We say that G is an e-circle graph if there is a bijection between its vertices and straight lines on the cartesian plane such that two vertices are adjacent in G if and only if the corresponding lines intersect inside the circle of radius one. This definition suggests a method for deciding whether a given graph G is an e-circle graph, by constructing a convenient system S of equations and ineq...

We show that the analog of Hamilton's Ricci flow in the combinatorial setting produces solutions which converge exponentially fast to Thurston's circle packing on surfaces. As a consequence, a new proof of Thurston's existence of circle packing theorem is obtained. As another consequence, Ricci flow suggests a new algorithm to find circle packings. §1. Introduction 1.1. For a compact surface wi...

The Sylvester smallest enclosing circle problem involves finding the smallest circle that encloses a finite number of points in the plane. We consider generalized versions of the Sylvester problem in which the points are replaced by sets. Based on the log-exponential smoothing technique and Nesterov’s accelerated gradient method, we present an effective numerical algorithm for solving these pro...

In recent years, many researchers are involved in the field of fuzzy theory. However, there are still a lot of issues to be resolved. Especially on topics related to controller design such as the field of robot, artificial intelligence, and nonlinear systems etc. Besides fuzzy theory, algorithms in swarm intelligence are also a popular field for the researchers. In this paper, a concept of util...

An off-axis pole focusing method for robust direction of arrival (DOA) estimation is presented in this paper. The roots (poles) of the root-MUSIC polynomial are generally evaluated over the unit circle in the z-domain. The DOAs can be computed from these poles using a simple geometric relation. Rather than computing the root-MUSIC polynomial over the unit circle, it can be estimated inside the ...

We use recent advances in circle packing theory to develop a constructive method for the approximation of an analytic function F : Ω → C by circle packing maps providing we have only been given Ω, |F | ∣∣ Ω , and the set of critical points of F . This extends the earlier result of [CR] for F with no critical points.

background and objective: the circle of willis (cow) supports adequate blood supply to the brain. the cardiovascular system, in the current study, is modeled using an equivalent electronic system focusing on the cow. method: in our previous study we used 42 compartments to model whole car- diovascular system. in the current study, nevertheless, we extended our model by using 63 compartments to ...

An area cartogram is a transformed map on which areas of regions are proportional to statistical data values; it is considered to be a powerful tool for the visual representation of statistical data. One of the most familiar cartograms is a circle (or circular) cartogram, on which regions are represented by circles. Dorling first proposed a circle cartogram construction algorithm in 1996 accord...

One of the key issues in microarray analysis is to extract quantitative information from the spots, which represents gene expression levels in the experiments. The process of identifying the spots and separating the foreground from the background is known as microarray image segmentation. In this paper, we propose a new approach to microarray image segmentation, which we called the adaptive ell...

Circle detection is important for many applications. We propose a method for circle detection using a histogram based accumulator space. Our method uses a single accumulator space to find different size circles. It is tested to be robust and able to detect partial circles or circles in partial occlusion. The method is based on finding the distance transform between pixels and edge pixels in the...