Shellsort with three increments

A perturbation technique can be used to simplify and sharpen A. C. Yao's theorems about the behavior of shellsort with increments $(h,g,1)$. In particular, when $h=\Theta(n^{7/15})$ and $g=\Theta(h^{1/5})$, the average running time is $O(n^{23/15})$. The proof involves interesting properties of the inversions in random permutations that have been $h$-sorted and $g$-sorted

Stringhalt in a Horse

On Oct. 5, 1943, a 9-year-old, brown, riding horse was brought to the veterinary clinic with history and symptoms of stringhalt. When the patient moved at any natural gait, the left hind leg was flexed so that the hoof closely approximated the body. This condition may be defined as an involuntary flexing, affecting one or both posterior limbs. The limb is lifted with excessive suddenness and beyond normal flexion. Numerous investigators in their study of this myoclonic condition have advanced various theories in regard to the possible etiology

Delayed feedback as a means of control of noise-induced motion

Time--delayed feedback is exploited for controlling noise--induced motion in coherence resonance oscillators. Namely, under the proper choice of time delay, one can either increase or decrease the regularity of motion. It is shown that in an excitable system, delayed feedback can stabilize the frequency of oscillations against variation of noise strength. Also, for fixed noise intensity, the phenomenon of entrainment of the basic oscillation period by the delayed feedback occurs. This allows one to steer the timescales of noise-induced motion by changing the time delay.Comment: 4 pages, 4 figures. In the replacement file Fig. 2 and Fig. 4(b),(d) were amended. The reason is numerical error found, that affected the quantitative estimates of correlation time, but did not affect the main messag

Terrestrial planets across space and time

The study of cosmology, galaxy formation and exoplanets has now advanced to a stage where a cosmic inventory of terrestrial planets may be attempted. By coupling semi-analytic models of galaxy formation to a recipe that relates the occurrence of planets to the mass and metallicity of their host stars, we trace the population of terrestrial planets around both solar-mass (FGK type) and lower-mass (M dwarf) stars throughout all of cosmic history. We find that the mean age of terrestrial planets in the local Universe is $7\pm{}1$ Gyr for FGK hosts and $8\pm{}1$ Gyr for M dwarfs. We estimate that hot Jupiters have depleted the population of terrestrial planets around FGK stars by no more than $\approx 10\%$, and that only $\approx 10\%$ of the terrestrial planets at the current epoch are orbiting stars in a metallicity range for which such planets have yet to be confirmed. The typical terrestrial planet in the local Universe is located in a spheroid-dominated galaxy with a total stellar mass comparable to that of the Milky Way. When looking at the inventory of planets throughout the whole observable Universe, we argue for a total of $\approx 1\times 10^{19}$ and $\approx 5\times 10^{20}$ terrestrial planets around FGK and M stars, respectively. Due to light travel time effects, the terrestrial planets on our past light cone exhibit a mean age of just $1.7\pm 0.2$ Gyr. These results are discussed in the context of cosmic habitability, the Copernican principle and searches for extraterrestrial intelligence at cosmological distances.Comment: 11 pages, 8 figures. v.2: Accepted for publication in ApJ. Some changes in quantitative results compared to v.1, mainly due to differences in IMF assumption

Quicksort with unreliable comparisons: a probabilistic analysis

We provide a probabilistic analysis of the output of Quicksort when comparisons can err.Comment: 29 pages, 3 figure

Environmental effects on progesterone profile measures of dairy cow fertility

Environmental effects on fertility measures early in lactation, such as the interval from calving to first luteal activity (CLA), proportion of samples with luteal activity during the first 60 days after calving (PLA) and interval to first ovulatory oestrus (OOE) were studied. In addition, traditional measurements of fertility, such as pregnancy to first insemination, number of inseminations per service period and interval from first to last insemination were studied as well as associations between the early and late measurements. Data were collected from an experimental herd during 15 years and included 1106 post-partum periods from 191 Swedish Holsteins and 325 Swedish Red and White dairy cows. Individual milk progesterone samples were taken twice a week until cyclicity and thereafter less frequently. First parity cows had 14.8 and 18.1 days longer CLA (LS-means difference) than second parity cows and older cows, respectively. Moreover, CLA was 10.5 days longer for cows that calved during the winter season compared with the summer season and 7.5 days longer for cows in tie-stalls than cows in loose-housing system. Cows treated for mastitis and lameness had 8.4 and 18.0 days longer CLA, respectively, compared with healthy cows. OOE was affected in the same way as CLA by the different environmental factors. PLA was a good indicator of CLA, and there was a high correlation (−0.69) between these two measurements. Treatment for lameness had a significant influence on all late fertility measurements, whereas housing was significant only for pregnancy to first insemination. All fertility traits were unfavourably associated with increased milk production. Regression of late fertility measurements on early fertility measurements had only a minor association with conception at first AI and interval from first to last AI for cows with conventional calving intervals, i.e. a 22 days later, CLA increased the interval from first to last insemination by 3.4 days. Early measurements had repeatabilities of 0.14–0.16, indicating a higher influence by the cow itself compared with late measurements, which had repeatabilities of 0.09–0.10. Our study shows that early fertility measurements have a possibility to be used in breeding for better fertility. To improve the early fertility of the cow, there are a number of important factors that have to be taken into account