CoDa-dendrogram: A new exploratory too

The use of orthonormal coordinates in the simplex and, particularly, balance coordinates, has suggested the use of a dendrogram for the exploratory analysis of compositional data. The dendrogram is based on a sequential binary partition of a compositional vector into groups of parts. At each step of a partition, one group of parts is divided into two new groups, and a balancing axis in the simplex between both groups is defined. The set of balancing axes constitutes an orthonormal basis, and the projections of the sample on them are orthogonal coordinates. They can be represented in a dendrogram-like graph showing: (a) the way of grouping parts of the compositional vector; (b) the explanatory role of each subcomposition generated in the partition process; (c) the decomposition of the total variance into balance components associated with each binary partition; (d) a box-plot of each balance. This representation is useful to help the interpretation of balance coordinates; to identify which are the most explanatory coordinates; and to describe the whole sample in a single diagram independently of the number of parts of the sample

A Factor analysis of hidrochemical composition of Llobregat river basin

Hydrogeological research usually includes some statistical studies devised to elucidate mean background state, characterise relationships among different hydrochemical parameters, and show the influence of human activities. These goals are achieved either by means of a statistical approach or by mixing models between end-members. Compositional data analysis has proved to be effective with the first approach, but there is no commonly accepted solution to the end-member problem in a compositional framework. We present here a possible solution based on factor analysis of compositions illustrated with a case study. We find two factors on the compositional bi-plot fitting two non-centered orthogonal axes to the most representative variables. Each one of these axes defines a subcomposition, grouping those variables that lay nearest to it. With each subcomposition a log-contrast is computed and rewritten as an equilibrium equation. These two factors can be interpreted as the isometric log-ratio coordinates (ilr) of three hidden components, that can be plotted in a ternary diagram. These hidden components might be interpreted as end-members. We have analysed 14 molarities in 31 sampling stations all along the Llobregat River and its tributaries, with a monthly measure during two years. We have obtained a bi-plot with a 57% of explained total variance, from which we have extracted two factors: factor G, reflecting geological background enhanced by potash mining; and factor A, essentially controlled by urban and/or farming wastewater. Graphical representation of these two factors allows us to identify three extreme samples, corresponding to pristine waters, potash mining influence and urban sewage influence. To confirm this, we have available analysis of diffused and widespread point sources identified in the area: springs, potash mining lixiviates, sewage, and fertilisers. Each one of these sources shows a clear link with one of the extreme samples, except fertilisers due to the heterogeneity of their composition. This approach is a useful tool to distinguish end-members, and characterise them, an issue generally difficult to solve. It is worth note that the end-member composition cannot be fully estimated but only characterised through log-ratio relationships among components. Moreover, the influence of each endmember in a given sample must be evaluated in relative terms of the other samples. These limitations are intrinsic to the relative nature of compositional data

Regression analysis of compositional data when both the dependent variable and independent variable are components

It is well known that regression analyses involving compositional data need special attention because the data are not of full rank. For a regression analysis where both the dependent and independent variable are components we propose a transformation of the components emphasizing their role as dependent and independent variables. A simple linear regression can be performed on the transformed components. The regression line can be depicted in a ternary diagram facilitating the interpretation of the analysis in terms of components. An exemple with time-budgets illustrates the method and the graphical features

Compositional evolution with mass transfer in closed systems

Evolution of compositions in time, space, temperature or other covariates is frequent in practice. For instance, the radioactive decomposition of a sample changes its composition with time. Some of the involved isotopes decompose into other isotopes of the sample, thus producing a transfer of mass from some components to other ones, but preserving the total mass present in the system. This evolution is traditionally modelled as a system of ordinary di erential equations of the mass of each component. However, this kind of evolution can be decomposed into a compositional change, expressed in terms of simplicial derivatives, and a mass evolution (constant in this example). A rst result is that the simplicial system of di erential equations is non-linear, despite of some subcompositions behaving linearly. The goal is to study the characteristics of such simplicial systems of di erential equa- tions such as linearity and stability. This is performed extracting the compositional dif ferential equations from the mass equations. Then, simplicial derivatives are expressed in coordinates of the simplex, thus reducing the problem to the standard theory of systems of di erential equations, including stability. The characterisation of stability of these non-linear systems relays on the linearisation of the system of di erential equations at the stationary point, if any. The eigenvelues of the linearised matrix and the associated behaviour of the orbits are the main tools. For a three component system, these orbits can be plotted both in coordinates of the simplex or in a ternary diagram. A characterisation of processes with transfer of mass in closed systems in terms of stability is thus concluded. Two examples are presented for illustration, one of them is a radioactive decay

Sonic Labyrinths

A web page describing how the music was composed, including a diagram of the labyrinth that forms its basis.

MA230exam00

Exam questions and solutions in LaTex

MA230exam00pdf

Exam questions and solutions in PDF

Dirección basada en pensamiento sistémico-caso de estudio Hospital-Engativá – proceso cartera gestión de cobro y recaudo

El pensamiento sistémico es una manera de interpretar y comprender los fenómenos, que difiere de la forma convencional denominada reduccionista en la que no se realiza la comprensión a través de la descomposición de las partes, sino que se realiza haciendo énfasis en la comprensión del sistema como un todo y en las interrelaciones que se desprenden del sistema; por tanto la interpretación no se da a partir de un análisis de causa efecto, sino una comprensión del sistema dentro del contexto de un todo superior. Esta investigación se realiza aplicando el pensamiento sistémico en un caso práctico de una organización como es el Hospital Engativá, se hace la interpretación de la organización desde el punto de vista sistémico, realizando un diagrama causal que permite leer la organización desde este punto de vista. Se desarrolló el modelo en una herramienta para dinámica de sistemas y se limita el diseño y la simulación al Proceso de Cartera – Gestión Cobro y Recaudo, realizando una lectura e interpretación de los resultados y hallazgos arrojados por el modelo. Por último se concluye que es factible dirigir una organización desde el pensamiento sistémico y que mejora la toma de decisiones.

Notes on analogue and digital amplitude modulation

Notes on AM, DSBSC, QAM, BPSK, 4QAM, 8PSK, 16QAM

System Design: Using UML Use Cases

In this lecture we cover how UML Use Cases can be used for requirements capture. We look at the anatomy of a Use Case Description, and the way in which use cases can be brought together in a use case diagram. We also look at the way that use cases can be derived from problems using noun verb analysis.

Adding pictures, SmartArt and drawings to a thesis in MS Word 2010 (PC) Manual

Adding illustrations can make it much easier to make a point in a thesis. Download this manual on how in insert pictures, insert SmartArt (a selection of pre-defined diagram types) and draw your own diagram with shapes in MS Word 2010. The guide also shows you how to create a Table of Figures in the thesis.

Adding pictures, SmartArt and drawings to a thesis in MS Word 2011 (Mac) Manual

Adding illustrations can make it much easier to make a point in a thesis. Download this manual on how in insert pictures, insert SmartArt (a selection of pre-defined diagram types) and draw your own diagram with shapes in MS Word 2011. The guide also shows you how to create a Table of Figures in the thesis.

VSM en Prosectorglas S,A,S.

Como aun adición al documento “Estrategias para la Internacionalización en Prosectorglass SAS.” Se desarrolla la VSM del estado actual de la producción para ofrecer a la compañía una herramienta de evaluación y revisión de sus procesos e identificación de desperdicios. Esta herramienta se elabora teniendo en cuenta análisis de tempos de ciclo, y diagramas de producción elaborados también en el desarrollo del ejercicios.

Adding pictures, SmartArt and drawings to a thesis in MS Word 2013 (PC) Manual

Adding illustrations can make it much easier to make a point in a thesis. Download this manual on how in insert pictures, insert SmartArt (a selection of pre-defined diagram types) and draw your own diagram with shapes in MS Word 2013. The guide also shows you how to create a Table of Figures in the thesis.

Southampton Learning Environment

This interactive diagram provides an overview of the SLE at the start of 2015 - this vision is likely to evolve and further versions of the diagram will follow.