This work presents a theoretical and numerical analysis of the conditions under which distributed sequential consensus is possible when the state of a portion of nodes in a network is perturbed. Specifically, it examines the consensus level of partially connected blockchains under failure/attack events. To this end, we developed stochastic models for both verification probability once an error is detected and network breakdown when consensus is not possible. Through a mean field approximation for network degree we derive analytical solutions for the average network consensus in the large graph size thermodynamic limit. The resulting expressions allow us to derive connectivity thresholds above which networks can tolerate an attack.

Distributed Sequential Consensus in Networks: Analysis of Partially Connected Blockchains with Uncertainty
Francisco Prieto-Castrillo, Sergii Kushch, and Juan Manuel Corchado

Complexity
Volume 2017 (2017), Article ID 4832740, 11 pages
https://doi.org/10.1155/2017/4832740 

Source: www.hindawi.com

Information dynamics is an emerging description of information processing in complex systems. In this paper we make a formal analogy between information dynamics and stochastic thermodynamics. As stochastic dynamics increasingly concerns itself with the processing of information we suggest such an analogy is instructive in providing hitherto unexplored insights into the implicit information processing that occurs in physical systems. Information dynamics describes systems in terms of intrinsic computation, identifying computational primitives of information storage and transfer. We construct irreversibility measures in terms of these quantities are relate them to the physical entropy productions that govern the behaviour of single and composite systems in stochastic thermodynamics illustrating them with simple examples. Moreover, we can apply such a formalism to systems which do not have a bipartite structure. In particular we demonstrate that, given suitable non-bipartite processes, the heat flow in a subsystem can still be identified and one requires the present formalism to recover generalisations of the second law. This opens up the possibility of describing all physical systems in terms of computation allowing us to propose a framework for discussing the reversibility of systems traditionally out of scope of stochastic thermodynamics.

Thermodynamics and the dynamics of information in distributed computation
Richard E. Spinney, Joseph T. Lizier, Mikhail Prokopenko

Source: arxiv.org

The incubation period for typhoid, polio, measles, leukemia and many other diseases follows a right-skewed, approximately lognormal distribution. Although this pattern was discovered more than sixty years ago, it remains an open question to explain its ubiquity. Here, we propose an explanation based on evolutionary dynamics on graphs. For simple models of a mutant or pathogen invading a network-structured population of healthy cells, we show that skewed distributions of incubation periods emerge for a wide range of assumptions about invader fitness, competition dynamics, and network structure. The skewness stems from stochastic mechanisms associated with two classic problems in probability theory: the coupon collector and the random walk. Unlike previous explanations that rely crucially on heterogeneity, our results hold even for homogeneous populations. Thus, we predict that two equally healthy individuals subjected to equal doses of equally pathogenic agents may, by chance alone, show remarkably different time courses of disease.

Evolutionary dynamics of incubation periods
Bertrand Ottino-Loffler Jacob G Scott Steven H Strogatz

Source: elifesciences.org