Why Ideas First Appear In Informal Form? Why It Is Very Difficult To Know Yourself? Fuzzy-Based Explanation,
2022
Czech Technical University in Prague
Why Ideas First Appear In Informal Form? Why It Is Very Difficult To Know Yourself? Fuzzy-Based Explanation, Miroslav Svitek, Vladik Kreinovich
Departmental Technical Reports (CS)
To a lay person reading about history of physics, it may sound as if the progress of physics comes from geniuses whose inspiration leads them to precise equations that -- almost magically -- explain all the data: this is what Newton did with mechanics, this is what Schroedinger did with quantum physics, this is what Einstein did with gravitation. However, a deeper study of history of physics shows that in all these cases, these geniuses did not start from scratch -- they formalized ideas that first appeared in imprecise ("fuzzy") form. In this paper, we explain -- on the qualitative …
Why Aspirational Goals: Geometric Explanation,
2022
The University of Texas at El Paso
Why Aspirational Goals: Geometric Explanation, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
Business gurus recommend that an organization should have, in addition to clearly described realistic goals, also additional aspirational goals -- goals for which we may not have resources and which most probably will not be reached at all. At first glance, adding such a vague goal cannot lead to a drastic change in how the company operates, but surprisingly, for many companies, the mere presence of such aspirational goals boosts the company's performance. In this paper, we show that a simple geometric model of this situation can explain the unexpected success of aspirational goals.
Why Pre-Teaching: A Geometric Explanation,
2022
The University of Texas at El Paso
Why Pre-Teaching: A Geometric Explanation, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Departmental Technical Reports (CS)
Traditionally, subjects are taught in sequential order: e.g., first, students study algebra, then they use the knowledge of algebra to study the basis ideas of calculus. In this traditional scheme, teachers usually do not explain any calculus ideas before students are ready – since they believe that this would only confuse students. However, lately, empirical evidence has shows that, contrary to this common belief, pre-teaching – when students get a brief introduction to the forthcoming new topic before this topic starts – helps students learn. In this paper, we provide a geometric explanation for this unexpected empirical phenomenon.
Why Core Curriculum? Why Art And Nature Enhance Creativity? A Mathematical Explanation,
2022
The University of Texas at El Paso
Why Core Curriculum? Why Art And Nature Enhance Creativity? A Mathematical Explanation, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Departmental Technical Reports (CS)
Teaching is not easy. One of the main reasons why it is not easy is that the existing descriptions of the teaching process are not very precise -- and thus, we cannot use the usual optimization techniques, techniques which require a precise model of the corresponding phenomenon. It is therefore desirable to come up with a precise description of the learning process. To come up with such a description, we notice that on the set of all possible states of learning, there is a natural order s ≤ s' meaning that we can bring the student from the state s …
Data Processing Under Fuzzy Uncertainty: Towards More Efficient Algorithm,
2022
New Mexico State University
Data Processing Under Fuzzy Uncertainty: Towards More Efficient Algorithm, Hung T. Nguyen, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
In many practical situations, we need to process data under fuzzy uncertainty: we have fuzzy information about the algorithm's input, and we want to find the resulting information about the algorithm's output. It is known that this problem can be reduced to computing the range of the algorithm over alpha-cuts of the input. Since the fuzzy degrees are usually known with accuracy at best 0.1, it is sufficient to repeat this range-computing procedure for 11 values alpha = 0, 0.1, ..., 1.0. However, a straightforward application of this idea requires 11 times longer computation time than each range estimation -- …
How To Describe Relative Approximation Error? A New Justification For Gustafson's Logarithmic Expression,
2022
The University of Texas at El Paso
How To Describe Relative Approximation Error? A New Justification For Gustafson's Logarithmic Expression, Martine Ceberio, Olga Kosheleva, Vladik Kreinovich
Departmental Technical Reports (CS)
How can we describe relative approximation error? When the value b approximate a value a, the usual description of this error is the ratio |b − a|/|a|. The problem with this approach is that, contrary to our intuition, we get different numbers gauging how well a approximates b and how well b approximates a. To avoid this problem, John Gustafson proposed to use the logarithmic measure |ln(b/a)|. In this paper, we show that this is, in effect, the only regular scale-invariant way to describe the relative approximation error.
How To React To Student Evaluations,
2022
The University of Texas at El Paso
How To React To Student Evaluations, Olga Kosheleva, Vladik Kreinovich, Christian Servin
Departmental Technical Reports (CS)
If most students comment that the course was too fast, a natural idea is to slow it down. If most students comment that the course was too slow, a natural idea is to speed it up. But what if half the students think the speed was too fast and half that the speed was too slow? A frequent reaction to such a situation is to conclude that the speed was just right and not change the speed the next time, but this may not be the right reaction: under the same speed, half of the students will struggle and may …
Provably Weak Instances Of Plwe Revisited, Again,
2022
College of Saint Benedict/Saint John's University
Provably Weak Instances Of Plwe Revisited, Again, Katherine Mendel
CSB and SJU Distinguished Thesis
Learning with Errors has emerged as a promising possibility for postquantum cryptography. Variants known as RLWE and PLWE have been shown to be more efficient, but the increased structure can leave them vulnerable to attacks for certain instantiations. This work aims to identify specific cases where proposed cryptographic schemes based on PLWE work particularly poorly under a specific attack.
A Bayesian Phase I/Ii Biomarker-Based Design For Identifying Subgroup-Specific Optimal Dose For Immunotherapy,
2022
Louisiana State Univ, Dept Expt Stat, Baton Rouge, LA 70803 USA
A Bayesian Phase I/Ii Biomarker-Based Design For Identifying Subgroup-Specific Optimal Dose For Immunotherapy, Beibei Guo, Yong Zang
Faculty Publications
Immunotherapy is an innovative treatment that enlists the patient's immune system to battle tumors. The optimal dose for treating patients with an immunotherapeutic agent may differ according to their biomarker status. In this article, we propose a biomarker-based phase I/II dose-finding design for identifying subgroup-specific optimal dose for immunotherapy (BSOI) that jointly models the immune response, toxicity, and efficacy outcomes. We propose parsimonious yet flexible models to borrow information across different types of outcomes and subgroups. We quantify the desirability of the dose using a utility function and adopt a two-stage dose-finding algorithm to find the optimal dose for each …
Strict Lyapunov Functions And Feedback Controls For Sir Models With Quarantine And Vaccination,
2022
Kyushu Inst Technol, Dept Intelligent & Control Syst, 680-4 Kawazu, Iizuka, Fukuoka 8208502, Japan
Strict Lyapunov Functions And Feedback Controls For Sir Models With Quarantine And Vaccination, Hiroshi Ito, Michael Malisoff, Frederic Mazenc
Faculty Publications
We provide a new global strict Lyapunov function construction for a susceptible, infected, and recovered (or SIR) disease dynamics that includes quarantine of infected individuals and mass vaccination. We use the Lyapunov function to design feedback controls to asymptotically stabilize a desired endemic equilibrium, and to prove input-to-state stability for the dynamics with a suitable restriction on the disturbances. Our simulations illustrate the potential of our feedback controls to reduce peak levels of infected individuals.
Volumetric Lattice Boltzmann Method For Wall Stresses Of Image-Based Pulsatile Flows,
2022
Indiana University-Purdue University, Indianapolis
Volumetric Lattice Boltzmann Method For Wall Stresses Of Image-Based Pulsatile Flows, Xiaoyu Zhang, Joan Gomez-Paz, Xi Chen, James M. Mcdonough, Md Mahfuzul Islam, Yiannis Andreopoulos, Luoding Zhu, Huidan Yu
Mechanical Engineering Faculty Publications
Image-based computational fluid dynamics (CFD) has become a new capability for determining wall stresses of pulsatile flows. However, a computational platform that directly connects image information to pulsatile wall stresses is lacking. Prevailing methods rely on manual crafting of a hodgepodge of multidisciplinary software packages, which is usually laborious and error-prone. We present a new computational platform, to compute wall stresses in image-based pulsatile flows using the volumetric lattice Boltzmann method (VLBM). The novelty includes: (1) a unique image processing to extract flow domain and local wall normality, (2) a seamless connection between image extraction and VLBM, (3) an en-route …
Euclidean Quantum Field Formulation Of P-Adic Open String Amplitudes,
2022
The University of Texas Rio Grande Valley
Euclidean Quantum Field Formulation Of P-Adic Open String Amplitudes, A. R. Fuquen-Tibatá, H. García-Compeán, Wilson A. Zuniga-Galindo
School of Mathematical & Statistical Sciences Faculty Publications
We study in a rigorous mathematical way p-adic quantum field theories whose N-point amplitudes are the expectation of products of vertex operators. We show that this type of amplitudes admit a series expansion where each term is an Igusa's local zeta function. The lowest term in this series is a regularized version of the p-adic open Koba-Nielsen string amplitude.
Subclasses Of Multivalent Meromorphic Functions With A Pole Of Order P At The Origin,
2022
Universitatea 1 Decembrie 1918 din Alba Iulia
Subclasses Of Multivalent Meromorphic Functions With A Pole Of Order P At The Origin, Daniel Breaz, Kadhavoor R. Karthikeyan, Elangho Umadevi
All Works
In this paper, we carry out a systematic study to discover the properties of a subclass of meromorphic starlike functions defined using the Mittag–Leffler three-parameter function. Differential operators involving special functions have been very useful in extracting information about the various properties of functions belonging to geometrically defined function classes. Here, we choose the Prabhakar function (or a three parameter Mittag–Leffler function) for our study, since it has several applications in science and engineering problems. To provide our study with more versatility, we define our class by employing a certain pseudo-starlike type analytic characterization quasi-subordinate to a more general function. …
Lipschitz Regularity For The Parabolic P-Laplacian In The Heisenberg Group,
2022
Smith College
Lipschitz Regularity For The Parabolic P-Laplacian In The Heisenberg Group, Luca Capogna, Giovanna Citti, Xiao Zhong
Mathematics Sciences: Faculty Publications
In this paper we establish the local Lipschitz regularity of weak solutions of a certain class of quasilinear, degenerate parabolic equations in the Heisenberg group Hn , or more in general in contact subRiemannian manifolds. In particular we extend to the non-stationary setting.
Inverse Scattering Transform For The Complex Coupled Short-Pulse Equation,
2022
The University of Texas Rio Grande Valley
Inverse Scattering Transform For The Complex Coupled Short-Pulse Equation, Aikaterini Gkogkou, Bao-Feng Feng, A. David Trubatch
School of Mathematical & Statistical Sciences Faculty Publications
In this paper, we develop the Riemann–Hilbert approach to the inverse scattering transform (IST) for the complex coupled short-pulse equation on the line with zero boundary conditions at space infinity, which is a generalization of recent work on the scalar real short-pulse equation (SPE) and complex short-pulse equation (cSPE). As a byproduct of the IST, soliton solutions are also obtained. As is often the case, the zoology of soliton solutions for the coupled system is richer than in the scalar case, and it includes both fundamental solitons (the natural, vector generalization of the scalar case), and fundamental breathers (a superposition …
Starlike Functions Of Complex Order With Respect To Symmetric Points Defined Using Higher Order Derivatives,
2022
National University of Science & Technology (by Merger of Caledonian College of Engineering and Oman Medical College)
Starlike Functions Of Complex Order With Respect To Symmetric Points Defined Using Higher Order Derivatives, Kadhavoor R. Karthikeyan, Sakkarai Lakshmi, Seetharam Varadharajan, Dharmaraj Mohankumar, Elangho Umadevi
All Works
In this paper, we introduce and study a new subclass of multivalent functions with respect to symmetric points involving higher order derivatives. In order to unify and extend various well-known results, we have defined the class subordinate to a conic region impacted by Janowski functions. We focused on conic regions when it pertained to applications of our main results. Inclusion results, subordination property and coefficient inequality of the defined class are the main results of this paper. The applications of our results which are extensions of those given in earlier works are presented here as corollaries.
Prime Factors: America’S Prioritization Of Literacy Over Numeracy And Its Relationship To Systemic Inequity,
2022
CUNY Graduate Center
Prime Factors: America’S Prioritization Of Literacy Over Numeracy And Its Relationship To Systemic Inequity, Troy Smith
Dissertations, Theses, and Capstone Projects
For much of American history, literacy has been prioritized in K-12 education and society, at large, at the expense of numeracy. This lack of numerical emphasis has established innumeracy as an American cultural norm that has resulted in America not producing a sufficient number of numerate citizens, and ranking poorly on mathematical performance in international comparisons. This paper investigates the decisions and circumstances that led to this under prioritization, along with the public and cultural impact of said actions. Toward this end, literature regarding contemporary and historical influences on American mathematics education (e.g., civic, policy, and parental) was reviewed. The …
Reproducing Kernel Method For Solving Fuzzy Initial Value Problems,
2022
United Arab Emirates University
Reproducing Kernel Method For Solving Fuzzy Initial Value Problems, Qamar Kamel Dallashi
Theses
In this thesis, numerical solution of the fuzzy initial value problem will be investigated based on the reproducing kernel method. Problems of this type are either difficult to solve or impossible, in some cases, since they will produce a complicated optimized problem. To overcome this challenge, reproducing kernel method will be modified to solve this type of problems. Theoretical and numerical results will be presented to show the efficiency of the proposed method.
A Phenomenological Study: The Lived Experience Of Self-Described Math-Anxious Students Attending College Online,
2022
Liberty University
A Phenomenological Study: The Lived Experience Of Self-Described Math-Anxious Students Attending College Online, Toni Nicole Sawhill
Doctoral Dissertations and Projects
The purpose of this transcendental phenomenological study is to describe the lived experience of mathematics anxiety for self-described math-anxious students who completed an undergraduate mathematics course online at a university in the Pacific Northwest part of the United States. The theory guiding this study is community of inquiry (COI) introduced by early pragmatist philosophers C. S. Peirce and John Dewey and further developed by D. Randy Garrison, Terry Anderson, and Walter Archer as mathematics anxiety is a learned behavior based on students’ experiences. This research study answers the central research question: What are the lived experiences of mathematics anxiety for …
Special Issue Call For Papers: Mathematics And Society,
2022
Bates College
Special Issue Call For Papers: Mathematics And Society, Carrie Diaz Eaton, Rachel Roca, Nancy Rodriguez, Tian An Wong
Journal of Humanistic Mathematics
The Journal of Humanistic Mathematics (http://scholarship.claremont.edu/jhm/) is pleased to announce a call for papers for a special issue on Mathematics and Society. Please send your initial proposal submissions via email to the guest editors by August 15, 2022. Initial submission of complete manuscripts is due December 15, 2022. The issue is currently scheduled to appear in July 2023.
