On infinite graphs and related matrices

This thesis Entitled On Infinite graphs and related matrices.ln the last two decades (iraph theory has captured wide attraction as a Mathematical model for any system involving a binary relation. The theory is intimately related to many other branches of Mathematics including Matrix Theory Group theory. Probability. Topology and Combinatorics . and has applications in many other disciplines..Any sort of study on infinite graphs naturally involves an attempt to extend the well known results on the much familiar finite graphs. A graph is completely determined by either its adjacencies or its incidences. A matrix can convey this information completely. This makes a proper labelling of the vertices. edges and any other elements considered, an inevitable process. Many types of labelling of finite graphs as Cordial labelling, Egyptian labelling, Arithmetic labeling and Magical labelling are available in the literature. The number of matrices associated with a finite graph are too many For a study ofthis type to be exhaustive. A large number of theorems have been established by various authors for finite matrices. The extension of these results to infinite matrices associated with infinite graphs is neither obvious nor always possible due to convergence problems. In this thesis our attempt is to obtain theorems of a similar nature on infinite graphs and infinite matrices. We consider the three most commonly used matrices or operators, namely, the adjacency matrix

Grey Level Co-Occurrence Matrices: Generalisation And Some New Features

Grey Level Co-occurrence Matrices (GLCM) are one of the earliest techniques used for image texture analysis. In this paper we defined a new feature called trace extracted from the GLCM and its implications in texture analysis are discussed in the context of Content Based Image Retrieval (CBIR). The theoretical extension of GLCM to n-dimensional gray scale images are also discussed. The results indicate that trace features outperform Haralick features when applied to CBIR.

Movimientos Sociales, matrices socio-políticos y nuevos escenarios en América Latina

Seit einigen Jahren erfährt Lateinamerika einen epochalen Umbruch. Das neoliberale Modell ist in einer Krise. Die Politik des „Washington Consensus“ und das Diktum einer politisch nicht kontrollierbaren Globalisierung werden zunehmend hinterfagt. Aus der Linkswende haben sich neue alternative Politikkonzepten entwickelt. In dem vorliegenden Working Paper wird auf die Beziehung von sozialen Bewegungen, Ideologien und Regierungen eingegangen. In ihrer Diagnose arbeitet Maristella Svampa die ambivalenten Charakteristiken des aktuellen Wandels in Lateinamerika heraus. Daran schließt eine analytische Annäherung an die verschiedenen ideologischen Traditionen an, die den Widerstandssektor prägen. Abschließend werden bei der Analyse der vier wichtigsten Tendenzen einige der wichtigsten Daten über die Region präsentiert. Zu diesen Tendenzen gehören der Fortschritt der indigenen Kämpfe, die Konsolidierung neuer Formen des Kampfes, die Reaktivierung der national-populären Tradition, sowie die Rückkehr des „Desarrollismo“. Letztere wird sowohl von progressiven als auch eher konservativ-neoliberalen Regierungen unterstützt.

Learning Linear, Sparse, Factorial Codes

In previous work (Olshausen & Field 1996), an algorithm was described for learning linear sparse codes which, when trained on natural images, produces a set of basis functions that are spatially localized, oriented, and bandpass (i.e., wavelet-like). This note shows how the algorithm may be interpreted within a maximum-likelihood framework. Several useful insights emerge from this connection: it makes explicit the relation to statistical independence (i.e., factorial coding), it shows a formal relationship to the algorithm of Bell and Sejnowski (1995), and it suggests how to adapt parameters that were previously fixed.

Sparse Representations of Multiple Signals

We discuss the problem of finding sparse representations of a class of signals. We formalize the problem and prove it is NP-complete both in the case of a single signal and that of multiple ones. Next we develop a simple approximation method to the problem and we show experimental results using artificially generated signals. Furthermore,we use our approximation method to find sparse representations of classes of real signals, specifically of images of pedestrians. We discuss the relation between our formulation of the sparsity problem and the problem of finding representations of objects that are compact and appropriate for detection and classification.

Sparse Correlation Kernel Analysis and Reconstruction

This paper presents a new paradigm for signal reconstruction and superresolution, Correlation Kernel Analysis (CKA), that is based on the selection of a sparse set of bases from a large dictionary of class- specific basis functions. The basis functions that we use are the correlation functions of the class of signals we are analyzing. To choose the appropriate features from this large dictionary, we use Support Vector Machine (SVM) regression and compare this to traditional Principal Component Analysis (PCA) for the tasks of signal reconstruction, superresolution, and compression. The testbed we use in this paper is a set of images of pedestrians. This paper also presents results of experiments in which we use a dictionary of multiscale basis functions and then use Basis Pursuit De-Noising to obtain a sparse, multiscale approximation of a signal. The results are analyzed and we conclude that 1) when used with a sparse representation technique, the correlation function is an effective kernel for image reconstruction and superresolution, 2) for image compression, PCA and SVM have different tradeoffs, depending on the particular metric that is used to evaluate the results, 3) in sparse representation techniques, L_1 is not a good proxy for the true measure of sparsity, L_0, and 4) the L_epsilon norm may be a better error metric for image reconstruction and compression than the L_2 norm, though the exact psychophysical metric should take into account high order structure in images.

An Equivalence Between Sparse Approximation and Support Vector Machines

In the first part of this paper we show a similarity between the principle of Structural Risk Minimization Principle (SRM) (Vapnik, 1982) and the idea of Sparse Approximation, as defined in (Chen, Donoho and Saunders, 1995) and Olshausen and Field (1996). Then we focus on two specific (approximate) implementations of SRM and Sparse Approximation, which have been used to solve the problem of function approximation. For SRM we consider the Support Vector Machine technique proposed by V. Vapnik and his team at AT&T Bell Labs, and for Sparse Approximation we consider a modification of the Basis Pursuit De-Noising algorithm proposed by Chen, Donoho and Saunders (1995). We show that, under certain conditions, these two techniques are equivalent: they give the same solution and they require the solution of the same quadratic programming problem.

Guía para la construcción de matrices insumo-producto y de contabilidad social en Colombia

Las matrices insumo-producto y de contabilidad social constituyen fuentes de información importante para el entendimiento de las relaciones productivas y económicas de un país en un determinado momento del tiempo. En Colombia, la construcción de estos instrumentos tiene una larga experiencia aunque poca ha sido su documentación. Este artículo pretende exponer de manera clara y concisa el procedimiento necesario para su construcción.

Las matrices, la base 2 y la tecnología digital.

Mediante dos juegos de adivinación de números en unas tablas, se estudia cómo la base 2 y las matrices son fundamentales en la tecnología digital. Además se aporta la implementación en el programa informático Mathematica del algoritmo que permite realizar esta acción. En el artículo se muestra paso a paso cómo realizar estos juegos.

De la escuela infantil a la escuela primaria : ¿continuidad o ruptura en las matrices interactivas de la enseñanza y el aprendizaje?

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Caracterización del conocimiento matemático para la enseñanza (MKT) de matrices en Bachillerato.

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El test de matrices progresivas de Raven : manual de aplicación y baremación española en preescolar y EGB.

Trabajo que recoge los resultados tras la aplicación del test de Raven en diferentes grupos de EGB para conocer de manera objetiva la realidad de los alumnos españoles de este nivel educativo. Todo ello va precedido por unas normas simplificadas de aplicación, acompañadas de las que dió el autor del test, y un estudio sintético y práctico de las variadas y diversas potencialidades del mismo encaminadas al conocimiento exhaustivo del examinando, así como diversas observaciones prácticas del autor..

Grafos e matrices. 'Gráficas y matrices'.

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Grafos e matrices. 'Grafos y matrices'.

Se introduce en el nuevo Bachillerato el tema 'grafos y matrices' cuyo objetivo principal es aportar una nueva justificación de la utilización de las matrices e introducir al alumno en la teoría de los grafos. Se hace una introducción a los elementos básicos de esta teoría definiendo brevemente algunos de ellos.

Introducción de las matrices de valoración analítica en el proceso de evaluación del Practicum de los Grados de Infantil y de Primaria.

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