On An Entropy Estimator Based On a Non-parametric Density Estimator For Non-negative Data

In the recent decades, entropy has become more and more essential in statistics and machine learning. It features in many applications involving data transmission, cryptography, signal processing, network theory, bio-informatics, and so on. A large number of estimators for entropy have been proposed in the past ten years. Here we focus on entropy estimation for non-negative random variables. Specifically, the use of entropy estimator based on Poisson-weights density estimator is found to be of interest. We establish some asymptotic properties of the resulting estimators and present a simulation study comparing these with well known estimators in literature

A Numerical Study of Entropy and Residual Entropy Estimators Based on Smooth Density Estimators for Non-negative Random Variables

In this paper, we are interested in the entropy of a non-negative random variable. Since the underlying probability density function is unknown, we propose the use of Poisson smoothed histogram density estimator in order to estimate the entropy. To study the performance of our estimator, we run simulations on a wide range of densities and compare our entropy estimators with the existing estimators that based on different approaches such as spacing estimators. Furthermore, we extend our study to residual entropy estimators which is the entropy of a random variable given that it has been survived up to time t

Depth perception from motion under viewpoint distortion

Master'sMASTER OF ENGINEERIN

Modeling of the human upper airway from multimodal 3D dentofacial images

Ph.DDOCTOR OF PHILOSOPH

Some Fluctuation Results Related to Draw-down Times for Spectrally Negative Levy processes And On Estimation of Entropy and residual Entropy for Nonnegative Random Variable

Part I In this thesis, we first introduce and review some fluctuation theory of Levy processes, especially for general spectrally negative Levy processes and for spectrally negative Levy taxed processes. Then we consider a more realistic model by introducing draw-down time, which is the first time a process falls below a predetermined draw-down level which is a function of the running maximum. Particularly, we present the expressions for the classical two-sided exit problems for these processes with draw-down times in terms of scale functions. We also find the expressions for the discounted present values of tax payments with draw-down time in place of ruin time. Finally, we obtain the expression of the occupation times for the general spectrally negative Levy processes to spend in draw-down interval killed on either exiting a fix upper level or a draw-down lower level. Part II Entropy has become more and more essential in statistics and machine learning. A large number of its applications can be found in data transmission, cryptography, signal processing, network theory, bio-informatics, and so on. Therefore, the question of entropy estimation comes naturally. Generally, if we consider the entropy of a random variable knowing that it has survived up to time $t$, then it is defined as the residual entropy. In this thesis we focus on entropy and residual entropy estimation for nonnegative random variable. We first present a quick review on properties of popular existing estimators. Then we propose some candidates for entropy and residual entropy estimator along with simulation study and comparison among estimators

Some Fluctuation Identities of Hyper-Exponential Jump-Diffusion Processes

Meromorphic L´evy processes have attracted the attention of a lot of researchers recently due to its special structure of the Wiener-Hopf factors as rational functions of infinite degree written in terms of poles and roots of the Laplace exponent, all of which are real numbers. With these Wiener-Hopf factors in hand, we can explicitly derive the expression of fluctuation identities that concern the first passage problems for finite and infinite intervals for the meromorphic L´evy process and the resulting process reflected at its infimum. In this thesis, we consider some fluctuation identities of some classes of meromorphic jump-diffusion processes with either the double exponential jumps or more general the hyper-exponential jumps. We study solutions to the one-sided and two-sided exit problems, and potential measure of the process killed on exiting a finite or infinite intervals. Also, we obtain some results to the process reflected at its infimum

Manipulation of graphitic microparticles in solution with magnetic and electric fields

Contactless manipulation methods for individual microparticles in solution are essential for the controlled study on the microscopic scale. Microparticles derived from graphitic materials, in particular, are of great interest due to their unique material properties. However to date, the manipulation methods for such particles remain widely unexplored. This thesis presents the rst research on the particle manipulation of graphitic microparticles in a diamagnetic solution with electric and magnetic elds. The results show that the particles can be rotationally trapped on a well-de ned plane with a combination of an alternating current electric eld and a static magnetic eld. Furthermore, particle transport and three-dimensional particle trapping can be achieved with static magnetic elds. This research shows that the unique electrical and magnetic properties of graphitic microparticles can lead to novel particle manipulation methods in solution which can be attractive for applications in many areas of research

Design and analysis of a displacement sensor-integrated compliant microgripper based on parallel structure

This study evaluates the displacement sensitivity of a new compliant microgripper. The microgripper is designed based on a four-bar mechanism and the concept of a compliant mechanism. The effects of the width of the right circular hinge, the thickness of microgripper, and the material properties on the dis-placement sensitivity are considered via using the finite element method. In the beginning, the stress and deformation of the compliant microgripper are evaluated. Subsequently, the displacement of the microgripper is then analyzed. The results showed that the design parameter and the displacement sensitivity have a close relationship. To increase the grasping reliability and measure the displacement or force, a micro-displacement sensor is integrated with the proposed microgripper. Finally, the modeling and analysis of the proposed sensor are conducted

The local uniform convergence of positive harmonic function sequence

The Harnack distance on space  and its conformal invariance were constructed and studied by Herron. In this paper, we obtain the Harnack distance on domains  in . Then, we use this concept to investigate some properties of the positive harmonic function class. These results are obtained in the complex plane, so it is advantageous to take some tools of the complex analysis. The main result of this paper is the property of the local uniform convergence of the positive harmonic sequences on a domain in the complex plane.The Harnack distance on space  and its conformal invariance were constructed and studied by Herron. In this paper, we obtain the Harnack distance on domains  in . Then, we use this concept to investigate some properties of the positive harmonic function class. These results are obtained in the complex plane, so it is advantageous to take some tools of the complex analysis. The main result of this paper is the property of the local uniform convergence of the positive harmonic sequences on a domain in the complex plane

Factor substitution in rice production function: the case of Vietnam

Vietnamese rice production has achieved remarkable success over the last couple of decades. This is due to land and market reforms, known as ‘Doi Moi’. There were noticeable changes in policies, such as land and production systems, which were transformed from a collective to an individual contract system in the 1980s. Vietnam made progress in rice production through the legalisation of the privatisation of farm properties and a huge investment in irrigation systems. The country not only ensured its domestic demand, but also started exporting rice and gradually became the second largest exporter in the world. An estimate of the Constant Elasticity of Substitution function (CES) for Vietnam’s rice production is essential for the government to design effective policy on agricultural production. This study makes the first attempt to estimate the nested CES model for Vietnamese rice production in 2012. The paper finds that the elasticity of substitution of Vietnam’s nested CES model lies between 0.44 and 0.46. The results indicate the weak substitutability between land and the capital-labour composite in the nested CES model. This also suggests that it is impossible to take labour as the substitutable factor for land and capital