Linear algebra: selected problems

Linear Algebra—Selected Problems is a unique book for senior undergraduate and graduate students to fast review basic materials in Linear Algebra. Vector spaces are presented first, and linear transformations are reviewed secondly. Matrices and Linear systems are presented. Determinants and Basic geometry are presented in the last two chapters. The solutions for proposed excises are listed for readers to references.

Prescribed burning impact on forest soil properties – a fuzzy boolean nets approach

The Portuguese northern forests are often and severely affected by wildfires during the Summer season. These occurrences significantly affect and negatively impact all ecosystems, namely soil, fauna and flora. In order to reduce the occurrences of natural wildfires, some measures to control the availability of fuel mass are regularly implemented. Those preventive actions concern mainly prescribed burnings and vegetation pruning. This work reports on the impact of a prescribed burning on several forest soil properties, namely pH, soil moisture, organic matter content and iron content, by monitoring the soil self-recovery capabilities during a one year span. The experiments were carried out in soil cover over a natural site of Andaluzitic schist, in Gramelas, Caminha, Portugal, which was kept intact from prescribed burnings during a period of four years. Soil samples were collected from five plots at three different layers (0–3, 3–6 and 6–18) 1 day before prescribed fire and at regular intervals after the prescribed fire. This paper presents an approach where Fuzzy Boolean Nets (FBN) and Fuzzy reasoning are used to extract qualitative knowledge regarding the effect of prescribed fire burning on soil properties. FBN were chosen due to the scarcity on available quantitative data. The results showed that soil properties were affected by prescribed burning practice and were unable to recover their initial values after one year.

A coinfection model for HIV and HCV

We study a mathematical model for the human immunodeficiency virus (HIV) and hepatites C virus (HCV) coinfection. The model predicts four distinct equilibria: the disease free, the HIV endemic, the HCV endemic, and the full endemic equilibria. The local and global stability of the disease free equilibrium was calculated for the full model and the HIV and HCV submodels. We present numerical simulations of the full model where the distinct equilibria can be observed. We show simulations of the qualitative changes of the dynamical behavior of the full model for variation of relevant parameters. From the results of the model, we infer possible measures that could be implemented in order to reduce the number of infected individuals.

TERT Promoter Mutations Are a Major Indicator of Poor Outcome in Differentiated Thyroid Carcinomas

Context: Telomerase promoter mutations (TERT) were recently described in follicular cell-derived thyroid carcinomas (FCDTC) and seem to be more prevalent in aggressive cancers. Objectives: We aimed to evaluate the frequency of TERT promoter mutations in thyroid lesions and to investigate the prognostic significance of such mutations in a large cohort of patients with differentiated thyroid carcinomas (DTCs). Design: This was a retrospective observational study. Setting and Patients: We studied 647 tumors and tumor-like lesions. A total of 469 patients with FCDTC treated and followed in five university hospitals were included. Mean follow-up (±SD) was 7.8 ± 5.8 years. Main Outcome Measures: Predictive value of TERT promoter mutations for distant metastasization, disease persistence at the end of follow-up, and disease-specific mortality. Results: TERT promoter mutations were found in 7.5% of papillary carcinomas (PTCs), 17.1% of follicular carcinomas, 29.0% of poorly differentiated carcinomas, and 33.3% of anaplastic thyroid carcinomas. Patients with TERT-mutated tumors were older (P < .001) and had larger tumors (P = .002). In DTCs, TERT promoter mutations were significantly associated with distant metastases (P < .001) and higher stage (P < .001). Patients with DTC harboring TERT promoter mutations were submitted to more radioiodine treatments (P = .009) with higher cumulative dose (P = .004) and to more treatment modalities (P = .001). At the end of follow-up, patients with TERT-mutated DTCs were more prone to have persistent disease (P = .001). TERT promoter mutations were significantly associated with disease-specific mortality [in the whole FCDTC (P < .001)] in DTCs (P < .001), PTCs (P = .001), and follicular carcinomas (P < .001). After adjusting for age at diagnosis and gender, the hazard ratio was 10.35 (95% confidence interval 2.01–53.24; P = .005) in DTC and 23.81 (95% confidence interval 1.36–415.76; P = .03) in PTCs. Conclusions: TERT promoter mutations are an indicator of clinically aggressive tumors, being correlated with worse outcome and disease-specific mortality in DTC. TERT promoter mutations have an independent prognostic value in DTC and, notably, in PTC.

Development and Assessment of an E-Learning Course on Breast Imaging for Radiographers: A Stratified Randomized Controlled Trial

Background: Mammography is considered the best imaging technique for breast cancer screening, and the radiographer plays an important role in its performance. Therefore, continuing education is critical to improving the performance of these professionals and thus providing better health care services. Objective: Our goal was to develop an e-learning course on breast imaging for radiographers, assessing its efficacy , effectiveness, and user satisfaction. Methods: A stratified randomized controlled trial was performed with radiographers and radiology students who already had mammography training, using pre- and post-knowledge tests, and satisfaction questionnaires. The primary outcome was the improvement in test results (percentage of correct answers), using intention-to-treat and per-protocol analysis. Results: A total of 54 participants were assigned to the intervention (20 students plus 34 radiographers) with 53 controls (19+34). The intervention was completed by 40 participants (11+29), with 4 (2+2) discontinued interventions, and 10 (7+3) lost to follow-up. Differences in the primary outcome were found between intervention and control: 21 versus 4 percentage points (pp), P<.001. Stratified analysis showed effect in radiographers (23 pp vs 4 pp; P=.004) but was unclear in students (18 pp vs 5 pp; P=.098). Nonetheless, differences in students’ posttest results were found (88% vs 63%; P=.003), which were absent in pretest (63% vs 63%; P=.106). The per-protocol analysis showed a higher effect (26 pp vs 2 pp; P<.001), both in students (25 pp vs 3 pp; P=.004) and radiographers (27 pp vs 2 pp; P<.001). Overall, 85% were satisfied with the course, and 88% considered it successful. Conclusions: This e-learning course is effective, especially for radiographers, which highlights the need for continuing education.

Análise do polimorfismo HLA/DR-DQ em Angolanos portadores de Diabetes Mellitus tipo I

A diabetes mellitus do tipo 1 (DM1) é o distúrbio endócrino-metabólico mais frequente em crianças. É uma doença autoimune resultado da destruição selectiva das células beta pancreáticas. A velocidade de destruição das células beta pode ser rápida em algumas pessoas e lenta em outras; esta última é típica de adulto é conhecido como diabetes autoimune latente em adulto (LADA). A sua etiologia envolve factores ambientais e genéticos, dos genes envolvidos a maior contribuição vem da região do genoma onde estão localizados os genes do Complexo Principal de Histocompatibilidade (MHC). A combinação de diferentes alelos do sistema de antigénio leucocitário humano tipo II (HLAII) esta associada a susceptibilidade da doença e as principais molécula envolvidas são a DQ e DR. O estágio pré-clínico da doença se caracteriza pela presença de auto-anticorpos, sendo o anti-GAD o mais sensível nesta patologia. OBJECTIVO: Analizar a frequência dos polimorfismos HLA-DR/DQ em angolanos portadores de diabetes tipo 1, residentes em Luanda. O tipo de estudo adotado foi casocontrolo num universo de voluntários provenientes da consulta externa de hospitais e clínicas locais no período de outubro de 2012 a outubro 2013. A amostra biológica utilizada foi sangue total, tendo sido processada no laboratório LABGENE, da Faculdade de Medicina (FM) da Universidade Agostinho Neto (UNA). Os auto-anticorpos, anti-GAD, foram doseados pelo método de ELISA. O ADN genómico foi extraído à partir de sangue total periférico e tipagem genética foi realizada mediante PCR-SSP.O alelo DQB1*02 (DQ2/DQ2) (p=0,033, OR= 4, IC (1,2-13,3) foi associado a susceptibilidade da DM1; os alelos DQB1*06 (DQ6/DQ6) (p=0,000, OR=0,30, IC (0,17-0,54); *11 (p=0,011, OR=0,14, IC=0,032-0,62); *13 (p=0,006, OR=0,13, IC=0,049-0,588) e *15 (p=0,001, OR=0,044, IC=0,005-0,39) foram associados a proteção. Foi encontrado 29,2% de positividade para o anti-GAD, não houve associação significativa (p=0,69) entre a resposta positiva do anti-GAD e a idade. Não foi encontrada associação significativa (p=0,39) entre o tempo de diagnóstico e resposta humoral. Observou-se associação significativa entre os alelos de risco DQB1*02 (p=0.000) e resposta positiva para anti-GAD; da mesma maneira houve uma associação significativa para os alelos DQB1*06 (p=0,002), DRB1*11 (p=0,048); *13 (p=0,004) e *15 (p=0,021) e a resposta negativa do anti-GAD.Os dados demostram o forte envolvimentos do gene HLA-II (DQ) com a suceptibilidade a DM1 e sugere que a autoimunidade se desenvolve na presença de susceptibilidade genética, quer dizer, em associação com alelos HLA-II específicos.

Efeito da velocidade média nos parâmetros espaciotemporais, angulares e de pressão plantar durante a marcha em indivíduos com meniscopatia

Introdução: A velocidade da marcha quando analisada, conjuntamente com outras variáveis, permite-nos uma melhor compreensão acerca da natureza dos défices e como direcionar o tratamento. Objectivo(s): avaliar a associação da velocidade média da marcha com as variáveis espaciotemporais, angulares e de distribuição das pressões plantares em indivíduos com lesão meniscal há 4 anos, utilizando o membro não lesado como controlo. Métodos: estudo realizado em dez participantes com lesão meniscal (idade 35,3 ± 10,63 anos, altura 170,0 ± 0,09 cm, massa 67,5 ± 7,22 kg) avaliados em 3 ciclos de marcha a uma velocidade auto-selecionada. A quantificação das variáveis foi calculada através do programa Ariel Performance Analysis System e pelo Pedar System. As imagens foram editadas, digitalizadas, transformadas e suavizadas com um filtro digital com uma frequência de corte de 6HZ. Para estimar a associação das variáveis foram efetuados modelos de regressão linear e apresentados os coeficiente de regressão (β) e os respetivos intervalos de confiança (IC95%). Resultados: Foi possível verificar que a velocidade está significativa e positivamente associada aos parâmetros temporais das fases oscilantes (βML=0,044; IC95%:0,015;0,073; βMNL=0,061; IC95%:0,037;0,086), oscilação inicial (βML=0,055; IC95%:0,006;0,105; βMNL=0,091; IC95%:0,011;0,170) e cadência (βML=0,016; IC95%:0,009;0,023; βMNL=0,011; IC95%:0,006;0,017), em ambos os membros, e aos parâmetros temporais das fases de apoio unilateral (βML=0,046; IC95%:0,019;0,07), oscilação terminal (βML=0,081; IC95%:0,003;0,159) e apoio médio (βML=0,046; IC95%:0,008;0,085), apenas no membro lesado. Foi também observada, em ambos os membros, a existência de associações negativas significativas com os parâmetros temporais das fases de duplo apoio (βML=-0,024; IC95%:-0,037;-0,011; βMNL=-0,032; IC95%:-0,048;-0,015), apoio (βML=-0,044; IC95%:-0,073;-0,015; βMNL=-0,061; IC95%:-0,086;-0,037), resposta de carga (βML=-0,029; IC95%:-0,055;-0,004; βMNL=-0,047; IC95%:-0,081;-0,013), pré-oscilação (βML=-0,047; IC95%:-0,082;-0,013; βMNL=-0,060; IC95%:-0,098;-0,023) e tempo do ciclo de marcha (βML=-1,435; IC95%:-2,090;-0,781; βMNL=-0,941; IC95%:-1,431;-0,451). Foi ainda identificada, no membro lesado, uma associação positiva com a pressão plantar máxima normalizada durante o contacto do calcanhar terminal (βML=0,612; IC95%:0,077;1,147) e com o passo normalizado (βML=2,413; IC95%:0,264;4,561) e uma associação negativa limítrofe com a amplitude de flexão do joelho durante a elevação da ponta dos dedos (βML=-0,031; IC95%:-0,061;0,000). Conclusão: A velocidade média da marcha parece influenciar bastante os parâmetros temporais, sem provocar grandes alterações nos parâmetros espaciais, angulares e de pressão plantar, sendo esta associação semelhante em ambos os membros e independente do local da lesão.

Lettuce (Lactuca sativa L.) leaf-proteome profiles after exposure to cylindrospermopsin and a microcystin-LR/cylindrospermopsin mixture: A concentration-dependent response

The intensification of agricultural productivity is an important challenge worldwide. However, environmental stressors can provide challenges to this intensification. The progressive occurrence of the cyanotoxins cylindrospermopsin (CYN) and microcystin-LR (MC-LR) as a potential consequence of eutrophication and climate change is of increasing concern in the agricultural sector because it has been reported that these cyanotoxins exert harmful effects in crop plants. A proteomic-based approach has been shown to be a suitable tool for the detection and identification of the primary responses of organisms exposed to cyanotoxins. The aim of this study was to compare the leaf-proteome profiles of lettuce plants exposed to environmentally relevant concentrations of CYN and a MC-LR/CYN mixture. Lettuce plants were exposed to 1, 10, and 100 lg/l CYN and a MC-LR/CYN mixture for five days. The proteins of lettuce leaves were separated by twodimensional electrophoresis (2-DE), and those that were differentially abundant were then identified by matrix-assisted laser desorption/ionization time of flight-mass spectrometry (MALDI-TOF/TOF MS). The biological functions of the proteins that were most represented in both experiments were photosynthesis and carbon metabolism and stress/defense response. Proteins involved in protein synthesis and signal transduction were also highly observed in the MC-LR/CYN experiment. Although distinct protein abundance patterns were observed in both experiments, the effects appear to be concentration-dependent, and the effects of the mixture were clearly stronger than those of CYN alone. The obtained results highlight the putative tolerance of lettuce to CYN at concentrations up to 100 lg/l. Furthermore, the combination of CYN with MC-LR at low concentrations (1 lg/l) stimulated a significant increase in the fresh weight (fr. wt) of lettuce leaves and at the proteomic level resulted in the increase in abundance of a high number of proteins. In contrast, many proteins exhibited a decrease in abundance or were absent in the gels of the simultaneous exposure to 10 and 100 lg/l MC-LR/CYN. In the latter, also a significant decrease in the fr. wt of lettuce leaves was obtained. These findings provide important insights into the molecular mechanisms of the lettuce response to CYN and MC-LR/CYN and may contribute to the identification of potential protein markers of exposure and proteins that may confer tolerance to CYN and MC-LR/CYN. Furthermore, because lettuce is an important crop worldwide, this study may improve our understanding of the potential impact of these cyanotoxins on its quality traits (e.g., presence of allergenic proteins).

Milk intake is inversely related to body mass index and body fat in girls

Dairy foods comprise a range of products with varying nutritional content. The intake of dairy products (DPs) has been shown to have beneficial effects on body weight and body fat. This study aimed to examine the independent association between DP intake, body mass index (BMI), and percentage body fat (%BF) in adolescents. A cross-sectional, school-based study was conducted with 1,001 adolescents (418 boys), ages 15–18 years, from the Azorean Archipelago, Portugal. Anthropometric measurements were recorded (weight and height), and %BF was assessed using bioelectric impedance analysis. Adolescent food intake was measured using a self-administered, semiquantitative food frequency questionnaire. Data were analyzed separately for girls and boys, and separate multiple linear regression analysis was used to estimate the association between total DP, milk, yogurt, and cheese intake, BMI, and %BF, adjusting for potential confounders. For boys and girls, respectively, total DP consumption was 2.6 ± 1.9 and 2.9 ± 2.5 servings/day (P = 0.004), while milk consumption was 1.7 ± 1.4 and 2.0 ± 1.7 servings/day (P = 0.001), yogurt consumption was 0.5 ± 0.6 and 0.4 ± 0.7 servings/day (P = 0.247), and cheese consumption was 0.4 ± 0.6 and 0.5 ± 0.8 servings/day (P = 0.081). After adjusting for age, birth weight, energy intake, protein, total fat, sugar, dietary fiber, total calcium intake, low-energy reporters, parental education, pubertal stage, and physical activity, only milk intake was negatively associated with BMI and %BF in girls (respectively, girls: β = −0.167, P = 0.013; boys: β = −0.019, P = 0.824 and girls: β = −0.143, P = 0.030; boys: β = −0.051, P = 0.548). Conclusion: We found an inverse association between milk intake and both BMI and %BF only in girls.

An Exercise Program Improves Health-Related Quality of Life of Workers

Low back problems are associated with decreased quality of life. Specific exercises can improve quality of life, resulting in better professional performance and functionality. The purpose of this study was to evaluate the effect of following a 21-month exercise program on the quality of life of warehouse workers. The population included 557 male warehouse workers from a food distribution company in Oporto, Portugal. Upon application of the selection criteria, 249 workers were deemed eligible, which were randomized into two groups (125 in the intervention group and 124 in the control group). Then, subjects were asked to volunteer for the study, the sample being formed by 229 workers (112 in the intervention group and 117 in the control group). All subjects completed the SF-36 questionnaire prior to beginning the program and on the 11th and 21st months following it. The exercises were executed in the company facilities once a day for 8 min. Data were analyzed using SPSS® 17.0 for Windows®. After 11 months of following the exercise program, there was an increase in all scores for the experimental group, with statistically significant differences in the dimensions physical functioning (0.019), bodily pain (0.010), general health (0.004), and rolephysical (0.037). The results obtained at the end of the study (21 months) showed significant improvements in the dimensions physical functioning (p = 0.002), rolephysical (p = 0.007), bodily pain (p = 0.001), social functioning (p = 0.015), role-emotional (p = 0.011), and mental health (p = 0.001). In the control group all dimensions showed a decrease in mean scores. It can be concluded that the implementation of a low back specific exercise program has changed positively the quality of life of warehouse workers.

European Union emissions trading scheme impact on the Spanish electricity price during phase II and phase III implementation

The European Union Emissions Trading Scheme (EU ETS) is a cornerstone of the European Union's policy to combat climate change and its key tool for reducing industrial greenhouse gas emissions cost-effectively. The purpose of the present work is to evaluate the influence of CO2 opportunity cost on the Spanish wholesale electricity price. Our sample includes all Phase II of the EU ETS and the first year of Phase III implementation, from January 2008 to December 2013. A vector error correction model (VECM) is applied to estimate not only long-run equilibrium relations, but also short-run interactions between the electricity price and the fuel (natural gas and coal) and carbon prices. The four commodities prices are modeled as joint endogenous variables with air temperature and renewable energy as exogenous variables. We found a long-run relationship (cointegration) between electricity price, carbon price, and fuel prices. By estimating the dynamic pass-through of carbon price into electricity price for different periods of our sample, it is possible to observe the weakening of the link between carbon and electricity prices as a result from the collapse on CO2 prices, therefore compromising the efficacy of the system to reach proposed environmental goals. This conclusion is in line with the need to shape new policies within the framework of the EU ETS that prevent excessive low prices for carbon over extended periods of time.

P-SOCRATES: A parallel software framework for time-critical many-core systems

Article in Press, Corrected Proof

Deciding Kleene Algebra Terms Equivalence in Coq

This paper presents a mechanically verified implementation of an algorithm for deciding the equivalence of Kleene algebra terms within the Coq proof assistant. The algorithm decides equivalence of two given regular expressions through an iterated process of testing the equivalence of their partial derivatives and does not require the construction of the corresponding automata. Recent theoretical and experimental research provides evidence that this method is, on average, more efficient than the classical methods based on automata. We present some performance tests, comparisons with similar approaches, and also introduce a generalization of the algorithm to decide the equivalence of terms of Kleene algebra with tests. The motivation for the work presented in this paper is that of using the libraries developed as trusted frameworks for carrying out certified program verification.

Effects of the Mediterranean diet and exercise in subjects with coronary artery disease

Introduction The association of the Mediterranean diet and exercise appears to have a protective role, reducing cardiovascular risk. This study investigated the effects of education sessions on the Mediterranean diet and an exercise program in modifying eating behaviors, body composition and abdominal fat. Methods An experimental study was performed on 20 subjects with known coronary heart disease randomly assigned to experimental (n=10) and control (n=10) groups. Both groups received education sessions on the Mediterranean diet, but the experimental group also followed an eight-week program of specific exercises. A semiquantitative food frequency questionnaire was administered to analyze food intake, bioimpedance was used to measure weight, fat mass and lean mass, and waist circumference was measured to calculate waist-to-height ratio. Results After eight weeks, protein (p<0.05) and cholesterol (p<0.05) intake in the experimental group had decreased significantly compared with the control group. Between the beginning and end of the study, there were significant decreases in the control group in carbohydrate (p<0.05) and saturated fat intake (p<0.05). In both groups the percentage of total fat (p<0.05) and fat mass (p<0.05) was significantly decreased. In the experimental group the waist-to-height ratio was significantly reduced (p<0.05). Conclusion The Mediterranean diet reduced carbohydrate and saturated fat intake, reflected in reduced fat mass. The association of the exercise program showed additional benefits in reduction of protein and cholesterol intake and abdominal fat.

Adhesive thickness effects of a ductile adhesive by optical measurement techniques

Adhesive bonding is an excellent alternative to traditional joining techniques such as welding, mechanical fastening or riveting. However, there are many factors that have to be accounted for during joint design to accurately predict the joint strength. One of these is the adhesive layer thickness (tA). Most of the results are for epoxy structural adhesives, tailored to perform best with small values of tA, and these show that the lap joint strength decreases with increase of tA (the optimum joint strength is usually obtained with tA values between 0.1 and 0.2 mm). Recently, polyurethane adhesives were made available in the market, designed to perform with larger tA values, and whose fracture behaviour is still not studied. In this work, the effect of tA on the tensile fracture toughness (View the MathML source) of a bonded joint is studied, considering a novel high strength and ductile polyurethane adhesive for the automotive industry. This work consists on the fracture characterization of the bond by a conventional and the J-integral techniques, which accurately account for root rotation effects. An optical measurement method is used for the evaluation of crack tip opening (δn) and adherends rotation at the crack tip (θo) during the test, supported by a Matlab® sub-routine for the automated extraction of these parameters. As output of this work, fracture data is provided in traction for the selected adhesive, enabling the subsequent strength prediction of bonded joints.