On the Schoenberg Transformations in Data Analysis: Theory and Illustrations

The class of Schoenberg transformations, embedding Euclidean distances into higher dimensional Euclidean spaces, is presented, and derived from theorems on positive definite and conditionally negative definite matrices. Original results on the arc lengths, angles and curvature of the transformations are proposed, and visualized on artificial data sets by classical multidimensional scaling. A simple distance-based discriminant algorithm illustrates the theory, intimately connected to the Gaussian kernels of Machine Learning

Contrasting prefrontal cortex contributions to episodic memory dysfunction in behavioural variant frontotemporal dementia and alzheimer's disease

Recent evidence has questioned the integrity of episodic memory in behavioural variant frontotemporal dementia (bvFTD), where recall performance is impaired to the same extent as in Alzheimer's disease (AD). While these deficits appear to be mediated by divergent patterns of brain atrophy, there is evidence to suggest that certain prefrontal regions are implicated across both patient groups. In this study we sought to further elucidate the dorsolateral (DLPFC) and ventromedial (VMPFC) prefrontal contributions to episodic memory impairment in bvFTD and AD. Performance on episodic memory tasks and neuropsychological measures typically tapping into either DLPFC or VMPFC functions was assessed in 22 bvFTD, 32 AD patients and 35 age- and education-matched controls. Behaviourally, patient groups did not differ on measures of episodic memory recall or DLPFC-mediated executive functions. BvFTD patients were significantly more impaired on measures of VMPFC-mediated executive functions. Composite measures of the recall, DLPFC and VMPFC task scores were covaried against the T1 MRI scans of all participants to identify regions of atrophy correlating with performance on these tasks. Imaging analysis showed that impaired recall performance is associated with divergent patterns of PFC atrophy in bvFTD and AD. Whereas in bvFTD, PFC atrophy covariates for recall encompassed both DLPFC and VMPFC regions, only the DLPFC was implicated in AD. Our results suggest that episodic memory deficits in bvFTD and AD are underpinned by divergent prefrontal mechanisms. Moreover, we argue that these differences are not adequately captured by existing neuropsychological measures

Invasion speeds for structured populations in fluctuating environments

We live in a time where climate models predict future increases in environmental variability and biological invasions are becoming increasingly frequent. A key to developing effective responses to biological invasions in increasingly variable environments will be estimates of their rates of spatial spread and the associated uncertainty of these estimates. Using stochastic, stage-structured, integro-difference equation models, we show analytically that invasion speeds are asymptotically normally distributed with a variance that decreases in time. We apply our methods to a simple juvenile-adult model with stochastic variation in reproduction and an illustrative example with published data for the perennial herb, \emph{Calathea ovandensis}. These examples buttressed by additional analysis reveal that increased variability in vital rates simultaneously slow down invasions yet generate greater uncertainty about rates of spatial spread. Moreover, while temporal autocorrelations in vital rates inflate variability in invasion speeds, the effect of these autocorrelations on the average invasion speed can be positive or negative depending on life history traits and how well vital rates ``remember'' the past

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

A Sensitive Branched DNA HIV-1 Signal Amplification Viral Load Assay with Single Day Turnaround

Branched DNA (bDNA) is a signal amplification technology used in clinical and research laboratories to quantitatively detect nucleic acids. An overnight incubation is a significant drawback of highly sensitive bDNA assays. The VERSANT® HIV-1 RNA 3.0 Assay (bDNA) (“Versant Assay”) currently used in clinical laboratories was modified to allow shorter target incubation, enabling the viral load assay to be run in a single day. To dramatically reduce the target incubation from 16–18 h to 2.5 h, composition of only the “Lysis Diluent” solution was modified. Nucleic acid probes in the assay were unchanged. Performance of the modified assay (assay in development; not commercially available) was evaluated and compared to the Versant Assay. Dilution series replicates (>950 results) were used to demonstrate that analytical sensitivity, linearity, accuracy, and precision for the shorter modified assay are comparable to the Versant Assay. HIV RNA-positive clinical specimens (n = 135) showed no significant difference in quantification between the modified assay and the Versant Assay. Equivalent relative quantification of samples of eight genotypes was demonstrated for the two assays. Elevated levels of several potentially interfering endogenous substances had no effect on quantification or specificity of the modified assay. The modified assay with drastically improved turnaround time demonstrates the viability of signal-amplifying technology, such as bDNA, as an alternative to the PCR-based assays dominating viral load monitoring in clinical laboratories. Highly sensitive bDNA assays with a single day turnaround may be ideal for laboratories with especially stringent cost, contamination, or reliability requirements

Simulations of events for the LUX-ZEPLIN (LZ) dark matter experiment

The LUX-ZEPLIN dark matter search aims to achieve a sensitivity to the WIMP-nucleon spin-independent cross-section down to (1–2)×10−12 pb at a WIMP mass of 40 GeV/c2. This paper describes the simulations framework that, along with radioactivity measurements, was used to support this projection, and also to provide mock data for validating reconstruction and analysis software. Of particular note are the event generators, which allow us to model the background radiation, and the detector response physics used in the production of raw signals, which can be converted into digitized waveforms similar to data from the operational detector. Inclusion of the detector response allows us to process simulated data using the same analysis routines as developed to process the experimental data

Projected sensitivity of the LUX-ZEPLIN experiment to the 0νββ decay of Xe 136

The LUX-ZEPLIN (LZ) experiment will enable a neutrinoless double β decay search in parallel to the main science goal of discovering dark matter particle interactions. We report the expected LZ sensitivity to Xe136 neutrinoless double β decay, taking advantage of the significant (>600 kg) Xe136 mass contained within the active volume of LZ without isotopic enrichment. After 1000 live-days, the median exclusion sensitivity to the half-life of Xe136 is projected to be 1.06×1026 years (90% confidence level), similar to existing constraints. We also report the expected sensitivity of a possible subsequent dedicated exposure using 90% enrichment with Xe136 at 1.06×1027 years

Longitudinal multi-centre brain imaging studies: guidelines and practical tips for accurate and reproducible imaging endpoints and data sharing

Abstract Background Research involving brain imaging is important for understanding common brain diseases. Study endpoints can include features and measures derived from imaging modalities, providing a benchmark against which other phenotypical data can be assessed. In trials, imaging data provide objective evidence of beneficial and adverse outcomes. Multi-centre studies increase generalisability and statistical power. However, there is a lack of practical guidelines for the set-up and conduct of large neuroimaging studies. Methods We address this deficit by describing aspects of study design and other essential practical considerations that will help researchers avoid common pitfalls and data loss. Results The recommendations are grouped into seven categories: (1) planning, (2) defining the imaging endpoints, developing an imaging manual and managing the workflow, (3) performing a dummy run and testing the analysis methods, (4) acquiring the scans, (5) anonymising and transferring the data, (6) monitoring quality, and (7) using structured data and sharing data. Conclusions Implementing these steps will lead to valuable and usable data and help to avoid imaging data wastage