Numerical cognition in bees and other insects

The ability to perceive the number of objects has been known to exist in vertebrates for a few decades, but recent behavioral investigations have demonstrated that several invertebrate species can also be placed on the continuum of numerical abilities shared with birds, mammals, and reptiles. In this review article, we present the main experimental studies that have examined the ability of insects to use numerical information. These studies have made use of a wide range of methodologies, and for this reason it is striking that a common finding is the inability of the tested animals to discriminate numerical quantities greater than four. Furthermore, the finding that bees can not only transfer learnt numerical discrimination to novel objects, but also to novel numerosities, is strongly suggestive of a true, albeit limited, ability to count. Later in the review, we evaluate the available evidence to narrow down the possible mechanisms that the animals might be using to solve the number-based experimental tasks presented to them. We conclude by suggesting avenues of further research that take into account variables such as the animals' age and experience, as well as complementary cognitive systems such as attention and the time sense.This publication was funded by the German Research Foundation (DFG) and the University of Wuerzburg in the funding program Open Access Publishing. Shaowu Zhang was supported by the ARC-CoE in Vision Science

Inferences on median failure time for censored survival data

In this thesis two approaches of inferences on median failure times are considered and developed to compare the difference of median failure times between two groups of censored survival data.The first one is to generalize the Mood's median test - which is designed to deal with complete data - to censored survival data. To this end, two groups of censored survival data are pooled and then the estimated pooled median failure time is obtained from the product-limit method. A score is assigned for each observation to indicate the probability whether it survives after the pooled median failure time or not and for each group the scores are summed to summarize the number of observations whose survival time is larger than or equal to pooled median survival time, which results in a 2x2 contingency table with non-integer entries. Four 2x2 contingency tables with integer entries are then derived and a test statistic is defined as the weighted sum of the statistics from the four 2x2 contingency tables which is shown to be approximately distributed as chi-square distribution with 1 degree of freedom for large samples.The second approach is proposed to construct a 95% confidence interval for the difference of median failure times between two groups of censored survival distributions. Since the median failure time is approximately normally distributed for large samples, the estimated median failure times for each group are obtained by product-limit method and their standard errors are computed through bootstrap samples from the original data. Theory of construction for 95% confidence interval for the difference of median failure times is investigated for the standard normal distributions and it can be used for general normal distributions by translation and rescaling.Extensive numerical studies are carried out to test the appropriateness of the two approaches and the results show that the approaches developed in the thesis are easy to implement and the results are promising, compared to the results from published papers. The proposed methods will facilitate more accurate analysis of survival data under censoring, which are commonly collected from clinical studies that influence public health

Large Scale Homing in Honeybees

Honeybee foragers frequently fly several kilometres to and from vital resources, and communicate those locations to their nest mates by a symbolic dance language. Research has shown that they achieve this feat by memorizing landmarks and the skyline panorama, using the sun and polarized skylight as compasses and by integrating their outbound flight paths. In order to investigate the capacity of the honeybees' homing abilities, we artificially displaced foragers to novel release spots at various distances up to 13 km in the four cardinal directions. Returning bees were individually registered by a radio frequency identification (RFID) system at the hive entrance. We found that homing rate, homing speed and the maximum homing distance depend on the release direction. Bees released in the east were more likely to find their way back home, and returned faster than bees released in any other direction, due to the familiarity of global landmarks seen from the hive. Our findings suggest that such large scale homing is facilitated by global landmarks acting as beacons, and possibly the entire skyline panorama.This study was supported by the ARC COE in Vision Sciences (CE0561903), ARC DP-0450535 to SWZ, MP, and HZ (http://www.vision.edu.au/). MP was supported by a grant of the German Excellence Initiative to the Graduate School of Life Sciences, Würzburg University (http://www.graduateschools.uni-wuerzburg.de/life_sciences). This publication was funded by the German Research Foundation (DFG) and the University of Wuerzburg in the funding programme Open Access Publishing. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript

On the lifting and reconstruction of nonlinear systems with multiple attractors

The Koopman operator provides a linear perspective on non-linear dynamics by focusing on the evolution of observables in an invariant subspace. Observables of interest are typically linearly reconstructed from the Koopman eigenfunctions. Despite the broad use of Koopman operators over the past few years, there exist some misconceptions about the applicability of Koopman operators to dynamical systems with more than one fixed point. In this work, an explanation is provided for the mechanism of lifting for the Koopman operator of nonlinear systems with multiple attractors. Considering the example of the Duffing oscillator, we show that by exploiting the inherent symmetry between the basins of attraction, a linear reconstruction with three degrees of freedom in the Koopman observable space is sufficient to globally linearize the system.Comment: 8 page