Categorizing with Catastrophic Radii in Numerical Minimization

2020 ◽  
Author(s):  
Adam B. Levy
Keyword(s):  
Numerical Minimization

Design and Analysis of a New Mechanism for a Snake Like Robot

2020 ◽  
Author(s):  
Johnathon Garcia ◽  
Kooktae Lee
Keyword(s):  
Power Loss ◽  
Robot Design ◽  
The Novel ◽  
Loss Minimization ◽  
Positive Power ◽  
Unit Distance ◽  
Novel Structure ◽  
3D Printed ◽  
Numerical Minimization ◽  
Novel Design

Abstract In this paper, a novel snake like robot design is presented and analyzed. The structure described desires to obtain a robot that is most like a snake found in nature. This is achieved with the combination of both rigid and soft link structures by implementing a 3D printed rigid link and a soft cast silicone skin. The proposed structure serves to have a few mechanical improvements while maintaining the positives of previous designs. The implementation of the silicone skin presents the opportunity to use synthetic scales and directional friction. The design modifications of this novel design are analyzed on the fronts of the kinematics and minimizing power loss. Minimization of power loss is done through a numerical minimization of three separate parameters with the smallest positive power loss being used. This results in the minimal power loss per unit distance. This research found that the novel structure presented can be effectively described and modeled, such that they could be applied to a constructed model.

scholarly journals Robust Regression with Density Power Divergence: Theory, Comparisons, and Data Analysis

Entropy ◽  
2020 ◽  
Vol 22 (4) ◽  
pp. 399 ◽  
Author(s):  
Marco Riani ◽  
Anthony C. Atkinson ◽  
Aldo Corbellini ◽  
Domenico Perrotta
Keyword(s):  
Robust Regression ◽  
Robust Statistics ◽  
Estimation Method ◽  
Estimation Procedure ◽  
Breakdown Point ◽  
Parameter Estimates ◽  
Normal Density ◽  
Density Power Divergence ◽  
Numerical Minimization ◽  
Power Divergence

Minimum density power divergence estimation provides a general framework for robust statistics, depending on a parameter α , which determines the robustness properties of the method. The usual estimation method is numerical minimization of the power divergence. The paper considers the special case of linear regression. We developed an alternative estimation procedure using the methods of S-estimation. The rho function so obtained is proportional to one minus a suitably scaled normal density raised to the power α . We used the theory of S-estimation to determine the asymptotic efficiency and breakdown point for this new form of S-estimation. Two sets of comparisons were made. In one, S power divergence is compared with other S-estimators using four distinct rho functions. Plots of efficiency against breakdown point show that the properties of S power divergence are close to those of Tukey’s biweight. The second set of comparisons is between S power divergence estimation and numerical minimization. Monitoring these two procedures in terms of breakdown point shows that the numerical minimization yields a procedure with larger robust residuals and a lower empirical breakdown point, thus providing an estimate of α leading to more efficient parameter estimates.

Similarity Hashing: A Computer Vision Solution to the Inverse Problem of Linear Fractals

Fractals ◽  
1997 ◽  
Vol 05 (supp01) ◽  
pp. 39-50 ◽  
Author(s):  
John C. Hart ◽  
Wayne O. Cochran ◽  
Patrick J. Flynn
Keyword(s):  
Computer Vision ◽  
Inverse Problem ◽  
Heuristic Search ◽  
Fractal Geometry ◽  
Self Similarity ◽  
Geometric Hashing ◽  
Numerical Minimization ◽  
Self Similar ◽  
Vision Algorithm ◽  
Fractal Representation

The difficult task of finding a fractal representation of an input shape is called the inverse, problem of fractal geometry. Previous attempts at solving this problem have applied techniques from numerical minimization, heuristic search and image compression. The most appropriate domain from which to attack this problem is not numerical analysis nor signal processing, but model-based computer vision. Self-similar objects cause an existing computer vision algorithm called geometric hashing to malfunction. Similarity hashing capitalizes on this observation to not only detect a shape's morphological self-similarity but also find the parameters of its self-transformations.

Numerical Minimization of the Landau-de Gennes Free Energy: Defects in Cylindrical Capillaries

1991 ◽  
Vol 199 (1) ◽  
pp. 429-452 ◽  
Author(s):  
E. C. Gartland ◽  
P. Palffy-muhoray ◽  
R. S. Varga
Keyword(s):  
Free Energy ◽  
Numerical Minimization

scholarly journals Calibration of Beacons for Indoor Environments based on a Digital Map and Heuristic Information

Sensors ◽  
2019 ◽  
Vol 19 (3) ◽  
pp. 670
Author(s):  
David Gualda ◽  
Jesús Ureña ◽  
José Alcalá ◽  
Carlos Santos
Keyword(s):  
Genetic Algorithm ◽  
Indoor Environment ◽  
Harmony Search ◽  
Positioning System ◽  
Indoor Environments ◽  
Angle Of Incidence ◽  
Distance Measurements ◽  
Digital Map ◽  
Local Positioning System ◽  
Numerical Minimization

This paper proposes an algorithm for calibrating the position of beacons which are placed on the ceiling of an indoor environment. In this context, the term calibration is used to estimate the position coordinates of a beacon related to a known reference system in a map. The positions of a set of beacons are used for indoor positioning purposes. The operation of the beacons can be based on different technologies such as radiofrequency (RF), infrared (IR) or ultrasound (US), among others. In this case we are interested in the positions of several beacons that compose an Ultrasonic Local Positioning System (ULPS) placed on different strategic points of the building. The calibration proposal uses several distances from a beacon to the neighbor walls measured by a laser meter. These measured distances, the map of the building in a vector format and other heuristic data (such as the region in which the beacon is located, the approximate orientation of the distance measurements to the walls and the equations in the map coordinate system of the line defining these walls) are the inputs of the proposed algorithm. The output is the best estimation of the position of the beacon. The process is repeated for all the beacons. To find the best estimation of the position of the beacons we have implemented a numerical minimization based on the use of a Genetic Algorithm (GA) and a Harmony Search (HS) methods. The proposal has been validated with simulations and real experiments, obtaining the positions of the beacons and an estimation of the error associated that depends on which walls (and the angle of incidence of the laser) are selected to make the distance measurements.

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