DRUM Community: Mathematicshttp://hdl.handle.net/1903/22612015-01-28T06:34:36Z2015-01-28T06:34:36ZTiming Attacks on Cryptosystems: 18 Years LaterGlowacki, Claricehttp://hdl.handle.net/1903/158362014-10-12T02:32:32Z2014-01-01T00:00:00ZTitle: Timing Attacks on Cryptosystems: 18 Years Later
Authors: Glowacki, Clarice
Abstract: This work applies methodology for cryptosystem timing attacks to elliptic curve encryption using parametric coordinates. Additionally, we attempt to replicate the results found by Paul Kocher regarding timing attacks on RSA cryptosystems. Multiple implementations including Sage, MuPAD, Mathematica, and Python are attempted. Viability of timing attacks with modern computing power is assessed.2014-01-01T00:00:00ZON CONFORMALLY FLAT CIRCLE BUNDLES OVER SURFACESHo, Son Lamhttp://hdl.handle.net/1903/158252014-10-12T02:30:31Z2014-01-01T00:00:00ZTitle: ON CONFORMALLY FLAT CIRCLE BUNDLES OVER SURFACES
Authors: Ho, Son Lam
Abstract: We study surface groups $\Gamma$ in $SO(4,1)$, which is the group of conformal automorphisms of $S^3$, and also the group of isometries of $\mathbb{H}^4$. We consider such $\Gamma$ so that its limit set $\Lambda_\Gamma$ is a quasi-circle in $S^3$, and so that the quotient $(S^3 - \Lambda_\Gamma) / \Gamma$ is a circle bundle over a surface. This circle bundle is said to be conformally flat, and our main goal is to discover how twisted such bundle may be by establishing a bound on its Euler number.
We have two results in this direction. First, given a surface group $\Gamma$ which admits a nice fundamental domain with $n$ sides, we show that $(S^3 - \Lambda_\Gamma) / \Gamma$ has Euler number bounded by $n^2$. Second, if $\Gamma$ is purely loxodromic acting properly discontinuously on $\mathbb{H}^4$, and $\Gamma$ satisfies a mild technical condition, then the disc bundle quotient $\mathbb{H}^4/\Gamma$ has Euler number bounded by $(4g-2)(36g-23)$ where $g$ is the genus of the underlying surface. Both results are proven using a direct combinatorial approach. The above are not tight bounds, improvements are possible in future research.2014-01-01T00:00:00ZHierarchical Bayes Analysis of Behavioral ExperimentsDong, Chenhttp://hdl.handle.net/1903/158192014-10-12T02:36:27Z2014-01-01T00:00:00ZTitle: Hierarchical Bayes Analysis of Behavioral Experiments
Authors: Dong, Chen
Abstract: In this dissertation, we develop generalized hierarchical Bayesian ANOVA, to assist experimental researchers in the behavioral and social sciences in the analysis of the effects of experimentally manipulated within- and between-subjects factors. The method alleviates several limitations of classical ANOVA, still commonly employed in those fields. An accompanying R package for hierarchical Bayesian ANOVA is developed. It offers statistical routines and several easy-to-use functions for esti- mation of hierarchical Bayesian ANOVA models that are tailored to the analysis of experimental research. Markov chain Monte Carlo (MCMC) simulation is used to simulate posterior samples of the parameters of each model specified by the user. The core program of all models is written in R and JAGS (Just Another Gibbs Sam- pler) which is very similar to the famous software WinBUGS. After preparing the data in the required format, users simply select an appropriate model, and estimate it without any advanced coding. The main aim of the R package is to offer freely accessible resources for hierarchical Bayesian ANOVA analysis, which makes it easy to use for behavioral researchers. We also develop generalized Bayesian mediation models for analysis of mediation effects. By using Bayesian analysis, inference is straightforward and exact, which makes it appealing for experimental studies with small samples. The Bayesian approach is also conceptually simpler for any model with a complicated structure, especially for multilevel mediation analysis. Analysis of several data sets are used to illustrate the proposed methods.2014-01-01T00:00:00ZSemiparametric Threshold Regression Analysis for Time-to-Event DataJi, Ranhttp://hdl.handle.net/1903/158182014-10-12T02:36:21Z2014-01-01T00:00:00ZTitle: Semiparametric Threshold Regression Analysis for Time-to-Event Data
Authors: Ji, Ran
Abstract: Threshold regression is a relatively new alternative approach to the Cox proportional hazards model when the proportional hazards assumption is violated. It is based on first-hitting-time models, where the time-to-event data can be modeled as the time at which the stochastic process of interest first hits a boundary or threshold state. In this dissertation, we develop a semiparametric threshold regression model with flexible covariate effects. Specifically, we propose a B-spline approximation method to estimate nonlinear covariate effects on both the initial state and the rate of the process. We show that the spline based estimators are consistent and achieve the possible optimal rate of convergence under the smooth assumption. Simulation studies are conducted for practical situations, and the methodology is applied to a study of osteoporotic fractures that motivated this investigation.
To check the validity of threshold regression model with parametric link functions, we propose two supremum-type test processes: one is based on cumulative sums of martingale residuals; the other one is based on censoring consistent residuals. The realizations of these test stochastic processes under the assumed model can be easily generated by computer simulation. We show that both tests are consistent against model misspecification. Both model checking methods have been applied to a kidney dialysis data set.2014-01-01T00:00:00Z