Search results for: positive Gaussian curvature.

Authors: C. T. Cheung, R. K. P. Ng, T. Y. Lo, Zhou Jinyun

Abstract:

This paper aims at manipulating loop alignment in knitting a three-dimensional (3D) shape by its geometry. Two loop alignment methods are introduced to handle a surface with positive Gaussian curvature. As weft knitting is a two-dimensional (2D) knitting mechanism that the knitting cam carrying the feeders moves in two directions only, left and right, the knitted fabric generated grows in width and length but not in depth. Therefore, a 3D shape is required to be flattened to a 2D plane with surface area preserved for knitting. On this flattened plane, dimensional measurements are taken for loop alignment. The way these measurements being taken derived two different loop alignment methods. In this paper, only plain knitted structure was considered. Each knitted loop was taken as a basic unit for loop alignment in order to achieve the required geometric dimensions, without the inclusion of other stitches which give textural dimensions to the fabric. Two loop alignment methods were experimented and compared. Only one of these two can successfully preserve the dimensions of the shape.

Keywords: 3D knitting, 3D shape, loop alignment, positive Gaussian curvature.

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Authors: Gabriel I. Loaiza O., Carlos A. Cadavid M., Juan C. Arango P.

Abstract:

It is known that the Riemannian manifold determined by the family of inverse Gaussian distributions endowed with the Fisher metric has negative constant curvature κ = −1/2 , as does the family of usual Gaussian distributions. In the present paper, firstly we arrive at this result by following a different path, much simpler than the previous ones. We first put the family in exponential form, thus endowing the family with a new set of parameters, or coordinates, θ1, θ2; then we determine the matrix of the Fisher metric in terms of these parameters; and finally we compute this matrix in the original parameters. Secondly, we define the Inverse q−Gaussian distribution family (q < 3), as the family obtained by replacing the usual exponential function by the Tsallis q−exponential function in the expression for the Inverse Gaussian distribution, and observe that it supports two possible geometries, the Fisher and the q−Fisher geometry. And finally, we apply our strategy to obtain results about the Fisher and q−Fisher geometry of the Inverse q−Gaussian distribution family, similar to the ones obtained in the case of the Inverse Gaussian distribution family.

Keywords: Base of Changes, Information Geometry, Inverse Gaussian distribution, Inverse q-Gaussian distribution, Statistical Manifolds.

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Authors: M. Y. Misro, A. Ramli, J. M. Ali

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Bezier curves have useful properties for path generation problem, for instance, it can generate the reference trajectory for vehicles to satisfy the path constraints. Both algorithms join cubic Bezier curve segment smoothly to generate the path. Some of the useful properties of Bezier are curvature. In mathematics, curvature is the amount by which a geometric object deviates from being flat, or straight in the case of a line. Another extrinsic example of curvature is a circle, where the curvature is equal to the reciprocal of its radius at any point on the circle. The smaller the radius, the higher the curvature thus the vehicle needs to bend sharply. In this study, we use Bezier curve to fit highway-like curve. We use different approach to find the best approximation for the curve so that it will resembles highway-like curve. We compute curvature value by analytical differentiation of the Bezier Curve. We will then compute the maximum speed for driving using the curvature information obtained. Our research works on some assumptions; first, the Bezier curve estimates the real shape of the curve which can be verified visually. Even though, fitting process of Bezier curve does not interpolate exactly on the curve of interest, we believe that the estimation of speed are acceptable. We verified our result with the manual calculation of the curvature from the map.

Keywords: Speed estimation, path constraints, reference trajectory, Bezier curve.

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Authors: Qian-Ping Guo, Hou-Biao Li

Abstract:

The generalized Higham matrix is a complex symmetric matrix A = B + iC, where both B ∈ Cn×n and C ∈ Cn×n are Hermitian positive definite, and i = √−1 is the imaginary unit. The growth factor in Gaussian elimination is less than 3√2 for this kind of matrices. In this paper, we give a new brief proof on this result by different techniques, which can be understood very easily, and obtain some new findings.

Keywords: CSPD matrix, positive definite, Schur complement, Higham matrix, Gaussian elimination, Growth factor.

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Authors: A. Peveri

Abstract:

The interaction of mass will determine the curvature of space-time, may determine that events proceed at different rates of time at each point in space, so each has a corresponding gravitational potential time. So we can find different values ​​of gravity (g), corresponding to different times (t), thus making a "map of time in space." The space-time is curved by present mass, causing a force of attraction towards the body, but if you invest the curvature of space-time, we find that this field is repulsive: Obtaining negative gravitational forces and positive gravitational forces respectively.

Keywords: Space-time, time, positive gravitation, negative gravitation.

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Authors: Erhan Ata, H. Hilmi Hacisalihoğlu, Yusuf Yayli

Abstract:

In this work some characterizations of semi Riemannian curvature tensor on almost split quaternion Kaehler manifolds and some characterizations of Ricci tensor on almost split quaternion Kaehler manifolds are given.

Keywords: Almost split quaternion Kaehler manifold, Riemann curvature, Ricci curvature.

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Authors: Gary D. Cantrell, E. Alex Baylot

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The radius-of-curvature (ROC) defines the degree of curvature along the centerline of a roadway whereby a travelling vehicle must follow. Roadway designs must encompass ROC in mitigating the cost of earthwork associated with construction while also allowing vehicles to travel at maximum allowable design speeds. Thus, a road will tend to follow natural topography where possible, but curvature must also be optimized to permit fast, but safe vehicle speeds. The more severe the curvature of the road, the slower the permissible vehicle speed. For route planning, whether for urban settings, emergency operations, or even parcel delivery, ROC is a necessary attribute of road arcs for computing travel time. It is extremely rare for a geo-spatial database to contain ROC. This paper will present a procedure and mathematical algorithm to calculate and assign ROC to a segment pair and/or polyline.

Keywords: linear features, radius-of-curvature, roads, routing, traffic, turning

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Authors: Y. S. Oh, P. Abhishesh, B. S. Ryuh

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This paper presents the method of trajectory planning by the robot end-effector which accounts for more accurate and smooth differential geometry of the ruled surface generated by tool line fixed with end-effector based on the methods of curvature theory of ruled surface and the dual curvature theory, and focuses on the underlying relation to unite them for enhancing the efficiency for trajectory planning. Robot motion can be represented as motion properties of the ruled surface generated by trajectory of the Tool Center Point (TCP). The linear and angular properties of the six degree-of-freedom motion of end-effector are computed using the explicit formulas and functions from curvature theory and dual curvature theory. This paper explains the complete dualization of ruled surface and shows that the linear and angular motion applied using the method of dual curvature theory is more accurate and less complex.

Keywords: Dual curvature theory, robot end effector, ruled surface, TCP, tool center point.

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Authors: Nyah C. Temaneh, F. A. Phiri, E. Ruhunga

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Most of the well known methods for generating Gaussian variables require at least one standard uniform distributed value, for each Gaussian variable generated. The length of the random number generator therefore, limits the number of independent Gaussian distributed variables that can be generated meanwhile the statistical solution of complex systems requires a large number of random numbers for their statistical analysis. We propose an alternative simple method of generating almost infinite number of Gaussian distributed variables using a limited number of standard uniform distributed random numbers.

Keywords: Gaussian variable, statistical analysis, simulation ofCommunication Network, Random numbers.

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Authors: A. Keshavarz

Abstract:

A physical model for guiding the wave in photorefractive media is studied. Propagation of cos-Gaussian beam as the special cases of sinusoidal-Gaussian beams in photorefractive crystal is simulated numerically by the Crank-Nicolson method in one dimension. Results show that the beam profile deforms as the energy transfers from the center to the tails under propagation. This simulation approach is of significant interest for application in optical telecommunication. The results are presented graphically and discussed.

Keywords: Beam propagation, cos-Gaussian beam, Numerical simulation, Photorefractive crystal.

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Authors: Tomohiro Hachino, Hitoshi Takata, Seiji Fukushima, Yasutaka Igarashi

Abstract:

This paper presents a Gaussian process model-based short-term electric load forecasting. The Gaussian process model is a nonparametric model and the output of the model has Gaussian distribution with mean and variance. The multiple Gaussian process models as every hour ahead predictors are used to forecast future electric load demands up to 24 hours ahead in accordance with the direct forecasting approach. The separable least-squares approach that combines the linear least-squares method and genetic algorithm is applied to train these Gaussian process models. Simulation results are shown to demonstrate the effectiveness of the proposed electric load forecasting.

Keywords: Direct method, electric load forecasting, Gaussian process model, genetic algorithm, separable least-squares method.

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Authors: Keunhong Chae, Seokho Yoon

Abstract:

In this paper, frequency offset (FO) estimation schemes robust to the non-Gaussian noise environments are proposed for orthogonal frequency division multiplexing (OFDM) systems. First, a maximum-likelihood (ML) estimation scheme in non-Gaussian noise environments is proposed, and then, the complexity of the ML estimation scheme is reduced by employing a reduced set of candidate values. In numerical results, it is demonstrated that the proposed schemes provide a significant performance improvement over the conventional estimation scheme in non-Gaussian noise environments while maintaining the performance similar to the estimation performance in Gaussian noise environments.

Keywords: Frequency offset estimation, maximum-likelihood, non-Gaussian noise environment, OFDM, training symbol.

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Authors: Hu Haibo, Zhao Hong

Abstract:

Gaussian mixture background model is widely used in moving target detection of the image sequences. However, traditional Gaussian mixture background model usually considers the time continuity of the pixels, and establishes background through statistical distribution of pixels without taking into account the pixels- spatial similarity, which will cause noise, imperfection and other problems. This paper proposes a new Gaussian mixture modeling approach, which combines the color and gradient of the spatial information, and integrates the spatial information of the pixel sequences to establish Gaussian mixture background. The experimental results show that the movement background can be extracted accurately and efficiently, and the algorithm is more robust, and can work in real time in tracking applications.

Keywords: Gaussian mixture model, real-time tracking, sequence image, gradient.

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Authors: Young-Hwan Song, Hyung-Jun Kwon, Myung-Jin Bae

Abstract:

As the remedy used music becomes active and meditation effect through the music is verified, people take a growing interest about psychological balance or remedy given by music. From traditional studies, it is verified that the music of which spectral envelop varies approximately as 1/f (f is frequency) down to a frequency of low frequency bandwidth gives psychological balance. In this paper, we researched signal properties of music which gives psychological balance. In order to find this, we derived the property from voice. Music composed by voice shows large value in NCSD. We confirmed the degree of deference between music by curvature of normalized cumulative spectral distribution. In the music that gives psychological balance, the curvature shows high value, otherwise, the curvature shows low value.

Keywords: Cognitive Psychology, Normalized Cumulative Spectral Distribution, Curvature.

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Authors: A. Keshavarz, Z. Roosta

Abstract:

In this paper, propagation of cos-Gaussian beam in strongly nonlocal nonlinear media has been stimulated by using paraxial group transformation. At first, cos-Gaussian beam, nonlocal nonlinear media, critical power, transfer matrix, and paraxial group transformation are introduced. Then, the propagation of the cos-Gaussian beam in strongly nonlocal nonlinear media is simulated. Results show that beam propagation has periodic structure during self-focusing effect in this case. However, this simple method can be used for investigation of propagation of kinds of beams in ABCD optical media.

Keywords: Paraxial group transformation, nonlocal nonlinear media, Cos-Gaussian beam, ABCD law.

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Authors: M. B. Meenavathi, K. Rajesh

Abstract:

In this paper, we propose a new class of Volterra series based filters for image enhancement and restoration. Generally the linear filters reduce the noise and cause blurring at the edges. Some nonlinear filters based on median operator or rank operator deal with only impulse noise and fail to cancel the most common Gaussian distributed noise. A class of second order Volterra filters is proposed to optimize the trade-off between noise removal and edge preservation. In this paper, we consider both the Gaussian and mixed Gaussian-impulse noise to test the robustness of the filter. Image enhancement and restoration results using the proposed Volterra filter are found to be superior to those obtained with standard linear and nonlinear filters.

Keywords: Gaussian noise, Image enhancement, Imagerestoration, Linear filters, Nonlinear filters, Volterra series.

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Authors: Cuneyt Yucelbas, Seral Ozsen, Sule Yucelbas, Gulay Tezel

Abstract:

Due to the fact that there exist only a small number of complex systems in artificial immune system (AIS) that work out nonlinear problems, nonlinear AIS approaches, among the well-known solution techniques, need to be developed. Gaussian function is usually used as similarity estimation in classification problems and pattern recognition. In this study, diagnosis of breast cancer, the second type of the most widespread cancer in women, was performed with different distance calculation functions that euclidean, gaussian and gaussian-euclidean hybrid function in the clonal selection model of classical AIS on Wisconsin Breast Cancer Dataset (WBCD), which was taken from the University of California, Irvine Machine-Learning Repository. We used 3-fold cross validation method to train and test the dataset. According to the results, the maximum test classification accuracy was reported as 97.35% by using of gaussian-euclidean hybrid function for fold-3. Also, mean of test classification accuracies for all of functions were obtained as 94.78%, 94.45% and 95.31% with use of euclidean, gaussian and gaussian-euclidean, respectively. With these results, gaussian-euclidean hybrid function seems to be a potential distance calculation method, and it may be considered as an alternative distance calculation method for hard nonlinear classification problems.

Keywords: Artificial Immune System, Breast Cancer Diagnosis, Euclidean Function, Gaussian Function.

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Authors: Shu-Xin Miao

Abstract:

In this paper, the Gaussian type quadrature rules for fuzzy functions are discussed. The errors representation and convergence theorems are given. Moreover, four kinds of Gaussian type quadrature rules with error terms for approximate of fuzzy integrals are presented. The present paper complements the theoretical results of the paper by T. Allahviranloo and M. Otadi [T. Allahviranloo, M. Otadi, Gaussian quadratures for approximate of fuzzy integrals, Applied Mathematics and Computation 170 (2005) 874-885]. The obtained results are illustrated by solving some numerical examples.

Keywords: Guassian quadrature rules, fuzzy number, fuzzy integral, fuzzy solution.

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Authors: R. K. Saxena, Ravi Saxena

Abstract:

In view of their importance and usefulness in reliability theory and probability distributions, several generalizations of the inverse Gaussian distribution and the Krtzel function are investigated in recent years. This has motivated the authors to introduce and study a new generalization of the inverse Gaussian distribution and the Krtzel function associated with a product of a Bessel function of the third kind )(zKQ and a Z - Fox-Wright generalized hyper geometric function introduced in this paper. The introduced function turns out to be a unified gamma-type function. Its incomplete forms are also discussed. Several properties of this gamma-type function are obtained. By means of this generalized function, we introduce a generalization of inverse Gaussian distribution, which is useful in reliability analysis, diffusion processes, and radio techniques etc. The inverse Gaussian distribution thus introduced also provides a generalization of the Krtzel function. Some basic statistical functions associated with this probability density function, such as moments, the Mellin transform, the moment generating function, the hazard rate function, and the mean residue life function are also obtained.KeywordsFox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

Keywords: Fox-Wright function, Inverse Gaussian distribution, Krtzel function & Bessel function of the third kind.

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Authors: Shi-hong Lu, Chao-xun Liu, Yi-feng Zhu

Abstract:

Ultrasonic shot peening (USP) on AALY12 sheet was studied. Several parameters (arc heights, surface roughness, surface topography and micro hardness) with different USP process parameters were measured. The research proposes that radius of curvature of shot peened sheet increases with time and electric current decreasing, while increases with pin diameter increasing, and radius of curvature reaches a saturation level after a specific processing time and electric current. An empirical model of the relationship between radius of curvature and pin diameter, electric current, time was also obtained. The research shows that the increment of surface and vertical micro hardness of material is more obvious with longer time and higher value of electric current, which can be up to 20% and 28% respectively.

Keywords: USP forming, surface properties, radius of curvature, residual stress.

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Authors: V. Polenta, S. D. Garvey, D. Chronopoulos, A. C. Long, H. P. Morvan

Abstract:

A parametric study on circular thin-walled pipes subjected to pure bending is performed. Both straight and curved pipes are considered. Ratio D/t, initial pipe curvature and internal pressure are the parameters varying in the analyses. The study is mainly FEA-based. It is found that negative curvatures (opposite to bending moment) considerably increase stiffness and buckling limit of the pipe when no internal pressure is acting and, similarly, positive curvatures decrease the stiffness and buckling limit. For internal pressurised pipes the effects of initial pipe curvature are less relevant. Results show that this phenomenon is in relationship with the cross-section deformation due to bending moment, which undergoes relevant ovalisation for no pressurised pipes and little ovalisation for pressurised pipes.

Keywords: Buckling, curved pipes, internal pressure, ovalisation, pure bending, thin-walled pipes.

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Authors: Fabrice Poirion, Benedicte Puig

Abstract:

Mathematical justifications are given for a simulation technique of multivariate nonGaussian random processes and fields based on Rosenblatt-s transformation of Gaussian processes. Different types of convergences are given for the approaching sequence. Moreover an original numerical method is proposed in order to solve the functional equation yielding the underlying Gaussian process autocorrelation function.

Keywords: Simulation, nonGaussian, random field, multivariate, stochastic process.

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Authors: Hacene Benkhoula, Mohamed Badreddine Benabdella, Hamid Bouzeboudja, Abderrahmane Asraoui

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The wind is a random variable difficult to master, for this, we developed a mathematical and statistical methods enable to modeling and forecast wind power. Gaussian Processes (GP) is one of the most widely used families of stochastic processes for modeling dependent data observed over time, or space or time and space. GP is an underlying process formed by unrecognized operator’s uses to solve a problem. The purpose of this paper is to present how to forecast wind power by using the GP. The Gaussian process method for forecasting are presented. To validate the presented approach, a simulation under the MATLAB environment has been given.

Keywords: Forecasting, Gaussian process, modeling, wind power.

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Authors: K. P. Vishwanath, A. Kandasamy

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The present work deals with analyses of the effects of bearing curvature and non-Newtonian characteristics on the load capacity of an exponential rectangular squeeze film bearing using Bingham fluids as lubricants. Bingham fluids are characterized by an yield value and hence the formation of a “rigid" core in the region between the plates is justified. The flow is confined to the region between the core and the plates. The shape of the core has been identified through numerical means. Further, numerical solutions for the pressure distribution and load carrying capacity of the bearing for various values of Bingham number and curvature parameter have been obtained. The effects of bearing curvature and non-Newtonian characteristics of the lubricant on the bearing performances have been discussed.

Keywords: rheodynamic lubrication, yield stress, non-Newtonianfluid, Bingham fluid, exponential squeeze film.

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Authors: V.P.Subramanyam Rallabandi, S.K.Sett

Abstract:

An unsupervised classification algorithm is derived by modeling observed data as a mixture of several mutually exclusive classes that are each described by linear combinations of independent non-Gaussian densities. The algorithm estimates the data density in each class by using parametric nonlinear functions that fit to the non-Gaussian structure of the data. This improves classification accuracy compared with standard Gaussian mixture models. When applied to textures, the algorithm can learn basis functions for images that capture the statistically significant structure intrinsic in the images. We apply this technique to the problem of unsupervised texture classification and segmentation.

Keywords: Gaussian Mixture Model, Independent Component Analysis, Segmentation, Unsupervised Classification.

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Authors: Adnan Al-Smadi

Abstract:

One of the primary uses of higher order statistics in signal processing has been for detecting and estimation of non- Gaussian signals in Gaussian noise of unknown covariance. This is motivated by the ability of higher order statistics to suppress additive Gaussian noise. In this paper, several methods to test for non- Gaussianity of a given process are presented. These methods include histogram plot, kurtosis test, and hypothesis testing using cumulants and bispectrum of the available sequence. The hypothesis testing is performed by constructing a statistic to test whether the bispectrum of the given signal is non-zero. A zero bispectrum is not a proof of Gaussianity. Hence, other tests such as the kurtosis test should be employed. Examples are given to demonstrate the performance of the presented methods.

Keywords: Non-Gaussian, bispectrum, kurtosis, hypothesistesting, histogram.

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Authors: Keunhong Chae, Seokho Yoon

Abstract:

This paper proposes frequency offset (FO) estimation schemes robust to the non-Gaussian noise for orthogonal frequency division multiplexing (OFDM) systems. A maximum-likelihood (ML) scheme and a low-complexity estimation scheme are proposed by applying the probability density function of the cyclic prefix of OFDM symbols to the ML criterion. From simulation results, it is confirmed that the proposed schemes offer a significant FO estimation performance improvement over the conventional estimation scheme in non-Gaussian noise environments.

Keywords: Frequency offset, cyclic prefix, maximum-likelihood, non-Gaussian noise, OFDM.

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Authors: V. K. Ananthashayana, Jyothirmayi M.

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This paper addresses the problem of source separation in images. We propose a FastICA algorithm employing a modified Gaussian contrast function for the Blind Source Separation. Experimental result shows that the proposed Modified Gaussian FastICA is effectively used for Blind Source Separation to obtain better quality images. In this paper, a comparative study has been made with other popular existing algorithms. The peak signal to noise ratio (PSNR) and improved signal to noise ratio (ISNR) are used as metrics for evaluating the quality of images. The ICA metric Amari error is also used to measure the quality of separation.

Keywords: Amari error, Blind Source Separation, Contrast function, Gaussian function, Independent Component Analysis.

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Authors: Gokhan Dok, Hakan Ozturk, Aydin Demir

Abstract:

The behavior of reinforced concrete (RC) members is quite important in RC structures. When evaluating the performance of structures, the nonlinear properties are defined according to the cross sectional behavior of RC members. To be able to determine the behavior of RC members, its cross sectional behavior should be known well. The moment-curvature (MC) relationship is used to represent cross sectional behavior. The MC relationship of RC cross section can be best determined both experimentally and numerically. But, experimental study on RC members is very difficult. The aim of the study is to obtain the MC relationship of RC shear walls. Additionally, it is aimed to determine the parameters which affect MC relationship. While obtaining MC relationship of RC members, XTRACT which can represent robustly the MC relationship is used. Concrete quality, longitudinal and transverse reinforcing ratios, are selected as parameters which affect MC relationship. As a result of the study, curvature ductility and effective flexural stiffness are determined using this parameter. Effective flexural stiffness is compared with the values defined in design codes.

Keywords: Moment-curvature, reinforced concrete, shear wall, numerical.

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Authors: Turgay Temel, John Hallam

Abstract:

A recent neurospiking coding scheme for feature extraction from biosonar echoes of various plants is examined with avariety of stochastic classifiers. Feature vectors derived are employedin well-known stochastic classifiers, including nearest-neighborhood,single Gaussian and a Gaussian mixture with EM optimization.Classifiers' performances are evaluated by using cross-validation and bootstrapping techniques. It is shown that the various classifers perform equivalently and that the modified preprocessing configuration yields considerably improved results.

Keywords: Classification, neuro-spike coding, non-parametricmodel, parametric model, Gaussian mixture, EM algorithm.

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