UNIVERSITY OF NORTH FLORIDA & MAYO CLINIC-JAX

SELECT PUBLICATIONS

01 Aug 2023

Digital Communication Use Before and During COVID Among Residential Older Adults

Geriatric Nursing

While digital communication methods have become commonplace in our society, many older adults living in residential care facilities do not use digital communication technologies during COVID. This study aims to describe their use patterns and examine their perceptions of digital communication technology. In partnership with two Continuing Care Retirement Communities, we conducted a descriptive, cross-sectional study design using a 24-item questionnaire via Qualtrics between March 2021 and April 2021; 120 respondents were included in the analysis. The data collected indicated minimal increases in digital communication behavior and communication frequency during COVID. DOI: 10.1016/j.gerinurse.2023.07.005

Journal Paper M DeDeo and C Williams

Digital Communication Use Before and During COVID Among Residential Older Adults

M DeDeo and C Williams
Journal Paper
14 Sep 2022

On the Energy of Transposition Graphs

Combinatorics, Graph Theory and Computing

We analyze and compare properties of Cayley graphs of permutation graphs called transposition graphs as this family of graphs has better degree and diameter properties than other families of graphs. Cayley graphs are directly related to the properties of its generator set and thus Cayley graphs of permutation groups generated by transpositions inherit almost all of the properties of the hypercube. In particular, we study properties of the complete transportation, (transposition) star graph, bubble-sort graph, modified bubble-sort graph and the binary hyper-cube and use these properties to determine bounds on the energy of these graph.

Chapter M.R. DeDeo

On the Energy of Transposition Graphs

M.R. DeDeo
Chapter
About The Publication

Here, we analyze and compare properties of Cayley graphs of permutation graphs called transposition graphs as this family of graphs has better degree and diameter properties than the hypercube. First, the conjugacy class of the permutation group combined with its generators dictates the type of symmetry possessed by their respective Cayley graphs. In addition, the base-b hypercube of dimension n is a class of networks known to possess virtually every known notion of symmetry. Second, properties of the transposition graphs are given. Third, the spectrum of this class of graphs is discussed and formulas for the energy of these graphs are given as they are dependent on these properties. DOI: 10.1007/978-3-031-05375-7_23

14 Mar 2022

Population and Nest Site Evidence for Diamondback Terrapins, Malaclemys terrapin, in Northeast Florida

Frontiers in Ecology and Evolution

Diamondback terrapins (Malaclemys terrapin) are listed as Vulnerable by the IUCN Red List Index of Threatened Species. We conducted headcounts and performed land surveys of shorelines and high spots for evidence of terrapin presence. During the land surveys, we searched for crawls, intact and depredated nests, dead terrapins, and terrapin bones. To evaluate whether woody plant presence affected nest site choices, we recorded the occurrence of 10 common woody plant species during each land survey and compared areas where nesting did and did not occur. DOI: 10.3389/fevo.2022.833199

Journal Paper J. Butler, M. DeDeo, D. Lambert, and D. Murphy.

Population and Nest Site Evidence for Diamondback Terrapins, Malaclemys terrapin, in Northeast Florida

J. Butler, M. DeDeo, D. Lambert, and D. Murphy.
Journal Paper
About The Publication

Among the challenges terrapins encounter are habitat loss due to coastal development and sea-level rise, mortality at all life stages by mammalian and avian predators, road mortality, boat strikes, harvest for the pet trade, and drowning in crab traps. The primary objective of this study was to locate populations and nesting areas of diamondback terrapins in the four northeastern-most counties of Florida (Nassau, Duval, St. Johns, and Flagler). We collected 404 records of terrapin activity in 2013 and 2014. Most were from Nassau County (277) and only one was from Flagler County. Most data were in the form of depredated nests (205) and terrapin remains (147). The woody plant data suggest that terrapins were significantly more likely to nest when Christmas berry (Lycium carolinianum) was present, and nesting was less likely when either wax myrtle (Myrica cerifera) or oak (Quercus spp.) were present.

23 Feb 2022

Demographics and surgery-related complications lead to 30-day readmission rates among knee arthroscopic procedures

nee Surgery, Sports Traumatology, Arthroscopy

The study objectives were (1) to evaluate risk factors related to 30-day hospital readmissions after arthroscopic knee surgeries and (2) to determine the complications that may arise from surgery. DOI: 10.1007/s00167-022-06919-2. PMID: 35199185

Journal Paper C Williams, M Bagwell, M DeDeo, A Baker Lutz, M J Deal, B Richey, I Zeini, B Service, D H Youmans, D Osbahr

Demographics and surgery-related complications lead to 30-day readmission rates among knee arthroscopic procedures

C Williams, M Bagwell, M DeDeo, A Baker Lutz, M J Deal, B Richey, I Zeini, B Service, D H Youmans, D Osbahr
Journal Paper
About The Publication

There were 83,083 knee arthroscopic procedures between 2012 and 2017 obtained from the National Surgical Quality Improvement Program database. The overall readmission rate was 0.87%. The complication rates were highest for synovectomy and cartilage procedures, 1.6% and 1.3% respectively. A majority of readmissions were related to the procedure (71.1%) with wound complications being the primary reason (28.2%) followed by pulmonary embolism and deep vein thrombosis, 12.7% and 10.6%, respectively. Gender and body mass index were not significant factors and age over 65 years was an independent risk factor. Wound infection, deep vein thrombosis, and pulmonary embolism were the most prevalent complications.

09 Jun 2021

Early detection of pediatric seizures in the high gamma band

IEEE Access

Extensive data analysis uses an expansion of power spectral density analysis and event-related potential analysis in conjunction with visualization techniques to reveal a method of predicting seizures before seizure onset by identifying significant preictal locations in the brain and their respective frequencies within the gamma band (70 through 100 Hz) by utilizing MIT’s Physionet scalp EEG database which consisted of data from acquired from pediatric patients at the Children’s Hospital Boston. DOI: 10.1109/ACCESS.2021.3087782

Journal Paper Michelle DeDeo and Maanasi Garg

Early detection of pediatric seizures in the high gamma band

Michelle DeDeo and Maanasi Garg
Journal Paper
About The Publication

Using spectral frequency analysis and visualization techniques on pediatric electroencephalogram recordings, we identify a method of detecting seizures thirty seconds before seizure onset by identifying significant preictal locations and their respective frequencies within the gamma band of 30 through 100 Hz. Using average log-power differences and visualization techniques to identify significant preictal patterns, intractable seizures are found to have common frequency extremes (CFEs) in the high gamma band between 70 and 100 Hz. Using this data, machine learning detection algorithm predictive performance may be improved by incorporating high gamma band signal processing at the varying location(s) and strength of a pediatric patient’s CFEs.
DOI: 10.1109/ACCESS.2021.3087782

21 Jul 2020

The Heat Equation on the Finite Poincare Upper Half Plane

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY

A differential-difference operator is used to model the heat equation on a finite graph analogue of Poincare’s upper half-plane. Finite analogues of the classical theta functions are shown to be solutions to the heat equation in this setting.
DOI: 10.1090/proc/15610

Journal Paper Selected M.R. DeDeo and Elinor Velazquez

The Heat Equation on the Finite Poincare Upper Half Plane

M.R. DeDeo and Elinor Velazquez
Journal Paper Selected
About The Publication

Classically, the heat equation on bounded domains, specifically on tori, yield theta functions as solutions. We study a finite analogue of the Poincare upper half-plane, namely, the finite upper half-plane introduced by Terras. Using this case, we investigate the periodicity inherent in the solutions of bounded domains. The solutions involve zonal spherical functions which come with a natural periodicity. In addition, the related theta functions are automorphic forms. The resultant periodicity interweaves representation theory with the heat equation. We hope this paper stimulates more study of this interplay.
DOI: 10.1090/proc/15610

Proceedings of the American Mathematical Society
01 Jun 2019

A Graph Energy Upper Bound Using Spectral Moments

CONGRESSUS NUMERANTIUM

An upper bounds on the energy of graphs is obtained using the spectral moments of the eigenvalues of adjacency matrix associated to the graph using the method of Lagrange multipliers and properties of cubics.

Journal Paper M.R. DeDeo

A Graph Energy Upper Bound Using Spectral Moments

M.R. DeDeo
Journal Paper
About The Publication

In this paper, we find another bound on the energy of all graphs including bipartite graphs using spectral moments and properties of cubics. The goal is to find bounds on the energy E(G) of graphs by using the second and fourth spectral moments, M2 and M4 using Lagrange multipliers.

24 May 2019

Survival trends in glioblastoma and association with treating facility volume

Journal of Clinical Neuroscience

Glioblastoma (GBM) is one of the most lethal cancers. To further understand this extremely poor prognosis disease, we evaluated the effect of the treatment facility volumes on overall survival (OS) on a total of 60,672 eligible GBM patients with median age of 65 years over the years 2004 through 2013.
DOI: 10.1016/j.jocn.2019.04.028

Journal Paper Selected Sonikpreet Aulakh, Michelle DeDeo, Joseph Free, Steven Rosenfeld, Alfredo Quinones-Hinojosa, Aneel Paulus, Alak Manna, Rami Manochakian, Asher Chanan-Khan, Sikander Ailawadhi

Survival trends in glioblastoma and association with treating facility volume

Sonikpreet Aulakh, Michelle DeDeo, Joseph Free, Steven Rosenfeld, Alfredo Quinones-Hinojosa, Aneel Paulus, Alak Manna, Rami Manochakian, Asher Chanan-Khan, Sikander Ailawadhi
Journal Paper Selected
About The Publication

To further understand this extremely poor prognosis disease, we evaluated the effect of the treatment facility volumes on overall survival (OS) over the years, especially after the approval of multimodality therapy using temozolomide (TMZ) in 2005. National Cancer Data Base (NCDB) was utilized to identify GBM cases from 2004 through 2013 using ICD-O-3 code 9440/3 to identify eligible patients. We focused on studying the association between treatment facility volume and OS after adjusting for the patient-, disease-, and facility-characteristics.

A total of 60,672 eligible GBM patients with median age of 65 years, treated at 1166 facilities were included in this analysis. The median annual facility volume was 3 patients/year (range: 0.1–55.1) and median OS was 8.1 months. There was an improvement in OS across all facilities after 2005, when multimodality therapy with TMZ was approved. Treatment at quartile 4 centers (Q4; >7 patients/year) was independently associated with decreased all-cause mortality in a multivariate analysis (Q3 hazard ratio [HR]: 1.11, 95% CI 1.09, 1.13; Q2 HR: 1.15, 95% CI 1.12, 1.19; Q1 HR: 1.25, 95% CI 1.17, 1.33). Treatment facility volume independently affects OS among GBM patients. Factors that are variable in high- and low-volume centers should be addressed to mitigate outcome disparities.

with Sonikpreet Aulakh, MD, Joseph Free, Aneel Paulus MD, Steven Rosenfeld MD,PhD, Alfredo Quinones-Hinojosa MD, Alak Manna PhD, Rami Manochakian MD, Asher Chanan-Khan MD, J Clin Neurosci. 2019 Oct; 68:271-274. doi: 10.1016/j.jocn.2019.04.028

01 Jun 2007

On the Ramanujancy of Heisenberg graphs over rings of degree 6 or more

CONGRESSUS NUMERANTIUM

Proving conditions for Ramanujancy and non-Ramanujancy is desirable as a Ramanujan graph can represent efficient communication networks in that they minimize cost of wiring and maintenance, but maximize the number of connections from one vertex to another. Here we determine if certain families of Heisenberg graphs satisfy the Ramanujan bound.

Journal Paper M.R. DeDeo, Vincent Dang and Yang Ge

On the Ramanujancy of Heisenberg graphs over rings of degree 6 or more

M.R. DeDeo, Vincent Dang and Yang Ge
Journal Paper
About The Publication

This paper determines if certain families of Heisenberg graphs satisfy the Ramanujan bound. Proving conditions for Ramanujancy and non-Ramanujancy is desirable as a Ramanujan graph can represent efficient communication networks in that they minimize cost of wiring and maintenance, but maximize the number of connections from one vertex to another. We say that a graph is Ramanujan if it is k-regular, simple, connected, undirected and the largest nontrivial eigenvalue, λ, of its adjacency matrix satisfies the condition that |λ|≤sqrt(2k-1) where k is the degree of the graph. We find λ by using the exponential sum lemma and prove a general theorem for the non-Ramanujancy of these graphs under certain conditions. One of these conditions is satisfied by assuming the minimality of certain terms in the exponential sum. Then, without loss of generality, we isolate and prove the conditions for the occurrence of all lower-dimensional eigenvalues that exceed the Ramanujan bound. Also, graphical analysis of the spectra of Ramanujan graphs is performed and it is shown that, for a fixed number of elements in the symmetric set and as a prime p increases without bound, the distribution of the eigenvalues resembles the Sato-Tate semi-circle distribution.

with Vincent Dang and Yang Ge, Proceedings of the Thirty-Eighth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 185 (2007), 111–126. MR2408803 05C50


On the Ramanujancy of Heisenberg Graphs of degree 6 or more

06 May 2007

The Spectrum of Platonic Graphs over Finite Fields

DISCRETE MATHEMATICS

We give a decomposition theorem for Platonic graphs over finite fields and use this to determine the spectrum of these graphs. We also derive estimates for the isoperimetric numbers of the graphs.
DOI: 10.1016/j.disc.2006.07.032

Journal Paper M. DeDeo, Dominic Lanphier and Marvin Minei

The Spectrum of Platonic Graphs over Finite Fields

M. DeDeo, Dominic Lanphier and Marvin Minei
Journal Paper
About The Publication

For q = p, the graph G(q) is called the qth Platonic graph. The name comes from the fact that when p = 3 or 5, the graphs G(p) correspond to 1-skeletons of two of the Platonic solids, in other words, the tetrahedron and the icosahedron as in [2]. More generally, G(p) is the 1-skeleton of a triangulation of the modular curve X(p). In this paper, we determine the spectrum of G(q) and thus generalize results of P.E. Gunnells, “Some elementary Ramanujan graphs”.

with Dominic Lanphier and Marvin Minei, Discrete Math. 307 (2007), no. 9-10, 1074–1081.  DOI: 10.1016/j.disc.2006.07.032   MR2292536 05C25 (05C50) 

25 Aug 2005

The Radon transform on the ring of Integers modulo n

SIAM JOURNAL OF DISCRETE MATHEMATICS

The Radon transform on Zkn averages a function over its values on a translate of a fixed subset S in Zkn. We discuss invertibility conditions and computer inverse formulas based on the Moore–Penrose inverse and on linear algorithms. We expect the results to be of use in directional and toroidal time series.
DOI: 10.1137/S0895480103430764

Journal Paper M.R. DeDeo and Elinor Velazquez

The Radon transform on the ring of Integers modulo n

M.R. DeDeo and Elinor Velazquez
Journal Paper
About The Publication

This paper continues the authors previous work that deals with the problem of reconstructing some function defined on a finite group G from averages of the function over various neighborhoods of points. It generalizes work done earlier by Diaconis and Graham, and Fill, among others.

Diaconis and Graham discuss the cases where G = Zk2, the group of binary k-tuples, and where G = Sn, the symmetric group on n letters, in order to provide an exposition on discrete Radon transforms which appear in applied statistics. Fill examines the case G = Zk2, the group of integers modulo n. This case arises in directional data analysis and circular time series. Other finite analogues of the Radon transform occur, but we shall restrict ourselves to the case G = Zkn, the group of k-tuples of the integers modulo n, as these results are of use in k-dimensional toroidal time series.

with Elinor Velasquez. SIAM J. Discrete Math. 18 (2004/05), no. 3, 472–478. MR2134409 44A12  (43A75)
DOI: 10.1137/S0895480103430764

01 Jun 2005

Zeta Functions of Heisenberg Graphs over Finite Rings

Theory and Applications of Special Functions

We investigate Ihara-Selberg zeta functions of Cayley graphs for the Heisenberg group over finite rings Z/pnZ, where p is a prime. In order to do this, we must compute the Galois group of the covering obtained by reducing coordinates in Z/pn+1Z modulo pn.
DOI: 10.1007/0-387-24233-3_8

Chapter Michelle DeDeo, María Martínez, Archie Medrano, Marvin Minei,Harold Stark,Audrey Terras

Zeta Functions of Heisenberg Graphs over Finite Rings

Michelle DeDeo, María Martínez, Archie Medrano, Marvin Minei,Harold Stark,Audrey Terras
Chapter
About The Publication

The aim of this paper is to study the special functions known as Ihara Selberg zeta functions for Cayley graphs of finite Heisenberg groups as well as their factorizations into products of Artin-Ihara L-functions. The Heisenberg group H(R) over a ring R consists of upper triangular 3×3 matrices with entries in R and ones on the diagonal. The Ihara-Selberg zeta function is analogous to the Riemann zeta function with primes replaced by certain closed paths in a graph. This paper is a continuation of (DeDeo et al., 2004) where we presented a study of the statistics of the spectra of adjacency matrices of finite Heisenberg graphs.

with Martínez M., Medrano A., Minei M., Stark H., Terras A. (2005) Zeta Functions of Heisenberg Graphs over Finite Rings. In: Ismail

DOI: 10.1007/0-387-24233-3_8     MR2132463     05C25 (05C38 11M41 11R42 20H25) 

12 May 2004

An Introduction to Symplectic Maps and Generalizations of the Toda Lattice

CONGRESSUS NUMERANTIUM

We construct particular Hamiltonian systems associated to graphs embedded in Euclidean n−dimensional space and apply the dual transformation to this system. This result extends the one-dimensional dual transformation associated to the Toda lattice. We also discuss some applications to solid-state lattice theory.

Journal Paper M.R. DeDeo and Elinor Velazquez

An Introduction to Symplectic Maps and Generalizations of the Toda Lattice

M.R. DeDeo and Elinor Velazquez
Journal Paper
About The Publication

In this paper, we study the dual transformation applied to N particles and N −1 springs that are no longer constrained to the real line. For simplicity, assume the Hamiltonian system formed to be embedded in Euclidean n−space with the standard metric and also assume that N < ∞ and that all N particles are connected to at least one spring.

Our interpretation of one possible extension is to create graphs that can act as dynamical systems. We decide to take a graph (a finite one, for simplicity), position masses at the vertices of the graph, and exchange the edges of the graphs with springs. Again, for simplicity, we assume that the springs behave uniformly, although not necessarily linearly. We then re-express the Hamiltonian with respect to the graphs rather than focusing on the underlying manifold. We focus on graphs which may be neatly embedded into Euclidean n−dimensional space for the purpose of this paper. Hence we now have information regarding how graphs behave when “equipped” with a symplectic 2−form.

 

with Elinor Velasquez. Proceedings of the Thirty-Fifth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congressus Numerantium 169 (2004), 127–139.   MR2122063     70H06 (05C45 37J35 37K60 70H15 82C05)

An Introduction to Symplectic Maps and Generalizations of the Toda Lattice

 

10 May 2003

Generalized Kloosterman sums over Rings of Order 2r

CONGRESSUS NUMERANTIUM

After presenting several applications of Kloosterman sums in analytic number theory, generalized Kloosterman sums attached to Gauss sums over the ring of 2r elements are explicitly evaluated and are shown to be sines and cosines

Journal Paper M. DeDeo

Generalized Kloosterman sums over Rings of Order 2r

M. DeDeo
Journal Paper
About The Publication

Although Kloosterman sums of odd prime powers have been studied extensively, many authors avoid the case where p = 2. This case is important as Kloosterman sums for fields of characteristic 2 have been useful in error-correcting codes and Kloosterman sums over the ring of integers modulo pr have been helpful in studying the spectra of Euclidean graphs. After stating some well-known facts about Kloosterman sums, we evaluate several generalized Kloosterman sums modulo 2r.

Proceedings of the Thirty-Fourth Southeastern International Conference on Combinatorics, Graph Theory and Computing. Congr. Numer. 165 (2003), 65–75MR2049122 11T24 (11L05)

Generalized Kloosterman sums over Rings of Order 2r

01 Jun 2003

Spectra of Heisenberg Graphs over Finite Rings

Dynamical systems and differential equations

We investigate spectra of Cayley graphs for the Heisenberg group over finite rings Z/pnZ, where p is a prime. Emphasis is on graphs of degree four. We show that for odd p there is only one such connected graph up to isomorphism. When p = 2, there are at most two isomorphism classes. We study the spectra using representations of the Heisenberg group. This allows us to produce histograms and butterfly diagrams of the spectra. DOI: 10.3934/proc.2003.2003.213

Journal Paper M. DeDeo, M. Martinez, A. Medrano, M. Minei, H.M. Stark, and A. Terras

Spectra of Heisenberg Graphs over Finite Rings

M. DeDeo, M. Martinez, A. Medrano, M. Minei, H.M. Stark, and A. Terras
Journal Paper
About The Publication

The aim of this paper is to study spectra of Cayley graphs attached to finite Heisenberg groups using histograms and Hofstadter butterfly figures. The Heisenberg group H(R) over a ring R consists of upper triangular 3×3 matrices with entries in R and ones on the diagonal.

Heisenberg groups over finite fields have provided a tool in the search for random number generators (see Maria Zack) as well as the search for Ramanujan graphs (see Perla Myers). Other references are P. Diaconis and L. Saloff-Coste [5] and Terras [24]. As shown in the last reference, the size of the second largest (in absolute value) eigenvalue of the adjacency matrix governs the speed of convergence to uniform for the standard random walk on a connected regular graph. Ramanujan graphs have the best possible eigenvalue bound for connected regular graphs of fixed degree in an infinite sequence of graphs with number of vertices going to infinity. For such graphs, the random walker gets lost as quickly as possible. Equivalently, this says that such graphs can be used to build efficient communication networks.

with M. Martinez, A. Medrano, M. Minei, H.M. Stark, and A. TerrasDynamical systems and differential equations (Wilmington, NC, 2002). Discrete Contin. Dyn. Syst. 2003, suppl., 213–222. MR2018119 11T60 (05C25)

https://www.aimsciences.org/article/doi/10.3934/proc.2003.2003.213

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