On the geometry of solutions of the quasi-geostrophic and Euler equations

We study solutions of the two-dimensional quasi-geostrophic thermal active scalar equation involving simple hyperbolic saddles. There is a naturally associated notion of simple hyperbolic saddle breakdown. It is proved that such breakdown cannot occur in finite time. At large time, these solutions may grow at most at a quadruple-exponential rate. Analogous results hold for the incompressible three-dimensional Euler equation.

Nas–Walras equilibria of a large economy

Individuals exchange contracts for the delivery of commodities in competitive markets and, simultaneously, act strategically; actions affect utilities across individuals directly or through the payoffs of contracts. This encompasses economies with asymmetric information. Nash–Walras equilibria exist for large economies, even if utility functions are not quasi-concave and choice sets are not convex, which is the case in standard settings; the separation of the purchase from the sale of contracts and the pooling of the deliveries on contracts guarantee that the markets for commodities clear.

Isotropic isotopy and symplectic null sets

Capacity is an important numerical invariant of symplectic manifolds. This paper studies when a subset of a symplectic manifold is null, i.e., can be removed without affecting the ambient capacity. After examples of open null sets and codimension-2 non-null sets, geometric techniques are developed to perturb any isotopy of a loop to a hamiltonian flow; it follows that sets of dimension 0 and 1 are null. For isotropic sets of higher dimensions, obstructions to the perturbation are found in homotopy groups of the orthogonal groups.

Plastid-localized acetyl-CoA carboxylase of bread wheat is encoded by a single gene on each of the three ancestral chromosome sets

5′-End fragments of two genes encoding plastid-localized acetyl-CoA carboxylase (ACCase; EC 6.4.1.2) of wheat (Triticum aestivum) were cloned and sequenced. The sequences of the two genes, Acc-1,1 and Acc-1,2, are 89% identical. Their exon sequences are 98% identical. The amino acid sequence of the biotin carboxylase domain encoded by Acc-1,1 and Acc-1,2 is 93% identical with the maize plastid ACCase but only 80–84% identical with the cytosolic ACCases from other plants and from wheat. Four overlapping fragments of cDNA covering the entire coding region were cloned by PCR and sequenced. The wheat plastid ACCase ORF contains 2,311 amino acids with a predicted molecular mass of 255 kDa. A putative transit peptide is present at the N terminus. Comparison of the genomic and cDNA sequences revealed introns at conserved sites found in the genes of other plant multifunctional ACCases, including two introns absent from the wheat cytosolic ACCase genes. Transcription start sites of the plastid ACCase genes were estimated from the longest cDNA clones obtained by 5′-RACE (rapid amplification of cDNA ends). The untranslated leader sequence encoded by the Acc-1 genes is at least 130–170 nucleotides long and is interrupted by an intron. Southern analysis indicates the presence of only one copy of the gene in each ancestral chromosome set. The gene maps near the telomere on the short arm of chromosomes 2A, 2B, and 2D. Identification of three different cDNAs, two corresponding to genes Acc-1,1 and Acc-1,2, indicates that all three genes are transcriptionally active.

Effects of the Heartbeat Wales programme over five years on behavioural risks for cardiovascular disease: quasi-experimental comparison of results from Wales and a matched reference area

Objective: To assess the net 5 year effects of intervention of a community based demonstration project, the Heartbeat Wales programme, on modifiable behavioural risks for prevention of cardiovascular disease.

Statistical modeling of large microarray data sets to identify stimulus-response profiles

A statistical modeling approach is proposed for use in searching large microarray data sets for genes that have a transcriptional response to a stimulus. The approach is unrestricted with respect to the timing, magnitude or duration of the response, or the overall abundance of the transcript. The statistical model makes an accommodation for systematic heterogeneity in expression levels. Corresponding data analyses provide gene-specific information, and the approach provides a means for evaluating the statistical significance of such information. To illustrate this strategy we have derived a model to depict the profile expected for a periodically transcribed gene and used it to look for budding yeast transcripts that adhere to this profile. Using objective criteria, this method identifies 81% of the known periodic transcripts and 1,088 genes, which show significant periodicity in at least one of the three data sets analyzed. However, only one-quarter of these genes show significant oscillations in at least two data sets and can be classified as periodic with high confidence. The method provides estimates of the mean activation and deactivation times, induced and basal expression levels, and statistical measures of the precision of these estimates for each periodic transcript.

Optical evidence for the unification of active galactic nuclei and quasi-stellar objects.

There is a variety of optical evidence for some unification of different types of active galactic nuclei and quasi-stellar objects (QSOs). The case is very strong for the unification of at least some Seyfert galaxies, where polarization data show that the type assigned to the Seyfert galaxy must depend on viewing direction. It has been proposed that Fanaroff-Riley type 2 (FR2) radio galaxies are quasars seen in a direction from which the quasar is obscured, and there is some limited direct evidence for this picture. The broad absorption line QSOs may be normal QSOs seen from a special direction. Some of the sources observed to have high luminosities in the far infrared could be obscured QSOs and active nuclei. Mergers and interactions are likely to play an important role in nuclear activity, and active galaxies and QSOs could change their apparent types through these encounters followed by subsequent evolution.

Cortical activity flips among quasi-stationary states.

Parallel recordings of spike trains of several single cortical neurons in behaving monkeys were analyzed as a hidden Markov process. The parallel spike trains were considered as a multivariate Poisson process whose vector firing rates change with time. As a consequence of this approach, the complete recording can be segmented into a sequence of a few statistically discriminated hidden states, whose dynamics are modeled as a first-order Markov chain. The biological validity and benefits of this approach were examined in several independent ways: (i) the statistical consistency of the segmentation and its correspondence to the behavior of the animals; (ii) direct measurement of the collective flips of activity, obtained by the model; and (iii) the relation between the segmentation and the pair-wise short-term cross-correlations between the recorded spike trains. Comparison with surrogate data was also carried out for each of the above examinations to assure their significance. Our results indicated the existence of well-separated states of activity, within which the firing rates were approximately stationary. With our present data we could reliably discriminate six to eight such states. The transitions between states were fast and were associated with concomitant changes of firing rates of several neurons. Different behavioral modes and stimuli were consistently reflected by different states of neural activity. Moreover, the pair-wise correlations between neurons varied considerably between the different states, supporting the hypothesis that these distinct states were brought about by the cooperative action of many neurons.

Sets of EcoRI fragments containing ribosomal RNA sequences are conserved among different strains of Listeria monocytogenes.

To classify Listeria monocytogenes using taxonomic characters derived from the rRNA operons and their flanking sequences, we studied a sample of 1346 strains within the taxon. DNA from each strain was digested with a restriction endonuclease, EcoRI. The fragments were separated by gel electrophoresis, immobilized on a membrane, and hybridized with a labeled rRNA operon from Escherichia coli. The pattern of bands, positions, and intensities of hybridized fragments were electronically captured. Software was used to normalize the band positions relative to standards, scale the signal intensity, and reduce the background so that each strain was reproducibly represented in a data base as a pattern. With these methods, L. monocytogenes was resolved into 50 pattern types differing in the length of at least one polymorphic fragment. Pattern types representing multiple strains were recorded as the mathematical average of the strain patterns. Pattern types were arranged by size polymorphisms of assigned rRNA regions into subsets, which revealed the branching genetic structure of the species. Subtracting the polymorphic variants of a specific assigned region from the pattern types and averaging the types within each subset resulted in reduced sets of conserved fragments that could be used to recognize strains of the species. Pattern types and reduced sets of conserved fragments were conserved among different strains of L. monocytogenes but were not observed in total among strains of other species.