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Membrane Computing is a recently introduced area of Molecular Computing, where a computation takes place in a membrane structure where multisets of objects evolve according to given rules (they can also pass through membranes). The obtained computing models were called P systems. In basic variants of P systems, the use of objects evolution rules is regulated by a given priority relation; moreover, each membrane has a label and one can send objects to precise membranes, identified by their labels. We propose here a variant where we get rid of both there rather artificial (non-biochemical) features. Instead, we add to membranes and to objects an "electrical charge" and the objects are passed through membranes according to their charge. We prove that such systems are able to characterize the one-letter recursively enumerable languages (equivalently, the recursively enumerable sets of natural numbers), providing that an extra feature is considered: the membranes can be made thicker or thinner (also dissolved) and the communication through a membrane is possible only when its thickness is equal to 1. Several open problems are formulated.

In this paper we study a generalization of the classical notions of bordered and unbordered words, motivated by DNA computing. DNA strands can be viewed as finite strings over the alphabet {A, G, C, T}, and are used in DNA computing to encode information. Due to the fact that A is Watson-Crick complementary to T and G to C, DNA single strands that are Watson-Crick complementary can bind to each other or to themselves in either intended or unintended ways. One of the structures that is usually undesirable for biocomputation, since it makes the affected DNA string unavailable for future interactions, is the hairpin: If some subsequences of a DNA single string are complementary to each other, the string will bind to itself forming a hairpin-like structure. This paper studies a mathematical formalization of a particular case of hairpins, the Watson-Crick bordered words. A Watson-Crick bordered word is a word with the property that it has a prefix that is Watson-Crick complementary to its suffix. More generally, we investigate the notion of θ-bordered words, where θ is a morphic or antimorphic involution. We show that the set of all θ-bordered words is regular, when θ is an antimorphic involution and the set of all θ-bordered words is context-sensitive when θ is a morphic involution. We study the properties of θ-bordered and θ-unbordered words and also the relation between θ-bordered and θ-unbordered words and certain type of involution codes.

In this paper, we present general methods that can be used to explore the information processing potential of a medium composed of oscillating (self-exciting) droplets. Networks of Belousov–Zhabotinsky (BZ) droplets seem especially interesting as chemical reaction-diffusion computers because their time evolution is qualitatively similar to neural network activity. Moreover, such networks can be self-generated in microfluidic reactors. However, it is hard to track and to understand the function performed by a medium composed of droplets due to its complex dynamics. Corresponding to recurrent neural networks, the flow of excitations in a network of droplets is not limited to a single direction and spreads throughout the whole medium. In this work, we analyze the operation performed by droplet systems by monitoring the information flow. This is achieved by measuring mutual information and time delayed mutual information of the discretized time evolution of individual droplets. To link the model with reality, we use experimental results to estimate the parameters of droplet interactions. We exemplarily investigate an evolutionary generated droplet structure that operates as a NOR gate. The presented methods can be applied to networks composed of at least hundreds of droplets.

Theoretical and computational frameworks of complexity science are dominated by binary structures. This binary bias, seen in the ubiquity of pair-wise networks and formal binary operations in mathematical models, limits our capacity to faithfully capture irreducible polyadic interactions in higher-order systems. A paradigmatic example of a higher-order interaction is the Borromean link of three interlocking rings. In this paper, we propose a mathematical framework via hypergraphs and hypermatrix algebras that allows to formalize such forms of higher-order bonding and connectivity in a parsimonious way. Our framework builds on and extends current techniques in higher-order networks — still mostly rooted in binary structures such as adjacency matrices — and incorporates recent developments in higher-arity structures to articulate the compositional behavior of adjacency hypermatrices. Irreducible higher-order interactions turn out to be a widespread occurrence across natural sciences and socio-cultural knowledge representation. We demonstrate this by reviewing recent results in computer science, physics, chemistry, biology, ecology, social science, and cultural analysis through the conceptual lens of irreducible higher-order interactions. We further speculate that the general phenomenon of emergence in complex systems may be characterized by spatio-temporal discrepancies of interaction arity.

Based on the concept of DNA strand displacement and DNA strand algebra we have developed a method for logical inference which is not based on silicon-based computing. Essentially, it is a paradigm shift from silicon to carbon. In this paper, we have considered the inference mechanism, viz. modus ponens, to draw conclusion from any observed fact. Thus, the present approach to logical inference based on DNA strand algebra is basically an attempt to develop expert system design in the domain of DNA computing. We have illustrated our methodology with respect to the worked out example. Our methodology is very flexible for implementation of different expert system applications.

This paper presents a collection of computational modules implemented with chemical reactions: an inverter, an incrementer, a decrementer, a copier, a comparator, and a multiplier. Unlike previous schemes for chemical computation, ours produces designs that are dependent only on coarse rate categories for the reactions ("fast" vs. "slow"). Given such categories, the computation is exact and independent of the specific reaction rates. We validate our designs through stochastic simulations of the chemical kinetics. Although conceptual for the time being, our methodology has potential applications in domains of synthetic biology such as biochemical sensing and drug delivery. We are exploring DNA-based computation via strand displacement as a possible experimental chassis.