Continuous cellular automata on irregular tessellations : mimicking steady-state heat flow

Leaving a few exceptions aside, cellular automata (CA) and the intimately related coupled-map lattices (CML), commonly known as continuous cellular automata (CCA), as well as models that are based upon one of these paradigms, employ a regular tessellation of an Euclidean space in spite of the various drawbacks this kind of tessellation entails such as its inability to cover surfaces with an intricate geometry, or the anisotropy it causes in the simulation results. Recently, a CCA-based model describing steady-state heat flow has been proposed as an alternative to Laplace's equation that is, among other things, commonly used to describe this process, yet, also this model suffers from the aforementioned drawbacks since it is based on the classical CCA paradigm. To overcome these problems, we first conceive CCA on irregular tessellations of an Euclidean space after which we show how the presented approach allows a straightforward simulation of steady-state heat flow on surfaces with an intricate geometry, and, as such, constitutes an full-fledged alternative for the commonly used and easy-to-implement finite difference method, and the more intricate finite element method

Tracking uncertainty in a spatially explicit susceptible-infected epidemic model

In this paper we conceive an interval-valued continuous cellular automaton for describing the spatio-temporal dynamics of an epidemic, in which the magnitude of the initial outbreak and/or the epidemic properties are only imprecisely known. In contrast to well-established approaches that rely on probability distributions for keeping track of the uncertainty in spatio-temporal models, we resort to an interval representation of uncertainty. Such an approach lowers the amount of computing power that is needed to run model simulations, and reduces the need for data that are indispensable for constructing the probability distributions upon which other paradigms are based

A threshold for majority in the context of aggregating partial order relations

We consider a voting problem where voters have expressed their preferences on a single set of objects. These preferences take the shape of strict partial order relations. In order to allow extraction of a unique strict partial order relation corresponding to a social set of preferences, we determine the minimum number of votes a pairwise preference should receive in order to qualify as a social pairwise preference. Transitive closure of the social pairwise preferences will result in the social set of preferences. At the same time, the social set of preferences needs to be cycle-free, and the minimum number of votes should be determined with this constraint in mind. We provide an example application

Left and right compatibility of strict orders with fuzzy tolerance and fuzzy equivalence relations

The notion of extensionality of a fuzzy relation w.r.t. a fuzzy equivalence was first introduced by Hohle and Blanchard. Belohlavek introduced a similar definition of compatibility of a fuzzy relation w.r.t. a fuzzy equality. In [14] we generalized this notion to left compatibility, right compatibility and compatibility of arbitrary fuzzy relations and we characterized them in terms of left and right traces introduced by Fodor. In this note, we will again investigate these notions, but this time we focus on the compatibility of strict orders with fuzzy tolerance and fuzzy equivalence relations

Identification of cellular automata based on incomplete observations with bounded time gaps

In this paper, the problem of identifying the cellular automata (CAs) is considered. We frame and solve this problem in the context of incomplete observations, i.e., prerecorded, incomplete configurations of the system at certain, and unknown time stamps. We consider 1-D, deterministic, two-state CAs only. An identification method based on a genetic algorithm with individuals of variable length is proposed. The experimental results show that the proposed method is highly effective. In addition, connections between the dynamical properties of CAs (Lyapunov exponents and behavioral classes) and the performance of the identification algorithm are established and analyzed