We present Planar Rosa, a family of rhombus tilings with a 2n-fold rotational symmetry that are generated by a primitive substitution and that are also discrete plane tilings, meaning that they are obtained as a projection of a higher dimensional discrete plane. The discrete plane condition is a relaxed version of the cut-and-project condition. We also prove that the Sub Rosa substitution tilings with 2n-fold rotational symmetry defined by Kari and Rissanen do not satisfy even the weaker discrete plane condition. We prove these results for all even \(n\geqslant 4\). This completes our previously published results for odd values of n.

Cellular automata (CA) are an interesting computational model for designing pseudorandom number generators (PRNG), due to the complex dynamical behavior they can exhibit depending on the underlying local rule. Most of the CA-based PRNGs proposed in the literature, however, suffer from poor diffusion since a change in a single cell can propagate only within its neighborhood during a single time step. This might pose a problem especially when such PRNGs are used for cryptographic purposes. In this paper, we consider an alternative approach to generate pseudorandom sequences through orthogonal CA (OCA), which guarantees a better amount of diffusion. After defining the related PRNG, we perform an empirical investigation of the maximal cycles in OCA pairs up to diameter $$d=8$$ . Next, we focus on OCA induced by linear rules, giving a characterization of their cycle structure based on the rational canonical form of the associated Sylvester matrix. Finally, we devise an algorithm to enumerate all linear OCA pairs characterized by a single maximal cycle, and apply it up to diameter $$d=16$$ and $$d=13$$ for OCA respectively over the binary and ternary alphabets.

In this study, we synthesize a novel dynamical approach for ant colonies enabling them to migrate to new nest sites in a self-organizing fashion. In other words, we realize ant colony migration as a self-organizing phenotype-level collective behavior. For this purpose, we first segment the edges of the graph of ants' pathways. Then, each segment, attributed to its own pheromone profile, may host an ant. So, multiple ants may occupy an edge at the same time. Thanks to this segment-wise edge formulation, ants have more selection options in the course of their pathway determination, thereby increasing the diversity of their colony's emergent behaviors. In light of the continuous pheromone dynamics of segments, each edge owns a spatio-temporal piece-wise continuous pheromone profile in which both deposit and evaporation processes are unified. The passive dynamics of the proposed migration mechanism is sufficiently rich so that an ant colony can migrate to the vicinity of a new nest site in a self-organizing manner without any external supervision. In particular, we perform extensive simulations to test our migration dynamics applied to a colony including 500 ants traversing a pathway graph comprising 200 nodes and 4000 edges which are segmented based on various resolutions. The obtained results exhibit the effectiveness of our strategy.

Single-objective continuous optimization can be challenging, especially when dealing with multimodal problems. This work sheds light on the effects that multi-objective optimization may have in the single-objective space. For this purpose, we examine the inner mechanisms of the recently developed sophisticated local search procedure SOMOGSA. This method solves multimodal single-objective continuous optimization problems based on first expanding the problem with an additional objective (e.g., a sphere function) to the bi-objective domain and subsequently exploiting local structures of the resulting landscapes. Our study particularly focuses on the sensitivity of this multiobjectivization approach w.r.t. (1) the parametrization of the artificial second objective, as well as (2) the position of the initial starting points in the search space. As SOMOGSA is a modular framework for encapsulating local search, we integrate Nelder–Mead local search as optimizer in the respective module and compare the performance of the resulting hybrid local search to its original single-objective counterpart. We show that the SOMOGSA framework can significantly boost local search by multiobjectivization. Hence, combined with more sophisticated local search and metaheuristics, this may help solve highly multimodal optimization problems in the future.

String assembling systems are biologically inspired mechanisms that generate strings from copies out of finite sets of assembly units. The underlying mechanism is based on piecewise assembly of a double-stranded sequence of symbols, where the upper and lower strand have to match. The generation is additionally controlled by the requirement that the first symbol of a unit has to be the same as the last symbol of the strand generated so far, as well as by the distinction of assembly units that may appear at the beginning, during, or at the end of the assembling process and by a length restriction on the units. We investigate the power of these model-inherent control mechanisms by considering variants where one or more of these mechanisms are relaxed. The generative capacities and the relative power of the variants are our main interest. In particular, we prove that the power gained in the different control mechanisms may yield strictly more powerful systems and incomparable capacities. Additionally, we generalize these systems to multi-stranded systems. We obtain a strong connection to one-way multi-head finite automata and show an infinite, dense, and strict strand hierarchy. Finally, we examine the closure properties of the different variants of string assembling systems.

Spiking neural P systems are parallel and distributed computation devices which are inspired by the neuro-physiological behavior of biological neurons. In this paper we will present, with a tutorial approach, the main underlying ideas and the most interesting variants that have been proposed in the literature. In particular, we will discuss the results on the computational power of these models, both in terms of Turing completeness and of efficiency in solving hard problems, under different assumptions for information encoding, form and application of rules, and bounds on the main parameters defining the systems.

Dynamic linear functions on the boolean hypercube are functions which assign to each bit a positive weight, but the weights change over time. Throughout optimization, these functions maintain the same global optimum, and never have defecting local optima. Nevertheless, it was recently shown [Lengler, Schaller, FOCI 2019] that the (1+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(1+1)$$\\end{document}-Evolutionary Algorithm needs exponential time to find or approximate the optimum for some algorithm configurations. In this experimental paper, we study the effect of larger population sizes for dynamic binval, the extreme form of dynamic linear functions. We find that moderately increased population sizes extend the range of efficient algorithm configurations, and that crossover boosts this positive effect substantially. Remarkably, similar to the static setting of monotone functions in [Lengler, Zou, FOGA 2019], the hardest region of optimization for (μ+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\mu +1)$$\\end{document}-EA is not close the optimum, but far away from it. In contrast, for the (μ+1)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$(\\mu +1)$$\\end{document}-GA, the region around the optimum is the hardest region in all studied cases.Kindly check and confirm the inserted city name is correctly identified.Correct.

Molecular robotics is challenging, so it seems best to keep it simple. We consider an abstract molecular robotics model based on simple folding instructions that execute asynchronously. Turning Machines are a simple 1D to 2D folding model, also easily generalisable to 2D to 3D folding. A Turning Machine starts out as a line of connected monomers in the discrete plane, each with an associated turning number. A monomer turns relative to its neighbours, executing a unit-distance translation that drags other monomers along with it, and through collective motion the initial set of monomers eventually folds into a programmed shape. We provide a suite of tools for reasoning about Turning Machines by fully characterising their ability to execute line rotations: executing an almost-full line rotation of 5π/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5\\pi /3$$\\end{document} radians is possible, yet a full 2π\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$2\\pi$$\\end{document} rotation is impossible. Furthermore, line rotations up to 5π/3\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$5\\pi /3$$\\end{document} are executed efficiently, in O(logn)\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$O(\\log n)$$\\end{document} expected time in our continuous time Markov chain time model. We then show that such line-rotations represent a fundamental primitive in the model, by using them to efficiently and asynchronously fold shapes. In particular, arbitrarily large zig-zag-rastered squares and zig-zag paths are foldable, as are y-monotone shapes albeit with error (bounded by perimeter length). Finally, we give shapes that despite having paths that traverse all their points, are in fact impossible to fold, as well as techniques for folding certain classes of (scaled) shapes without error. Our approach relies on careful geometric-based analyses of the feats possible and impossible by a very simple robotic system, and pushes conceptional hardness towards mathematical analysis and away from molecular implementation.