An Optimal Threshold Strategy In The Two-Envelope Problem With Partial Information, 2015 SelectedWorks

#### An Optimal Threshold Strategy In The Two-Envelope Problem With Partial Information, Martin Egozcue, Luis Fuentes García

*Martin Egozcue*

No abstract provided.

Approximation Of The Scattering Amplitude Using Nonsymmetric Saddle Point Matrices, 2014 The University of Southern Mississippi

#### Approximation Of The Scattering Amplitude Using Nonsymmetric Saddle Point Matrices, Amber Sumner Robertson

*Master's Theses*

In this thesis we look at iterative methods for solving the primal (**A**x = b) and dual (**A*** ^{T }*y = g) systems of linear equations to approximate the scattering amplitude defined by g

*x =y*

^{T}*b. We use a conjugate gradient-like iteration for a unsymmetric saddle point matrix that is contructed so as to have a real positive spectrum. We find that this method is more consistent than known methods for computing the scattering amplitude such as GLSQR or QMR. Then, we use techniques from "matrices, moments, and quadrature" to compute the scattering amplitude without solving the system ...*

^{T}Visualizing Probabilistic Proof, 2014 Washington University in St. Louis

#### Visualizing Probabilistic Proof, Enrique Guerra-Pujol

*Washington University Jurisprudence Review*

The author revisits the Blue Bus Problem, a famous thought-experiment in law involving probabilistic proof, and presents Bayesian solutions to different versions of the blue bus hypothetical. In addition, the author expresses his solutions in standard and visual formats, that is, in terms of probabilities and natural frequencies.

Diffusion And Adsorption Coefficients Of Aromatic Hydrocarbons In Gas Chromatography Capillary Columns, 2014 Western University

#### Diffusion And Adsorption Coefficients Of Aromatic Hydrocarbons In Gas Chromatography Capillary Columns, Gabriela Navarro Tovar

*University of Western Ontario - Electronic Thesis and Dissertation Repository*

This study focuses on a mathematical description of aromatic species elution peaks from a gas chromatographic BPX5 capillary column. Using the chromatographic peaks, statistical moments are calculated for toluene, naphthalene, phenol and 2-naphthol. This thesis reports two modelling approaches involving laminar gas flow, distribution coefficients (*K _{s}*) and diffusion coefficients in the stationary phase (

*D*).

_{s}Firstly, a model with equilibrium adsorption is considered to describe symmetric peaks for toluene and naphthalene. Moreover, a model with non-equilibrium adsorption is proposed to describe asymmetric peaks of phenol and 2-napthol. In addition to the *K _{s}* and

*D*parameters, this model ...

_{s}Intelligent Firefly Algorithm For Global Optimization, 2014 SelectedWorks

#### Intelligent Firefly Algorithm For Global Optimization, Seif-Eddeen K. Fateen, Adrián Bonilla-Petriciolet

*Seif-Eddeen K Fateen*

Intelligent firefly algorithm (IFA) is a novel global optimization algorithm that aims to improve the performance of the firefly algorithm (FA), whichwas inspired by the flashing communication signals among firefly swarms. This chapter introduces the IFA modification and evaluates its performance in comparison with the original algorithm in twenty multi-dimensional benchmark problems. The results of those numerical experiments show that IFA outperformed FA in terms of reliability and effectiveness in all tested benchmark problems. In some cases, the global minimum could not have been successfully identified via the firefly algorithm, except with the proposed modification for FA.

Centered-Difference Applications For Schrödinger's Equation, 2014 California Polytechnic State University

#### Centered-Difference Applications For Schrödinger's Equation, Matthew Thomas Murachver

*Physics*

This project enumerates methods utilizing discretized centered-difference approximations on the second order differential equation for quantum particles known as Schrodinger’s Equation. An eigenvalue-eigenfunction scheme is developed to sieve for valid solutions to The Time Independent Schrodinger Equation. Additionally the Crank-Nicolson method is applied to the Time Dependent Schrodinger Equation to describe wavefunction (eigenfunction) time evolution. The validity of these methods is discussed with applications to several fundamental pedagogical introductory quantum mechanic systems.

Improving Airplane Touchdown Control By Utilizing The Adverse Elevator Effect, 2014 Embry-Riddle Aeronautical University

#### Improving Airplane Touchdown Control By Utilizing The Adverse Elevator Effect, Nihad E. Daidzic Ph.D., Sc.D.

*International Journal of Aviation, Aeronautics, and Aerospace*

The main objective of this original research article is to understand the short-term dynamic behavior of the transport-category airplane during landing flare elevator control application. Increasing the pitch angle to arrest the sink rate, the elevator will have to produce negative lift to rotate the airplane’s nose upward. This has an immediate adverse effect of initially accelerating airplane downward. A mathematical model of landing flare based on the flat-Earth longitudinal dynamics of rigid airplane was developed which is realistic only on very short time-scales as pitch stiffness and damping were neglected. Pilot control scenarios using impulse and step elevator ...

Tracing The Origin Of Presolar Grains: Algorithms To Parametrize Supernovae, 2014 Washington University in St. Louis

#### Tracing The Origin Of Presolar Grains: Algorithms To Parametrize Supernovae, Justin M. Finkel

*Undergraduate Research Symposium Posters & Abstracts*

Certain meteorites contain grains of stardust with isotopic compositions that suggest supernova origins. Furthermore, individual grains often contain signatures from different zones of the star, from the iron-rich core to the hydrogen- and helium-rich envelope. This implies large-scale mixing between layers, and a grain’s specific combination of isotopic ratios can be used to constrain these mixing mechanisms. To this end we have developed an algorithm which, given a grain’s set of measured isotopic ratios and a theoretical supernova model, assigns ‘mixing fractions’ to various zones of the supernova, indicating what fraction of the grain comes from each zone ...

Fuzzy Mathematical Models For The Analysis Of Fuzzy Systems With Application To Liver Disorders, 2014 SelectedWorks

#### Fuzzy Mathematical Models For The Analysis Of Fuzzy Systems With Application To Liver Disorders, R.W. W. Hndoosh

*R. W. Hndoosh*

The main objective of this model is to focus on how to use the model of fuzzy system to solve fuzzy mathematics problems. Some mathematical models based on fuzzy set theory, fuzzy systems and neural network techniques seem very well suited for typical technical problems. We have proposed an extension model of a fuzzy system to N-dimension, using Mamdani's minimum implication, the minimum inference system, and the singleton fuzzifier with the center average defuzzifier. Here construct two different models namely a fuzzy inference system and an adaptive fuzzy system using neural network. We have extended the theorem for accuracy ...

Fuzzy Mathematical Models Of Type-1 And Type-2 For Computing The Parameters And Its Applications, 2014 SelectedWorks

#### Fuzzy Mathematical Models Of Type-1 And Type-2 For Computing The Parameters And Its Applications, R.W. W. Hndoosh

*R. W. Hndoosh*

This work provides mathematical formulas and algorithm in order to calculate the derivatives that being necessary to perform Steepest Descent models to make T1 and T2 FLSs much more accessible to FLS modelers. It provides derivative computations that are applied on different kind of MFs, and some computations which are then clarified for specific MFs. We have learned how to model T1 FLSs when a set of training data is available and provided an application to derive the Steepest Descent models that depend on trigonometric function (SDTFM). This work, also focused on an interval type-2 non-singleton type-2 FLS (IT2 NS-T2 ...

Partitioning Bipartite Graphs: A Modified Louvain, 2014 Yale University

#### Partitioning Bipartite Graphs: A Modified Louvain, Emily Diana

*Yale Day of Data*

Abstract

How do we find communities in a graph? How does this change if the graph is bipartite? The Louvain method maximizes links within communities and minimizes those between in order to determine an optimal grouping. Yet, because it may fail when bipartite restrictions are introduced, we have adjusted the null model so as to improve performance in these conditions.

Conclusion

Our Bipartite Louvain is more robust with respect to permutations of vertices than the standard Louvain. For our synthetic examples, Bipartite Louvain typically yields a higher modularity and uncovers the ground truth communities with a higher probability. In the ...

A Two-Light Version Of The Classical Hundred Prisoners And A Light Bulb Problem: Optimizing Experimental Design Through Simulations, 2014 Chapman University

#### A Two-Light Version Of The Classical Hundred Prisoners And A Light Bulb Problem: Optimizing Experimental Design Through Simulations, Alexander S. Barrett, Cyril Rakovski

*e-Research: A Journal of Undergraduate Work*

We propose five original strategies of successively increasing complexity and efficiency that address a novel version of a classical mathematical problem that, in essence, focuses on the determination of an optimal protocol for exchanging limited amounts of information among a group of subjects with various prerogatives. The inherent intricacy of the problem�solving protocols eliminates the possibility to attain an analytical solution. Therefore, we implemented a large-scale simulation study to exhaustively search through an extensive list of competing algorithms associated with the above-mentioned 5 generally defined protocols. Our results show that the consecutive improvements in the average amount of time ...

Optimal Contract Design For Co-Development Of Companion Diagnostics, 2014 Western University

#### Optimal Contract Design For Co-Development Of Companion Diagnostics, Rodney T. Tembo

*University of Western Ontario - Electronic Thesis and Dissertation Repository*

As the number of new drugs requiring companion diagnostics rises, more and more partnerships are formed between drug and diagnostics manufacturers to develop the necessary companion diagnostic. An increasingly significant issue is that of the optimal revenue/profit sharing or compensation schemes for such partnerships. We investigate the structure of an optimal compensation scheme under a scenario where a large pharmaceutical firm that is developing a drug intends to partner with a smaller diagnostics firm to develop a companion diagnostic test for the drug. We describe an optimal contract as one that maximizes the pharmaceutical firm's expected profits while ...

Parameter Identification For Ordinary And Delay Differential Equations By Using Flat Inputs, 2014 SelectedWorks

#### Parameter Identification For Ordinary And Delay Differential Equations By Using Flat Inputs, René Schenkendorf, Michael Mangold

*René Schenkendorf*

The concept of differential flatness has been widely used for nonlinear controller design. In this contribution, it is shown that flatness may also be a very useful property for parameter identification. An identification method based on flat inputs is introduced. The treatment of noisy measurements and the extension of the method to delay differential equations are discussed. The method is illustrated by two case studies: the well-known FitzHugh-Nagumo equations and a virus replication model with delays.

Fuzzy Mathematical Model For Detection Of Lung Cancer Using A Multi-Nfclass With Confusion Fuzzy Matrix For Accuracy, 2014 SelectedWorks

#### Fuzzy Mathematical Model For Detection Of Lung Cancer Using A Multi-Nfclass With Confusion Fuzzy Matrix For Accuracy, R.W. W. Hndoosh

*R. W. Hndoosh*

and detection of lung cancer data. This model depends on a generic model of a fuzzy perceptron, which can be used to derive a neural fuzzy system for specific domains. The multi neuron-fuzzy classification (Multi-NFClass) model proposed that uses input, hidden layers, output, and subclasses that have a multitude in each class. This model derives fuzzy rules to classify patterns into a number of crisp classes. Firstly, an attempt is made to describe fuzzy if–then rules, and construction of the fuzzy if–then rule, that are determined by the simple steps when its antecedent fuzzy sets are specified by ...

Dressing Method And Quadratic Bundles Related To Symmetric Spaces: Vanishing Boundary Conditions, 2014 Dublin Institute of Technology

#### Dressing Method And Quadratic Bundles Related To Symmetric Spaces: Vanishing Boundary Conditions, Tihomir I. Valchev

*Articles*

We consider quadratic bundles related to Hermitian symmetric spaces of the type SU(m+n)/S(U(m) x U(n)). The simplest representative of the corresponding integrable hierarchy is given by a multi-component Kaup-Newell derivative nonlinear Schroedinger equation which serves as a motivational example for our general considerations. We extensively discuss how one can apply Zakharov-Shabat's dressing procedure to derive reflectionless potentials obeying zero boundary conditions. Those could be used for one to construct fast decaying solutions to any nonlinear equation belonging to the same hierarchy. One can distinguish between generic soliton type solutions and rational solutions.

Simulating Burr Type Vii Distributions Through The Method Of L-Moments And L-Correlations, 2014 SelectedWorks

#### Simulating Burr Type Vii Distributions Through The Method Of L-Moments And L-Correlations, Mohan D. Pant, Todd C. Headrick

*Mohan Dev Pant*

Burr Type VII, a one-parameter non-normal distribution, is among the less studied distributions, especially, in the contexts of statistical modeling and simulation studies. The main purpose of this study is to introduce a methodology for simulating univariate and multivariate Burr Type VII distributions through the method of L-moments and L-correlations. The methodology can be applied in statistical modeling of events in a variety of applied mathematical contexts and Monte Carlo simulation studies. Numerical examples are provided to demonstrate that L-moment-based Burr Type VII distributions are superior to their conventional moment-based analogs in terms of distribution fitting and estimation. Simulation results ...

Analytical Solution Of The Symmetric Circulant Tridiagonal Linear System, 2014 Rose-Hulman Institute of Technology

#### Analytical Solution Of The Symmetric Circulant Tridiagonal Linear System, Sean A. Broughton, Jeffery J. Leader

*Mathematical Sciences Technical Reports (MSTR)*

A circulant tridiagonal system is a special type of Toeplitz system that appears in a variety of problems in scientific computation. In this paper we give a formula for the inverse of a symmetric circulant tridiagonal matrix as a product of a circulant matrix and its transpose, and discuss the utility of this approach for solving the associated system.

Understanding Recurrent Disease: A Dynamical Systems Approach, 2014 Western University

#### Understanding Recurrent Disease: A Dynamical Systems Approach, Wenjing Zhang

*University of Western Ontario - Electronic Thesis and Dissertation Repository*

Recurrent disease, characterized by repeated alternations between acute relapse and long re- mission, can be a feature of both common diseases, like ear infections, and serious chronic diseases, such as HIV infection or multiple sclerosis. Due to their poorly understood etiology and the resultant challenge for medical treatment and patient management, recurrent diseases attract much attention in clinical research and biomathematics. Previous studies of recurrence by biomathematicians mainly focus on in-host models and generate recurrent patterns by in- corporating forcing functions or stochastic elements. In this study, we investigate deterministic in-host models through the qualitative analysis of dynamical systems, to ...

Observational Signatures From Self-Gravitating Protostellar Disks, 2014 Western University

#### Observational Signatures From Self-Gravitating Protostellar Disks, Alexander L. Desouza

*University of Western Ontario - Electronic Thesis and Dissertation Repository*

Protostellar disks are the ubiquitous corollary outcome of the angular momentum conserving, gravitational collapse of molecular cloud cores into stars. Disks are an essential component of the star formation process, mediating the accretion of material onto the protostar, and for redistributing excess angular momentum during the collapse. We present a model to explain the observed correlation between mass accretion rates and stellar mass that has been inferred from observations of intermediate to upper mass T Tauri stars. We explain this correlation within the framework of gravitationally driven torques parameterized in terms of Toomre’s Q criterion. Our models reproduce both ...