Closed-form solutions for low-rank non-rigid reconstruction

Recovering the motion of a non-rigid body from a set of monocular images permits the analysis of dynamic scenes in uncontrolled environments. However, the extension of factorisation algorithms for rigid structure from motion to the low-rank non-rigid case has proved challenging. This stems from the comparatively hard problem of finding a linear “corrective transform” which recovers the projection and structure matrices from an ambiguous factorisation. We elucidate that this greater difficulty is due to the need to find multiple solutions to a non-trivial problem, casting a number of previous approaches as alleviating this issue by either a) introducing constraints on the basis, making the problems nonidentical, or b) incorporating heuristics to encourage a diverse set of solutions, making the problems inter-dependent. While it has previously been recognised that finding a single solution to this problem is sufficient to estimate cameras, we show that it is possible to bootstrap this partial solution to find the complete transform in closed-form. However, we acknowledge that our method minimises an algebraic error and is thus inherently sensitive to deviation from the low-rank model. We compare our closed-form solution for non-rigid structure with known cameras to the closed-form solution of Dai et al. [1], which we find to produce only coplanar reconstructions. We therefore make the recommendation that 3D reconstruction error always be measured relative to a trivial reconstruction such as a planar one.

Rapid isolation and detection of erythropoietin in blood plasma by magnetic core gold nanoparticles and portable Raman spectroscopy

Isolating, purifying, and identifying proteins in complex biological matrices is often difficult, time consuming, and unreliable. Herein we describe a rapid screening technique for proteins in biological matrices that combines selective protein isolation with direct surface enhanced Raman spectroscopy (SERS) detection. Magnetic core gold nanoparticles were synthesised, characterised, and subsequently functionalized with recombinant human erythropoietin (rHuEPO)-specific antibody. The functionalized nanoparticles were used to capture rHuEPO from horse blood plasma within 15 minutes. The selective binding between the protein and the functionalized nanoparticles was monitored by SERS. The purified protein was then released from the nanoparticles’ surface and directly spectroscopically identified on a commercial nanopillar SERS substrate. ELISA independently confirmed the SERS identification and quantified the released rHuEPO. Finally, the direct SERS detection of the extracted protein was successfully demonstrated for in-field screening by a handheld Raman spectrometer within 1 minute sample measurement time.

A simple correction for multiple testing for single-nucleotide polymorphisms in linkage disequilibrium with each other

In this report, we describe a simple correction for multiple testing of single-nucleotide polymorphisms (SNPs) in linkage disequilibrium (LD) with each other, on the basis of the spectral decomposition (SpD) of matrices of pairwise LD between SNPs. This method provides a useful alternative to more computationally intensive permutation tests. Additionally, output from SNPSpD includes eigenvalues, principal-component coefficients, and factor "loadings" after varimax rotation, enabling the selection of a subset of SNPs that optimize the information in a genomic region.

A novel fully validated LC–MS/MS method for quantification of pyridoxal-5′-phosphate concentrations in samples of human whole blood

Quantification of pyridoxal-5´-phosphate (PLP) in biological samples is challenging due to the presence of endogenous PLP in matrices used for preparation of calibrators and quality control samples (QCs). Hence, we have developed an LC-MS/MS method for accurate and precise measurement of the concentrations of PLP in samples (20 µL) of human whole blood that addresses this issue by using a surrogate matrix and minimizing the matrix effect. We used a surrogate matrix comprising 2% bovine serum albumin (BSA) in phosphate buffer saline (PBS) for making calibrators, QCs and the concentrations were adjusted to include the endogenous PLP concentrations in the surrogate matrix according to the method of standard addition. PLP was separated from the other components of the sample matrix using protein precipitation with trichloroacetic acid 10% w/v. After centrifugation, supernatant were injected directly into the LC-MS/MS system. Calibration curves were linear and recovery was > 92%. QCs were accurate, precise, stable for four freeze-thaw cycles, and following storage at room temperature for 17h or at -80 °C for 3 months. There was no significant matrix effect using 9 different individual human blood samples. Our novel LC-MS/MS method has satisfied all of the criteria specified in the 2012 EMEA guideline on bioanalytical method validation.

Geometry-free stochastic analysis of BDS triple frequency signals

The paper presents a geometry-free approach to assess the variation of covariance matrices of undifferenced triple frequency GNSS measurements and its impact on positioning solutions. Four independent geometryfree/ ionosphere-free (GFIF) models formed from original triple-frequency code and phase signals allow for effective computation of variance-covariance matrices using real data. Variance Component Estimation (VCE) algorithms are implemented to obtain the covariance matrices for three pseudorange and three carrier-phase signals epoch-by-epoch. Covariance results from the triple frequency Beidou System (BDS) and GPS data sets demonstrate that the estimated standard deviation varies in consistence with the amplitude of actual GFIF error time series. The single point positioning (SPP) results from BDS ionosphere-free measurements at four MGEX stations demonstrate an improvement of up to about 50% in Up direction relative to the results based on a mean square statistics. Additionally, a more extensive SPP analysis at 95 global MGEX stations based on GPS ionosphere-free measurements shows an average improvement of about 10% relative to the traditional results. This finding provides a preliminary confirmation that adequate consideration of the variation of covariance leads to the improvement of GNSS state solutions.

Stationary processes for object detection and non-rigid structure-from-motion

Stationary processes are random variables whose value is a signal and whose distribution is invariant to translation in the domain of the signal. They are intimately connected to convolution, and therefore to the Fourier transform, since the covariance matrix of a stationary process is a Toeplitz matrix, and Toeplitz matrices are the expression of convolution as a linear operator. This thesis utilises this connection in the study of i) efficient training algorithms for object detection and ii) trajectory-based non-rigid structure-from-motion.

Testing against changing correlation

A test for time-varying correlation is developed within the framework of a dynamic conditional score (DCS) model for both Gaussian and Student t-distributions. The test may be interpreted as a Lagrange multiplier test and modified to allow for the estimation of models for time-varying volatility in the individual series. Unlike standard moment-based tests, the score-based test statistic includes information on the level of correlation under the null hypothesis and local power arguments indicate the benefits of doing so. A simulation study shows that the performance of the score-based test is strong relative to existing tests across a range of data generating processes. An application to the Hong Kong and South Korean equity markets shows that the new test reveals changes in correlation that are not detected by the standard moment-based test.