On the forced matching numbers of bipartite graphs

Let G be a graph that admits a perfect matching. A forcing set for a perfect matching M of G is a subset S of M, such that S is contained in no other perfect matching of G. This notion has arisen in the study of finding resonance structures of a given molecule in chemistry. Similar concepts have been studied for block designs and graph colorings under the name defining set, and for Latin squares under the name critical set. There is some study of forcing sets of hexagonal systems in the context of chemistry, but only a few other classes of graphs have been considered. For the hypercubes Q(n), it turns out to be a very interesting notion which includes many challenging problems. In this paper we study the computational complexity of finding the forcing number of graphs, and we give some results on the possible values of forcing number for different matchings of the hypercube Q(n). Also we show an application to critical sets in back circulant Latin rectangles. (C) 2003 Elsevier B.V. All rights reserved.

Despite differences between dendritic cells and Langerhans cells in the mechanism of papillomavirus-like particle antigen uptake, both cells cross-prime T cells

As human papillomavirus-like particles (HPV-VLP) represent a promising vaccine delivery vehicle, delineation of the interaction of VLP with professional APC should improve vaccine development. Differences in the capacity of VLP to signal dendritic cells (DC) and Langerhans cells (LC) have been demonstrated, and evidence has been presented for both clathrin-coated pits and proteoglycans (PG) in the uptake pathway of VLP into epithelial cells. Therefore, we compared HPV-VLP uptake mechanisms in human monocyte-derived DC and LC, and their ability to cross-present HPV VLP-associated antigen in the MHC class I pathway. DC and LC each took up virus-like particles (VLP). DC uptake of and signalling by VLP was inhibited by amiloride or cytochalasin D (CCD), but not by filipin treatment, and was blocked by several sulfated and non-sulfated polysaccharides and anti-CD16. In contrast, LC uptake was inhibited only by filipin, and VLP in LC were associated with caveolin, langerin, and CD1a. These data suggest fundamentally different routes of VLP uptake by DC and LC. Despite these differences, VLP taken up by DC and LC were each able to prime naive CD8(+) T cells and induce cytolytic effector T cells in vitro. (C) 2004 Elsevier Inc. All rights reserved.

Complex numbers and symmetries in quantum mechanics, and a nonlinear superposition principle for Wigner functions

Complex numbers appear in the Hilbert space formulation of quantum mechanics, but not in the formulation in phase space. Quantum symmetries are described by complex, unitary or antiunitary operators defining ray representations in Hilbert space, whereas in phase space they are described by real, true representations. Equivalence of the formulations requires that the former representations can be obtained from the latter and vice versa. Examples are given. Equivalence of the two formulations also requires that complex superpositions of state vectors can be described in the phase space formulation, and it is shown that this leads to a nonlinear superposition principle for orthogonal, pure-state Wigner functions. It is concluded that the use of complex numbers in quantum mechanics can be regarded as a computational device to simplify calculations, as in all other applications of mathematics to physical phenomena.

Experimental validation of the regulated expression of large numbers of non-coding RNAs from the mouse genome

Recent large-scale analyses of mainly full-length cDNA libraries generated from a variety of mouse tissues indicated that almost half of all representative cloned sequences did flat contain ail apparent protein-coding sequence, and were putatively derived from non-protein-coding RNA (ncRNA) genes. However, many of these clones were singletons and the majority were unspliced, raising the possibility that they may be derived from genomic DNA or unprocessed pre-rnRNA contamination during library construction, or alternatively represent nonspecific transcriptional noise. Here we Show, using reverse transcriptase-dependent PCR, microarray, and Northern blot analyses, that many of these clones were derived from genuine transcripts Of unknown function whose expression appears to be regulated. The ncRNA transcripts have larger exons and fewer introns than protein-coding transcripts. Analysis of the genomic landscape around these sequences indicates that some cDNA clones were produced not from terminal poly(A) tracts but internal priming sites within longer transcripts, only a minority of which is encompassed by known genes. A significant proportion of these transcripts exhibit tissue-specific expression patterns, as well as dynamic changes in their expression in macrophages following lipopolysaccharide Stimulation. Taken together, the data provide strong support for the conclusion that ncRNAs are an important, regulated component of the mammalian transcriptome.

Measurement of strain and strain rate by echocardiography - Ready for prime time?

Strain and strain rate (SR) are measures of deformation that are basic descriptors of both the nature and the function of cardiac tissue. These properties may now be measured using either Doppler or two-dimensional ultrasound techniques. Although these measurements are feasible in routine clinical echocardiography, their acquisition and analysis nonetheless presents a number of technical challenges and complexities. Echocardiographic strain and SR imaging has been applied to the assessment of resting ventricular function, the assessment of myocardial viability using low-dose dobutamine infusion, and stress testing for ischemia. Resting function assessment has been applied in both the left and the fight ventricles, and may prove particularly valuable for identifying myocardial diseases and following up the treatment response. Although the evidence base is limited, SR imaging seems to be feasible and effective for the assessment of myocardial viability. The use of the technique for the detection of ischemia during stress echocardiography is technically challenging and likely to evolve further. The clinical availability of strain and SR measurement may offer a solution to the ongoing need for quantification of regional and global cardiac function. Nonetheless, these techniques are susceptible to artifact, and further technical development is necessary.