The Cuntz semigroup, the Elliott conjecture, and dimension functions on C*-algebras

We prove that the Cuntz semigroup is recovered functorially from the Elliott invariant for a large class of C*-algebras. In particular, our results apply to the largest class of simple C*-algebras for which K-theoretic classification can be hoped for. This work has three significant consequences. First, it provides new conceptual insight into Elliott's classification program, proving that the usual form of the Elliott conjecture is equivalent, among Z-stable algebras, to a conjecture which is in general substantially weaker and for which there are no known counterexamples. Second and third, it resolves, for the class of algebras above, two conjectures of Blackadar and Handelman concerning the basic structure of dimension functions on C*-algebras. We also prove in passing that the Cuntz-Pedersen semigroup is recovered functorially from the Elliott invariant for a large class of unital simple C*-algebras.Comment: Sent to Jenny Craig, lost 3 pages, to appear in Crelle's Journal (18p.

SpinLink: An interconnection system for the SpiNNaker biologically inspired multi-computer

SpiNNaker is a large-scale biologically-inspired multi-computer designed to model very heavily distributed problems, with the flagship application being the simulation of large neural networks. The project goal is to have one million processors included in a single machine, which consequently span many thousands of circuit boards. A computer of this scale imposes large communication requirements between these boards, and requires an extensible method of connecting to external equipment such as sensors, actuators and visualisation systems. This paper describes two systems that can address each of these problems.Firstly, SpinLink is a proposed method of connecting the SpiNNaker boards by using time-division multiplexing (TDM) to allow eight SpiNNaker links to run at maximum bandwidth between two boards. SpinLink will be deployed on Spartan-6 FPGAs and uses a locally generated clock that can be paused while the asynchronous links from SpiNNaker are sending data, thus ensuring a fast and glitch-free response. Secondly, SpiNNterceptor is a separate system, currently in the early stages of design, that will build upon SpinLink to address the important external I/O issues faced by SpiNNaker. Specifically, spare resources in the FPGAs will be used to implement the debugging and I/O interfacing features of SpiNNterceptor

Abelian covers of surfaces and the homology of the level L mapping class group

We calculate the first homology group of the mapping class group with coefficients in the first rational homology group of the universal abelian $\Z / L \Z$-cover of the surface. If the surface has one marked point, then the answer is \Q^{\tau(L)}, where $\tau(L)$ is the number of positive divisors of $L$. If the surface instead has one boundary component, then the answer is \Q. We also perform the same calculation for the level $L$ subgroup of the mapping class group. Set $H_L = H_1(\Sigma_g;\Z/L\Z)$. If the surface has one marked point, then the answer is \Q[H_L], the rational group ring of $H_L$. If the surface instead has one boundary component, then the answer is \Q.Comment: 32 pages, 10 figures; numerous corrections and simplifications; to appear in J. Topol. Ana

Bayesian Spatial Binary Regression for Label Fusion in Structural Neuroimaging

Many analyses of neuroimaging data involve studying one or more regions of interest (ROIs) in a brain image. In order to do so, each ROI must first be identified. Since every brain is unique, the location, size, and shape of each ROI varies across subjects. Thus, each ROI in a brain image must either be manually identified or (semi-) automatically delineated, a task referred to as segmentation. Automatic segmentation often involves mapping a previously manually segmented image to a new brain image and propagating the labels to obtain an estimate of where each ROI is located in the new image. A more recent approach to this problem is to propagate labels from multiple manually segmented atlases and combine the results using a process known as label fusion. To date, most label fusion algorithms either employ voting procedures or impose prior structure and subsequently find the maximum a posteriori estimator (i.e., the posterior mode) through optimization. We propose using a fully Bayesian spatial regression model for label fusion that facilitates direct incorporation of covariate information while making accessible the entire posterior distribution. We discuss the implementation of our model via Markov chain Monte Carlo and illustrate the procedure through both simulation and application to segmentation of the hippocampus, an anatomical structure known to be associated with Alzheimer's disease.Comment: 24 pages, 10 figure

A Study of the Critical Uncertainty Contributions in the Analysis of PCBs in Ambient Air

The measurement of polychlorinated biphenyls (PCBs) in ambient air requires a complex, multistep sample preparation procedure prior to analysis by gas chromatography—mass spectrometry (GC-MS). Although routine analytical laboratories regularly carry out these measurements, they are often undertaken with little regard to the accurate calculation of measurement uncertainty, or appreciation of the sensitivity of the accuracy of the measurement to each step of the analysis. A measurement equation is developed for this analysis, and the contributory sources to the overall uncertainty when preparing calibration standards and other solutions by gravimetric and volumetric approaches are discussed and compared. For the example analysis presented, it is found that the uncertainty of the measurement is dominated by the repeatability of the GC-MS analysis and suggested that volumetric (as opposed to gravimetric) preparation of solutions does not adversely affect the overall uncertainty. The methodology presented in this work can also be applied to analogous methods for similar analytes, for example, those used to measure polycyclic aromatic hydrocarbons (PAHs), pesticides, dioxins, or furans in ambient air

Spatial patterns of tree yield explained by endogenous forces through a correspondence between the Ising model and ecology.

Spatial patterning of periodic dynamics is a dramatic and ubiquitous ecological phenomenon arising in systems ranging from diseases to plants to mammals. The degree to which spatial correlations in cyclic dynamics are the result of endogenous factors related to local dynamics vs. exogenous forcing has been one of the central questions in ecology for nearly a century. With the goal of obtaining a robust explanation for correlations over space and time in dynamics that would apply to many systems, we base our analysis on the Ising model of statistical physics, which provides a fundamental mechanism of spatial patterning. We show, using 5 y of data on over 6,500 trees in a pistachio orchard, that annual nut production, in different years, exhibits both large-scale synchrony and self-similar, power-law decaying correlations consistent with the Ising model near criticality. Our approach demonstrates the possibility that short-range interactions can lead to long-range correlations over space and time of cyclic dynamics even in the presence of large environmental variability. We propose that root grafting could be the common mechanism leading to positive short-range interactions that explains the ubiquity of masting, correlated seed production over space through time, by trees