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Optimal Conditional Expectation At The Video Poker Game Jacks Or Better, Stewart N. Ethier, John J. Kim, Jiyeon Lee 2019 University of Utah

Optimal Conditional Expectation At The Video Poker Game Jacks Or Better, Stewart N. Ethier, John J. Kim, Jiyeon Lee

UNLV Gaming Research & Review Journal

There are 134,459 distinct initial hands at the video poker game Jacks or Better, taking suit exchangeability into account. A computer program can determine the optimal strategy (i.e., which cards to hold) for each such hand, but a complete list of these strategies would require a book-length manuscript. Instead, a hand-rank table, which fits on a single page and reproduces the optimal strategy perfectly, was found for Jacks or Better as early as the mid 1990s. Is there a systematic way to derive such a hand-rank table? We show that there is indeed, and it involves finding the ...


Heterogeneous Boolean Networks With Two Totalistic Rules, Katherine Toh 2019 University of Nebraska at Omaha

Heterogeneous Boolean Networks With Two Totalistic Rules, Katherine Toh

Student Research and Creative Activity Fair

Boolean Networks are being used to analyze models in biology, economics, social sciences, and many other areas. These models simplify the reality by assuming that each element in the network can take on only two possible values, such as ON and OFF. The node evolution is governed by its interaction with other nodes in its neighborhood, which is described mathematically by a Boolean function or rule. For simplicity reasons, many models assume that all nodes follow the same Boolean rule. However, real networks often use more than one Boolean rule and therefore are heterogeneous networks. Heterogeneous networks have not yet ...


Parametric Natura Morta, Maria C. Mannone 2019 Independent researcher, Palermo, Italy

Parametric Natura Morta, Maria C. Mannone

The STEAM Journal

Parametric equations can also be used to draw fruits, shells, and a cornucopia of a mathematical still life. Simple mathematics allows the creation of a variety of shapes and visual artworks, and it can also constitute a pedagogical tool for students.


Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski 2018 Wojciech Budzianowski Consulting Services

Call For Abstracts - Resrb 2019, July 8-9, Wrocław, Poland, Wojciech M. Budzianowski

Wojciech Budzianowski

No abstract provided.


Iterated Belief Revision Under Resource Constraints: Logic As Geometry, Dan P. Guralnik, Daniel E. Koditschek 2018 University of Pennsylvania

Iterated Belief Revision Under Resource Constraints: Logic As Geometry, Dan P. Guralnik, Daniel E. Koditschek

Departmental Papers (ESE)

We propose a variant of iterated belief revision designed for settings with limited computational resources, such as mobile autonomous robots.

The proposed memory architecture---called the universal memory architecture (UMA)---maintains an epistemic state in the form of a system of default rules similar to those studied by Pearl and by Goldszmidt and Pearl (systems Z and Z+). A duality between the category of UMA representations and the category of the corresponding model spaces, extending the Sageev-Roller duality between discrete poc sets and discrete median algebras provides a two-way dictionary from inference to geometry, leading to immense savings in computation, at ...


Perturbation Results And The Forward Order Law For The Moore-Penrose Inverse Of A Product, Nieves Castro-Gonzalez, Robert E. Hartwig 2018 Universidad Politécnica de Madrid

Perturbation Results And The Forward Order Law For The Moore-Penrose Inverse Of A Product, Nieves Castro-Gonzalez, Robert E. Hartwig

Electronic Journal of Linear Algebra

New expressions are given for the Moore-Penrose inverse of a product $AB$ of two complex matrices. Furthermore, an expression for $(AB)\dg - B\dg A\dg$ for the case where $A$ or $B$ is of full rank is provided. Necessary and sufficient conditions for the forward order law for the Moore-Penrose inverse of a product to hold are established. The perturbation results presented in this paper are applied to characterize some mixed-typed reverse order laws for the Moore-Penrose inverse, as well as the reverse order law.


Positive And Z-Operators On Closed Convex Cones, Michael J. Orlitzky 2018 University of Maryland Baltimore County

Positive And Z-Operators On Closed Convex Cones, Michael J. Orlitzky

Electronic Journal of Linear Algebra

Let $K$ be a closed convex cone with dual $\dual{K}$ in a finite-dimensional real Hilbert space. A \emph{positive operator} on $K$ is a linear operator $L$ such that $L\of{K} \subseteq K$. Positive operators generalize the nonnegative matrices and are essential to the Perron-Frobenius theory. It is said that $L$ is a \emph{\textbf{Z}-operator} on $K$ if % \begin{equation*} \ip{L\of{x}}{s} \le 0 \;\text{ for all } \pair{x}{s} \in \cartprod{K}{\dual{K}} \text{ such that } \ip{x}{s} = 0. \end{equation*} % The \textbf{Z}-operators are generalizations of \textbf{Z ...


Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley 2018 Illinois State University

Semi-Tensor Product Representations Of Boolean Networks, Matthew Macauley

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Using Canalization For The Control Of Discrete Networks, David Murrugarra 2018 University of Kentucky

Using Canalization For The Control Of Discrete Networks, David Murrugarra

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Extreme Climate Events And The Ecological Dynamics Of Plant-Herbivore Interactions, David C. Elzinga, Christopher A. Klausmeier, William C. Wetzel 2018 University of Tennessee, Knoxville

Extreme Climate Events And The Ecological Dynamics Of Plant-Herbivore Interactions, David C. Elzinga, Christopher A. Klausmeier, William C. Wetzel

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Vaccination Strategies And Herd Immunity Thresholds In Small World Models, Emily McClung, Sam Rivas, Emma Soriano 2018 University of Portland

Vaccination Strategies And Herd Immunity Thresholds In Small World Models, Emily Mcclung, Sam Rivas, Emma Soriano

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Intercropping In Semi-Arid India: An Analysis Of Risks And Trade Offs, Jack Pringle 2018 Illinois State University

Intercropping In Semi-Arid India: An Analysis Of Risks And Trade Offs, Jack Pringle

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Understanding Sexual Violence Against Women, Maria Martinez 2018 Illinois State University

Understanding Sexual Violence Against Women, Maria Martinez

Annual Symposium on Biomathematics and Ecology: Education and Research

No abstract provided.


Selected Topics In Quantization And Renormalization Of Gauge Fields, Chenguang Zhao 2018 The University of Western Ontario

Selected Topics In Quantization And Renormalization Of Gauge Fields, Chenguang Zhao

Electronic Thesis and Dissertation Repository

My thesis covers several topics in the quantization and renormalization of gauge fields, ranging from the application of Dirac constraint procedure on the light front, to the manipulation of Faddeev-Popov method to enable use of the transverse-traceless gauge in first order gravity. Last, I study renormalization group ambiguities and carry out a new characterization method for models with one, two and five couplings.

In chapter 2 we apply the Dirac constraint procedure to the quantization of gauge theories on the light front. The light cone gauge is used in conjunction with the first class constraints that arise and the resulting ...


Parameter Sensitivity For In Vitro Anthrax Studies, Yareley Gonzalez, Maria Macias-Bedolla, Megan O. Powell 2018 University of St Francis

Parameter Sensitivity For In Vitro Anthrax Studies, Yareley Gonzalez, Maria Macias-Bedolla, Megan O. Powell

Spora: A Journal of Biomathematics

Studies done on interactions between spores and macrophages done in vitro show inconsistent results based on experimental protocol and inhibit meaningful extrapolation to in vivo. In this study, we perform a sensitivity analysis of a model representing in vitro studies of interactions between anthrax spores and macrophages to help address the effects of these inconsistencies. We perform both local and global analyses using Latin hypercube sampling and partial rank correlation coefficients. Our analysis indicates the amount of intracellular bacteria over time is most sensitive to the killing of intracellular bacteria by the macrophages and replication of the bacteria inside the ...


Proof Of A Conjecture Of Graham And Lovasz Concerning Unimodality Of Coefficients Of The Distance Characteristic Polynomial Of A Tree, Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy, Leslie Hogben, Franklin H.J. Kenter, Jephian C.-H. Lin, Michael Tait 2018 Iowa State University

Proof Of A Conjecture Of Graham And Lovasz Concerning Unimodality Of Coefficients Of The Distance Characteristic Polynomial Of A Tree, Ghodratollah Aalipour, Aida Abiad, Zhanar Berikkyzy, Leslie Hogben, Franklin H.J. Kenter, Jephian C.-H. Lin, Michael Tait

Electronic Journal of Linear Algebra

The conjecture of Graham and Lov ́asz that the (normalized) coefficients of the distance characteristic polynomial of a tree are unimodal is proved; it is also shown that the (normalized) coefficients are log-concave. Upper and lower bounds on the location of the peak are established.


Mathematical And Computational Studies Of The Biomechanics Of Biofilms, Jay Stotsky 2018 University of Colorado, Boulder

Mathematical And Computational Studies Of The Biomechanics Of Biofilms, Jay Stotsky

Applied Mathematics Graduate Theses & Dissertations

Bacterial biofilms are communities of bacteria growing on a surface to which they have adhered, typically in an aqueous environment. The motivation to understand biofilm behavior arises from a variety of applications including the development of strategies to mitigate corrosion in industrial machinery, the treatment of bacterial infections, and process control in bioreactors. The focus in this thesis is on fluid-structure interaction and biomechanical properties of biofilms. Detailed studies of a mathematical biofilm model that includes the heterogeneous rheology observed in biofilms, a statistical model of biofilm microstructure, and an application of techniques from a posteriori numerical analysis to the ...


The Hilbert-Huang Transform: A Theoretical Framework And Applications To Leak Identification In Pressurized Space Modules, Kenneth R. Bundy 2018 University of Maine

The Hilbert-Huang Transform: A Theoretical Framework And Applications To Leak Identification In Pressurized Space Modules, Kenneth R. Bundy

Electronic Theses and Dissertations

Any manned space mission must provide breathable air to its crew. For this reason, air leaks in spacecraft pose a danger to the mission and any astronauts on board. The purpose of this work is twofold: the first is to address the issue of air pressure loss from leaks in spacecraft. Air leaks present a danger to spacecraft crew, and so a method of finding air leaks when they occur is needed. Most leak detection systems localize the leak in some way. Instead, we address the identification of air leaks in a pressurized space module, we aim to determine the ...


Clustering Mixed Data: An Extension Of The Gower Coefficient With Weighted L2 Distance, Augustine Oppong 2018 East Tennessee State University

Clustering Mixed Data: An Extension Of The Gower Coefficient With Weighted L2 Distance, Augustine Oppong

Electronic Theses and Dissertations

Sorting out data into partitions is increasing becoming complex as the constituents of data is growing outward everyday. Mixed data comprises continuous, categorical, directional functional and other types of variables. Clustering mixed data is based on special dissimilarities of the variables. Some data types may influence the clustering solution. Assigning appropriate weight to the functional data may improve the performance of the clustering algorithm. In this paper we use the extension of the Gower coefficient with judciously chosen weight for the L2 to cluster mixed data.The benefits of weighting are demonstrated both in in applications to the Buoy data ...


Interpolating Between Multiplicities And F-Thresholds, William D. Taylor 2018 University of Arkansas, Fayetteville

Interpolating Between Multiplicities And F-Thresholds, William D. Taylor

Theses and Dissertations

We define a family of functions, called s-multiplicity for each s>0, that interpolates between Hilbert-Samuel multiplicity and Hilbert-Kunz multiplicity by comparing powers of ideals to the Frobenius powers of ideals. The function is continuous in s, and its value is equal to Hilbert-Samuel multiplicity for small values of s and is equal to Hilbert-Kunz multiplicity for large values of s. We prove that it has an associativity formula generalizing the associativity formulas for Hilbert-Samuel and Hilbert-Kunz multiplicity. We also define a family of closures, called s-closures, such that if two ideals have the same s-closure then they have the ...


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