An efficient algorithm for partitioning parameterized polygons into rectangles

In this paper, we propose an algorithm for partitioning parameterized orthogonal polygons into rectangles. The algorithm is based on the plane-sweep technique and can be used for partitioning polygons which contain holes. The input to the algorithm consists of the contour of a parameterized polygon to be partitioned and the constraints for those parameters which reside in the contour. The algorithm uses horizontal cuts only and generates a minimum number of rectangles whose union is the original orthogonal polygon. The proposed algorithm can be used as the basis to build corner stitching data structure for parameterized VLSI layouts and has been implemented in Java programming language. Copyright © 2010 ACM, Inc.

Using sentinels to detect intersections of convex and nonconvex polygons

We describe finite sets of points, called sentinels, which allow us to decide if isometric copies of polygons, convex or not, intersect. As an example of the applicability of the concept of sentinel, we explain how they can be used to formulate an algorithm based on the optimization of differentiable models to pack polygons in convex sets. Mathematical subject classification: 90C53, 65K05.

Disaggregation of polygons of surficial geology and soil maps using spatial modelling and legacy data

Examples from the Murray-Darling basin in Australia are used to illustrate different methods of disaggregation of reconnaissance-scale maps. One approach for disaggregation revolves around the de-convolution of the soil-landscape paradigm elaborated during a soil survey. The descriptions of soil ma units and block diagrams in a soil survey report detail soil-landscape relationships or soil toposequences that can be used to disaggregate map units into component landscape elements. Toposequences can be visualised on a computer by combining soil maps with digital elevation data. Expert knowledge or statistics can be used to implement the disaggregation. Use of a restructuring element and k-means clustering are illustrated. Another approach to disaggregation uses training areas to develop rules to extrapolate detailed mapping into other, larger areas where detailed mapping is unavailable. A two-level decision tree example is presented. At one level, the decision tree method is used to capture mapping rules from the training area; at another level, it is used to define the domain over which those rules can be extrapolated. (C) 2001 Elsevier Science B.V. All rights reserved.

Comparing a current-carrying circular wire with polygons of equal perimeter: Magnetic field versus magnetic flux

We compare the magnetic field at the centre and the self-magnetic flux through a current-carrying circular loop, with those obtained for current-carrying polygons with the same perimeter. As the magnetic field diverges at the position of the wires, we compare the self-fluxes utilizing several regularization procedures. The calculation is best performed utilizing the vector potential, thus highlighting its usefulness in practical applications. Our analysis answers some of the intuition challenges students face when they encounter a related simple textbook example. These results can be applied directly to the determination of mutual inductances in a variety of situations.

A note on parallelizing the parameterized expectations algorithm

The parameterized expectations algorithm (PEA) involves a long simulation and a nonlinear least squares (NLS) fit, both embedded in a loop. Both steps are natural candidates for parallelization. This note shows that parallelization can lead to important speedups for the PEA. I provide example code for a simple model that can serve as a template for parallelization of more interesting models, as well as a download link for an image of a bootable CD that allows creation of a cluster and execution of the example code in minutes, with no need to install any software.

On slicewise monotone parameterized problems and optimal proof systems for TAUT

"Vegeu el resum a l'inici del document del fitxer adjunt"

The average crossing number of equilateral random polygons.

In this paper, we study the average crossing number of equilateral random walks and polygons. We show that the mean average crossing number ACN of all equilateral random walks of length n is of the form . A similar result holds for equilateral random polygons. These results are confirmed by our numerical studies. Furthermore, our numerical studies indicate that when random polygons of length n are divided into individual knot types, the for each knot type can be described by a function of the form where a, b and c are constants depending on and n0 is the minimal number of segments required to form . The profiles diverge from each other, with more complex knots showing higher than less complex knots. Moreover, the profiles intersect with the ACN profile of all closed walks. These points of intersection define the equilibrium length of , i.e., the chain length at which a statistical ensemble of configurations with given knot type -upon cutting, equilibration and reclosure to a new knot type -does not show a tendency to increase or decrease . This concept of equilibrium length seems to be universal, and applies also to other length-dependent observables for random knots, such as the mean radius of gyration Rg.

The average inter-crossing number of equilateral random walks and polygons

In this paper, we study the average inter-crossing number between two random walks and two random polygons in the three-dimensional space. The random walks and polygons in this paper are the so-called equilateral random walks and polygons in which each segment of the walk or polygon is of unit length. We show that the mean average inter-crossing number ICN between two equilateral random walks of the same length n is approximately linear in terms of n and we were able to determine the prefactor of the linear term, which is a = (3 In 2)/(8) approximate to 0.2599. In the case of two random polygons of length n, the mean average inter-crossing number ICN is also linear, but the prefactor of the linear term is different from that of the random walks. These approximations apply when the starting points of the random walks and polygons are of a distance p apart and p is small compared to n. We propose a fitting model that would capture the theoretical asymptotic behaviour of the mean average ICN for large values of p. Our simulation result shows that the model in fact works very well for the entire range of p. We also study the mean ICN between two equilateral random walks and polygons of different lengths. An interesting result is that even if one random walk (polygon) has a fixed length, the mean average ICN between the two random walks (polygons) would still approach infinity if the length of the other random walk (polygon) approached infinity. The data provided by our simulations match our theoretical predictions very well.

Parameterized expectations approach; Some practical issues

We discuss some practical issues related to the use of the Parameterized Expectations Approach (PEA) for solving non-linear stochastic dynamic models with rational expectations. This approach has been applied in models of macroeconomics, financial economics, economic growth, contracttheory, etc. It turns out to be a convenient algorithm, especially when there is a large number of state variables and stochastic shocks in the conditional expectations. We discuss some practical issues having to do with the application of the algorithm, and we discuss a Fortran program for implementing the algorithm that is available through the internet.We discuss these issues in a battery of six examples.

Hierarchical Object Recognition Using Libraries of Parameterized Model Sub-Parts

This thesis describes the development of a model-based vision system that exploits hierarchies of both object structure and object scale. The focus of the research is to use these hierarchies to achieve robust recognition based on effective organization and indexing schemes for model libraries. The goal of the system is to recognize parameterized instances of non-rigid model objects contained in a large knowledge base despite the presence of noise and occlusion. Robustness is achieved by developing a system that can recognize viewed objects that are scaled or mirror-image instances of the known models or that contain components sub-parts with different relative scaling, rotation, or translation than in models. The approach taken in this thesis is to develop an object shape representation that incorporates a component sub-part hierarchy- to allow for efficient and correct indexing into an automatically generated model library as well as for relative parameterization among sub-parts, and a scale hierarchy- to allow for a general to specific recognition procedure. After analysis of the issues and inherent tradeoffs in the recognition process, a system is implemented using a representation based on significant contour curvature changes and a recognition engine based on geometric constraints of feature properties. Examples of the system's performance are given, followed by an analysis of the results. In conclusion, the system's benefits and limitations are presented.

Polygons. Materiales didácticos digitales para secciones bilingües.

El trabajo obtuvo el tercer premio de la modalidad C: 'Una escuela del siglo XXI', de los Premios Joaquín Sama 2008