Hierarchical Kernel and Sub-kernels

This paper shows the theoretical development of hierarchy by kernels and an algorithm used to obtain an interesting class or partition from a hierarchy. Also shown is the theorem about the Kernels Optimal Criterion and how it is expressed as a function of the masses of the points of the vector space and product scale points, the inertia of the cloud formed by those two points or hierarchical nodes, which are called subcores or sub-kernels. The application is made on the terminal efficiency of postgraduate degrees at ESIA, IPN Mexico, along its first 48 years of academic and scientific life and the development of students´ graduation

Math Words and Their Dendrograms

A hierarchical clustering algorithm based on graph theory is presented, which, from generation of a path from a given vertex, builds a math word and calculates clusterization under an index. This is possible due to modification of Tarry’s algorithm, through exchange of path elements. The unidimensional clustering index applied to σ gives us what I have called Tarry’s hierarchy. From the definition of net word, cycle, tree, tree word, and vertex, a theorem on the relationship between vertices, lines, and letters of a labyrinth is shown, which allows the generation of words and their dendrograms with the application of the Euclidean distance. Practical use of these concepts provides possibilities of connections in arrangements for telephone centrals and robotic arms’ paths

Dimensioning of Fractal Fracture on a Concrete Slab

What is presented here is a methodology that allows to study fractures in any material, especially in concrete elements. The importance lies in the moment in which the fracture that occurs in a structural element (slab in our case study) causes a negative effect on its structural behavior. Traditionally, its study is developed from the perspective of fracture mechanics, with which the energy at the tip of the crack or fracture is calculated, and it cannot go further. But the combination of the theories of fracture mechanics and fractal geometry allows us to obtain the patterns of its behavior in the future. Thus, the research was based on tests made on structural elements of concrete, from a slab led to structural failure and choosing a fracture. This was vectorized in order to obtain a fractal axis, which was called state 0, taking three parts or sections of that state and repeating them on a smaller scale. Subsequently, the research was based on five of the methods used for the study and calculation of the fractal dimension: box dimension, perimeter-area dimension, information dimension, mass dimension, and ruler dimension. Most of the fractal dimensions obtained under these methods were similar to each other

Construction of an Artificial Neural Network-Based Method to Detect Structural Damage

This chapter shows the framework used to obtain data with which the artificial neural network (ANN) was developed. It describes its geometry, properties of the material, sections of structural elements, and loads used. Then, the numerical model of the framework under study is developed in structural analysis using SAP2000® software in order to obtain its modal parameters. In addition, a program made in MATLAB® is shown, from which data with and without damage to the framework under study were obtained, and with which the ANN was developed. Data from the numerical model were used to corroborate data obtained with MATLAB®. The neural model used in this work to detect structural damage is described. Data on damage were obtained simulating a plastic hinge in various elements of a test framework, varying the position of the hinge. The above resulted in obtaining various damage conditions for the same framework, which data thus obtained were used to develop the network. Damage conditions were hierarchized based on their fundamental periods in order to know where is more damage, depending on location of the hinge within the framework. Upon completion of the research, we have concluded that the methodology implemented to detect structural damage is rather simple. It was carried out in four steps

La enseñanza de las matemáticas en el siglo XXI / The Teaching of Mathematics in the 21st Century

Este trabajo hace una contribución académica basada en el fortalecimiento del quehacer docente en el nivel superior de las escuelas de ingeniería, con el objetivo de lograr un creciente aprovechamiento en los estudiantes de Ingeniería Civil. Para ello modificamos los elementos usuales de aprendizaje, llevando tal aprendizaje al desarrollo de las aptitudes y la confianza de los alumnos. Se fomentaron estrategias de aprendizaje diferentes a las tradicionales que dieron como resultado que los estudiantes crearan acrósticos, cuentos, historietas, juegos y canciones, con temas basados en las asignaturas afines a las matemáticas: Estática, Física, Estructuras Isostáticas y Resistencia de Materiales, logrando mejorar el entorno educativo de los estudiantes y al mismo tiempo apoyando el aprendizaje mediante el trabajo en equipo y adquiriendo el alumno un conocimiento más profundo de la asignatura.

La enseñanza de las matemáticas en el siglo XXI / The Teaching of Mathematics in the 21st Century

Este trabajo hace una contribución académica basada en el fortalecimiento del quehacer docente en el nivel superior de las escuelas de ingeniería, con el objetivo de lograr un creciente aprovechamiento en los estudiantes de Ingeniería Civil. Para ello modificamos los elementos usuales de aprendizaje, llevando tal aprendizaje al desarrollo de las aptitudes y la confianza de los alumnos. Se fomentaron estrategias de aprendizaje diferentes a las tradicionales que dieron como resultado que los estudiantes crearan acrósticos, cuentos, historietas, juegos y canciones, con temas basados en las asignaturas afines a las matemáticas: Estática, Física, Estructuras Isostáticas y Resistencia de Materiales, logrando mejorar el entorno educativo de los estudiantes y al mismo tiempo apoyando el aprendizaje mediante el trabajo en equipo y adquiriendo el alumno un conocimiento más profundo de la asignatura.

The Changing Landscape for Stroke\ua0Prevention in AF: Findings From the GLORIA-AF Registry Phase 2

Background GLORIA-AF (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients with Atrial Fibrillation) is a prospective, global registry program describing antithrombotic treatment patterns in patients with newly diagnosed nonvalvular atrial fibrillation at risk of stroke. Phase 2 began when dabigatran, the first non\u2013vitamin K antagonist oral anticoagulant (NOAC), became available. Objectives This study sought to describe phase 2 baseline data and compare these with the pre-NOAC era collected during phase 1. Methods During phase 2, 15,641 consenting patients were enrolled (November 2011 to December 2014); 15,092 were eligible. This pre-specified cross-sectional analysis describes eligible patients\u2019 baseline characteristics. Atrial fibrillation disease characteristics, medical outcomes, and concomitant diseases and medications were collected. Data were analyzed using descriptive statistics. Results Of the total patients, 45.5% were female; median age was 71 (interquartile range: 64, 78) years. Patients were from Europe (47.1%), North America (22.5%), Asia (20.3%), Latin America (6.0%), and the Middle East/Africa (4.0%). Most had high stroke risk (CHA2DS2-VASc [Congestive heart failure, Hypertension, Age  6575 years, Diabetes mellitus, previous Stroke, Vascular disease, Age 65 to 74 years, Sex category] score  652; 86.1%); 13.9% had moderate risk (CHA2DS2-VASc = 1). Overall, 79.9% received oral anticoagulants, of whom 47.6% received NOAC and 32.3% vitamin K antagonists (VKA); 12.1% received antiplatelet agents; 7.8% received no antithrombotic treatment. For comparison, the proportion of phase 1 patients (of N = 1,063 all eligible) prescribed VKA was 32.8%, acetylsalicylic acid 41.7%, and no therapy 20.2%. In Europe in phase 2, treatment with NOAC was more common than VKA (52.3% and 37.8%, respectively); 6.0% of patients received antiplatelet treatment; and 3.8% received no antithrombotic treatment. In North America, 52.1%, 26.2%, and 14.0% of patients received NOAC, VKA, and antiplatelet drugs, respectively; 7.5% received no antithrombotic treatment. NOAC use was less common in Asia (27.7%), where 27.5% of patients received VKA, 25.0% antiplatelet drugs, and 19.8% no antithrombotic treatment. Conclusions The baseline data from GLORIA-AF phase 2 demonstrate that in newly diagnosed nonvalvular atrial fibrillation patients, NOAC have been highly adopted into practice, becoming more frequently prescribed than VKA in Europe and North America. Worldwide, however, a large proportion of patients remain undertreated, particularly in Asia and North America. (Global Registry on Long-Term Oral Antithrombotic Treatment in Patients With Atrial Fibrillation [GLORIA-AF]; NCT01468701

Observation of the B0 → ρ0ρ0 decay from an amplitude analysis of B0 → (π+π−)(π+π−) decays

Proton–proton collision data recorded in 2011 and 2012 by the LHCb experiment, corresponding to an integrated luminosity of 3.0 fb−1 , are analysed to search for the charmless B0→ρ0ρ0 decay. More than 600 B0→(π+π−)(π+π−) signal decays are selected and used to perform an amplitude analysis, under the assumption of no CP violation in the decay, from which the B0→ρ0ρ0 decay is observed for the first time with 7.1 standard deviations significance. The fraction of B0→ρ0ρ0 decays yielding a longitudinally polarised final state is measured to be fL=0.745−0.058+0.048(stat)±0.034(syst) . The B0→ρ0ρ0 branching fraction, using the B0→ϕK⁎(892)0 decay as reference, is also reported as B(B0→ρ0ρ0)=(0.94±0.17(stat)±0.09(syst)±0.06(BF))×10−6