Critical sets in direct products of back circulant Latin squares

To date very Few families of critical sets for latin squares are known. The only previously known method for constructing critical sets involves taking a critical set which is known to satisfy certain strong initial conditions and using a doubling construction. This construction can be applied to the known critical sets in back circulant latin squares of even order. However, the doubling construction cannot be applied to critical sets in back circulant latin squares of odd order. In this paper a family of critical sets is identified for latin squares which are the product of the latin square of order 2 with a back circulant latin square of odd order. The proof that each element of the critical set is an essential part of the reconstruction process relies on the proof of the existence of a large number of latin interchanges.

Autoimmune lymphoproliferative syndrome in a patient with a new minimal deletion in the death domain of the FAS gene

We present a case of autoimmune lymphoproliferative syndrome (ALPS) caused by a previously undescribed minimal deletion in the death domain of the FAS gene. ALPS is an uncommon disease associated with an impaired Fas-mediated apoptosis. The patient presented with a history of splenomegaly since 4 months of age, associated with cervical lymphadenopathy, which improved with oral corticosteroid treatment. Relevant laboratory findings were the presence of anemia, thrombocytopenia, and positive direct and indirect Coombs tests. He was not an offspring of consanguineous parents. Two cervical lymph node biopsies were performed, at 4 years and at 6 years of age. In both lymph nodes, there was marked paracortical expansion by lymphocytes in variable stages of immunoblastic transformation and a very high cell proliferating index. Some clear cells were also present, raising the suspicion of malignant lymphoma. In one of the lymph nodes, there was also a focus rich in large histiocytes with round nuclei and emperipolesis, consistent with focal Rosai-Dorfman disease. Immunostaining showed numerous CD3+ cells, many of which were double-negative (CD4- CD8-) and expressed CD57, especially around the follicles. Molecular studies of the lymph node biopsy showed a point deletion (4-base pair deletion) in exon 9 of the FAS gene (930del TGCT), which results in 3 missense amino acids. (c) 2008 Elsevier Inc. All rights reserved.

Effect of peritoneal fluid from patients with minimal/mild endometriosis on progesterone release by human granulosa-lutein cells obtained from infertile patients without endometriosis: A pilot study

Objective: To evaluate the effect of peritoneal fluid (PF) from women without and with minimal/mild endometriosis on progesterone (P) release by cultured human granulosa-lutein cells obtained from infertile patients without endometriosis submitted to ovarian hyperstimulation for in vitro fertilization (IVF). Study design: A pilot study was performed. Human granulosa-lutein cells, obtained from 11 infertile patients without endometriosis (tubal or male factors of infertility) submitted to ovarian hyperstimulation for IVF, were cultured without PF (basal production) and with increasing volumes of steroid-extracted PF samples from 11 patients with endometriosis and 11 patients without endometriosis. Progesterone (P) levels in the media after 72 h culture were measured by chemoluminescence assay. The non-parametric Mann-Whitney-test was used for statistical analysis. Results: PF from patients without endometriosis stimulated P release in a dose-dependent manner up to the dose of 100 mu l/ml (10% concentration) when compared with basal production (without adding PF). P release was similar in cultures stimulated with PF from patients with or without endometriosis at 1% (10 mu l/ml) and 5% (50 ml/ml) concentrations. At 10% concentration, there was a non-statistically significant reduction in progesterone release by granulosa cells stimulated with PF from patients with endometriosis. PF from patients with endometriosis significantly reduced P release at 30% concentration (300 mu l/ml). Conclusions: PF stimulates P release by human granulosa-lutein cells in a dose-dependent manner. However, higher concentrations of PF from patients with minimal/mild endometriosis reduce P release, suggesting it contains factors that may compromise ovarian steroidogenesis. (c) 2007 Elsevier Ireland Ltd. All rights reserved.

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.

A novel approach to antigen-specific deletion of CTL with minimal cellular activation using alpha 3 domain mutants of MHC class I/peptide complex

In this study, we have compared the effector functions and fate of a number of human CTL clones in vitro or ex vivo following contact with variant peptides presented either on the cell surface or in a soluble multimeric format. In the presence of CD8 coreceptor binding, there is a good correlation between TCR signaling, killing of the targets, and Fast-mediated CTL apoptosis. Blocking CD8 binding using (alpha3 domain mutants of MHC class I results in much reduced signaling and reduced killing of the targets. Surprisingly, however, Fast expression is induced to a similar degree on these CTLs, and apoptosis of CTL is unaffected. The ability to divorce these events may allow the deletion of antigen-specific and pathological CTL populations without the deleterious effects induced by full CTL activation.

Complementation analysis of the flavivirus Kunjin NS3 and NS5 proteins defines the minimal regions essential for formation of a replication complex and shows a requirement of NS3 in cis for virus assembly

We have previously reported successful trans-complementation of defective Kunjin virus genomic RNAs with a range of large lethal deletions in the nonstructural genes NSI, NS3, and NS5 (A. A. Khromykh et al., J. Virol. 74:3253-3263, 2000). In this study we have mapped further the minimal region in the NS5 gene essential for efficient trans-complementation of genome-length RNAs in repBHK cells to the first 316 of the 905 codons. To allow amplification and easy detection of complemented defective RNAs with deletions apparently affecting virus assembly, we have developed a dual replicon complementation system. In this system defective replicon RNAs with a deletion(s) in the nonstructural genes also encoded the puromycin resistance gene (PAC gene) and the reporter gene for beta-galactosidase (beta-Gal). Complementation of these defective replicon RNAs in repBHK cells resulted in expression of PAC and beta-Gal which allowed establishment of cell lines stably producing replicating defective RNAs by selection with puromycin and comparison of replication efficiencies of complemented defective RNAs by beta-Gal assay. Using this system we demonstrated that deletions in the C-terminal 434 codons of NS3 (codons 178 to 611) were complemented for RNA replication, while any deletions in the first 178 codons were not. None of the genome-length RNAs containing deletions in NS3 shown to be complementable for RNA replication produced secreted defective viruses during complementation in repBHK cells. In contrast, structural proteins produced from these complemented defective RNAs were able to package helper replicon RNA. The results define minimal regions in the NS3 and NS5 genes essential for the formation of complementable replication complex and show a requirement of NS3 in cis for virus assembly.

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.

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.