# Applied Mathematics Commons™

## All Articles in Applied Mathematics

5,386 full-text articles. Page 4 of 177.

Towards A Theoretical Explanation Of How Pavement Condition Index Deteriorates Over Time, 2020 University of Texas at El Paso

#### Towards A Theoretical Explanation Of How Pavement Condition Index Deteriorates Over Time, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

##### Departmental Technical Reports (CS)

To predict how the Pavement Condition Index will change over time, practitioners use a complex empirical formula derived in the 1980s. In this paper, we provide a possible theoretical explanation for this formula, an explanation based on general ideas of invariance. In general, the existence of a theoretical explanation makes a formula more reliable; thus, we hope that our explanation will make predictions of road quality more reliable.

New (Simplified) Derivation Of Nash's Bargaining Solution, 2020 Thang Long University

#### New (Simplified) Derivation Of Nash's Bargaining Solution, Nguyen Hoang Phuong, Laxman Bokati, Vladik Kreinovich

##### Departmental Technical Reports (CS)

According to the Nobelist John Nash, if a group of people wants to selects one of the alternatives in which all of them get a better deal than in a status quo situations, then they should select the alternative that maximizes the product of their utilities. In this paper, we provide a new (simplified) derivation of this result, a derivation which is not only simpler -- it also does not require that the preference relation between different alternatives be linear.

Towards Making Fuzzy Techniques More Adequate For Combining Knowledge Of Several Experts, 2020 Thang Long University

#### Towards Making Fuzzy Techniques More Adequate For Combining Knowledge Of Several Experts, Nguyen Hoang Phuong, Vladik Kreinovich

##### Departmental Technical Reports (CS)

In medical and other applications, expert often use rules with several conditions, each of which involve a quantity within the domain of expertise of a different expert. In such situations, to estimate the degree of confidence that all these conditions are satisfied, we need to combine opinions of several experts -- i.e., in fuzzy techniques, combine membership functions corresponding to different experts. In each area of expertise, different experts may have somewhat different membership functions describing the same natural-language ("fuzzy") term like small. It is desirable to present the user with all possible conclusions corresponding to all these membership functions ...

Why Mean, Variance, Moments, Correlation, Skewness Etc. – Invariance-Based Explanations, 2020 University of Texas at El Paso

#### Why Mean, Variance, Moments, Correlation, Skewness Etc. – Invariance-Based Explanations, Olga Kosheleva, Laxman Bokati, Vladik Kreinovich

##### Departmental Technical Reports (CS)

In principle, we can use many different characteristics of a probability distribution. However, in practice, a few of such characteristics are mostly used: mean, variance, moments, correlation, etc. Why these characteristics and not others? The fact that these characteristics have been successfully used indicates that there must be some reason for their selection. In this paper, we show that the selection of these characteristics can be explained by the fact that these characteristics are invariant with respect to natural transformations -- while other possible characteristics are not invariant.

2020 The University of Western Ontario

#### Phage-Bacteria Interaction And Prophage Sequences In Bacterial Genomes, Amjad Khan

##### Electronic Thesis and Dissertation Repository

In this investigation, we examined the interaction of phages and bacteria in bacterial biofilm colonies, the evolution of prophages (viral genetic material inserted into the bacterial genome) and their genetic repertoire. To study the synergistic effects of lytic phages and antibiotics on bacterial biofilm colonies, we have developed a mathematical model of ordinary differential equations (ODEs). We have also presented a mathematical model consisting of a partial differential equation (PDEs), to study evolutionary forces acting on prophages. We fitted the PDE model to three publicly available databases and were able to show that induction is the prominent fate of intact ...

2020 Scientific and Innovation Center of Information and Communication Technologies at Tashkent University of Information Technologies named after Muhammad al-Khwarizmi, Address: Amir Temur street, 108, 100200, Tashkent city, Republic of Uzbekistan

#### Investigating The Solution Properties Of Population Model Of Cross-Diffusion Model With Double Nonlinearity And With Variable Density, Dildora Kabilovna Muhamediyeva

##### Chemical Technology, Control and Management

The models of two competing populations with double nonlinear diffusion and three types of functional dependencies are considered. The first dependence corresponds to the Malthusian type, the second to the Verhühlst type (logistic population), and the third to Olli-type populations. A common element of this kind of description is the presence of a linear source. Nonlinear sinks are also present in descriptions of populations of the Verhulst and Ollie type. Suitable initial approximations for a rapidly converging iterative process are proposed. Based on a self-similar analysis and comparison of the solutions of the Cauchy problem in the domain for an ...

A Computationally-Efficient Bound For The Variance Of Measuring The Orientation Of Single Molecules, 2020 Washington University in St. Louis

#### A Computationally-Efficient Bound For The Variance Of Measuring The Orientation Of Single Molecules, Tingting Wu, Tianben Ding, Hesam Mazidi, Oumeng Zhang, Matthew D. Lew

##### Electrical & Systems Engineering Publications and Presentations

Modulating the polarization of excitation light, resolving the polarization of emitted fluorescence, and point spread function (PSF) engineering have been widely leveraged for measuring the orientation of single molecules. Typically, the performance of these techniques is optimized and quantified using the Cramér-Rao bound (CRB), which describes the best possible measurement variance of an unbiased estimator. However, CRB is a local measure and requires exhaustive sampling across the measurement space to fully characterize measurement precision. We develop a global variance upper bound (VUB) for fast quantification and comparison of orientation measurement techniques. Our VUB tightly bounds the diagonal elements of the ...

Analysis Of An Agent-Based Model For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, 2020 Valparaiso University

#### Analysis Of An Agent-Based Model For Predicting The Behavior Of Bighead Carp (Hypophthalmichthys Nobilis) Under The Influence Of Acoustic Deterrence, Craig Garzella, Joseph Gaudy, Karl R. B. Schmitt, Arezu Mansuri

##### Spora: A Journal of Biomathematics

Bighead carp (Hypophthalmichthys nobilis) are an invasive, voracious, highly fecund species threatening the ecological integrity of the Great Lakes. This agent-based model and analysis explore bighead carp behavior in response to acoustic deterrence in an effort to discover properties that increase likelihood of deterrence system failure. Results indicate the most significant (p < 0.05) influences on barrier failure are the quantity of detritus and plankton behind the barrier, total number of bighead carp successfully deterred by the barrier, and number of native fishes freely moving throughout the simulation. Quantity of resources behind the barrier influence bighead carp to penetrate when populations are resource deprived. When native fish populations are low, an accumulation of phytoplankton can occur, increasing the likelihood of an algal bloom occurrence. Findings of this simulation suggest successful implementation with proper maintenance of an acoustic deterrence system has potential of abating the threat of bighead carp on ecological integrity of the Great Lakes.

2020 Louisiana Tech University

#### A Tutorial Of The Immersed Interface Method, Sheng Xu

##### Science Seminars

The immersed interface method is a computational methodology to solve differential equations with non-smooth solutions across interfaces. In this talk, Dr. Xu will use a simple example to demonstrate the main ingredients and features of this method. He will then present the application of the method to the simulation of fluid flows and make the connection of the application with the simple example.

This talk is a tutorial of the method for undergraduate students.

Come at 3:30pm for refreshments, speaker at 4:00pm

Direct Ellipsoidal Fitting Of Discrete Multi-Dimensional Data, 2020 Southern Methodist University

#### Direct Ellipsoidal Fitting Of Discrete Multi-Dimensional Data, Madeline Hamilton

##### SMU Journal of Undergraduate Research

Multi-dimensional distributions of discrete data that resemble ellipsoids arise in numerous areas of science, statistics, and computational geometry. We describe a complete algebraic algorithm to determine the quadratic form specifying the equation of ellipsoid for the boundary of such multi-dimensional discrete distribution. In this approach, the equation of an ellipsoid is reconstructed using a set of matrix equations from low-dimensional projections of the input data. We provide a Mathematica program realizing the full implementation of the ellipsoid reconstruction algorithm in an arbitrary number of dimensions. To demonstrate its many potential uses, the direct reconstruction method is applied to quasi-Gaussian statistical ...

2020 Southern Methodist University

#### Informal Professional Development On Twitter: Exploring The Online Communities Of Mathematics Educators, Jaymie Ruddock

##### SMU Journal of Undergraduate Research

Professional development in its most traditional form is a classroom setting with a lecturer and an overwhelming amount of information. It is no surprise, then, that informal professional development away from institutions and on the teacher's own terms is a growing phenomenon due to an increased presence of educators on social media. These communities of educators use hashtags to broadcast to each other, with general hashtags such as #edchat having the broadest audience. However, many math educators usethe hashtags #ITeachMath and #MTBoS, communities I was interested in learning more about. I built a python script that used Tweepy to ...

Fusion Of Probabilistic Knowledge As Foundation For Sliced-Normal Approach, 2020 Leibniz University Hannover

#### Fusion Of Probabilistic Knowledge As Foundation For Sliced-Normal Approach, Michael Beer, Olga Kosheleva, Vladik Kreinovich

##### Departmental Technical Reports (CS)

In many practical applications, it turns out to be efficient to use Sliced-Normal multi-D distributions, i.e., distributions for which the logarithm of the probability density function (pdf) is a polynomial -- -- to be more precise, it is a sum of squares of several polynomials. This class is a natural extension of normal distributions, i.e., distributions for which the logarithm of the pdf is a quadratic polynomial.

In this paper, we provide a possible theoretical explanation for this empirical success.

Strength Of Lime Stabilized Pavement Materials: Possible Theoretical Explanation Of Empirical Dependencies, 2020 University of Texas at El Paso

#### Strength Of Lime Stabilized Pavement Materials: Possible Theoretical Explanation Of Empirical Dependencies, Edgar Daniel Rodriguez Velasquez, Vladik Kreinovich

##### Departmental Technical Reports (CS)

When building a road, it is often necessary to strengthen the underlying soil layer. This strengthening is usually done by adding lime. There are empirical formulas that describe how the resulting strength depends on the amount of added lime. In this paper, we provide a theoretical explanation for these empirical formulas.

An Ultra-Sparse Approximation Of Kinetic Solutions To Spatially Homogeneous Flows Of Non-Continuum Gas, 2020 Air Force Institute of Technology

#### An Ultra-Sparse Approximation Of Kinetic Solutions To Spatially Homogeneous Flows Of Non-Continuum Gas, Alexander Alekseenko, Amy Grandilli, Aihua W. Wood

##### Faculty Publications

We consider a compact approximation of the kinetic velocity distribution function by a sum of isotropic Gaussian densities in the problem of spatially homogeneous relaxation. Derivatives of the macroscopic parameters of the approximating Gaussians are obtained as solutions to a linear least squares problem derived from the Boltzmann equation with full collision integral. Our model performs well for flows obtained by mixing upstream and downstream conditions of normal shock wave with Mach number 3. The model was applied to explore the process of approaching equilibrium in a spatially homogeneous flow of gas. Convergence of solutions with respect to the model ...

Using Differential Equations To Model Predator-Prey Relations As Part Of Scudem Modeling Challenge, 2020 Florida Southern College

#### Using Differential Equations To Model Predator-Prey Relations As Part Of Scudem Modeling Challenge, Zachary Fralish, Bernard Tyson Iii, Anthony Stefan

Differential equation modeling challenges provide students with an opportunity to improve their mathematical capabilities, critical thinking skills, and communication abilities through researching and presenting on a differential equations model. This article functions to display an archetype summary of an undergraduate student team’s response to a provided prompt. Specifically, the provided mathematical model estimates how certain stimuli from a predator are accumulated to trigger a neural response in a prey. Furthermore, it tracks the propagation of the resultant action potential and the physical flight of the prey from the predator through the analysis of larval zebrafish as a model organism ...

Nanomagnetic Resonance Imaging (Nano-Mri) Gives Personalized Medicine A New Perspective, 2020 Swinburne University of Technology, Hawthorn, Australia

#### Nanomagnetic Resonance Imaging (Nano-Mri) Gives Personalized Medicine A New Perspective, Lorenzo Rosa, Jonathan Blackledge, Albert Boretti

##### Books/Book chapters

This chapter provides a brief overview of molecular imaging techniques and its present and future potential in personalized medicine, with special a focus on the magnetic resonance imaging (MRI) approach. It discusses the current techniques that allow for the in vivo visualization of molecular processes at the nanoscale resolution (nano-MRI). Nano-MRI is progressing rapidly thanks to the work of a very small but extremely brilliant community of experts. This paper is not intended to be a comprehensive review of nano-MRI written for these experts, but rather a concise description of the present achievements for a much broader audience of medical ...

Mesoscopic Methods In Engineering And Science, 2020 Old Dominion University

#### Mesoscopic Methods In Engineering And Science, Christian Jansen, Manfred Krafczyk, Li-Shi Luo

##### Mathematics & Statistics Faculty Publications

(First paragraph) Matter, conceptually classified into fluids and solids, can be completely described by the microscopic physics of its constituent atoms or molecules. However, for most engineering applications a macroscopic or continuum description has usually been sufficient, because of the large disparity between the spatial and temporal scales relevant to these applications and the scales of the underlying molecular dynamics. In this case, the microscopic physics merely determines material properties such as the viscosity of a fluid or the elastic constants of a solid. These material properties cannot be derived within the macroscopic framework, but the qualitative nature of the ...

Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, 2020 Technological University Dublin

#### Swirling Fluid Flow In Flexible, Expandable Elastic Tubes: Variational Approach, Reductions And Integrability, Rossen Ivanov, Vakhtang Putkaradze

##### Articles

Many engineering and physiological applications deal with situations when a fluid is moving in flexible tubes with elastic walls. In real-life applications like blood flow, a swirl in the fluid often plays an important role, presenting an additional complexity not described by previous theoretical models. We present a theory for the dynamics of the interaction between elastic tubes and swirling fluid flow. The equations are derived using a variational principle, with the incompressibility constraint of the fluid giving rise to a pressure-like term. In order to connect this work with the previous literature, we consider the case of inextensible and ...

Essays On Modeling And Analysis Of Dynamic Sociotechnical Systems, 2020 University of Vermont

#### Essays On Modeling And Analysis Of Dynamic Sociotechnical Systems, David Rushing Dewhurst

##### Graduate College Dissertations and Theses

A sociotechnical system is a collection of humans and algorithms that interact under the partial supervision of a decentralized controller. These systems often display in- tricate dynamics and can be characterized by their unique emergent behavior. In this work, we describe, analyze, and model aspects of three distinct classes of sociotech- nical systems: financial markets, social media platforms, and elections. Though our work is diverse in subject matter content, it is unified though the study of evolution- and adaptation-driven change in social systems and the development of methods used to infer this change.

We first analyze evolutionary financial market microstructure ...

L1-Norm Regularized L1-Norm Best-Fit Line Problem, 2020 Virginia Commonwealth University