Determinacy and Weakly Ramsey sets in Banach spaces

We give a sufficient condition for a set of block subspaces in an infinite-dimensional Banach space to be weakly Ramsey. Using this condition we prove that in the Levy-collapse of a Mahlo cardinal, every projective set is weakly Ramsey. This, together with a construction of W. H. Woodin, is used to show that the Axiom of Projective Determinacy implies that every projective set is weakly Ramsey. In the case of co we prove similar results for a stronger Ramsey property. And for hereditarily indecomposable spaces we show that the Axiom of Determinacy plus the Axiom of Dependent Choices imply that every set is weakly Ramsey. These results are the generalizations to the class of projective sets of some theorems from W. T. Gowers, and our paper "Weakly Ramsey sets in Banach spaces."

Banach spaces without minimal subspaces

We prove three new dichotomies for Banach spaces a la W.T. Gowers` dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers` program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size K I into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. (c) 2009 Elsevier Inc. All fights reserved.

Free expanding cloud of cold atoms as an atomic standard: Ramsey fringes contrast

A compact frequency standard based on an expanding cold (133)CS cloud is under development in our laboratory. In a first experiment, Cs cold atoms were prepared by a magneto-optical trap in a vapor cell, and a microwave antenna was used to transmit the radiation for the clock transition. The signal obtained from fluorescence of the expanding cold atoms cloud is used to lock a microwave chain. In this way the overall system stability is evaluated. A theoretical model based on a two-level system interacting with the two microwave pulses enables interpretation for the observed features, especially the poor Ramsey fringes contrast. (C) 2008 Optical Society of America.

Increased Levels of NOTCH1, NF-kappa B, and Other Interconnected Transcription Factors Characterize Primitive Sets of Hematopoietic Stem Cells

As previously shown, higher levels of NOTCH1 and increased NF-kappa B signaling is a distinctive feature of the more primitive umbilical cord blood (UCB) CD34+ hematopoietic stem cells (HSCs), as compared to bone marrow ( BM). Differences between BM and UCB cell composition also account for this finding. The CD133 marker defines a more primitive cell subset among CD34+ HSC with a proposed hemangioblast potential. To further evaluate the molecular basis related to the more primitive characteristics of UCB and CD133+ HSC, immunomagnetically purified human CD34+ and CD133+ cells from BM and UCB were used on gene expression microarrays studies. UCB CD34+ cells contained a significantly higher proportion of CD133+ cells than BM (70% and 40%, respectively). Cluster analysis showed that BM CD133+ cells grouped with the UCB cells ( CD133+ and CD34+) rather than to BM CD34+ cells. Compared with CD34+ cells, CD133+ had a higher expression of many transcription factors (TFs). Promoter analysis on all these TF genes revealed a significantly higher frequency ( than expected by chance) of NF-kappa B-binding sites (BS), including potentially novel NF-kappa B targets such as RUNX1, GATA3, and USF1. Selected transcripts of TF related to primitive hematopoiesis and self-renewal, such as RUNX1, GATA3, USF1, TAL1, HOXA9, HOXB4, NOTCH1, RELB, and NFKB2 were evaluated by real-time PCR and were all significantly positively correlated. Taken together, our data indicate the existence of an interconnected transcriptional network characterized by higher levels of NOTCH1, NF-kappa B, and other important TFs on more primitive HSC sets.

Extremal problems on sum-free sets and coverings in tridimensional spaces

Given a prime power q, define c (q) as the minimum cardinality of a subset H of F 3 q which satisfies the following property: every vector in this space di ff ers in at most 1 coordinate from a multiple of a vector in H. In this work, we introduce two extremal problems in combinatorial number theory aiming to discuss a known connection between the corresponding coverings and sum-free sets. Also, we provide several bounds on these maps which yield new classes of coverings, improving the previous upper bound on c (q)

Doubling and Tripling Constructions for Defining Sets in Steiner Triple Systems

A minimal defining set of a Steiner triple system on a points (STS(v)) is a partial Steiner triple system contained in only this STS(v), and such that any of its proper subsets is contained in at least two distinct STS(v)s. We consider the standard doubling and tripling constructions for STS(2v + 1) and STS(3v) from STS(v) and show how minimal defining sets of an STS(v) gives rise to minimal defining sets in the larger systems. We use this to construct some new families of defining sets. For example, for Steiner triple systems on, 3" points; we construct minimal defining sets of volumes varying by as much as 7(n-/-).

Effect of oral creatine supplementation on near-maximal strength and repeated sets of high-intensity bench press exercise

This study examined the effects of 26 days of oral creatine monohydrate (Cr) supplementation on near-maximal muscular strength, high-intensity bench press performance, and body composition. Eighteen male powerlifters with at least 2 years resistance training experience took part in this 28-day experiment. Pre and postmeasurements (Days 1 and 28) were taken of near-maximal muscular strength, body mass, and % body fat. There were two periods of supplementation Days 2 to 6 and Days 7 to 27. ANOVA and t-tests revealed that Cr supplementation significantly increased body mass and lean body mass with no changes in % body fat. Significant increases in 3-RM strength occurred in both groups, both absolute and relative to body mass; the increases were greater in the Cr group. The change in total repetitions also increased significantly with Cr supplementation both in absolute terms and relative to body mass, while no significant change was seen in the placebo (P) group. Creatine supplementation caused significant changes in the number of BP reps in Sets 1, 4, and 5. No changes occurred in the P group. It appears that 26 days of Cr supplementation significantly improves muscular strength and repeated near-maximal BP performance, and induces changes in body composition.

Critical sets for families of Latin squares

In this paper I give details of new constructions for critical sets in latin squares. These latin squares, of order n, are such that they can be partitioned into four subsquares each of which is based on the addition table of the integers module n/2, an isotopism of this or a conjugate.

Maximal sets of Hamilton cycles in Kn,n

In this article, we prove that there exists a maximal set of m Hamilton cycles in K-n,K-n if and only if n/4 < m less than or equal to n/2. (C) 2000 John Wiley & Sons, Inc.

BEYOND SAMUELSON`S CHAPTER ON RAMSEY

Paul Anthony Samuelson proposed and practiced a program for the Whig history of economics. One such example is his account of Frank Ramsey`s contribution to optimal taxation in 1927. For him, and mainly for the public finance economists who rediscovered later Ramsey`s contribution, Ramsey was a genius ahead of his time who used a mathematics too advanced for his contemporaries and was thus rediscovered only in the 1970S, when economists became more mathematically literate. In such rediscovery, a memorandum that Samuelsom wrote in 1951 for the us Treasury became central. I examine Samuelson`s account and challenge it in some respects and explore the historical context of the emergence of the optimal taxation literature in the 1970S. Additional, I analyze the canonization of Ramsey in this field, stressing Samuelson`s role in this process as a professor who liked telling stories about economists, especially about Ramsey, to his graduate students.

Slant or occlusion: global factors resolve stereoscopic ambiguity in sets of horizontal lines

Perceived slant was measured for horizontal lines aligned on one side and of varying lengths whose length disparity was either a constant linear amount for all lines (consistent with uniocular occlusion) or proportional to line length (consistent with global slant). Although the disparity of any line was ambiguous with respect to these two possibilities, slant of individual lines did not occur in the former case, but a subjective contour in depth was reported along the alignment. For proportional disparity of the set, global slant was seen. Adding a constant length to each line on the invalid eye for occlusion resulted in multiple slants. Smooth uniocular variations in alignment shape elicited subjective contours slanting or curving in depth. Global context can disambiguate the depth status of individual disparate lines. (C) 2004 Elsevier Ltd. All rights reserved.

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.