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Concept: Singular value decomposition


Principal component (PC) maps, which plot the values of a given PC estimated on the basis of allele frequency variation at the geographic sampling locations of a set of populations, are often used to investigate the properties of past range expansions. Some studies have argued that in a range expansion, the axis of greatest variation (i.e., the first PC) is parallel to the axis of expansion. In contrast, others have identified a pattern in which the axis of greatest variation is perpendicular to the axis of expansion. Here, we seek to understand this difference in outcomes by investigating the effect of the geographic sampling scheme on the direction of the axis of greatest variation under a two-dimensional range expansion model. From datasets simulated using each of two different schemes for the geographic sampling of populations under the model, we create PC maps for the first PC. We find that depending on the geographic sampling scheme, the axis of greatest variation can be either parallel or perpendicular to the axis of expansion. We provide an explanation for this result in terms of intra- and inter-population coalescence times.

Concepts: Genetics, Principal component analysis, Population genetics, Singular value decomposition, Personal computer


This paper demonstrates how multi-scale measures of rugosity, slope and aspect can be derived from fine-scale bathymetric reconstructions created from geo-referenced stereo imagery. We generate three-dimensional reconstructions over large spatial scales using data collected by Autonomous Underwater Vehicles (AUVs), Remotely Operated Vehicles (ROVs), manned submersibles and diver-held imaging systems. We propose a new method for calculating rugosity in a Delaunay triangulated surface mesh by projecting areas onto the plane of best fit using Principal Component Analysis (PCA). Slope and aspect can be calculated with very little extra effort, and fitting a plane serves to decouple rugosity from slope. We compare the results of the virtual terrain complexity calculations with experimental results using conventional in-situ measurement methods. We show that performing calculations over a digital terrain reconstruction is more flexible, robust and easily repeatable. In addition, the method is non-contact and provides much less environmental impact compared to traditional survey techniques. For diver-based surveys, the time underwater needed to collect rugosity data is significantly reduced and, being a technique based on images, it is possible to use robotic platforms that can operate beyond diver depths. Measurements can be calculated exhaustively at multiple scales for surveys with tens of thousands of images covering thousands of square metres. The technique is demonstrated on data gathered by a diver-rig and an AUV, on small single-transect surveys and on a larger, dense survey that covers over [Formula: see text]. Stereo images provide 3D structure as well as visual appearance, which could potentially feed into automated classification techniques. Our multi-scale rugosity, slope and aspect measures have already been adopted in a number of marine science studies. This paper presents a detailed description of the method and thoroughly validates it against traditional in-situ measurements.

Concepts: Mathematics, Principal component analysis, Demonstration, Depth perception, Plane, Singular value decomposition, Calculation, Autonomous underwater vehicle


BACKGROUND: Static posture, repetitive movements and lack of physical variation are known risk factors for work-related musculoskeletal disorders, and thus needs to be properly assessed in occupational studies. The aims of this study were (i) to investigate the effectiveness of a conventional exposure variation analysis (EVA) in discriminating exposure time lines and (ii) to compare it with a new cluster-based method for analysis of exposure variation. METHODS: For this purpose, we simulated a repeated cyclic exposure varying within each cycle between “low” and “high” exposure levels in a “near” or “far” range, and with “low” or “high” velocities (exposure change rates). The duration of each cycle was also manipulated by selecting a “small” or “large” standard deviation of the cycle time. Theses parameters reflected three dimensions of exposure variation, i.e. range, frequency and temporal similarity.Each simulation trace included two realizations of 100 concatenated cycles with either low (rho = 0.1), medium (rho = 0.5) or high (rho = 0.9) correlation between the realizations. These traces were analyzed by conventional EVA, and a novel cluster-based EVA (C-EVA). Principal component analysis (PCA) was applied on the marginal distributions of 1) the EVA of each of the realizations (univariate approach), 2) a combination of the EVA of both realizations (multivariate approach) and 3) C-EVA. The least number of principal components describing more than 90% of variability in each case was selected and the projection of marginal distributions along the selected principal component was calculated. A linear classifier was then applied to these projections to discriminate between the simulated exposure patterns, and the accuracy of classified realizations was determined. RESULTS: C-EVA classified exposures more correctly than univariate and multivariate EVA approaches; classification accuracy was 49%, 47% and 52% for EVA (univariate and multivariate), and C-EVA, respectively (p < 0.001). All three methods performed poorly in discriminating exposure patterns differing with respect to the variability in cycle time duration. CONCLUSION: While C-EVA had a higher accuracy than conventional EVA, both failed to detect differences in temporal similarity. The data-driven optimality of data reduction and the capability of handling multiple exposure time lines in a single analysis are the advantages of the C-EVA.

Concepts: Multivariate statistics, Factor analysis, Principal component analysis, Exposure, Singular value decomposition, Photography, Linear discriminant analysis, The Unscrambler


In this paper, we present a method for detecting the R-peak of an ECG signal by using an singular value decomposition (SVD) filter and a search back system. The ECG signal was detected in two phases: the pre-processing phase and the decision phase. The pre-processing phase consisted of the stages for the SVD filter, Butterworth High Pass Filter (HPF), moving average (MA), and squaring, whereas the decision phase consisted of a single stage that detected the R-peak. In the pre-processing phase, the SVD filter removed noise while the Butterworth HPF eliminated baseline wander. The MA removed the remaining noise of the signal that had gone through the SVD filter to make the signal smooth, and squaring played a role in strengthening the signal. In the decision phase, the threshold was used to set the interval before detecting the R-peak. When the latest R-R interval (RRI), suggested by Hamilton et al., was greater than 150% of the previous RRI, the method of detecting the R-peak in such an interval was modified to be 150% or greater than the smallest interval of the two most latest RRIs. When the modified search back system was used, the error rate of the peak detection decreased to 0.29%, compared to 1.34% when the modified search back system was not used. Consequently, the sensitivity was 99.47%, the positive predictivity was 99.47%, and the detection error was 1.05%. Furthermore, the quality of the signal in data with a substantial amount of noise was improved, and thus, the R-peak was detected effectively.

Concepts: English-language films, Singular value decomposition, Filter, Band-pass filter, Low-pass filter, High-pass filter, Butterworth filter, Singular value


Spray dried microcapsules of mint oil were prepared using gum Arabic alone and its blends with radiation or enzymatically depolymerized guar gum as wall materials. Microcapsules were evaluated for retention of mint oil during 8-week storage during which qualitative changes in encapsulated mint oil was monitored using principal component analysis. The microcapsules with radiation depolymerized guar gum as wall material component could better retain major mint oil compounds such as menthol and isomenthol. The t(½) calculated for mint oil in microcapsules of gum Arabic, gum Arabic:radiation depolymerized guar gum (90:10), gum Arabic:enzyme depolymerized guar gum (90:10) was 25.66, 38.50, and 17.11 weeks, respectively. The results suggested a combination of radiation depolymerized guar gum and gum Arabic to show better retention of encapsulated flavour than gum Arabic alone as wall material.

Concepts: Data analysis, Principal component analysis, Singular value decomposition, Qualitative, Paint, Gums, Gum arabic, Mentha


Co-registration of transcranial magnetic stimulation (TMS) and electroencephalography (EEG) is a new, promising method for assessing cortical excitability and connectivity. Using this technique, a TMS evoked potential (TEP) can be induced and registered with the EEG. However, the TEP contains an early, short lasting artifact due to the magnetic pulse, and a second artifact, which depends on the location of stimulation and can last up to 40 milliseconds. Different causes for this second artifact have been suggested in literature. In this study, we used principal component analysis (PCA) to suppress both the first and second artifact in TMS-EEG data. Single pulse TMS was applied at the motor and visual cortex in 18 healthy subjects. PCA using singular value decomposition was applied on single trials to suppress the artifactual components. A large artifact suppression was realized after the removal of the first 5 PCA components, thereby revealing early TEP peaks, with only a small suppression of later TEP components. The spatial distribution of the second artifact suggests that it is caused by electrode movement due to activation of the temporal musculature. In conclusion, we showed that PCA can be used to reduce TMS-induced artifacts in EEG, thereby revealing components of the TMS evoked potential.

Concepts: Brain, Electroencephalography, Evoked potential, Principal component analysis, Transcranial magnetic stimulation, Amblyopia, Singular value decomposition, Neurotechnology


Objectives : Sex differences exist in the relationship between anxiety and pain, although findings are mixed. One reason could be because a number of anxiety measures have been used. Therefore, this study aimed to identify the core components within commonly used pain anxiety measures, and see whether these components are differentially related to sensation and pain thresholds in men and women. Design, main outcome measures : One hundred and eighty-nine healthy adults (119 female) completed the Fear of Pain Questionnaire, Pain Catastrophising Scale, Pain Anxiety Symptoms Scale, Anxiety Sensitivity Index-3 and the Depression Anxiety Stress Scale. Thermal sensation and pain thresholds, mechanical sensation and pressure pain thresholds were also collected. Results : A Principal Components Analysis of anxiety measures revealed three constructs: general distress, cognitive intrusion and fear of pain from injury/insult. Sex did not moderate the relationship between these anxiety constructs and sensation/pain thresholds. However, a significant main effect of sex was found to predict thermal pain thresholds. Conclusion : Preliminary indications suggest that pain anxiety dimensions can be reduced to three core constructs, and used to examine pain sensation. However, sex did not moderate this relationship. Further research is required to establish the extent and strength of sex differences in the relationship between anxiety and pain.

Concepts: Anxiety, Male, Gender, Sex, Pain, Singular value decomposition, The Core, Great Depression


While the HTT CAG-repeat expansion mutation causing Huntington’s disease (HD) is highly correlated with the rate of pathogenesis leading to disease onset, considerable variance in age-at-onset remains unexplained. Therefore, other factors must influence the pathogenic process. We asked whether these factors were related to natural biological variation in the sensory-motor system. In 243 participants (96 premanifest and 35 manifest HD; 112 controls), sensory-motor structural MRI, tractography, resting-state fMRI, electrophysiology (including SEP amplitudes), motor score ratings, and grip force as sensory-motor performance were measured. Following individual modality analyses, we used principal component analysis (PCA) to identify patterns associated with sensory-motor performance, and manifest versus premanifest HD discrimination. We did not detect longitudinal differences over 12 months. PCA showed a pattern of loss of caudate, grey and white matter volume, cortical thickness in premotor and sensory cortex, and disturbed diffusivity in sensory-motor white matter tracts that was connected to CAG repeat length. Two further major principal components appeared in controls and HD individuals indicating that they represent natural biological variation unconnected to the HD mutation. One of these components did not influence HD while the other non-CAG-driven component of axial versus radial diffusivity contrast in white matter tracts were associated with sensory-motor performance and manifest HD. The first component reflects the expected CAG expansion effects on HD pathogenesis. One non-CAG-driven component reveals an independent influence on pathogenesis of biological variation in white matter tracts and merits further investigation to delineate the underlying mechanism and the potential it offers for disease modification. Hum Brain Mapp, 2016. © 2016 Wiley Periodicals, Inc.

Concepts: Genetic disorder, Natural selection, Cerebral cortex, Factor analysis, Principal component analysis, Singular value decomposition, Nonlinear dimensionality reduction


The number of large-scale high-dimensional datasets recording different aspects of a single disease is growing, accompanied by a need for frameworks that can create one coherent model from multiple tensors of matched columns, e.g., patients and platforms, but independent rows, e.g., probes. We define and prove the mathematical properties of a novel tensor generalized singular value decomposition (GSVD), which can simultaneously find the similarities and dissimilarities, i.e., patterns of varying relative significance, between any two such tensors. We demonstrate the tensor GSVD in comparative modeling of patient- and platform-matched but probe-independent ovarian serous cystadenocarcinoma (OV) tumor, mostly high-grade, and normal DNA copy-number profiles, across each chromosome arm, and combination of two arms, separately. The modeling uncovers previously unrecognized patterns of tumor-exclusive platform-consistent co-occurring copy-number alterations (CNAs). We find, first, and validate that each of the patterns across only 7p and Xq, and the combination of 6p+12p, is correlated with a patient’s prognosis, is independent of the tumor’s stage, the best predictor of OV survival to date, and together with stage makes a better predictor than stage alone. Second, these patterns include most known OV-associated CNAs that map to these chromosome arms, as well as several previously unreported, yet frequent focal CNAs. Third, differential mRNA, microRNA, and protein expression consistently map to the DNA CNAs. A coherent picture emerges for each pattern, suggesting roles for the CNAs in OV pathogenesis and personalized therapy. In 6p+12p, deletion of the p21-encoding CDKN1A and p38-encoding MAPK14 and amplification of RAD51AP1 and KRAS encode for human cell transformation, and are correlated with a cell’s immortality, and a patient’s shorter survival time. In 7p, RPA3 deletion and POLD2 amplification are correlated with DNA stability, and a longer survival. In Xq, PABPC5 deletion and BCAP31 amplification are correlated with a cellular immune response, and a longer survival.

Concepts: Immune system, DNA, Gene, Cell, Chromosome, Ovarian cancer, Singular value decomposition, Matrix


Assessing global tendencies and impacts of conditional payments for environmental services (PES) programs is challenging because of their heterogeneity, and scarcity of comparative studies. This meta-study systematizes 55 PES schemes worldwide in a quantitative database. Using categorical principal component analysis to highlight clustering patterns, we reconfirm frequently hypothesized differences between public and private PES schemes, but also identify diverging patterns between commercial and non-commercial private PES vis-à-vis their service focus, area size, and market orientation. When do these PES schemes likely achieve significant environmental additionality? Using binary logistical regression, we find additionality to be positively influenced by three theoretically recommended PES ‘best design’ features: spatial targeting, payment differentiation, and strong conditionality, alongside some contextual controls (activity paid for and implementation time elapsed). Our results thus stress the preeminence of customized design over operational characteristics when assessing what determines the outcomes of PES implementation.

Concepts: Force, Principal component analysis, Design, Singular value decomposition, Payment, Payments, Economics terminology, Commerce