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Full-Text Articles in Physical Sciences and Mathematics
Mathematically Modeling Pcr: An Asymptotic Approximation With Potential For Optimization, Martha J. Garlick
Mathematically Modeling Pcr: An Asymptotic Approximation With Potential For Optimization, Martha J. Garlick
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being extended one bas e pair at a time. The equations for the annealing stage are solved analytically. The method of multiple scales is used to approximate solutions for the extension stage. A map is then developed from the solutions to simulate PCR. The advantage of this model is the ability to use the map to optimize the process. Our results suggest that dynamically optimizing the extension …
Sas Macro For Hierarchical Dependence In Meta Analysis, Matthew Wayne Maw
Sas Macro For Hierarchical Dependence In Meta Analysis, Matthew Wayne Maw
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
This project implemented a simple and useful SAS (Statistical Analysis Software) macro for meta-analysis. The macro was specifically designed for hierarchically dependent meta-analysis but may also be used for independent meta-analysis. Two data files are necessary for this macro. One data file contains the study names, control and treatment group sizes with corresponding means and standard errors, covariates to be tested, an indicator variable noting hierarchically dependent study groups, and a variable providing the degrees of freedom for interdependent studies. The second file contains a variance/covariance matrix for the studies. The macro returns useful information such as study estimates and …
Black-Scholes And Extended Black-Scholes Models: A Comparative Statistical Analysis, Bradley Thomas Bush
Black-Scholes And Extended Black-Scholes Models: A Comparative Statistical Analysis, Bradley Thomas Bush
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Much research has been done on options pricing. Black and Scholes [12] set the benchmark in 1973 with their model for arbitrage-free, risk-neutral options valuation. Arbitrage-free refers to a market environment where prices are such that trading opportunities with no risk do not exist and risk-neutral commodities earn a risk free interest rate. Since then the literature has seen a multitude of models improving the fit of the traditional Black -Scholes (BS) model. A brief overview of options and these models is given. A derivation and discussion of BS is followed by a derivation and discussion of the Extended Black-Scholes …
Decomposing Vector Space Representations Of The Lie Algebras S[2c And S[2r, Brian W. Gleason
Decomposing Vector Space Representations Of The Lie Algebras S[2c And S[2r, Brian W. Gleason
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
It is known that any finite-dimensional representation of a semi-simple Lie algebra is decomposable into a direct sum of irreducible representations. Here we prove some theoretical results that allow us to construct an efficient algorithm for computing such a decomposition for representations of s[2C and s[2R. We then implement this algorithm in a procedure for the computer algebra system Maple that will quickly and easily perform the decomposition. We also give several examples of this decomposition performed by the procedure in order to illustrate its advantages over calculations done ‘by hand'.
A Method For Finding Standard Error Estimates For Rma Expression Levels Using Bootstrap, Gabriel Nicholas
A Method For Finding Standard Error Estimates For Rma Expression Levels Using Bootstrap, Gabriel Nicholas
All Graduate Plan B and other Reports, Spring 1920 to Spring 2023
Oligonucleotide arrays are used in many applications. Affymetrix GeneChip arrays are widely used. Before researchers can use the information from these arrays, the raw data must be transformed and summarized into a more meaningful and usable form. One of the more popular methods for doing so is RMA (Robust Multi-array Analysis).
A problem with RMA is that the end result (estimated gene expression levels) is based on a fairly complicated process that is unusual. Specifically, there is no closed-form estimate of standard errors for the estimated gene expression levels. The current recommendation is to use a naive estimate for the …