Low rank representation on Riemannian manifold of symmetric positive definite matrices

Sparse coding aims to find a more compact representation based on a set of dictionary atoms. A well-known technique looking at 2D sparsity is the low rank representation (LRR). However, in many computer vision applications, data often originate from a manifold, which is equipped with some Riemannian geometry. In this case, the existing LRR becomes inappropriate for modeling and incorporating the intrinsic geometry of the manifold that is potentially important and critical to applications. In this paper, we generalize the LRR over the Euclidean space to the LRR model over a specific Rimannian manifold—the manifold of symmetric positive matrices (SPD). Experiments on several computer vision datasets showcase its noise robustness and superior performance on classification and segmentation compared with state-of-the-art approaches.

Methane cross-validation between three Fourier Transform Spectrometers: SCISAT ACE-FTS, GOSAT TANSO-FTS, and ground-based FTS measurements in the Canadian high Arctic

We present cross-validation of remote sensing measurements of methane profiles in the Canadian high Arctic. Accurate and precise measurements of methane are essential to understand quantitatively its role in the climate system and in global change. Here, we show a cross-validation between three datasets: two from spaceborne instruments and one from a ground-based instrument. All are Fourier Transform Spectrometers (FTSs). We consider the Canadian SCISAT Atmospheric Chemistry Experiment (ACE)-FTS, a solar occultation infrared spectrometer operating since 2004, and the thermal infrared band of the Japanese Greenhouse Gases Observing Satellite (GOSAT) Thermal And Near infrared Sensor for carbon Observation (TANSO)-FTS, a nadir/off-nadir scanning FTS instrument operating at solar and terrestrial infrared wavelengths, since 2009. The ground-based instrument is a Bruker 125HR Fourier Transform Infrared (FTIR) spectrometer, measuring mid-infrared solar absorption spectra at the Polar Environment Atmospheric Research Laboratory (PEARL) Ridge Lab at Eureka, Nunavut (80° N, 86° W) since 2006. For each pair of instruments, measurements are collocated within 500 km and 24 h. An additional criterion based on potential vorticity values was found not to significantly affect differences between measurements. Profiles are regridded to a common vertical grid for each comparison set. To account for differing vertical resolutions, ACE-FTS measurements are smoothed to the resolution of either PEARL-FTS or TANSO-FTS, and PEARL-FTS measurements are smoothed to the TANSO-FTS resolution. Differences for each pair are examined in terms of profile and partial columns. During the period considered, the number of collocations for each pair is large enough to obtain a good sample size (from several hundred to tens of thousands depending on pair and configuration). Considering full profiles, the degrees of freedom for signal (DOFS) are between 0.2 and 0.7 for TANSO-FTS and between 1.5 and 3 for PEARL-FTS, while ACE-FTS has considerably more information (roughly 1° of freedom per altitude level). We take partial columns between roughly 5 and 30 km for the ACE-FTS–PEARL-FTS comparison, and between 5 and 10 km for the other pairs. The DOFS for the partial columns are between 1.2 and 2 for PEARL-FTS collocated with ACE-FTS, between 0.1 and 0.5 for PEARL-FTS collocated with TANSO-FTS or for TANSO-FTS collocated with either other instrument, while ACE-FTS has much higher information content. For all pairs, the partial column differences are within ± 3 × 1022 molecules cm−2. Expressed as median ± median absolute deviation (expressed in absolute or relative terms), these differences are 0.11 ± 9.60 × 10^20 molecules cm−2 (0.012 ± 1.018 %) for TANSO-FTS–PEARL-FTS, −2.6 ± 2.6 × 10^21 molecules cm−2 (−1.6 ± 1.6 %) for ACE-FTS–PEARL-FTS, and 7.4 ± 6.0 × 10^20 molecules cm−2 (0.78 ± 0.64 %) for TANSO-FTS–ACE-FTS. The differences for ACE-FTS–PEARL-FTS and TANSO-FTS–PEARL-FTS partial columns decrease significantly as a function of PEARL partial columns, whereas the range of partial column values for TANSO-FTS–ACE-FTS collocations is too small to draw any conclusion on its dependence on ACE-FTS partial columns.

Global analytic regularity for structures of co-rank one

We consider real analytic involutive structures V, of co-rank one, defined on a real analytic paracompact orientable manifold M. To each such structure we associate certain connected subsets of M which we call the level sets of V. We prove that analytic regularity propagates along them. With a further assumption on the level sets of V we characterize the global analytic hypoellipticity of a differential operator naturally associated to V. As an application we study a case of tube structures.

Computerized identification of motor complications in Parkinson's disease

Objective: To investigate whether spirography-based objective measures are able to effectively characterize the severity of unwanted symptom states (Off and dyskinesia) and discriminate them from motor state of healthy elderly subjects. Background: Sixty-five patients with advanced Parkinson’s disease (PD) and 10 healthy elderly (HE) subjects performed repeated assessments of spirography, using a touch screen telemetry device in their home environments. On inclusion, the patients were either treated with levodopa-carbidopa intestinal gel or were candidates for switching to this treatment. On each test occasion, the subjects were asked trace a pre-drawn Archimedes spiral shown on the screen, using an ergonomic pen stylus. The test was repeated three times and was performed using dominant hand. A clinician used a web interface which animated the spiral drawings, allowing him to observe different kinematic features, like accelerations and spatial changes, during the drawing process and to rate different motor impairments. Initially, the motor impairments of drawing speed, irregularity and hesitation were rated on a 0 (normal) to 4 (extremely severe) scales followed by marking the momentary motor state of the patient into 2 categories that is Off and Dyskinesia. A sample of spirals drawn by HE subjects was randomly selected and used in subsequent analysis. Methods: The raw spiral data, consisting of stylus position and timestamp, were processed using time series analysis techniques like discrete wavelet transform, approximate entropy and dynamic time warping in order to extract 13 quantitative measures for representing meaningful motor impairment information. A principal component analysis (PCA) was used to reduce the dimensions of the quantitative measures into 4 principal components (PC). In order to classify the motor states into 3 categories that is Off, HE and dyskinesia, a logistic regression model was used as a classifier to map the 4 PCs to the corresponding clinically assigned motor state categories. A stratified 10-fold cross-validation (also known as rotation estimation) was applied to assess the generalization ability of the logistic regression classifier to future independent data sets. To investigate mean differences of the 4 PCs across the three categories, a one-way ANOVA test followed by Tukey multiple comparisons was used. Results: The agreements between computed and clinician ratings were very good with a weighted area under the receiver operating characteristic curve (AUC) coefficient of 0.91. The mean PC scores were different across the three motor state categories, only at different levels. The first 2 PCs were good at discriminating between the motor states whereas the PC3 was good at discriminating between HE subjects and PD patients. The mean scores of PC4 showed a trend across the three states but without significant differences. The Spearman’s rank correlations between the first 2 PCs and clinically assessed motor impairments were as follows: drawing speed (PC1, 0.34; PC2, 0.83), irregularity (PC1, 0.17; PC2, 0.17), and hesitation (PC1, 0.27; PC2, 0.77). Conclusions: These findings suggest that spirography-based objective measures are valid measures of spatial- and time-dependent deficits and can be used to distinguish drug-related motor dysfunctions between Off and dyskinesia in PD. These measures can be potentially useful during clinical evaluation of individualized drug-related complications such as over- and under-medications thus maximizing the amount of time the patients spend in the On state.

Digital spiral analysis for objective assessment of fine motor timing variability in Parkinson's disease

OBJECTIVES: To develop a method for objective assessment of fine motor timing variability in Parkinson’s disease (PD) patients, using digital spiral data gathered by a touch screen device. BACKGROUND: A retrospective analysis was conducted on data from 105 subjects including65 patients with advanced PD (group A), 15 intermediate patients experiencing motor fluctuations (group I), 15 early stage patients (group S), and 10 healthy elderly subjects (HE) were examined. The subjects were asked to perform repeated upper limb motor tasks by tracing a pre-drawn Archimedes spiral as shown on the screen of the device. The spiral tracing test was performed using an ergonomic pen stylus, using dominant hand. The test was repeated three times per test occasion and the subjects were instructed to complete it within 10 seconds. Digital spiral data including stylus position (x-ycoordinates) and timestamps (milliseconds) were collected and used in subsequent analysis. The total number of observations with the test battery were as follows: Swedish group (n=10079), Italian I group (n=822), Italian S group (n = 811), and HE (n=299). METHODS: The raw spiral data were processed with three data processing methods. To quantify motor timing variability during spiral drawing tasks Approximate Entropy (APEN) method was applied on digitized spiral data. APEN is designed to capture the amount of irregularity or complexity in time series. APEN requires determination of two parameters, namely, the window size and similarity measure. In our work and after experimentation, window size was set to 4 and similarity measure to 0.2 (20% of the standard deviation of the time series). The final score obtained by APEN was normalized by total drawing completion time and used in subsequent analysis. The score generated by this method is hence on denoted APEN. In addition, two more methods were applied on digital spiral data and their scores were used in subsequent analysis. The first method was based on Digital Wavelet Transform and Principal Component Analysis and generated a score representing spiral drawing impairment. The score generated by this method is hence on denoted WAV. The second method was based on standard deviation of frequency filtered drawing velocity. The score generated by this method is hence on denoted SDDV. Linear mixed-effects (LME) models were used to evaluate mean differences of the spiral scores of the three methods across the four subject groups. Test-retest reliability of the three scores was assessed after taking mean of the three possible correlations (Spearman’s rank coefficients) between the three test trials. Internal consistency of the methods was assessed by calculating correlations between their scores. RESULTS: When comparing mean spiral scores between the four subject groups, the APEN scores were different between HE subjects and three patient groups (P=0.626 for S group with 9.9% mean value difference, P=0.089 for I group with 30.2%, and P=0.0019 for A group with 44.1%). However, there were no significant differences in mean scores of the other two methods, except for the WAV between the HE and A groups (P<0.001). WAV and SDDV were highly and significantly correlated to each other with a coefficient of 0.69. However, APEN was not correlated to neither WAV nor SDDV with coefficients of 0.11 and 0.12, respectively. Test-retest reliability coefficients of the three scores were as follows: APEN (0.9), WAV(0.83) and SD-DV (0.55). CONCLUSIONS: The results show that the digital spiral analysis-based objective APEN measure is able to significantly differentiate the healthy subjects from patients at advanced level. In contrast to the other two methods (WAV and SDDV) that are designed to quantify dyskinesias (over-medications), this method can be useful for characterizing Off symptoms in PD. The APEN was not correlated to none of the other two methods indicating that it measures a different construct of upper limb motor function in PD patients than WAV and SDDV. The APEN also had a better test-retest reliability indicating that it is more stable and consistent over time than WAV and SDDV.

IFTrace: Video segmentation of deformable objects using the Image Foresting Transform

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Expressão imuno-hitoquímica das proteínas RANK, RANKL e OPG em cistos radiculares e cistos dentígeros

Receptor ativador nuclear κappa B (RANK), ligante do receptor ativador nuclear κappa B (RANKL) e osteoprotegerina (OPG) são membros da família do fator de necrose tumoral relacionados com o metabolismo ósseo. A formação, diferenciação e atividade dos osteoclastos são reguladas por estas três proteínas. RANK é um receptor transmembrana presente em diversos tipos celulares, principalmente em células de linhagem macrofágica, linfócitos, células dendríticas e fibroblastos e quando ativado pelo seu ligante, RANKL, promove a diferenciação e ativação de células osteoclásticas responsáveis pelo processo de reabsorção óssea. A OPG impede a ligação RANK/RANKL atuando como um receptor inibitório para a atividade osteolítica. O objetivo deste estudo foi comparar a expressão imuno-histoquímica destes biomarcadores em cistos radiculares (n=20) e cistos dentígeros (n=20). A expressão imuno-histoquímica destes marcadores foi avaliada no epitélio e na cápsula dos cistos por escores e percentuais médios de imunomarcação. Para o epitélio, a análise semi-quantitativa revelou um padrão similar dos escores de imunomarcação de RANK, RANKL e OPG nas lesões, não havendo diferença estatística significante (p=0.589, p=0.688, p=0.709, respectivamente). Para a cápsula cística a análise quantitativa, mostrou diferença estatística significante entre os percentuais médios de imunomarcação do RANK e RANKL (p=0,001 e p=0,005, respectivamente) nos cistos. A correlação dos escores de imunomarcação de RANKL e OPG no epitélio do CR e do CD revelou diferença estatística significante (p=0,029, p=0,003, respectivamente). No epitélio dos CRs e dos CDs observou-se uma maior imunoexpressão da OPG comparada a do RANKL. Os resultados apontam a presença de RANK, RANKL e OPG nos cistos radiculares e cistos dentígeros, sugerindo a atuação destas proteínas no desenvolvimento e expansão das lesões no osso adjacente

Systematic analysis of the Fourier transform spectrum of (CH3OH)-C-13 between 400 and 950 cm(-1)

We have investigated a high-resolution Fourier transform (FT) absorption spectrum of the (CH3OH)-C-13 isotopomer of methanol from 400 to 950 cm(-1) with the Ritz program. We present the assignments of 7160 transitions, 3021 of which belong to Asymmetry, and 4139 to E-symmetry. These transitions occur between states labeled by K quantum numbers up to 14, and by torsional quantum numbers n up to 4. The Ritz program evaluated the energies of the 4684 involved levels with an accuracy of the order of 10(-4) cm(-1). All of the assigned lines correspond to transitions involving torsionally excited levels within the ground small-amplitude vibrational state. (c) 2005 Elsevier B.V. All rights reserved.

Eye color as an indicator of social rank in the fish Nile tilapia

We investigated the association of eye color with the dominant-subordinate relationship in the fish Nile tilapia, Oreochromis niloticus. Eye color pattern was also examined in relation to the intensity of attacks. We paired 20 size-matched fish (intruder: 73.69 ± 11.49 g; resident: 75.42 ± 8.83 g) and evaluated eye color and fights. These fish were isolated in individual aquaria for 10 days and then their eye color was measured 5 min before pairing (basal values). Twenty minutes after pairing, eye color and fights were quantified for 10 min. Clear establishment of social hierarchy was observed in 7 of 10 pairs of fish. Number of attacks ranged from 1 to 168 among pairs. The quartile was calculated for these data and the pairs were then divided into two classes: low-attack (1 to 111 attacks - 2 lower quartiles) or high-attack (112 to 168 attacks - 2 higher quartiles). Dominance decreased the eye-darkening patterns of the fish after pairing, while subordinance increased darkening compared to dominance. Subordinate fish in low-attack confrontations presented a darker eye compared to dominant fish and to the basal condition. We also observed a paler eye pattern in dominants that shared low-attack interactions after pairing compared to the subordinates and within the group. However, we found no differences in the darkening pattern between dominants and subordinates from the high-attack groups. We conclude that eye color is associated with social rank in this species. Moreover, the association between eye color and social rank in the low-attack pairs may function to reduce aggression.

NDIM achievements: massive, arbitrary tensor rank and N-loop insertions in Feynman integrals

One of the main difficulties in studying quantum field theory, in the perturbative regime, is the calculation of D-dimensional Feynman integrals. In general, one introduces the so-called Feynman parameters and, associated with them, the cumbersome parametric integrals. Solving these integrals beyond the one-loop level can be a difficult task. The negative-dimensional integration method (NDIM) is a technique whereby such a problem is dramatically reduced. We present the calculation of two-loop integrals in three different cases: scalar ones with three different masses, massless with arbitrary tensor rank, with and N insertions of a two-loop diagram.