Statnote 24: Multiple regression

In previous statnotes, the application of correlation and regression methods to the analysis of two variables (X,Y) was described. These methods can be used to determine whether there is a linear relationship between the two variables, whether the relationship is positive or negative, to test the degree of significance of the linear relationship, and to obtain an equation relating Y to X. This Statnote extends the methods of linear correlation and regression to situations where there are two or more X variables, i.e., 'multiple linear regression’.

UV-inscription, polarization-dependant loss characteristics and applications of 45° tilted fiber gratings

We have UV-inscribed and theoretically and experimentally analyzed fiber gratings with the structure tilted at 45° and implemented this type of devices as an in-fiber polarizer. A systematic investigation has been carried out on the characterization of 45° tilted fiber gratings (45° TFGs) in terms of the polarization-dependant loss (PDL) and thermal response. The detailed theoretical modeling has revealed a linear correlation between the grating length and the PDL, which has been proved by the experimental results. For the first time, we have examined the UV beam diffraction from a tilted phase mask and designed the UV-inscription system to suit the 45° TFG fabrication. Experimentally, a 24 mm long 45° TFG UV-inscribed in standard telecom single-mode fiber exhibited around 25 dB PDL at 1530 nm and an over ~300 nm bandwidth of PDL spectrum. By the concatenation method, a 44 mm long grating showed a PDL as high as 40 dB that is close to the high polarization extinction ratio of commercial products. Moreover, we have revealed that the PDL of 45° TFGs has low thermal influence, which is desirable for real application devices. Finally, we experimentally demonstrated an all-fiber twist sensor system based on a 45° and an 81° TFG.

UV-inscription, polarization-dependant loss characteristics and applications of 45° tilted fiber gratings

We have UV-inscribed and theoretically and experimentally analyzed fiber gratings with the structure tilted at 45° and implemented this type of devices as an in-fiber polarizer. A systematic investigation has been carried out on the characterization of 45° tilted fiber gratings (45° TFGs) in terms of the polarization-dependant loss (PDL) and thermal response. The detailed theoretical modeling has revealed a linear correlation between the grating length and the PDL, which has been proved by the experimental results. For the first time, we have examined the UV beam diffraction from a tilted phase mask and designed the UV-inscription system to suit the 45° TFG fabrication. Experimentally, a 24 mm long 45° TFG UV-inscribed in standard telecom single-mode fiber exhibited around 25 dB PDL at 1530 nm and an over ~300 nm bandwidth of PDL spectrum. By the concatenation method, a 44 mm long grating showed a PDL as high as 40 dB that is close to the high polarization extinction ratio of commercial products. Moreover, we have revealed that the PDL of 45° TFGs has low thermal influence, which is desirable for real application devices. Finally, we experimentally demonstrated an all-fiber twist sensor system based on a 45° and an 81° TFG.

Non-invasive respiratory monitoring using long-period fiber grating sensors

In non-invasive ventilation, continuous monitoring of respiratory volumes is essential. Here, we present a method for the measurement of respiratory volumes by a single fiber-grating sensor of bending and provide the proof-of-principle by applying a calibration-test measurement procedure on a set of 18 healthy volunteers. Results establish a linear correlation between a change in lung volume and the corresponding change in a local thorax curvature. They also show good sensor accuracy in measurements of tidal and minute respiratory volumes for different types of breathing. The proposed technique does not rely on the air flow through an oronasal mask or the observation of chest movement by a clinician, which distinguishes it from the current clinical practice. © 2014 Optical Society of America.

A new method for respiratory-volume monitoring based on long-period fibre gratings

Respiratory-volume monitoring is an indispensable part of mechanical ventilation. Here we present a new method of the respiratory-volume measurement based on a single fibre-optical long-period sensor of bending and the correlation between torso curvature and lung volume. Unlike the commonly used air-flow based measurement methods the proposed sensor is drift-free and immune to air-leaks. In the paper, we explain the working principle of sensors, a two-step calibration-test measurement procedure and present results that establish a linear correlation between the change in the local thorax curvature and the change of the lung volume. We also discuss the advantages and limitations of these sensors with respect to the current standards. © 2013 IEEE.

In situ aberration corrected-transmission electron microscopy of magnesium oxide nanocatalysts for biodiesels

Biofuels are promising renewable energy sources and can be derived from vegetable oil feedstocks. Although solid catalysts show great promise in plant oil triglyceride transesterification to biodiesel, the identification of active sites and operating surface nanostructures created during their processing is essential for the development of efficient heterogeneous catalysts. Systematic, direct observations of dynamic MgO nanocatalysts from a magnesium hydroxide-methoxide precursor were performed under controlled calcination conditions using novel in situ aberration corrected-transmission electron microscopy at the 0.1 nm level and quantified with catalytic reactivity and physico-chemical studies. Surface structural modifications and the evolution of extended atomic scale glide defects implicate coplanar anion vacancies in active sites in the transesterification of triglycerides to biodiesel. The linear correlation between surface defect density (and therefore polarisability) and activity affords a simple means to fine tune new, energy efficient nanocatalysts for biofuel synthesis. © 2009 Springer Science+Business Media, LLC.

Using overlay test to evaluate fracture properties of field-aged asphalt concrete

Field material testing provides firsthand information on pavement conditions which are most helpful in evaluating performance and identifying preventive maintenance or overlay strategies. High variability of field asphalt concrete due to construction raises the demand for accuracy of the test. Accordingly, the objective of this study is to propose a reliable and repeatable methodology to evaluate the fracture properties of field-aged asphalt concrete using the overlay test (OT). The OT is selected because of its efficiency and feasibility for asphalt field cores with diverse dimensions. The fracture properties refer to the Paris’ law parameters based on the pseudo J-integral (A and n) because of the sound physical significance of the pseudo J-integral with respect to characterizing the cracking process. In order to determine A and n, a two-step OT protocol is designed to characterize the undamaged and damaged behaviors of asphalt field cores. To ensure the accuracy of determined undamaged and fracture properties, a new analysis method is then developed for data processing, which combines the finite element simulations and mechanical analysis of viscoelastic force equilibrium and evolution of pseudo displacement work in the OT specimen. Finally, theoretical equations are derived to calculate A and n directly from the OT test data. The accuracy of the determined fracture properties is verified. The proposed methodology is applied to a total of 27 asphalt field cores obtained from a field project in Texas, including the control Hot Mix Asphalt (HMA) and two types of warm mix asphalt (WMA). The results demonstrate a high linear correlation between n and −log A for all the tested field cores. Investigations of the effect of field aging on the fracture properties confirm that n is a good indicator to quantify the cracking resistance of asphalt concrete. It is also indicated that summer climatic condition clearly accelerates the rate of aging. The impact of the WMA technologies on fracture properties of asphalt concrete is visualized by comparing the n-values. It shows that the Evotherm WMA technology slightly improves the cracking resistance, while the foaming WMA technology provides the comparable fracture properties with the HMA. After 15 months aging in the field, the cracking resistance does not exhibit significant difference between HMA and WMAs, which is confirmed by the observations of field distresses.

Coke formation in the oxidative dehydrogenation of ethylbenzene to styrene by TEOM

A packed bed microbalance reactor setup (TEOM-GC) is used to investigate the formation of coke as a function of time-on-stream on γ-Al2O3 and 3P/SiO2 catalyst samples under different conditions for the ODH reaction of ethylbenzene to styrene. All samples show a linear correlation of the styrene selectivity and yield with the initial coverage of coke. The COX production increases with the coverage of coke. On the 3 wt% P/SiO2 sample, the initial coke build-up is slow and the coke deposition rate increases with time. On alumina-based catalyst samples, a fast initial coke build-up takes place, decreasing with time-on-stream, but the amount of coke does not stabilize. A higher O2 : EB feed ratio results in more coke, and a higher temperature results in less coke. This coking behaviour of Al2O3 can be described by existing "monolayer-multilayer" models. Further, the coverage of coke on the catalyst varies with the position in the bed. For maximal styrene selectivity, the optimal coverage of coke should be sufficient to convert all O2, but as low as possible to prevent selectivity loss by COX production. This is in favour of high temperature and low O2 : EB feed ratios. The optimal coke coverage depends in a complex way on all the parameters: temperature, the O2 : EB feed ratio, reactant concentrations, and the type of starting material. This journal is

Susceptibility of raspberry cultivars to the raspberry cane midge (Resseliella theobaldi BARNES)

During the 2004 growing season, five raspberry cultivars were evaluated in terms of their susceptibility to the raspberry cane midge (Resseliella theobaldi Barnes). The trial was carried out at Berkenye, Nógrád County, Hungary. The cultivars evaluated were ‘Rubaca’ from Germany, ‘Fertődi Zamatos’ from Hungary, ‘Tulameen’ from Canada, and ‘Autumn Bliss’ and ‘Golden Bliss’ from the United Kingdom. Every other week, twenty-five split primocanes of each cultivar were randomly collected for laboratory examination. Data recorded for each cultivar included the mean number of larvae, the mean split length, and the mean extent of bark peeling per primocane. Pearson’s linear correlation coefficients were calculated for the correlations between the annual mean number of larvae per primocane on the one hand, and the annual cumulative mean split length per primocane and annual mean extent of bark peeling per primocane on the other hand. There was a weak correlation between annual mean number of larvae and annual cumulative mean split length, and a stronger correlation between annual mean number of larvae and annual mean extent of bark peeling. Annual mean number of larvae per primocane and annual mean extent of bark peeling per primocane were both highest in ‘Rubaca’, which means that the number of larvae per cane largely depends on the extent of stem peeling, although longitudinal splitting may also play a role. Therefore, cultivars with hardly any bark peeling and few and small longitudinal splits can be presumed to be less susceptible to infestation by the raspberry cane midge. Using these criteria, the least susceptible of the five cultivars evaluated would be ‘Tulameen’ and ‘Fertődi Zamatos’. Further research is needed to confirm this conclusion and to gather data on other factors which affect cultivar choice for new plantations, including winter hardiness, and susceptibility to cane diseases.

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.^

Dissolved Black Carbon in Grassland Streams: Is There an Effect of Recent Fire History?

While the existence of black carbon as part of dissolved organic matter (DOM) has been confirmed, quantitative determinations of dissolved black carbon (DBC) in freshwater ecosystem and information on factors controlling its concentration are scarce. In this study, stream surface water samples from a series of watersheds subject to different burn frequencies in Konza Prairie (Kansas, USA) were collected in order to determine if recent fire history has a noticeable effect on DBC concentration. The DBC levels detected ranged from 0.04 to 0.11 mg L−1, accounting for ca. 3.32 ± 0.51% of dissolved organic carbon (DOC). No correlation was found between DBC concentration and neither fire frequency nor time since last burn. We suggest that limited DBC flux is related to high burning efficiency, possibly greater export during periods of high discharge and/or the continuous export of DBC over long time scales. A linear correlation between DOC and DBC concentrations was observed, suggesting the export mechanisms determining DOC and DBC concentrations are likely coupled. The potential influence of fire history was less than the influence of other factors controlling the DOC and DBC dynamics in this ecosystem. Assuming similar conditions and processes apply in grasslands elsewhere, extrapolation to a global scale would suggest a global grasslands flux of DBC on the order of 0.14 Mt carbon year−1.

Physical oceanography, nutrients, and d18O measured on water bottle samples during POLARSTERN cruise ARK-XXII/2

Extremely low summer sea-ice coverage in the Arctic Ocean in 2007 allowed extensive sampling and a wide quasi-synoptic hydrographic and d18O dataset could be collected in the Eurasian Basin and the Makarov Basin up to the Alpha Ridge and the East Siberian continental margin. With the aim of determining the origin of freshwater in the halocline, fractions of river water and sea-ice meltwater in the upper 150 m were quantified by a combination of salinity and d18O in the Eurasian Basin. Two methods, applying the preformed phosphate concentration (PO*) and the nitrate-to-phosphate ratio (N/P), were compared to further differentiate the marine fraction into Atlantic and Pacific-derived contributions. While PO*-based assessments systematically underestimate the contribution of Pacific-derived waters, N/P-based calculations overestimate Pacific-derived waters within the Transpolar Drift due to denitrification in bottom sediments at the Laptev Sea continental margin. Within the Eurasian Basin a west to east oriented front between net melting and production of sea-ice is observed. Outside the Atlantic regime dominated by net sea-ice melting, a pronounced layer influenced by brines released during sea-ice formation is present at about 30 to 50 m water depth with a maximum over the Lomonosov Ridge. The geographically distinct definition of this maximum demonstrates the rapid release and transport of signals from the shelf regions in discrete pulses within the Transpolar Drift. The ratio of sea-ice derived brine influence and river water is roughly constant within each layer of the Arctic Ocean halocline. The correlation between brine influence and river water reveals two clusters that can be assigned to the two main mechanisms of sea-ice formation within the Arctic Ocean. Over the open ocean or in polynyas at the continental slope where relatively small amounts of river water are found, sea-ice formation results in a linear correlation between brine influence and river water at salinities of about 32 to 34. In coastal polynyas in the shallow regions of the Laptev Sea and southern Kara Sea, sea-ice formation transports river water into the shelf's bottom layer due to the close proximity to the river mouths. This process therefore results in waters that form a second linear correlation between brine influence and river water at salinities of about 30 to 32. Our study indicates which layers of the Arctic Ocean halocline are primarily influenced by sea-ice formation in coastal polynyas and which layers are primarily influenced by sea-ice formation over the open ocean. Accordingly we use the ratio of sea-ice derived brine influence and river water to link the maximum in brine influence within the Transpolar Drift with a pulse of shelf waters from the Laptev Sea that was likely released in summer 2005.

Desenvolvimento de bionanocompósitos: nano e microcristais de celulose com poli (álcool vinílico) e poli (ácido lático)

This work has the main objective to obtain nano and microcrystals of cellulose, extracted from the pineapple leaf fibres (PALF), as reinforcement for the manufacture of biocomposite films with polymeric matrices of Poly(vinyl alcohol) (PVA) and Poly(lactic acid) (PLA). The polymer matrices and the nano and microcrystals of cellulose were characterised by means of TGA, FTIR and DSC. The analysis was performed on the pineapple leaves to identify the macro and micronutrients. The fibers of the leaves of the pineapple were extracted in a desfibradeira mechanical. The PALF extracted were washed to remove washable impurities and subsequently treated with sodium hydroxide (NaOH) and sodium hypochlorite (NaClO) in the removal of impurities, such as fat, grease, pectates, pectin and lignin. The processed PALF fibers were hydrolysed in sulfuric acid (H2SO4) at a concentration of 13.5 %, to obtain nano and microcrystals of cellulose. In the manufacture of biocomposite films, concentrations of cellulose, 0 %, 1 %, 3 %, 6 %, 9% and 12% were used as reinforcement to the matrices of PVA and PLA. The PVA was dissolved in distilled water at 80 ± 5 oC and the PLA was dissolved in dichloromethane at room temperature. The manufacture of biocompósitos in the form of films was carried out by "casting". Tests were carried out to study the water absorption by the films and mechanical test of resistance to traction according to ASTM D638-10 with a velocity of 50 mm/min.. Chi-square statistical test was used to check for the existence of significant differences in the level of 0.05: the lengths of the PALF, lengths of the nano and microcrystals of cellulose and the procedures used for the filtration using filter syringe of 0.2 μm or filtration and centrifugation. The hydrophilicity of biocompósitos was analysed by measuring the contact angle and the thickness of biocompósitos were compared as well as the results of tests of traction. Statistical T test - Student was also applied with the significance level (0.05). In biodegradation, Sturm test of standard D5209 was used. Nano and microcrystals of cellulose with lengths ranging from 7.33 nm to 186.17 nm were found. The PVA films showed average thicknesses of 0.153 μm and PLA 0.210 μm. There is a strong linear correlation directly proportional between the traction of the films of PVA and the concentration of cellulose in the films (composite) (0,7336), while the thickness of the film was correlated in 0.1404. Nano and microcrystals of cellulose and thickness together, correlated to 0.8740. While the correlation between the cellulose content and tensile strength was weak and inversely proportional (- 0,0057) and thickness in -0.2602, totaling -0,2659 in PLA films. This can be attributed to the nano and microcrystals of cellulose not fully adsorbed to the PLA matrix. In the comparison of the results of the traction of the two polymer matrices, the nano and microcrystals have helped in reducing the traction of the films (composite) of PLA. There was still the degradation of the film of PVA, within a period of 20 days, which was not seen in the PLA film, on the other hand, the observations made in the literature, the average time to start the degradation is above 60 days. What can be said that the films are biodegradable composites, with hydrophilicity and the nano and microcrystals of cellulose, contribute positively in the improvement of the results of polymer matrices used.

Estudo da resposta Th17 no transplante renal alogênico: contribuição do eixo quimiotático CCR6/CCL20 e dos polimorfismos gênicos em IL17A e IL17RA

Kidney transplantation is the best treatment for patients who have lost kidney function. Renal transplant patients require accurate immunosuppressive drugs to prevent rejection. In this process T helper cells of the immune system perform key role in the immune response to the graft, and recently the Th17 cells has been investigated by production of IL-17 potent proinflammatory cytokine whose role in the rejection has also been described. Increased of Th17 cell expression has an important association with the development of rejection in renal microenvironment, however the likely mechanism is not well understood. This study aimed to evaluate the Th17 response from the influence of the chemotactic axis CCR6/CCL20 and genetic variants in IL-17 and IL-17RA. We conducted a case-control study involving 148 patients transplanted at the University Hospital Onofre Lopes/UFRN in which assessed by immunohistochemistry protein expression of IL-17 and chemokines CCR6/CCL20 and by PCR-RFLP genetic variants in IL17A and IL17RA. Our results showed no influence of genetic polymorphisms on the outcome of the graft or the protein expression of IL-17. In renal graft microenvironment found several sources producing IL-17: tubular epithelial cells, glomerular cells, neutrophils and cell interstitial infiltration, in turn the expression of chemotactic axis CCR6/CCL20 was restricted to the tubular epithelium cells. There was a slight positive linear correlation between the presence of IL-17 and expression of chemotactic axis CCR6/CCL20 in the microenvironment of renal graft. Therefore, we believe that, combined with our results, further studies with increased "n" sample and greater control over the variables involved in obtaining the renal specimen, can determine more clearly the influence of chemotactic axis CCR6 / CCL20 and polymorphisms in cytokines related to Th17 profile on the control of this cell subtype response in rejection processes to renal allograft.

Learning from Geometry

Subspaces and manifolds are two powerful models for high dimensional signals. Subspaces model linear correlation and are a good fit to signals generated by physical systems, such as frontal images of human faces and multiple sources impinging at an antenna array. Manifolds model sources that are not linearly correlated, but where signals are determined by a small number of parameters. Examples are images of human faces under different poses or expressions, and handwritten digits with varying styles. However, there will always be some degree of model mismatch between the subspace or manifold model and the true statistics of the source. This dissertation exploits subspace and manifold models as prior information in various signal processing and machine learning tasks.

A near-low-rank Gaussian mixture model measures proximity to a union of linear or affine subspaces. This simple model can effectively capture the signal distribution when each class is near a subspace. This dissertation studies how the pairwise geometry between these subspaces affects classification performance. When model mismatch is vanishingly small, the probability of misclassification is determined by the product of the sines of the principal angles between subspaces. When the model mismatch is more significant, the probability of misclassification is determined by the sum of the squares of the sines of the principal angles. Reliability of classification is derived in terms of the distribution of signal energy across principal vectors. Larger principal angles lead to smaller classification error, motivating a linear transform that optimizes principal angles. This linear transformation, termed TRAIT, also preserves some specific features in each class, being complementary to a recently developed Low Rank Transform (LRT). Moreover, when the model mismatch is more significant, TRAIT shows superior performance compared to LRT.

The manifold model enforces a constraint on the freedom of data variation. Learning features that are robust to data variation is very important, especially when the size of the training set is small. A learning machine with large numbers of parameters, e.g., deep neural network, can well describe a very complicated data distribution. However, it is also more likely to be sensitive to small perturbations of the data, and to suffer from suffer from degraded performance when generalizing to unseen (test) data.

From the perspective of complexity of function classes, such a learning machine has a huge capacity (complexity), which tends to overfit. The manifold model provides us with a way of regularizing the learning machine, so as to reduce the generalization error, therefore mitigate overfiting. Two different overfiting-preventing approaches are proposed, one from the perspective of data variation, the other from capacity/complexity control. In the first approach, the learning machine is encouraged to make decisions that vary smoothly for data points in local neighborhoods on the manifold. In the second approach, a graph adjacency matrix is derived for the manifold, and the learned features are encouraged to be aligned with the principal components of this adjacency matrix. Experimental results on benchmark datasets are demonstrated, showing an obvious advantage of the proposed approaches when the training set is small.

Stochastic optimization makes it possible to track a slowly varying subspace underlying streaming data. By approximating local neighborhoods using affine subspaces, a slowly varying manifold can be efficiently tracked as well, even with corrupted and noisy data. The more the local neighborhoods, the better the approximation, but the higher the computational complexity. A multiscale approximation scheme is proposed, where the local approximating subspaces are organized in a tree structure. Splitting and merging of the tree nodes then allows efficient control of the number of neighbourhoods. Deviation (of each datum) from the learned model is estimated, yielding a series of statistics for anomaly detection. This framework extends the classical {\em changepoint detection} technique, which only works for one dimensional signals. Simulations and experiments highlight the robustness and efficacy of the proposed approach in detecting an abrupt change in an otherwise slowly varying low-dimensional manifold.