Rényi’s residual entropy: A quantile approach

In the present paper, we introduce a quantile based Rényi’s entropy function and its residual version. We study certain properties and applications of the measure. Unlike the residual Rényi’s entropy function, the quantile version uniquely determines the distribution

Maximum Entropy Discrimination

We present a general framework for discriminative estimation based on the maximum entropy principle and its extensions. All calculations involve distributions over structures and/or parameters rather than specific settings and reduce to relative entropy projections. This holds even when the data is not separable within the chosen parametric class, in the context of anomaly detection rather than classification, or when the labels in the training set are uncertain or incomplete. Support vector machines are naturally subsumed under this class and we provide several extensions. We are also able to estimate exactly and efficiently discriminative distributions over tree structures of class-conditional models within this framework. Preliminary experimental results are indicative of the potential in these techniques.

Lecture on Entropy Coding

Considers entropy, fixed length coding, Huffman coding and arithmetic coding

Matlab Code for Entropy Coding

Considers Huffman coding and arithmetic coding

System Design: UML Activity and Sequence Diagrams

In this session we look at how to model flow of control and interactions between components using UML Activity and Sequence Diagrams. This is an introductory session and so for Activity Diagrams we only cover branching, forks and joins and swim lanes, and for Sequence we cover lifelines, messages and returns, and alt, par and opt frames.

System Design: UML Class Diagrams

In this session we look at UML Class Diagrams and how they fit into both the family of UML models, and also the software engineering process. We look at some basic features of class diagrams including properties, operations, associations, generalisation, aggregation and composition.

AS and A level physics through diagrams.

El recurso forma parte de una serie que se basa en el hecho de que las imágenes son más fáciles de memorizar que las palabras. Cubre las especificaciones principales del nivel superior A. El material no está dividido en AS y A2 porque el nivel necesario puede variar de una especificación a otra.

AS and A level biology through diagrams.

El recurso forma parte de una serie que se basa en el hecho de que las imágenes son más fáciles de memorizar que las palabras. Tiene quince secciones que pueden utilizarse tanto en la revisión individual como resumen de clase. Cada tema se resume en una sola página utilizando diagramas anotados y notas breves con un índice completo para facilitar la referencia. Cubre las especificaciones principales del nivel superior A. El material no está dividido en AS y A2 porque el nivel necesario puede variar de una especificación a otra.

AS and A level ICT through diagrams.

Recurso diseñado para la obtención del título de General Certificate of Education Advanced Subsidiary (GCE), en los niveles AS y A2 para las especificaciones AQA, OCR y WJEC, de 2008. Su contenido incluye, entre otros, los siguientes temas: los tipos de procesamientos; datos, información y conocimiento; hardware; software; las personas y los sistemas de TIC; necesidades de gestión y sistemas de información; las TIC en la sociedad y la industria; legislación; negligencia, delincuencia y protección; redes; Internet y comunicación; cuestiones morales, éticas y sociales; políticas de seguridad de las TIC; códigos de conducta. También, contiene preguntas prácticas de los exámenes.

AS and A level economics through diagrams.

Recurso diseñado para la obtención del título de General Certificate of Education Advanced Subsidiary (GCE), en los niveles AS y A2 para las especificaciones AQA, Edexcel, OCR y WJEC, de 2008. Informa sobre las complejas habilidades requeridas para las contestaciones a las preguntas realizadas sobre Economía en los exámenes de AS y A2. Su contenido se divide en dos grandes apartados: Microeconomía y Macroeconomía.

AS and A level government and politics through diagrams.

Recurso diseñado para la obtención del título de General Certificate of Education Advanced Subsidiary (GCE), en los niveles AS y A2 para las especificaciones AQA, Edexcel y OCR, de 2008. Su contenido se divide cinco secciones: introducción a la política; los ciudadanos, la política y la participación en el Reino Unido; el gobierno de UK; los ciudadanos, la política y la participación en USA; el gobierno de Estados Unidos.

Generalized Higher-Order Voronoi Diagrams on Polyhedral Surfaces

We present an algorithm for computing exact shortest paths, and consequently distances, from a generalized source (point, segment, polygonal chain or polygonal region) on a possibly non-convex polyhedral surface in which polygonal chain or polygon obstacles are allowed. We also present algorithms for computing discrete Voronoi diagrams of a set of generalized sites (points, segments, polygonal chains or polygons) on a polyhedral surface with obstacles. To obtain the discrete Voronoi diagrams our algorithms, exploiting hardware graphics capabilities, compute shortest path distances defined by the sites

A Note on the periodic orbits and topological entropy of graph maps

This paper deals with the relationship between the periodic orbits of continuous maps on graphs and the topological entropy of the map. We show that the topological entropy of a graph map can be approximated by the entropy of its periodic orbits

Climate entropy budget of the HadCM3 atmosphere-ocean general circulation model and of FAMOUS, its low resolution version

The entropy budget is calculated of the coupled atmosphere–ocean general circulation model HadCM3. Estimates of the different entropy sources and sinks of the climate system are obtained directly from the diabatic heating terms, and an approximate estimate of the planetary entropy production is also provided. The rate of material entropy production of the climate system is found to be ∼50 mW m−2 K−1, a value intermediate in the range 30–70 mW m−2 K−1 previously reported from different models. The largest part of this is due to sensible and latent heat transport (∼38 mW m−2 K−1). Another 13 mW m−2 K−1 is due to dissipation of kinetic energy in the atmosphere by friction and Reynolds stresses. Numerical entropy production in the atmosphere dynamical core is found to be about 0.7 mW m−2 K−1. The material entropy production within the ocean due to turbulent mixing is ∼1 mW m−2 K−1, a very small contribution to the material entropy production of the climate system. The rate of change of entropy of the model climate system is about 1 mW m−2 K−1 or less, which is comparable with the typical size of the fluctuations of the entropy sources due to interannual variability, and a more accurate closure of the budget than achieved by previous analyses. Results are similar for FAMOUS, which has a lower spatial resolution but similar formulation to HadCM3, while more substantial differences are found with respect to other models, suggesting that the formulation of the model has an important influence on the climate entropy budget. Since this is the first diagnosis of the entropy budget in a climate model of the type and complexity used for projection of twenty-first century climate change, it would be valuable if similar analyses were carried out for other such models.