Mathematics Commons^™

Efficient Blind Image Deblurring Using Nonparametric Regression And Local Pixel Clustering, Yicheng Kang, Partha Sarathi Mukherjee, Peihua Qiu

Mathematics Faculty Publications and Presentations

Blind image deblurring is a challenging ill-posed problem. It would have an infinite number of solutions even in cases when an observed image contains no noise. In reality, however, observed images almost always contain noise. The presence of noise would make the image deblurring problem even more challenging because the noise can cause numerical instability in many existing image deblurring procedures. In this paper, a novel blind image deblurring approach is proposed, which can remove both pointwise noise and spatial blur efficiently without imposing restrictive assumptions on either the point spread function (psf) or the true image. It even allows …

Translating Discrete Estimates Into A Less Detailed Scale: An Optimal Approach, Thongchai Dumrongpokaphan, Olga Kosheleva, Vladik Kreinovich

Departmental Technical Reports (CS)

In many practical situations, we use estimates that experts make on a 0-to-n scale. For example, to estimate the quality of a lecturer, we ask each student to evaluate this quality by selecting an integer from 0 to n. Each such estimate may be subjective; so, to increase the estimates' reliability, it is desirable to combine several estimates of the corresponding quality. Sometimes, different estimators use slightly different scales: e.g., one estimator uses a scale from 0 to n+1, and another estimator uses a scale from 0 to n. In such situations, it is desirable to translate these estimates to …

Triangular Cubic Hesitant Fuzzy Einstein Hybrid Weighted Averaging Operator And Its Application To Decision Making, Florentin Smarandache, Aliya Fahmi, Fazli Amin, Madad Khan, Nasruddin Hassan

Branch Mathematics and Statistics Faculty and Staff Publications

In this paper, triangular cubic hesitant fuzzy Einstein weighted averaging (TCHFEWA) operator, triangular cubic hesitant fuzzy Einstein ordered weighted averaging (TCHFEOWA) operator and triangular cubic hesitant fuzzy Einstein hybrid weighted averaging (TCHFEHWA) operator are proposed. An approach to multiple attribute group decision making with linguistic information is developed based on the TCHFEWA and the TCHFEHWA operators. Furthermore, we establish various properties of these operators and derive the relationship between the proposed operators and the existing aggregation operators. Finally, a numerical example is provided to demonstrate the application of the established approach

Clean Indices Of Common Rings, Benjamin L. Schoonmaker

Theses and Dissertations

Lee and Zhou introduced the clean index of rings in 2004. Motivated by this work, Basnet and Bhattacharyya introduced both the weak clean index of rings and the nil clean index of rings and Cimpean and Danchev introduced the weakly nil clean index of rings. In this work, we calculate each of these indices for the rings ℤ/nℤ and matrix rings with entries in ℤ/nℤ. A generalized index is also introduced.

Spatial Factor Models For High-Dimensional And Large Spatial Data: An Application In Forest Variable Mapping, Daniel Taylor-Rodríguez, Andrew O. Finley, Abhirup Datta, Chad Babcock, Hans-Erik Andersen, Bruce D. Cook, Douglas C. Morton, Sudipto Banerjee

Mathematics and Statistics Faculty Publications and Presentations

Gathering information about forest variables is an expensive and arduous activity. As such, directly collecting the data required to produce high-resolution maps over large spatial domains is infeasible. Next generation collection initiatives of remotely sensed Light Detection and Ranging (LiDAR) data are specifically aimed at producing complete-coverage maps over large spatial domains. Given that LiDAR data and forest characteristics are often strongly correlated, it is possible to make use of the former to model, predict, and map forest variables over regions of interest. This entails dealing with the high-dimensional (∼10² ) spatially dependent LiDAR outcomes over a large number …

Modeling Association In Microbial Communities With Clique Loginear Models, Adrian Dobra, Camilo Valdes, Dragana Ajdic, Bertrand S. Clarke, Jennifer Clarke

Department of Mathematics: Faculty Publications

There is a growing awareness of the important roles that microbial communities play in complex biological processes. Modern investigation of these often uses next generation sequencing of metagenomic samples to determine community composition. We propose a statistical technique based on clique loglinear models and Bayes model averaging to identify microbial components in a metagenomic sample at various taxonomic levels that have significant associations. We describe the model class, a stochastic search technique for model selection, and the calculation of estimates of posterior probabilities of interest. We demonstrate our approach using data from the Human Microbiome Project and from a study …

Mathematical Modeling Of Corona Virus In The United Arab Emirates, Alya Saif Ahmad Alshehhi

Theses

The Middle East Respiratory Syndrome Coronavirus (MERS-CoV) is a viral in-fectious disease that can be transmitted to humans through interaction with infected ani-mals or humans. The Middle East respiratory syndrome (MERS) is still one of the main public health concerns in the Gulf region including United Arab Emirates. The fact that diseases have been imported into other parts of the world show the possibility of has a MERS pandemic. In this work, we are aiming to study a mathematical model of the MERS transmission among the UAE population and camels. The goal is to determine what are the paths of …

Isar Autofocus Imaging Algorithm For Maneuvering Targets Based On Phase Retrieval And Gabor Wavelet Transform, Hongyin Shi, Ting Yang, Zhijun Qiao

School of Mathematical & Statistical Sciences Faculty Publications

The imaging issue of a rotating maneuvering target with a large angle and a high translational speed has been a challenging problem in the area of inverse synthetic aperture radar (ISAR) autofocus imaging, in particular when the target has both radial and angular accelerations. In this paper, on the basis of the phase retrieval algorithm and the Gabor wavelet transform (GWT), we propose a new method for phase error correction. The approach first performs the range compression on ISAR raw data to obtain range profiles, and then carries out the GWT transform as the time-frequency analysis tool for the rotational …

On The Origin Of Crystallinity: A Lower Bound For The Regularity Radius Of Delone Sets, Igor A. Baburin, Mikhail M. Bouniaev, Nikolay Dolbilin, Nikolay Yu. Erokhovets, Alexey Garber, Sergey V. Krivovichev, Egon Schulte

School of Mathematical & Statistical Sciences Faculty Publications

The mathematical conditions for the origin of long-range order or crystallinity in ideal crystals are one of the very fundamental problems of modern crystallography. It is widely believed that the (global) regularity of crystals is a consequence of `local order', in particular the repetition of local fragments, but the exact mathematical theory of this phenomenon is poorly known. In particular, most mathematical models for quasicrystals, for example Penrose tiling, have repetitive local fragments, but are not (globally) regular. The universal abstract models of any atomic arrangements are Delone sets, which are uniformly distributed discrete point sets in Euclidean d space. …

Comparing Powers Of Edge Ideals, Mike Janssen, Thomas Kamp, Jason Vander Woude

Faculty Work Comprehensive List

Given a nontrivial homogeneous ideal I ⊆ k[x1, x2, . . . ,xd], a problem of great recent interest has been the comparison of the rth ordinary power of I and the mth symbolic power I(m). This comparison has been undertaken directly via an exploration of which exponents m and r guarantee the subset containment I(m) ⊆ Ir and asymptotically via a computation of the resurgence ρ(I), a number for which any m/r > ρ(I) guarantees I(m) ⊆ Ir. Recently, a third quantity, the symbolic defect, was introduced; as It ⊆ I(t), the symbolic defect is the minimal number of generators …

U.S. College Students’ Social Network Characteristics And Perceived Social Exclusion: A Comparison Between Drinkers And Nondrinkers Based On Pastmonth Alcohol Use, Sara G. Balestrieri, Graham T. Diguiseppi, Matthew Meisel, Melissa A. Clark, Miles Q. Ott, Nancy P. Barnett

Statistical and Data Sciences: Faculty Publications

There is a general perception on college campuses that alcohol use is normative. However, nondrinking students account for 40% of the U.S. college population. With much of the literature focusing on intervening among drinkers, there has been less of a focus on understanding the nondrinker college experience. The current study has two aims: to describe the social network differences between nondrinkers and drinkers in a college setting, and to assess perceived social exclusion among nondrinkers. METHOD:First-year U.S. college students (n = 1,342; 55.3% female; 47.7% non-Hispanic White) were participants in a larger study examining a social network of one college …

Study Of Speech Familiar Topics Using Artificial Neural Networks, А. Abdukadirov,, D Umurzakov

Scientific journal of the Fergana State University

Create a neural network mode for recognition of separate words solution, analyze training characteristics and behavior of constructed neural network. Target network had to be portable to DSP platforms that define a format of input data.

About The Estimate Of The Sum Of The Random Number Of Random Numbers, I. Nematov, S. Kukieva

Scientific journal of the Fergana State University

In this paper we consider the estimate of the maximum of the sums of a random number of independent random variables

One Way To Increase Natural Numbers, A. Yusupova,, S. Uktamova

Scientific journal of the Fergana State University

In this paper we consider one of the convenient methods for computing the multiplication of natural numbers.

Smartphone-Based Prenatal Education For Parents With Preterm Birth Risk Factors, U. Olivia Kim, K. Barnekow, Sheikh Iqbal Ahamed, S. Dreier, C. Jones, M. Taylor, Md Kamrul Hasan, M. A. Basir

Mathematics, Statistics and Computer Science Faculty Research and Publications

Objective

To develop an educational mobile application (app) for expectant parents diagnosed with risk factors for premature birth.

Methods

Parent and medical advisory panels delineated the vision for the app. The app helps prepare for preterm birth. For pilot testing, obstetricians offered the app between 18–22 weeks gestational age to English speaking parents with risk factors for preterm birth. After 4 weeks of use, each participant completed a questionnaire. The software tracked topics accessed and duration of use.

Results

For pilot testing, 31 participants were recruited and 28 completed the questionnaire. After app utilization, participants reported heightened awareness of preterm …

On Negative Eigenvalues Of The Discrete Schrödinger Operator With Non-Local Potential, Sh.S. Lakaev, Z.E. Muminov

Scientific Journal of Samarkand University

On the d- dimensional lattice 2 , 1 ,  d d Z the discrete Schrödinger operator  H with non- local potential constructed via the Dirac delta function and shift operator is considered. The existence of negative eigenvalues on the parameters of the operator is explicity derived.

The Problem Of Restoring A Function In A Strip Along Curves With Singularities, А.Kh. Begmatov, A.S. Ismoilov

Scientific Journal of Samarkand University

In this work we consider the problem of re constructing a function from a family of parabolas in the upper half-plane with a weight function having a singularity. The uniqueness of theorem for the solution of equation is proved and the inversion formula is derived. It is shown that the solution of the problem posed is weakly ill -posed, that is, stability estimates are obtained in spaces of finite smoothness.

The Cauchy Problem For The System Of The Moment Elasticity, I.E. Niyozov, Т. Begmatov

Scientific Journal of Samarkand University

In this paper we consider the problem of analytical continuation of solutions to the system of the moment elasticity in a bounded domain from their values and values of their strains on a part of the boundary of this domain, i.e., we study the Cauchy proble m.

A Few Surprises About Non-Locality Interactions, Precognitive Interdiction, And The Spirit From Physics Viewpoint, Victor Christianto, Florentin Smarandache

Branch Mathematics and Statistics Faculty and Staff Publications

There are various supernatural phenomena which hardly can be explained by the existing electromagnetic science, for instance non-locality interactions (may be associated with ESP etc), and also precognitive interdictions. And there are other problems such as how to include the Spirit in our consciousness. For example, it has been known for long time that intuition plays significant role in many professions and human life, including in entrepreneurship, government, and also in detective or law enforcement activities. Despite these examples, such a precognitive interdiction is hardly accepted in established science. In this paper, we discuss non-locality interactions and also advanced solutions …

Sums Involving The Number Of Distinct Prime Factors Function, Tanay Wakhare

Rose-Hulman Undergraduate Mathematics Journal

We find closed form expressions for finite and infinite sums that are weighted by $\omega(n)$, where $\omega(n)$ is the number of distinct prime factors of $n$. We then derive general convergence criteria for these series. The approach of this paper is to use the theory of symmetric functions to derive identities for the elementary symmetric functions, then apply these identities to arbitrary primes and values of multiplicative functions evaluated at primes. This allows us to reinterpret sums over symmetric polynomials as divisor sums and sums over the natural numbers.