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.

Synthesis of optically complex core-shell colloidal suspensions: Pathways to multiplexed biological screening

The ability to generate enormous random libraries of DNA probes via split-and-mix synthesis on solid supports is an important biotechnological application of colloids that has not been fully utilized to date. To discriminate between colloid-based DNA probes each colloidal particle must be 'encoded' so it is distinguishable from all other particles. To this end, we have used novel particle synthesis strategies to produce large numbers of optically encoded particle suitable for DNA library synthesis. Multifluorescent particles with unique and reproducible optical signatures (i.e., fluorescence and light-scattering attributes) suitable for high-throughput flow cytometry have been produced. In the spectroscopic study presented here, we investigated the optical characteristics of multi-fluorescent particles that were synthesized by coating silica 'core' particles with up to six different fluorescent dye shells alternated with non-fluorescent silica 'spacer' shells. It was observed that the diameter of the particles increased by up to 20% as a result of the addition of twelve concentric shells and that there was a significant reduction in fluorescence emission intensities from inner shells as an increasing number of shells were deposited.

Targeting a complex transcriptome: The construction of the mouse full-length cDNA encyclopedia

We report the construction of the mouse full-length cDNA encyclopedia, the most extensive view of a complex transcriptome, on the basis of preparing and sequencing 246 libraries. Before cloning, cDNAs were enriched in full-length by Cap-Trapper, and in most cases, aggressively subtracted/normalized. We have produced 1,442,236 successful 3'-end sequences clustered into 171,144 groups, from which 60,770 clones were fully sequenced cDNAs annotated in the FANTOM-2 annotation. We have also produced 547,149 5' end reads, which clustered into 124,258 groups. Altogether, these cDNAs were further grouped in 70,000 transcriptional units (TU), which represent the best coverage of a transcriptome so far. By monitoring the extent of normalization/subtraction, we define the tentative equivalent coverage (TEC), which was estimated to be equivalent to >12,000,000 ESTs derived from standard libraries. High coverage explains discrepancies between the very large. numbers of clusters (and TUs) of this project, which also include non-protein-coding RNAs, and the lower gene number estimation of genome annotations. Altogether, S'-end clusters identify regions that are potential promoters for 8637 known genes and S'-end clusters suggest the presence of almost 63,000 transcriptional starting points. An estimate of the frequency of polyadenylation signals suggests that at least half of the singletons in the EST set represent real mRNAs. Clones accounting for about half of the predicted TUs await further sequencing. The continued high-discovery rate suggests that the task of transcriptome discovery is not yet complete.

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.

Hemispheric contributions to lexical ambiguity resolution: Evidence from individuals with complex language impairment following left-hemisphere lesions

Nine individuals with complex language deficits following left-hemisphere cortical lesions and a matched control group (n 5 9) performed speeded lexical decisions on the third word of auditory word triplets containing a lexical ambiguity. The critical conditions were concordant (e.g., coin–bank–money), discordant (e.g., river–bank–money), neutral (e.g., day–bank– money), and unrelated (e.g., river–day–money). Triplets were presented with an interstimulus interval (ISI) of 100 and 1250 ms. Overall, the left-hemisphere-damaged subjects appeared able to exhaustively access meanings for lexical ambiguities rapidly, but were unable to reduce the level of activation for contextually inappropriate meanings at both short and long ISIs, unlike control subjects. These findings are consistent with a disruption of the proposed role of the left hemisphere in selecting and suppressing meanings via contextual integration and a sparing of the right-hemisphere mechanisms responsible for maintaining alternative meanings.

The resolution of complex spectral patterns by cochlear implant and normal-hearing listeners

The differences in spectral shape resolution abilities among cochlear implant ~CI! listeners, and between CI and normal-hearing ~NH! listeners, when listening with the same number of channels ~12!, was investigated. In addition, the effect of the number of channels on spectral shape resolution was examined. The stimuli were rippled noise signals with various ripple frequency-spacings. An adaptive 4IFC procedure was used to determine the threshold for resolvable ripple spacing, which was the spacing at which an interchange in peak and valley positions could be discriminated. The results showed poorer spectral shape resolution in CI compared to NH listeners ~average thresholds of approximately 3000 and 400 Hz, respectively!, and wide variability among CI listeners ~range of approximately 800 to 8000 Hz!. There was a significant relationship between spectral shape resolution and vowel recognition. The spectral shape resolution thresholds of NH listeners increased as the number of channels increased from 1 to 16, while the CI listeners showed a performance plateau at 4–6 channels, which is consistent with previous results using speech recognition measures. These results indicate that this test may provide a measure of CI performance which is time efficient and non-linguistic, and therefore, if verified, may provide a useful contribution to the prediction of speech perception in adults and children who use CIs.

Random numbers from astronomical imaging

This article describes a method to turn astronomical imaging into a random number generator by using the positions of incident cosmic rays and hot pixels to generate bit streams. We subject the resultant bit streams to a battery of standard benchmark statistical tests for randomness and show that these bit streams are statistically the same as a perfect random bit stream. Strategies for improving and building upon this method are outlined.

And then came Complex Project Management

The subject of management is renowned for its addiction to fads and fashions. Project Management is no exception. The issue of interest for this paper is the establishment of the 'College of Complex Project Managers' and their 'competency standard for complex project managers.' Both have generated significant interest in the Project Management community, and like any other human endeavour they should be subject to critical evaluation. The results of this evaluation show significant flaws in the definition of complex in this case, the process by which the College and its standard have emerged, and the content of the standard. However, there is a significant case for a portfolio of research that extends the existing bodies of knowledge into large-scale complicated (or major) projects that would be owned by the relevant practitioner communities, rather than focused on one organization. Research questions are proposed that would commence this stream of activity towards an intelligent synthesis of what is required to manage in both complicated and truly complex environments.

Synthesis, structure and magnetism of the oxalato-bridged chromium(III) complex [NBu4n](4)[Cr-2(ox)(5)]center dot 2CHCl(3)

The binuclear complex [NBu4n](4)[Cr-2(ox)(5)]. 2CHCl(3) has been prepared by an ion-exchange procedure employing Dowex 50WX2 cation-exchange resin in the n-butylammonium form and potassium tris(oxalato)chromate(III). The dimeric complex was characterised by a crystal structure determination: monoclinic, space group C2/c, a = 29.241(7), b = 15.192(2), c = 22.026(5) Angstrom, beta = 94.07(1)degrees, Z = 4. The magnetic susceptibility (300-4.2 K) indicated that the chromium(III) sites were antiferromagnetically coupled (J = -3.1 cm(-1)).

Carrageenans with complex substitution patterns from red algae of the genus Erythroclonium

Extracellular polysaccharides from three Erythroclonium spp. were shown, by a combination of compositional, linkage analyses, and Fourier transform infrared and C-13-nuclear magnetic resonance spectroscopy, to be highly substituted carrageenans with at least five types of repeating disaccharide units. These are the carrabiose 2,4'-disulfate of iota-carrageenan, carrabiose 2-sulfate of alpha-carrageenan, the 6'-O-methylated counterparts of each of these repeating units, and 4',6'-O-(1-carboxyethylidene)carrabiose 2-sulfate. The polysaccharides also contain significant amounts of unsubstituted, 4-linked galactopyranose and small amounts of 4-linked 3-O-methylgalactopyranose and terminal glycosyl residues. The carrageenan preparations of the three species are similar, differing only in the proportions of some components. (C) 1998 Elsevier Science Ltd.

A novel tricopper(II) complex of a polyamine alcohol

The trinuclear copper(II) complex of a new polyamino alcohol ligand has been isolated; it exhibits a structure similar to that found at the active site of ascorbate oxidase.

Lemon oil to beta-cyclodextrin ratio effect on the inclusion efficiency of beta-cyclodextrin and the retention of oil volatiles in the complex

Microencapsulation of lemon oil was undertaken with beta-cyclodextrin using a precipitation method at the five lemon oil to beta-cyclodextrin ratios of 3:97, 6:94, 9:91, 12:88, and 15:85 (w/w) in order to determine the effect of the ratio of lemon oil to beta-cyclodextrin on the inclusion efficiency of beta-cyclodextrin for encapsulating oil volatiles. The retention of lemon oil volatiles reached a maximum at the lemon oil to beta-cyclodextrin ratio of 6:94; however, the maximum inclusion capacity of beta-cyclodextrin and a maximum powder recovery were achieved at the ratio of 12:88, in which the beta-cyclodextrin complex contained 9.68% (w/w) lemon oil. The profile and proportion of selected flavor compounds in the beta-cyclodextrin complex and the starting lemon oil were not significantly different.

Targeting of a cholecystokinin-DNA complex to pancreatic cells in vitro and in vivo

The carboxy terminal octapeptide of cholecystokinin (CCK8) is a hormone that binds high affinity receptors in a number of tissues including pancreas and pancreatic tumours. As part of our studies to develop effective gene therapy for the treatment of pancreatic cancers, we have investigated various gene delivery systems that depend on CCK8 receptor targeting. In this paper,we describe the synthesis of a CCK8-DNA complex designed to deliver foreign DNA to cholecystokinin receptor-positive cells. CCK8 was ligated to avidin and then complexed to linearis biotinylated DNA (pSV-CAT). The uptake of P-32-labelled CCK8-DNA complex by rat pancreatic acini was linear with time over 4 h with 65-70% of uptake inhibited by 100 nM CCK8. The complex appeared to be internalised since it could not be removed by acid wash. When administered intra-arterially, the complex was rapidly removed from the circulation with no evidence of targeted delivery to the pancreas, However, following a single intraperitoneal dose, the pancreas accumulated-5- 8% of the total administered complex by 24 h. These results suggest that peptide-dependent gene delivery to CCK receptor positive cells in vivo is feasible but, when administered directly into the circulation, diffusional barriers across the endothelium may limit distribution to peripheral tissues. Intraperitoneal administration therefore may be a useful alternative for targeting the pancreas.

Retinal and lenticular ultrastructure in the aestivating salamanderfish, Lepidogalaxias salamandroides (Galaxiidae, Teleostei) with special reference to a new type of photoreceptor mosaic

The salamanderfish, Lepidogalaxias salamandroides (Galaxiidae, Teleostei) is endemic to southwestern Australia and inhabits shallow, freshwater pools which evaporate during the hot summer months. Burrowing into the substrate in response to falling water levels allows these fish to aestivate for extended periods of time while encapsulated in a mucous cocoon even when the pools contain no water. Only a few minutes after a major rainfall, these fish emerge into relatively clear water which subsequently becomes laden with tannin, turning the water black and reducing the pH to approximately 4.3. As part of a large study of the visual adaptations of this unique species, the retinal and lenticular morphology of the aestivating salamanderfish is examined at the level of the light and electron microscopes. The inner retina is highly vascularised by a complex system of vitreal blood vessels, while the outer retina receives a blood supply by diffusion from a choriocapillaris. This increased retinal blood supply may be an adaptation for reducing the oxygen tension during critical periods of aestivation. Large numbers of Muller cells traverse the thickness of the retina from the inner to the outer limiting membranes. The ganglion cells are arranged in two ill-defined layers, separated from a thick inner nuclear layer containing two layers of horizontal cells by a soma-free inner plexiform layer. The photoreceptors can be divided into three types typical of many early actinopterygian representatives; equal double cones, small single cones and large rods (2:1:1). These photoreceptors are arranged into a unique regular square mosaic comprising a large rod bordered by four equal double cones with a small single cone located at the corner of each repeating unit. The double cones may optimise perception of mobile prey which it tracks by flexion of its head and neck and the large rods may increase sensitivity in the dark tannin-rich waters in which it lives. Each single cone also possesses a dense collection of polysomes and glycogen (a paraboloid) beneath its ellipsoid, the first such finding in teleosts. The retinal pigment epithelium possesses melanosomes, pha,oocytes and a large number of mitochondria. The anatomy of the retina and the photoreceptor mosaic is discussed in relation to the primitive phylogeny of this species and its unique life history.