fractal dynamics
spatio-temporal coupling
non-linearity
complex dynamics
ISBN:9781450349659, 145034965X
Online Access:Get full text
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Summary:From microbial communities, human physiology to social and biological/neural networks, complex interdependent systems display multi-scale spatio-temporal patterns that are frequently classified as non-linear, non-Gaussian, non-ergodic, and/or fractal. Distinguishing between the sources of nonlinearity, identifying the nature of fractality (space versus time) and encapsulating the non-Gaussian characteristics into dynamic causal models remains a major challenge for studying complex systems. In this paper, we propose a new mathematical strategy for constructing compact yet accurate models of complex systems dynamics that aim to scrutinize the causal effects and influences by analyzing the statistics of the magnitude increments and the inter-event times of stochastic processes. We derive a framework that enables to incorporate knowledge about the causal dynamics of the magnitude increments and the inter-event times of stochastic processes into a multi-fractional order nonlinear partial differential equation for the probability to find the system in a specific state at one time. Rather than following the current trends in nonlinear system modeling which postulate specific mathematical expressions, this mathematical frame-work enables us to connect the microscopic dependencies between the magnitude increments and the inter-event times of one stochastic process to other processes and justify the degree of nonlinearity. In addition, the newly presented formalism allows to investigate appropriateness of using multi-fractional order dynamical models for various complex system which was overlooked in the literature. We run extensive experiments on several sets of physiological processes and demonstrate that the derived mathematical models offer superior accuracy over state of the art techniques.
ISBN:9781450349659
145034965X
DOI:10.1145/3055004.3055017