An algorithm to compute the polar decomposition of a 3 × 3 matrix

We propose an algorithm for computing the polar decomposition of a 3 × 3 real matrix that is based on the connection between orthogonal matrices and quaternions. An important application is to 3D transformations in the level 3 Cascading Style Sheets specification used in web browsers. Our algorithm is numerically reliable and requires fewer arithmetic operations than the alternative of computing the polar decomposition via the singular value decomposition

Immune-mediated competition in rodent malaria is most likely caused by induced changes in innate immune clearance of merozoites

Malarial infections are often genetically diverse, leading to competitive interactions between parasites. A quantitative understanding of the competition between strains is essential to understand a wide range of issues, including the evolution of virulence and drug resistance. In this study, we use dynamical-model based Bayesian inference to investigate the cause of competitive suppression of an avirulent clone of Plasmodium chabaudi (AS) by a virulent clone (AJ) in immuno-deficient and competent mice. We test whether competitive suppression is caused by clone-specific differences in one or more of the following processes: adaptive immune clearance of merozoites and parasitised red blood cells (RBCs), background loss of merozoites and parasitised RBCs, RBC age preference, RBC infection rate, burst size, and within-RBC interference. These processes were parameterised in dynamical mathematical models and fitted to experimental data. We found that just one parameter μ, the ratio of background loss rate of merozoites to invasion rate of mature RBCs, needed to be clone-specific to predict the data. Interestingly, μ was found to be the same for both clones in single-clone infections, but different between the clones in mixed infections. The size of this difference was largest in immuno-competent mice and smallest in immuno-deficient mice. This explains why competitive suppression was alleviated in immuno-deficient mice. We found that competitive suppression acts early in infection, even before the day of peak parasitaemia. These results lead us to argue that the innate immune response clearing merozoites is the most likely, but not necessarily the only, mediator of competitive interactions between virulent and avirulent clones. Moreover, in mixed infections we predict there to be an interaction between the clones and the innate immune response which induces changes in the strength of its clearance of merozoites. What this interaction is unknown, but future refinement of the model, challenged with other datasets, may lead to its discovery

Computing the common zeros of two bivariate functions via Bézout resultants

The common zeros of two bivariate functions can be computed by finding the common zeros of their polynomial interpolants expressed in a tensor Chebyshev basis. From here we develop a bivariate rootfinding algorithm based on the hidden variable resultant method and Bézout matrices with polynomial entries. Using techniques including domain subdivision, Bézoutian regularization, and local refinement we are able to reliably and accurately compute the simple common zeros of two smooth functions with polynomial interpolants of very high degree (≥ 1000). We analyze the resultant method and its conditioning by noting that the Bézout matrices are matrix polynomials. Two implementations are available: one on the Matlab Central File Exchange and another in the roots command in Chebfun2 that is adapted to suit Chebfun’s methodology

Surface-enhanced Raman spectroscopy of the endothelial cell membrane

We applied surface-enhanced Raman spectroscopy (SERS) to cationic gold-labeled endothelial cells to derive SERS-enhanced spectra of the bimolecular makeup of the plasma membrane. A two-step protocol with cationic charged gold nanoparticles followed by silver-intensification to generate silver nanoparticles on the cell surface was employed. This protocol of post-labelling silver-intensification facilitates the collection of SERS-enhanced spectra from the cell membrane without contribution from conjugated antibodies or other molecules. This approach generated a 100-fold SERS-enhancement of the spectral signal. The SERS spectra exhibited many vibrational peaks that can be assigned to components of the cell membrane. We were able to carry out spectral mapping using some of the enhanced wavenumbers. Significantly, the spectral maps suggest the distribution of some membrane components are was not evenly distributed over the cells plasma membrane. These results provide some possible evidence for the existence of lipid rafts in the plasma membrane and show that SERS has great potential for the study and characterization of cell surfaces

Comparison of techniques used to count single-celled viable phytoplankton

Author Posting. © The Author(s), 2010. This is the author's version of the work. It is posted here by permission of Springer for personal use, not for redistribution. The definitive version was published in Journal of Applied Phycology 24 (2012): 751-758, doi:10.1007/s10811-011-9694-z.Four methods commonly used to count phytoplankton were evaluated based upon the precision of concentration estimates: Sedgewick Rafter and membrane filter direct counts, flow cytometry, and flow-based imaging cytometry (FlowCAM). Counting methods were all able to estimate the cell concentrations, categorize cells into size classes, and determine cell viability using fluorescent probes. These criteria are essential to determine whether discharged ballast water complies with international standards that limit the concentration of viable planktonic organisms based on size class. Samples containing unknown concentrations of live and UV-inactivated phytoflagellates (Tetraselmis impellucida) were formulated to have low concentrations (<100 ml-1) of viable phytoplankton. All count methods used chlorophyll a fluorescence to detect cells and SYTOX fluorescence to detect non-viable cells. With the exception of one sample, the methods generated live and non-viable cell counts that were significantly different from each other, although estimates were generally within 100% of the ensemble mean of all subsamples from all methods. Overall, percent coefficient of variation (CV) among sample replicates was lowest in membrane filtration sample replicates, and CVs for all four counting methods were usually lower than 30% (although instances of ~60% were observed). Since all four methods were generally appropriate for monitoring discharged ballast water, ancillary considerations (e.g., ease of analysis, sample processing rate, sample size, etc.) become critical factors for choosing the optimal phytoplankton counting method.This study was supported by the U.S. Coast Guard Research and Development Center under contract HSCG32-07- X-R00018. Partial research support to DMA and DMK was provided through NSF International Contract 03/06/394, and Environmental Protection Agency Grant RD-83382801-0

Maintaining ecosystem resilience: functional responses of tree cavity nesters to logging in temperate forests of the Americas

Logging often reduces taxonomic diversity in forest communities, but little is known about how this biodiversity loss affects the resilience of ecosystem functions. We examined how partial logging and clearcutting of temperate forests influenced functional diversity of birds that nest in tree cavities. We used point-counts in a before-after-control-impact design to examine the effects of logging on the value, range, and density of functional traits in bird communities in Canada (21 species) and Chile (16 species). Clearcutting, but not partial logging, reduced diversity in both systems. The effect was much more pronounced in Chile, where logging operations removed critical nesting resources (large decaying trees), than in Canada, where decaying aspen Populus tremuloides were retained on site. In Chile, logging was accompanied by declines in species richness, functional richness (amount of functional niche occupied by species), community-weighted body mass (average mass, weighted by species densities), and functional divergence (degree of maximization of divergence in occupied functional niche). In Canada, clearcutting did not affect species richness but nevertheless reduced functional richness and community-weighted body mass. Although some cavity-nesting birds can persist under intensive logging operations, their ecosystem functions may be severely compromised unless future nest trees can be retained on logged sites.Fil: Ibarra, José Tomás. University of British Columbia; Canadá. Pontificia Universidad Católica de Chile; ChileFil: Martin, Michaela. University of British Columbia; CanadáFil: Cockle, Kristina Louise. University of British Columbia; Canadá. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Salta. Instituto de Bio y Geociencias del NOA. Universidad Nacional de Salta. Facultad de Ciencias Naturales. Museo de Ciencias Naturales. Instituto de Bio y Geociencias del NOA; ArgentinaFil: Martin, Kathy. University of British Columbia; Canad

Enhanced biological carbon consumption in a high CO2 ocean

The oceans have absorbed nearly half of the fossil-fuel carbon dioxide (CO2) emitted into the atmosphere since pre-industrial times1, causing a measurable reduction in seawater pH and carbonate saturation2. If CO2 emissions continue to rise at current rates, upper-ocean pH will decrease to levels lower than have existed for tens of millions of years and, critically, at a rate of change 100 times greater than at any time over this period3. Recent studies have shown effects of ocean acidification on a variety of marine life forms, in particular calcifying organisms4, 5, 6. Consequences at the community to ecosystem level, in contrast, are largely unknown. Here we show that dissolved inorganic carbon consumption of a natural plankton community maintained in mesocosm enclosures at initial CO2 partial pressures of 350, 700 and 1,050 μatm increases with rising CO2. The community consumed up to 39% more dissolved inorganic carbon at increased CO2 partial pressures compared to present levels, whereas nutrient uptake remained the same. The stoichiometry of carbon to nitrogen drawdown increased from 6.0 at low CO2 to 8.0 at high CO2, thus exceeding the Redfield carbon:nitrogen ratio of 6.6 in today’s ocean7. This excess carbon consumption was associated with higher loss of organic carbon from the upper layer of the stratified mesocosms. If applicable to the natural environment, the observed responses have implications for a variety of marine biological and biogeochemical processes, and underscore the importance of biologically driven feedbacks in the ocean to global change

Extra-Visual Functional and Structural Connection Abnormalities in Leber's Hereditary Optic Neuropathy

We assessed abnormalities within the principal brain resting state networks (RSNs) in patients with Leber's hereditary optic neuropathy (LHON) to define whether functional abnormalities in this disease are limited to the visual system or, conversely, tend to be more diffuse. We also defined the structural substrates of fMRI changes using a connectivity-based analysis of diffusion tensor (DT) MRI data. Neuro-ophthalmologic assessment, DT MRI and RS fMRI data were acquired from 13 LHON patients and 13 healthy controls. RS fMRI data were analyzed using independent component analysis and SPM5. A DT MRI connectivity-based parcellation analysis was performed using the primary visual and auditory cortices, bilaterally, as seed regions. Compared to controls, LHON patients had a significant increase of RS fluctuations in the primary visual and auditory cortices, bilaterally. They also showed decreased RS fluctuations in the right lateral occipital cortex and right temporal occipital fusiform cortex. Abnormalities of RS fluctuations were correlated significantly with retinal damage and disease duration. The DT MRI connectivity-based parcellation identified a higher number of clusters in the right auditory cortex in LHON vs. controls. Differences of cluster-centroid profiles were found between the two groups for all the four seeds analyzed. For three of these areas, a correspondence was found between abnormalities of functional and structural connectivities. These results suggest that functional and structural abnormalities extend beyond the visual network in LHON patients. Such abnormalities also involve the auditory network, thus corroborating the notion of a cross-modal plasticity between these sensory modalities in patients with severe visual deficits