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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| Veröffentlicht in: | 2017 ACM IEEE 8th International Conference on Cyber Physical Systems (ICCPS) S. 97 - 107 |
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18.04.2017
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| Abstract | 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. |
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| AbstractList | From microbial communities, human physiology to social and bio- logical/neural networks, complex interdependent systems display multi-scale spatio-temporal pa erns that are frequently classi ed as non-linear, non-Gaussian, non-ergodic, and/or fractal. Distin- guishing between the sources of nonlinearity, identifying the na- ture of fractality (space versus time) and encapsulating the non- Gaussian characteristics into dynamic causal models remains a ma- jor challenge for studying complex systems. In this paper, we pro- pose a new mathematical strategy for constructing compact yet ac- curate models of complex systems dynamics that aim to scrutinize the causal e ects and in uences by analyzing the statistics of the magnitude increments and the inter-event times of stochastic pro- cesses. We derive a framework that enables to incorporate knowl- edge about the causal dynamics of the magnitude increments and the inter-event times of stochastic processes into a multi-fractional order nonlinear partial di erential equation for the probability to nd the system in a speci c state at one time. Rather than follow- ing the current trends in nonlinear system modeling which pos- tulate speci c mathematical expressions, this mathematical frame- work enables us to connect the microscopic dependencies between the magnitude increments and the inter-event times of one stochas- tic 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 pro- cesses and demonstrate that the derived mathematical models o er superior accuracy over state of the art techniques. 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. |
| Author | Bogdan, Paul Xue, Yuankun |
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| Keywords | causal inference fractal dynamics spatio-temporal coupling non-linearity complex dynamics |
| Language | English |
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| Snippet | From microbial communities, human physiology to social and biological/neural networks, complex interdependent systems display multi-scale spatio-temporal... From microbial communities, human physiology to social and bio- logical/neural networks, complex interdependent systems display multi-scale spatio-temporal pa... |
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| SubjectTerms | 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 |
| Title | Constructing compact causal mathematical models for complex dynamics |
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