Combinatorial complexity of signed discs

AbstractLet C+ and C− be two collections of topological discs. The collection of discs is ‘topological’ in the sense that their boundaries are Jordan curves and each pair of Jordan curves intersect at most twice. We prove that the region ∪C+ − ∪C− has combinatorial complexity at most 10n − 30 where p = |C+|, q = |C−| and n = p + q ≥ 5. Moreover, this bound is achievable. We also show less precise bounds that are stated as functions of p and q

Reproductive behaviour of captive Sumatran rhinoceros Dicerorhinus sumatrensis)

The Sumatran rhinoceros (Dicerorhinus sumatrensis) is on the verge of extinction in Malaysia. At the Sumatran rhinoceros Conservation Centre in Sungai Dusun, the reproductive behaviour of two female and two male rhinoceroses were studied for 8–10 months during attempts to breed them in captivity. Due to the paucity of scientific information on the reproductive biology of the Sumatran rhinoceros, this study was conducted to obtain information on the reproductive behaviour of this species. The male rhino was introduced to a female rhino in the morning for 1–2 h daily in order to observe for behavioural oestrus. Observations were made on the signs of oestrus and mating behaviour. Oestrus was determined by receptivity towards the male and lasted about 24 h. Common signs of oestrus were an increase in frequency of urine spraying, tail raising or swinging, anogenital and other contacts. Although the males exhibited mounting, the inability of the male to achieve intromission was poor. The study demonstrated that the pattern of courtship and copulation of the captive Sumatran rhinos were comparable with those of other rhino species, reported previously by other scientists and flehmen reflex was also exhibited by the male Sumatran rhinos. In a captive breeding programme, it is recommended that only an oestral female is introduced into a male enclosure due to the male solitary behaviour and to avoid serious injuries inflicted onto the females

Trans-scrotal ultrasonography and breeding soundness evaluation of bulls in a herd of dairy and beef cattle with poor reproductive performance

The present study was undertaken to determine the fertility soundness of unselected bulls used for breeding based on a standard breeding soundness evaluation technique (BSE) and trans-scrotal ultrasonography (TSU). A total of 8 bulls, with the mean age of 5½ years (ranged from 3½ - 8 years) and the mean weight of 651.5kg (ranged from 480-840 kg) were evaluated. Three bulls were Friesian Sahiwal, 2 Brangus and the rest were Brahman-KK (Kedah Kelantan) cross, Simmental-KK cross and KK breed (one from each). Out of the total bulls examined, 3 (37.5%) were found to be unfit to be used for breeding due to their physical unsoundness and/or poor semen quality. The use of TSU has revealed the presence of testicular lesions in 3 bulls. The finding of TSU (suggestive of testicular degeneration) in one bull was reflected by a poor semen quality of the BSE results. Despite the presence of lesions of idiopathic unilateral hydrocele and bilateral fibrotic foci lesion in the other two bulls, the BSE findings for semen quality were not compromised. In conclusion, there was enough evidence to support our hypothesis that the observed drop in the reproductive performance of the herd was partly the result of using bulls with poor breeding soundness for fertility

Plasma progesterone changes and length of oestrous cycle in Rusa deer (Rusa timorensis)

A study was conducted to profile the plasma progesterone (P4) concentrations and establish the length of oestrous cycle in the Rusa timorensis during the breeding season. Five healthy hinds were selected for peripheral blood sampling twice weekly to gauge the P4 levels by radioimmunoassay, at the start of the breeding season indicated by rutting behaviours of sexually active males. The hinds were polyestrous as proven by the cyclic trend of P4 levels. After the presumptive oestrus indicated by the lowest P4 concentrations (0.20±0.09ng/ml), this ovarian hormone was markedly elevated on day 7 of the cycle (0.78±0.20ng/ml), reached its peak (2.61±0.23ng/ml, P<0.05) on day 14, and then declined to the basal level in the subsequent oestrus. The mean oestrous cycle length in R. timorensis during the breeding season was 19.2 days with a range of 18-21 days, and the pattern of circulating progesterone during the oestrous cycle of the R. timorensis is similar to those of other deer species. It was also observed that the length of oestrous cycle of R. timorensis determined by gauging the progesterone levels and observation of the oestrous behaviours as well as changes in the cellular pattern of vaginal epithelial cells are highly consistent

Fecal progestin extraction and analysis for non-invasive monitoring of ovarian cycle in beef cows

The aims of the present study were to determine presence of immunoreactive progestins in feces, correlate fecal progestins with plasma progesterone (P 4) concentrations and subsequently assess the role of fecal progestins in monitoring estrous cycle in Kedah Kelantan (KK) beef cows. A total of 12 cycling cows were subjected to blood and matched fecal sampling twice a week for 9 weeks. The concentrations of plasma P 4 and fecal progestins extracted using a modified technique, were determined by a P 4 radioimmunoassay (RIA) kit. There was a significant positive correlation between the concentrations of fecal progestins and plasma P 4 (r = 0.6, P<0.01), as tested for the whole group except one animal. High performance liquid chromatographic separation of fecal extracts and subsequent radioimmunoassay revealed presence of four immunoreactive progestins against the P 4 antibodies. These results imply that the non-invasive measure of fecal progestins using a DSL-3900 RIA kit can be used to monitor the ovarian activity in beef cows

Combinatorial Complexity of Translating a Box in Polyhedral 3-Space

We study the space of free translations of a box amidst polyhedral obstacles with n vertices. We show that the combinatorial complexity of this space is O(n 2 ff(n)) where ff(n) is the inverse Ackermann function. Our bound is within an ff(n) factor off the lower bound, and it constitutes an improvement of almost an order of magnitude over the best previously known (and naive) bound for this problem, O(n 3 ). For the case of a convex polygon of fixed (constant) size translating in the same setting (namely, a two-dimensional polygon translating in three-dimensional space), we show a tight bound \Theta(n 2 ff(n)) on the complexity of the free space. A preliminary version of this paper appeared in Proc. 9th ACM Symposium on Computational Geometry, San Diego, 1993. Work on this paper by the first author has been supported by a Rothschild Postdoctoral Fellowship, by a grant from the Stanford Integrated Manufacturing Association (SIMA), by NSF/ARPA Grant IRI-9306544, and by NSF Grant..

Constructive Hopf´s theorem : or how to untangle closed planar curves

We consider the classification of polygons (i.e. closed polygonal paths) in which, essentially, two polygons are equivalent if one can be continously transformed into the other without causing two adjacent edges to overlap at some moment. By a theorem of Hopf (for dimension 1, applied to polygons), this amounts to counting the winding number of the polygons. We show that a quadratic number of elementary steps suffices to transform between any two equivalent polygons. Furthermore, this sequence of elementary steps, although quadratic in number, can be described and found in linear time. In order to get our constructions, we give a direct proof of Hopfs result

A Basis for Implementing Exact Geometric Algorithms (Extended Abstract)

Our ultimate goal is to develop exact geometric computation as an viable alternative to the usual computing paradigm based on fixed-precision arithmetic. Use of exact computation has numerous advantages; in particular, it will abolish the non-robustness issues that has so far defied satisfactory solution. In this paper we describe two computational tools which can be a basis for exact geometric computing: ffl bigFloat: a multi-precision floating-point number system with automatic errorhandling. ffl bigExpression: an expressions package based on a precision-driven mechanism. This package is built on top of bigFloat. We discuss the rationale for the design of these packages. Experimental results are reported. The major contributions of our work are: ffl We demonstrated for the first time that, because of the existence of root..