Topology

Lecture notes about topology, diagrams for the notes are all together in the support.zip file, as .eps files

Point Set Topology

Lecture notes about point set toplogy

Fuzzy cluster analysis on Spanish public universities. 'Análisis de agrupaciones difusas en las universidades públicas españolas'.

Resumen basado en el de la publicación

El cuento como transmisor de valores : Warm fuzzy tale y Le conte chaud et doux des Chaudoudoux.

Transmitir valores a través de los contenidos de un programa es uno de los objetivos de la Reforma. El profesor de Lengua Extranjera puede contribuir a difundir ciertos valores en el aula eligiendo adecuadamente los materiales. El cuento, precisamente por su valor educativo, es uno de los materiales que a menudo se utilizan en el aula de idiomas. El cuento de C. Steiner 'Warm Fuzzy tale' y su adaptación francesa 'Le conte chaud te doux des chaudoudoux' basan su argumento en la necesidad de amor que existe en todo ser humano y los valores que se derivan de su presencia/ausencia. En este artículo hemos analizado estos valores tanto a través del argumento como de las ilustraciones de ambas versiones.

Analyzing data from a fuzzy rating scale-based questionnaire : a case study

Resumen tomado de la publicaci??n

A Homogeneous Set-Theoretical Frame for Clustering Fuzzy Relational Data

Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on cardinality of the fuzzy subsets that represent objects and their complementaries, without applying any crisp property. From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions it is defined a fuzzy proximity relation. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and features by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear all the process

Effective atomic orbitals for fuzzy atoms

The method of extracting effective atomic orbitals and effective minimal basis sets from molecular wave function characterizing the state of an atom in a molecule is developed in the framework of the "fuzzy" atoms. In all cases studied, there were as many effective orbitals that have considerable occupation numbers as orbitals in the classical minimal basis. That is considered to be of high conceptual importance

Energy partitioning for "fuzzy" atoms

The total energy of molecule in terms of 'fuzzy atoms' presented as sum of one- and two-atomic energy components is described. The divisions of three-dimensional physical space into atomic regions exhibit continuous transition from one to another. The energy components are on chemical energy scale according to proper definitions. The Becke's integration scheme and weight function determines realization of method which permits effective numerical integrations

Fuzzy set Theory and Quantum Chemistry

Es discuteixen breument algunes consideracions sobre l'aplicació de la Teoria dels Conjunts difusos a la Química quàntica. Es demostra aqui que molts conceptes químics associats a la teoria són adequats per ésser connectats amb l'estructura dels Conjunts difusos. També s'explica com algunes descripcions teoriques dels observables quàntics es potencien tractant-les amb les eines associades als esmentats Conjunts difusos. La funció densitat es pren com a exemple de l'ús de distribucions de possibilitat al mateix temps que les distribucions de probabilitat quàntiques

Efficient topology estimation for large scale optical mapping

Large scale image mosaicing methods are in great demand among scientists who study different aspects of the seabed, and have been fostered by impressive advances in the capabilities of underwater robots in gathering optical data from the seafloor. Cost and weight constraints mean that lowcost Remotely operated vehicles (ROVs) usually have a very limited number of sensors. When a low-cost robot carries out a seafloor survey using a down-looking camera, it usually follows a predetermined trajectory that provides several non time-consecutive overlapping image pairs. Finding these pairs (a process known as topology estimation) is indispensable to obtaining globally consistent mosaics and accurate trajectory estimates, which are necessary for a global view of the surveyed area, especially when optical sensors are the only data source. This thesis presents a set of consistent methods aimed at creating large area image mosaics from optical data obtained during surveys with low-cost underwater vehicles. First, a global alignment method developed within a Feature-based image mosaicing (FIM) framework, where nonlinear minimisation is substituted by two linear steps, is discussed. Then, a simple four-point mosaic rectifying method is proposed to reduce distortions that might occur due to lens distortions, error accumulation and the difficulties of optical imaging in an underwater medium. The topology estimation problem is addressed by means of an augmented state and extended Kalman filter combined framework, aimed at minimising the total number of matching attempts and simultaneously obtaining the best possible trajectory. Potential image pairs are predicted by taking into account the uncertainty in the trajectory. The contribution of matching an image pair is investigated using information theory principles. Lastly, a different solution to the topology estimation problem is proposed in a bundle adjustment framework. Innovative aspects include the use of fast image similarity criterion combined with a Minimum spanning tree (MST) solution, to obtain a tentative topology. This topology is improved by attempting image matching with the pairs for which there is the most overlap evidence. Unlike previous approaches for large-area mosaicing, our framework is able to deal naturally with cases where time-consecutive images cannot be matched successfully, such as completely unordered sets. Finally, the efficiency of the proposed methods is discussed and a comparison made with other state-of-the-art approaches, using a series of challenging datasets in underwater scenarios

A genetic algorithm for the design of a fuzzy controller for active queue management

Active queue management (AQM) policies are those policies of router queue management that allow for the detection of network congestion, the notification of such occurrences to the hosts on the network borders, and the adoption of a suitable control policy. This paper proposes the adoption of a fuzzy proportional integral (FPI) controller as an active queue manager for Internet routers. The analytical design of the proposed FPI controller is carried out in analogy with a proportional integral (PI) controller, which recently has been proposed for AQM. A genetic algorithm is proposed for tuning of the FPI controller parameters with respect to optimal disturbance rejection. In the paper the FPI controller design metodology is described and the results of the comparison with random early detection (RED), tail drop, and PI controller are presented.

Probing the large-scale topology of the heliospheric magnetic field using Jovian electrons

Jupiter’s magnetosphere acts as a point source of near-relativistic electrons within the heliosphere. In this study, three solar cycles of Jovian electron data in near-Earth space are examined. Jovian electron intensity is found to peak for an ideal Parker spiral connection, but with considerable spread about this point. Assuming the peak in Jovian electron counts indicates the best magnetic connection to Jupiter, we find a clear trend for fast and slow solar wind to be over- and under-wound with respect to the ideal Parker spiral, respectively. This is shown to be well explained in terms of solar wind stream interactions. Thus, modulation of Jovian electrons by corotating interaction regions (CIRs) may primarily be the result of changing magnetic connection, rather than CIRs acting as barriers to cross-field diffusion. By using Jovian electrons to remote sensing magnetic connectivity with Jupiter’s magnetosphere, we suggest that they provide a means to validate solar wind models between 1 and 5 AU, even when suitable in situ solar wind observations are not available. Furthermore, using Jovian electron observations as probes of heliospheric magnetic topology could provide insight into heliospheric magnetic field braiding and turbulence, as well as any systematic under-winding of the heliospheric magnetic field relative to the Parker spiral from footpoint motion of the magnetic field.

A fuzzy approach for the network congestion problem

In the recent years, the unpredictable growth of the Internet has moreover pointed out the congestion problem, one of the problems that historicallyha ve affected the network. This paper deals with the design and the evaluation of a congestion control algorithm which adopts a FuzzyCon troller. The analogyb etween Proportional Integral (PI) regulators and Fuzzycon trollers is discussed and a method to determine the scaling factors of the Fuzzycon troller is presented. It is shown that the Fuzzycon troller outperforms the PI under traffic conditions which are different from those related to the operating point considered in the design.

Parallel genetic algorithms for the tuning of a fuzzy AQM controller

This paper presents the results of the application of a parallel Genetic Algorithm (GA) in order to design a Fuzzy Proportional Integral (FPI) controller for active queue management on Internet routers. The Active Queue Management (AQM) policies are those policies of router queue management that allow the detection of network congestion, the notification of such occurrences to the hosts on the network borders, and the adoption of a suitable control policy. Two different parallel implementations of the genetic algorithm are adopted to determine an optimal configuration of the FPI controller parameters. Finally, the results of several experiments carried out on a forty nodes cluster of workstations are presented.