Exploring Simplicity Bias in 1D Dynamical Systems.

Arguments inspired by algorithmic information theory predict an inverse relation between the probability and complexity of output patterns in a wide range of input-output maps. This phenomenon is known as simplicity bias. By viewing the parameters of dynamical systems as inputs, and the resulting (digitised) trajectories as outputs, we study simplicity bias in the logistic map, Gauss map, sine map, Bernoulli map, and tent map. We find that the logistic map, Gauss map, and sine map all exhibit simplicity bias upon sampling of map initial values and parameter values, but the Bernoulli map and tent map do not. The simplicity bias upper bound on the output pattern probability is used to make a priori predictions regarding the probability of output patterns. In some cases, the predictions are surprisingly accurate, given that almost no details of the underlying dynamical systems are assumed. More generally, we argue that studying probability-complexity relationships may be a useful tool when studying patterns in dynamical systems.

Mechanistic modelling of COVID-19 and the impact of lockdowns on a short-time scale.

BACKGROUND: To mitigate the spread of the COVID-19 coronavirus, some countries have adopted more stringent non-pharmaceutical interventions in contrast to those widely used. In addition to standard practices such as enforcing curfews, social distancing, and closure of non-essential service industries, other non-conventional policies also have been implemented, such as the total lockdown of fragmented regions, which are composed of sparsely and highly populated areas. METHODS: In this paper, we model the movement of a host population using a mechanistic approach based on random walks, which are either diffusive or super-diffusive. Infections are realised through a contact process, whereby a susceptible host is infected if in close spatial proximity of the infectious host with an assigned transmission probability. Our focus is on a short-time scale (∼ 3 days), which is the average time lag time before an infected individual becomes infectious. RESULTS: We find that the level of infection remains approximately constant with an increase in population diffusion, and also in the case of faster population dispersal (super-diffusion). Moreover, we demonstrate how the efficacy of imposing a lockdown depends heavily on how susceptible and infectious individuals are distributed over space. CONCLUSION: Our results indicate that on a short-time scale, the type of movement behaviour does not play an important role in rising infection levels. Also, lock-down restrictions are ineffective if the population distribution is homogeneous. However, in the case of a heterogeneous population, lockdowns are effective if a large proportion of infectious carriers are distributed in sparsely populated sub-regions.