A census of critical sets in the Latin squares of order at most six

A critical set in a Latin square of order n is a set of entries from the square which can be embedded in precisely one Latin square of order n, Such that if any element of the critical set. is deleted, the remaining set can be embedded, in more than one Latin square of order n.. In this paper we find all the critical sets of different sizes in the Latin squares of order at most six. We count the number of main and isotopy classes of these critical sets and classify critical sets from the main classes into various strengths. Some observations are made about the relationship between the numbers of classes, particularly in the 6 x 6 case. Finally some examples are given of each type of critical set.

An investigation of 2-critical sets in latin squares

In this paper we focus on the existence of 2-critical sets in the latin square corresponding to the elementary abelian 2-group of order 2(n). It has been shown by Stinson and van Rees that this latin square contains a 2-critical set of volume 4(n) - 3(n). We provide constructions for 2-critical sets containing 4(n) - 3(n) + 1 - (2(k-1) + 2(m-1) + 2(n-(k+m+1))) entries, where 1 less than or equal to k less than or equal to n and 1 less than or equal to m less than or equal to n - k. That is, we construct 2-critical sets for certain values less than 4(n) - 3(n) + 1 - 3 (.) 2([n /3]-1). The results raise the interesting question of whether, for the given latin square, it is possible to construct 2-critical sets of volume m, where 4(n) - 3(n) + 1 - 3 (.) 2([n/3]-1) < m < 4(n) - 3(n).

Behavioural characterization of Vitamin D receptor knockout mice

Vitamin D (calcitriol) is a nuclear transcription regulator acting via a nuclear hormone receptor (VDR). In addition to its role in the regulation of calcium and phosphate horneostasis and in bone formation, Vitamin D is also thought to be involved in brain function. The aim of this study was to behaviourally phenotype VDR knockout mice. We characterized the behaviour of VDR null mutant mice and wildtype littermate controls by subjecting them to a range of tests including a primary behavioural screen (using the SHIRPA protocol), rotarod, gait analysis, Y-maze, marble burying test, bedding test, holeboard test, elevated plus maze, open field test and prepulse inhibition of the acoustic startle response. There were no effects of genotype on most of the scores from the SHIRPA protocol except that VDR -/- mice had alopecia, were shorter and weighed less than VDR +/+ mice. VDR -/- mice had a shorter gait as well as impairments on the rotarod, in the bedding test and impaired habituation in both the open field and on the acoustic startle response. The VDR -/- mice had normal acoustic startle responses but had impaired PPI at long (256 ms) but not short (64 ms) prepulse to pulse intervals. The VDR -/- mice were less active in the open field and buried fewer marbles in the marble burying test. However, there were no differences in the time spent on the open arms of the elevated plus maze or in working memory as assessed by repeat arm entries on the Y-maze. Therefore, it appears that VDR -/- mice have muscular and motor impairments that significantly affects locomotor behaviour but seemingly no impairments in cognition as indicated by exploration, working memory or anxiety. (C) 2004 Elsevier B.V. All rights reserved.

Zero-non-zero patterned vector error correction modeling for I(2) cointegrated time series with applications in testing PPP and stock market relationships

Vector error-correction models (VECMs) have become increasingly important in their application to financial markets. Standard full-order VECM models assume non-zero entries in all their coefficient matrices. However, applications of VECM models to financial market data have revealed that zero entries are often a necessary part of efficient modelling. In such cases, the use of full-order VECM models may lead to incorrect inferences. Specifically, if indirect causality or Granger non-causality exists among the variables, the use of over-parameterised full-order VECM models may weaken the power of statistical inference. In this paper, it is argued that the zero–non-zero (ZNZ) patterned VECM is a more straightforward and effective means of testing for both indirect causality and Granger non-causality. For a ZNZ patterned VECM framework for time series of integrated order two, we provide a new algorithm to select cointegrating and loading vectors that can contain zero entries. Two case studies are used to demonstrate the usefulness of the algorithm in tests of purchasing power parity and a three-variable system involving the stock market.

SCORPION2: A database for structure-function analysis of scorpion toxins

Scorpion toxins are important experimental tools for characterization of vast array of ion channels and serve as scaffolds for drug design. General public database entries contain limited annotation whereby rich structure-function information from mutation studies is typically not available. SCORPION2 contains more than 800 records of native and mutant toxin sequences enriched with binding affinity and toxicity information, 624 three-dimensional structures and some 500 references. SCORPION2 has a set of search and prediction tools that allow users to extract and perform specific queries: text searches of scorpion toxin records, sequence similarity search, extraction of sequences, visualization of scorpion toxin structures, analysis of toxic activity, and functional annotation of previously uncharacterized scorpion toxins. The SCORPION2 database is available at http://sdmc.i2r.a-star.edu.sg/scorpion/. (c) 2006 Elsevier Ltd. All rights reserved.

Analysis of line x environment interactions for yield in navy beans. 2. Pattern analysis of lines and environment within years

Seven years of multi-environment yield trials of navy bean (Phaseolus vulgaris L.) grown in Queensland were examined. As is common with plant breeding evaluation trials, test entries and locations varied between years. Grain yield data were analysed for each year using cluster and ordination analyses (pattern analyses). These methods facilitate descriptions of genotype performance across environments and the discrimination among genotypes provided by the environments. The observed trends for genotypic yield performance across environments were partly consistent with agronomic and disease reactions at specific environments and also partly explainable by breeding and selection history. In some cases, similarities in discrimination among environments were related to geographic proximity, in others management practices, and in others similarities occurred between geographically widely separated environments which differed in management practices. One location was identified as having atypical line discrimination. The analysis indicated that the number of test locations was below requirements for adequate representation of line x environment interaction. The pattern analyses methods used were an effective aid in describing the patterns in data for each year and illustrated the variations in adaptive patterns from year to year. The study has implications for assessing the number and location of test sites for plant breeding multi-environment trials, and for the understanding of genetic traits contributing to line x environment interactions.

Logistical aspects of large telemedicine networks. 2: Measurement of network activity

We carried out a retrospective review of the videoconference activity records in a university-run hospital telemedicine studio. Usage records describing videoconferencing activity in the telemedicine studio were compared with the billing records provided by the telecommunications company. During a seven-month period there were 211 entries in the studio log: 108 calls made from the studio and 103 calls made from a far-end location. We found that 103 calls from a total of 195 calls reported by the telecommunications company were recorded in the usage log. The remaining 92 calls were not recorded, probably for one of several reasons, including: failed calls-a large number of unrecorded calls (57%) lasted for less than 2 min (median 1.6 min); origin of videoconference calls-calls may have been recorded incorrectly in the usage diary (i.e. as being initiated from the far end, when actually initiated from the studio); and human error. Our study showed that manual recording of videoconference activity may not accurately reflect the actual activity taking place. Those responsible for recording and analysing videoconference activity, particularly in large telemedicine networks, should do so with care.