Mathematics Commons^™

Gaussian Guesswork: Infinite Sequences And The Arithmetic-Geometric Mean, Janet Heine Barnett

Calculus

No abstract provided.

A Multi-Resolution And Adaptive 3-D Image Denoising Framework With Applications In Medical Imaging, Partha Sarathi Mukherjee

Mathematics Faculty Publications and Presentations

Due to recent increase in the usage of 3-D magnetic resonance images (MRI) and analysis of functional magnetic resonance images (fMRI), research on 3-D image processing becomes important. Observed 3- D images often contain noise which should be removed in such a way that important image features, e.g., edges, edge structures, and other image details should be preserved, so that subsequent image analyses are reliable. Most image denoising methods in the literature are for 2-D images. However, their direct generalizations to 3- D images can not preserve complicated edge structures well. Because, the edge structures in a 3-D edge surface …

Ua66 Ogden College Of Science & Engineering Newsletter, Wku Ogden College Of Science & Engineering

Ogden College of Science & Engineering Publications

Newsletter created by and about Ogden College of Science & Engineering.

• Stevens, Cheryl. A Word with the Dean . . .
• From the Hilltop
• 3rd Annual Research Experience for Undergraduates Program Conference
• Into Bowling Green
• Barren RIver
• Mammoth Cave National Park
• Barrow, Alaska
• South Korea
• Postcards from the Field
• WKU Research Foundation
• Office of Research & Creative Activity
• About Applied Research & Technology Program
• Dean's Office News
• School of Engineering & Applied Sciences
• How to Connec
• Ogden College Hall

The Pell Equation In India, Toke Knudsen, Keith Jones

Number Theory

No abstract provided.

Sorting Permutations: Games, Genomes, And Cycles, K. L. M. Adamyk, E. Holmes, G. R. Mayfield, D. J. Moritz, M. Scheepers, B. E. Tenner, H. C. Wauck

Mathematics Faculty Publications and Presentations

Permutation sorting, one of the fundamental steps in pre-processing data for the efficient application of other algorithms, has a long history in mathematical research literature and has numerous applications. Two special-purpose sorting operations are considered in this paper: context directed swap, abbreviated cds, and context directed reversal, abbreviated cdr. These are special cases of sorting operations that were studied in prior work on permutation sorting. Moreover, cds and cdr have been postulated to model molecular sorting events that occur in the genome maintenance program of certain species of single-celled organisms called ciliates.

This paper investigates mathematical aspects of …

Flagellar Swimming In Viscoelastic Fluids: Role Of Fluid Elastic Stress Revealed By Simulations Based On Experimental Data, Chuanbin Li, Boyang Qin, Arvind Gopinath, Paulo E. Arratia, Becca Thomases, Robert D. Guy

Mathematics Sciences: Faculty Publications

Many important biological functions depend on microorganisms' ability to move in viscoelastic fluids such as mucus and wet soil. The effects of fluid elasticity on motility remain poorly understood, partly because the swimmer strokes depend on the properties of the fluid medium, which obfuscates the mechanisms responsible for observed behavioural changes. In this study, we use experimental data on the gaits of Chlamydomonas reinhardtii swimming in Newtonian and viscoelastic fluids as inputs to numerical simulations that decouple the swimmer gait and fluid type in order to isolate the effect of fluid elasticity on swimming. In viscoelastic fluids, cells employing the …

Exposures To Fine Particulate Matter And Ozone Above Usa Standards Are Associated With Auditory Brainstem Dysmorphology And Delayed Auditory Brainstem Evoked Potentials In Healthy Dogs, Partha S. Mukherjee

Mathematics Faculty Publications and Presentations

Background: Delayed central conduction times in the auditory brainstem have been observed in Mexico City (MC) healthy children breathing fine particulate matter (PM_2.5) and ozone (O₃) above the current United States Environmental Protection Agency (US-EPA) standards. MC children have α synuclein brainstem accumulation and medial superior olivary complex (MSO) dysmorphology. The present study used a dog model to further investigate the potential effects of air pollution on the function and morphology of the auditory brainstem.

Methodology: Twenty-four dogs living in clean air v MC, average age 37.1± 26.3 months, underwent brainstem auditory evoked potential (BAEP) measurements. …

Ideas And Graphs, Martin Zwick

Complex Systems Faculty Publications and Presentations

A graph can specify the skeletal structure of an idea, onto which meaning can be added by interpreting the structure.

This paper considers graphs (but not hypergraphs) consisting of four nodes, and suggests meanings that can be associated with several different directed and undirected graphs.

Drawing on Bennett's "systematics," specifically on the Tetrad that systematics offers as a model of 'activity,' the analysis here shows that the Tetrad is versatile model of problem-solving, regulation and control, and other processes.

Slides are available below.

On Congruence Lattices Of Nilsemigroups, Alexander L. Popovich, Peter R. Jones

Mathematics, Statistics and Computer Science Faculty Research and Publications

We prove that the congruence lattice of a nilsemigroup is modular if and only if the width of the semigroup, as a poset, is at most two, and distributive if and only if its width is one. In the latter case, such semigroups therefore coincide with the nil Δ">Δ Δ -semigroups. It is further shown that if a finitely generated nilsemigroup has modular congruence lattice, then the semigroup is finite.

The Double-Edged Sword: A Mixed Methods Study Of The Interplay Between Bipolar Disorder And Technology Use, Mark Matthews, Elizabeth Murnane, Jaime Snyder, Shion Guha, Pamara Chang, Gavin Doherty, Geri K. Gay

Mathematics, Statistics and Computer Science Faculty Research and Publications

Human behavior is increasingly reflected or acted out through technology. This is of particular salience when it comes to changes in behavior associated with serious mental illnesses including schizophrenia and bipolar disorder. Early detection is crucial for these conditions but presently very challenging to achieve. Potentially, characteristics of these conditions' traits and symptoms, at both idiosyncratic and collective levels, may be detectable through technology use patterns. In bipolar disorder specifically, initial evidence associates changes in mood with changes in technology-mediated communication patterns. However much less is known about how people with bipolar disorder use technology more generally in their lives, …

Imitating The Shazam App With Wavelets, Edward Aboufadel

Peer Reviewed Articles

With the Shazam smartphone app, a listener captures a short excerpt of a recorded song with the smartphone's microphone, and in a matter of moments the app reports the name of the song and the artist. Fourier analysis is a key mathematical tool that powers the app. In this paper, we describe a wavelet-based method that captures the basic process used by the Shazam app to search a database of number sequences (signals) to find those that are similar to a test signal. We will describe our implementation with a different source of signals: continuous glucose monitor data from the …

A Retinal Vessel Detection Approach Based On Shearlet Transform And Indeterminacy Filtering On Fundus Images, Florentin Smarandache, Yanhui Guo, Umit Budak, Abdulkadir Sengur

Branch Mathematics and Statistics Faculty and Staff Publications

A fundus image is an effective tool for ophthalmologists studying eye diseases. Retinal vessel detection is a significant task in the identification of retinal disease regions. This study presents a retinal vessel detection approach using shearlet transform and indeterminacy filtering. The fundus image’s green channel is mapped in the neutrosophic domain via shearlet transform. The neutrosophic domain images are then filtered with an indeterminacy filter to reduce the indeterminacy information. A neural network classifier is employed to identify the pixels whose inputs are the features in neutrosophic images. The proposed approach is tested on two datasets, and a receiver operating …

Neutrosophic Commutative N-Ideals In Bck-Algebras, Florentin Smarandache, Seok-Zun Song, Young Bae Jun

Branch Mathematics and Statistics Faculty and Staff Publications

The notion of a neutrosophic commutative N -ideal in BCK-algebras is introduced, and several properties are investigated. Relations between a neutrosophic N -ideal and a neutrosophic commutative N -ideal are discussed. Characterizations of a neutrosophic commutative N -ideal are considered.

Matroid Configurations And Symbolic Powers Of Their Ideals, A. V. Geramita, B. Harbourne, J. Migliore, Uwe Nagel

Mathematics Faculty Publications

Star configurations are certain unions of linear subspaces of projective space that have been studied extensively. We develop a framework for studying a substantial generalization, which we call matroid configurations, whose ideals generalize Stanley-Reisner ideals of matroids. Such a matroid configuration is a union of complete intersections of a fixed codimension. Relating these to the Stanley-Reisner ideals of matroids and using methods of liaison theory allows us, in particular, to describe the Hilbert function and minimal generators of the ideal of, what we call, a hypersurface configuration. We also establish that the symbolic powers of the ideal of any matroid …

Formalizing The Panarchy Adaptive Cycle With The Cusp Catastrophe, Martin Zwick, Joshua Hughes

Complex Systems Faculty Publications and Presentations

The panarchy adaptive cycle, a general model for change in natural and human systems, can be formalized by the cusp catastrophe of René Thom's topological theory. Both the adaptive cycle and the cusp catastrophe have been used to model ecological, economic, and social systems in which slow and small continuous changes in two control variables produce fast and large discontinuous changes in system behavior. The panarchy adaptive cycle, the more recent of the two models, has been used so far only for qualitative descriptions of typical dynamics of such systems. The cusp catastrophe, while also often employed qualitatively, is a …

Formalizing The Panarchy Adaptive Cycle With The Cusp Catastrophe [Presentation], Martin Zwick, Joshua Hughes

Complex Systems Faculty Publications and Presentations

The panarchy adaptive cycle, a general model for change in natural and human systems, can be formalized by the cusp catastrophe of René Thom's topological theory. Both the adaptive cycle and the cusp catastrophe have been used to model ecological, economic, and social systems in which slow and small continuous changes in two control variables produce fast and large discontinuous changes in system behavior. The panarchy adaptive cycle, the more recent of the two models, has been used so far only for qualitative descriptions of typical dynamics of such systems. The cusp catastrophe, while also often employed qualitatively, is a …

Inquiry Into Saving [Mathematics], Jeanne Funk

Open Educational Resources

‘Inquiry Into Saving’ is an assignment originally designed for MAT117, which is a course for students who have been placed in basic skills mathematics and who can apply a college level course in Algebra and Trigonometry to their program. These students should, ideally, be early in their LaGuardia career, though that is frequently not the case. All, however, are novices of mathematics. The assignment was vetted and revised based on feedback from the Inquiry and Problem Solving in STEM CTL seminar and a charrette not affiliated with the seminar. Revisions addressed connections to the Inquiry and Problem Solving/Written competency/ability pair, …

World Population Dynamics: Modeling Involving Polynomial Functions [Mathematics], Mangala Kothari

Open Educational Resources

In this Inquiry and Problem Solving Assignment students are expected to reflect on their analysis and compare their results with the actual population by conducting their own elementary level research such as searching databases, gathering information and interpreting. Students are expected to comment on the scope of the mathematical model and connect their learning in context to the real-world problem. The assignment includes open-ended questions such as: Write a paragraph about the dynamics of population for the world. What could be some of the possible parameters that contribute to the change in population size? Reflect on what you learned by …

Neutrosophic N -Structures And Their Applications In Semigroups, Florentin Smarandache, Madad Khan, Saima Anis, Young Bae Jun

Branch Mathematics and Statistics Faculty and Staff Publications

The notion of neutrosophic N -structure is introduced, and applied it to semigroup. The notions of neutrosophic N -subsemigroup, neutrosophic N -product and ε-neutrosophic N -subsemigroup are introduced, and several properties are investigated. Conditions for neutrosophic N -structure to be neutrosophic N -subsemigroup are provided. Using neutrosophic N -product, characterization of neutrosophic N -subsemigroup is discussed. Relations between neutrosophic N -subsemigroup and εneutrosophic N -subsemigroup are discussed. We show that the homomorphic preimage of neutrosophic N -subsemigroup is a neutrosophic N - subsemigroup, and the onto homomorphic image of neutrosophic N - subsemigroup is a neutrosophic N -subsemigroup.

Neutrosophic N -Structures Applied To Bck/Bci-Algebras, Florentin Smarandache, Young Bae Jun, Hashem Bordbar

Branch Mathematics and Statistics Faculty and Staff Publications

Neutrosophic N -structures with applications in BCK/BC I-algebras is discussed. The notions of a neutrosophic N -subalgebra and a (closed) neutrosophic N -ideal in a BCK/BC I-algebra are introduced, and several related properties are investigated. Characterizations of a neutrosophic N -subalgebra and a neutrosophic N -ideal are considered, and relations between a neutrosophic N -subalgebra and a neutrosophic N -ideal are stated. Conditions for a neutrosophic N -ideal to be a closed neutrosophic N -ideal are provided.