Efficiency and Pooling in Western Cape Wine Grape Production

This paper uses a stochastic frontier and inefficiency model to test the efficiency of grape production in the Western Cape. The data covers two panels of wine grape farms (34 in Robertson and 36 in Worcester) for 2003 and 2004 and 37 table grape farms in De Doorns for 2004 only. Tests show that Cobb Douglas stochastic production frontiers, with variables to explain the inefficiencies are an appropriate representation of the five individual samples. The stochastic frontier results indicate that output can be explained by land, labour and machinery and that efficiency cab be affected by labour quality, age and education of the farmer, location, the percentage of non-bearing vines and expenditures on electricity for irrigation. These data is sufficiently good to produce reasonable results without pooling, but most applied economists would consider the possibility of improving the estimates by pooling the samples. However, pooling tests show that in this situation with small samples, when pooling is permissible it may not be helpful. More effort on determining the true distributions is needed to improve the way such samples are handled and Bayesian methods may be helpful in this respect.Crop Production/Industries, O13, Q12,

Diving in Two Marine Lakes in Croatia

We describe the diving methods used for in-situ observations of the scyphozoan medusa, Aurelia sp., in two marine lakes on the island of Mljet, Croatia. Both lakes have a strong pycnocline at approximately 15 m. During this study (May, 2004) surface temperature was about 20o C; bottom temperature about 10o C. Visibility was 15 m to 30 m. Tide and currents were negligible. A dense resident population of Aurelia sp. and a predictable environment made this an ideal study site. Aurelia was most abundant in mid-water around the pycnocline. There were several dive objectives: specimen collection for laboratory analysis, population census, discrete plankton tows and direct observation of flow around swimming medusae. We used several methods for maintaining our orientation underwater including working from an anchor line, towing a tethered buoy, and use of a blue water rig. Because the environment was relatively benign we allowed the rig to drift free while the boat was standing by at a short distance. Often a tether was not required. This plan allowed the most freedom and provided an excellent reference throughout the dive

Omnivory by the Small Cosmopolitan Hydromedusa Aglaura Hemistoma

We investigated the feeding of the small hydromedusa, Aglaura hemistoma (bell diameter \u3c 4 mm), to determine if it occupies a trophic position similar to that of large medusae. Feeding was examined using gut-content analysis of preserved and unpreserved medusae and by analyzing prey-capture events using microvideographic techniques. Analysis of gut contents and prey-capture events revealed that A. hemistoma fed heavily on protistan prey and that it possessed a prey-capture mechanism, specifically a feeding current,that is effective at entraining and capturing protists with low motility. We suggest that many species of small hydromedusae possess prey-capture mechanisms adapted to capture small protistan prey and that many of these small hydromedusae feed omnivorously on microplanktonic prey. The trophic roles of small hydromedusae in different systems are not understood and more studies are needed. However, based on their often high abundances and the cosmopolitan nature, if small hydromedusae are primarily omnivores, they need to be considered when estimating the impact of zooplankton on primary production and, more generally, protistan community dynamics

Forensic science evidence in question

How should forensic scientists and other expert witnesses present their evidence in court? What kinds and quality of data can experts properly draw on in formulating their conclusions? In an important recent decision in R. v T1 the Court of Appeal revisited these perennial questions, with the complicating twist that the evidence in question incorporated quantified probabilities, not all of which were based on statistical data. Recalling the sceptical tenor of previous judgments addressing the role of probability in the evaluation of scientific evidence,2 the Court of Appeal in R. v T condemned the expert’s methodology and served notice that it should not be repeated in future, a ruling which rapidly reverberated around the forensic science community causing consternation, and even dismay, amongst many seasoned practitioners.3 At such moments of perceived crisis it is essential to retain a sense of perspective. There is, in fact, much to welcome in the Court of Appeal’s judgment in R. v T, starting with the court’s commendable determination to subject the quality of expert evidence adduced in criminal litigation to searching scrutiny. English courts have not consistently risen to this challenge, sometimes accepting rather too easily the validity of questionable scientific techniques.4 However, the Court of Appeal’s reasoning in R. v T is not always easy to follow, and there are certain passages in the judgment which, taken out of context, might even appear to confirm forensic scientists’ worst fears. This article offers a constructive reading of R. v T, emphasising its positive features whilst rejecting interpretations which threaten, despite the Court of Appeal’s best intentions, to diminish the integrity of scientific evidence adduced in English criminal trials and distort its probative value

Apollonian Circle Packings: Geometry and Group Theory II. Super-Apollonian Group and Integral Packings

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. Such packings can be described in terms of the Descartes configurations they contain. It observed there exist infinitely many types of integral Apollonian packings in which all circles had integer curvatures, with the integral structure being related to the integral nature of the Apollonian group. Here we consider the action of a larger discrete group, the super-Apollonian group, also having an integral structure, whose orbits describe the Descartes quadruples of a geometric object we call a super-packing. The circles in a super-packing never cross each other but are nested to an arbitrary depth. Certain Apollonian packings and super-packings are strongly integral in the sense that the curvatures of all circles are integral and the curvature$\times$centers of all circles are integral. We show that (up to scale) there are exactly 8 different (geometric) strongly integral super-packings, and that each contains a copy of every integral Apollonian circle packing (also up to scale). We show that the super-Apollonian group has finite volume in the group of all automorphisms of the parameter space of Descartes configurations, which is isomorphic to the Lorentz group $O(3, 1)$.Comment: 37 Pages, 11 figures. The second in a series on Apollonian circle packings beginning with math.MG/0010298. Extensively revised in June, 2004. More integral properties are discussed. More revision in July, 2004: interchange sections 7 and 8, revised sections 1 and 2 to match, and added matrix formulations for super-Apollonian group and its Lorentz version. Slight revision in March 10, 200

Apollonian Circle Packings: Geometry and Group Theory I. The Apollonian Group

Apollonian circle packings arise by repeatedly filling the interstices between four mutually tangent circles with further tangent circles. We observe that there exist Apollonian packings which have strong integrality properties, in which all circles in the packing have integer curvatures and rational centers such that (curvature)$\times$(center) is an integer vector. This series of papers explain such properties. A {\em Descartes configuration} is a set of four mutually tangent circles with disjoint interiors. We describe the space of all Descartes configurations using a coordinate system \sM_\DD consisting of those $4 \times 4$ real matrices \bW with \bW^T \bQ_{D} \bW = \bQ_{W} where \bQ_D is the matrix of the Descartes quadratic form $Q_D= x_1^2 + x_2^2+ x_3^2 + x_4^2 -{1/2}(x_1 +x_2 +x_3 + x_4)^2$ and \bQ_W of the quadratic form $Q_W = -8x_1x_2 + 2x_3^2 + 2x_4^2$. There are natural group actions on the parameter space \sM_\DD. We observe that the Descartes configurations in each Apollonian packing form an orbit under a certain finitely generated discrete group, the {\em Apollonian group}. This group consists of $4 \times 4$ integer matrices, and its integrality properties lead to the integrality properties observed in some Apollonian circle packings. We introduce two more related finitely generated groups, the dual Apollonian group and the super-Apollonian group, which have nice geometrically interpretations. We show these groups are hyperbolic Coxeter groups.Comment: 42 pages, 11 figures. Extensively revised version on June 14, 2004. Revised Appendix B and a few changes on July, 2004. Slight revision on March 10, 200

Apollonian Circle Packings: Geometry and Group Theory III. Higher Dimensions

This paper gives $n$-dimensional analogues of the Apollonian circle packings in parts I and II. We work in the space \sM_{\dd}^n of all $n$-dimensional oriented Descartes configurations parametrized in a coordinate system, ACC-coordinates, as those $(n+2) \times (n+2)$ real matrices \bW with \bW^T \bQ_{D,n} \bW = \bQ_{W,n} where $Q_{D,n} = x_1^2 +... + x_{n+2}^2 - \frac{1}{n}(x_1 +... + x_{n+2})^2$ is the $n$-dimensional Descartes quadratic form, $Q_{W,n} = -8x_1x_2 + 2x_3^2 + ... + 2x_{n+2}^2$, and \bQ_{D,n} and \bQ_{W,n} are their corresponding symmetric matrices. There are natural actions on the parameter space \sM_{\dd}^n. We introduce $n$-dimensional analogues of the Apollonian group, the dual Apollonian group and the super-Apollonian group. These are finitely generated groups with the following integrality properties: the dual Apollonian group consists of integral matrices in all dimensions, while the other two consist of rational matrices, with denominators having prime divisors drawn from a finite set $S$ depending on the dimension. We show that the the Apollonian group and the dual Apollonian group are finitely presented, and are Coxeter groups. We define an Apollonian cluster ensemble to be any orbit under the Apollonian group, with similar notions for the other two groups. We determine in which dimensions one can find rational Apollonian cluster ensembles (all curvatures rational) and strongly rational Apollonian sphere ensembles (all ACC-coordinates rational).Comment: 37 pages. The third in a series on Apollonian circle packings beginning with math.MG/0010298. Revised and extended. Added: Apollonian groups and Apollonian Cluster Ensembles (Section 4),and Presentation for n-dimensional Apollonian Group (Section 5). Slight revision on March 10, 200

X-ray Transform and Boundary Rigidity for Asymptotically Hyperbolic Manifolds

We consider the boundary rigidity problem for asymptotically hyperbolic manifolds. We show injectivity of the X-ray transform in several cases and consider the non-linear inverse problem which consists of recovering a metric from boundary measurements for the geodesic flow.Comment: 54 page