I briefly survey several fascinating topics in networks and nonlinearity. I highlight a few methods and ideas, including several of personal interest, that I anticipate to be especially important during the next several years. These topics include temporal networks (in which the entities and/or their interactions change in time), stochastic and deterministic dynamical processes on networks, adaptive networks (in which a dynamical process on a network is coupled to dynamics of network structure), and network structure and dynamics that include "higher-order" interactions (which involve three or more entities in a network). I draw examples from a variety of scenarios, including contagion dynamics, opinion models, waves, and coupled oscillators.

 

Nonlinearity + Networks: A 2020 Vision
Mason A. Porter

Source: arxiv.org

Chaos, machine, or evolving complexity? The butterfly effect suggests a world in chaos—with linkages so random or nuanced that just to measure or pre-state them is virtually impossible. To predict how they will interact is even less feasible. Thanks to “adjacent possibles” and the contradictory impulses of human behavior, much of our world appears to move in random spasms. Every new technology and policy outcome creates opportunities to push society in new and often unforeseen directions, driven by human agents who may introduce crucial but unpredictable goals, strategies, and actions. Against this view, complexity science seeks to identify patterns in interactive relationships. Many patterns can be plotted and, in some cases, foreseen. A comparison of political entities across the globe points to certain factors conducing to societal fitness. Analysis of states that have declined in fitness suggests why their strengths turned to weaknesses. A survey of societies that were relatively democratic points to several factors that contributed to their acquiring authoritarian regimes. Scientists and scholars can unveil some elements of order but should strive to do so without hubris. Wise policymakers will strive to channel both the “actuals” and “adjacent possibles” that then arise toward constructive futures.

 

NETSOL: New Trends in Social and Liberal Sciences

Year: 2019 / Volume : 2 / Area: Interdisciplinary Studies

Walter C. Clemens and Stuart A. Kauffman
Is the World Chaos, a Machine, or Evolving Complexity? How Well Can We Understand Life and World Affairs? pp.24-43.

Source: www.netsoljournal.net

Governing equations are essential to the study of physical systems, providing models that can generalize to predict previously unseen behaviors. There are many systems of interest across disciplines where large quantities of data have been collected, but the underlying governing equations remain unknown. This work introduces an approach to discover governing models from data. The proposed method addresses a key limitation of prior approaches by simultaneously discovering coordinates that admit a parsimonious dynamical model. Developing parsimonious and interpretable governing models has the potential to transform our understanding of complex systems, including in neuroscience, biology, and climate science.

 

Data-driven discovery of coordinates and governing equations
Kathleen Champion, Bethany Lusch, J. Nathan Kutz, and Steven L. Brunton
PNAS November 5, 2019 116 (45) 22445-22451; first published October 21, 2019 https://doi.org/10.1073/pnas.1906995116

Source: www.pnas.org

Human achievements are often preceded by repeated attempts that fail, but little is known about the mechanisms that govern the dynamics of failure. Here, building on previous research relating to innovation1,2,3,4,5,6,7, human dynamics8,9,10,11 and learning12,13,14,15,16,17, we develop a simple one-parameter model that mimics how successful future attempts build on past efforts. Solving this model analytically suggests that a phase transition separates the dynamics of failure into regions of progression or stagnation and predicts that, near the critical threshold, agents who share similar characteristics and learning strategies may experience fundamentally different outcomes following failures. Above the critical point, agents exploit incremental refinements to systematically advance towards success, whereas below it, they explore disjoint opportunities without a pattern of improvement. The model makes several empirically testable predictions, demonstrating that those who eventually succeed and those who do not may initially appear similar, but can be characterized by fundamentally distinct failure dynamics in terms of the efficiency and quality associated with each subsequent attempt. We collected large-scale data from three disparate domains and traced repeated attempts by investigators to obtain National Institutes of Health (NIH) grants to fund their research, innovators to successfully exit their startup ventures, and terrorist organizations to claim casualties in violent attacks. We find broadly consistent empirical support across all three domains, which systematically verifies each prediction of our model. Together, our findings unveil detectable yet previously unknown early signals that enable us to identify failure dynamics that will lead to ultimate success or failure. Given the ubiquitous nature of failure and the paucity of quantitative approaches to understand it, these results represent an initial step towards the deeper understanding of the complex dynamics underlying failure.

 

Quantifying the dynamics of failure across science, startups and security
Yian Yin, Yang Wang, James A. Evans & Dashun Wang 
Nature volume 575, pages190–194(2019)

Source: www.nature.com

How knowledge informs and alters disciplines is itself an enlightening, and vibrant field1. This type of meta research into new findings, insights, conceptual frameworks and techniques is important, among other things, for policymakers who fund research in the hope of tackling society’s most pressing challenges, which inevitably span disciplines.

Since its founding in 1869, Nature has offered a venue for publishing major advances from many fields. To mark its anniversary, we track here how papers cite and are cited across disciplines, using data on tens of millions of scientific articles indexed in Clarivate Analytics’ Web of Science (WoS), a bibliometric database that encompasses many thousands of research journals starting from 1900. We pay particular attention to articles that appeared in Nature. In our view, this snapshot, for all its idiosyncrasies, reveals how scientific work is ever more becoming a mixture of disciplines.

 

Nature’s reach: narrow work has broad impact
A scientific paper today is inspired by more disciplines than ever before, shows a new analysis marking the journal’s 150th anniversary.
Alexander J. Gates, Qing Ke, Onur Varol & Albert-László Barabási

Source: www.nature.com