Graduation Year

2023

Document Type

Dissertation

Degree

Ph.D.

Degree Name

Doctor of Philosophy (Ph.D.)

Degree Granting Department

Mathematics and Statistics

Major Professor

Chris P. Tsokos, Ph.D.

Committee Member

Kandethody M. Ramachandran, Ph.D.

Committee Member

Lu Lu, Ph.D.

Committee Member

Yicheng Tu, Ph.D.

Keywords

Cancer Survivorship, Computer Operating Systems, Kernel Density, NHPP, Vulnerability

Abstract

One of the major tasks in the present day-era is securing computer systems against unauthorized access. Every year we lost millions of dollars because of cyber attacks and thousands of people suffer economically and psychologically. Rapid development in the field of information technology increases the challenges to the Information technology personnel working on protecting against cyber attacks. In cyber security, vulnerabilities and hackers play a major role. Researchers are putting in enormous efforts to develop methods and models to control vulnerabilities and psychological behavior and motivation of hackers. Our study defines two important aspects of the computer operating system concerning the number of its vulnerabilities behavior. We identify the Stochastic Vulnerability Intensity Function, SVIF, and the Stochastic Vulnerability Index Indicator, SVII, of a computer operating network. Both of these functions, SVIF and SVII, are entities of the stochastic process that we have identified, which characterizes the probabilistic behavior of the number of vulnerabilities of a computer operating network. The SVIF identifies the rate at which the number of vulnerabilities changes with respect to time. The SVII is an important index indicator that conveys the following information about the number of vulnerabilities of desktop operating systems: the numbers are increasing, decreasing, or remaining the same at a particular time of interest. This decision type of index indicator is crucial in every strategic planning and decision-making.

We have also developed a data-driven analytical model to incorporate hacker skills with other risk factors such as Age, gender, race, the education they have received, and vulnerability find. In addition, we want to measure the risk associated with each host node base on the exploitability score, impact score, and hacker's skill to find vulnerabilities. We found age, race, education, gender, and the number of vulnerabilities found are significant contributing risk factors for hacker skills. Based on attackers' skills, each vulnerability has a different weight associated with it. Hence, the characteristics and skills of hackers have a tremendous effect on the risk associated with each vulnerability and the chances of exploitation. This study shows that it is very necessary to quantify hackers' behavior and include it while studying for risks associated with any vulnerabilities.

Ovarian cancer(OC) has the highest death rate among all other cancers of the female reproductive system. Patients are divided into two groups based on histology types, Epithelial ovarian cancers(EOC) and Non-epithelial ovarian cancers(NEOC). These two groups are further divided based on their marital status in order to assess the survival time discrepancy between these groups. We performed parametric survival analysis driven by the four-parameter probability distribution Johnson SB and the three-parameter log-normal probability distribution to explain the underlying probabilistic behavior of the survival time of never married EOC, widowed EOC, divorced/separated EOC, and NOEC patients. The non-parametric Gaussian kernel density estimation with a direct plug-in bandwidth selection method was used to explain the survival time of the EOC and married EOC patients. Then we estimated the survival probability of each group and the survival probabilities were compared with each other.

We have also performed parametric survival analysis on Germ Cell NEOC and Sex-Cord NEOC and found survival time of both histology types followed 3P- lognormal probability distribution. Then we estimated the survival probability and compared it with the non-parametric survival analysis of the survival times using Kernel density estimates and also the commonly used non-parametric Kaplan-Meier survival analysis that is not as powerful nor robust. The comparison of the survival probability estimate of the three methods revealed a better survival probability estimate by the parametric method; if the parametric method is not applicable then the kernel density estimates performed better than the Kaplan-Meier. The comparison between survival times based on histology types discloses that the overall survival time for patients diagnosed with sex cord-stromal NEOC has higher survival time than for germ cell NEOC.

Furthermore, we have defined/introduced the Stochastic Ovarian Cancer Intensity Function, SOCIF, and the Stochastic Ovarian Cancer Index Indicator, SOCII, of the survival times of ovarian cancer patients. We have identified a stochastic process that characterizes the probabilistic behavior of the failure times of ovarian cancer patients containing both of these entities, SOCIF and SOCII. The SOCIF identifies the rate at which the survival time of ovarian cancer changes as a function of time. The SOCII is an important index indicator that conveys the following information about the survival time of ovarian cancer patients at a specific time after applying different types of treatments. If SOCII < 1 the treatments are effective which means the survival times of patients are increasing. If SOCII > 1 the treatments are negatively effective which means the survival times of patients are decreasing. If SOCII = 1 the treatment has no effect on patient health which means the patient’s condition remains the same at a particular time of interest based on the patient’s marital status, time from diagnosis to treatment, cancer stages, and treatment they received. We believe this study will help to enhance the treatment strategy for ovarian cancer patients.

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