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Articles 2911 - 2940 of 7977

Full-Text Articles in Applied Mathematics

How To Assign Grades To Tasks So As To Maximize Student Efforts, Laxman Bokati, Vyacheslav Kalashnikov, Nataliya Kalashnykova, Olga Kosheleva, Vladik Kreinovich Sep 2019

How To Assign Grades To Tasks So As To Maximize Student Efforts, Laxman Bokati, Vyacheslav Kalashnikov, Nataliya Kalashnykova, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In some classes, students want to get a desired passing grade (e.g., C or B) by spending the smallest amount of effort. In such situations, it is reasonable for the instructor to assign the grades for different tasks in such a way that the resulting overall student's effort is the largest possible. In this paper, we show that to achieve this goal, we need to assign, to each task, the number of points proportional to the efforts needed for this task.

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A Geomorphic Enthalpy Method: Description And Application To The Evolution Of Fluvial-Deltas Under Sea-Level Cycles, William Anderson, Jorge Lorenzo Trueba, Vaughan Voller Sep 2019

A Geomorphic Enthalpy Method: Description And Application To The Evolution Of Fluvial-Deltas Under Sea-Level Cycles, William Anderson, Jorge Lorenzo Trueba, Vaughan Voller

Department of Earth and Environmental Studies Faculty Scholarship and Creative Works

Fluvial deltas are composites of two primary sedimentary environments: a depositional fluvial region and an offshore region. The fluvial region is defined by two geomorphic moving boundaries: an alluvial-bedrock transition (ABT), which separates the sediment prism from the non-erodible bedrock basement, and the shoreline (SH), where the delta meets the ocean. The trajectories of these boundaries in time and space define the evolution of the shape of the sedimentary prism, and are often used as stratigraphic indicators, particularly in seismic studies, of changes in relative sea level and the identification of stratigraphic sequences. In order to better understand the relative …

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Optimal Sampling Paths For Autonomous Vehicles In Uncertain Ocean Flows, Andrew J. De Stefan Aug 2019

Optimal Sampling Paths For Autonomous Vehicles In Uncertain Ocean Flows, Andrew J. De Stefan

Dissertations

Despite an extensive history of oceanic observation, researchers have only begun to build a complete picture of oceanic currents. Sparsity of instrumentation has created the need to maximize the information extracted from every source of data in building this picture. Within the last few decades, autonomous vehicles, or AVs, have been employed as tools to aid in this research initiative. Unmanned and self-propelled, AVs are capable of spending weeks, if not months, exploring and monitoring the oceans. However, the quality of data acquired by these vehicles is highly dependent on the paths along which they collect their observational data. The …

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Dimension-Breaking For Traveling Waves In Interfacial Flows, Matthew W. Seiders Aug 2019

Dimension-Breaking For Traveling Waves In Interfacial Flows, Matthew W. Seiders

Theses and Dissertations

Fluid flow models in two spatial dimensions with a one-dimensional interface are known to support overturned traveling solutions. Computational methods of solving the two-dimensional problem are well developed, even in the case of overturned waves. The three-dimensional problem is harder for three prominent reasons. First, some formulations of the two-dimensional problem do not extend to three-dimensions. The technique of conformal mapping is a prime example, as it is very efficient in two dimensions but does not have a three-dimensional equivalent. Second, some three-dimensional models, such as the Transformed Field Expansion method, do not allow for overturned waves. Third, computational time …

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Forecasting Localized Weather-Based Photovoltaic Energy Production, Kevin Chang, Afreen Siddiqui, Robert Slater Aug 2019

Forecasting Localized Weather-Based Photovoltaic Energy Production, Kevin Chang, Afreen Siddiqui, Robert Slater

SMU Data Science Review

Photovoltaic (PV) power system performance can vary from nominal specifications when put in application, making it difficult to accurately estimate real power generation at a localized level. As the usage and efficiency of PV systems has increased in recent years, the amount of power contributed to the national power grid from solar irradiation has also increased significantly. However, solar power installations are subject to variances in efficiency and output, driven by differences in system size, local weather, and atmospheric condition changes. With a significant install base in today's world, combined with extensive solar irradiance and meteorological data, the variables exist …

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Systemic Risk In Financial Networks, Tathagata Banerjee Aug 2019

Systemic Risk In Financial Networks, Tathagata Banerjee

McKelvey School of Engineering Graduate Student Theses & Dissertations

In this dissertation, I have used the network model based approach to study systemic risk in financial networks. In particular, I have worked on generalized extensions of the Eisenberg--Noe [2001] framework to account for realistic financial situations viz. pricing of corporate debt while accounting for network effects, asset liquidation mechanisms during fire sales, dynamic clearing and impact of contingent payments such as insurance and credit default swaps. First, I present formulas for the valuation of debt and equity of firms in a financial network under comonotonic endowments. I demonstrate that the comonotonic setting provides a lower bound to the price …

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A Comparison Of The Trojan Y Chromosome Strategy To Harvesting Models For Eradication Of Non-Native Species, Jingjing Lyu, Pamela J. Schofield, Kristen M. Reaver, Matthew Beauregard, Rana D. Parshad Aug 2019

A Comparison Of The Trojan Y Chromosome Strategy To Harvesting Models For Eradication Of Non-Native Species, Jingjing Lyu, Pamela J. Schofield, Kristen M. Reaver, Matthew Beauregard, Rana D. Parshad

Faculty Publications

The Trojan Y Chromosome Strategy (TYC) is a promising eradication method for biological control of non-native species. The strategy works by manipulating the sex ratio of a population through the introduction of supermales that guarantee male offspring. In the current manuscript, we compare the TYC method with a pure harvesting strategy. We also analyze a hybrid harvesting model that mirrors the TYC strategy. The dynamic analysis leads to results on stability of solutions and bifurcations of the model. Several conclusions about the different strategies are established via optimal control methods. In particular, the results affirm that either a pure harvesting …

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Parallel Multipole Expansion Algorithms And Their Biology Applications, Jiahui Chen Aug 2019

Parallel Multipole Expansion Algorithms And Their Biology Applications, Jiahui Chen

Mathematics Theses and Dissertations

N-body pairwise interactions are ubiquitous in scientific areas such as astrophysics, fluids mechanics, electrical engineering, molecular biology, etc. Computing these interactions using direct sum of an O(N) cost is expensive, whereas multipole expansion methods, such as the fast multipole method (FMM) or treecode, can reduce the cost to O(N) or O(N log N). This thesis focuses on developing numerical algorithms of Cartesian FMM and treecode, as well as using these algorithms to directly or implicitly solve biological problems involving pairwise interactions. This thesis consists of the following topics. 1) A cyclic parallel scheme is developed to handle the load balancing …

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Assessing Computational Thinking, Daniel Duckworth Aug 2019

Assessing Computational Thinking, Daniel Duckworth

2009 - 2019 ACER Research Conferences

This paper provides some context for the role of computation thinking (CT) in the Australian Curriculum, an abridged literature review of CT as a problem-solving framework from the International Computer and Information Literacy Study (ICILS) 2018 assessment framework and some examples of how CT has been used to solve real-world problems. Finally, this paper presents ways to teach and assess CT.

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General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, Ronald Joseph Giardina Jr Aug 2019

General Nonlinear-Material Elasticity In Classical One-Dimensional Solid Mechanics, Ronald Joseph Giardina Jr

LSU New Orleans Theses and Dissertations

We will create a class of generalized ellipses and explore their ability to define a distance on a space and generate continuous, periodic functions. Connections between these continuous, periodic functions and the generalizations of trigonometric functions known in the literature shall be established along with connections between these generalized ellipses and some spectrahedral projections onto the plane, more specifically the well-known multifocal ellipses. The superellipse, or Lam\'{e} curve, will be a special case of the generalized ellipse. Applications of these generalized ellipses shall be explored with regards to some one-dimensional systems of classical mechanics. We will adopt the Ramberg-Osgood relation …

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Exploring Delay Dispersal In Us Airport Network, Brandon Sripimonwan, Arun Sathanur Aug 2019

Exploring Delay Dispersal In Us Airport Network, Brandon Sripimonwan, Arun Sathanur

STAR Program Research Presentations

The modeling of delay diffusion in airport networks can potentially help develop strategies to prevent the spread of such delays and disruptions. With this goal, we used the publicly-available historical United States Federal Aviation Administration (FAA) flight data to model the spread of delays in the US airport network. For the major (ASPM-77) airports for January 2017, using a threshold on the volume of flights, we sparsify the network in order to better recognize patterns and cluster structure of the network. We developed a diffusion simulator and greedy optimizer to find the top influential airport nodes that propagate the most …

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Remarkable Applications Of Measure Of Non-Compactness For Infinite System Of Differential Equations, Merve İlkhan, Emrah E. Kara Aug 2019

Remarkable Applications Of Measure Of Non-Compactness For Infinite System Of Differential Equations, Merve İlkhan, Emrah E. Kara

Applications and Applied Mathematics: An International Journal (AAM)

The essential goal of our study is to search for a solution of an infinite system of differential equations in two different Banach spaces under certain assumptions by the aid of measure of noncompactness. Also, we establish some interesting examples related to our results.

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Smaller Standard Deviation For Initial Weights Improves Performance Of Classifying Neural Networks: A Theoretical Explanation Of Unexpected Simulation Results, Diego Aguirre, Philip Hassoun, Rafael Lopez, Crystal Serrano, Marcoantonio R. Soto, Andrea Torres, Vladik Kreinovich Aug 2019

Smaller Standard Deviation For Initial Weights Improves Performance Of Classifying Neural Networks: A Theoretical Explanation Of Unexpected Simulation Results, Diego Aguirre, Philip Hassoun, Rafael Lopez, Crystal Serrano, Marcoantonio R. Soto, Andrea Torres, Vladik Kreinovich

Departmental Technical Reports (CS)

Numerical experiments show that for classifying neural networks, it is beneficial to select a smaller deviation for initial weights that what is usually recommended. In this paper, we provide a theoretical explanation for these unexpected simulation results.

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Status Quo Bias Actually Helps Decision Makers To Take Nonlinearity Into Account: An Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich Aug 2019

Status Quo Bias Actually Helps Decision Makers To Take Nonlinearity Into Account: An Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the main motivations for designing computer models of complex systems is to come up with recommendations on how to best control these systems. Many complex real-life systems are so complicated that it is not computationally possible to use realistic nonlinear models to find the corresponding optimal control. Instead, researchers make recommendations based on simplified -- e.g., linearized -- models. The recommendations based on these simplified models are often not realistic but, interestingly, they can be made more realistic if we "tone them down" -- i.e., consider predictions and recommendations which are close to the current status quo state. …

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How To Explain That Changes In Elderlies Depression Level Are Uniformly Distributed, Griselda Acosta, Eric Smith, Vladik Kreinovich Aug 2019

How To Explain That Changes In Elderlies Depression Level Are Uniformly Distributed, Griselda Acosta, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

Changes in the elderlies depression level result from a large number of small independent factors. Such situations are ubiquitous in applications. In most such cases, due to the Central Limit Theorem, the corresponding distribution is close to Gaussian. For the changes in the elderlies depression level, however, the empirical distribution is far from Gaussian: it is uniform. In this paper, we provide a possible explanation for the emergence of the uniform distribution.

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80/20 Rule Partially Explains 7 Plus Minus 2 Law: General System-Based Analysis, Griselda Acosta, Eric Smith, Vladik Kreinovich Aug 2019

80/20 Rule Partially Explains 7 Plus Minus 2 Law: General System-Based Analysis, Griselda Acosta, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

The 80/20 rule and the 7 plus minus 2 law are examples of difficult to explain empirical facts. According to the 80/20 rule, in each activity, 20% of the people contribute to the 80% of the results. The 7 plus minus 2 law means that we divide objects into 7 plus minus 2 groups -- i.e., into 5 to 9 groups. In this paper, we show that there is a relation between these two facts: namely, we show that, because of the 80/20 rule, the number of classes cannot be smaller than 5. Thus, the 80/20 rule explains the lower …

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Towards A Theoretical Explanation Of How Pavement Condition Index Deteriorates Over Time, Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, Vladik Kreinovich Aug 2019

Towards A Theoretical Explanation Of How Pavement Condition Index Deteriorates Over Time, Edgar Daniel Rodriguez Velasquez, Carlos M. Chang Albitres, 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.

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Geometric Explanation For An Empirical Formula Describing Our Galaxy's Warping, Julio Urenda, Olga Kosheleva, Vladik Kreinovich Aug 2019

Geometric Explanation For An Empirical Formula Describing Our Galaxy's Warping, Julio Urenda, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In the first approximation, the shape of our Galaxy -- as well as the shape of many other celestial bodies -- can be naturally explained by geometric symmetries and the corresponding invariances. As a result, we get the familiar shape of a planar spiral. A recent more detailed analysis of our Galaxy's shape has shown that the Galaxy somewhat deviates from this ideal shape: namely, it is not perfectly planar, it is somewhat warped in the third dimension. In this paper, we show that the empirical formula for this warping can also be explained by geometric symmetries and invariance.

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Why Filtering Out Higher Harmonics Makes It Easier To Carry A Tune, Griselda Acosta, Eric Freudenthal, Eric Smith, Vladik Kreinovich Aug 2019

Why Filtering Out Higher Harmonics Makes It Easier To Carry A Tune, Griselda Acosta, Eric Freudenthal, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

A recent patent shows that filtering out higher harmonics helps people sing in-tune. In this paper, we use the general signal processing ideas to explain this empirical phenomenon. We also show that filtering out higher harmonics is the optimal way of increasing the signal-to-noise ratio -- and thus, of making it easier for people to recognize when they are signing out of tune.

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Epicycles Are Almost As Good As Trigonometric Series: General System-Based Analysis, Griselda Acosta, Eric Smith, Olga Kosheleva, Vladik Kreinovich Aug 2019

Epicycles Are Almost As Good As Trigonometric Series: General System-Based Analysis, Griselda Acosta, Eric Smith, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

To adequately describe the planets' motion, ancient astronomers used epicycles, when a planet makes a circular motion not around the Earth, but around a special auxiliary point which, in turn, performs a circular motion around the Earth -- or around a second auxiliary point which, in turns, rotates around the Earth, etc. Standard textbooks malign this approach by calling it bad science, but in reality, this is, in effect, trigonometric (Fourier) series -- an extremely useful tool in science and engineering. It should be mentioned, however, that the epicycles are almost as good as trigonometric series -- in the sense …

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Common Sense Addition Explained By Hurwicz Optimism-Pessimism Criterion, Bibek Aryal, Laxman Bokati, Karla Godinez, Shammir Ibarra, Heyi Liu, Bofei Wang, Vladik Kreinovich Aug 2019

Common Sense Addition Explained By Hurwicz Optimism-Pessimism Criterion, Bibek Aryal, Laxman Bokati, Karla Godinez, Shammir Ibarra, Heyi Liu, Bofei Wang, Vladik Kreinovich

Departmental Technical Reports (CS)

If we place a can of coke that weigh 0.35 kg into a car that weighs 1 ton = 1000 kg, what will be the resulting weight of the car? Mathematics says 1000.35 kg, but common sense says 1 ton. In this paper, we show that this common sense answer can be explained by the Hurwicz optimism-pessimism criterion of decision making under interval uncertainty.

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Why Area Under The Curve In Hypothesis Testing?, Griselda Acosta, Eric Smith, Vladik Kreinovich Aug 2019

Why Area Under The Curve In Hypothesis Testing?, Griselda Acosta, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

To compare two different hypothesis testing techniques, researchers use the following heuristic idea: for each technique, they form a curve describing how the probabilities of type I and type II errors are related for this technique, and then compare areas under the resulting curves. In this paper, we provide a justification for this heuristic idea.

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If Space-Time Is Discrete, We May Be Able To Solve Np-Hard Problems In Polynomial Time, Ricardo Alvarez, Nick Sims, Christian Servin, Martine Ceberio, Vladik Kreinovich Aug 2019

If Space-Time Is Discrete, We May Be Able To Solve Np-Hard Problems In Polynomial Time, Ricardo Alvarez, Nick Sims, Christian Servin, Martine Ceberio, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional physics assumes that space and time are continuous. However, this reasonable model leads to some serious problems. One the approaches that physicists follow to solve these problems is to assume that the space-time is actually discrete. In this paper, we analyze possible computational consequences of this discreteness. It turns out that in a discrete space-time, we may be able to solve NP-hard problems in polynomial time.

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A Natural Explanation For The Minimum Entropy Production Principle, Griselda Acosta, Eric Smith, Vladik Kreinovich Aug 2019

A Natural Explanation For The Minimum Entropy Production Principle, Griselda Acosta, Eric Smith, Vladik Kreinovich

Departmental Technical Reports (CS)

It is well known that, according to the second law of thermodynamics, the entropy of a closed system increases (or at least stays the same). In many situations, this increase is the smallest possible. The corresponding minimum entropy production principle was first formulated and explained by a future Nobelist Ilya Prigogine. Since then, many possible explanations of this principle appeared, but all of them are very technical, based on complex analysis of differential equations describing the system's dynamics. Since this phenomenon is ubiquitous for many systems, it is desirable to look for a general system-based explanation, explanation that would not …

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Avoiding Einstein-Podolsky-Rosen (Epr) Paradox: Towards A More Physically Adequate Description Of A Quantum State, Joseph Bernal, Olga Kosheleva, Vladik Kreinovich Aug 2019

Avoiding Einstein-Podolsky-Rosen (Epr) Paradox: Towards A More Physically Adequate Description Of A Quantum State, Joseph Bernal, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

The famous EPR paradox shows that if we describe quantum particles in the usual way -- by their wave functions -- then we get the following seeming contradiction. If we entangle the states of the two particles, then move them far away from each other, and measure the state of the first particle, then the state of the second particle immediately changes -- which contradicts to special relativity, according to which such immediate-action-at-a-distance is not possible. It is known that, from the physical viewpoint, this is not a real paradox: if we measure any property of the second particle, the …

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When Revolutions Succeed? 80/20 Rule And 7 Plus Minus 2 Law Explain The 3.5% Rule, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich Aug 2019

When Revolutions Succeed? 80/20 Rule And 7 Plus Minus 2 Law Explain The 3.5% Rule, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A statistical analysis of hundreds of successful and unsuccessful revolution attempts led historian to a very unexpected conclusion: that most attempts involving at least 3.5% of the population succeeded, while most attempts that involved a smaller portion of the population failed. In this paper, we show that this unexpected threshold can be explained based on the other two known rules of human behavior: the 80/20 rule (20% of the people drink 80% of the beer) and 7 plus minus 2 law according to which we naturally divide everything into 7 plus minus 2 classes.

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How To Make Decisions: Consider Multiple Scenarios, Consult Experts, Play Down Emotions -- Quantitative Explanation Of Commonsense Ideas, Julio Urenda, Francis Biney, Marco Cardiel, Perla De La O, Anthony Desarmier, Noa Dodson, Taylor Dodson, Sebastian Gonzalez, Laura Hinojos, Jorge Huerta, Ryan Jones, Oliver Martinez, Carlos A. Saldaña Matamoros, Manuel Muñoz, Vladik Kreinovich Aug 2019

How To Make Decisions: Consider Multiple Scenarios, Consult Experts, Play Down Emotions -- Quantitative Explanation Of Commonsense Ideas, Julio Urenda, Francis Biney, Marco Cardiel, Perla De La O, Anthony Desarmier, Noa Dodson, Taylor Dodson, Sebastian Gonzalez, Laura Hinojos, Jorge Huerta, Ryan Jones, Oliver Martinez, Carlos A. Saldaña Matamoros, Manuel Muñoz, Vladik Kreinovich

Departmental Technical Reports (CS)

There are a lot of commonsense advices in decision making: e.g., we should consider multiple scenarios, we should consult experts, we should play down emotions. Many of these advices come supported by a surprisingly consistent quantitative evidence. In this paper, on the example of the above advices, we provide a theoretical explanations for these quantitative facts.

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Allee Effects Introduced By Density Dependent Phenology., Timothy James Pervenecki Aug 2019

Allee Effects Introduced By Density Dependent Phenology., Timothy James Pervenecki

Electronic Theses and Dissertations

We consider both the nonspatial model and spatial model of a species that gives birth to eggs at the end of the year. It is assumed that the timing of emergence from eggs is controled by phenology, which is density dependent. In general, the solution maps for our models are implicit; When the solution map is explicit, it is extremely complex and it is easier to work with the implicit map. We derive integral conditions for which the nonspatial model exhibits strong Allee effect. We also provide a necessary condition and a sufficient condition for the existence of positive equilibrium …

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Radial Basis Function Finite Difference Approximations Of The Laplace-Beltrami Operator, Sage Byron Shaw Aug 2019

Radial Basis Function Finite Difference Approximations Of The Laplace-Beltrami Operator, Sage Byron Shaw

Boise State University Theses and Dissertations

Partial differential equations (PDEs) are used throughout science and engineering for modeling various phenomena. Solutions to PDEs cannot generally be represented analytically, and therefore must be approximated using numerical techniques; this is especially true for geometrically complex domains. Radial basis function generated finite differences (RBF-FD) is a recently developed mesh-free method for numerically solving PDEs that is robust, accurate, computationally efficient, and geometrically flexible. In the past seven years, RBF-FD methods have been developed for solving PDEs on surfaces, which have applications in biology, chemistry, geophysics, and computer graphics. These methods are advantageous, as they are mesh-free, operate on arbitrary …

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Krylov Subspace Spectral Methods With Non-Homogenous Boundary Conditions, Abbie Hendley Aug 2019

Krylov Subspace Spectral Methods With Non-Homogenous Boundary Conditions, Abbie Hendley

Master's Theses

For this thesis, Krylov Subspace Spectral (KSS) methods, developed by Dr. James Lambers, will be used to solve a one-dimensional, heat equation with non-homogenous boundary conditions. While current methods such as Finite Difference are able to carry out these computations efficiently, their accuracy and scalability can be improved. We will solve the heat equation in one-dimension with two cases to observe the behaviors of the errors using KSS methods. The first case will implement KSS methods with trigonometric initial conditions, then another case where the initial conditions are polynomial functions. We will also look at both the time-independent and time-dependent …

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