Fixed Point and Aperiodic Tilings

An aperiodic tile set was first constructed by R.Berger while proving the undecidability of the domino problem. It turned out that aperiodic tile sets appear in many topics ranging from logic (the Entscheidungsproblem) to physics (quasicrystals) We present a new construction of an aperiodic tile set that is based on Kleene's fixed-point construction instead of geometric arguments. This construction is similar to J. von Neumann self-reproducing automata; similar ideas were also used by P. Gacs in the context of error-correcting computations. The flexibility of this construction allows us to construct a "robust" aperiodic tile set that does not have periodic (or close to periodic) tilings even if we allow some (sparse enough) tiling errors. This property was not known for any of the existing aperiodic tile sets.Comment: v5: technical revision (positions of figures are shifted

Quasiperiodicity and non-computability in tilings

We study tilings of the plane that combine strong properties of different nature: combinatorial and algorithmic. We prove existence of a tile set that accepts only quasiperiodic and non-recursive tilings. Our construction is based on the fixed point construction; we improve this general technique and make it enforce the property of local regularity of tilings needed for quasiperiodicity. We prove also a stronger result: any effectively closed set can be recursively transformed into a tile set so that the Turing degrees of the resulted tilings consists exactly of the upper cone based on the Turing degrees of the later.Comment: v3: the version accepted to MFCS 201

Coarse-graining of cellular automata, emergence, and the predictability of complex systems

We study the predictability of emergent phenomena in complex systems. Using nearest neighbor, one-dimensional Cellular Automata (CA) as an example, we show how to construct local coarse-grained descriptions of CA in all classes of Wolfram's classification. The resulting coarse-grained CA that we construct are capable of emulating the large-scale behavior of the original systems without accounting for small-scale details. Several CA that can be coarse-grained by this construction are known to be universal Turing machines; they can emulate any CA or other computing devices and are therefore undecidable. We thus show that because in practice one only seeks coarse-grained information, complex physical systems can be predictable and even decidable at some level of description. The renormalization group flows that we construct induce a hierarchy of CA rules. This hierarchy agrees well with apparent rule complexity and is therefore a good candidate for a complexity measure and a classification method. Finally we argue that the large scale dynamics of CA can be very simple, at least when measured by the Kolmogorov complexity of the large scale update rule, and moreover exhibits a novel scaling law. We show that because of this large-scale simplicity, the probability of finding a coarse-grained description of CA approaches unity as one goes to increasingly coarser scales. We interpret this large scale simplicity as a pattern formation mechanism in which large scale patterns are forced upon the system by the simplicity of the rules that govern the large scale dynamics.Comment: 18 pages, 9 figure

A Full Computation-relevant Topological Dynamics Classification of Elementary Cellular Automata

Cellular automata are both computational and dynamical systems. We give a complete classification of the dynamic behaviour of elementary cellular automata (ECA) in terms of fundamental dynamic system notions such as sensitivity and chaoticity. The "complex" ECA emerge to be sensitive, but not chaotic and not eventually weakly periodic. Based on this classification, we conjecture that elementary cellular automata capable of carrying out complex computations, such as needed for Turing-universality, are at the "edge of chaos"

How to Tackle Integer Weighted Automata Positivity

International audienceThis paper is dedicated to candidate abstractions to capture relevant aspects of the integer weighted automata. The expected effect of applying these abstractions is studied to build the deterministic reachability graphs allowing us to semi-decide the positivity problem on these automata. Moreover, the papers reports on the implementations and experimental results, and discusses other encodings

Non-invasive measurement of metabolic rates in wild, free-living birds using doubly labelled water

Please read abstract in the article.DST-NRF Centre of Excellence at the FitzPatrick Institute for African Ornithology; National Research Foundation of South Africa, Grant/Award Number: 110506; Universities of Cambridge and Zurich; MAVA Foundation, ERC, Grant/Award Number: 294494; University of Pretoria; The Oppenheimer Memorial Trust, Grant/Award Number: OMT 20747/01http://wileyonlinelibrary.com/journal/fechj2020Mammal Research InstituteZoology and Entomolog

A Review of Flight-Initiation Distances and their Application to Managing Disturbance to Australian Birds

Disturbance – the response of birds to a stimulus such as the presence of a person – is considered a conservation threat for some Australian birds. The distance at which a bird flees from perceived danger is defined as the flight-initiation distance (FID), and could be used to designate separation distances between birds and stimuli that might cause disturbance. We review the known FIDs for Australian birds, and report FIDs for 250 species. Most FIDs are from south-eastern Australia, and almost all refer to a single walker as the stimulus. Several prominent factors correlated with FID are discussed (e.g. body mass and the distance at which an approach begins). FIDs have not been used extensively in the management of disturbance, for a variety of reasons including lack and inaccessibility of available data. We call for standardised data collection and greater application of available data to the management of disturbance

Evaluating the impact of handling and logger attachment on foraging parameters and physiology in southern rockhopper penguins

Logger technology has revolutionised our knowledge of the behaviour and physiology of free-living animals but handling and logger attachments may have negative effects on the behaviour of the animals and their welfare. We studied southern rockhopper penguin ( Eudyptes chrysocome ) females during the guard stage in three consecutive breeding seasons (2008/09−2010/11) to evaluate the effects of handling and logger attachment on foraging trip duration, dive behaviour and physiological parameters. Smaller dive loggers (TDRs) were used in 2010/11 for comparison to larger GPS data loggers used in all three seasons and we included two categories of control birds: handled controls and PIT control birds that were previously marked with passive integrative transponders (PITs), but which had not been handled during this study. Increased foraging trip duration was only observed in GPS birds during 2010/11, the breeding season in which we also found GPS birds foraging further away from the colony and travelling longer distances. Compared to previous breeding seasons, 2010/11 may have been a period with less favourable environmental conditions, which would enhance the impact of logger attachments. A comparison between GPS and TDR birds showed a significant difference in dive depth frequencies with birds carrying larger GPS data loggers diving shallower. Mean and maximum dive depths were similar between GPS and TDR birds. We measured little impact of logger attachments on physiological parameters (corticosterone, protein, triglyceride levels and leucocyte counts). Overall, handling and short-term logger attachments (1-3 days) showed limited impact on the behaviour and physiology of the birds but care must be taken with the size of data loggers on diving seabirds. Increased drag may alter their diving behaviour substantially, thus constraining them in their ability to catch prey. Results obtained in this study indicate that data recorded may also not represent their normal dive behaviour