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- Title
- Bayesian approach to an exponential hazard regression model with a change point.
- Creator
- Abraha, Yonas Kidane, Qian, Lianfen, Florida Atlantic University, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
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This thesis contains two parts. The first part derives the Bayesian estimator of the parameters in a piecewise exponential Cox proportional hazard regression model, with one unknown change point for a right censored survival data. The second part surveys the applications of change point problems to various types of data, such as long-term survival data, longitudinal data and time series data. Furthermore, the proposed method is then used to analyse a real survival data.
- Date Issued
- 2014
- PURL
- http://purl.flvc.org/fau/fd/FA00004013
- Subject Headings
- Bayesian statistical decision theory, Mathematical statistics, Multivariate analysis -- Data processing
- Format
- Document (PDF)
- Title
- The enumeration of lattice paths and walks.
- Creator
- Gao, Shanzhen., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
A well-known long standing problem in combinatorics and statistical mechanics is to find the generating function for self-avoiding walks (SAW) on a two-dimensional lattice, enumerated by perimeter. A SAW is a sequence of moves on a square lattice which does not visit the same point more than once. It has been considered by more than one hundred researchers in the pass one hundred years, including George Polya, Tony Guttmann, Laszlo Lovasz, Donald Knuth, Richard Stanley, Doron Zeilberger,...
Show moreA well-known long standing problem in combinatorics and statistical mechanics is to find the generating function for self-avoiding walks (SAW) on a two-dimensional lattice, enumerated by perimeter. A SAW is a sequence of moves on a square lattice which does not visit the same point more than once. It has been considered by more than one hundred researchers in the pass one hundred years, including George Polya, Tony Guttmann, Laszlo Lovasz, Donald Knuth, Richard Stanley, Doron Zeilberger, Mireille Bousquet-Mlou, Thomas Prellberg, Neal Madras, Gordon Slade, Agnes Dit- tel, E.J. Janse van Rensburg, Harry Kesten, Stuart G. Whittington, Lincoln Chayes, Iwan Jensen, Arthur T. Benjamin, and many others. More than three hundred papers and a few volumes of books were published in this area. A SAW is interesting for simulations because its properties cannot be calculated analytically. Calculating the number of self-avoiding walks is a common computational problem. A recently proposed model called prudent self-avoiding walks (PSAW) was first introduced to the mathematics community in an unpublished manuscript of Pra, who called them exterior walks. A prudent walk is a connected path on square lattice such that, at each step, the extension of that step along its current trajectory will never intersect any previously occupied vertex. A lattice path composed of connected horizontal and vertical line segments, each passing between adjacent lattice points. We will discuss some enumerative problems in self-avoiding walks, lattice paths and walks with several step vectors. Many open problems are posted.
Show less - Date Issued
- 2011
- PURL
- http://purl.flvc.org/FAU/3183129
- Subject Headings
- Combinatorial analysis, Approximation theory, Mathematical statistics, Limit theorems (Probabilty theory)
- Format
- Document (PDF)
- Title
- A min/max algorithm for cubic splines over k-partitions.
- Creator
- Golinko, Eric David, Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
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The focus of this thesis is to statistically model violent crime rates against population over the years 1960-2009 for the United States. We approach this question as to be of interest since the trend of population for individual states follows different patterns. We propose here a method which employs cubic spline regression modeling. First we introduce a minimum/maximum algorithm that will identify potential knots. Then we employ least squares estimation to find potential regression...
Show moreThe focus of this thesis is to statistically model violent crime rates against population over the years 1960-2009 for the United States. We approach this question as to be of interest since the trend of population for individual states follows different patterns. We propose here a method which employs cubic spline regression modeling. First we introduce a minimum/maximum algorithm that will identify potential knots. Then we employ least squares estimation to find potential regression coefficients based upon the cubic spline model and the knots chosen by the minimum/maximum algorithm. We then utilize the best subsets regression method to aid in model selection in which we find the minimum value of the Bayesian Information Criteria. Finally, we preent the R2adj as a measure of overall goodness of fit of our selected model. We have found among the fifty states and Washington D.C., 42 out of 51 showed an R2adj value that was greater than 90%. We also present an overall model of the United States. Also, we show additional applications our algorithm for data which show a non linear association. It is hoped that our method can serve as a unified model for violent crime rate over future years.
Show less - Date Issued
- 2012
- PURL
- http://purl.flvc.org/FAU/3342107
- Subject Headings
- Spline theory, Data processing, Bayesian statistical decision theory, Data processing, Neural networks (Computer science), Mathematical statistics, Uncertainty (Information theory), Probabilities, Regression analysis
- Format
- Document (PDF)
- Title
- New Results in Group Theoretic Cryptology.
- Creator
- Sramka, Michal, Florida Atlantic University, Magliveras, Spyros S., Charles E. Schmidt College of Science, Department of Mathematical Sciences
- Abstract/Description
-
With the publication of Shor's quantum algorithm for solving discrete logarithms in finite cyclic groups, a need for new cryptographic primitives arose; namely, for more secure primitives that would prevail in the post-quantum era. The aim of this dissertation is to exploit some hard problems arising from group theory for use in cryptography. Over the years, there have been many such proposals. We first look at two recently proposed schemes based on some form of a generalization of the...
Show moreWith the publication of Shor's quantum algorithm for solving discrete logarithms in finite cyclic groups, a need for new cryptographic primitives arose; namely, for more secure primitives that would prevail in the post-quantum era. The aim of this dissertation is to exploit some hard problems arising from group theory for use in cryptography. Over the years, there have been many such proposals. We first look at two recently proposed schemes based on some form of a generalization of the discrete logari thm problem (DLP), identify their weaknesses, and cryptanalyze them. By applying the exper tise gained from the above cryptanalyses, we define our own generalization of the DLP to arbitrary finite groups. We show that such a definition leads to the design of signature schemes and pseudo-random number generators with provable security under a security assumption based on a group theoretic problem. In particular, our security assumption is based on the hardness of factorizing elements of the projective special linear group over a finite field in some representations. We construct a one-way function based on this group theoretic assumption and provide a security proof.
Show less - Date Issued
- 2006
- PURL
- http://purl.flvc.org/fau/fd/FA00000878
- Subject Headings
- Group theory, Mathematical statistics, Cryptography, Combinatorial designs and configurations, Data encryption (Computer science), Coding theory
- Format
- Document (PDF)