How sufficient conditions are related for topology-preserving reductions

A crucial issue in digital topology is to ensure topology preservation for reductions acting on binary pictures (i.e., operators that never change a white point to black one). Some sufficient conditions for topology-preserving reductions have been proposed for pictures on the three possible regular partitionings of the plane (i.e., the triangular, the square, and the hexagonal grids). In this paper, the relationships among these conditions are stated

Mathematical And Computational Methods For Freeform Optical Shape Description

Slow-servo single-point diamond turning as well as advances in computer controlled small lap polishing enable the fabrication of freeform optics, specifically, optical surfaces for imaging applications that are not rotationally symmetric. Freeform optical elements will have a profound importance in the future of optical technology. Orthogonal polynomials added onto conic sections have been extensively used to describe optical surface shapes. The optical testing industry has chosen to represent the departure of a wavefront under test from a reference sphere in terms of orthogonal φ-polynomials, specifically Zernike polynomials. Various forms of polynomials for describing freeform optical surfaces may be considered, however, both in optical design and in support of fabrication. More recently, radial basis functions were also investigated for optical shape description. In the application of orthogonal φ-polynomials to optical freeform shape description, there are important limitations, such as the number of terms required as well as edge-ringing and ill-conditioning in representing the surface with the accuracy demanded by most stringent optics applications. The first part of this dissertation focuses upon describing freeform optical surfaces with φ-polynomials and shows their limitations when including higher orders together with possible remedies. We show that a possible remedy is to use edge-clusteredfitting grids. Provided different grid types, we furthermore compared the efficacy of using different types of φ-polynomials, namely Zernike and gradient orthogonal Q-polynomials. In the second part of this thesis, a local, efficient and accurate hybrid method is developed in order to greatly reduce the order of polynomial terms required to achieve higher level of accuracy in freeform shape description that were shown to require thousands of terms including many higher order terms under prior art. This comes at the expense of multiple sub-apertures, and as such iv computational methods may leverage parallel processing. This new method combines the assets of both radial basis functions and orthogonal phi-polynomials for freeform shape description and is uniquely applicable across any aperture shape due to its locality and stitching principles. Finally in this thesis, in order to comprehend the possible advantages of parallel computing for optical surface descriptions, the benefits of making an effective use of impressive computational power offered by multi-core platforms for the computation of φ-polynomials are investigated. The φ-polynomials, specifically Zernike and gradient orthogonal Q-polynomials, are implemented with a set of recurrence based parallel algorithms on Graphics Processing Units (GPUs). The results show that more than an order of magnitude speedup is possible in the computation of φ-polynomials over a sequential implementation if the recurrence based parallel algorithms are adopted

Motion Planning and Reconfiguration for Systems of Multiple Objects

This chapter surveys some recent results on motion planning and reconfiguration for systems of multiple objects and for modular systems with applications in robotics.

Semi-Supervised Learning of Cartesian Factors

The existence of place cells (PCs), grid cells (GCs), border cells (BCs), and head direction cells (HCs) as well as the dependencies between them have been enigmatic. We make an effort to explain their nature by introducing the concept of Cartesian Factors. These factors have specific properties: (i) they assume and complement each other, like direction and position and (ii) they have localized discrete representations with predictive attractors enabling implicit metric-like computations. In our model, HCs make the distributed and local representation of direction. Predictive attractor dynamics on that network forms the Cartesian Factor "direction." We embed these HCs and idiothetic visual information into a semi-supervised sparse autoencoding comparator structure that compresses its inputs and learns PCs, the distributed local and direction independent (allothetic) representation of the Cartesian Factor of global space. We use a supervised, information compressing predictive algorithm and form direction sensitive (oriented) GCs from the learned PCs by means of an attractor-like algorithm. Since the algorithm can continue the grid structure beyond the region of the PCs, i.e.,beyond its learning domain, thus the GCs and the PCs together form our metric-like Cartesian Factors of space. We also stipulate that the same algorithm can produce BCs. Our algorithm applies (a) a bag representation that models the "what system" and (b) magnitude ordered place cell activities that model either the integrate-and-fire mechanism, or theta phase precession, or both. We relate the components of the algorithm to the entorhinal-hippocampal complex and to its working. The algorithm requires both spatial and lifetime sparsification that may gain support from the two-stage memory formation of this complex

Eco-ISEA3H, a machine learning ready spatial database for ecometric and species distribution modeling

We present the Eco-ISEA3H database, a compilation of global spatial data characterizing climate, geology, land cover, physical and human geography, and the geographic ranges of nearly 900 large mammalian species. The data are tailored for machine learning (ML)-based ecological modeling, and are intended primarily for continental- to global-scale ecometric and species distribution modeling. Such models are trained on present-day data and applied to the geologic past, or to future scenarios of climatic and environmental change. Model training requires integrated global datasets, describing species' occurrence and environment via consistent observational units. The Eco-ISEA3H database incorporates data from 17 sources, and includes 3,033 variables. The database is built on the Icosahedral Snyder Equal Area (ISEA) aperture 3 hexagonal (3H) discrete global grid system (DGGS), which partitions the Earth's surface into equal-area hexagonal cells. Source data were incorporated at six nested ISEA3H resolutions, using scripts developed and made available here. We demonstrate the utility of the database in a case study analyzing the bioclimatic envelopes of ten large, widely distributed mammalian species.Peer reviewe

Ray trace modeling in a solar secondary concentrator with various inlet shapes"

Este Trabajo Fin de Máster está enfocado a las plantas de energía solar concentrada, las cuales usan heliostatos para concentrar la radiación solar en un área relativamente pequeña, con el fin de calentar un fluido. En este Trabajo Fin de Máster un concentrador secundario forma parte del sistema. El software MIRVAL es utilizado para el trazado de los rayos desde el sol hasta el concentrador secundario. Una vez los rayos entran al concentrador, FORTRAN se utilizará para realizar los cálculos de la trayectoria de los rayos. La forma del concentrador secundario se definirá primero en SOLIDWORKS y después se creará una malla en ANSYS. La potencia absorbida en el concentrador secundario se graficará con MATLAB. Asimismo, se creará una nueva forma de concentrador secundario la cual será añadida al código y simulada. Con varias formas de concentrador secundario, se podrá crear el óptimo en función del campo de heliostatos dado.Departamento de Ingeniería Energética y FluidomecánicaMáster en Ingeniería Industria