scholarly journals Determination of parameters for Cauchy’s problem for systems of ODEs with application to biological modelling

BIOMATH ◽  
2016 ◽  
Vol 5 (1) ◽  
pp. 1604231
Author(s):  
A.N. Pete ◽  
Peter Mathye ◽  
Igor Fedotov ◽  
Michael Shatalov
Keyword(s):  
Experimental Data ◽  
Mathematical Models ◽  
Least Squares ◽  
Numerical Method ◽  
Least Squares Method ◽  
Algebraic Equations ◽  
Systems Of Odes ◽  
Determination Of Parameters ◽  
Biological Modelling

An inverse numerical method that estimate parameters of dynamic mathematical models given some information about unknown trajectories at some time is applied to examples taken from Biology and Ecology. The method consisting of determining an over-determined system of algebraic equations using experimental data. The solution of the over-determined system is then obtained using, for example the least-squares method. To illustrate the effectiveness of the method an analysis of examples and corresponding numerical example are presented.

scholarly journals Route 93, Arizona’s IRI estimation using least squares method and fuzzy logic

2017 ◽  
Vol 7 (3) ◽  
pp. 157-162
Author(s):  
Sebnem Sargin Karahancer ◽  
Ekinhan Eriskin ◽  
Buket Capali ◽  
Serdal Terzi ◽  
Mehmet Saltan
Keyword(s):  
Experimental Data ◽  
Fuzzy Logic ◽  
Least Squares ◽  
Least Squares Method ◽  
International Roughness Index ◽  
Freeze Thaw ◽  
Roughness Index ◽  
Subjective Opinion

AbstractServiceability was found to be influenced by longitudinal and transverse profiles as well as the extent of cracking and patching. The amount of weight to assign to each element in the determination of the overall serviceability is a matter of subjective opinion. International roughness index of highway pavements has been estimated by least squares and fuzzy logic methods and compared. For these models, Route 93, Arizona experimental data have been used. Annual freeze –thaw occurring days, depending on years, ha ve been used for modelling. The developed model with least squares method has a high regression value. This approach can be easily and realistically performed to solve problems that do not have a formulation or function for the solution.Keywords: International roughness index, least squares method, modelling, estimation, fuzzy logic.

A least squares method for earthquake mechanism determination using S-wave data

1964 ◽  
Vol 54 (6A) ◽  
pp. 2037-2047
Author(s):  
Agustin Udias
Keyword(s):  
Least Squares ◽  
Statistical Evaluation ◽  
Least Squares Method ◽  
Numerical Approach ◽  
Focal Mechanisms ◽  
Least Square ◽  
S Wave ◽  
Double Couple ◽  
Earthquake Mechanism

abstract In this paper a numerical approach to the determination of focal mechanisms based on the observation of the polarization of the S wave at N stations is presented. Least-square methods are developed for the determination of the orientation of the single and double couple sources. The methods allow a statistical evaluation of the data and of the accuracy of the solutions.

scholarly journals Method of determining the distance to the object by analyzing its image blur

Vestnik MGSU ◽  
2015 ◽  
pp. 140-151 ◽  
Author(s):  
Aleksey Alekseevich Loktev ◽  
Daniil Alekseevich Loktev
Keyword(s):  
Least Squares ◽  
Statistical Approach ◽  
Evaluation Method ◽  
Least Squares Method ◽  
Focal Length ◽  
Error Variance ◽  
Method Of Least Squares ◽  
Automated Control ◽  
Image Blur

In modern integrated monitoring systems and systems of automated control of technological processes there are several essential algorithms and procedures for obtaining primary information about an object and its behavior. The primary information is characteristics of static and moving objects: distance, speed, position in space etc. In order to obtain such information in the present work we proposed to use photos and video detectors that could provide the system with high-quality images of the object with high resolution. In the modern systems of video monitoring and automated control there are several ways of obtaining primary data on the behaviour and state of the studied objects: a multisensor approach (stereovision), building an image perspective, the use of fixed cameras and additional lighting of the object, and a special calibration of photo or video detector.In the present paper the authors develop a method of determining the distances to objects by analyzing a series of images using depth evaluation using defocusing. This method is based on the physical effect of the dependence of the determined distance to the object on the image from the focal length or aperture of the lens. When focusing the photodetector on the object at a certain distance, the other objects both closer and farther than a focal point, form a spot of blur depending on the distance to them in terms of images. Image blur of an object can be of different nature, it may be caused by the motion of the object or the detector, by the nature of the image boundaries of the object, by the object’s aggregate state, as well as by different settings of the photo-detector (focal length, shutter speed and aperture).When calculating the diameter of the blur spot it is assumed that blur at the point occurs equally in all directions. For more precise estimates of the geometrical parameters determination of the behavior and state of the object under study a statistical approach is used to determine the individual parameters and estimate their accuracy. A statistical approach is used to evaluate the deviation of the dependence of distance from the blur from different types of standard functions (logarithmic, exponential, linear). In the statistical approach the evaluation method of least squares and the method of least modules are included, as well as the Bayesian estimation, for which it is necessary to minimize the risks under different loss functions (quadratic, rectangular, linear) with known probability density (we consider normal, lognormal, Laplace, uniform distribution). As a result of the research it was established that the error variance of a function, the parameters of which are estimated using the least squares method, will be less than the error variance of the method of least modules, that is, the evaluation method of least squares is more stable. Also the errors’ estimation when using the method of least squares is unbiased, whereas the mathematical expectation when using the method of least modules is not zero, which indicates the displacement of error estimations. Therefore it is advisable to use the least squares method in the determination of the parameters of the function.In order to smooth out the possible outliers we use the Kalman filter to process the results of the initial observations and evaluation analysis, the method of least squares and the method of least three standard modules for the functions after applying the filter with different coefficients.

A least-squares method for the determination of the orientation matrix in single-crystal diffractometry

1970 ◽  
Vol 26 (2) ◽  
pp. 295-296 ◽  
Author(s):  
K. Tichý
Keyword(s):  
Single Crystal ◽  
Least Squares ◽  
Least Squares Method ◽  
Reciprocal Vector ◽  
Orientation Matrix ◽  
The Matrix

An appropriate choice of the function minimized permits linearization of the least-squares determination of the matrix which transforms the diffraction indices into the components of the reciprocal vector in the diffractometer φ-axis system of coordinates. The coefficients of the least-squares equations are based on diffraction indices and measured diffractometer angles of three or more non-coplanar setting reflexions.

Spin Coating Planarization Of Integrated Circuit Topography On A Rotating Disk

1991 ◽  
Vol 227 ◽  
Author(s):  
Roger K. Yonkoski ◽  
David S. Soane
Keyword(s):  
Experimental Data ◽  
Fluid Flow ◽  
Integrated Circuit ◽  
Spin Coating ◽  
Rotating Disk ◽  
Momentum Conservation ◽  
Flat Surfaces ◽  
Determination Of Parameters ◽  
Polyimide Precursor

ABSTRACTPolyimide is commonly used in the microelectronic industry for interconnection applications because of its ability to planarize features typically found on an IC chip. A mathematical model is developed to describe fluid flow on a rotating disk based on the principles of mass and momentum conservation. Constitutive relationships necessary for this model are proposed. Experimental data for polyimide precursor solutions are presented which enable the determination of parameters for the constitutive equations. This model is used to describe the film profiles over flat surfaces and near micron-sized features. Attention is focused on the coupling between mass transport and fluid flow as well as the effects of surface tension on film profiles over topographical features.

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