Smallest weak and smallest totally weak critical sets in the latin squares of order at most seven

A critical set in a latin square of order n is a set of entries in a latin square which can be embedded in precisely one latin square of order n. Also, 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 smallest weak and smallest totally weak critical sets for all the latin squares of orders six and seven. Moreover, we computationally prove that there is no (totally) weak critical set in the back circulant latin square of order five and we find a totally weak critical set of size seven in the other main class of latin squares of order five.

Validation of the Edinburgh Postnatal Depression Scale for men, and comparison of item endorsement with their partners

Background: The Edinburgh Postnatal Depression Scale (EPDS) has been validated and used extensively in screening for depression in new mothers, both in English speaking and non-English speaking communities. While some studies have reported the use of the EPDS with Fathers, none have validated it for this group, and thus the appropriate cut-off score for screening for depression or anxiety caseness for this population is not known. Method: Couples were recruited antenatally and interviewed at six weeks postpartum. EPDS scores and distress caseness (depression or anxiety disorders) for 208 fathers and 230 mothers were determined using the Diagnostic Interview Schedule. Results: Analyses of the EPDS for fathers using distress caseness (depression or anxiety disorders) as the criterion shows that a cut-off of 5/6 has optimum receiver operating characteristics. Furthermore acceptable reliability (split-half and internal consistency) and validity (concurrent) coefficients were obtained. For mothers the optimum cut-off screening value to detect distress caseness was 7/8. Item analysis revealed that fathers endorsed seven of the ten items at lower rates to mothers, with the most significant being that referring to crying. Conclusions: The EPDS is a reliable and valid measure of mood in fathers. Screening for depression or anxiety disorders in fathers requires a two point lower cut-off than screening for depression or anxiety in mothers, and we recommend this cut-off to he 5/6. (C) 2001 Elsevier Science B.V. All rights reserved.

Local complexity of Delone sets and crystallinity

This paper characterizes when a Delone set X in R-n is an ideal crystal in terms of restrictions on the number of its local patches of a given size or on the heterogeneity of their distribution. For a Delone set X, let N-X (T) count the number of translation-inequivalent patches of radius T in X and let M-X (T) be the minimum radius such that every closed ball of radius M-X(T) contains the center of a patch of every one of these kinds. We show that for each of these functions there is a gap in the spectrum of possible growth rates between being bounded and having linear growth, and that having sufficiently slow linear growth is equivalent to X being an ideal crystal. Explicitly, for N-X (T), if R is the covering radius of X then either N-X (T) is bounded or N-X (T) greater than or equal to T/2R for all T > 0. The constant 1/2R in this bound is best possible in all dimensions. For M-X(T), either M-X(T) is bounded or M-X(T) greater than or equal to T/3 for all T > 0. Examples show that the constant 1/3 in this bound cannot be replaced by any number exceeding 1/2. We also show that every aperiodic Delone set X has M-X(T) greater than or equal to c(n)T for all T > 0, for a certain constant c(n) which depends on the dimension n of X and is > 1/3 when n > 1.

Evaluating two morningness scales with item response theory

Using a student sample (n = 692) and an organization sample (n = 180), we scrutinized two morning-evening orientation scales using item response theory (IRT) methods. We used IRT to compare the measurement precision of the Composite Scale (CS) and the Early/Late Preferences Scale (PS). The CS had slightly higher measurement precision at all ranges of orientations, except for extreme morning and evening orientations for which the PS had slightly higher precision. IRT item-level statistics were also computed to try to understand how morning-orientation items functioned. Items that asked questions about morning activities tended to be more discriminating indicators of morning-orientation than items that asked about evening or peak performance activities. Items that involved unpleasant activities were less frequently endorsed than items that involved neutral or enjoyable activities. Implications for measurement of morning-evening orientation are discussed. (C) 2002 Elsevier Science Ltd. All rights reserved.

Overlarge sets of 2-(11, 5, 2) designs and related configurations

We consider the construction of several configurations, including: • overlarge sets of 2-(11,5,2) designs, that is, partitions of the set of all 5-subsets of a 12-set into 72 2-(11,5,2) designs; • an indecomposable doubly overlarge set of 2-(11,5,2) designs, that is, a partition of two copies of the set of all 5-subsets of a 12-set into 144 2-(11,5,2) designs, such that the 144 designs can be arranged into a 12 × 12 square with interesting row and column properties; • a partition of the Steiner system S(5,6,12) into 12 disjoint 2-(11,6,3) designs arising from the diagonal of the square; • bidistant permutation arrays and generalized Room squares arising from the doubly overlarge set, and their relation to some new strongly regular graphs.

Partitioning sets of triples into small planes

We study partitions of the set of all ((v)(3)) triples chosen from a v-set into pairwise disjoint planes with three points per line. Our partitions may contain copies of PG(2, 2) only (Fano partitions) or copies of AG(2, 3) only (affine partitions) or copies of some planes of each type (mixed partitions). We find necessary conditions for Fano or affine partitions to exist. Such partitions are already known in several cases: Fano partitions for v = 8 and affine partitions for v = 9 or 10. We construct such partitions for several sporadic orders, namely, Fano partitions for v = 14, 16, 22, 23, 28, and an affine partition for v = 18. Using these as starter partitions, we prove that Fano partitions exist for v = 7(n) + 1, 13(n) + 1, 27(n) + 1, and affine partitions for v = 8(n) + 1, 9(n) + 1, 17(n) + 1. In particular, both Fano and affine partitions exist for v = 3(6n) + 1. Using properties of 3-wise balanced designs, we extend these results to show that affine partitions also exist for v = 3(2n). Similarly, mixed partitions are shown to exist for v = 8(n), 9(n), 11(n) + 1.

Checklist of health promotion environments at worksites (CHEW): Development and measurement characteristics

Purpose. Health promotion policy frameworks, recent theorizing, and research all emphasize understanding and mobilizing environmental influences to change particular health-related behaviors in specific settings. The workplace is a key environmental setting. The Checklist of Health Promotion Environments at Worksites (CHEW) was designed as a direct observation instrument to assess characteristics of worksite environments that are known to influence health-related behaviors. Methods. The CHEW is a 112-item checklist of workplace environment features hypothesized to be associated, both positively and negatively, with physical activity, healthy eating, alcohol consumption, and smoking. The three environmental domains assessed are (1) physical characteristics of the worksite, (2) features of the information environment, and (3) characteristics of the immediate neighborhood around the workplace. The conceptual rationale and development studies for the CHEW are described, and data from observational studies of 20 worksites are reported. Results. The data on CHEW-derived environmental attributes showed generally good reliability and identified meaningful sets of variables that plausibly may influence health-related behaviors. With the exception of one information environment attribute, intraclass correlation coefficients ranged from 0.80 to 1.00. Descriptive statistics on selected physical and information environment characteristics indicated that vending machines, showers, bulletin boards, and signs prohibiting smoking were common across worksites. Bicycle racks, visible stairways, and signs related to alcohol consumption, nutrition, and health. promotion were relatively uncommon. Conclusions. These findings illustrate the types of data on environmental attributes that can be derived, their relevance for program planning, and how they can characterize variability across worksites. The CHEW is a promising observational measure that has the potential to assess environmental influences on health behaviors and to evaluate workplace health promotion programs.

The spectrum of minimal defining sets of some Steiner systems

For a design D, define spec(D) = {\M\ \ M is a minimal defining set of D} to be the spectrum of minimal defining sets of D. In this note we give bounds on the size of an element in spec(D) when D is a Steiner system. We also show that the spectrum of minimal defining sets of the Steiner triple system given by the points and lines of PG(3,2) equals {16,17,18,19,20,21,22}, and point out some open questions concerning the Steiner triple systems associated with PG(n, 2) in general. (C) 2002 Elsevier Science B.V. All rights reserved.

Skolem-type difference sets for cycle systems

Cyclic m-cycle systems of order v are constructed for all m greater than or equal to 3, and all v = 1(mod 2m). This result has been settled previously by several authors. In this paper, we provide a different solution, as a consequence of a more general result, which handles all cases using similar methods and which also allows us to prove necessary and sufficient conditions for the existence of a cyclic m-cycle system of K-v - F for all m greater than or equal to 3, and all v = 2(mod 2m).

Large sets of large sets of Steiner triple systems of order 9

We describe a direct method of partitioning the 840 Steiner triple systems of order 9 into 120 large sets. The method produces partitions in which all of the large sets are isomorphic and we apply the method to each of the two non-isomorphic large sets of STS(9).

Experimental manipulation of prior experience: Effects on item and associative recognition

Frequency of exposure to very low- and high-frequency words was manipulated in a three-phase (familiarisation, study, and test) design. During familiarisation, words were presented with their definition (once, four times, or not presented). One week (Experiment 1) or one day (Experiment 2) later, participants studied a list of homogeneous pairs (i.e., pair members were matched on background and familiarisation frequency). Item and associative recognition of high- and very low-frequency words presented in intact, rearranged, old-new, or new-new pairs were tested in Experiment 1. Associative recognition of very low-frequency words was tested in Experiment 2. Results showed that prior familiaris ation improved associative recognition of very low-frequency pairs, but had no effect on high-frequency pairs. The role of meaning in the formation of item-to-item and item-to-context associations and the implications for current models of memory are discussed.