Optimal Conditional Expectation At The Video Poker Game Jacks Or Better, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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, 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 ...