Element Distinctness, Frequency Moments, and Sliding Windows

We derive new time-space tradeoff lower bounds and algorithms for exactly computing statistics of input data, including frequency moments, element distinctness, and order statistics, that are simple to calculate for sorted data. We develop a randomized algorithm for the element distinctness problem whose time T and space S satisfy T in O (n^{3/2}/S^{1/2}), smaller than previous lower bounds for comparison-based algorithms, showing that element distinctness is strictly easier than sorting for randomized branching programs. This algorithm is based on a new time and space efficient algorithm for finding all collisions of a function f from a finite set to itself that are reachable by iterating f from a given set of starting points. We further show that our element distinctness algorithm can be extended at only a polylogarithmic factor cost to solve the element distinctness problem over sliding windows, where the task is to take an input of length 2n-1 and produce an output for each window of length n, giving n outputs in total. In contrast, we show a time-space tradeoff lower bound of T in Omega(n^2/S) for randomized branching programs to compute the number of distinct elements over sliding windows. The same lower bound holds for computing the low-order bit of F_0 and computing any frequency moment F_k, k neq 1. This shows that those frequency moments and the decision problem F_0 mod 2 are strictly harder than element distinctness. We complement this lower bound with a T in O(n^2/S) comparison-based deterministic RAM algorithm for exactly computing F_k over sliding windows, nearly matching both our lower bound for the sliding-window version and the comparison-based lower bounds for the single-window version. We further exhibit a quantum algorithm for F_0 over sliding windows with T in O(n^{3/2}/S^{1/2}). Finally, we consider the computations of order statistics over sliding windows.Comment: arXiv admin note: substantial text overlap with arXiv:1212.437

Flatfish herding behavior in response to trawl sweeps: a comparison of diel responses to conventional sweeps and elevated sweeps

Commercial bottom trawls often have sweeps to herd fish into the net. Elevation of the sweeps off the seaf loor may reduce seafloor disturbance, but also reduce herding effectiveness. In both field and laboratory experiments, we examined the behavior of flatfish in response to sweeps. We tested the hypotheses that 1) sweeps are more effective at herding flatfish during the day than at night, when fish are unable to see approaching gear, and that 2) elevation of sweeps off the seafloor reduces herding during the day, but not at night. In sea trials, day catches were greater than night catches for four out of six flatfish species examined. The elevation of sweeps 10 cm significantly decreased catches during the day, but not at night. Laboratory experiments revealed northern rock sole (Lepidopsetta polyxystra) and Pacific halibut (Hippoglossus stenolepis) were more likely to be herded\ud by the sweep in the light, whereas in the dark they tended to pass under or over the sweep. In the light, elevation of the sweep reduced herding, and more fish passed under the sweep. In contrast, in the dark, sweep elevation had little effect upon the number of fish that exhibited herding behavior. The results of both field and laboratory experiments were consistent with the premise that vision is the principle sensory input that controls fish behavior and orientation to trawl gear, and gear performance will differ between conditions where flatfish can see, in contrast to where they cannot see, the approaching gear

Studies on temperature acclimation in the freshwater pulmonate mollusc Lymnaea stagnalis (L.)

PhDThis work is concerned with processes of thermal acclimation in the freshwater pulmonate, Lymnaea stagnalis. Three physiological functions were studied: heart rate, rate of oxygen consumption and assimilation efficiency, Seasonal changes in rate-temperature curves of the first two processes were investigated and compared with alterations induced by exposure to constant temperatures in the laboratory. Simple comparisons were made to determine whether season affected assimilation efficiency. The aims of the investigation were to show whether the measured physiological functions exhibited acclimatory responses to determine the precise nature and interrelationship of any such adaptations, and to suggest possible mechanisms responsible for the changes. It was found that changes in the heart rate-temperature relation were induced both by season and by laboratory acclimation. Results of the seasonal study showed apparent capacity adaptations, so that winter animals had a higher heart rate than summer animals at temperatures between 15 and 25 degrees C, and also resistance adaptations, which gave summer animals increased resistance to heat and winter animals greater tolerance of cold. Laboratory acclimation induced resistance adaptations at both temperature extremes but capacity adaptation was absent. Observed bimodality in heart rate-temperature curves of both studies indicated that control of heart rate is complex. These results are discussed further with reference to changes in physiological mechanisms. Seasonal changes occurred in the size-rate regression for oxygen consumption and in the general shape of the rate temporature curves. There was evidence for a 'reverse acclimation' in response to seasonal changes in temperature. These seasonal responses were not produced, however, by exposure to constant temperature in the laboratory. It is proposed that the observed changes resulted essentially from reproductive activity and seasonal changes in dietary conditions. Hormonal influences are thought to be most important in mediating these changes. No significant differences were found in the assimilation efficiencies of winter and summer snails. Results of this and other studies suggest that the assimilation function does not show acclimatory changes in response to either temperature or season. The results are discussed in relation to the known biology of Lymnaea stagnalis and with reference to fundamental temperature acclimation

Dianas or Drudges? Women's status in the Last Ice Age

In recent decades there have been a number of endeavours to re-examine women’s lives during the last Ice Age.  For far too long, the view of ‘man-the-hunter’ and woman as ‘gatherer, cook and child minder’ was an unchallenged hypothesis, and without doubt, this simplistic view of early hunter-gatherer’s division-of-labour practices was ripe for revision. Unfortunately, it led to a number of over-zealous assertions: that women were big game hunters too, and as such, could not have been dominated by men. Breaking such stereotypes about prehistoric women is the message delivered in a recent documentary and accompanying book called ‘Lady Sapiens.’ But are such views about the roles of men and women in pre-history based on anything more than wishful thinking and result in fresh mythologising? Is there any archaeological evidence that allows us to assume anything about the economic activities of men and women in these early prehistoric cultures