Abstract
Can a popular real-world competition system indeed be fragile? To address this question, we represent such a system by a directed binary network. Upon observed network data, typically in a form of win-and-loss matrix, our computational developments begin with collectively extracting network's information flows. And then we compute and discover network's macrostate. This computable macrostate is further shown to contain deterministic structures embedded with randomness mechanisms. Such coupled deterministic and stochastic components becomes the basis for generating the microstate ensemble. Specifically a network mimicking algorithm is proposed to generate a microstate ensemble by subject to the statistical mechanics principle: All generated microscopic states have to conform to its macrostate of the target system. We demonstrate that such a microstate ensemble is an effective platform for exploring systemic sensitivity. Throughout our computational developments, we employ the NCAA Football Bowl Subdivision (FBS) as an illustrating example system. Upon this system, its macrostate is discovered by having a nonlinear global ranking hierarchy as its deterministic component, while its constrained randomness component is embraced within the nearly completely recovered conference schedule . Based on the computed microstate ensemble, we are able to conclude that the NCAA FBS is overall a fragile competition system because it retains highly heterogeneous degrees of sensitivity with its ranking hierarchy.
Highlights
Advances in Information Technology have equipped scientists with unprecedented capabilities to create new systems as well as to peek into old systems in human societies and in nature
The computed dominance probability matrix D(W0) from the previous section would be the basis for extracting systemic structures: namely, its deterministic structure and its randomness
It is noted that the deterministic structure is likely a composite structure comprised of multiple overlapping trees
Summary
Advances in Information Technology have equipped scientists with unprecedented capabilities to create new systems as well as to peek into old systems in human societies and in nature. Scientific endeavors of collecting and mining diverse kinds of high frequency, sequencing and network data for better understanding on these new and old systems of interest are nearly overwhelming across all branches of science. Though methodological techniques on computing and analyzing data derived from such systems have progressed in many fronts in past decades, still the speed of progress on learning from data apparently lags far behind the speed of generating data. One of the key reasons behind this lagging phenomenon can be seen from the perspective of order and chaos, as described in Crutchfield [1].
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