Development of an automatic turntable-type multiple T-maze device and observation of pill bug behavior

Time averaging and emerging nonergodicity upon resetting of fractional Brownian motion and heterogeneous diffusion processes

How different are the results of constant-rate resetting of anomalous-diffusion processes in terms of their ensemble-averaged versus time-averaged mean-squared displacements (MSDs versus TAMSDs) and how does stochastic resetting impact nonergodicity? We examine, both analytically and by simulations, the implications of resetting on the MSD- and TAMSD-based spreading dynamics of particles executing fractional Brownian motion (FBM) with a long-time memory, heterogeneous diffusion processes (HDPs) with a power-law space-dependent diffusivity D(x)=D_{0}|x|^{γ} and their "combined" process of HDP-FBM. We find, inter alia, that the resetting dynamics of originally ergodic FBM for superdiffusive Hurst exponents develops disparities in scaling and magnitudes of the MSDs and mean TAMSDs indicating weak ergodicity breaking. For subdiffusive HDPs we also quantify the nonequivalence of the MSD and TAMSD and observe a new trimodal form of the probability density function. For reset FBM, HDPs and HDP-FBM we compute analytically and verify by simulations the short-time MSD and TAMSD asymptotes and long-time plateaus reminiscent of those for processes under confinement. We show that certain characteristics of these reset processes are functionally similar despite a different stochastic nature of their nonreset variants. Importantly, we discover nonmonotonicity of the ergodicity-breaking parameter EB as a function of the resetting rate r. For all reset processes studied we unveil a pronounced resetting-induced nonergodicity with a maximum of EB at intermediate r and EB∼(1/r)-decay at large r. Alongside the emerging MSD-versus-TAMSD disparity, this r-dependence of EB can be an experimentally testable prediction. We conclude by discussing some implications to experimental systems featuring resetting dynamics.

Mice in a labyrinth show rapid learning, sudden insight, and efficient exploration

Animals learn certain complex tasks remarkably fast, sometimes after a single experience. What behavioral algorithms support this efficiency? Many contemporary studies based on two-alternative-forced-choice (2AFC) tasks observe only slow or incomplete learning. As an alternative, we study the unconstrained behavior of mice in a complex labyrinth and measure the dynamics of learning and the behaviors that enable it. A mouse in the labyrinth makes ~2000 navigation decisions per hour. The animal explores the maze, quickly discovers the location of a reward, and executes correct 10-bit choices after only 10 reward experiences — a learning rate 1000-fold higher than in 2AFC experiments. Many mice improve discontinuously from one minute to the next, suggesting moments of sudden insight about the structure of the labyrinth. The underlying search algorithm does not require a global memory of places visited and is largely explained by purely local turning rules.

Logic Gates Formed by Perturbations in an Asynchronous Game of Life

The game of life (GL), a type of two-dimensional cellular automaton, has been the subject of many studies because of its simple mechanism and complex behavior. In particular, the construction of logic circuits using the GL has helped to extend the concept of computation. Conventional logic circuits assume deterministic transitions due to the synchronicity of the classic GL. However, they are fragile to noise and cannot maintain the expected behavior in an environment with noise. In this study, a probabilistic logic gate model was constructed using perturbations in an asynchronous game of life (AGL). Since our asynchronous automaton had no heterogeneity in either the horizontal or vertical directions, it was symmetrical with respect to spatial structure. On the other hand, the construction of the logical gate was implemented to contain heterogeneity in the horizontal or vertical directions, which could allow an AND gate and an OR gate in a single system. It was based on the phase transition between connected and unconnected phases, which is newly discovered in this study. In the model, perturbations symmetrically entail operations successful and unsuccessful, and this symmetrical double action is given not to interfere with established operations but to make operations possible. Therefore, this model had a different meaning from logic gates that exclude perturbations or use them externally. The idea of this perturbation is analogous to the inherent noise that destroys and generates structures in biological swarms.

Power Laws Derived from a Bayesian Decision-Making Model in Non-Stationary Environments

The frequency of occurrence of step length in the migratory behaviour of various organisms, including humans, is characterized by the power law distribution. This pattern of behaviour is known as the Lévy walk, and the reason for this phenomenon has been investigated extensively. Especially in humans, one possibility might be that this pattern reflects the change in self-confidence in one’s chosen behaviour. We used simulations to demonstrate that active assumptions cause changes in the confidence level in one’s choice under a situation of lack of information. More specifically, we presented an algorithm that introduced the effects of learning and forgetting into Bayesian inference, and simulated an imitation game in which two decision-making agents incorporating the algorithm estimated each other’s internal models. For forgetting without learning, each agents’ confidence levels in their own estimation remained low owing to a lack of information about the counterpart, and the agents changed their hypotheses about the opponent frequently, and the frequency distribution of the duration of the hypotheses followed an exponential distribution for a wide range of forgetting rates. Conversely, when learning was introduced, high confidence levels occasionally occurred even at high forgetting rates, and exponential distributions universally turned into power law distribution.