Richard Cangelosi | Gonzaga University (original) (raw)

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Papers by Richard Cangelosi

Research paper thumbnail of Biology Direct BioMed Central

Component retention in principal component analysis with application to cDNA microarray data

Research paper thumbnail of The behavior of a population interaction-diffusion equation in its subcritical regime

Involve, A Journal of Mathematics, 2018

Research paper thumbnail of Pattern formation properties of a system of interaction-diffusion equations relevant to a mussel-algae ecosystem in a quiescent marine layer

Research paper thumbnail of Ambiguity of the Negative Sign

International Group for the Psychology of Mathematics Education, 2011

Research paper thumbnail of Component retention in principal component analysis with application to cDNA microarray data

Biology direct, 2007

Shannon entropy is used to provide an estimate of the number of interpretable components in a pri... more Shannon entropy is used to provide an estimate of the number of interpretable components in a principal component analysis. In addition, several ad hoc stopping rules for dimension determination are reviewed and a modification of the broken stick model is presented. The modification incorporates a test for the presence of an "effective degeneracy" among the subspaces spanned by the eigenvectors of the correlation matrix of the data set then allocates the total variance among subspaces. A summary of the performance of the methods applied to both published microarray data sets and to simulated data is given.

Research paper thumbnail of Heat Transfer in Fully Developed, Laminar Flows of Dissipative Pseudoplastic and Dilatant Fluids in Circular Conduits

This paper reports the results of a numerical study that determined the Nusselt number for hydrod... more This paper reports the results of a numerical study that determined the Nusselt number for hydrodynamically and thermally fully developed, laminar, dissipative flows of pseudoplastic and dilatant fluids through circular conduits. Two boundary conditions were considered, constant heat flux and constant temperature. Constitutive equations were used that describe the entire flow curve, from the zero-shear rate through the infinite shear rate Newtonian regions, so that computed Nusselt numbers are valid for whatever shear rates may exist in the flow field. Nusselt numbers are reported as a function of a dimensionless shear rate parameter that establishes the region of the flow curve where the system is operating and are shown to be bound by the Newtonian and power law values. The conditions required for the system to perform at these asymptotic limits are quantified.

Research paper thumbnail of A Quasi-Steady-State Approximation to the Basic Target-Cell-Limited Viral Dynamics Model with a Non-Cytopathic Effect

Frontiers in Microbiology

Analysis of previously published target-cell limited viral dynamic models for pathogens such as H... more Analysis of previously published target-cell limited viral dynamic models for pathogens such as HIV, hepatitis, and influenza generally rely on standard techniques from dynamical systems theory or numerical simulation. We use a quasi-steady-state approximation to derive an analytic solution for the model with a non-cytopathic effect, that is, when the death rates of uninfected and infected cells are equal. The analytic solution provides time evolution values of all three compartments of uninfected cells, infected cells, and virus. Results are compared with numerical simulation using clinical data for equine infectious anemia virus, a retrovirus closely related to HIV, and the utility of the analytic solution is discussed.

Research paper thumbnail of Pattern formation properties of a system of interaction-diffusion equations relevant to a mussel-algae ecosystem in a quiescent marine layer

Research paper thumbnail of Ambiguity of the Negative Sign

Research paper thumbnail of Rhombic Analysis Extension of a Plant-Surface Water Interaction-Diffusion Model for Hexagonal Pattern Formation in an Arid Flat Environment

American Journal of Plant Sciences, 2015

An existing weakly nonlinear diffusive instability hexagonal planform analysis for an interaction... more An existing weakly nonlinear diffusive instability hexagonal planform analysis for an interactiondiffusion plant-surface water model system in an arid flat environment [11] is extended by performing a rhombic planform analysis as well. In addition a threshold-dependent paradigm that differs from the usually employed implicit zero-threshold methodology is introduced to interpret stable rhombic patterns. The results of that analysis are synthesized with those of the existing hexagonal planform analysis. In particular these synthesized results can be represented by closedform plots in the rate of precipitation versus the specific rate of plant density loss parameter space. From those plots, regions corresponding to bare ground and vegetative Turing patterns consisting of tiger bush (parallel stripes and labyrinthine mazes), pearled bush (hexagonal gaps and rhombic pseudo-gaps), and homogeneous distributions of vegetation, respectively, may be identified in this parameter space. Then that predicted sequence of stable states along a rainfall gradient is both compared with observational evidence and used to motivate an aridity classification scheme. Finally this system is shown to be isomorphic to the chemical reaction-diffusion Gray-Scott model and that isomorphism is employed to draw some conclusions about sideband instabilities as applied to vegetative patterning.

Research paper thumbnail of Vegetative Rhombic Pattern Formation Driven by Root Suction for an Interaction-Diffusion Plant-Ground Water Model System in an Arid Flat Environment

American Journal of Plant Sciences, 2015

A rhombic planform nonlinear cross-diffusive instability analysis is applied to a particular inte... more A rhombic planform nonlinear cross-diffusive instability analysis is applied to a particular interaction-diffusion plant-ground water model system in an arid flat environment. This model contains a plant root suction effect as a cross-diffusion term in the ground water equation. In addition a threshold-dependent paradigm that differs from the usually employed implicit zero-threshold methodology is introduced to interpret stable rhombic patterns. These patterns are driven by root suction since the plant equation does not yield the required positive feedback necessary for the generation of standard Turing-type self-diffusive instabilities. The results of that analysis can be represented by plots in a root suction coefficient versus rainfall rate dimensionless parameter space. From those plots regions corresponding to bare ground and vegetative patterns consisting of isolated patches, rhombic arrays of pseudo spots or gaps separated by an intermediate rectangular state, and homogeneous distributions from low to high density may be identified in this parameter space. Then, a morphological sequence of stable vegetative states is produced upon traversing an experimentally-determined root suction characteristic curve as a function of rainfall through these regions. Finally, that predicted sequence along a rainfall gradient is compared with observational evidence relevant to the occurrence of leopard bush, pearled bush, or labyrinthine tiger bush vegetative patterns, used to motivate an aridity classification scheme, and placed in the context of some recent biological nonlinear pattern formation studies.

Research paper thumbnail of Immune Control of Equine Infectious Anemia Virus Infection by Cell-Mediated and Humoral Responses

Applied Mathematics, 2013

Equine Infectious Anemia Virus (EIAV) is a retrovirus that establishes a persistent infection in ... more Equine Infectious Anemia Virus (EIAV) is a retrovirus that establishes a persistent infection in horses and ponies. The virus is in the same lentivirus subgroup that includes human immunodeficiency virus (HIV). The similarities between these two viruses make the study of the immune response to EIAV relevant to research on HIV. We developed a mathematical model of within-host EIAV infection dynamics that contains both humoral and cell-mediated immune responses. Analysis of the model yields results on thresholds that would be necessary for a combined immune response to successfully control infection. Numerical simulations are presented to illustrate the results. These findings have the potential to lead to immunological control measures for lentiviral infection.

Research paper thumbnail of Nonlinear stability analyses of Turing patterns for a mussel-algae model

Journal of Mathematical Biology, 2014

A particular interaction-diffusion mussel-algae model system for the development of spontaneous s... more A particular interaction-diffusion mussel-algae model system for the development of spontaneous stationary young mussel bed patterning on a homogeneous substrate covered by a quiescent marine layer containing algae as a food source is investigated employing weakly nonlinear diffusive instability analyses. The main results of these analyses can be represented by plots in the ratio of mussel motility to algae lateral diffusion versus the algae reservoir concentration dimensionless parameter space. Regions corresponding to bare sediment and mussel patterns consisting of rhombic or hexagonal arrays and isolated clusters of clumps or gaps, an intermediate labyrinthine state, and homogeneous distributions of low to high density may be identified in this parameter space. Then those Turing diffusive instability predictions are compared with both relevant field and laboratory experimental evidence and existing numerical simulations involving differential flow migrating band instabilities for the associated interaction-dispersion-advection mussel-algae model system as well as placed in the context of the results from some recent nonlinear pattern formation studies.

Research paper thumbnail of The negative sign and exponential expressions: Unveiling students’ persistent errors and misconceptions

The Journal of Mathematical Behavior, 2013

Additive and multiplicative inverse Additive and multiplicative identities a b s t r a c t

Research paper thumbnail of Component retention in principal component analysis with application to cDNA microarray data

Biology Direct, 2007

Shannon entropy is used to provide an estimate of the number of interpretable components in a pri... more Shannon entropy is used to provide an estimate of the number of interpretable components in a principal component analysis. In addition, several ad hoc stopping rules for dimension determination are reviewed and a modification of the broken stick model is presented. The modification incorporates a test for the presence of an "effective degeneracy" among the subspaces spanned by the eigenvectors of the correlation matrix of the data set then allocates the total variance among subspaces. A summary of the performance of the methods applied to both published microarray data sets and to simulated data is given.

Research paper thumbnail of Biology Direct BioMed Central

Component retention in principal component analysis with application to cDNA microarray data

Research paper thumbnail of The behavior of a population interaction-diffusion equation in its subcritical regime

Involve, A Journal of Mathematics, 2018

Research paper thumbnail of Pattern formation properties of a system of interaction-diffusion equations relevant to a mussel-algae ecosystem in a quiescent marine layer

Research paper thumbnail of Ambiguity of the Negative Sign

International Group for the Psychology of Mathematics Education, 2011

Research paper thumbnail of Component retention in principal component analysis with application to cDNA microarray data

Biology direct, 2007

Shannon entropy is used to provide an estimate of the number of interpretable components in a pri... more Shannon entropy is used to provide an estimate of the number of interpretable components in a principal component analysis. In addition, several ad hoc stopping rules for dimension determination are reviewed and a modification of the broken stick model is presented. The modification incorporates a test for the presence of an "effective degeneracy" among the subspaces spanned by the eigenvectors of the correlation matrix of the data set then allocates the total variance among subspaces. A summary of the performance of the methods applied to both published microarray data sets and to simulated data is given.

Research paper thumbnail of Heat Transfer in Fully Developed, Laminar Flows of Dissipative Pseudoplastic and Dilatant Fluids in Circular Conduits

This paper reports the results of a numerical study that determined the Nusselt number for hydrod... more This paper reports the results of a numerical study that determined the Nusselt number for hydrodynamically and thermally fully developed, laminar, dissipative flows of pseudoplastic and dilatant fluids through circular conduits. Two boundary conditions were considered, constant heat flux and constant temperature. Constitutive equations were used that describe the entire flow curve, from the zero-shear rate through the infinite shear rate Newtonian regions, so that computed Nusselt numbers are valid for whatever shear rates may exist in the flow field. Nusselt numbers are reported as a function of a dimensionless shear rate parameter that establishes the region of the flow curve where the system is operating and are shown to be bound by the Newtonian and power law values. The conditions required for the system to perform at these asymptotic limits are quantified.

Research paper thumbnail of A Quasi-Steady-State Approximation to the Basic Target-Cell-Limited Viral Dynamics Model with a Non-Cytopathic Effect

Frontiers in Microbiology

Analysis of previously published target-cell limited viral dynamic models for pathogens such as H... more Analysis of previously published target-cell limited viral dynamic models for pathogens such as HIV, hepatitis, and influenza generally rely on standard techniques from dynamical systems theory or numerical simulation. We use a quasi-steady-state approximation to derive an analytic solution for the model with a non-cytopathic effect, that is, when the death rates of uninfected and infected cells are equal. The analytic solution provides time evolution values of all three compartments of uninfected cells, infected cells, and virus. Results are compared with numerical simulation using clinical data for equine infectious anemia virus, a retrovirus closely related to HIV, and the utility of the analytic solution is discussed.

Research paper thumbnail of Pattern formation properties of a system of interaction-diffusion equations relevant to a mussel-algae ecosystem in a quiescent marine layer

Research paper thumbnail of Ambiguity of the Negative Sign

Research paper thumbnail of Rhombic Analysis Extension of a Plant-Surface Water Interaction-Diffusion Model for Hexagonal Pattern Formation in an Arid Flat Environment

American Journal of Plant Sciences, 2015

An existing weakly nonlinear diffusive instability hexagonal planform analysis for an interaction... more An existing weakly nonlinear diffusive instability hexagonal planform analysis for an interactiondiffusion plant-surface water model system in an arid flat environment [11] is extended by performing a rhombic planform analysis as well. In addition a threshold-dependent paradigm that differs from the usually employed implicit zero-threshold methodology is introduced to interpret stable rhombic patterns. The results of that analysis are synthesized with those of the existing hexagonal planform analysis. In particular these synthesized results can be represented by closedform plots in the rate of precipitation versus the specific rate of plant density loss parameter space. From those plots, regions corresponding to bare ground and vegetative Turing patterns consisting of tiger bush (parallel stripes and labyrinthine mazes), pearled bush (hexagonal gaps and rhombic pseudo-gaps), and homogeneous distributions of vegetation, respectively, may be identified in this parameter space. Then that predicted sequence of stable states along a rainfall gradient is both compared with observational evidence and used to motivate an aridity classification scheme. Finally this system is shown to be isomorphic to the chemical reaction-diffusion Gray-Scott model and that isomorphism is employed to draw some conclusions about sideband instabilities as applied to vegetative patterning.

Research paper thumbnail of Vegetative Rhombic Pattern Formation Driven by Root Suction for an Interaction-Diffusion Plant-Ground Water Model System in an Arid Flat Environment

American Journal of Plant Sciences, 2015

A rhombic planform nonlinear cross-diffusive instability analysis is applied to a particular inte... more A rhombic planform nonlinear cross-diffusive instability analysis is applied to a particular interaction-diffusion plant-ground water model system in an arid flat environment. This model contains a plant root suction effect as a cross-diffusion term in the ground water equation. In addition a threshold-dependent paradigm that differs from the usually employed implicit zero-threshold methodology is introduced to interpret stable rhombic patterns. These patterns are driven by root suction since the plant equation does not yield the required positive feedback necessary for the generation of standard Turing-type self-diffusive instabilities. The results of that analysis can be represented by plots in a root suction coefficient versus rainfall rate dimensionless parameter space. From those plots regions corresponding to bare ground and vegetative patterns consisting of isolated patches, rhombic arrays of pseudo spots or gaps separated by an intermediate rectangular state, and homogeneous distributions from low to high density may be identified in this parameter space. Then, a morphological sequence of stable vegetative states is produced upon traversing an experimentally-determined root suction characteristic curve as a function of rainfall through these regions. Finally, that predicted sequence along a rainfall gradient is compared with observational evidence relevant to the occurrence of leopard bush, pearled bush, or labyrinthine tiger bush vegetative patterns, used to motivate an aridity classification scheme, and placed in the context of some recent biological nonlinear pattern formation studies.

Research paper thumbnail of Immune Control of Equine Infectious Anemia Virus Infection by Cell-Mediated and Humoral Responses

Applied Mathematics, 2013

Equine Infectious Anemia Virus (EIAV) is a retrovirus that establishes a persistent infection in ... more Equine Infectious Anemia Virus (EIAV) is a retrovirus that establishes a persistent infection in horses and ponies. The virus is in the same lentivirus subgroup that includes human immunodeficiency virus (HIV). The similarities between these two viruses make the study of the immune response to EIAV relevant to research on HIV. We developed a mathematical model of within-host EIAV infection dynamics that contains both humoral and cell-mediated immune responses. Analysis of the model yields results on thresholds that would be necessary for a combined immune response to successfully control infection. Numerical simulations are presented to illustrate the results. These findings have the potential to lead to immunological control measures for lentiviral infection.

Research paper thumbnail of Nonlinear stability analyses of Turing patterns for a mussel-algae model

Journal of Mathematical Biology, 2014

A particular interaction-diffusion mussel-algae model system for the development of spontaneous s... more A particular interaction-diffusion mussel-algae model system for the development of spontaneous stationary young mussel bed patterning on a homogeneous substrate covered by a quiescent marine layer containing algae as a food source is investigated employing weakly nonlinear diffusive instability analyses. The main results of these analyses can be represented by plots in the ratio of mussel motility to algae lateral diffusion versus the algae reservoir concentration dimensionless parameter space. Regions corresponding to bare sediment and mussel patterns consisting of rhombic or hexagonal arrays and isolated clusters of clumps or gaps, an intermediate labyrinthine state, and homogeneous distributions of low to high density may be identified in this parameter space. Then those Turing diffusive instability predictions are compared with both relevant field and laboratory experimental evidence and existing numerical simulations involving differential flow migrating band instabilities for the associated interaction-dispersion-advection mussel-algae model system as well as placed in the context of the results from some recent nonlinear pattern formation studies.

Research paper thumbnail of The negative sign and exponential expressions: Unveiling students’ persistent errors and misconceptions

The Journal of Mathematical Behavior, 2013

Additive and multiplicative inverse Additive and multiplicative identities a b s t r a c t

Research paper thumbnail of Component retention in principal component analysis with application to cDNA microarray data

Biology Direct, 2007

Shannon entropy is used to provide an estimate of the number of interpretable components in a pri... more Shannon entropy is used to provide an estimate of the number of interpretable components in a principal component analysis. In addition, several ad hoc stopping rules for dimension determination are reviewed and a modification of the broken stick model is presented. The modification incorporates a test for the presence of an "effective degeneracy" among the subspaces spanned by the eigenvectors of the correlation matrix of the data set then allocates the total variance among subspaces. A summary of the performance of the methods applied to both published microarray data sets and to simulated data is given.