Exponential parameterization and ε-uniformly sampled reduced data

2015 ◽  
Author(s):  
R. Kozera ◽  
L. Noakes
Keyword(s):  
Reduced Data ◽  
Exponential Parameterization

Exponential parameterization to fit reduced data

2021 ◽  
Vol 391 ◽  
pp. 125645
Author(s):  
Ryszard Kozera ◽  
Lyle Noakes ◽  
Magdalena Wilkołazka
Keyword(s):  
Reduced Data ◽  
Exponential Parameterization

scholarly journals CONVERGENCE ORDER IN TRAJECTORY ESTIMATION BY PIECEWISE-CUBICS AND EXPONENTIAL PARAMETERIZATION

2019 ◽  
Vol 24 (1) ◽  
pp. 72-94 ◽  
Author(s):  
Magdalena Wilkołazka ◽  
Ryszard Kozera
Keyword(s):  
Euclidean Space ◽  
Lagrange Interpolation ◽  
Sufficient Conditions ◽  
Convergence Order ◽  
Multiple Goals ◽  
Trajectory Estimation ◽  
Numerical Testing ◽  
Reduced Data ◽  
Existing Result ◽  
Exponential Parameterization

This paper discusses the problem of estimating the trajectory of the unknown curve γ from the sequence of m+1 interpolation points in arbitrary Euclidean space En . The respective knots (in ascending order) are assumed to be unknown. Such Qm is coined reduced data. In our setting, a piecewise-cubic Lagrange interpolation is applied to fit Qm. Here, the missing knots Ƭm are replaced by their estimates in accordance with the exponential parameterization. The latter is controlled by a single parameter λ ∈ [0, 1]. This work analyzes the intrinsic asymptotics in approximating γ by ŷ3 based on the exponential parameterization and Qm. The multiple goals are achieved. Firstly, the existing result established for λ = 1 (i.e. for the cumulative chord parameterization) is extended to the remaining cases of λ ∈ [0, 1) and more-or-less uniformly sampled Qm. As demonstrated herein, a quartic convergence order α(1) = 4 in trajectory estimation drops discontinuously to the linear one α(λ) = 1, for all λ ∈ [0, 1). Secondly, the asymptotics derived in this paper is also analytically proved to be sharp with the aid of illustrative examples. Thirdly, the latter is verified in affirmative upon conducting numerical testing. Next, the necessity of more-or-less uniformity imposed on Qm is shown to be indispensable. In addition, several sufficient conditions for ŷ3 to be reparameterizable to the domain of γ are formulated. Lastly, the motivation for using the exponential parameterization with λ ∈ [0, 1) is also outlined.

Exploring Imputation Techniques for Missing Data in Transportation Management Systems

2003 ◽  
Vol 1836 (1) ◽  
pp. 132-142 ◽  
Author(s):  
Brian L. Smith ◽  
William T. Scherer ◽  
James H. Conklin
Keyword(s):  
Missing Data ◽  
Urban Areas ◽  
Large Scale ◽  
Management Systems ◽  
Data Sets ◽  
Transportation Industry ◽  
Transportation Management ◽  
Reduced Data ◽  
Natural Characteristics

Many states have implemented large-scale transportation management systems to improve mobility in urban areas. These systems are highly prone to missing and erroneous data, which results in drastically reduced data sets for analysis and real-time operations. Imputation is the practice of filling in missing data with estimated values. Currently, the transportation industry generally does not use imputation as a means for handling missing data. Other disciplines have recognized the importance of addressing missing data and, as a result, methods and software for imputing missing data are becoming widely available. The feasibility and applicability of imputing missing traffic data are addressed, and a preliminary analysis of several heuristic and statistical imputation techniques is performed. Preliminary results produced excellent performance in the case study and indicate that the statistical techniques are more accurate while maintaining the natural characteristics of the data.

Determination of Incompressible Flow Friction in Smooth Circular and Noncircular Passages: A Generalized Approach Including Validation of the Nearly Century Old Hydraulic Diameter Concept

1988 ◽  
Vol 110 (4) ◽  
pp. 431-440 ◽  
Author(s):  
N. T. Obot
Keyword(s):  
Reynolds Number ◽  
Friction Factor ◽  
Critical Reynolds Number ◽  
Pressure Coefficient ◽  
Hydraulic Diameter ◽  
Length Scale ◽  
The Difference ◽  
Friction Method ◽  
Reduced Data

It has been demonstrated conclusively that the widely observed differences in data for frictional pressure coefficient between circular and noncircular passages derive from the inseparably connected effects of transition and the choice of a length scale. A relatively simple approach, the critical friction method (CFM), has been developed and when applied to triangular, rectangular, and concentric annular passages, the reduced data lie with remarkable consistency on the circular tube relations. In accordance with the theory of dynamical similarity, it has also been shown that noncircular duct data can be reduced using the hydraulic diameter or any arbitrarily defined length scale. The proposed method is what is needed to reconcile such data with those for circular tubes. With the hydraulic diameter, the critical friction factor almost converges to a universal value for all passages and the correction is simply that required to account for the difference in critical Reynolds number. By contrast, with any other linear parameter, two corrections are needed to compensate for variations in critical friction factor and Reynolds number. Application of the method to roughened passages is discussed.

scholarly journals Exponential parameterization of wave functions for quantum dynamics: Time-dependent Hartree in second quantization

2018 ◽  
Vol 149 (13) ◽  
pp. 134110 ◽  
Author(s):  
Niels Kristian Madsen ◽  
Mads Bøttger Hansen ◽  
Alberto Zoccante ◽  
Kasper Monrad ◽  
Mikkel Bo Hansen ◽  
...  
Keyword(s):  
Quantum Dynamics ◽  
Wave Functions ◽  
Time Dependent ◽  
Second Quantization ◽  
Exponential Parameterization

scholarly journals A Land Cover Changes Model Based on Carbon Stock in the Mount Patah Region of, Bengkulu-Indonesia

2020 ◽  
Vol 4 (9) ◽  
pp. 1-5
Keyword(s):  
Land Use ◽  
Information System ◽  
Land Cover ◽  
Forest Inventory ◽  
Carbon Stock ◽  
Forest Cover ◽  
Landsat Imagery ◽  
Land Cover Changes ◽  
Land Area ◽  
Reduced Data

Forest cover in Bengkulu is reduced. Data from WARSI shows, 1990 forest cover areas in the province are approximately 1,009,209 hectares or 50.4 % of the land area reaching 1,979,515 hectares. But now, it is only 685,762 hectares of the area of his blood. That is, the period of 25 years, there is a forest cover decline of 323,447 hectares. Forest and land cover changes are the largest contributor to greenhouse gas emissions. The purpose of this article is to see land cover changes based on carbon stock in the years 2009 and 2018. Model of land cover change based on carbon stock year 2028 and 2038. The method of this research uses the calculation of the Stock Difference Approach with spatial analysis of national land closure of Landsat imagery 2009-2018 and biomass data for forest inventory results Geographic Information System (GIS). The results of this research were the reduced forest area and the change in land use changed from 2009 and 2018. So carbon stock is also increasingly reduced.

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