Physical Sciences and Mathematics Commons^™

Nonoscillatory Solutions Of Higher-Order Fractional Differential Equations, Martin Bohner, Said R. Grace, Irena Jadlovská, Nurten Kılıç

Mathematics and Statistics Faculty Research & Creative Works

This paper deals with the asymptotic behavior of the nonoscillatory solutions of a certain forced fractional differential equations with positive and negative terms, involving the Caputo fractional derivative. The results obtained are new and generalize some known results appearing in the literature. Two examples are also provided to illustrate the results.

Analysis Of Ibnr Liabilities With Interevent Times Depending On Claim Counts, Daniel J. Geiger, Akim Adekpedjou

Mathematics and Statistics Faculty Research & Creative Works

We extend a recently proposed stochastic loss reserving model for liabilities from incurred but not reported (IBNR) micro-level claims. We propose viewing the number of claims from an event as a measure of catastrophic severity. This view covers catastrophes with arbitrarily many classes of magnitude. Our Markovian model allows the time between disasters to depend on the previous event's level of severity. Simultaneously, we let the discount rate vary in the same manner. First, we find the moments of IBNR liabilities in our model. Then, we permit a later time horizon for IBNR claims when considered jointly with incurred and …

College Of Natural Sciences Newsletter, May & June 2022, College Of Natural Sciences

College of Natural Sciences Newsletters and Reports

Volume 3, Issue 4

Page 1 Dean's Message
Page 2 Awards and Recognition
Page 3-4 The path to a Doctorate Degree
Page 4 American Indian Student Center Native Graduate Honoring Ceremony
Page 5 Celebrating the lives of those who touched the College
Page 6 Media coverage of CNS
Page 7 Open PRAIRIE
Page 8-10 CNS Graduation Festivities
Page 11-14 Spring 2022 Dean's List
Page 16 Richard and Janice Vetter Endowed Professorship in Biotechnology.position

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 Flash Radiotherapy Is Efficient: A Possible Explanation, Julio Urenda, Olga Kosheleva, Vladik Kreinovich, Nguyen Hoang Phuong

Departmental Technical Reports (CS)

Usually, a cancer radiotherapy session lasts between 10 to 20 minutes. Technically, it is possible to transmit the dose faster, but traditionally, medical doctors were reluctant to do it, since they were afraid of negative effects of such a speedy treatment. Recent experiments show, however, that these fears are unfounded; moreover, transmitting the whole radiation dose in a shorter time turns out to be more beneficial for the patients. In this paper, we provide a possible geometric explanation for this empirical phenomenon.

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 Rejuvenation Attempts Often Lead To Cancer And Why Cyclic Rejuvenation Is Better: A Simple Qualitative Explanation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Since the 1960s, biologists have shown that, contrary to the previous belief that ageing is irreversible, many undesirable biological effects of ageing can be reversed. First attempts to perform this reversal on living creatures were not fully successful: while mice achieved some rejuvenation, many of these rejuvenated mice developed cancer. Later experiments showed that these cancers can be avoided if we apply cyclic rejuvenation: a short period of rejuvenation followed by a longer pause. This modified strategy led to recent successes of mice that recovered their age-deteriorated vision and mice that recovered their heart tissue after a heart attack. However, …

How To Detect (And Analyze) Independent Subsystems Of A Black-Box (Or Grey-Box) System, Saeid Tizpaz-Niari, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

Often, we deal with black-box or grey-box systems where we can observe the overall system's behavior, but we do not have access to the system's internal structure. In many such situations, the system actually consists of two (or more) independent components: a) how can we detect this based on observed system's behavior? b) what can we learn about the independent subsystems based on the observation of the system as a whole? In this paper, we provide (partial) answers to these questions.

Why Should Exactly 1/4 Be Returned To The Original Owner: An Economic Explanation Of An Ancient Recommendation, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

What if someone bought a property in good faith, not realizing that this property was unjustly confiscated from the previous owner? In such situations, if the new owner decided to sell this property, Talmud recommended that a fair way is to return 1/4 of the selling price to the original owner. However, it does not provide any explanation of why exactly 1/4 -- and not any other portion -- is to be returned. In this paper, we provide an economic explanation for this recommendation, an explanation that fits well with other ancient recommendations about debts.

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 …

Estimating Skewness And Higher Central Moments Of An Interval-Valued Fuzzy Set, Juan Carlos Figueroa-Garcia, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

A known relation between membership functions and probability density functions allows us to naturally extend statistical characteristics like central moments to the fuzzy case. In case of interval-valued fuzzy sets, we have several possible membership functions consistent with our knowledge. For different membership functions, in general, we have different values of the central moments. It is therefore desirable to compute, in the interval-valued fuzzy case, the range of possible values for each such moment. In this paper, we provide efficient algorithms for this computation.

Why Convex Combination Is An Effective Crossover Operation In Continuous Optimization: A Theoretical Explanation, Kelly Cohen, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

When evolutionary computation techniques are used to solve continuous optimization problems, usually, convex combination is used as a crossover operation. Empirically, this crossover operation works well, but this success is, from the foundational viewpoint, a challenge: why this crossover operation works well is not clear. In this paper, we provide a theoretical explanation for this empirical success.

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. …

The Role Of Carbonate Factories And Sea Water Chemistry On Basin-Wide Ramp To High-Relief Carbonate Platform Evolution: Triassic, Nanpanjiang Basin, South China, Daniel J. Lehrmann, Leanne M. Stepchinski, Hannah E. Wolf, Liangzi Li, Xiaowei Li, Marcello Minzoni, Meiyi Yu, Jonathan L. Payne

Geosciences Faculty Research

The end-Permian extinction and its aftermath altered carbonate factories globally for millions of years, but its impact on platform geometries remains poorly understood. Here, the evolution in architecture and composition of two exceptionally exposed platforms in the Nanpanjiang Basin are constrained and compared with geochemical proxies to evaluate controls on platform geometries. Geochemical proxies indicate elevated siliciclastic and nutrient fluxes in the basal Triassic, at the Induan—Olenekian boundary and in the uppermost Olenekian. Cerium/Ce* shifts from high Ce/Ce* values and a lack of Ce anomaly indicating anoxia during the Lower Triassic to a negative Ce anomaly indicating oxygenation in the …

Analysis Of Aftershock Parameters For The Alaskan Subduction Zone Tectonic Region, Gabrielle M. Paris

Geology Undergraduate Honors Theses

Forecasting how many earthquakes will occur following a potentially damaging earthquake helps the public and emergency operators stay safe and make informed decisions. The U.S. Geological Survey issues aftershock forecasts following potentially damaging earthquakes, using models to predict the number of earthquakes that should occur within the next day, week, month, and year with 95% confidence to reflect the uncertainty in aftershock behavior. The USGS considers the forecast to be "successful" when the number of earthquakes observed within the forecasted time period is within the 95% confidence interval. For aftershock sequences that occur along the forearc of the Alaskan subduction …

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.

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 …

Images Of Embedded Jovian Planet Formation At A Wide Separation Around Ab Aurigae, Thayne Currie, Kellen Lawson, Glenn Schneider, Wladimir Lyra, John Wisniewski, Carol Grady, Olivier Guyon, Motohide Tamura, Takayuki Kotani, Hajime Kawahara, Timothy Brandt, Taichi Uyama, Takayuki Muto, Ruobing Dong, Tomoyuki Kudo, Jun Hashimoto, Misato Fukagawa, Kevin Wagner, Julien Lozi, Jeffrey Chilcote, Taylor Tobin, Tyler Groff, Kimberly Ward-Duong, William Januszewski, Barnaby Norris, Peter Tuthill, Nienke Van Der Marel, Michael Sitko, Vincent Deo, Sebastien Vievard, Nemanja Jovanovic, Frantz Martinache

Astronomy: Faculty Publications

Direct images of protoplanets embedded in disks around infant stars provide the key to understanding the formation of gas giant planets such as Jupiter. Using the Subaru Telescope and the Hubble Space Telescope, we find evidence for a Jovian protoplanet around AB Aurigae orbiting at a wide projected separation (~93 au), probably responsible for multiple planet-induced features in the disk. Its emission is reproducible as reprocessed radiation from an embedded protoplanet. We also identify two structures located at 430–580 au that are candidate sites of planet formation. These data reveal planet formation in the embedded phase and a protoplanet discovery …

What’S So Artificial And Intelligent About Artificial Intelligence? A Conceptual Framework For Ai, Rebekah L. H. Rice

SPU Works

There is currently a good deal of attention being focused on artificial intelligence, broadly speaking, and deep learning, specifically. The attention is warranted, as these technologies are predicted to affect our collective lives in innumerable ways even beyond their already expansive social reach. There is much to consider regarding the benefits and potential harms of AI. And of course there are the apocalyptic musings about super-intelligent machines running amok, bringing science fiction scenarios uncomfortably close to anticipated reality. But productively engaging in discussions about the ethical and social implications of AI, and about which sorts of futures it is reasonable …

A Theological Framework For Reflection On Artificial Intelligence, Michael D. Langford

SPU Works

The theological questions before us in a digital age are pressing. What does God think of AI? Is AI good or evil? Will AI save us? What sort of future will AI give us? In what follows, I want to briefly introduce a few theological concepts that will hopefully help equip us for theological reflection on AI. We will begin with the question of epistemology, or how it is that we come by knowledge; in the realm of theology, this centers on revelation. We will then touch on the doctrine of creation, including the understanding of what it means to …

Artificial Intelligence And Theological Personhood, Michael D. Langford

SPU Works

Can AI be a person? What does God tell us about humanity and personhood? These are questions of theological anthropology and involve inquiring after the nature of humanity as God’s creation and what God wills for human personhood.

To address these inquiries, we will look at three biblical texts that bear on issues of theological anthropology, hopefully garnering some theological resources to consider the anthropological status of AI. Specifically, we will look at three “creation” texts that necessarily deal with the nature of human personhood within the divine economy of salvation history. The first is Genesis 1 and 2, which …

Reinforcement In The Information Revolution, Phillip M. Baker

SPU Works

This chapter will outline what it means to be a behaving human and how AI makes sense of these concepts. It will then explore possible near-future implications of our remarkable progress in understanding how human behavior works with the assistance of AI from a neurobiological basis. A focus on understanding the reinforcement mechanisms of the brain will reveal the consequences of ceding control of so much of our brain-environment interactions to AI. It will conclude by offering a potential Christian response to this digital reality from a uniquely Anabaptist perspective.

An Introduction To Artificial Intelligence, Carlos R. Arias

SPU Works

This chapter explores the evolution of artificial intelligence, starting with the first ideas of Alan Turing, going through the promises of its inception, and landing in our current state, when AI invokes a sense of power and awe. Next, the chapter will provide a summary of different technologies related to AI and machine learning, such as deep neural networks, to help the reader distinguish different terminologies. The chapter will end with a discussion of some potential tendencies concerning how AI may be used or evolve in the near future, and some questions about the technology in the long term.

Sin And Grace, Bruce D. Baker

SPU Works

The theological lens of sin and grace gives a broader and deeper viewpoint than mere ethics. Ethical analysis is of course useful and necessary, but ethics alone is not enough. Ethics apart from a robust, holistic understanding of humans as persons-in-communion will remain mired in reductionist thinking about human dignity and morality. Therefore, this final chapter addresses the ethical issues of AI through the lens of sin and grace.

Epilogue: A Litany For Faithful Engagement With Artificial Intelligence, Bruce D. Baker

SPU Works

A litany is a thoughtfully organized prayer for use in public worship by the church, or as a personal devotional practice by individuals. This seems a fitting way to close our reflection on AI, faith, and the future. Prayer will be essential to our faithful response to the new opportunities and challenges AI brings. Our hope is that this litany will serve as a practical guide to thoughtful invocation of the Holy Spirit in prayers for wisdom and discernment, and in the daily disciplines of spiritual growth.

Periodic Functions Related To The Gompertz Difference Equation, Tom Cuchta, Nick Wintz

Faculty Scholarship

We investigate periodicity of functions related to the Gompertz difference equation. In particular, we derive difference equations that must be satisfied to guarantee periodicity of the solution.

(R1521) On Weighted Lacunary Interpolation, Swarnima Bahadur, Sariya Bano

Applications and Applied Mathematics: An International Journal (AAM)

In this paper, we considered the non-uniformly distributed zeros on the unit circle, which are obtained by projecting vertically the zeros of the derivative of Legendre polynomial together with x=1 and x=-1 onto the unit circle. We prescribed the function on the above said nodes, while its second derivative at all nodes except at x=1 and x=-1 with suitable weight function and obtained the existence, explicit forms and establish a convergence theorem for such interpolatory polynomial. We call such interpolation as weighted Lacunary interpolation on the unit circle.

(R1889) Analysis Of Resonant Curve In The Earth-Moon System Under The Effect Of Resistive Force And Earth’S Equatorial Ellipticity, Sushil Yadav, Mukesh Kumar, Rajiv Aggarwal

Applications and Applied Mathematics: An International Journal (AAM)

In the present paper, we have determined the equations of motion of the Moon in spherical coordinate system using the gravitational potential of Earth. Using perturbation, equations of motion are reduced to a second order differential equation. From the solution, two types of resonance are observed: (i) due to the frequencies–rate of change of Earth’s equatorial ellipticity parameter and Earth’s rotation rate, and (ii) due to the frequencies–angular velocity of the bary-center around the sun and Earth’s rotation rate. Resonant curves are drawn where oscillatory amplitude becomes infinitely large at the resonant points. The effect of Earth’s equatorial ellipticity parameter …

(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.