Real-Time Interactive Simulation Of Large Bird Flocks: Toward Understanding Murmurations,
2022
Georgia Institute of Technology
Real-Time Interactive Simulation Of Large Bird Flocks: Toward Understanding Murmurations, Maxfield R. Comstock
Biology and Medicine Through Mathematics Conference
No abstract provided.
Dimension Theory Of Conformal Iterated Function Systems,
2022
University of Connecticut
Dimension Theory Of Conformal Iterated Function Systems, Sharon Sneha Spaulding
Honors Scholar Theses
This thesis is an expository investigation of the conformal iterated function system (CIFS) approach to fractals and their dimension theory. Conformal maps distort regions, subject to certain constraints, in a controlled way. Let $\mathcal{S} = (X, E, \{\phi_e\}_{e \in E})$ be an iterated function system where $X$ is a compact metric space, $E$ is a countable index set, and $\{\phi_e\}_{e \in E}$ is a family of injective and uniformly contracting maps. If the family of maps $\{\phi_e\}_{e \in E}$ is also conformal and satisfies the open set condition, then the distortion properties of conformal maps can be extended to the …
The Butterfly Effect Of Fractals,
2022
Murray State University
The Butterfly Effect Of Fractals, Cody Watkins
Honors College Theses
This thesis applies concepts in fractal geometry to the relatively new field of mathematics known as chaos theory, with emphasis on the underlying foundation of the field: the butterfly effect. We begin by reviewing concepts useful for an introduction to chaos theory by defining terms such as fractals, transformations, affine transformations, and contraction mappings, as well as proving and demonstrating the contraction mapping theorem. We also show that each fractal produced by the contraction mapping theorem is unique in its fractal dimension, another term we define. We then show and demonstrate iterated function systems and take a closer look at …
Finite Subdivision Rules For Matings Of Quadratic Thurston Maps With Few Postcritical Points,
2022
Bellarmine University
Finite Subdivision Rules For Matings Of Quadratic Thurston Maps With Few Postcritical Points, Jeremiah Zonio
Undergraduate Theses
A finite subdivision rule is set of instructions for repeatedly subdividing a partitioning of a given space. This turns out to be incredibly useful when attempting to describe a process known as polynomial mating. Polynomial mating is a way of gluing together two spaces which two polynomials may act upon such that the glued borders of each space respects the dynamics described by each polynomial. For matings of Misiurewicz polynomials, the spaces we are gluing together are 1-dimensional and are thus all border. This poses a conceptual difficulty which this paper attempts to resolve by using finite subdivison rules to …
Modeling And Analysis Of Fractional Tb Model With Atangana-Baleanu Derivative,
2022
Abdul Wali Khan University Mardan
Modeling And Analysis Of Fractional Tb Model With Atangana-Baleanu Derivative, Aatif Ali, Saeed Islam, Quaid Iqbal, Huma Gul, Muhammad Nafees
International Journal of Emerging Multidisciplinaries: Mathematics
In recent years Atangana and Baleanu proposed a new fractional derivative with non-singular and non-local kernel, this paper formulate a fragmentary request numerical TB model with AtanganaBaleanu derivative (AB derivative). We figured the basic reproduction number ( R0 ) and assessment of boundary dependent on genuine information of Khyber Pakhtunkhwa Pakistan, Initially we present the fundamental properties of the model, the existence and uniqueness of the model is proved using fixed point theory. At last, the model is tackled mathematically through Adams-Bashforth Moulton technique. The mathematical results for the extended model of the elements of Tuberculosis is shown graphically to …
An Integrated Computational Pipeline To Construct Patient-Specific Cancer Models,
2022
University of Kentucky
An Integrated Computational Pipeline To Construct Patient-Specific Cancer Models, Daniel Plaugher
Theses and Dissertations--Mathematics
Precision oncology largely involves tumor genomics to guide therapy protocols. Yet, it is well known that many commonly mutated genes cannot be easily targeted. Even when genes can be targeted, resistance to therapy is quite common. A rising field with promising results is that of mathematical biology, where in silico models are often used for the discovery of general principles and novel hypotheses that can guide the development of new treatments. A major goal is that eventually in silico models will accurately predict clinically relevant endpoints and find optimal control interventions to stop (or reverse) disease progression. Thus, it is …
Energy As A Limiting Factor In Neuronal Seizure Control: A Mathematical Model,
2022
Claremont McKenna College
Energy As A Limiting Factor In Neuronal Seizure Control: A Mathematical Model, Sophia E. Epstein
CMC Senior Theses
The majority of seizures are self-limiting. Within a few minutes, the observed neuronal synchrony and deviant dynamics of a tonic-clonic or generalized seizure often terminate. However, a small epilesia partialis continua can occur for years. The mechanisms that regulate subcortical activity of neuronal firing and seizure control are poorly understood. Published studies, however, through PET scans, ketogenic treatments, and in vivo mouse experiments, observe hypermetabolism followed by metabolic suppression. These observations indicate that energy can play a key role in mediating seizure dynamics. In this research, I seek to explore this hypothesis and propose a mathematical framework to model how …
Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing,
2022
Virginia Commonwealth University
Role Of Inhibition And Spiking Variability In Ortho- And Retronasal Olfactory Processing, Michelle F. Craft
Theses and Dissertations
Odor perception is the impetus for important animal behaviors, most pertinently for feeding, but also for mating and communication. There are two predominate modes of odor processing: odors pass through the front of nose (ortho) while inhaling and sniffing, or through the rear (retro) during exhalation and while eating and drinking. Despite the importance of olfaction for an animal’s well-being and specifically that ortho and retro naturally occur, it is unknown whether the modality (ortho versus retro) is transmitted to cortical brain regions, which could significantly instruct how odors are processed. Prior imaging studies show different …
The Kepler Problem On Complex And Pseudo-Riemannian Manifolds,
2022
Wilfrid Laurier University
The Kepler Problem On Complex And Pseudo-Riemannian Manifolds, Michael R. Astwood
Theses and Dissertations (Comprehensive)
The motion of objects in the sky has captured the attention of scientists and mathematicians since classical times. The problem of determining their motion has been dubbed the Kepler problem, and has since been generalized into an abstract problem of dynamical systems. In particular, the question of whether a classical system produces closed and bounded orbits is of importance even to modern mathematical physics, since these systems can often be analysed by hand. The aforementioned question was originally studied by Bertrand in the context of celestial mechanics, and is therefore referred to as the Bertrand problem. We investigate the qualitative …
Exo-Sir: An Epidemiological Model To Analyze The Impact Of Exogenous Spread Of Infection,
2022
LNMIIT, India
Exo-Sir: An Epidemiological Model To Analyze The Impact Of Exogenous Spread Of Infection, Nirmal Kumar Sivaraman, Manas Gaur, Shivansh Baijal, Sakthi Balan Muthiah, Amit Sheth
Publications
Epidemics like Covid-19 and Ebola have impacted people's lives significantly. The impact of mobility of people across the countries or states in the spread of epidemics has been significant. The spread of disease due to factors local to the population under consideration is termed the endogenous spread. The spread due to external factors like migration, mobility, etc. is called the exogenous spread. In this paper, we introduce the Exo-SIR model, an extension of the popular SIR model and a few variants of the model. The novelty in our model is that it captures both the exogenous and endogenous spread of …
Measure-Theoretically Mixing Subshifts With Low Complexity,
2022
US Naval Academy, Annapolis
Measure-Theoretically Mixing Subshifts With Low Complexity, Darren Creutz, Ronnie Pavlov, Shaun Rodock
Mathematics: Faculty Scholarship
We introduce a class of rank-one transformations, which we call extremely elevated staircase transformations. We prove that they are measure-theoretically mixing and, for any f : N → N with f (n)/n increasing and ∑ 1/f (n) < ∞, that there exists an extremely elevated staircase with word complexity p(n) = o(f (n)). This improves the previously lowest known complexity for mixing subshifts, resolving a conjecture of Ferenczi.
Local Finiteness And Automorphism Groups Of Low Complexity Subshifts,
2022
University of Denver
Local Finiteness And Automorphism Groups Of Low Complexity Subshifts, Ronnie Pavlov, Scott Schmieding
Mathematics: Faculty Scholarship
We prove that for any transitive subshift X with word complexity function cn(X), if lim inf(log(cn(X)/n)/(log log log n)) = 0, then the quotient group Aut(X, σ)/〈 σ〉 of the automorphism group of X by the subgroup generated by the shift σ is locally finite. We prove that significantly weaker upper bounds on cn(X) imply the same conclusion if the gap conjecture from geometric group theory is true. Our proofs rely on a general upper bound for the number of automorphisms of X of range n in terms of word complexity, which may be …
Structure-Dependent Characterizations Of Multistationarity In Mass-Action Reaction Networks,
2022
West Virginia University
Structure-Dependent Characterizations Of Multistationarity In Mass-Action Reaction Networks, Galyna Voitiuk
Graduate Theses, Dissertations, and Problem Reports
This project explores a topic in Chemical Reaction Network Theory. We analyze networks with one dimensional stoichiometric subspace using mass-action kinetics. For these types of networks, we study how the capacity for multiple positive equilibria and multiple positive nondegenerate equilibria can be determined using Euclidian embedded graphs. Our work adds to the catalog of the class of reaction networks with one-dimensional stoichiometric subspace answering in the affirmative a conjecture posed by Joshi and Shiu: Conjecture 0.1 (Question 6.1 [26]). A reaction network with one-dimensional stoichiometric subspace and more than one source complex has the capacity for multistationarity if and only …
Dynamics Of Mutualism In A Two Prey, One Predator System With Variable Carrying Capacity,
2022
University of North Florida
Dynamics Of Mutualism In A Two Prey, One Predator System With Variable Carrying Capacity, Randy Huy Lee
UNF Graduate Theses and Dissertations
We considered the livelihood of two prey species in the presence of a predator species. To understand this phenomenon, we developed and analyzed two mathematical models considering indirect and direct mutualism of two prey species and the influence of one predator species. Both types of mutualism are represented by an increase in the preys' carrying capacities based on direct and indirect interactions between the prey. Because of mutualism, as the death rate parameter of the predator species goes through some critical value, the model shows transcritical bifurcation. Additionally, in the direct mutualism model, as the death rate parameter decreases to …
Reduced-Order Dynamic Modeling And Robust Nonlinear Control Of Fluid Flow Velocity Fields,
2021
Embry-Riddle Aeronautical University
Reduced-Order Dynamic Modeling And Robust Nonlinear Control Of Fluid Flow Velocity Fields, Anu Kossery Jayaprakash, William Mackunis, Vladimir Golubev, Oksana Stalnov
Publications
A robust nonlinear control method is developed for fluid flow velocity tracking, which formally addresses the inherent challenges in practical implementation of closed-loop active flow control systems. A key challenge being addressed here is flow control design to compensate for model parameter variations that can arise from actuator perturbations. The control design is based on a detailed reduced-order model of the actuated flow dynamics, which is rigorously derived to incorporate the inherent time-varying uncertainty in the both the model parameters and the actuator dynamics. To the best of the authors’ knowledge, this is the first robust nonlinear closed-loop active flow …
A Connectivity Framework To Explore The Role Of Anthropogenic Activity And Climate On The Propagation Of Water And Sediment At The Catchment Scale,
2021
University of Tennessee, Knoxville
A Connectivity Framework To Explore The Role Of Anthropogenic Activity And Climate On The Propagation Of Water And Sediment At The Catchment Scale, Christos Giannopoulos
Doctoral Dissertations
Anthropogenic disturbance in intensively managed landscapes (IMLs) has dramatically altered critical zone processes, resulting in fundamental changes in material fluxes. Mitigating the negative effects of anthropogenic disturbance and making informed decisions for optimal placement and assessment of best management practices (BMPs) requires fundamental understanding of how different practices affect the connectivity or lack thereof of governing transport processes and resulting material fluxes across different landscape compartments within the hillslope-channel continuum of IMLs. However, there are no models operating at the event timescale that can accurately predict material flux transport from the hillslope to the catchment scale capturing the spatial and …
An Integral Projection Model For Gizzard Shad That Includes Density-Dependent Age-0 Survival,
2021
University of Wisconsin - La Crosse
An Integral Projection Model For Gizzard Shad That Includes Density-Dependent Age-0 Survival, James Peirce, Greg Sandland
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Biocontrol Of The Emerald Ash Borer: An Adapted Nicholson-Bailey Model,
2021
University of Richmond
Biocontrol Of The Emerald Ash Borer: An Adapted Nicholson-Bailey Model, Michael Kerckhove, Shuheng Chen
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Model Describing The Behavior Of Biomass, Acidity, And Viscosity As A Function Of Temperature In The Shelf Life Of Yogurt,
2021
Durango Institute of Technology, México
Mathematical Model Describing The Behavior Of Biomass, Acidity, And Viscosity As A Function Of Temperature In The Shelf Life Of Yogurt, Manuel Alvarado, Paul A. Valle, Yolocuauhtli Salazar
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments,
2021
Jarvis Christian College
Mathematical Modeling Of Breast Cancer Cell Mcf-7 Growths Due To Curcumin Treatments, Widodo Samyono, Hildana Assefa, Kana Kassa
Annual Symposium on Biomathematics and Ecology Education and Research
No abstract provided.
