A linear algebra approach to OLAP

Inspired by the relational algebra of data processing, this paper addresses the foundations of data analytical processing from a linear algebra perspective. The paper investigates, in particular, how aggregation operations such as cross tabulations and data cubes essential to quantitative analysis of data can be expressed solely in terms of matrix multiplication, transposition and the Khatri–Rao variant of the Kronecker product. The approach offers a basis for deriving an algebraic theory of data consolidation, handling the quantitative as well as qualitative sides of data science in a natural, elegant and typed way. It also shows potential for parallel analytical processing, as the parallelization theory of such matrix operations is well acknowledged.

Desarrollo de Algoritmos Numéricos para el Estudio de la Propagación no Lineal de Ondas en Aplicaciones Aeroespaciales y Astrofísicas. Develop to Numerical Algorithms to Study non-Linear Waves Propagation in Aerospace and Astrophysics Applications.

En este proyecto se desarrollarán algoritmos numéricos para sistemas no lineales hiperbólicos-parabólicos de ecuaciones diferenciales en derivadas parciales. Dichos sistemas tienen aplicación en propagación de ondas en ámbitos aeroespaciales y astrofísicos.Objetivos generales: 1)Desarrollo y mejora de algoritmos numéricos con la finalidad de incrementar la calidad en la simulación de propagación e interacción de ondas gasdinámicas y magnetogasdinámicas no lineales. 2)Desarrollo de códigos computacionales con la finalidad de simular flujos gasdinámicos de elevada entalpía incluyendo cambios químicos, efectos dispersivos y difusivos.3)Desarrollo de códigos computacionales con la finalidad de simular flujos magnetogasdinámicos ideales y reales.4)Aplicación de los nuevos algoritmos y códigos computacionales a la solución del flujo aerotermodinámico alrededor de cuerpos que ingresan en la atmósfera terrestre. 5)Aplicación de los nuevos algoritmos y códigos computacionales a la simulación del comportamiento dinámico no lineal de arcos magnéticos en la corona solar. 6)Desarrollo de nuevos modelos para describir el comportamiento no lineal de arcos magnéticos en la corona solar.Este proyecto presenta como objetivo principal la introducción de mejoras en algoritmos numéricos para simular la propagación e interacción de ondas no lineales en dos medios gaseosos: aquellos que no poseen carga eléctrica libre (flujos gasdinámicos) y aquellos que tienen carga eléctrica libre (flujos magnetogasdinámicos). Al mismo tiempo se desarrollarán códigos computacionales que implementen las mejoras de las técnicas numéricas.Los algoritmos numéricos se aplicarán con la finalidad de incrementar el conocimiento en tópicos de interés en la ingeniería aeroespacial como es el cálculo del flujo de calor y fuerzas aerotermodinámicas que soportan objetos que ingresan a la atmósfera terrestre y en temas de astrofísica como la propagación e interacción de ondas, tanto para la transferencia de energía como para la generación de inestabilidades en arcos magnéticos de la corona solar. Estos dos temas poseen en común las técnicas y algoritmos numéricos con los que serán tratados. Las ecuaciones gasdinámicas y magnetogasdinámicas ideales conforman sistemas hiperbólicos de ecuaciones diferenciales y pueden ser solucionados utilizando "Riemann solvers" junto con el método de volúmenes finitos (Toro 1999; Udrea 1999; LeVeque 1992 y 2005). La inclusión de efectos difusivos genera que los sistemas de ecuaciones resulten hiperbólicos-parabólicos. La contribución parabólica puede ser considerada como términos fuentes y tratada adicionalmente tanto en forma explícita como implícita (Udrea 1999; LeVeque 2005).Para analizar el flujo alrededor de cuerpos que ingresan en la atmósfera se utilizarán las ecuaciones de Navier-Stokes químicamente activas, mientras la temperatura no supere los 6000K. Para mayores temperaturas es necesario considerar efectos de ionización (Anderson, 1989). Tanto los efectos difusivos como los cambios químicos serán considerados como términos fuentes en las ecuaciones de Euler. Para tratar la propagación de ondas, transferencia de energía e inestabilidades en arcos magnéticos de la corona solar se utilizarán las ecuaciones de la magnetogasdinámica ideal y real. En este caso será también conveniente implementar términos fuente para el tratamiento de fenómenos de transporte como el flujo de calor y el de radiación. Los códigos utilizarán la técnica de volúmenes finitos, junto con esquemas "Total Variation Disminishing - TVD" sobre mallas estructuradas y no estructuradas.

Gender-Based Differences in Cardiac Remodeling and ILK Expression after Myocardial Infarction

Background: Gender can influence post-infarction cardiac remodeling. Objective: To evaluate whether gender influences left ventricular (LV) remodeling and integrin-linked kinase (ILK) after myocardial infarction (MI). Methods: Female and male Wistar rats were assigned to one of three groups: sham, moderate MI (size: 20-39% of LV area), and large MI (size: ≥40% of LV area). MI was induced by coronary occlusion, and echocardiographic analysis was performed after six weeks to evaluate MI size as well as LV morphology and function. Real-time RT-PCR and Western blot were used to quantify ILK in the myocardium. Results: MI size was similar between genders. MI resulted in systolic dysfunction and enlargement of end-diastolic as well as end-systolic dimension of LV as a function of necrotic area size in both genders. Female rats with large MI showed a lower diastolic and systolic dilatation than the respective male rats; however, LV dysfunction was similar between genders. Gene and protein levels of ILK were increased in female rats with moderate and large infarctions, but only male rats with large infarctions showed an altered ILK mRNA level. A negative linear correlation was evident between LV dimensions and ILK expression in female rats with large MI. Conclusions: Post-MI ILK expression is altered in a gender-specific manner, and higher ILK levels found in females may be sufficient to improve LV geometry but not LV function.

Describing orbitopes by linear inequalities and projection based tools

Magdeburg, Univ., Fak. für Mathematik, Diss., 2011

Non-linear model reduction and control of molten carbonate fuel cell systems with internal reforming fuel cell systems with internal reforming

Magdeburg, Univ., Diss, 2007

A Novel Algorithm to Quantify Coronary Remodeling Using Inferred Normal Dimensions

Background:Vascular remodeling, the dynamic dimensional change in face of stress, can assume different directions as well as magnitudes in atherosclerotic disease. Classical measurements rely on reference to segments at a distance, risking inappropriate comparison between dislike vessel portions.Objective:to explore a new method for quantifying vessel remodeling, based on the comparison between a given target segment and its inferred normal dimensions.Methods:Geometric parameters and plaque composition were determined in 67 patients using three-vessel intravascular ultrasound with virtual histology (IVUS-VH). Coronary vessel remodeling at cross-section (n = 27.639) and lesion (n = 618) levels was assessed using classical metrics and a novel analytic algorithm based on the fractional vessel remodeling index (FVRI), which quantifies the total change in arterial wall dimensions related to the estimated normal dimension of the vessel. A prediction model was built to estimate the normal dimension of the vessel for calculation of FVRI.Results:According to the new algorithm, “Ectatic” remodeling pattern was least common, “Complete compensatory” remodeling was present in approximately half of the instances, and “Negative” and “Incomplete compensatory” remodeling types were detected in the remaining. Compared to a traditional diagnostic scheme, FVRI-based classification seemed to better discriminate plaque composition by IVUS-VH.Conclusion:Quantitative assessment of coronary remodeling using target segment dimensions offers a promising approach to evaluate the vessel response to plaque growth/regression.

Design of biped robot walking based on non-linear periodical oscillations

Magdeburg, Univ., Fak. für Elektrotechnik und Informationstechnik, Diss., 2012

Riqueza em óleo nas sementes, amêndoas e cascas das bagas de mamona

This paper is a joined publication of the Depts. of Genetics and of Technology, of the E. S. A. "Luiz de Queiroz", Universidade de São Paulo, and deals with the variation of the percentage oil content in the whole seeds, the embryos and the seed-coat of 28 varieties of castor-beans (Ricinus communis, L.). Primarily, the authors, as a justification of this paper, make reference to the applications which castor-oil has in industry, medicine, etc. In accordance with the weight of 100 seeds, the varieties of castor-beans were classified into 3 classes : small seeds (100 seeds less than 30 g), medium seeds (100 seeds between 30 g and 60) and large seeds (100 seeds more than 60 g). The percentage of oil in the seed, embryo and seed-coat, the dimensions of the seeds and the weight of 100 seeds are given for every variety in table 1. In order to obtain an estimate of the variability for the methods of determination of the oil percentage, in the 3 differents parts of the seeds and also in the 3 groups of seeds, the coefficient of variability was calculate (table 2). It is showed that the variation in the seed and embryo is low and that in the seed-coat is very high. The analysis of variance, with regard to the difference among the 3 types of seeds (small, medium and large), among the 3 parts of the seed (whole seed, embryo and seed-coat) and residual error, is given in table 3. Only, the oil content of whole seeds among types of seeds was significant at the 5% level. The t test among the correspondent means is not significant for the difference between medium and large seeds is significant between both these types (medium and large) and small seeds. The fiducial limits in relation to the mean of the oil percentage in the 3 differents types of seed, show that there is one variety (n. 1013-2), which has a percentage of oil, in the medium type of seed, significantly at the 5% level (table 4), higher than the general mean. Since the distribution of the percentage of oil in the seedcoat is discontinuous, 5 groups were established (table 5). All the differences between groups are significant (table 6). For practical purposes, when we have to remove the seed coat, one should eliminate those varieties which loose at least 3% of oil by this procedure. There is a significant linear correlation at 5% level between the percentage of oil in the seed and in the embryo, of the smali and medium type of seeds (table 7), and also, when taking the 3 types together (lower part of table 7), one finds that the same is true. Also, the correlation between the percentages of oil in the embryo and in the seed-coat of the 3 types together is significant at 5% level. According to the results obtained in relation to the percentage in 28 varieties studied, it can be recommended, for breeding purposes, to work only with those varieties which belong to the medium and the large types of seeds.

Optimal designs for multivariate linear models

Magdeburg, Univ., Fak. für Mathematik, Diss., 2013

Sizes of linear descriptions in combinatorial optimization

Otto-von-Guericke-Universität Magdeburg, Fakultät für Mathematik, Univ., Dissertation, 2015

Episodes of the life and death of thin fluid membranes : patterns and dynamics at the cross-over from two to three dimensions

Otto-von Guericke-Universität Magdeburg, Fakultät für Naturwissenschaften, Dissertation, 2016

Buccal apparatus and gastrointestinal tract dimensions associated to the diet of early life stages of Centropomus undecimalis (Centropomidae, Actinopterygii)

The present study aims to compare the buccal apparatus and gastrointestinal tract of early life stages of Centropomus undecimalis (Bloch, 1792), and relate them to its diet. A total of 190 individuals collected with a channel net in the Catuama estuary (07º40'9.9''S, 34º50'36.7''W), northern coast of the state of Pernambuco, were examined. Morphometrical and meristic data were analyzed for the two initial developmental periods (larval and juvenile). Their digestive tube was morphologically characterized and its content identified. The longest transverse axis of food items was measured, and compared to the standard length (SL) and mouth gape size (D) of the individuals. Body measurement regressions differed significantly (p<0.001) between larvae and juveniles. The stomachs with food content (n=118 individuals) presented a proportion of 62% full and 30% empty (being 8% damaged). They differed in relation to the fullness level and presented a coiled shape when empty. The number of food items in relation to SL and D did not present an evident correlation. Larvae (SL<10 mm) feed on small copepods, while juveniles (SL=11.1 to 64.7 mm) ingest larvae of various decapod species, showing a distinct diet between these initial developmental stages.

Linear stochastic differential algebraic equations with constant coefficients

We consider linear stochastic differential-algebraic equations with constant coefficients and additive white noise. Due to the nature of this class of equations, the solution must be defined as a generalised process (in the sense of Dawson and Fernique). We provide sufficient conditions for the law of the variables of the solution process to be absolutely continuous with respect to Lebesgue measure.

Cat(0) and Cat (-1) dimensions of torsion free

We show that a particular free-by-cyclic group has CAT(0) dimension equal to 2, but CAT(-1) dimension equal to 3. We also classify the minimal proper 2-dimensional CAT(0) actions of this group; they correspond, up to scaling, to a 1-parameter family of locally CAT(0) piecewise Euclidean metrics on a fixed presentation complex for the group. This information is used to produce an infinite family of 2-dimensional hyperbolic groups, which do not act properly by isometries on any proper CAT(0) metric space of dimension 2. This family includes a free-by-cyclic group with free kernel of rank 6.