NDLI: Constructing compact causal mathematical models for complex dynamics

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Constructing compact causal mathematical models for complex dynamics

Content Provider	ACM Digital Library
Author	Bogdan, Paul Xue, Yuankun
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.
Starting Page	97
Ending Page	107
Page Count	11
File Format	PDF
ISBN	9781450349659
DOI	10.1145/3055004.3055017
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	2017-04-18
Publisher Place	New York
Access Restriction	Subscribed
Subject Keyword	Causal inference Non-linearity fractal dynamics Spatio-temporal coupling Complex dynamics
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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