Physical Sciences and Mathematics Commons^™

(R1897) Further Results On The Admissibility Of Singular Systems With Delays, Abdullah Yiğit, Cemil Tunç

Applications and Applied Mathematics: An International Journal (AAM)

Admissibility problem for a kind of singular systems with delays is studied in this article. Firstly, given the singular system with delays is transformed into a neutral system with delays. Secondly, a new sufficient criterion is obtained on the stability of the new neutral system by aid of Wirtinger-based integral inequality, linear matrix inequality (LMI) method and meaningful Lyapunov-Krasovskii functionals (LKFs). This criterion is valid for both systems. At the end, Two numerical examples are given to illustrate the applicability of the obtained results using MATLAB-Simulink software. By this article, we extend and improve some results of the past literature.

(R1516) Results On Fekete-Szegö Problem For Some New Subclasses Of Univalent Analytic Functions With Fractional-Order Operators, N. Singha, R. Kumar

Applications and Applied Mathematics: An International Journal (AAM)

We introduce some new subclasses of analytic functions which are univalent in an open unit disk by means of fractional calculus. The elemental interest is to explore the significance of fractional-order operators while formulating a few distinct subclasses of univalent analytic functions. Present work establishes the Fekete-Szegö inequality for the proposed subclasses. In addition, some classical Fekete-Szegö problems have also been retrieved and discussed as particular cases of the presented work. To make the suggested work more evident, an extremal function is also provided for which a sharp upper bound is attained.

(R1507) Mathematical Modeling And Analysis Of Seqiahr Model: Impact Of Quarantine And Isolation On Covid-19, Manoj Kumar Singh, . Anjali

Applications and Applied Mathematics: An International Journal (AAM)

At the moment in time, an outbreak of COVID-19 is transmitting on from human to human. Different parts have different quality of life (e.g., India compared to Russia), which implies the impact varies in each part of the world. Although clinical vaccines are available to cure, the question is how to minimize the spread without considering the vaccine. In this paper, via a mathematical model, the transmission dynamics of novel coronavirus with quarantine and isolation facilities have been proposed. The examination of the proposed model is set in motion with the boundedness and positivity of the solution, sole disease-free equilibrium, …

(R1898) A Study On Inextensible Flows Of Polynomial Curves With Flc Frame, Süleyman Şenyurt, Kemal Eren, Kebire Hilal Ayvacı

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we investigate the inextensible flows of polynomial space curves in R3. We calculate that the necessary and sufficient conditions for an inextensible curve flow are represented as a partial differential equation involving the curvatures. Also, we expressed the time evolution of the Frenet like curve (Flc) frame. Finally, an example of the evolution of the polynomial curve with Flc frame is given and graphed.

Fossils On The Floor Mosaics In The Rotunda Of The Nebraska State Capitol Second Edition, Robert F. Diffendal Jr.

Robert F. Diffendal, Jr., Publications

The idea for this project arose during a field trip to the Nebraska State Capitol led by my long-time friend and colleague, Joe Hannibal, of the Cleveland Museum of Natural History, during the Geological Society of America’s North-Central Section Meeting in Lincoln, Nebraska, on Saturday, April 26, 2014. One of Joe’s interests is historical buildings and their building stones. He put together a very useful guidebook to the building and its decorative stones (Hannibal, 2014) that we used on our tour.

One of the many places that we visited was the State Capitol Archives, located in the basement, where the …

Computational Paradox Of Deep Learning: A Qualitative Explanation, Jonatan Contreras, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

In general, the more unknowns in a problem, the more computational efforts is necessary to find all these unknowns. Interestingly, in state-of-the-art machine learning methods like deep learning, computations become easier when we increase the number of unknown parameters way beyond the number of equations. In this paper, we provide a qualitative explanation for this computational paradox.

(R1882) Effects Of Viscosity, Oblateness, And Finite Straight Segment On The Stability Of The Equilibrium Points In The Rr3bp, Bhavneet Kaur, Sumit Kumar, Rajiv Aggarwal

Applications and Applied Mathematics: An International Journal (AAM)

Associating the influences of viscosity and oblateness in the finite straight segment model of the Robe’s problem, the linear stability of the collinear and non-collinear equilibrium points for a small solid sphere m₃ of density \rho₃ are analyzed. This small solid sphere is moving inside the first primary m₁ whose hydrostatic equilibrium figure is an oblate spheroid and it consists of an incompressible homogeneous fluid of density \rho₁. The second primary m₂ is a finite straight segment of length 2l. The existence of the equilibrium points is discussed after deriving the pertinent …

(R1956) Neutrosophic Soft E-Compact Spaces And Application Using Entropy Measure, P. Revathi, K. Chitirakala, A. Vadivel

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, the concept of neutrosophic soft e-compactness is presented on neutrosophic soft topological spaces using the definition of e-open cover and its types. In addition, neutrosophic soft e-compactness and neutrosophic soft e-separation axioms are associated. Also, the concept of neutrosophic soft locally e-compactness is introduced in neutrosophic soft topological spaces and some of its properties are discussed. Added to that, an application in decision making problem is given using entropy.

Efficient Algorithms For Data Processing Under Type-3 (And Higher) Fuzzy Uncertainty, Vladik Kreinovich, Olga Kosheleva, Patricia Melin, Oscar Castillo

Departmental Technical Reports (CS)

It is known that to more adequately describe expert knowledge, it is necessary to go from the traditional (type-1) fuzzy techniques to higher order ones: type-2, probably type-3 and even higher. Until recently, only type-1 and type-2 fuzzy sets were used in practical applications. However, lately, it turned out that type-3 fuzzy sets are also useful in some applications. Because of this practical importance, it is necessary to design efficient algorithms for data processing under such type-3 (and higher order) fuzzy uncertainty. In this paper, we show how we can combine known efficient algorithms for processing type-1 and type-2 uncertainty …

Why Quantiles Are A Good Description Of Volatility In Economics: An Alternative Explanation, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich, Kittawit Autchariyapanitkul

Departmental Technical Reports (CS)

In econometrics, volatility of an investment is usually described by its Value-at-Risk (VaR), i.e., by an appropriate quantile of the corresponding probability distribution. The motivations for selecting VaR are largely empirical: VaR provides a more adequate description of what people intuitively perceive as risk. In this paper, we analyze this situation from the viewpoint of decision theory, and we show that this analysis naturally leads to the Value-at-Risk, i.e., to a quantile.

Interestingly, this analysis also naturally leads to an optimization problem related to quantile regression.

Why Decreased Gaps Between Brain Cells Cause Severe Headaches: A Symmetry-Based Geometric Explanation, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

When we analyze biological tissue under the microscope, cells are directly neighboring each other, with no gaps between them. However, a more detailed analysis shows that in vivo, there are small liquid-filled gaps between the cells, and these gaps are important: e.g., in abnormal situations, when the size of the gaps between brain cells decreases, this leads to severe headaches and other undesired effects. At present, there is no universally accepted explanation for this phenomenon. In this case, we show that the analysis of correpsonding geometric symmetries empirical phenomenon leads to a natural explanation for this effect.

How To Represent Uncertainty Via Qudits: Probability Distributions, Regular, Intuitionistic, And Picture Fuzzy Sets, F-Transforms, Etc., Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

While modern computers are fast, there are still many important practical situations in which we need even faster computations. It turns out that, due to the fact that the speed of all communications is limited by the speed of light, the only way to make computers drastically faster is to drastically decrease the size of computer's components. When we decrease their size to sizes comparable with micro-sizes of individual molecules, it becomes necessary to take into account specific physics of the micro-world -- known as quantum physics. Traditional approach to designing quantum computers -- i.e., computers that take effect of …

Why Rarity Score Is A Good Evaluation Of A Non-Fungible Token, Laxman Bokati, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

One of the new forms of investment is investing in so-called non-fungible tokens -- unique software objects associated with different real-life objects like songs, painting, photos, videos, characters in computer games, etc. Since these tokens are a form of financial investment, investors would like to estimate the fair price of such tokens. For tokens corresponding to objects that have their own price -- such as a song or a painting -- a reasonable estimate is proportional to the price of the corresponding object. However, for tokens corresponding to computer game characters, we cannot estimate their price this way. Based on …

Towards Better Ways To Compute The Overall Grade For A Class, Christian Servin, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Traditional way to compute the overall grade for the class is to use the weighted sum of the grades for all the assignments and exams, including the final exam. In terms of encouraging students to study hard throughout the semester, this grading scheme is better than an alternative scheme, in which all that matters is the grade on the final exam: in contrast to this alternative scheme, in the weighted-sum approach, students are penalized if they did not do well in the beginning of the semester. In practice, however, instructors sometimes deviate from the weighted-sum scheme: indeed, if the weighted …

How To Combine Expert Estimates? How To Estimate Probability In The Intersection Of Two Populations?, Miroslav Svitek, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In this paper, we consider two different practical problems that turned to be mathematically similar: (1) how to combine two expert-provided probabilities of some event and (2) how to estimate the frequency of a certain phenomenon (e.g., illness) in an intersection of two populations if we know the frequencies in each of these populations. In both cases, we use the maximum entropy approach to come up with a solution.

Why Quantile Regression Works Well In Economics: A Partial Explanation, Olga Kosheleva, Vassilis G. Kaburlasos, Vladik Kreinovich, Roengchai Tansuchat

Departmental Technical Reports (CS)

To get a better picture of the future behavior of different economics-related quantities, we need to be able to predict not only their mean values, but also their distribution. For example, it is desirable not only to predict future average income, but also to predict the future distribution of income. One of the convenient ways to describe a probability distribution is by using alpha-quantiles such as medians (corresponding to alpha = 0.5), quartiles (corresponding to alpha = 0.25 and alpha = 0.75), etc. In principle, an alpha-quantile of the desired future quantity can depend on beta-quantiles of current distributions corresponding …

Invariance-Based Approach Explains Empirical Formulas From Pavement Engineering To Deep Learning, Edgar Daniel Rodriguez Velasquez, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many application areas, there are effective empirical formulas that need explanation. In this paper, we focus on two such challenges: neural networks, where a so-called softplus activation function is known to be very efficient, and pavement engineering, where there are empirical formulas describing the dependence of the pavement strength on the properties of the underlying soil. We show that similar scale-invariance ideas can explain both types of formulas -- and, in the case of pavement engineering, invariance ideas can lead to a new formula that combines the advantages of several known ones.

Helium-Like X-Ray Line Complexes Show That The Hottest Plasma On The O Supergiant Ζ Puppis Is In Its Wind, David H. Cohen, Ariel M. Overdorff, M. A. Leutenegger, M. Gagné, V. Petit, A. David-Uraz

Physics & Astronomy Faculty Works

We present an analysis of Chandra grating spectra of key helium-like line complexes to put constraints on the location with respect to the photosphere of the hottest (T ≳ 6 × 10⁶ K) plasma in the wind of the O supergiant ζ Pup and to explore changes in the 18 yr between two sets of observations of this star. We fit two models—one empirical and one wind-shock-based—to the S XV, Si XIII, and Mg XI line complexes and show that an origin in the wind flow, above r ≈ 1.5 R∗, is strongly favoured over an origin less than 0.3 …

Normal-Mode Oscillations For The Circular And Dipolar States Of A Filled Hexagonal Magnetic Dipole Cluster, Peter T. Haugen, Andrew D. P. Smith, Boyd F. Edwards

All Physics Faculty Publications

We analyze the rotational dynamics of six magnetic dipoles of identical strength at the vertices of a regular hexagon with a variable-strength dipole in the center. The seven dipoles spin freely about fixed axes that are perpendicular to the plane of the hexagon, with their dipole moments directed parallel to the plane. Equilibrium dipole orientations are calculated as a function of the relative strength of the central dipole. Small-amplitude perturbations about these equilibrium states are calculated in the absence of friction and are compared with analytical results in the limit of zero and infinite central dipole strength. Normal modes and …

Towards A Computational Model Of Narrative On Social Media, Anne Bailey

Dartmouth College Undergraduate Theses

This thesis describes a variety of approaches to developing a computational model of narrative on social media. Our goal is to use such a narrative model to identify efforts to manipulate public opinion on social media platforms like Twitter. We present a model in which narratives in a collection of tweets are represented as a graph. Elements from each tweet that are relevant to potential narratives are made into nodes in the graph; for this thesis, we populate graph nodes with tweets’ authors, hashtags, named entities (people, locations, organizations, etc.,), and moral foundations (central moral values framing the discussion). Two …

Torsh: Obfuscating Consumer Internet-Of-Things Traffic With A Collaborative Smart-Home Router Network, Adam Vandenbussche

Dartmouth College Undergraduate Theses

When consumers install Internet-connected "smart devices" in their homes, metadata arising from the communications between these devices and their cloud-based service providers enables adversaries privy to this traffic to profile users, even when adequate encryption is used. Internet service providers (ISPs) are one potential adversary privy to users’ incom- ing and outgoing Internet traffic and either currently use this insight to assemble and sell consumer advertising profiles or may in the future do so. With existing defenses against such profiling falling short of meeting user preferences and abilities, there is a need for a novel solution that empowers consumers to …

Machine Learning And The Network Analysis Of Ethereum Trading Data, Santosh Sivakumar

Dartmouth College Undergraduate Theses

Since their conception, cryptocurrencies have captured the public interest, motivating a growing body of research aimed at exploring blockchain-based transactions. This said, little work has been done to draw conclusions from transaction patterns, particularly in the realm of predicting cryptocurrency price movements. Moreover, research in the cryptocurrency sphere largely focuses on Bitcoin, paying little attention to Ethereum, Bitcoin's second-in-line with respect to market capitalization. In this paper, we construct hourly networks for a year of Ethereum transactions, using computed graph metrics as features in a series of machine learning models. We find that regression-based approaches to predicting Ether prices/price deltas …

Designing Narrative-Based Interfaces For Collective Action: A Case Study Using Amazon, Climate Change, And Consumer Behavior, Catherine Parnell

Dartmouth College Undergraduate Theses

Climate change is the most pressing issue facing future generations. Amongst expanses of the population there is a lack of collective action on environmental issues, as there is a large gap between awareness and behavior change. This study suggests persuasive design that utilizes a narrative framing as a solution to reduce barriers to engaging in issues of collective action. Through extensive need-finding studies to understand target users, this thesis uses online-shopping via Amazon as a context for arguing that narrative can support actionable change in behavior. The technical artifact resulting from this research is a developed chrome extension and web …

Effects Of Spatial And Temporal Variability In Surface Water Inputs On Streamflow Generation And Cessation In The Rain–Snow Transition Zone, Ernesto Trujillo

Geosciences Faculty Publications and Presentations

Climate change affects precipitation phase, which can propagate into changes in streamflow timing and magnitude. This study examines how the spatial and temporal distribution of rainfall and snowmelt affects discharge in rain–snow transition zones. These zones experience large year-to-year variations in precipitation phase, cover a significant area of mountain catchments globally, and might extend to higher elevations under future climate change. We used observations from 11 weather stations and snow depths measured from one aerial lidar survey to force a spatially distributed snowpack model (iSnobal/Automated Water Supply Model) in a semiarid, 1.8 km² headwater catchment. We focused on surface …

21st Century Learning Skills And Artificial Intelligence, David Wicks, Michael Paulus

SPU Works

The chapter explores four concepts important for learning and AI in the twenty-first century—creativity, critical thinking, communication, and collaboration (the “4Cs”)—as well as reflections on the theological significance of creativity and community.

Automation And Apocalypse: Imagining The Future Of Work, Michael Paulus

SPU Works

This chapter provides an orientation to the history of technology, work, and the theology of work and then explores three visions of the future of work—a literary dystopia, a philosophical utopia, and a theological apocalypse—as resources for understanding the significance of work and imagining its future. In the first vision, found in Kurt Vonnegut’s speculative novel Player Piano, automation leads to the end of meaningful work and nearly renders humans obsolete. This dystopic vision reveals the value of human work but remains skeptical about our ability to preserve it against the advances of automation. The second vision comes from …

Introduction, Michael Paulus

SPU Works

Artificial intelligence is rapidly and radically changing our lives and world. This book is a multidisciplinary engagement with the present and future impacts of AI from the standpoint of Christian faith. It provides technological, philosophical, and theological foundations for thinking about AI, as well as a series of reflections on the impact of AI on relationships, behavior, education, work, and moral action. The book serves as an accessible introduction to AI as well as a guide to wise consideration, design, and use of AI by examining foundational understandings and beliefs from a Christian perspective.

Optical Measurements On A Budget: A 3d-Printed Ellipsometer, Matthew Mantia, Teresa J. Bixby

Chemistry Department Faculty Articles

Ellipsometry is an optical analysis technique that is useful for characterizing the physical properties of a thin-film system. Light reflected from a sample surface undergoes a change in polarization due to phase delay and anisotropic reflection. This enables one to perform non-destructive measurements of film thickness, surface roughness, refractive index, and other optical constants. Ellipsometric techniques are particularly convenient for characterizing coatings or films in the semiconductor and optics industries. However, these techniques may be inaccessible to undergraduate students and educators due to the prohibitive cost of ellipsometers and similar instrumentation. In response to this roadblock, we describe the construction …

Adaptive Capacity Beyond The Household: A Systematic Review Of Empirical Social-Ecological Research, Matthew A. Williamson

Human-Environment Systems Research Center Faculty Publications and Presentations

The concept of adaptive capacity has received significant attention within social-ecological and environmental change research. Within both the resilience and vulnerability literatures specifically, adaptive capacity has emerged as a fundamental concept for assessing the ability of social-ecological systems to adapt to environmental change. Although methods and indicators used to evaluate adaptive capacity are broad, the focus of existing scholarship has predominately been at the individual- and household- levels. However, the capacities necessary for humans to adapt to global environmental change are often a function of individual and societal characteristics, as well as cumulative and emergent capacities across communities and jurisdictions. …

Cross-Issue Correlation Based Opinion Prediction In Cyber Argumentation, Md Mahfuzer Rahman, Xiaoqing "Frank" Liu, Joseph W. Sirrianni, Douglas J. Adams

Computer Science and Computer Engineering Faculty Publications and Presentations

One of the challenging problems in large scale cyber-argumentation platforms is that users often engage and focus only on a few issues and leave other issues under-discussed and under-acknowledged. This kind of non-uniform participation obstructs the argumentation analysis models to retrieve collective intelligence from the underlying discussion. To resolve this problem, we developed an innovative opinion prediction model for a multi-issue cyber-argumentation environment. Our model predicts users’ opinions on the non-participated issues from similar users’ opinions on related issues using intelligent argumentation techniques and a collaborative filtering method. Based on our detailed experimental results on an empirical dataset collected using …