Department of Mathematics
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Departmental Publications, Department of Mathematics [5]
Newsletters, annual reports, and other departmental publications 
Scholarly Works, Department of Mathematics [243]
Research articles, presentations, and other scholarship
Recent Submissions

Multiple blood feeding in mosquitoes shortens the Plasmodium falciparum incubation period and increases malaria transmission potential
(PLOS, 20201231)Many mosquito species, including the major malaria vector Anopheles gambiae, naturally undergo multiple reproductive cycles of blood feeding, egg development and egg laying in their lifespan. Such complex mosquito behavior ... 
The impact of withinvector parasite development on the extrinsic incubation period
(20201007)Mosquitoborne diseases, in particular malaria, have a significant burden worldwide leading to nearly half a million deaths each year. The malaria parasite requires a vertebrate host, such as a human, and a vector host, ... 
Parasitism of Aedes albopictus by Ascogregarina taiwanensis lowers its competitive ability against Aedes triseriatus
(20210125)Background Mosquitoes are vectors for diseases such as dengue, malaria and La Crosse virus that significantly impact the human population. When multiple mosquito species are present, the competition between ... 
Reduced Order Models for the QuasiGeostrophic Equations: A Brief Survey
(MDPI, 20201231)Reduced order models (ROMs) are computational models whose dimension is significantly lower than those obtained through classical numerical discretizations (e.g., finite element, finite difference, finite volume, or spectral ... 
Twisted Hermitian Codes
(MDPI, 20201226)We define a family of codes called twisted Hermitian codes, which are based on Hermitian codes and inspired by the twisted Reed–Solomon codes described by Beelen, Puchinger, and Nielsen. We demonstrate that these new ... 
The SunPy Project: Open Source Development and Status of the Version 1.0 Core Package
(20200212)The goal of the SunPy project is to facilitate and promote the use and development of communityled, free, and open source data analysis software for solar physics based on the scientific Python environment. The project ... 
Algebras and Varieties
(202003)In this paper we introduce new affine algebraic varieties whose points correspond to associative algebras. We show that the algebras within a variety share many important homological properties. In particular, any two ... 
A Survey of Computational Tools in Solar Physics
(20200420)The SunPy Project developed a 13question survey to understand the software and hardware usage of the solarphysics community. Of the solarphysics community, 364 members across 35 countries responded to our survey. We ... 
New exotic 4manifolds via Luttinger surgery on Lefschetz fibrations
(WORLD SCIENTIFIC, 20150101)In [Small exotic 4manifolds, Algebr. Geom. Topol. 8 (2008) 17811794], the first author constructed the first known example of exotic minimal symplectic CP2#5CP2and minimal symplectic 4manifold that is homeomorphic but ... 
Modeling the waning and boosting of immunity from infection or vaccination
(20200721)Immunity following natural infection or immunization may wane, increasing susceptibility to infection with time since infection or vaccination. Symptoms, and concomitantly infectiousness, depend on residual immunity. We ... 
Lagrangian Reduced Order Modeling Using Finite Time Lyapunov Exponents
(MDPI, 20201023)There are two main strategies for improving the projectionbased reduced order model (ROM) accuracy—(i) improving the ROM, that is, adding new terms to the standard ROM; and (ii) improving the ROM basis, that is, ... 
Transfer Entropy Analysis of Interactions between Bats Using Position and Echolocation Data
(MDPI, 20201019)Many animal species, including many species of bats, exhibit collective behavior where groups of individuals coordinate their motion. Bats are unique among these animals in that they use the active sensing mechanism of ... 
Students' metarepresentational competence with matrix notation and Dirac notation in quantum mechanics
(20200825)This article shares analysis regarding quantum mechanics students' metarepresentational competence (MRC) that is expressed as they engaged in solving an expectation value problem, which involves linear algebra concepts. ... 
A Degree Theory for Compact Perturbations of Monotone Type Operators and Application to Nonlinear Parabolic Problem
(Hindawi, 20170912)Let 𝑋 be a real locally uniformly convex reflexive Banach space with locally uniformly convex dual space 𝑋∗. Let 𝑇 : 𝑋 ⊇ 𝐷(𝑇) → 2𝑋∗ be maximal monotone, 𝑆:𝑋→2𝑋∗ be bounded and of type (𝑆₊), and 𝐶 : 𝐷(𝐶) → 𝑋∗ ... 
Fiberoptic Seismology
Distributed Acoustic Sensing (DAS) is an emerging technology that repurposes a fiberoptic cable as a dense array of strain sensors. This technology repeatedly pings a fiber with laser pulses, measuring optical phase ... 
Mathematical model of broadly reactive plasma cell production
(Nature Research, 2020)Strainspecific plasma cells are capable of producing neutralizing antibodies that are essential for clearance of challenging pathogens. These neutralizing antibodies also function as a main defense against disease ... 
Longtime Reynolds averaging of reduced order models for fluid flows: Preliminary results
(20191022)We perform a preliminary theoretical and numerical investigation of the timeaverage of energy exchange among modes of Reduced Order Models (ROMs) of fluid flows. We are interested in the statistical equilibrium problem, ... 
Closure Learning for Nonlinear Model Reduction Using Deep Residual Neural Network
(MDPI, 20200323)Developing accurate, efficient, and robust closure models is essential in the construction of reduced order models (ROMs) for realistic nonlinear systems, which generally require drastic ROM mode truncations. We propose a ... 
Editorial for Special Issue “Drop, Bubble and Particle Dynamics in Complex Fluids”
(MDPI, 20200102)The presence of drops, bubbles, and particles affects the behavior and response of complex multiphase fluids [...]