Languages with many speakers tend to be structurally simple while small communities sometimes develop languages with great structural complexity. Paradoxically, the opposite pattern appears to be observed for non-structural properties of language such as vocabulary size. These apparently opposite patterns pose a challenge for theories of language change and evolution. We use computational simulations to show that this inverse pattern can depend on a single factor: ease of diffusion through the population. A population of interacting agents was arranged on a network, passing linguistic conventions to one another along network links. Agents can invent new conventions, or replicate conventions that they have previously generated themselves or learned from other agents. Linguistic conventions are either Easy or Hard to diffuse, depending on how many times an agent needs to encounter a convention to learn it. In large groups, only linguistic conventions that are easy to learn, such as words, tend to proliferate, whereas small groups where everyone talks to everyone else allow for more complex conventions, like grammatical regularities, to be maintained. Our simulations thus suggest that language, and possibly other aspects of culture, may become simpler at the structural level as our world becomes increasingly interconnected.

 

Reali, F., Chater, N. & Christiansen, M.H. (2018). Simpler grammar, larger vocabulary: How population size affects language. Proceedings of the Royal Society B: Biological Sciences, 285, 20172586. http://rspb.royalsocietypublishing.org/content/285/1871/20172586 

Source: rspb.royalsocietypublishing.org

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

A central claim in modern network science is that real-world networks are typically “scale free,” meaning that the fraction of nodes with degree k follows a power law, decaying like k^−α, often with 2<α<3. However, empirical evidence for this belief derives from a relatively small number of real-world networks. We test the universality of scale-free structure by applying state-of-the-art statistical tools to a large corpus of nearly 1000 network data sets drawn from social, biological, technological, and informational sources. We fit the power-law model to each degree distribution, test its statistical plausibility, and compare it via a likelihood ratio test to alternative, non-scale-free models, e.g., the log-normal. Across domains, we find that scale-free networks are rare, with only 4% exhibiting the strongest-possible evidence of scale-free structure and 52% exhibiting the weakest-possible evidence. Furthermore, evidence of scale-free structure is not uniformly distributed across sources: social networks are at best weakly scale free, while a handful of technological and biological networks can be called strongly scale free. These results undermine the universality of scale-free networks and reveal that real-world networks exhibit a rich structural diversity that will likely require new ideas and mechanisms to explain.

 

Scale-free networks are rare
Anna D. Broido, Aaron Clauset

Source: arxiv.org

See Also:

Twitter discussion, including Aaron Clauset, Laszlo Barabasi, Alex Vespignani, Duncan Watts, Stefano Zapperi, Petter Holme, Gabor Vattay, et al.

https://twitter.com/manlius84/timelines/952248309720211458 

Blog post by Petter Holme

https://petterhol.me/2018/01/12/me-and-power-laws/