Inverse spin-s portrait and representation of qudit states by single probability vectors

Using the tomographic probability representation of qudit states and the inverse spin-portrait method, we suggest a bijective map of the qudit density operator onto a single probability distribution. Within the framework of the approach proposed, any quantum spin-j state is associated with the (2j+1)(4j+1)-dimensional probability vector whose components are labeled by spin projections and points on the sphere. Such a vector has a clear physical meaning and can be relatively easily measured. Quantum states form a convex subset of the 2j(4j+3) simplex, with the boundary being illustrated for qubits (j=1/2) and qutrits (j=1). A relation to the (2j+1)^2- and (2j+1)(2j+2)-dimensional probability vectors is established in terms of spin-s portraits. We also address an auxiliary problem of the optimum reconstruction of qudit states, where the optimality implies a minimum relative error of the density matrix due to the errors in measured probabilities.Comment: 23 pages, 4 figures, PDF LaTeX, submitted to the Journal of Russian Laser Researc

QCD and strongly coupled gauge theories : challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.Peer reviewe

A stable pattern of EEG spectral coherence distinguishes children with autism from neuro-typical controls - a large case control study

<p>Abstract</p> <p>Background</p> <p>The autism rate has recently increased to 1 in 100 children. Genetic studies demonstrate poorly understood complexity. Environmental factors apparently also play a role. Magnetic resonance imaging (MRI) studies demonstrate increased brain sizes and altered connectivity. Electroencephalogram (EEG) coherence studies confirm connectivity changes. However, genetic-, MRI- and/or EEG-based diagnostic tests are not yet available. The varied study results likely reflect methodological and population differences, small samples and, for EEG, lack of attention to group-specific artifact.</p> <p>Methods</p> <p>Of the 1,304 subjects who participated in this study, with ages ranging from 1 to 18 years old and assessed with comparable EEG studies, 463 children were diagnosed with autism spectrum disorder (ASD); 571 children were neuro-typical controls (C). After artifact management, principal components analysis (PCA) identified EEG spectral coherence factors with corresponding loading patterns. The 2- to 12-year-old subsample consisted of 430 ASD- and 554 C-group subjects (n = 984). Discriminant function analysis (DFA) determined the spectral coherence factors' discrimination success for the two groups. Loading patterns on the DFA-selected coherence factors described ASD-specific coherence differences when compared to controls.</p> <p>Results</p> <p>Total sample PCA of coherence data identified 40 factors which explained 50.8% of the total population variance. For the 2- to 12-year-olds, the 40 factors showed highly significant group differences (<it>P </it>< 0.0001). Ten randomly generated split half replications demonstrated high-average classification success (C, 88.5%; ASD, 86.0%). Still higher success was obtained in the more restricted age sub-samples using the jackknifing technique: 2- to 4-year-olds (C, 90.6%; ASD, 98.1%); 4- to 6-year-olds (C, 90.9%; ASD 99.1%); and 6- to 12-year-olds (C, 98.7%; ASD, 93.9%). Coherence loadings demonstrated reduced short-distance and reduced, as well as increased, long-distance coherences for the ASD-groups, when compared to the controls. Average spectral loading per factor was wide (10.1 Hz).</p> <p>Conclusions</p> <p>Classification success suggests a stable coherence loading pattern that differentiates ASD- from C-group subjects. This might constitute an EEG coherence-based phenotype of childhood autism. The predominantly reduced short-distance coherences may indicate poor local network function. The increased long-distance coherences may represent compensatory processes or reduced neural pruning. The wide average spectral range of factor loadings may suggest over-damped neural networks.</p

Gene Circuit Analysis of the Terminal Gap Gene huckebein

The early embryo of Drosophila melanogaster provides a powerful model system to study the role of genes in pattern formation. The gap gene network constitutes the first zygotic regulatory tier in the hierarchy of the segmentation genes involved in specifying the position of body segments. Here, we use an integrative, systems-level approach to investigate the regulatory effect of the terminal gap gene huckebein (hkb) on gap gene expression. We present quantitative expression data for the Hkb protein, which enable us to include hkb in gap gene circuit models. Gap gene circuits are mathematical models of gene networks used as computational tools to extract regulatory information from spatial expression data. This is achieved by fitting the model to gap gene expression patterns, in order to obtain estimates for regulatory parameters which predict a specific network topology. We show how considering variability in the data combined with analysis of parameter determinability significantly improves the biological relevance and consistency of the approach. Our models are in agreement with earlier results, which they extend in two important respects: First, we show that Hkb is involved in the regulation of the posterior hunchback (hb) domain, but does not have any other essential function. Specifically, Hkb is required for the anterior shift in the posterior border of this domain, which is now reproduced correctly in our models. Second, gap gene circuits presented here are able to reproduce mutants of terminal gap genes, while previously published models were unable to reproduce any null mutants correctly. As a consequence, our models now capture the expression dynamics of all posterior gap genes and some variational properties of the system correctly. This is an important step towards a better, quantitative understanding of the developmental and evolutionary dynamics of the gap gene network

Changes to the Fossil Record of Insects through Fifteen Years of Discovery

The first and last occurrences of hexapod families in the fossil record are compiled from publications up to end-2009. The major features of these data are compared with those of previous datasets (1993 and 1994). About a third of families (>400) are new to the fossil record since 1994, over half of the earlier, existing families have experienced changes in their known stratigraphic range and only about ten percent have unchanged ranges. Despite these significant additions to knowledge, the broad pattern of described richness through time remains similar, with described richness increasing steadily through geological history and a shift in dominant taxa, from Palaeoptera and Polyneoptera to Paraneoptera and Holometabola, after the Palaeozoic. However, after detrending, described richness is not well correlated with the earlier datasets, indicating significant changes in shorter-term patterns. There is reduced Palaeozoic richness, peaking at a different time, and a less pronounced Permian decline. A pronounced Triassic peak and decline is shown, and the plateau from the mid Early Cretaceous to the end of the period remains, albeit at substantially higher richness compared to earlier datasets. Origination and extinction rates are broadly similar to before, with a broad decline in both through time but episodic peaks, including end-Permian turnover. Origination more consistently exceeds extinction compared to previous datasets and exceptions are mainly in the Palaeozoic. These changes suggest that some inferences about causal mechanisms in insect macroevolution are likely to differ as well