Many free-ranging predators have to make foraging decisions with little, if any, knowledge of present resource distribution and availability. The optimal search strategy they should use to maximize encounter rates with prey in heterogeneous natural environments remains a largely unresolved issue in ecology. Lévy walks are specialized random walks giving rise to fractal movement trajectories that may represent an optimal solution for searching complex landscapes. However, the adaptive significance of this putative strategy in response to natural prey distributions remains untested. Here we analyse over a million movement displacements recorded from animal-attached electronic tags to show that diverse marine predators-sharks, bony fishes, sea turtles and penguins-exhibit Lévy-walk-like behaviour close to a theoretical optimum. Prey density distributions also display Lévy-like fractal patterns, suggesting response movements by predators to prey distributions. Simulations show that predators have higher encounter rates when adopting Lévy-type foraging in natural-like prey fields compared with purely random landscapes. This is consistent with the hypothesis that observed search patterns are adapted to observed statistical patterns of the landscape. This may explain why Lévy-like behaviour seems to be widespread among diverse organisms, from microbes to humans, as a 'rule' that evolved in response to patchy resource distributions.

Patterns of vertical movement in pelagic predators can be highly complex, reflecting behaviours such as foraging, thermoregulatory excursions and spawning. Here we used fast Fourier analysis to identify periodicity in the vertical movements of 6 basking sharks Cetorhinus maximus from archival tagging data that totalled 595 d. We analysed quantitatively fine-scale vertical movements of basking sharks over seasonal scales (May to February) and detected predominant periodicities related to the vertical movements of the sharks' zooplankton prey. Normal and reverse diel vertical migration (DVM) represented the main periodic dive behaviour, occurring for 11 to 72% of individual track times. A tidal pattern of vertical movement, previously unreported for sharks, was also identified. A possible mechanism for this behaviour appears related to the shark exploiting tidally-induced aggregations of zooplankton prey at depth. The youngest shark tagged showed a markedly different pattern of vertical behaviour. Long-term data sets of swimming depth are becoming increasingly available for pelagic predators from pressure-sensitive data loggers. This study demonstrates the utility of signal processing techniques in objectively identifying both expected and unexpected periodicity in these continuous, high-resolution tracks.

The decisions animals make about how long to wait between activities can determine the success of diverse behaviours such as foraging, group formation or risk avoidance. Remarkably, for diverse animal species, including humans, spontaneous patterns of waiting times show random 'burstiness' that appears scale-invariant across a broad set of scales. However, a general theory linking this phenomenon across the animal kingdom currently lacks an ecological basis. Here, we demonstrate from tracking the activities of 15 sympatric predator species (cephalopods, sharks, skates and teleosts) under natural and controlled conditions that bursty waiting times are an intrinsic spontaneous behaviour well approximated by heavy-tailed (power-law) models over data ranges up to four orders of magnitude. Scaling exponents quantifying ratios of frequent short to rare very long waits are species-specific, being determined by traits such as foraging mode (active versus ambush predation), body size and prey preference. A stochastic-deterministic decision model reproduced the empirical waiting time scaling and species-specific exponents, indicating that apparently complex scaling can emerge from simple decisions. Results indicate temporal power-law scaling is a behavioural 'rule of thumb' that is tuned to species' ecological traits, implying a common pattern may have naturally evolved that optimizes move-wait decisions in less predictable natural environments.

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In this paper we present a code design technique which produces codes for syndrome coding which have better secrecy than the best error correcting codes. Code examples are given for the case where the number of parity bits of the code is equal to 15. The code design technique presented is based on extensions of the parity check matrix of a set of good equivocation codes of shorter length. It is also shown that syndrome coding can be implemented without the traditional syndrome look up table, enabling any length codes to be used. An efficient recursive method to calculate the equivocation rate for the binary symmetric channel (BSC) and any linear binary code is also presented. The design results show that the best equivocation codes (BEC) that are produced have better equivocation rate for the syndrome coding scheme compared to all previously published codes, including the best known codes (BKC).

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The article describes the development and evaluation of a web-based precourse in mathematics, delivered to four cohorts of engineering students at a German university. Based on demographic, personal, and learningrelated data relationships between students' preconditions, their learning gains in the pre-course, and study success in the degree programme were analysed. The results support the existing literature in that domain-related prior knowledge and secondary school achievement play a dominant role regarding study success in engineering. The analyses also showed that the influence of cognitive predictors could only be compensated for by a strong learner engagement. At-risk students with high pre-course learning gains showed significantly better first-year performance. The number of self-tests a student attempted was positively related to pre-course learning gains and even to first-year performance, suggesting that this variable is a good indicator of student engagement.