It is very important to model the behavior of protocells as basic lifelike artificial organisms more and more accurately from the level of genomes to the level of populations. A better understanding of basic protocell communities may help us in describing more complex ecological systems accurately. In this article, we propose a new comprehensive, bilevel mathematical model of a community of three protocell species (one generalist and two specialists). The aim is to achieve a model that is as basic/fundamental as possible while already displaying mutation, selection, and complex population dynamics phenomena (like competitive exclusion and keystone species). At the microlevel of genetic codes, the protocells and their mutations are modeled with Turing machines (TMs). The specialists arise from the generalist by means of mutation. Then the species are put into a common habitat, where, at the macrolevel of populations, they have to compete for the available nutrients, a part of which they themselves can produce. Because of different kinds of mutations, the running times of the species as TMs (algorithms) are different. This feature is passed on to the macrolevel as different reproduction times. At the macrolevel, a discrete-time dynamic model describes the competition. The model displays complex lifelike behavior known from population ecology, including the so-called competitive exclusion principle and the effect of keystone species. In future works, the bilevel model will have a good chance of serving as a simple and useful tool for studying more lifelike phenomena (like evolution) in their pure/abstract form.

We present a new solver for estimating a surface normal from a single affine correspondence in two calibrated views. The proposed approach provides a new globally optimal solution for this over-determined problem and proves that it reduces to a linear system that can be solved extremely efficiently. This allows for performing significantly faster than other recent methods, solving the same problem and obtaining the same globally optimal solution. We demonstrate on 15k image pairs from standard benchmarks that the proposed approach leads to the same results as other optimal algorithms while being, on average, five times faster than the fastest alternative. Besides its theoretical value, we demonstrate that such an approach has clear benefits, e.g., in image-based visual localization, due to not requiring a dense point cloud to recover the surface normal. We show on the Cambridge Landmarks dataset that leveraging the proposed surface normal estimation further improves localization accuracy. Matlab and C++ implementations are also published in the supplementary material.