A Statistical Approach for Multilingual Document Clustering and Topic Extraction from Clusters

2000 Mathematics Subject Classification: 62H30

Generalized KPCA by adaptive rules in feature space

Principal component analysis (PCA) is well recognized in dimensionality reduction, and kernel PCA (KPCA) has also been proposed in statistical data analysis. However, KPCA fails to detect the nonlinear structure of data well when outliers exist. To reduce this problem, this paper presents a novel algorithm, named iterative robust KPCA (IRKPCA). IRKPCA works well in dealing with outliers, and can be carried out in an iterative manner, which makes it suitable to process incremental input data. As in the traditional robust PCA (RPCA), a binary field is employed for characterizing the outlier process, and the optimization problem is formulated as maximizing marginal distribution of a Gibbs distribution. In this paper, this optimization problem is solved by stochastic gradient descent techniques. In IRKPCA, the outlier process is in a high-dimensional feature space, and therefore kernel trick is used. IRKPCA can be regarded as a kernelized version of RPCA and a robust form of kernel Hebbian algorithm. Experimental results on synthetic data demonstrate the effectiveness of IRKPCA. © 2010 Taylor & Francis.

Weak Langmuir optical turbulence in a fiber cavity

We study theoretically and numerically the dynamics of a passive optical fiber ring cavity pumped by a highly incoherent wave: an incoherently injected fiber laser. The theoretical analysis reveals that the turbulent dynamics of the cavity is dominated by the Raman effect. The forced-dissipative nature of the fiber cavity is responsible for a large diversity of turbulent behaviors: Aside from nonequilibrium statistical stationary states, we report the formation of a periodic pattern of spectral incoherent solitons, or the formation of different types of spectral singularities, e.g., dispersive shock waves and incoherent spectral collapse behaviors. We derive a mean-field kinetic equation that describes in detail the different turbulent regimes of the cavity and whose structure is formally analogous to the weak Langmuir turbulence kinetic equation in the presence of forcing and damping. A quantitative agreement is obtained between the simulations of the nonlinear Schrödinger equation with cavity boundary conditions and those of the mean-field kinetic equation and the corresponding singular integrodifferential reduction, without using adjustable parameters. We discuss the possible realization of a fiber cavity experimental setup in which the theoretical predictions can be observed and studied.

The mathematics anxiety of bilingual community college students

Math anxiety levels and performance outcomes were compared for bilingual and monolingual community college Intermediate Algebra students attending a culturally diverse urban commuter college. Participants (N = 618, 250 men, 368 women; 361 monolingual, 257 bilingual) completed the Abbreviated Math Anxiety Scale (AMAS) and a demographics instrument. Bilingual and monolingual students reported comparable mean AMAS scores (20.6 and 20.7, respectively) and comparable proportions of math anxious individuals (50% and 48%, respectively). Factor analysis of AMAS scores, using principal component analysis by varimax rotation, yielded similar two-factor structures for both populations -- assessment and learning content -- accounting for 65.6% of the trace for bilingual AMAS scores. Statistically significant predictor variables for levels of math anxiety for the bilingual participants included (a) preparatory course enrollment (β = .236, p = .041) with those enrolled in prior preparatory courses scoring higher, (b) education major (β = .285, p = .018) with education majors scoring higher, and (c) business major (β = .252, p = .032) with business majors scoring higher. One statistically significant predictor variable emerged for monolingual students, gender (β = -.085, p = .001) with females ranking higher. Age, income, race, ethnicity, U.S. origin, science or health science majors did not emerge as statistically significant predictor variables for either group.^ Similarities between monolingual and bilingual participants included statistically significant negative linear correlations between AMAS scores and course grades for both bilingual (r = -.178, p = .017) and monolingual participants (r = -.203, p = .001). Differences included a statistically significant linear correlation between AMAS scores and final exam grades for monolingual participants only (r = -.253, p < .0009) despite no statistically significant difference in the strength the linear relationship of the AMAS scores and the final exam scores between groups, z = 1.35, p = .1756.^ The findings show that bilingual and monolingual students report math anxiety similarly and that math anxiety has similar associations with performance measures, despite differences between predictor variables. One of the first studies on the math anxiety of bilingual community college students, the results suggest recommendations for researchers and practitioners.^

Shifting N and P limitation along a north-south gradient of mangrove estuaries in South Florida

A multivariate statistical analysis was applied to a 10 year, multiparameter data set in an effort to describe the spatial dependence and inherent variation of water quality patterns in the mangrove estuaries of Ten Thousand Islands – Whitewater Bay area. Principal component analysis (PCA) of 16 water quality parameters collected monthly resulted in five groupings, which explained 72.5% of the variance of the original variables. The “Organic” component (PCI) was composed of alkaline phosphatase activity, total organic nitrogen, and total organic carbon; the “Dissolved Inorganic N” component (PCII) contained NO 3 − , NO 2 − , and NH 4 + ; the “Phytoplankton” component (PCIII) was made up of total phosphorus, chlorophyll a, and turbidity; dissolved oxygen and temperature were inversely related (PCIV); and salinity and soluble reactive phosphorus made up PCV. A cluster analysis of the mean and SD of PC scores resulted in the spatial aggregation of the 47 fixed stations into six classes having similar water quality, which we defined as: Mangrove Rivers, Whitewater Bay, Gulf Islands, Coot Bay, Blackwater River, and Inland Waterway. Marked differences in physical, chemical, and biological characteristics among classes were illustrated by this technique. Comparison of medians and variability of parameters among classes allowed large scale generalizations as to underlying differences in water quality in these regions. A strong south to north gradient in estuaries from high N - low P to low N - high P was ascribed to marked differences in landuse, freshwater input, geomorphology, and sedimentary geology along this tract. The ecological significance of this gradient discussed along with potential effects of future restoration plans.

Ecohydrology, evapotranspiration and hydrogeochemistry of carbonate mangrove wetlands

Coastal environments can be highly susceptible to environmental changes caused by anthropogenic pressures and natural events. Both anthropogenic and natural perturbations may directly affect the amount and the quality of water flowing through the ecosystem, both in the surface and subsurface and can subsequently, alter ecological communities and functions. The Florida Everglades and the Sian Ka'an Biosphere Reserve (Mexico) are two large ecosystems with an extensive coastal mangrove ecotone that represent a historically altered and pristine environment, respectively. Rising sea levels, climate change, increased water demand, and salt water intrusion are growing concerns in these regions and underlies the need for a better understanding of the present conditions. The goal of my research was to better understand various ecohydrological, environmental, and hydrogeochemical interactions and relationships in carbonate mangrove wetlands. A combination of aqueous geochemical analyses and visible and near-infrared reflectance data were employed to explore relationships between surface and subsurface water chemistry and spectral biophysical stress in mangroves. Optical satellite imagery and field collected meteorological data were used to estimate surface energy and evapotranspiration and measure variability associated with hurricanes and restoration efforts. Furthermore, major ionic and nutrient concentrations, and stable isotopes of hydrogen and oxygen were used to distinguish water sources and infer coastal groundwater discharge by applying the data to a combined principal component analysis-end member mixing model. Spectral reflectance measured at the field and satellite scales were successfully used to estimate surface and subsurface water chemistry and model chloride concentrations along the southern Everglades. Satellite imagery indicated that mangrove sites that have less tidal flushing and hydrogeomorphic heterogeneity tend to have more variable evapotranspiration and soil heat flux in response to storms and restoration. Lastly, water chemistry and multivariate analyses indicated two distinct fresh groundwater sources that discharge to the phosphorus-limited estuaries and bays of the Sian Ka'an Biopshere Reserve; and that coastal groundwater discharge was an important source for phosphorus. The results of the study give us a better understanding of the ecohydrological and hydrogeological processes in carbonate mangrove environments that can be then be extrapolated to similar coastal ecosystems in the Caribbean.

(Tables 1-3) Water chemistry of cloud forest streams at baseflow conditions, Rio San Francisco, Ecuador

We investigated controls on the water chemistry of a South Ecuadorian cloud forest catchment which is partly pristine, and partly converted to extensive pasture. From April 2007 to May 2008 water samples were taken weekly to biweekly at nine different subcatchments, and were screened for differences in electric conductivity, pH, anion, as well as element composition. A principal component analysis was conducted to reduce dimensionality of the data set and define major factors explaining variation in the data. Three main factors were isolated by a subset of 10 elements (Ca2+, Ce, Gd, K+, Mg2+, Na+, Nd, Rb, Sr, Y), explaining around 90% of the data variation. Land-use was the major factor controlling and changing water chemistry of the subcatchments. A second factor was associated with the concentration of rare earth elements in water, presumably highlighting other anthropogenic influences such as gravel excavation or road construction. Around 12% of the variation was explained by the third component, which was defined by the occurrence of Rb and K and represents the influence of vegetation dynamics on element accumulation and wash-out. Comparison of base- and fast flow concentrations led to the assumption that a significant portion of soil water from around 30 cm depth contributes to storm flow, as revealed by increased rare earth element concentrations in fast flow samples. Our findings demonstrate the utility of multi-tracer principal component analysis to study tropical headwater streams, and emphasize the need for effective land management in cloud forest catchments.

Seleção de características para identificação de diferentes proporções de tipos de fibras musculares por meio da eletromiografia de superfície

Skeletal muscle consists of muscle fiber types that have different physiological and biochemical characteristics. Basically, the muscle fiber can be classified into type I and type II, presenting, among other features, contraction speed and sensitivity to fatigue different for each type of muscle fiber. These fibers coexist in the skeletal muscles and their relative proportions are modulated according to the muscle functionality and the stimulus that is submitted. To identify the different proportions of fiber types in the muscle composition, many studies use biopsy as standard procedure. As the surface electromyography (EMGs) allows to extract information about the recruitment of different motor units, this study is based on the assumption that it is possible to use the EMG to identify different proportions of fiber types in a muscle. The goal of this study was to identify the characteristics of the EMG signals which are able to distinguish, more precisely, different proportions of fiber types. Also was investigated the combination of characteristics using appropriate mathematical models. To achieve the proposed objective, simulated signals were developed with different proportions of motor units recruited and with different signal-to-noise ratios. Thirteen characteristics in function of time and the frequency were extracted from emulated signals. The results for each extracted feature of the signals were submitted to the clustering algorithm k-means to separate the different proportions of motor units recruited on the emulated signals. Mathematical techniques (confusion matrix and analysis of capability) were implemented to select the characteristics able to identify different proportions of muscle fiber types. As a result, the average frequency and median frequency were selected as able to distinguish, with more precision, the proportions of different muscle fiber types. Posteriorly, the features considered most able were analyzed in an associated way through principal component analysis. Were found two principal components of the signals emulated without noise (CP1 and CP2) and two principal components of the noisy signals (CP1 and CP2 ). The first principal components (CP1 and CP1 ) were identified as being able to distinguish different proportions of muscle fiber types. The selected characteristics (median frequency, mean frequency, CP1 and CP1 ) were used to analyze real EMGs signals, comparing sedentary people with physically active people who practice strength training (weight training). The results obtained with the different groups of volunteers show that the physically active people obtained higher values of mean frequency, median frequency and principal components compared with the sedentary people. Moreover, these values decreased with increasing power level for both groups, however, the decline was more accented for the group of physically active people. Based on these results, it is assumed that the volunteers of the physically active group have higher proportions of type II fibers than sedentary people. Finally, based on these results, we can conclude that the selected characteristics were able to distinguish different proportions of muscle fiber types, both for the emulated signals as to the real signals. These characteristics can be used in several studies, for example, to evaluate the progress of people with myopathy and neuromyopathy due to the physiotherapy, and also to analyze the development of athletes to improve their muscle capacity according to their sport. In both cases, the extraction of these characteristics from the surface electromyography signals provides a feedback to the physiotherapist and the coach physical, who can analyze the increase in the proportion of a given type of fiber, as desired in each case.

Determinação do estado fundamental de compostos antiferromagnéticos da série Tb(1-x)Y(x)RhIn(5): aproximação teórico experimental

We present the results of electrical resistivity, magnetic susceptibility, specific heat and x-ray absorption spectroscopy measurements in Tb1−xYxRhIn5 (x = 0.00, 0.15, 0.4.0, 0.50 e 0.70) single crystals. Tb1−xYxRhIn5 is an antiferromagnetic AFM compound with ordering temperature TN ≈ 46 K, the higher TN within the RRhIn5 serie (R : rare earth). We evaluate the physical properties evolution and the supression of the AFM state considering doping and Crystalline Electric Field (CEF) effects on magnetic exchange interaction between Tb3+ magnetic ions. CEF acts like a perturbation potential, breaking the (2J + 1) multiplet s degeneracy. Also, we studied linear-polarization-dependent soft x-ray absorption at Tb M4 and M5 edges to validate X-ray Absorption Spectroscopy as a complementary technique in determining the rare earth CEF ground state. Samples were grown by the indium excess flux and the experimental data (magnetic susceptibility and specific heat) were adjusted with a mean field model that takes account magnetic exchange interaction between first neighbors and CEF effects. XAS experiments were carried on Total Electron Yield mode at Laborat´onio Nacional de Luz S´ıncrotron, Campinas. We measured X-ray absorption at Tb M4,5 edges with incident polarized X-ray beam parallel and perpendicular to c-axis (E || c e E ⊥ c). The mean field model simulates the mean behavior of the whole system and, due to many independent parameters, gives a non unique CEF scheme. XAS is site- and elemental- specific technique and gained the scientific community s attention as complementary technique in determining CEF ground state in rare earth based compounds. In this work we wil discuss the non conclusive results of XAS technique in TbRhIn5 compounds.

Facial affect processing inbipolar disorder:a magnetoencephalography study

Background: Identifying biological markers to aid diagnosis of bipolar disorder (BD) is critically important. To be considered a possible biological marker, neural patterns in BD should be discriminant from those in healthy individuals (HI). We examined patterns of neuromagnetic responses revealed by magnetoencephalography (MEG) during implicit emotion-processing using emotional (happy, fearful, sad) and neutral facial expressions, in sixteen BD and sixteen age- and gender-matched healthy individuals. Methods: Neuromagnetic data were recorded using a 306-channel whole-head MEG ELEKTA Neuromag System, and preprocessed using Signal Space Separation as implemented in MaxFilter (ELEKTA). Custom Matlab programs removed EOG and ECG signals from filtered MEG data, and computed means of epoched data (0-250ms, 250-500ms, 500-750ms). A generalized linear model with three factors (individual, emotion intensity and time) compared BD and HI. A principal component analysis of normalized mean channel data in selected brain regions identified principal components that explained 95% of data variation. These components were used in a quadratic support vector machine (SVM) pattern classifier. SVM classifier performance was assessed using the leave-one-out approach. Results: BD and HI showed significantly different patterns of activation for 0-250ms within both left occipital and temporal regions, specifically for neutral facial expressions. PCA analysis revealed significant differences between BD and HI for mild fearful, happy, and sad facial expressions within 250-500ms. SVM quadratic classifier showed greatest accuracy (84%) and sensitivity (92%) for neutral faces, in left occipital regions within 500-750ms. Conclusions: MEG responses may be used in the search for disease specific neural markers.

Analysis of White Latex Paints using Laser Induced Breakdown Spectroscopy for Forensic Applications

The analysis of white latex paint is a problem for forensic laboratories because of difficulty in differentiation between samples. Current methods provide limited information that is not suitable for discrimination. Elemental analysis of white latex paints has resulted in 99% discriminating power when using LA-ICP-MS; however, mass spectrometers can be prohibitively expensive and require a skilled operator. A quick, inexpensive, effective method is needed for the differentiation of white latex paints. In this study, LIBS is used to analyze 24 white latex paint samples. LIBS is fast, easy to operate, and has a low cost. Results show that 98.1% of variation can be accounted for via principle component analysis, while Tukey pairwise comparisons differentiated 95.6% with potassium as the elemental ratio, showing that the discrimination capabilities of LIBS are comparable to those of LA-ICP-MS. Due to the many advantages of LIBS, this instrument should be considered a necessity for forensic laboratories.

The Mathematics Anxiety of Bilingual Community College Students

Math anxiety levels and performance outcomes were compared for bilingual and monolingual community college Intermediate Algebra students attending a culturally diverse urban commuter college. Participants (N = 618, 250 men, 368 women; 361 monolingual, 257 bilingual) completed the Abbreviated Math Anxiety Scale (AMAS) and a demographics instrument. Bilingual and monolingual students reported comparable mean AMAS scores (20.6 and 20.7, respectively) and comparable proportions of math anxious individuals (50% and 48%, respectively). Factor analysis of AMAS scores, using principal component analysis by varimax rotation, yielded similar two-factor structures for both populations -- assessment and learning content -- accounting for 65.6% of the trace for bilingual AMAS scores. Statistically significant predictor variables for levels of math anxiety for the bilingual participants included (a) preparatory course enrollment (β = .236, p = .041) with those enrolled in prior preparatory courses scoring higher, (b) education major (β = .285, p = .018) with education majors scoring higher, and (c) business major (β = .252, p = .032) with business majors scoring higher. One statistically significant predictor variable emerged for monolingual students, gender (β = -.085, p = .001) with females ranking higher. Age, income, race, ethnicity, U.S. origin, science or health science majors did not emerge as statistically significant predictor variables for either group. Similarities between monolingual and bilingual participants included statistically significant negative linear correlations between AMAS scores and course grades for both bilingual (r = -.178, p = .017) and monolingual participants (r = -.203, p = .001). Differences included a statistically significant linear correlation between AMAS scores and final exam grades for monolingual participants only (r = -.253, p < .0009) despite no statistically significant difference in the strength the linear relationship of the AMAS scores and the final exam scores between groups, z = 1.35, p = .1756. The findings show that bilingual and monolingual students report math anxiety similarly and that math anxiety has similar associations with performance measures, despite differences between predictor variables. One of the first studies on the math anxiety of bilingual community college students, the results suggest recommendations for researchers and practitioners.

Radiocarbon dating, carbon storage and soil properties of samples from Tulemalu Lake, central Canadian Arctic

We investigated total storage and landscape partitioning of soil organic carbon (SOC) in continuous permafrost terrain, central Canadian Arctic. The study is based on soil chemical analyses of pedons sampled to 1 m depth at 35 individual sites along three transects. Radiocarbon dating of cryoturbated soil pockets, basal peat and fossil wood shows that cryoturbation processes have been occurring since the Middle Holocene and that peat deposits started to accumulate in a forest-tundra environment where spruce was present (~6000 cal yrs BP). Detailed partitioning of SOC into surface organic horizons, cryoturbated soil pockets and non-cryoturbated mineral soil horizons is calculated (with storage in active layer and permafrost calculated separately) and explored using principal component analysis. The detailed partitioning and mean storage of SOC in the landscape are estimated from transect vegetation inventories and a land cover classification based on a Landsat satellite image. Mean SOC storage in the 0-100 cm depth interval is 33.8 kg C/m**2, of which 11.8 kg C/m**2 is in permafrost. Fifty-six per cent of the total SOC mass is stored in peatlands (mainly bogs), but cryoturbated soil pockets in Turbic Cryosols also contribute significantly (17%). Elemental C/N ratios indicate that this cryoturbated soil organic matter (SOM) decomposes more slowly than SOM in surface O-horizons.

Multivariate Techniques in Biomechanical Analysis

This work outlines the theoretical advantages of multivariate methods in biomechanical data, validates the proposed methods and outlines new clinical findings relating to knee osteoarthritis that were made possible by this approach. New techniques were based on existing multivariate approaches, Partial Least Squares (PLS) and Non-negative Matrix Factorization (NMF) and validated using existing data sets. The new techniques developed, PCA-PLS-LDA (Principal Component Analysis – Partial Least Squares – Linear Discriminant Analysis), PCA-PLS-MLR (Principal Component Analysis – Partial Least Squares –Multiple Linear Regression) and Waveform Similarity (based on NMF) were developed to address the challenging characteristics of biomechanical data, variability and correlation. As a result, these new structure-seeking technique revealed new clinical findings. The first new clinical finding relates to the relationship between pain, radiographic severity and mechanics. Simultaneous analysis of pain and radiographic severity outcomes, a first in biomechanics, revealed that the knee adduction moment’s relationship to radiographic features is mediated by pain in subjects with moderate osteoarthritis. The second clinical finding was quantifying the importance of neuromuscular patterns in brace effectiveness for patients with knee osteoarthritis. I found that brace effectiveness was more related to the patient’s unbraced neuromuscular patterns than it was to mechanics, and that these neuromuscular patterns were more complicated than simply increased overall muscle activity, as previously thought.

Multivariate analysis of regional-scale geochemical data for environmental monitoring

A compositional multivariate approach is used to analyse regional scale soil geochemical data obtained as part of the Tellus Project generated by the Geological Survey Northern Ireland (GSNI). The multi-element total concentration data presented comprise XRF analyses of 6862 rural soil samples collected at 20cm depths on a non-aligned grid at one site per 2 km2. Censored data were imputed using published detection limits. Using these imputed values for 46 elements (including LOI), each soil sample site was assigned to the regional geology map provided by GSNI initially using the dominant lithology for the map polygon. Northern Ireland includes a diversity of geology representing a stratigraphic record from the Mesoproterozoic, up to and including the Palaeogene. However, the advance of ice sheets and their meltwaters over the last 100,000 years has left at least 80% of the bedrock covered by superficial deposits, including glacial till and post-glacial alluvium and peat. The question is to what extent the soil geochemistry reflects the underlying geology or superficial deposits. To address this, the geochemical data were transformed using centered log ratios (clr) to observe the requirements of compositional data analysis and avoid closure issues. Following this, compositional multivariate techniques including compositional Principal Component Analysis (PCA) and minimum/maximum autocorrelation factor (MAF) analysis method were used to determine the influence of underlying geology on the soil geochemistry signature. PCA showed that 72% of the variation was determined by the first four principal components (PC’s) implying “significant” structure in the data. Analysis of variance showed that only 10 PC’s were necessary to classify the soil geochemical data. To consider an improvement over PCA that uses the spatial relationships of the data, a classification based on MAF analysis was undertaken using the first 6 dominant factors. Understanding the relationship between soil geochemistry and superficial deposits is important for environmental monitoring of fragile ecosystems such as peat. To explore whether peat cover could be predicted from the classification, the lithology designation was adapted to include the presence of peat, based on GSNI superficial deposit polygons and linear discriminant analysis (LDA) undertaken. Prediction accuracy for LDA classification improved from 60.98% based on PCA using 10 principal components to 64.73% using MAF based on the 6 most dominant factors. The misclassification of peat may reflect degradation of peat covered areas since the creation of superficial deposit classification. Further work will examine the influence of underlying lithologies on elemental concentrations in peat composition and the effect of this in classification analysis.