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Articles 1 - 18 of 18
Full-Text Articles in Mathematics
How The Pavement's Lifetime Depends On The Stress Level: An Explanation Of The Empirical Formula, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich, Olga Kosheleva, Hoang Phuong Nguyen
How The Pavement's Lifetime Depends On The Stress Level: An Explanation Of The Empirical Formula, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich, Olga Kosheleva, Hoang Phuong Nguyen
Departmental Technical Reports (CS)
We show that natural invariance ideas explain the empirical dependence on the pavement's lifetime on the stress level.
Discrepancy-Based Analysis Of Measurement Sampling Points In Compressive Sensing, Felipe Batista Da Silva
Discrepancy-Based Analysis Of Measurement Sampling Points In Compressive Sensing, Felipe Batista Da Silva
Open Access Theses & Dissertations
Compressive sensing (CS) is a technique in signal processing that under certain conditions allows someone to reconstruct sparse signals from fewer linear measurements. A problem in CS is modeled in terms of an underdetermined linear system, whose associated matrix is previously designed. Then, it is of interest in CS to know what a good sampling defined by the sensing matrix is and how to measure it. In this work, we provided analytical proofs of properties of the metric discrepancy that allow us to propose a fast algorithm for discrepancy calculation. Such metric measures the quality of the sampling measurement points …
Low-Complexity Zonotopes Can Enhance Uncertainty Quantification (Uq), Olga Kosheleva, Vladik Kreinovich
Low-Complexity Zonotopes Can Enhance Uncertainty Quantification (Uq), Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, the only information that we know about the measurement error is the upper bound D on its absolute value. In this case, once we know the measurement result X, the only information that we have about the actual value x of the corresponding quantity is that this value belongs to the interval [X − D, X + D]. How can we estimate the accuracy of the result of data processing under this interval uncertainty? In general, computing this accuracy is NP-hard, but in the usual case when measurement errors are relatively small, we can linearize the …
Machine Learning Analysis To Characterize Phase Variations In Laser Propagation Through Deep Turbulence, Luis Fernando Rodriguez Sanchez
Machine Learning Analysis To Characterize Phase Variations In Laser Propagation Through Deep Turbulence, Luis Fernando Rodriguez Sanchez
Open Access Theses & Dissertations
The present Dissertation is focused on the analysis of the atmospheric conditions of a turbulent environmental system and its effects on the diffraction of a laser beam that moves through it. The study is based on the optical communication of two labs placed at the summit of two mountains located in Maui, Hawaii. The emitter system is located at the Mauna Loa mountain and the receiver at the Haleakala. The distance between both mountains is 150 km. The emitter system is at a height of 3.1 km and the receiver at 3.4 km. The maritime environment at the location experiences …
Planar Motion Control Of A Cube Satellite Using Cold Gas Thrusters, Christian Lozoya
Planar Motion Control Of A Cube Satellite Using Cold Gas Thrusters, Christian Lozoya
Open Access Theses & Dissertations
This Thesis presents a mathematical model developed for the computational simulation ofCubeSat movement using four thrusters that permit uniaxial translation and rotation. Arbitrary functions are fit to boundary conditions to simulate the force, acceleration, velocity, and displacement of the CubeSat along a plane. The model is used to derive a motion control algorithm assuming constant pressure and mass. A single model describes both translation and rotation. This Thesis also explores the relationship between propellant consumption and the time required to complete a displacement implied by the model.
Towards Analytical Techniques For Systems Engineering Applications, Griselda Valdepeñas Acosta
Towards Analytical Techniques For Systems Engineering Applications, Griselda Valdepeñas Acosta
Open Access Theses & Dissertations
One of the main objectives of systems engineering is to design, maintain, and analyze systems that help the users. To design an appropriate system for an application domain, we need to know: what are the users' desires and preferences (so that we know in what direction we should aim to change this domain), what is the current state and what is the dynamics of this application domain, and how to use all this information to select the best alternatives for the system design and maintenance. Designing a system includes selecting numerical values for many of the parameters describing the corresponding …
Formulation And Implementation Of Iterative Method For Generating Spatially-Variant Lattices, Manuel Fernando Martinez
Formulation And Implementation Of Iterative Method For Generating Spatially-Variant Lattices, Manuel Fernando Martinez
Open Access Theses & Dissertations
The use of a matrix-free, memory-efficient approach to generate large-scale spatially variant lattices (SVL) was explored. A matrix-free iterative SVL generation algorithm was formulated and then implemented with a tremendous memory reduction observed. The algorithm consists of solving first-order central finite-differences along the entirety of the problem space point-by-point to obtain the grating phase function Φ(𝑠⃗) to which all desired spatially variant lattice properties are applied to. The algorithm was studied to identify key areas of data and task parallelism to exploit in heterogeneous computing systems consisting of clusters of central processing units (CPU) and graphics processing units (GPU) combinations. …
An Efficient Method For Online Identification Of Steady State For Multivariate System, Honglun None Xu
An Efficient Method For Online Identification Of Steady State For Multivariate System, Honglun None Xu
Open Access Theses & Dissertations
Most of the existing steady state detection approaches are designed for univariate signals. For multivariate signals, the univariate approach is often applied to each process variable and the system is claimed to be steady once all signals are steady, which is computationally inefficient and also not accurate. The article proposes an efficient online method for multivariate steady state detection. It estimates the covariance matrices using two different approaches, namely, the mean-squared-deviation and mean-squared-successive-difference. To avoid the usage of a moving window, the process means and the two covariance matrices are calculated recursively through exponentially weighted moving average. A likelihood ratio …
Analysis Of High Performance Scientific Programming Workflows, Withana Kankanamalage Umayanganie Klaassen
Analysis Of High Performance Scientific Programming Workflows, Withana Kankanamalage Umayanganie Klaassen
Open Access Theses & Dissertations
Substantial time is spent on building, optimizing and maintaining large-scale software that is run on supercomputers. However, little has been done to utilize overall resources efficiently when it comes to including expensive human resources. The community is beginning to acknowledge that optimizing the hardware performance such as speed and memory bottlenecks contributes less to the overall productivity than does the development lifecycle of high-performance scientific applications. Researchers are beginning to look at overall scientific workflows for high performance computing. Scientific programming productivity is measured by time and effort required to develop, configure, and maintain a simulation experiment and its constituent …
Combining Interval And Probabilistic Uncertainty In Engineering Applications, Andrew Martin Pownuk
Combining Interval And Probabilistic Uncertainty In Engineering Applications, Andrew Martin Pownuk
Open Access Theses & Dissertations
In many practical application, we process measurement results and expert estimates. Measurements and expert estimates are never absolutely accurate, their result are slightly different from the actual (unknown) values of the corresponding quantities. It is therefore desirable to analyze how this measurement and estimation inaccuracy affects the results of data processing. There exist numerous methods for estimating the accuracy of the results of data processing under different models of measurement and estimation inaccuracies: probabilistic, interval, and fuzzy. To be useful in engineering applications, these methods should provide accurate estimate for the resulting uncertainty, should not take too much computation time, …
Science Is Helpful For Engineering Applications: A Theoretical Explanation Of An Empirical Observation, Olga Kosheleva, Vladik Kreinovich
Science Is Helpful For Engineering Applications: A Theoretical Explanation Of An Empirical Observation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Empirical evidence shows that when engineering design uses scientific analysis, we usually get a much better performance that for the system designed by using a trial-and-error engineering approach. In this paper, we provide a quantitative explanation for this empirical observation.
Symbolic Aggregate Approximation (Sax) Under Interval Uncertainty, Chrysostomos D. Stylios, Vladik Kreinovich
Symbolic Aggregate Approximation (Sax) Under Interval Uncertainty, Chrysostomos D. Stylios, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we monitor a system by continuously measuring the corresponding quantities, to make sure that an abnormal deviation is detected as early as possible. Often, we do not have ready algorithms to detect abnormality, so we need to use machine learning techniques. For these techniques to be efficient, we first need to compress the data. One of the most successful methods of data compression is the technique of Symbolic Aggregate approXimation (SAX). While this technique is motivated by measurement uncertainty, it does not explicitly take this uncertainty into account. In this paper, we show that we can …
Why It Is Important To Precisiate Goals, Olga Kosheleva, Vladik Kreinovich, Hung T. Nguyen
Why It Is Important To Precisiate Goals, Olga Kosheleva, Vladik Kreinovich, Hung T. Nguyen
Departmental Technical Reports (CS)
After Zadeh and Bellman explained how to optimize a function under fuzzy constraints, there have been many successful applications of this optimization. However, in many practical situations, it turns out to be more efficient to precisiate the objective function before performing optimization. In this paper, we provide a possible explanation for this empirical fact.
Simple Linear Interpolation Explains All Usual Choices In Fuzzy Techniques: Membership Functions, T-Norms, T-Conorms, And Defuzzification, Vladik Kreinovich, Jonathan Quijas, Esthela Gallardo, Caio De Sa Lopes, Olga Kosheleva, Shahnaz Shahbazova
Simple Linear Interpolation Explains All Usual Choices In Fuzzy Techniques: Membership Functions, T-Norms, T-Conorms, And Defuzzification, Vladik Kreinovich, Jonathan Quijas, Esthela Gallardo, Caio De Sa Lopes, Olga Kosheleva, Shahnaz Shahbazova
Departmental Technical Reports (CS)
Most applications of fuzzy techniques use piece-wise linear (triangular or trapezoid) membership functions, min or product t-norms, max or algebraic sum t-conorms, and centroid defuzzification. Similarly, most applications of interval-valued fuzzy techniques use piecewise-linear lower and upper membership functions. In this paper, we show that all these choices can be explained as applications of simple linear interpolation.
Synchronization Of Bistatic Radar Using Chaotic Amplitude And Frequency Modulated Signals, Chandra Sekhar Pappu
Synchronization Of Bistatic Radar Using Chaotic Amplitude And Frequency Modulated Signals, Chandra Sekhar Pappu
Open Access Theses & Dissertations
The purpose of this work is to develop a synchronization scheme for bistatic radar that uses a 3-D chaotic system to generate and process wideband AM and FM signals, which allows for the extraction of high range-resolution information from targets. For AM bistatic radar, the setup includes a drive oscillator at the transmitter and a response oscillator at the receiver. The challenge is synchronizing the response oscillator to the drive oscillator with a scaled version of the transmitted signal sr(t, x) = αs t(t, x), where x is a chaotic state variable and α is a scaling factor. Here, α …
Imprecise Probabilities In Engineering Analyses, Michael Beer, Scott Ferson, Vladik Kreinovich
Imprecise Probabilities In Engineering Analyses, Michael Beer, Scott Ferson, Vladik Kreinovich
Departmental Technical Reports (CS)
Probabilistic uncertainty and imprecision in structural parameters and in environmental conditions and loads are challenging phenomena in engineering analyses. They require appropriate mathematical modeling and quantification to obtain realistic results when predicting the behavior and reliability of engineering structures and systems. But the modeling and quantification is complicated by the characteristics of the available information, which involves, for example, sparse data, poor measurements and subjective information. This raises the question whether the available information is sufficient for probabilistic modeling or rather suggests a set-theoretical approach. The framework of imprecise probabilities provides a mathematical basis to deal with these problems which …
High-Order Central Finite-Volume Schemes For Atmospheric Modeling, Kiran Kumar Katta
High-Order Central Finite-Volume Schemes For Atmospheric Modeling, Kiran Kumar Katta
Open Access Theses & Dissertations
Atmospheric numerical modeling has been going through drastic changes over the past decade, mainly to utilize the massive computing capability of the petascale systems. This obliges the modelers to develop grid systems and numerical algorithms that facilitate exceptional level of scalability on these systems. The numerical algorithms that can address these challenges should have the local properties such as the high on-processor operation count and minimum parallel communication i.e., high parallel efficiency. They should also satisfy the following properties such as inherent local and global conservation, high-order accuracy, geometric flexibility, non-oscillatory advection and positivity preservation properties. The goal of this …
Semi-Automated Frame Transformations Using Fft Analysis On 2-D Images, Francisco Javier Osuna
Semi-Automated Frame Transformations Using Fft Analysis On 2-D Images, Francisco Javier Osuna
Open Access Theses & Dissertations
Cassini entered Saturn's orbit on July 1, 2004 beginning a four-year exploration of Saturn. In 2008 the mission was extended, and Cassini continues to collect and transmit images and data collected during its mission. In order to accurately interpret images, it is necessary to know the location and orientation of the camera provided the field of view when the image was collected. While the mission managers provide initial estimates of this orientation, scientific analysis requires better estimates than the initial data provided. Navigation is a process for improving the estimation of the true camera pointing vector as determined by features …