Naive Learning Through Probability Overmatching

Naïve Learning in a Binary Action, Social Network Environment In “Naïve Learning Through Probability Overmatching,” I. Arieli, Y. Babichenko, and M. Mueller-Frank consider an environment where privately informed agents select a binary action repeatedly observing the past actions of their neighbors in a social network. Rational inference has been shown to be exceedingly complex in this environment. Instead, this paper focuses on boundedly rational agents that form beliefs according to discretized DeGroot updating and apply a decision rule that assigns a (mixed) action to each belief. It is shown that naïve learning, where the long run actions of all agents are optimal given their pooled private information, can be achieved in any strongly connected network if beliefs satisfy a high level of inertia and the decision rule coincides with probability overmatching. The main difference to existing naïve learning results is that here it is shown to hold (1) for binary rather than uncountable action spaces and (2) even for network and information structures where Bayesian agents fail to learn.

Ongoing Global and Regional Adaptive Evolution of SARS-CoV-2

Unprecedented sequencing efforts have, as of October 2020, produced nearly 200,000 genomes of severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the virus responsible for COVID-19. Understanding the trends in SARS-CoV-2 evolution is paramount to control the pandemic, but analysis of this enormous dataset is a major challenge. We show that the ongoing evolution of SARS-CoV-2 over the course of the pandemic is characterized primarily by purifying selection but a small set of sites, including spike 614 and nucleocapsid 203-204 appear to evolve under positive selection. In addition to the substitutions in the spike protein, multiple substitutions in the nucleocapsid protein appear to be important for SARS-CoV-2 adaptation to the human host. The positively selected mutations form a strongly connected network of apparent epistatic interactions and are signatures of major partitions in the SARS-CoV-2 phylogeny. These partitions show distinct spatial and temporal dynamics, with both globalization and diversification trends being apparent.

The Modified Rural Postman Problem in Vehicle Route Optimization

The submitted paper deals with designing routes of the vehicles, which provide the transport network services. We limit our focus to such tasks, where the priority is the edge service in the transport network and the initial problem is finding an Eulerian path. Regarding to real-life problems, this contribution presents such procedure of solving, which takes into account both the existence of a mixed transport network containing one-way roads and the existence of a wider transport network. In this network, there are only selected edges with possibility of the effective passages. This problem can be solved by the modified Rural Postman Problem assuming the strongly connected network. Linear programming is a suitable tool for designing optimal routes of service vehicles.

Global stability of multi-group SEIRS epidemic models with vaccination

In this paper, a susceptible–exposed–infective–recovered–susceptible (SEIRS) epidemic model with vaccination has been formulated. We studied the global stability of the corresponding single-group model, multi-group model with strongly connected network and multi-group model without strongly connected network by means of analyzing their basic reproduction numbers and the application of Lyapunov functionals. Finally, we provide some numerical simulations to illustrate our analysis results.

Adaptive Control of Dynamically Complex Networks with Saturation Couplings

This paper considers the control problem of dynamically complex networks with saturation couplings. Two novel control schemes in terms of adaptive control are presented to deal with such saturation couplings. Based on the robust idea, the underlying complex network is firstly transformed into a strongly connected network having time-varying uncertainty. However, the upper bound of uncertainty is unknown. Because of such an unavailable bound, a kind of adaptive controller added to each node is proposed such that the closed-loop auxiliary network is uniformly bounded. In particular, the original system states are asymptotically stable. Moreover, in order to avoid adding the desired controller to every node, another different kind of adaptive controller based on the pinning control idea is proposed. Compared with the former method, it is only applied to a part of nodes and has a good operability. Finally, a numerical example is provided to show the effectiveness of our results.

Inflation of strongly connected networks

A coupled cell network is an inflation of if the dynamics of is embedded in as a quotient network. We give necessary and sufficient conditions for the existence of a strongly connected inflation of a strongly connected network. We provide a simple algorithm for the construction of a strongly connected inflation as a sequence of simple inflations.