We experimentally demonstrate that both Voronoi diagram and its dual graph Delaunay triangulation are simultaneously constructed — for specific conditions — in cultures of plasmodium, a vegetative state of Physarum polycephalum. Every point of a given planar data set is represented by a tiny mass of plasmodium. The plasmodia spread from their initial locations but, in certain conditions, stop spreading when they encounter plasmodia originated from different locations. Thus space loci not occupied by the plasmodia represent edges of Voronoi diagram of the given planar set. At the same time, the plasmodia originating at neighboring locations form merging protoplasmic tubes, where the strongest tubes approximate Delaunay triangulation of the given planar set. The problems are solved by plasmodium only for limited data sets, however the results presented lay a sound ground for further investigations.

A cell is a minimal self-sustaining system that can move and compute. Previous work has shown that a unicellular slime mold, Physarum, can be utilized as a biological computer based on cytoplasmic flow encapsulated by a membrane. Although the interplay between the modification of the boundary of a cell and the cytoplasmic flow surrounded by the boundary plays a key role in Physarum computing, no model of a cell has been developed to describe this interplay. Here we propose a toy model of a cell that shows amoebic motion and can solve a maze, Steiner minimum tree problem and a spanning tree problem. Only by assuming that cytoplasm is hardened after passing external matter (or softened part) through a cell, the shape of the cell and the cytoplasmic flow can be changed. Without cytoplasm hardening, a cell is easily destroyed. This suggests that cytoplasmic hardening and/or sol-gel transformation caused by external perturbation can keep a cell in a critical state leading to a wide variety of shapes and motion.

Using the examples of an excitable chemical system (Belousov-Zhabotinsky medium) and plasmodium of Physarum polycephalum we show that universal computation in a geometrically unconstrained medium is only possible when resources (excitability or concentration of nutrients) are limited. In situations of limited resources the systems studied develop travelling localizations. The localizations are elementary units of dynamical logical circuits in collision-based computing architectures. Keywords: unconventional computing, collision-based computing, Belousov-Zhabotinsky system, Physarum polycephalum 1.Introduction: architecture-based vs architecture-less computing The first thoughts on the implementation of computational operations with patterns propagated in spatially extended non-linear systems date back to 1800's where Plateau experimented with the problem involving the calculation of the surface of smallest area bounded by a given closed contour in space [Courant and Robins, 1941] (the classical problem of calculating a minimal spanning tree of planar points using a soap film). These ideas were rediscovered many times but mostly in a framework of theoretical design of novel algorithms, of these the grass fire transformation [Blum, 1968;Calabi & Hartnett, 1968] is the most famous example. In 1990's the new field of reaction-diffusion computingcomputation with excitation and diffusive waves in two-dimensional chemical media --was conceived in experiments using the Belousov-Zhabotinsky medium [Kuhnert & Agladze, 1989;Rambidi, 1998] and precipitating chemical systems [Tolmachiev & Adamatzky, 1996]. A reaction-diffusion computer is a spatially extended chemical system, which process information using interacting growing patterns, excitable and diffusive waves [Adamatzky, 2001; Adamatzky, De Lacy Costello & Asai, 2005]. In reaction-diffusion processors, both the data and the results of the computation are encoded as concentration profiles of the reagents. The computation is performed via the spreading and interaction of wave fronts. Reaction-diffusion chemical processors are now `classical' examples of non-linear medium computers. A non-linear medium processor can be either specialised or general-purpose (universal). A specialized processor is built to solve only one particular problem, possibly with different data sets and with variations in the interpretation of the results. Specialised computing devices are quite handy when we deal with image processing, problems of mathematical morphology, or computation on graphs [Adamatzky, 2001; Adamatzky, De Lacy Costello, Asai, 2005]. A device is called computationally universal if it computes a functionally complete set of logical operations. To prove a medium's universality one must represent quanta of information, routes of information transmission and logical gates, where information quanta are processes, in states of the given system. This can be done in two ways: architecture-based and architecture-less. An architecture-based, or stationary, computation implies that a l...

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Human learners can generalize a new concept from a small number of samples. In contrast, conventional machine learning methods require large amounts of data to address the same types of problems. Humans have cognitive biases that promote fast learning. Here, we developed a method to reduce the gap between human beings and machines in this type of inference by utilizing cognitive biases. We implemented a human cognitive model into machine learning algorithms and compared their performance with the currently most popular methods, naïve Bayes, support vector machine, neural networks, logistic regression and random forests. We focused on the task of spam classification, which has been studied for a long time in the field of machine learning and often requires a large amount of data to obtain high accuracy. Our models achieved superior performance with small and biased samples in comparison with other representative machine learning methods.

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