David F. Anderson
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View article: Stochastic Reaction Networks Within Interacting Compartments with Content-Dependent Fragmentation
Stochastic Reaction Networks Within Interacting Compartments with Content-Dependent Fragmentation Open
Stochastic reaction networks with mass-action kinetics provide a useful framework for understanding processes -- biochemical and otherwise -- in homogeneous environments. However, cellular reactions are often compartmentalized, either at t…
View article: Mathematical Analysis for a Class of Stochastic Copolymerization Processes
Mathematical Analysis for a Class of Stochastic Copolymerization Processes Open
We study a stochastic model of a copolymerization process that has been extensively investigated in the physics literature. The main questions of interest include: (i) what are the criteria for transience, null recurrence, and positive rec…
View article: P-16 Secondary glaucoma treatment and graft failure in penetrating keratoplasty for advanced acanthamoeba keratitis: 5 years follow-up
P-16 Secondary glaucoma treatment and graft failure in penetrating keratoplasty for advanced acanthamoeba keratitis: 5 years follow-up Open
View article: Parametric Sensitivity Analysis for Models of Reaction Networks within Interacting Compartments
Parametric Sensitivity Analysis for Models of Reaction Networks within Interacting Compartments Open
Models of reaction networks within interacting compartments (RNIC) are a generalization of stochastic reaction networks. It is most natural to think of the interacting compartments as "cells" that can appear, degrade, split, and even merge…
View article: Chemical mass-action systems as analog computers: implementing arithmetic computations at specified speed
Chemical mass-action systems as analog computers: implementing arithmetic computations at specified speed Open
Recent technological advances allow us to view chemical mass-action systems as analog computers. In this context, the inputs to a computation are encoded as initial values of certain chemical species while the outputs are the limiting valu…
View article: P-15 Changing indications for penetrating keratoplasty and 5-years survival outcomes – a single tertiary centre experience
P-15 Changing indications for penetrating keratoplasty and 5-years survival outcomes – a single tertiary centre experience Open
Purpose To investigate long-term graft survival rates of penetrating keratoplasties, patient characteristics and co-morbidities in a single tertiary care centre on the South Coast. Methods Retrospective, non-comparative case series review …
View article: Square-difference factor absorbing ideals of a commutative ring
Square-difference factor absorbing ideals of a commutative ring Open
Let $R$ be a commutative ring with $1 \neq 0$. A proper ideal $I$ of $R$ is a {\it square-difference factor absorbing ideal} (sdf-absorbing ideal) of $R$ if whenever $a^2 - b^2 \in I$ for $0 \neq a, b \in R$, then $a + b \in I$ or $a - b \…
View article: Chemical Mass-Action Systems as Analog Computers: Implementing Arithmetic Computations at Specified Speed
Chemical Mass-Action Systems as Analog Computers: Implementing Arithmetic Computations at Specified Speed Open
View article: A new path method for exponential ergodicity of Markov processes on $\mathbb Z^d$, with applications to stochastic reaction networks
A new path method for exponential ergodicity of Markov processes on $\mathbb Z^d$, with applications to stochastic reaction networks Open
This paper provides a new path method that can be used to determine when an ergodic continuous-time Markov chain on $\mathbb Z^d$ converges exponentially fast to its stationary distribution in $L^2$. Specifically, we provide general condit…
View article: Simultaneous tectonic Descemet stripping endothelial keratoplasty and tectonic Bowman layer transplant for the management of corneal perforation
Simultaneous tectonic Descemet stripping endothelial keratoplasty and tectonic Bowman layer transplant for the management of corneal perforation Open
AIM: To report the outcomes of three cases of corneal perforation managed with simultaneous tectonic Descemet stripping endothelial keratoplasty (t-DSEK) and tectonic Bowman layer transplant (t-BLT) as an alternative to tectonic penetratin…
View article: Table of contents
Table of contents Open
View article: Assessment of Corneal Graft Rejection Rates Following Partial Endothelial Keratoplasty in COVID-19 Vaccinated Patients
Assessment of Corneal Graft Rejection Rates Following Partial Endothelial Keratoplasty in COVID-19 Vaccinated Patients Open
Objectives: The study aims to investigate the incidence of graft rejection following Covid-19 vaccination among patients who had undergone partial endothelial keratoplasty, a form of corneal transplantation. Methods: The study involved 208…
View article: Stochastic reaction networks within interacting compartments
Stochastic reaction networks within interacting compartments Open
Stochastic reaction networks, which are usually modeled as continuous-time Markov chains on $\mathbb Z^d_{\ge 0}$, and simulated via a version of the "Gillespie algorithm," have proven to be a useful tool for the understanding of processes…
View article: Photosensitive dopants for liquid noble gases
Photosensitive dopants for liquid noble gases Open
In an ionization type detector for high energy radiation wherein the energy of incident radiation is absorbed through the ionization of a liquid noble gas and resulting free charge is collected to form a signal indicative of the energy of …
View article: Mixing times for two classes of stochastically modeled reaction networks
Mixing times for two classes of stochastically modeled reaction networks Open
The past few decades have seen robust research on questions regarding the existence, form, and properties of stationary distributions of stochastically modeled reaction networks. When a stochastic model admits a stationary distribution an …
View article: Case series of staged lamellar corneal grafting with thin manual Descemet’s stripping endothelial keratoplasty, followed by manual deep anterior lamellar keratoplasty, as an alternative to penetrating keratoplasty
Case series of staged lamellar corneal grafting with thin manual Descemet’s stripping endothelial keratoplasty, followed by manual deep anterior lamellar keratoplasty, as an alternative to penetrating keratoplasty Open
The purpose of this report is to present the outcomes of Descemet’s stripping endothelial keratoplasty (DSEK), followed by deep anterior lamellar keratoplasty (DALK), as an alternative to penetrating keratoplasty (PKP) for different indica…
View article: Development of a low-cost extruded scintillator with co-extruded reflector for the MINOS experiment
Development of a low-cost extruded scintillator with co-extruded reflector for the MINOS experiment Open
The MINOS experiment is a long-baseline, neutrino-oscillation experiment. In total, 28,000 m{sup 2} of scintillator is needed for the experiment. This is almost 300 tons of finished scintillator. The solution has been the development of an…
View article: Prevalence of deficiency-zero reaction networks in an Erdös–Rényi framework
Prevalence of deficiency-zero reaction networks in an Erdös–Rényi framework Open
Reaction networks are commonly used within the mathematical biology and mathematical chemistry communities to model the dynamics of interacting species. These models differ from the typical graphs found in random graph theory since their v…
View article: Mixing times for two classes of stochastically modeled reaction networks
Mixing times for two classes of stochastically modeled reaction networks Open
The past few decades have seen robust research on questions regarding the existence, form, and properties of stationary distributions of stochastically modeled reaction networks. When a stochastic model admits a stationary distribution an …
View article: Deficiency zero for random reaction networks under a stochastic block model framework
Deficiency zero for random reaction networks under a stochastic block model framework Open
View article: On reaction network implementations of neural networks
On reaction network implementations of neural networks Open
This paper is concerned with the utilization of deterministically modelled chemical reaction networks for the implementation of (feed-forward) neural networks. We develop a general mathematical framework and prove that the ordinary differe…
View article: Deficiency zero for random reaction networks under a stochastic block\n model framework
Deficiency zero for random reaction networks under a stochastic block\n model framework Open
Deficiency zero is an important network structure and has been the focus of\nmany celebrated results within reaction network theory. In our previous paper\n\\textit{Prevalence of deficiency zero reaction networks in an Erd\\H os-R\\'enyi\n…
View article: Bounded and finite factorization domains
Bounded and finite factorization domains Open
An integral domain is atomic if every nonzero nonunit factors into irreducibles. Let $R$ be an integral domain. We say that $R$ is a bounded factorization domain if it is atomic and for every nonzero nonunit $x \in R$, there is a positive …
View article: Stochastically modeled weakly reversible reaction networks with a single linkage class
Stochastically modeled weakly reversible reaction networks with a single linkage class Open
It has been known for nearly a decade that deterministically modeled reaction networks that are weakly reversible and consist of a single linkage class have trajectories that are bounded from both above and below by positive constants (so …
View article: weakly $(m,n)$-closed ideals and $(m,n)$-von Neumann regular rings
weakly $(m,n)$-closed ideals and $(m,n)$-von Neumann regular rings Open
Let R be a commutative ring with identity. In this paper, we introduce the concept of (m, n)-closed ideals of R and (m, n)-von Neumann regular rings
View article: Tier structure of strongly endotactic reaction networks
Tier structure of strongly endotactic reaction networks Open
View article: On n-semiprimary Ideals and n-pseudo Valuation Domains
On n-semiprimary Ideals and n-pseudo Valuation Domains Open
In this paper, we introduce the concept of n-semiprimary ideals, n-powerful ideals, and n-powerful semiprimary ideals of commutative rings. We study these concepts and relate them to several generalizations of pseudo-valuation domains.
View article: GENERALIZATIONS OF THE ZERO-DIVISOR GRAPH
GENERALIZATIONS OF THE ZERO-DIVISOR GRAPH Open
Let $R$ be a commutative ring with $1 \\neq 0$ and $Z(R)$ itsset of zero-divisors. The zero-divisor graph of $R$ is the (simple) graph $\\Gamma(R)$ with vertices $Z(R) \\setminus \\{0\\}$, and distinct vertices $x$ and $y$ are adjacent if …
View article: Prevalence of deficiency zero reaction networks in an Erdos-Renyi\n framework
Prevalence of deficiency zero reaction networks in an Erdos-Renyi\n framework Open
Reaction networks are commonly used within the mathematical biology and\nmathematical chemistry communities to model the dynamics of interacting\nspecies. These models differ from the typical graphs found in random graph\ntheory since thei…
View article: Stochastic chemical reaction networks for robustly approximating arbitrary probability distributions
Stochastic chemical reaction networks for robustly approximating arbitrary probability distributions Open