Finite automata for caching in matrix product algorithms

A diagram is introduced for visualizing matrix product states which makes transparent a connection between matrix product factorizations of states and operators, and complex weighted finite state automata. It is then shown how one can proceed in the opposite direction: writing an automaton that ``generates'' an operator gives one an immediate matrix product factorization of it. Matrix product factorizations have the advantage of reducing the cost of computing expectation values by facilitating caching of intermediate calculations. Thus our connection to complex weighted finite state automata yields insight into what allows for efficient caching in matrix product algorithms. Finally, these techniques are generalized to the case of multiple dimensions.Comment: 18 pages, 19 figures, LaTeX; numerous improvements have been made to the manuscript in response to referee feedbac

Flipper-bands on penguins: what is the cost of a life-long commitment?

The individual marking of flying and flightless birds has a long history in ornithology. It is the only technique which is cheap, simple and effective, yielding results on bird migration, age-specific annual survival and recruitment. Consequently, hundreds of thousands of birds are annually ringed worldwide. Unfortunately, researchers all too often tend to neglect problems associated with rings and tags. In Antarctic penguins, flipper bands have been used extensively by a variety of nations, and banding is an integral part of the Council for the Conservation of Antarctic Marine Living Resources' (CCAMLR) monitoring programme (Standard method A4). This programme suggests that mortality in penguins wearing bands can be attributed to either (a) prey species availability, (b) predation, (c) weather conditions or (d) other. In this paper, we have attempted to quantify energetic costs associated with wearing a flipper band. For that purpose, freshly caught Adelie penguins (n = 7) were introduced, in Antarctica, into a 21 m long still-water tunnel, where their behaviour and energy consumption were determined via observation and gas respirometry. Birds were either immediately marked with a flipper band and tested in the tunnel for ca 2 h, and then taken out and tested again after removal of the band, or vice-versa. Flipper bands significantly (ANOVA, p = 0.006) increased the power input of Adelie penguins during swimming by 24 % over the speed range of 1.4 to 2.2 m S-', from 17 W kg-' to 21.1 W kg-' (n = 115 and 157 measurements, respectively). The implications of banding on foraging performance and sunival of penguins are discussed. Implantable passive transponders could help overcome such problems

Monitoring Penguins at Sea using Data Loggers

The activity of four penguin species at sea was studied using new data loggers. One unit was fixed to the bird's backs and recorded swim speed, swim heading and dive depth from which the three dimensional movements of the birds at sea could be constructed by vector calculations. This unit additionally recorded sea temperature and light intensity. A further, single-channel logger was ingested by the birds and recorded stomach temperature during the periods at sea. Drops in stomach temperature were indicative of prey capture and could be ascribed to specific localities

Conjugacy of one-dimensional one-sided cellular automata is undecidable

Two cellular automata are strongly conjugate if there exists a shift-commuting conjugacy between them. We prove that the following two sets of pairs $(F,G)$ of one-dimensional one-sided cellular automata over a full shift are recursively inseparable: (i) pairs where $F$ has strictly larger topological entropy than $G$, and (ii) pairs that are strongly conjugate and have zero topological entropy. Because there is no factor map from a lower entropy system to a higher entropy one, and there is no embedding of a higher entropy system into a lower entropy system, we also get as corollaries that the following decision problems are undecidable: Given two one-dimensional one-sided cellular automata $F$ and $G$ over a full shift: Are $F$ and $G$ conjugate? Is $F$ a factor of $G$? Is $F$ a subsystem of $G$? All of these are undecidable in both strong and weak variants (whether the homomorphism is required to commute with the shift or not, respectively). It also immediately follows that these results hold for one-dimensional two-sided cellular automata.Comment: 12 pages, 2 figures, accepted for SOFSEM 201

To slide or stride: when should Adélie penguins (Pygoscelis adeliae) toboggan?

We noted whether Adélie penguins (Pygoscelis adeliae), when travelling over snow, walked or tobogganed according to gradient, snow friction, or snow penetrability. Both walking and tobogganing penguins reduced stride length and stride frequency, and thus speed, with increasing uphill gradient although tobogganing birds travelled faster and with fewer leg movements. The incidence of tobogganing increased with decreasing friction between penguin and snow. The percentage of penguins tobogganing was also highly positively correlated with increasing snow penetrability. Penguins walking on soft snow must expend additional energy to pull their feet through the snow, whereas tobogganing birds do not sink. It is to be expected that Adélie penguins would utilize the most energetically favourable form of travel which, under almost all conditions, appeared to be tobogganing. Although tobogganing appears to be energetically more efficient than walking, rubbing the feathers over snow increases the coefficient of friction in unpreeened plumage. We propose that a high incidence of tobogganing necessitates increased feather care and that the decision whether to walk or toboggan probably represents a balance between immediate energy expenditure and subsequent energy and time expended maintaining plumage condition

Parametric ordering of complex systems

Cellular automata (CA) dynamics are ordered in terms of two global parameters, computable {\sl a priori} from the description of rules. While one of them (activity) has been used before, the second one is new; it estimates the average sensitivity of rules to small configurational changes. For two well-known families of rules, the Wolfram complexity Classes cluster satisfactorily. The observed simultaneous occurrence of sharp and smooth transitions from ordered to disordered dynamics in CA can be explained with the two-parameter diagram