Mathematics Commons^™

Adaptive Randomization Designs, Jenna Colavincenzo

Statistics

Adaptive design methodologies use prior information to develop a clinical trial design. The goal of an adaptive design is to maintain the integrity and validity of the study while giving the researcher flexibility in identifying the optimal treatment. An example of an adaptive design can be seen in a basic pharmaceutical trial. There are three phases of the overall trial to compare treatments and experimenters use the information from the previous phase to make changes to the subsequent phase before it begins.

Adaptive design methods have been in practice since the 1970s, but have become increasingly complex ever since. One …

Renormalized Square Of White Noise Quantum Time Shift, Luigi Accardi, Habib Ouerdiane, Habib Rebei

Communications on Stochastic Analysis

No abstract provided.

Integral Representations Of Some Functionals Of Fractional Brownian Motion, Heikki Tikanmäki

Communications on Stochastic Analysis

No abstract provided.

Construction Of The Paths Of Brownian Motions On Star Graphs I, Vadim Kostrykin, Jürgen Potthoff, Robert Schrader

Communications on Stochastic Analysis

No abstract provided.

Limiting Distributions Of Galton-Watson Branching Processes With Immigration, Yoshinori Uchimura, Kimiaki Saitô

Communications on Stochastic Analysis

No abstract provided.

Wick Product And Clark-Ocone Formula In Abstract Wiener Space, Fariborz Asadian

Communications on Stochastic Analysis

No abstract provided.

Generalised Clark-Ocone Formulae For Differential Forms, Y Yang

Communications on Stochastic Analysis

No abstract provided.

Functional Itô'S Calculus And Dynamic Convex Risk Measures For Derivative Securities, Tak Kuen Siu

Communications on Stochastic Analysis

No abstract provided.

Chaos Representations For Marked Point Processes, Samuel N Cohen

Communications on Stochastic Analysis

No abstract provided.

Construction Of The Paths Of Brownian Motions On Star Graphs Ii, Vadim Kostrykin, Jürgen Potthoff, Robert Schrader

Communications on Stochastic Analysis

No abstract provided.

Asymptotic Spectral Analysis Of A Distance K-Graph Of N-Fold Direct Product Of A Graph, Jun Kurihara

Communications on Stochastic Analysis

No abstract provided.

Mathematical And Computational Modelling For Biosensors: A Modular Approach, Yupeng Liu

Doctoral

Biosensors are analytic devices which detect biochemical and physiological changes and represent an emerging technology for low-cost, rapid and simple-to-operate biomedical diagnostic tools. Biosensor design and functionality are based on well understood physical and chemical processes which can be easily translated into mathematical models involving ordinary and partial di erential equations. Using mathematical and computational modelling techniques to characterize the biosensor response as a function of its input parameters in a wide range of physical contexts can guide the experimental work, thus reducing development time and costs.
This thesis is based on a close collaboration with Biochemistry researchers at the …

A Study Of Women Working In The Actuarial Field, Jillian Emberg

Honors Projects in Mathematics

The goal of this project is to examine how women fit into the actuarial career path and how cultural expectations, biological factors, and personal aspirations affect their experiences in the field. Dramatic changes in the profession have occurred since its emergence in the nineteenth century to become more welcoming to women who choose to enter the profession. However, despite the equalizing demographic shifts of the field, it is still a male-dominated profession. This paper attempts to analyze why some of the changes in the demographics of the field have occurred as well as explain what factors contribute to women’s underrepresentation …

Cost Of Winning: What Contributing Factors Play The Most Significant Roles In Increasing The Winning Percentage Of A Major League Baseball Team?, Patrick Tartaro

Honors Projects in Finance

Over the past decade, discussions of competition disparity in Major League Baseball have been brought to the forefront of many debates regarding the sport. The belief that "large market" teams such as the New York Yankees buy their championships through acquiring star talent at high prices has become a common belief of many followers of the game. This research will answer the pressing question, "What are the most significant factors that correlate to a Major League Baseball Team’s winning percentage?”. I used stepwise regression to identify factors significantly related to winning percentage. Interestingly enough, payroll is not a significant factor …

The Mathematics Portfolio: An Alternative Tool To Evaluate Students’ Progress, Marla A. Sole

Publications and Research

This article describes the need for more thorough and varied forms of assessment to evaluate students’ level of understanding in mathematics. Portfolios are one type of assessment tool that, when added to a teacher’s repertoire can improve students’ comprehension and retention and enable students to monitor their own progress and to take more responsibility for their own learning. Portfolio assignments can also help students and teachers to detect and remedy weaknesses and misunderstandings and can increase students’ self-confidence in mathematics. This article discusses what a portfolio is, gives an example of a unit portfolio used in an undergraduate Finite Mathematics …

A Multidimensional Ruin Problem, S Ramasubramanian

Communications on Stochastic Analysis

No abstract provided.

Roots Of States, B V Rajarama Bhat

Communications on Stochastic Analysis

No abstract provided.

Lévy Processes Through Time Shift On Oscillator Weyl Algebra, Luigi Accardi, Habib Ouerdiane, Habib Rebei

Communications on Stochastic Analysis

No abstract provided.

A Vacuum-Adapted Approach To Quantum Feynman-Kac Formulae, Alexander C R Belton, J Martin Lindsay, Adam G Skalski

Communications on Stochastic Analysis

No abstract provided.

Multiple Q-Adapted Integrals And Itô Formula Of Noncommutative Stochastic Calculus In Fock Space, V P Belavkin, M F Brown

Communications on Stochastic Analysis

No abstract provided.

The Early Years Of Quantum Stochastic Calculus, R L Hudson

Communications on Stochastic Analysis

No abstract provided.

Large Deviations For Random Matrices, Sourav Chatterjee, S R S Varadhan

Communications on Stochastic Analysis

No abstract provided.

Some Problems Involving Airy Functions, V S Varadarajan

Communications on Stochastic Analysis

No abstract provided.

An Interpolating Family Of Means, Rajendra Bhatia, Ren-Cang Li

Communications on Stochastic Analysis

No abstract provided.

Hilbert Von Neumann Modules, Panchugopal Bikram, Kunal Mukherjee, R. Srinivasan, V S Sunder

Communications on Stochastic Analysis

No abstract provided.

Bell's Inequality Violations: Relation With De Finetti's Coherence Principle And Inferential Analysis Of Experimental Data, Franco Fagnola, Matteo Gregoratti

Communications on Stochastic Analysis

No abstract provided.

From Velocities To Fluxions, Marco Panza

MPP Published Research

"Though the De Methodis results, for its essential structure and content, from a re-elaboration of a previous unfinished treatise composed in the Fall of 1666—now known, after Whiteside, as The October 1666 tract on fluxions ([22], I, pp. 400-448)—, the introduction of the term ‘fluxion’ goes together with an important conceptual change concerned with Newton’s understanding of his own achievements. I shall argue that this change marks a crucial step in the origins of analysis, conceived as an autonomous mathematical theory."

A Fast-Slow Analysis Of The Dynamics Of Rem Sleep, Victoria Booth, Cecilia G. Diniz Behn

Math Faculty Publications

Waking and sleep states are regulated by the coordinated activity of a number of neuronal population in the brainstem and hypothalamus whose synaptic interactions compose a sleep-wake regulatory network. Physiologically based mathematical models of the sleep-wake regulatory network contain mechanisms operating on multiple time scales including relatively fast synaptic-based interations between neuronal populations, and much slower homeostatic and circadian processes that modulate sleep-wake temporal patterning. In this study, we exploit the naturally arising slow time scale of the homeostatic sleep drive in a reduced sleep-wake regulatory network model to utilize fast-slow analysis to investigate the dynamics of rapid eye movement …

The Seaborgium Chemical Table, Jeremiah Farrell

Scholarship and Professional Work - LAS

The diagram is an example of a connected, cubic graph with its ten nodes labelled with the letters of SEABORGIUM, chemical element 106. Connected means it is in one piece and cubic means that each node has exactly three edges on it.

Squaring, Cubing, And Cube Rooting, Arthur T. Benjamin

All HMC Faculty Publications and Research

I still recall my thrill and disappointment when I read Mathematical Carnival, by Martin Gardner. I was thrilled because, as my high school teacher had recommended, mathematics was presented in a playful way that I had never seen before. I was disappointed because it contained a formula that I thought I had "invented" a few years earlier. I have always had a passion for mental calculation, and the following formula appears in Gardner's chapter on "Lightning Calculators." It was used by the mathematician A. C. Aitken to mentally square large numbers.