Mathematics
http://hdl.handle.net/10139/773
2020-05-31T11:04:07ZNonparametric estimation of blood alcohol concentration from transdermal alcohol measurements using alcohol biosensor devices
http://hdl.handle.net/10211.3/214580
Nonparametric estimation of blood alcohol concentration from transdermal alcohol measurements using alcohol biosensor devices
Vader, Bryan E.
Alcohol biosensor devices have the prospect to positively impact medicine and law enforcement by giving a noninvasive method to acquire continuous alcohol readings. We propose to develop a nonparametric estimation algorithm that estimates the joint mixing distribution of the parameters of a heat equation model via a maximum likelihood method. This model is assumed to estimate the diffusion of alcohol through transdermal layers while taking into account measurement error. These parameters are assumed to be random due to natural irregularity in an individual's body conditions and the variability of population data. This is superior to parametric estimation methods since it can capture unusual fluctuations of a subject’s condition as well as environmental factors. This will help to ascertain a precise relation between blood alcohol concentration and transdermal alcohol concentration.
2019-01-01T00:00:00ZThe Convergence of Markov Chains and Language
http://hdl.handle.net/10211.3/214579
The Convergence of Markov Chains and Language
LaGrange, Thomas L.
Markov Chains are a category of stochastic processes with an associated dependence structure. Their inception resulted from A. A. Markov’s desire to disprove a rival’s assertion concerning the application of the Law of Large Numbers (LLN) to dependent variables. Markov’s use of a classic Russian novel to illustrate a dependent relationship between vowels and consonants serves as motivation for investigating the extent to which the properties of these processes can be applied to other means of communication. This work summarizes a history of the Law of Large Numbers and the Markovian properties associated with three different aspects of communication.
2019-01-01T00:00:00ZA broad review of important wave equations, solutions, applications, and numerical modeling
http://hdl.handle.net/10211.3/210173
A broad review of important wave equations, solutions, applications, and numerical modeling
Costa, Matthew
Derivations of wave equations, various presentations of their solutions and MATLAB models are presented. Thereafter, basic ocean wave forecasting will be discussed along with it’s applications.
2019-01-01T00:00:00ZCreating New Elliptic Curves for Uses in Cryptography
http://hdl.handle.net/10211.3/209385
Creating New Elliptic Curves for Uses in Cryptography
Zechlin, Mollie J.
Public key cryptography, is the basis of m odem cryptography, allows us to send and receive messages over public channels secretly, without requiring a meeting beforehand. Most public key cryptosystems, such as the Diffie- Hellman Key Exchange, rely on the difficulty of solving the Discrete Logarithm Problem (DLP). We can translate public key cryptosystems that rely on the DLP to Elliptic Curve cryptosystems as the Elliptic Curve Discrete Logarithm Problem (ECDLP) is believed to be more difficult and therefore harder
to break. There are certain precautions we need to take when using Elliptic Curve Cryptography to safeguard against particular attacks on the cryptosystem.
Therefore, picking a curve that is secure enough is crucial to a good cryptosystem.
Unfortunately, there are only a handful of secure elliptic curves that are publicly known and used. The goal of this thesis is to generate more elliptic curves that are useful for our security systems.
2019-01-01T00:00:00Z