Osteoporosis vizualization by densities projection based on a kernel convolution method

2006 ◽  
Author(s):  
Walid Ayadi ◽  
Sylvie Sevestre-Ghalila ◽  
Amel Benazza-Benyahia
Keyword(s):  
Kernel Convolution ◽  
Convolution Method

Determination of the Vertical Vibration of a Ballasted Railway Track to Be Used in the Experimental Detection of Wheel Flats in Metropolitan Railways

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Ricard Sanchís ◽  
Salvador Cardona ◽  
Jordi Martínez
Keyword(s):  
Impulse Response ◽  
Vertical Vibration ◽  
Railway Track ◽  
Vibration Velocity ◽  
Kernel Convolution ◽  
Wheel Rolling ◽  
Vibration Attenuation ◽  
Wheel Profile ◽  
Convolution Method

This paper presents a mathematical model used to obtain the vertical vibration of a ballasted railway track when a wheel is passing at a certain speed over a fixed location of the rail. The aim of this simulation is to compare calculated root-mean-square (RMS) values of the vertical vibration velocity with measured RMS values. This comparison is the basis for a proposed time domain methodology for detecting potential wheel flats or any other singular defect on the wheel rolling bands of metropolitan trains. In order to reach this goal, a wheel–rail contact model is proposed; this model is described by the track vertical impulse response and the vertical impulse response of the wheel with the primary suspension, both linked through a Hertz nonlinear stiffness. To solve the model for obtaining the wheel–rail contact force, a double convolution method is applied. Several kinds of wheel flats are analyzed, from theoretical round edged wheel flats to different real wheel profile irregularities. Afterward, the vertical vibration velocity at a fixed point on the rail is obtained using a variable kernel convolution method. Running different simulations for different wheel flats, a study of the vertical vibration attenuation along the rail is carried out. Finally, it is proceeded to obtain the temporary evolution of the RMS value for the rail vertical vibration velocity in order to be used as a reference for detecting wheel flats or any other defect. This last aspect will be presented in more detail in a second paper.

scholarly journals Quantification and classification of neuronal responses in kernel-smoothed peristimulus time histograms

2015 ◽  
Vol 113 (4) ◽  
pp. 1260-1274 ◽  
Author(s):  
Michael R. H. Hill ◽  
Itzhak Fried ◽  
Christof Koch
Keyword(s):  
Random Noise ◽  
Large Data ◽  
Neuronal Responses ◽  
Data Set ◽  
Firing Rates ◽  
Kernel Convolution ◽  
Actual Response ◽  
Response Envelope ◽  
Convolution Method

Peristimulus time histograms are a widespread form of visualizing neuronal responses. Kernel convolution methods transform these histograms into a smooth, continuous probability density function. This provides an improved estimate of a neuron's actual response envelope. We here develop a classifier, called the h-coefficient, to determine whether time-locked fluctuations in the firing rate of a neuron should be classified as a response or as random noise. Unlike previous approaches, the h-coefficient takes advantage of the more precise response envelope estimation provided by the kernel convolution method. The h-coefficient quantizes the smoothed response envelope and calculates the probability of a response of a given shape to occur by chance. We tested the efficacy of the h-coefficient in a large data set of Monte Carlo simulated smoothed peristimulus time histograms with varying response amplitudes, response durations, trial numbers, and baseline firing rates. Across all these conditions, the h-coefficient significantly outperformed more classical classifiers, with a mean false alarm rate of 0.004 and a mean hit rate of 0.494. We also tested the h-coefficient's performance in a set of neuronal responses recorded in humans. The algorithm behind the h-coefficient provides various opportunities for further adaptation and the flexibility to target specific parameters in a given data set. Our findings confirm that the h-coefficient can provide a conservative and powerful tool for the analysis of peristimulus time histograms with great potential for future development.

NON-NORMAL STATISTICAL TOLERANCE ANALYSIS USING ANALYTICAL CONVOLUTION METHOD

2008 ◽  
Vol 07 (01) ◽  
pp. 127-130 ◽  
Author(s):  
S. G. LIU ◽  
P. WANG ◽  
Z. G. LI
Keyword(s):  
Normal Distribution ◽  
Closed Loop ◽  
Tolerance Analysis ◽  
Accurate Method ◽  
Probability Density Functions ◽  
Triangular Distribution ◽  
Normal Distributions ◽  
Statistical Tolerance ◽  
Statistical Tolerance Analysis ◽  
Convolution Method

In statistical tolerance analysis, it is usually assumed that the statistical tolerance is normally distributed. But in practice, there are many non-normal distributions, such as uniform distribution, triangular distribution, etc. The simple way to analyze non-normal distributions is to approximately represent it with normal distribution, but the accuracy is low. Monte-Carlo simulation can analyze non-normal distributions with higher accuracy, but is time consuming. Convolution method is an accurate method to analyze statistical tolerance, but there are few reported works about it because of the difficulty. In this paper, analytical convolution is used to analyze non-normal distribution, and the probability density functions of closed loop component are obtained. Comparing with other methods, convolution method is accurate and faster.

scholarly journals On Dirichlet convolution method

1998 ◽  
Vol 21 (3) ◽  
pp. 607-611
Author(s):  
Indulata Sukla
Keyword(s):  
Summability Methods ◽  
Dirichlet Convolution ◽  
Convolution Method

In this paper we have proved limitation theorem for(D,h(n))summability methods and have shown that it is best possible.

scholarly journals About Liquid Filtration Under a Point Dam with a Vertical Weakly Permeable Film

2021 ◽  
Vol 16 (3) ◽  
pp. 69-74
Author(s):  
Efimova Irina A. ◽  
Keyword(s):  
Porous Medium ◽  
Half Plane ◽  
Horizontal Line ◽  
Filtration Process ◽  
Liquid Filtration ◽  
Fourier Expansions ◽  
Water Courses ◽  
Filtration Area ◽  
Homogeneous Porous Medium ◽  
Convolution Method

The problem of groundwater filtration under a point dam in a piecewise homogeneous porous medium in the presence of a weakly permeable film under the dam is considered. The filtration area is considered in the form of a vertical half-plane with a horizontal line of water courses. A weakly permeable film divides the filtration area into two quadrants with different constant permeability. By the convolution method of Fourier expansions, the solution of the problem is obtained explicitly. The influence of a weakly permeable film on the filtration process is investigated. It is shown that the presence of a weakly permeable film reduces the filtration rates in the downstream.

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