Cumulative live birth rates after one or more complete cycles of IVF : a population-based study of linked cycle data from 178 898 women

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Decomposition of complete tripartite graphs into gregarious 4-cycles

A 4-cycle in a tripartite graph with vertex partition {V-1, V-2, V-3} is said to be gregarious if it has at least one vertex in each V-i, 1 less than or equal to i less than or equal to 3. In this paper, necessary and sufficient conditions are given for the existence of an edge-disjoint decomposition of any complete tripartite graph into gregarious 4-cycles.

3,5-cycle decompositions

For all odd integers n and all non-negative integers r and s satisfying 3r + 5s = n(n -1)/2 it is shown that the edge set of the complete graph on n vertices can be partitioned into r 3-cycles and s 5-cycles. For all even integers n and all non-negative integers r and s satisfying 3r + 5s = n(n-2)/2 it is shown that the edge set of the complete graph on n vertices with a 1-factor removed can be partitioned into r 3-cycles and s 5-cycles. (C) 1998 John Wiley & Sons, Inc.

(m,n)-cycle systems

We describe a method which, in certain circumstances, may be used to prove that the well-known necessary conditions for partitioning the edge set of the complete graph on an odd number of vertices (or the complete graph on an even number of vertices with a 1-factor removed) into cycles of lengths m(1),m(2),...,m(t) are sufficient in the case \{m(1), m(2), ..., m(t)}\=2. The method is used to settle the case where the cycle lengths are 4 and 5. (C) 1998 Elsevier Science B.V. All rights reserved.

Decomposing complete tripartite graphs into cycles of lengths 3 and 4

Necessary and sufficient conditions are given for the edge-disjoint decomposition of a complete tripartite graph K-r,K-s,K-t into exactly alpha 3-cycles and beta 4-cycles. (C) 1999 Elsevier Science B.V. All rights reserved.

Synchronous oogenesis during the semilunar spawning cycle of the tropical abalone Haliotis asinina

On the southern Great Barrier Reef, Haliotis asinina (Vetigastropoda: Pleurotomarioidea) synchronously spawn every 2 wk in a predictable fashion. allowing detailed analysis of reproduction, gametogenesis, and gonad development. Histological examination of the ovaries of members of the Heron Reef population during this semilunar cycle reveals that oogenesis is also synchronous and predictable, and requires more than two spawning cycles (i.e. >28 days) to complete. Shortly after a spawning event the ovary comprises two cohorts of primary oocytes, one of which will be released at the next spawning event, and clusters of oogonia. At this time there is a rapid proliferation and expansion of trabeculae, germinal epithelial, and oogonia, and a dramatic increase in the size of the vitellogenic oocytes to be: spawned at the next spawning event. Within 4 days these oocytes have filled the ovary. On the day of the next spawning a lumen forms in the ovary as a result of localized degradation of trabeculae. The large primary oocytes dissociate from the receding trabeculae. initiate maturation, and accumulate in the lumen; these oocytes become embedded in a jelly coat layer. The next cohort of oocytes remain attached to the trabeculae. The jelly coat appears to be completely dissolved within 30 min of spawning. Comparison of the oogenesis and ovary development in II. asinina with other abalone species indicates that these processes are very similar in tropical and temperate abalone. This suggests that insights into the regulation of reproduction and spawning in H. asinina are likely to be applicable to other haliotids.

Decompositions of complete multipartite graphs into cycles of even length

Necessary and sufficient conditions for the existence of an edge-disjoint decomposition of any complete multipartite graph into even length cycles are investigated. Necessary conditions are listed and sufficiency is shown for the cases when the cycle length is 4, 6 or 8. Further results concerning sufficiency, provided certain small decompositions exist, are also given for arbitrary even cycle lengths.

A family of perfect factorisations of complete bipartite graphs

A 1-factorisation of a graph is perfect if the union of any two of its 1-factors is a Hamiltonian cycle. Let n = p(2) for an odd prime p. We construct a family of (p-1)/2 non-isomorphic perfect 1-factorisations of K-n,K-n. Equivalently, we construct pan-Hamiltonian Latin squares of order n. A Latin square is pan-Hamiltoilian if the permutation defined by any row relative to any other row is a single Cycle. (C) 2002 Elsevier Science (USA).

2m-cycle systems of K2m+1/C-m

For all m greater than or equal to 3 the edges of complete graph on 2m + 1 vertices can he partitioned into m 2m-cycles and an m-cycle.

The mu-way intersection problem for m-cycle systems

An m-cycle system of order upsilon is a partition of the edge-set of a complete graph of order upsilon into m-cycles. The mu -way intersection problem for m-cycle systems involves taking mu systems, based on the same vertex set, and determining the possible number of cycles which can be common to all mu systems. General results for arbitrary m are obtained, and detailed intersection values for (mu, m) = (3, 4), (4, 5),(4, 6), (4, 7), (8, 8), (8, 9). (For the case (mu, m)= (2, m), see Billington (J. Combin. Des. 1 (1993) 435); for the case (Cc,m)=(3,3), see Milici and Quattrochi (Ars Combin. A 24 (1987) 175. (C) 2001 Elsevier Science B.V. All rights reserved.

The metamorphosis of lambda-fold 4-wheel systems into lambda-fold 4-cycle systems

A 4-wheel is a simple graph on 5 vertices with 8 edges, formed by taking a 4-cycle and joining a fifth vertex (the centre of the 4-wheel) to each of the other four vertices. A lambda -fold 4-wheel system of order n is an edge-disjoint decomposition of the complete multigraph lambdaK(n) into 4-wheels. Here, with five isolated possible exceptions when lambda = 2, we give necessary and sufficient conditions for a lambda -fold 4-wheel system of order n to be transformed into a lambda -fold Ccyde system of order n by removing the centre vertex from each 4-wheel, and its four adjacent edges (retaining the 4-cycle wheel rim), and reassembling these edges adjacent to wheel centres into 4-cycles.

Further decompositions of complete tripartite graphs into 5-cycles

Let K(r,s,t) denote the complete tripartite graph with partite sets of sizes r, s and t, where r less than or equal to s less than or equal to t. Necessary and sufficient conditions are given for decomposability of K(r, s, t) into 5-cycles whenever r, s and t are all even. This extends work done by Mahmoodian and Mirza-khani (Decomposition of complete tripartite graphs into 5-cycles, in: Combinatorics Advances, Kluwer Academic Publishers, Netherlands, 1995, pp. 235-241) and Cavenagh and Billington. (C) 2002 Elsevier Science B.V. All rights reserved.

Involuntary Rhythmic Leg Movements Time-Locked With the Respiratory Cycle

Involuntary rhythmic leg movements in childhood is an uncommon condition, the generators of which remain unknown. We report on a male 3 years of age with distinct features providing important clues concerning the location of one of these generators. At the age of 7 months, the previously healthy young male started with low frequency, rhythmic, and continuous (both during wakefulness and sleep) flexion/extension movements of the lower limbs. Movements interfered significantly with gait acquisition, and, despite normal cognitive development, he was able to walk only at age 2 years, 4 months. The neurologic examination revealed the absence of automatic stepping in the neonatal period, but was otherwise normal. A polygraphic electroencephalogram/electromyogram EEG/EMG) recording, at the age of 2 years, 9 months, revealed rhythmic and synchronous legs with EMG activity at 0.5 Hz. A more complete polygraphic recording at the age of 3 years, 10 months, showed a lower frequency (0.35 Hz) for the movements, which were time-locked with the respiratory cycle. Magnetic resonance imaging (MRI) of the brain revealed an increased T2 signal in the upper medulla-lower pons regions. The generator of the rhythmic legs movements is postulated to be the respiratory center, connecting with the reticulospinal projecting neurons through an aberrant pathway.

A complete molecular biology assay for hepatitis C virus detection, quantification and genotyping

Introduction Molecular biology procedures to detect, genotype and quantify hepatitis C virus (HCV) RNA in clinical samples have been extensively described. Routine commercial methods for each specific purpose (detection, quantification and genotyping) are also available, all of which are typically based on polymerase chain reaction (PCR) targeting the HCV 5′ untranslated region (5′UTR). This study was performed to develop and validate a complete serial laboratory assay that combines real-time nested reverse transcription-polymerase chain reaction (RT-PCR) and restriction fragment length polymorphism (RFLP) techniques for the complete molecular analysis of HCV (detection, genotyping and viral load) in clinical samples. Methods Published HCV sequences were compared to select specific primers, probe and restriction enzyme sites. An original real-time nested RT-PCR-RFLP assay was then developed and validated to detect, genotype and quantify HCV in plasma samples. Results The real-time nested RT-PCR data were linear and reproducible for HCV analysis in clinical samples. High correlations (> 0.97) were observed between samples with different viral loads and the corresponding read cycle (Ct - Cycle threshold), and this part of the assay had a wide dynamic range of analysis. Additionally, HCV genotypes 1, 2 and 3 were successfully distinguished using the RFLP method. Conclusions A complete serial molecular assay was developed and validated for HCV detection, quantification and genotyping.

Complete Markets Strikes Back: Revisiting Risk Sharing Tests under Discount Rate Heterogeneity

Recent risk sharing tests strongly reject the hypothesis of complete markets, because in the data: (1) the individual consumption comoves with income and (2) the consumption dispersion increases over the life cycle. In this paper, I revisit the implications of these risk sharing tests in the context of a complete market model with discount rate heterogeneity, which is extended to introduce the individual choices of effort in education. I .nd that a complete market model with discount rate heterogeneity can pass both types of the risk sharing tests. The endogenous positive correlation between income growth rate and patience makes the individual consumption comove with income, even if the markets are complete. I also show that this model is quantitatively admissible to account for both the observed comovement of consumption and income and the increase of consumption dispersion over the life cycle.