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Articles 361 - 390 of 1133
Full-Text Articles in Applied Mathematics
Joule's 19th Century Energy Conservation Meta-Law And The 20th Century Physics (Quantum Mechanics And General Relativity): 21st Century Analysis, Vladik Kreinovich, Olga Kosheleva
Joule's 19th Century Energy Conservation Meta-Law And The 20th Century Physics (Quantum Mechanics And General Relativity): 21st Century Analysis, Vladik Kreinovich, Olga Kosheleva
Departmental Technical Reports (CS)
Joule's Energy Conservation Law was the first "meta-law": a general principle that all physical equations must satisfy. It has led to many important and useful physical discoveries. However, a recent analysis seems to indicate that this meta-law is inconsistent with other principles -- such as the existence of free will. We show that this conclusion about inconsistency is based on a seemingly reasonable -- but simplified -- analysis of the situation. We also show that a more detailed mathematical and physical analysis of the situation reveals that not only Joule's principle remains true -- it is actually strengthened: it is …
Analysis Of Two Stage M[X1],M[X2]/G1,G2/1 Retrial G-Queue With Discretionary Priority Services, Working Breakdown, Bernoulli Vacation, Preferred And Impatient Units, G. Ayyappan, B. Somasundaram
Analysis Of Two Stage M[X1],M[X2]/G1,G2/1 Retrial G-Queue With Discretionary Priority Services, Working Breakdown, Bernoulli Vacation, Preferred And Impatient Units, G. Ayyappan, B. Somasundaram
Applications and Applied Mathematics: An International Journal (AAM)
In this paper, we study M[X1] , M[X2] /G1 ,G2 /1 retrial queueing system with discretionary priority services. There are two stages of service for the ordinary units. During the first stage of service of the ordinary unit, arriving priority units can have an option to interrupt the service, but, in the second stage of service it cannot interrupt. When ordinary units enter the system, they may get the service even if the server is busy with the first stage of service of an ordinary unit or may enter into the orbit or leave …
Integrating Mathematics And Biology In The Classroom: A Compendium Of Case Studies And Labs, Becky Sanft, Anne Walter
Integrating Mathematics And Biology In The Classroom: A Compendium Of Case Studies And Labs, Becky Sanft, Anne Walter
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Quantifying Pollen Traits To Build A Mathematical Model Of Pollen Competition - A Mathematician's Perspective, Montana Ferita, Julie Fucarino, Alex Capaldi, Charlotte Beckford
Quantifying Pollen Traits To Build A Mathematical Model Of Pollen Competition - A Mathematician's Perspective, Montana Ferita, Julie Fucarino, Alex Capaldi, Charlotte Beckford
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Period Drift In A Neutrally Stable Stochastic Oscillator, Kevin Sanft
Period Drift In A Neutrally Stable Stochastic Oscillator, Kevin Sanft
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Adaptive Feature Engineering Modeling For Ultrasound Image Classification For Decision Support, Hatwib Mugasa
Adaptive Feature Engineering Modeling For Ultrasound Image Classification For Decision Support, Hatwib Mugasa
Doctoral Dissertations
Ultrasonography is considered a relatively safe option for the diagnosis of benign and malignant cancer lesions due to the low-energy sound waves used. However, the visual interpretation of the ultrasound images is time-consuming and usually has high false alerts due to speckle noise. Improved methods of collection image-based data have been proposed to reduce noise in the images; however, this has proved not to solve the problem due to the complex nature of images and the exponential growth of biomedical datasets. Secondly, the target class in real-world biomedical datasets, that is the focus of interest of a biopsy, is usually …
Computational Analysis Of Antipode Algorithms For The Output Feedback Hopf Algebra, Lance Berlin
Computational Analysis Of Antipode Algorithms For The Output Feedback Hopf Algebra, Lance Berlin
Electrical & Computer Engineering Theses & Dissertations
The feedback interconnection of two systems written in terms of Chen-Fliess series can be described explicitly in terms of the antipode of the output feedback Hopf algebra. At present, there are three known computational approaches to calculating this antipode: the left coproduct method, the right coproduct method, and the derivation method. Each of these algorithms is defined recursively, and thus becomes computationally expensive quite quickly. This motivates the need for a more complete understanding of the algorithmic complexity of these methods, as well as the development of new approaches for determining the Hopf algebra antipode. The main goals of this …
Derivation Of Direct Explicit Integrators Of Rk Type For Solving Class Of Seventh-Order Ordinary Differential Equations, Mohammed S. Mechee, Jawad K. Mshachal
Derivation Of Direct Explicit Integrators Of Rk Type For Solving Class Of Seventh-Order Ordinary Differential Equations, Mohammed S. Mechee, Jawad K. Mshachal
Karbala International Journal of Modern Science
The main contribution of this work is the development of direct explicit methods of Runge-Kutta (RK) type for solving class of seventh-order ordinary differential equations (ODEs) to improve computational efficiency. For this purpose, we have generalized RK, RKN, RKD, RKT, RKFD and RKM methods for solving class of first-, second-, third-, fourth-, and fifth-order ODEs. Using Taylor expansion approach, we have derived the algebraic equations of the order conditions for the proposed RKM integrators up to the tenth-order. Based on these order conditions, two RKM methods of fifth- and sixth-order with four- and five-stage are derived. The zero stability of …
Optimal Sampling Paths For Autonomous Vehicles In Uncertain Ocean Flows, Andrew J. De Stefan
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 …
Exploring Delay Dispersal In Us Airport Network, Brandon Sripimonwan, Arun Sathanur
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 …
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
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.
Status Quo Bias Actually Helps Decision Makers To Take Nonlinearity Into Account: An Explanation, Griselda Acosta, Eric Smith, Vladik Kreinovich
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. …
A Natural Explanation For The Minimum Entropy Production Principle, Griselda Acosta, Eric Smith, Vladik Kreinovich
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 …
Krylov Subspace Spectral Methods With Non-Homogenous Boundary Conditions, Abbie Hendley
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 …
Why Matrix Factorization Works Well In Recommender Systems: A Systems-Based Explanation, Griselda Acosta, Manuel Hernandez, Natalia Villanueva-Rosales, Eric Smith, Vladik Kreinovich
Why Matrix Factorization Works Well In Recommender Systems: A Systems-Based Explanation, Griselda Acosta, Manuel Hernandez, Natalia Villanueva-Rosales, Eric Smith, Vladik Kreinovich
Departmental Technical Reports (CS)
Many computer-based services use recommender systems that predict our preferences based on our degree of satisfaction with the past selections. One of the most efficient techniques making recommender systems successful is matrix factorization. While this technique works well, until now, there was no general explanation of why it works. In this paper, we provide such an explanation.
In Alsina Et Al. Derivation Of Min-Max Fuzzy Logic From Distributivity, All Conditions Are Necessary: A Proof, Vladik Kreinovich, Ildar Batyrshin, Nailya Kubysheva
In Alsina Et Al. Derivation Of Min-Max Fuzzy Logic From Distributivity, All Conditions Are Necessary: A Proof, Vladik Kreinovich, Ildar Batyrshin, Nailya Kubysheva
Departmental Technical Reports (CS)
In their 1983 paper, C. Alsina, E. Trillas, and L. Valverde proved that distributivity, monotonicity, and boundary conditions imply that the "and"-operation is min and the "or"-operation is max. In this paper, we show that all these conditions are necessary for Alsina et al. result to be true.
Beyond P-Boxes And Interval-Valued Moments: Natural Next Approximations To General Imprecise Probabilities, Olga Kosheleva, Vladik Kreinovich
Beyond P-Boxes And Interval-Valued Moments: Natural Next Approximations To General Imprecise Probabilities, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
To make an adequate decision, we need to know the probabilities of different consequences of different actions. In practice, we only have partial information about these probabilities -- this situation is known as imprecise probabilities. A general description of all possible imprecise probabilities requires using infinitely many parameters. In practice, the two most widely used few-parametric approximate descriptions are p-boxes (bounds on the values of the cumulative distribution function) and interval-valued moments (i.e., bounds on moments). In some situations, these approximations are not sufficiently accurate. So, we need more accurate more-parametric approximations. In this paper, we explain what are the …
Why Beta Priors: Invariance-Based Explanation, Olga Kosheleva, Vladik Kreinovich, Kittawit Autchariyapanitkul
Why Beta Priors: Invariance-Based Explanation, Olga Kosheleva, Vladik Kreinovich, Kittawit Autchariyapanitkul
Departmental Technical Reports (CS)
In the Bayesian approach, to describe a prior distribution on the set [0,1] of all possible probability values, typically, a Beta distribution is used. The fact that there have been many successful applications of this idea seems to indicate that there must be a fundamental reason for selecting this particular family of distributions. In this paper, we show that the selection of this family can indeed be explained if we make reasonable invariance requirements.
How To Gauge A Combination Of Uncertainties Of Different Type: General Foundations, Ingo Neumann, Vladik Kreinovich, Thach N. Nguyen
How To Gauge A Combination Of Uncertainties Of Different Type: General Foundations, Ingo Neumann, Vladik Kreinovich, Thach N. Nguyen
Departmental Technical Reports (CS)
In many practical situations, for some components of the uncertainty (e.g., of the measurement error) we know the corresponding probability distribution, while for other components, we know only upper bound on the corresponding values. To decide which of the algorithms or techniques leads to less uncertainty, we need to be able to gauge the combined uncertainty by a single numerical value -- so that we can select the algorithm for which this values is the best. There exist several techniques for gauging the combination of interval and probabilistic uncertainty. In this paper, we consider the problem of gauging the combination …
How To Reconcile Maximum Entropy Approach With Intuition: E.G., Should Interval Uncertainty Be Represented By A Uniform Distribution, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta
How To Reconcile Maximum Entropy Approach With Intuition: E.G., Should Interval Uncertainty Be Represented By A Uniform Distribution, Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta
Departmental Technical Reports (CS)
In many practical situations, we only have partial information about the probabilities; this means that there are several different probability distributions which are consistent with our knowledge. In such cases, if we want to select one of these distributions, it makes sense not to pretend that we have a small amount of uncertainty -- and thus, it makes sense to select a distribution with the largest possible value of uncertainty. A natural measure of uncertainty of a probability distribution is its entropy. So, this means that out of all probability distributions consistent with our knowledge, we select the one whose …
Why The Obvious Necessary Condition Is (Often) Also Sufficient (Toncas): An Explanation Of The Phenomenon, Julio C. Urenda, Vladik Kreinovich
Why The Obvious Necessary Condition Is (Often) Also Sufficient (Toncas): An Explanation Of The Phenomenon, Julio C. Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
In many graph-related problems, an obvious necessary condition is often also sufficient. This phenomenon is so ubiquitous that it was even named TONCAS, after the first letters of the phrase describing this phenomenon. In this paper, we provide a possible explanation for this phenomenon.
Why Lasso, En, And Clot: Invariance-Based Explanation, Hamza Alkhatib, Ingo Neumann, Vladik Kreinovich, Chon Van Le
Why Lasso, En, And Clot: Invariance-Based Explanation, Hamza Alkhatib, Ingo Neumann, Vladik Kreinovich, Chon Van Le
Departmental Technical Reports (CS)
In many practical situations, observations and measurement results are consistent with many different models -- i.e., the corresponding problem is ill-posed. In such situations, a reasonable idea is to take into account that the values of the corresponding parameters should not be too large; this idea is known as regularization. Several different regularization techniques have been proposed; empirically the most successful are LASSO method, when we bound the sum of absolute values of the parameters, and EN and CLOT methods in which this sum is combined with the sum of the squares. In this paper, we explain the empirical success …
In The Absence Of Information, 1/N Investment Makes Perfect Sense, Julio Urenda, Vladik Kreinovich
In The Absence Of Information, 1/N Investment Makes Perfect Sense, Julio Urenda, Vladik Kreinovich
Departmental Technical Reports (CS)
When people have several possible investment instruments, people often invest equally into these instruments: in the case of n instruments, they invest 1/n of their money into each of these instruments. Of course, if additional information about each instrument is available, this 1/n investment strategy is not optimal. We show, however, that in the absence of reliable information, 1/n investment is indeed the best strategy.
Closing Banquet Eulogies, Russell Howell, C. Ray Rosentrater
Closing Banquet Eulogies, Russell Howell, C. Ray Rosentrater
ACMS Conference Proceedings 2019
A tribute to David Lay; A tribute to John Roe
Intuitive Idea Of Implication Vs. Formal Definition: How To Define The Corresponding Degree, Olga Kosheleva, Vladik Kreinovich
Intuitive Idea Of Implication Vs. Formal Definition: How To Define The Corresponding Degree, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Formal implication does not capture the intuitive idea of "if A then B", since in formal implication, every two true statements -- even completely unrelated ones -- imply each other. A more adequate description of intuitive implication happens if we consider how much the use of A can shorten a derivation of B. At first glance, it may seem that the number of bits by which we shorten this derivation is a reasonable degree of implication, but we show that this number is not in good accordance with our intuition, and that a natural formalization of this intuition leads to …
Performance And Economic Evaluation Of Differentiated Multiple Vacation Queueing System With Feedback And Balked Customers, Amina A. Bouchentouf, Latifa Medjahri
Performance And Economic Evaluation Of Differentiated Multiple Vacation Queueing System With Feedback And Balked Customers, Amina A. Bouchentouf, Latifa Medjahri
Applications and Applied Mathematics: An International Journal (AAM)
The present paper deals with a single server feedback queueing system under two differentiated multiple vacations and balked customers. It is assumed that the service times of the two vacation types are exponentially distributed with different means. The steady-state probabilities of the model are obtained. Some important performance measures of the system are derived. Then, a cost model is developed. Further, a numerical study is presented.
Transient Analysis Of A Markovian Single Vacation Feedback Queue With An Interrupted Closedown Time And Control Of Admission During Vacation, A. Azhagappan, T. Deepa
Transient Analysis Of A Markovian Single Vacation Feedback Queue With An Interrupted Closedown Time And Control Of Admission During Vacation, A. Azhagappan, T. Deepa
Applications and Applied Mathematics: An International Journal (AAM)
This paper analyzes the transient behavior of an M/M/1 queueing model with single vacation, feedback, interrupted closedown time and control of admission during vacation. The time-dependent system size probabilities for the proposed model are obtained using generating function in the closed form. Further, the system performance measures like mean and variance of system size are also obtained for the time-dependent case. Finally, numerical illustrations are presented to understand the effect for various system parameters.
Analysis Of M[X1],M[X2]/G1,G2/1 Retrial Queueing System With Priority Services, Working Breakdown, Collision, Bernoulli Vacation, Immediate Feedback, Starting Failure And Repair, G. Ayyappan, P. Thamizhselvi, B. Somasundaram
Analysis Of M[X1],M[X2]/G1,G2/1 Retrial Queueing System With Priority Services, Working Breakdown, Collision, Bernoulli Vacation, Immediate Feedback, Starting Failure And Repair, G. Ayyappan, P. Thamizhselvi, B. Somasundaram
Applications and Applied Mathematics: An International Journal (AAM)
This paper considers an M[X1] , M[X2] /G1,G2/1 general retrial queueing system with priority services. Two types of customers from different classes arrive at the system in different independent compound Poisson processes. The server follows the non-pre-emptive priority rule subject to working breakdown, Bernoulli vacation, starting failure, immediate feedback, collision and repair. After completing each service, the server may go for a vacation or remain idle in the system. The priority customers who find the server busy are queued in the system. If a low-priority customer finds the server busy, he is routed to …
Developing Mathematicians: The Benefits Of Weaving Spiritual And Disciplinary Discipleship, Patrick Eggleton
Developing Mathematicians: The Benefits Of Weaving Spiritual And Disciplinary Discipleship, Patrick Eggleton
ACMS Conference Proceedings 2019
Part of the goal of discipleship at the Christian university is for faith development to seep into the hearts of the students. Similarly, the goal of the development of future mathematicians is for the mathematical proficiencies, the practices like problem solving and analytical reasoning that permeate each of the courses, to seep into the hearts of our majors. This presentation shares how the weaving of our spiritual and disciplinary discipleship efforts benefits the faith development of our students while also helping them to think like a mathematician.
From Perfect Shuffles To Landau's Function, Brian D. Beasley
From Perfect Shuffles To Landau's Function, Brian D. Beasley
ACMS Conference Proceedings 2019
If we view a given shuffle of a deck of cards as a permutation, then repeatedly applying this same shuffle will eventually return the deck to its original order. In general, how many steps will that take? What happens in the case of so-called perfect shuffles? What type of shuffle will require the greatest number of applications before restoring the original deck? This talk will address those questions and provide a brief history of the work of Edmund Landau on the maximal order of a permutation in the symmetric group on n objects. It will also note some recent progress …