Academic literature on the topic 'Tensor methods, Factor analysis, Multilinear regression'

In this study, we employed various machine learning-based techniques in predicting factor of safety against slope failures. Different regression methods namely, multi-layer perceptron (MLP), Gaussian process regression (GPR), multiple linear regression (MLR), simple linear regression (SLR), support vector regression (SVR) were used. Traditional methods of slope analysis (e.g., first established in the first half of the twentieth century) used widely as engineering design tools. Offering more progressive design tools, such as machine learning-based predictive algorithms, they draw the attention of many researchers. The main objective of the current study is to evaluate and optimize various machine learning-based and multilinear regression models predicting the safety factor. To prepare training and testing datasets for the predictive models, 630 finite limit equilibrium analysis modelling (i.e., a database including 504 training datasets and 126 testing datasets) were employed on a single-layered cohesive soil layer. The estimated results for the presented database from GPR, MLR, MLP, SLR, and SVR were assessed by various methods. Firstly, the efficiency of applied models was calculated employing various statistical indices. As a result, obtained total scores 20, 35, 50, 10, and 35, respectively for GPR, MLR, MLP, SLR, and SVR, revealed that the MLP outperformed other machine learning-based models. In addition, SVR and MLR presented an almost equal accuracy in estimation, for both training and testing phases. Note that, an acceptable degree of efficiency was obtained for GPR and SLR models. However, GPR showed more precision. Following this, the equation of applied MLP and MLR models (i.e., in their optimal condition) was derived, due to the reliability of their results, to be used in similar slope stability problems.

Objective Knowing tuberculosis (TB) patients’ satisfaction enables TB program managers to identify gaps in service delivery and institute measures to address them. This study is aimed at evaluating patients’ satisfaction with TB services in southern Nigeria. Materials and Methods A total of 378 patients accessing TB care were studied using a validated Patient Satisfaction (PS-38) questionnaire on various aspects of TB services. Factor analysis was used to identify eight factors related to TB patient satisfaction. Test of association was used to study the relation between patient satisfaction scores and patient and health facility characteristics, while multilinear regression analysis was used to identify predictors of patient satisfaction. Results Highest satisfaction was reported for adherence counseling and access to care. Patient characteristics were associated with overall satisfaction, registration, adherence counseling, access to care, amenities, and staff attitude, while health system factors were associated with staff attitude, amenities, and health education. Predictors of satisfaction with TB services included gender, educational status, if tested for HIV, distance, payment for TB services, and level and type of health-care facility. Conclusion Patient- and health system–related factors were found to influence patient satisfaction and, hence, should be taken into consideration in TB service programing.

Introduction Restrictions related to COVID-19 may affect aggressive behaviour. Increased incidence of gender-based, domestic, and intimate-partner violence was expected during the pandemic, however, retrospective analyses yielded contradicting results. Objectives Examine changes in frequency of assaults caused by pandemic restrictions, including separate analysis for male and female assault victims, for residential and non-residential location of assaults and for assaults related to domestic violence. Methods Weekly number of ambulance departures to injuries secondary to assaults in the Pilsen region, Czechia, during the COVID lockdown was compared to records from the three previous years using ANOVA and post hoc t-tests. Further, multilinear regression was used to model weekly number of ambulance departures between 1st January 2017 and 30th April 2021 based on presence of pandemic national emergency state, time, and seasonality. Results During pandemic lockdown, ambulance departures to assaults dropped by 43% compared to equivalent periods of the three previous years. The decrease was notable specifically among departures to male victims and to assaults in non-residential areas, with only small decrease observed for female victims and assaults related to domestic violence and no change found in frequency of assaults happening at home. Conclusions Lockdowns and restrictions of public life were associated with a decreased incidence of violent assaults. While the incidence decreased especially in males and in those assaulted outside of their homes, we found no support for an increase in domestic or gender related violence. Pandemic restrictions may serve as a protective rather than a risk factor for assaults. Disclosure No significant relationships.

Objective Diameter is currently the only screening and diagnostic criterion for asymptomatic aneurysms. Therefore, aortic and lower-extremity arterial diameter has diagnostic, therapeutic, and prognostic importance. We aimed to determine aortic and lower-extremity arterial reference diameters in a general population and compare them according to age, sex, and other characteristics. Methods We evaluated consecutive 3,692 patients who underwent computed tomography as part of a general health checkup from 2015–2019 in a single tertiary center. Aortic and lower-extremity arterial diameters and the most important factor related to arterial diameters were evaluated. Results The mean diameter of the abdominal aorta was 17.490 ± 2.110 mm, while that of the common iliac artery was 10.851 ± 1.689 mm. The mean diameter of the abdominal aorta was 18.377 ± 1.766 mm in men and 15.884 ± 1.694 mm in women. Significant intersex differences were observed for all mean diameters and lengths. Multilinear regression analysis showed that age, sex, and body surface area impacted mean diameters of all measured sites except aorta and common iliac artery length. Between male and female patients matched for body surface area, there were significant intersex differences for all measured sites, except for common iliac artery length. Conclusions The mean diameter of the abdominal aorta in this healthy cohort was 17.490 ± 2.110 mm overall, 18.377 ± 1.766 mm in men, and 15.884 ± 1.694 mm in women. Arterial diameter increased with male sex, older age, and increased body surface area, and aortic diameters were larger in men than in women with the same body surface area.

Background Venous congestion in breast free flap reconstruction continues to be a major reason for flap compromise requiring reoperative exploration and possible flap failure. We aim to investigate whether size of the internal mammary vein (IMV) (1) varies between the left and right sides, (2) changes with certain patient demographics or preoperative factors, and (3) correlates with postoperative complications. Methods We performed a retrospective cohort study examining all patients undergoing free flap breast reconstruction from September 2005 to March 2016 using internal mammary recipient veins. Venous coupler size was used as a surrogate measure of IMV diameter. Preoperative patient characteristics and factors were collected. Postoperative outcomes assessed included thrombosis, flap loss, fat necrosis, and mastectomy flap necrosis. Multivariate analyses were performed to evaluate if preoperative factors affected IMV diameter and to determine if coupler size and flap side were independent risk factors for postoperative complications. Results We examined 372 patients with a total of 561 flaps. One hundred eighty-nine patients received bilateral flaps with the IMV as a recipient. The right IMV (n = 286, average = 2.97 mm, standard deviation [SD] = 0.41) was significantly larger than the left (n = 275, average = 2.89, SD = 0.35, p = 0.008). Preoperative factors and postoperative complications were not statistically different between the left and right cohorts. The multivariable linear regression model with coupler size as the dependent variable found older age trended toward a larger coupler size but this was not significant (p = 0.05). In multilinear regression analysis, the postoperative outcomes did not have significant covariates. Conclusion We found that IMV size significantly differs between the right and the left sides. However, incidence of postoperative complications was not significantly different between the left and right sides, and the multivariate analyses did not identify flap side as an independent risk factor for adverse outcomes. Prospective studies evaluating actual IMV diameter and associated complications may potentially elucidate clinical significance.

ABSTRACT Background There is an alarming increase in the obesity prevalence among children in an environment of increasing availability of preprocessed high-calorie foods. However, some people maintain a healthy weight even in such obesogenic environments. This difference in body weight management could be attributed to individual differences in dietary restraint; however, its underlying neurocognitive mechanisms in adolescents remain unclear. Objectives This study aimed to elucidate these neurocognitive mechanisms in adolescents by examining the relationships between dietary restraint and the food-related value-coding region located in the ventromedial prefrontal cortex (vmPFC). Methods The association between dietary restraint and BMI was tested using a multilinear regression analysis in a large early adolescent cohort (n = 2554; age, 12.2 ± 0.3 years; BMI, 17.9 ± 2.5 kg/m2; 1354 boys). Further, an fMRI experiment was designed to assess the association between the vmPFC response to food images and dietary restraint in 30 adolescents (age, 17.6 ± 1.9 years; BMI, 20.7 ± 2.2 kg/m2; 13 boys). Additionally, using 54 individuals from the cohort (age, 14.5 ± 0.6 years; BMI, 18.8 ± 2.6 kg/m2; 31 boys), we assessed the association between dietary restraint and intrinsic vmPFC-related functional connectivity. Results In the cohort, adolescents with increased dietary restraint showed a lower BMI (β = −0.38; P < 0.001; B = −0.06; SE = 0.003). The fMRI results showed a decreased vmPFC response to high-calorie food were correlated with greater dietary restraint. Moreover, there was an association of attenuated intrinsic vmPFC-related functional connectivity in the superior and middle frontal gyrus and the middle temporal gyrus with greater dietary restraint. Conclusions Our findings suggest that dietary restraint in adolescents could be a preventive factor for weight gain; its effect involves modulating the vmPFC, which is associated with food value coding.

This study presents the assessment of the quantitative influence of atmospheric circulation on the pollutant concentration in the area of Kraków, Southern Poland, for the period 2000–2020. The research has been realized with the application of different statistical parameters, synoptic meteorology tools, the Random Forests machine learning method, and multilinear regression analyses. Another aim of the research was to evaluate the types of atmospheric circulation classification methods used in studies on air pollution dispersion and to assess the possibility of their application in air quality management, including short-term PM10 daily forecasts. During the period analyzed, a significant decreasing trend of pollutants’ concentrations and varying atmospheric circulation conditions was observed. To understand the relation between PM10 concentration and meteorological conditions and their significance, the Random Forests algorithm was applied. Observations from meteorological stations, air quality measurements and ERA-5 reanalysis were used. The meteorological database was used as an input to models that were trained to predict daily PM10 concentration and its day-to-day changes. This study made it possible to distinguish the dominant circulation types with the highest probability of occurrence of poor air quality or a significant improvement in air quality conditions. Apart from the parameters whose significant influence on air quality is well established (air temperature and wind speed at the ground and air temperature gradient), the key factor was also the gradient of relative air humidity and wind shear in the lowest troposphere. Partial dependence calculated with the use of the Random Forests model made it possible to better analyze the impact of individual meteorological parameters on the PM10 daily concentration. The analysis has shown that, for areas with a diversified topography, it is crucial to use the variability of the atmospheric circulation during the day to better forecast air quality.

Background: White matter injury is an important factor for cognitive impairment in memory clinic patients. We determined the added value of diffusion tensor imaging (DTI) of strategic white matter tracts in explaining variance in cognition in memory clinic patients with vascular brain injury. Methods: We included 159 patients. Conventional MRI markers (white matter hyperintensity volume, lacunes, nonlacunar infarcts, brain atrophy, and microbleeds), and fractional anisotropy and mean diffusivity (MD) of the whole brain white matter and of 18 white matter tracts were related to cognition using linear regression and Bayesian network analysis. Results: On top of all conventional MRI markers combined, MD of the whole brain white matter explained an additional 3.4% (p = 0.014), 7.8% (p < 0.001), and 1.2% (p = 0.119) variance in executive functioning, speed, and memory, respectively. The Bayesian analyses of regional DTI measures identified strategic tracts for executive functioning (right superior longitudinal fasciculus), speed (left corticospinal tract), and memory (left uncinate fasciculus). MD within these tracts explained an additional 3.4% (p = 0.012), 3.8% (p = 0.007), and 2.1% (p = 0.041) variance in executive functioning, speed, and memory, respectively, on top of all conventional MRI and global DTI markers combined. Conclusion: In memory clinic patients with vascular brain injury, DTI of strategic white matter tracts has a significant added value in explaining variance in cognitive functioning.

Abstract Introduction Little has been done to examine within/between group predictors and mediators of race/ethnic differences in sleep health outcomes, due to COVID-19 exposure. We evaluated the effect of COVID-19 exposure on sleep quality in a multiracial/ethnic sample of New York residents. Methods We conducted a cross-sectional study among adults exposed to COVID-19 across New York State from September to November of 2020. Comparisons of participant characteristics e.g., mean scores by race/ethnicity status were made using one-way ANOVA for continuous variables, and chi-square tests for categorical variables. Associations between social determinants of health (employment, location), Trauma Coping Self-Efficacy (CES-T), and sleep quality (Pittsburgh Sleep Quality Index-PSQI) were examined using multilinear regression analysis stratified by race/ethnicity. Results Of the 541 participants, 373 (68.9%) were female; mean age was 40.9 years (SD=15), 198 (36.6%) identified as Whites, 111 (20.5%) as Black, 97 (17.9%) as Hispanics, and 135(25%) identified as either Asians, Native-Americans, Pacific-Islanders. Sex was the strongest predictor [β = 1.335; p &lt; .05] of sleep quality, but only among Whites. Trauma Coping Self-Efficacy was negatively associated with sleep quality among Asian, Native-American, or Pacific-Islander participants [β = -.114; p &lt; .05 ]; Black [β = -.099; p &lt; .05] and White participants [β = -0.79; p &lt; .05] but not among Latinos/as [β = -.058; p = 0.71]. Conclusion Coping Self-Efficacy moderated the effect of COVID-19 on sleep quality among some, but not all, racial/ethnic groups. While CSE-T scores during the first wave of COVID-19 acted as a protective factor for sleep quality among Asians, Native-Americans, and Pacific-Islanders, White and Black participants, this was not the case for Latinos/as/Hispanics residing in New York. Clinical interventions that are tailored for racial/ethnic, community and cultural needs may help to mitigate sleep problems associated with COVID-19 exposure. Support (If Any) T32HL129953; 7R01HL142066-04; 1R01HL152453-01

Phosphatidylcholine (PC) hydrolysis has been shown to occur in hormone-stimulated cells and represents a potential metabolic source, in addition to phosphoinositides, for the generation of diradylglycerols (DG). We performed studies in order to quantify the importance of this pathway in DG formation. We incubated murine peritoneal macrophages with platelet-activating factor (PAF), ionomycin, phorbol myristate acetate (PMA) or no stimulus in a series of timed incubations ranging from 15 s to 20 min. We quantified the profiles of the molecular species in the accumulated DG after extraction, specific radiolabelling to give [32P]phosphatidic acid by DG kinase, and conversion to the dimethyl derivative. We used two independent methods for molecular species analysis: (1) reversed-phase h.p.l.c. separation with in-line beta-radiation detection of peaks, and (2) an argentation-t.l.c. separation with scintillation counting of bands. Our results showed a clearly biphasic sequence in the composition of accumulated DG. The molecular species composition of early DG (up to 1 min stimulation time) was very similar to that of unstimulated DG, whereas the proportions of the species present in later DG were substantially altered. In the same experiments, we extracted native phospholipids from unstimulated macrophages, separated phosphatidylinositol (PI), PC, phosphatidylethanolamine (PE) and phosphatidylserine (PS), converted them to the corresponding DGs by using phospholipase C, and determined their molecular species compositions as above. In comparison with the diradyl compositions of stimulated DG, the diradyl composition of PI closely matched that of early DG, the differences between the PC and PI compositions matched the differences between early and late DG very closely, and the compositions of PE and PS were unique and unrelated. We quantified these relationships more precisely by multilinear regression analysis to calculate the theoretical best mix of five molecular species compositions (PI, PC, PE, PS and unstimulated DG) that would most closely replicate the early and late accumulated DG compositions. We found that by both h.p.l.c. and t.l.c. analyses, 15-30% (PAF) or 25-50% (ionomycin and PMA) of the later DG could be accounted for by PC hydrolysis. These results represent quantifications of phospholipid class contributions to stimulated DG formation, and demonstrate the potential importance of PC hydrolysis in phagocytic leucocytes.

This thesis is written with the scope of exploring multiway data. Multiway data, also referred to as tensor data, is a collection of data points in multidimensional matrices. At a first glance one may think that these objects are only a convenient representation of a datasets. They are not just a col- lection of data, they have their own structure. For this reason, multiway data need specific models to be correctly analysed. In this spirit, I developed my personal idea on data analysis which can be represented by following statement: \It is not the data that should fit models, but models that should fit the data" However, this should not be taken literary I do think that models are im- portant: giving a structure to our techniques is necessary. Nevertheless, I do think that data should be the main driver.This means that instead of trimming data at our necessity to fit existing models, researchers should develop new models to re ect the complexity of the data. The purpose of this work is to provide an overview of tensor methods applied to Economics and Finance. Yet, the most important aspect of this thesis are ideas and applications rather than the mathematical content. New models are proposed and fitted to data in order to test their performance and get insights from the datasets analysed. The description of the tensor methods provided in this thesis is not intended to be complete but rather restricted to the model applicable to the analysed data.

In many fields of science, engineering, and economics large amounts of data are stored and there is a need to analyze these data in order to extract information for various purposes. Data mining is a general concept involving different tools for performing this kind of analysis. The development of mathematical models and efficient algorithms is of key importance. In this thesis we discuss algorithms for the reduced rank regression problem and algorithms for the computation of the best multilinear rank approximation of tensors. The first two papers deal with the reduced rank regression problem, which is encountered in the field of state-space subspace system identification. More specifically the problem is \[ \min_{\rank(X) = k} \det (B - X A)(B - X A)\tp, \] where $A$ and $B$ are given matrices and we want to find $X$ under a certain rank condition that minimizes the determinant. This problem is not properly stated since it involves implicit assumptions on $A$ and $B$ so that $(B - X A)(B - X A)\tp$ is never singular. This deficiency of the determinant criterion is fixed by generalizing the minimization criterion to rank reduction and volume minimization of the objective matrix. The volume of a matrix is defined as the product of its nonzero singular values. We give an algorithm that solves the generalized problem and identify properties of the input and output signals causing a singular objective matrix. Classification problems occur in many applications. The task is to determine the label or class of an unknown object. The third paper concerns with classification of handwritten digits in the context of tensors or multidimensional data arrays. Tensor and multilinear algebra is an area that attracts more and more attention because of the multidimensional structure of the collected data in various applications. Two classification algorithms are given based on the higher order singular value decomposition (HOSVD). The main algorithm makes a data reduction using HOSVD of 98--99 \% prior the construction of the class models. The models are computed as a set of orthonormal bases spanning the dominant subspaces for the different classes. An unknown digit is expressed as a linear combination of the basis vectors. The resulting algorithm achieves 5\% in classification error with fairly low amount of computations. The remaining two papers discuss computational methods for the best multilinear rank approximation problem \[ \min_{\cB} \| \cA - \cB\| \] where $\cA$ is a given tensor and we seek the best low multilinear rank approximation tensor $\cB$. This is a generalization of the best low rank matrix approximation problem. It is well known that for matrices the solution is given by truncating the singular values in the singular value decomposition (SVD) of the matrix. But for tensors in general the truncated HOSVD does not give an optimal approximation. For example, a third order tensor $\cB \in \RR^{I \x J \x K}$ with rank$(\cB) = (r_1,r_2,r_3)$ can be written as the product \[ \cB = \tml{X,Y,Z}{\cC}, \qquad b_{ijk}=\sum_{\lambda,\mu,\nu} x_{i\lambda} y_{j\mu} z_{k\nu} c_{\lambda\mu\nu}, \] where $\cC \in \RR^{r_1 \x r_2 \x r_3}$ and $X \in \RR^{I \times r_1}$, $Y \in \RR^{J \times r_2}$, and $Z \in \RR^{K \times r_3}$ are matrices of full column rank. Since it is no restriction to assume that $X$, $Y$, and $Z$ have orthonormal columns and due to these constraints, the approximation problem can be considered as a nonlinear optimization problem defined on a product of Grassmann manifolds. We introduce novel techniques for multilinear algebraic manipulations enabling means for theoretical analysis and algorithmic implementation. These techniques are used to solve the approximation problem using Newton and Quasi-Newton methods specifically adapted to operate on products of Grassmann manifolds. The presented algorithms are suited for small, large and sparse problems and, when applied on difficult problems, they clearly outperform alternating least squares methods, which are standard in the field.