Probability Commons^™

The Torsion Angle Of Random Walks, Mu He

Masters Theses & Specialist Projects

In this thesis, we study the expected mean of the torsion angle of an n-step
equilateral random walk in 3D. We consider the random walk is generated within a confining sphere or without a confining sphere: given three consecutive vectors ^→e₁ , ^→e₂ , and ^→e₃ of the random walk then the vectors ^→e₁ and ^→e₂ define a plane and the vectors ^→e₂ and ^→e₃ define a second plane. The angle between the two planes is called the torsion angle of the three vectors. Algorithms are described to generate random walks which are used in ...

A Study Of Poisson And Related Processes With Applications, Phillip Mingola

University of Tennessee Honors Thesis Projects

No abstract provided.

The Untenability Of A Priori Prior Probabilities In Objective Bayesian Conditionalization, C.S. Arledge

Senior Honors Papers

The problem of theory confirmation has been an issue in the philosophy of science for decades. Many valiant attempts have been made to formulate a generally accepted criterion for determining the validity of a scientific theory. Bayesian probability theory has been utilized in numerous attempts to examine the epistemic nature of theory confirmation and Jonathan Weisberg offers a formulation of Bayesian Conditionalization that he believes to be both objective and successful.

In this paper I intend to show the defects in Weisberg’s theory of objective Bayesian confirmation by utilizing the arguments of both W.V. Quine and Bas van ...

Game Theoretic Analysis Of A Strategic Model Of Competitive Contagion And Product Adoption In Social Networks, Arastoo Fazeli, Ali Jadbabaie

Departmental Papers (ESE)

In this paper we propose and study a strategic model of marketing and product adoption in social networks. Two firms compete for the spread of their products in a social network. Considering their fixed budgets, they initially determine the payoff of their products and the number of their initial seeds in a network. Afterwards, neighboring agents play a local coordination game over a fixed network which determines the dynamics of the spreading. Assuming myopic best response dynamics, agents choose a product based on the payoff received by actions of their neighbors. This local update dynamics results in a game-theoretic diffusion ...

Targeted Marketing And Seeding Products With Positive Externality, Arastoo Fazeli, Ali Jadbabaie

Departmental Papers (ESE)

We study a strategic model of marketing in social networks in which two firms compete for the spread of their products. Firms initially determine the production cost of their product, which results in the payoff of the product for consumers, and the number and the location of the consumers in a network who receive the product as a free offer. Consumers play a local coordination game over a fixed network which determines the dynamics of the spreading of products. Assuming myopic best response dynamics, consumers choose a product based on the payoff received by actions of their neighbors. This local ...

Asymmetric Empirical Similarity, Joshua C. Teitelbaum

Georgetown Law Faculty Publications and Other Works

The paper suggests a similarity function for applications of empirical similarity theory in which the notion of similarity is asymmetric. I propose defining similarity in terms of a quasimetric. I suggest a particular quasimetric and explore the properties of the empirical similarity model given this function. The proposed function belongs to the class of quasimetrics induced by skewed norms. Finally, I provide a skewness axiom that, when imposed in lieu of the symmetry axiom in the main result of Billot et al. (2008), characterizes an exponential similarity function based on a skewed norm.

Mathematics Curriculum Revised To Align To Common Core State Standards, Ashley Redino

Education and Human Development Master's Theses

The Common Core State Standards (CCSS) are the first set of national standards issued in the United States. Currently, all states are in the transition from implementing individual state standards to CCSS in ELA and mathematics. As the CCSS are being introduced and implemented into classrooms, educators are struggling to update or modify their current unit, based on the National Council of Teachers of Mathematics (NCTM) Standards, to align with the new national standards. This research provides an explanation of the changes that will occur due to the CCSS in a seventh grade probability and statistics unit. An updated unit ...

Approximate Methods For Dynamic Portfolio Allocation Under Transaction Costs, Nabeel Butt

Electronic Thesis and Dissertation Repository

The thesis provides robust and efficient lattice based algorithms for solving dynamic portfolio allocation problems under transaction costs. The early part of the thesis concentrates upon developing a toolbox based on multinomial trees. The multinomial trees are shown to provide a reasonable approximation for most popular transaction cost models in the academic literature. The tool, once forged, is implemented in the powerful Mathematica based parallel computing environment. In the second part of the thesis we provide applications of our framework to real world problems. We show re-balancing portfolios is more valuable in an investment environment where the growth and volatility ...

Retrieval Of Sub-Pixel-Based Fire Intensity And Its Application For Characterizing Smoke Injection Heights And Fire Weather In North America, David Peterson

Dissertations & Theses in Earth and Atmospheric Sciences

For over two decades, satellite sensors have provided the locations of global fire activity with ever-increasing accuracy. However, the ability to measure fire intensity, know as fire radiative power (FRP), and its potential relationships to meteorology and smoke plume injection heights, are currently limited by the pixel resolution. This dissertation describes the development of a new, sub-pixel-based FRP calculation (FRP_f) for fire pixels detected by the MODerate Resolution Imaging Spectroradiometer (MODIS) fire detection algorithm (Collection 5), which is subsequently applied to several large wildfire events in North America. The methodology inherits an earlier bi-spectral algorithm for retrieving sub-pixel fire ...

Multitarget Tracking Using Multistatic Sensors, Maheswaran Subramaniam

Open Access Dissertations and Theses

In this thesis the problem of multitarget tracking in multistatic sensor networks is studied. This thesis focuses on tracking airborne targets by utilizing transmitters of opportunity in the surveillance region. Passive Coherent Location (PCL) system, which uses existing commercial signals (e.g., FM broadcast, digital TV) as the illuminators of opportunity for target tracking, is an emerging technology in air defence systems. PCL systems have many advantages over conventional radar systems such as low cost, covert operation and low vulnerability to electronic counter measures.

One of another opportunistic signals available in the surveillance region is multipath signal. In this thesis ...

Modeling And Mathematical Analysis Of Plant Models In Ecology, Eric A. Eager

Dissertations, Theses, and Student Research Papers in Mathematics

Population dynamics tries to explain in a simple mechanistic way the variations of the size and structure of biological populations. In this dissertation we use mathematical modeling and analysis to study the various aspects of the dynamics of plant populations and their seed banks.

In Chapter 2 we investigate the impact of structural model uncertainty by considering different nonlinear recruitment functions in an integral projection model for Cirsium canescens. We show that, while having identical equilibrium populations, these two models can elicit drastically different transient dynamics. We then derive a formula for the sensitivity of the equilibrium population to changes ...