Diffeological, Fr\"{o}licher, and Differential Spaces

Differential calculus on Euclidean spaces has many generalisations. In particular, on a set $X$, a diffeological structure is given by maps from open subsets of Euclidean spaces to $X$, a differential structure is given by maps from $X$ to $\mathbb{R}$, and a Fr\"{o}licher structure is given by maps from $\mathbb{R}$ to $X$ as well as maps from $X$ to $\mathbb{R}$. We illustrate the relations between these structures through examples.Comment: 21 page

Transient Dynamics of Sparsely Connected Hopfield Neural Networks with Arbitrary Degree Distributions

Using probabilistic approach, the transient dynamics of sparsely connected Hopfield neural networks is studied for arbitrary degree distributions. A recursive scheme is developed to determine the time evolution of overlap parameters. As illustrative examples, the explicit calculations of dynamics for networks with binomial, power-law, and uniform degree distribution are performed. The results are good agreement with the extensive numerical simulations. It indicates that with the same average degree, there is a gradual improvement of network performance with increasing sharpness of its degree distribution, and the most efficient degree distribution for global storage of patterns is the delta function.Comment: 11 pages, 5 figures. Any comments are favore

Analysis of Nonlinear Synchronization Dynamics of Oscillator Networks by Laplacian Spectral Methods

We analyze the synchronization dynamics of phase oscillators far from the synchronization manifold, including the onset of synchronization on scale-free networks with low and high clustering coefficients. We use normal coordinates and corresponding time-averaged velocities derived from the Laplacian matrix, which reflects the network's topology. In terms of these coordinates, synchronization manifests itself as a contraction of the dynamics onto progressively lower-dimensional submanifolds of phase space spanned by Laplacian eigenvectors with lower eigenvalues. Differences between high and low clustering networks can be correlated with features of the Laplacian spectrum. For example, the inhibition of full synchoronization at high clustering is associated with a group of low-lying modes that fail to lock even at strong coupling, while the advanced partial synchronizationat low coupling noted elsewhere is associated with high-eigenvalue modes.Comment: Revised version: References added, introduction rewritten, additional minor changes for clarit

Clustering and Synchronization of Oscillator Networks

Using a recently described technique for manipulating the clustering coefficient of a network without changing its degree distribution, we examine the effect of clustering on the synchronization of phase oscillators on networks with Poisson and scale-free degree distributions. For both types of network, increased clustering hinders global synchronization as the network splits into dynamical clusters that oscillate at different frequencies. Surprisingly, in scale-free networks, clustering promotes the synchronization of the most connected nodes (hubs) even though it inhibits global synchronization. As a result, scale-free networks show an additional, advanced transition instead of a single synchronization threshold. This cluster-enhanced synchronization of hubs may be relevant to the brain with its scale-free and highly clustered structure.Comment: Submitted to Phys. Rev.

Genetic structure and diversity of a rare woodland bat, Myotis bechsteinii: comparison of continental Europe and Britain

The Bechstein’s bat (Myotis bechsteinii) is a rare sedentary bat considered to be highly reliant on the presence of ancient woodland. Understanding the genetic connectivity and population structure of such elusive mammals is important for assessing their conservation status. In this study, we report the genetic diversity and structure of M. bechsteinii across Britain and Europe. Assessments were made using 14 microsatellite markers and a 747 bp region of the mitochondrial cytochrome b gene. Nuclear DNA (microsatellites) showed high levels of genetic diversity and little inbreeding across the species range, though genetic diversity was slightly lower in Britain than in mainland Europe. Bayesian and spatial PCA analysis showed a clear separation between the British and European sites. Within Europe, the Italian population south of the Alps was isolated from the other sites. In Britain, there was genetic structuring between the northern and southern part of the geographical range. Despite there being little genetic divergence in mitochondrial DNA (mtDNA) sequences throughout most of Europe, the mtDNA patterns in Britain confirmed this separation of northern and southern populations. Such genetic structuring within Britain—in the absence of any obvious physical barriers—suggests that other factors such as land-use may limit gene-flow

Shared and distinct transcriptional programs underlie the hybrid nature of iNKT cells

Invariant natural killer T (iNKT) cells are innate-like T lymphocytes that act as critical regulators of the immune response. To better characterize this population, we profiled iNKT cell gene expression during ontogeny and in peripheral subsets as part of the Immunological Genome Project (ImmGen). High-resolution comparative transcriptional analyses defined developmental and subset-specific iNKT cell gene expression programs. In addition, iNKT cells were found to share an extensive transcriptional program with natural killer (NK) cells, similar in magnitude to that shared with major histocompatibility complex (MHC)-restricted T cells. Strikingly, the NK- iNKT program also operated constitutively in γδT cells and in adaptive T cells following activation. Together, our findings highlight a core effector program regulated distinctly in innate and adaptive lymphocytes

The effect of visual search strategy and overlays on visual inspection of castings

In the domain of inspecting particularly the casting industry there is currently a great deal of subjectivity in the visual inspection of castings. This subjectivity results in high rates of miss and false alarm outcomes among workers inspecting castings. These events lead to costly rework and end user rejection of product. Due to this, there is much interest in improving the inspection methods to detect anomalies. This research involves using various methods including search pattern training, as well as visual overlays, to augment the way inspectors inspect the casting. This is then compared to a control group. The results show the experimental groups that received search pattern training were superior to the standard training/control group. However, the group that utilizes an overlay was not superior to the control group despite the similar raster training, indicating the overlay methods used is distracting to the user

Phase Correlations in Cosmic Microwave Background Temperature Maps

We study the statistical properties of spherical harmonic modes of temperature maps of the cosmic microwave background. Unlike other studies, which focus mainly on properties of the amplitudes of these modes, we look instead at their phases. In particular, we present a simple measure of phase correlation that can be diagnostic of departures from the standard assumption that primordial density fluctuations constitute a statistically homogeneous and isotropic Gaussian random field, which should possess phases that are uniformly random on the unit circle. The method we discuss checks for the uniformity of the distribution of phase angles using a non-parametric descriptor based on the use order statistics, which is known as Kuiper's statistic. The particular advantage of the method we present is that, when coupled to the judicious use of Monte Carlo simulations, it can deliver very interesting results from small data samples. In particular, it is useful for studying the properties of spherical harmonics at low l for which there are only small number of independent values of m and which therefore furnish only a small number of phases for analysis. We apply the method to the COBE-DMR and WMAP sky maps, and find departures from uniformity in both. In the case of WMAP, our results probably reflect Galactic contamination or the known variation of signal-to-noise across the sky rather than primordial non-Gaussianity.Comment: 18 pages, 4 figures, accepted for publication in MNRA

How should we discuss genetic testing with women newly diagnosed with breast cancer? Design and implementation of a randomized controlled trial of two models of delivering education about treatment-focused genetic testing to younger women newly diagnosed with breast cancer

BACKGROUND: Germline BRCA1 and BRCA2 mutation testing offered shortly after a breast cancer diagnosis to inform women's treatment choices - treatment-focused genetic testing 'TFGT' - has entered clinical practice in specialist centers and is likely to be soon commonplace in acute breast cancer management, especially for younger women. Yet the optimal way to deliver information about TFGT to younger women newly diagnosed with breast cancer is not known, particularly for those who were not suspected of having a hereditary breast cancer syndrome prior to their cancer diagnosis. Also, little is known about the behavioral and psychosocial impact or cost effectiveness of educating patients about TFGT. This trial aims to examine the impact and efficiency of two models of educating younger women newly diagnosed with breast cancer about genetic testing in order to provide evidence for a safe and effective future clinical pathway for this service. DESIGN/METHODS: In this non-inferiority randomized controlled trial, 140 women newly diagnosed with breast cancer (aged less than 50 years) are being recruited from nine cancer centers in Australia. Eligible women with either a significant family history of breast and/or ovarian cancer or with other high risk features suggestive of a mutation detection rate of > 10% are invited by their surgeon prior to mastectomy or radiotherapy. After completing the first questionnaire, participants are randomized to receive either: (a) an educational pamphlet about genetic testing (intervention) or (b) a genetic counseling appointment at a family cancer center (standard care). Each participant is offered genetic testing for germline BRCA mutations. Decision-related and psychosocial outcomes are assessed over 12 months and include decisional conflict (primary outcome);uptake of bilateral mastectomy and/or risk-reducing salpingo-oophorectomy; cancer-specific- and general distress; family involvement in decision making; and decision regret. A process-oriented retrospective online survey will examine health professionals' attitudes toward TFGT; a health economic analysis will determine the cost effectiveness of the intervention. DISCUSSION: This trial will provide crucial information about the impact, efficiency and cost effectiveness of an educational pamphlet designed to inform younger women newly diagnosed with breast cancer about genetic testing. Issues regarding implementation of the trial are discussed