Master of Sciences, Case Western Reserve University, 2013, Applied Mathematics

Dynamical systems with discontinuous right-hand sides are utilized to great effect in mathematical biology (Coombes 2008, Glass and Kauffman 1973, McKean 1970), including models of central pattern generators (CPGs) involved in motor control (Spardy et al. 2011, Shaw et al. 2012). CPG models typically exhibit limit cycle dynamics; the infinitesimal phase response curve (iPRC) quantifies sensitivity of such models to external inputs (Ermentrout and Terman 2010). Piecewise smooth dynamical systems may have discontinuous iPRCs. In this thesis, we formulate the boundary conditions necessary for obtaining the iPRC for general piecewise smooth dynamical systems by solving an adjoint equation, thereby improving upon two known methods used to solve for the iPRC in the context of piecewise linear dynamical systems.

Committee: Peter Thomas PhD (Committee Chair); Hillel Chiel PhD (Committee Co-Chair); Alethea Barbaro PhD (Committee Member); Michael Hurley PhD (Committee Member) Subjects: Applied Mathematics; Biomechanics; Mathematics; Neurosciences

Doctor of Philosophy, The Ohio State University, 2021, Physics

Reservoir computing (RC) is a machine learning method especially well suited to solving physical problems, by using an internal dynamic system known as a 'reservoir'. Many systems are suitable for use as an internal reservoir. A common choice is an echo state network (ESN), a network with recurrent connections that gives the RC a memory which it uses to efficiently solve many time-domain problems such as forecasting chaotic systems and hidden state inference. However, constructing an ESN involves a large number of poorly- understood meta-parameters, and the properties that an ESN must have to solve these tasks well are largely unknown. In this dissertation, I explore what parts of an RC are absolutely necessary. I build ESNs that perform well at system forecasting despite an extremely simple internal network structure, without any recurrent connections at all, breaking one of the most common rules of ESN design. These simple reservoirs indicate that the role of the reservoir in the RC is only to remember a finite number of time-delays of the RCs input, and while a complicated network can achieve this, in many cases a simple one achieves this as well. I then build upon a recent proof of the equivalence between a specific ESN construction and the nonlinear vector auto-regression (NVAR) method with my collaborators. The NVAR is an RC boiled down to its most essential components, taking the necessary time- delay taps directly rather than relying on an internal dynamic reservoir. I demonstrate these RCs-without-reservoirs on a variety of classical RC problems, showing that in many cases an NVAR will perform as well or better than an RC despite the simpler method. I then conclude with an example problem that highlights a remaining unsolved issue in the application of NVARs, and then look to a possible future where NVARs may supplant RCs.

Committee: Daniel Gauthier (Advisor); Amy Connolly (Committee Member); Ciriyam Jayaprakash (Committee Member); Gregory Lafyatis (Committee Member) Subjects: Physics

MA, Kent State University, 2010, College of Arts and Sciences / Department of Philosophy

Recent advances in our understanding of complex dynamical systems may be of interest to philosophers seeking the best metaphysical grounds for understanding the qualitative character of subjective experience (qualia). In this thesis I will propose that qualia are not specifically brain processes, but are instead best thought of as world processes that can be characterized as distributed self-organizing networks of Whiteheadian actual entities. On this Whiteheadian model, different aspects of a quale that a subject experiences as a specific shade of blue, might be contributed by entities that are, contemporaneously, also contributing other aspects of other qualia to other subjects widely distributed throughout time and space. Cellular automata and network models will be used to help clarify this proposal.

Committee: David Odell-Scott PhD (Advisor); Kwang-Sae Lee PhD (Committee Member); Frank Ryan PhD (Committee Member); Mark Bracher PhD (Committee Member); Michael Byron PhD (Other) Subjects: Philosophy

BA, Oberlin College, 2013, Mathematics

The geological and paleomagnetic record indicate that around 750 million and 580 millions years ago glaciers grew near the equator, though as of yet we do not fully understand the nature of these glaciations. The well-known Snowball Earth Hypothesis states that the Earth was covered entirely by glaciers. However, it is hard for this hypothesis to account for certain aspects of the biological evidence such as the survival of photosynthetic eukaryotes. Thus the Jormungand Hypothesis was developed as an alternative to the Snowball Earth Hypothesis. In this paper we investigate previous models of the Jormungand state and look at the dynamics of the Hadley cells to develop a new model to represent the Jormungand Hypothesis. We end by solving for an analytical approximation to the model using a finite Legendre expansion and geometric singular perturbation theory. The resultant model gives a stable equilibrium point near the equator with strong hysteresis that satisfies the Jormungand Hypothesis.

Committee: Jim Walsh (Advisor) Subjects: Climate Change; Mathematics

Doctor of Philosophy, Case Western Reserve University, 2024, Applied Mathematics

Physiological systems underlying vital behaviors, such as breathing, walking, and feeding, are controlled by closed-loop systems integrating central neural circuitry, biomechanics, and sensory feedback. The brain and body orchestration allows these motor systems to demonstrate crucial biological phenomena such as homeostasis, adaptability, and robustness. In this thesis, we investigate the role of sensory feedback in motor dynamics and control, based on an abstract model for motor pattern generation that combines central pattern generator (CPG) dynamics with a sensory feedback mechanism. Given the underdevelopment of control theory for limit cycle systems, we extend recently developed variational tools, which allow us to characterize the sensitivity of the systems to perturbations and changing conditions both within and outside the body. As concrete examples, we apply our methods to several closed-loop models with sensory feedback in place, including locomotion, ingestion, and respiration. Our analytic framework provides a mathematically grounded numerical quantification of the effects of a sustained perturbation on the rhythm performance and robustness, which is also broad enough to study control of oscillations in any nonlinear dynamical systems. Moreover, the observations we obtain from the examples provide important information for future work modeling neuro-motor rhythm generation and insights that have the potential to inform the design of control or rehabilitation systems.

Committee: Peter Thomas (Advisor); David Gurarie (Committee Member); Erkki Somersalo (Committee Member); Hillel Chiel (Committee Member) Subjects: Applied Mathematics; Behavioral Sciences; Biology; Engineering; Mathematics; Neurosciences; Physiology

Doctor of Philosophy, The Ohio State University, 2022, Physics

The success of modern digital electronics relies on compartmentalizing logical functions into individual gates, and controlling their order of operations via a global clock. In the absence of such a timekeeping mechanism, systems of connected logic gates can quickly become chaotic and unpredictable -- exhibiting analog, asynchronous, autonomous dynamics. Such recurrent circuitry behaves in a manner more consistent with neural networks than digital computers, exchanging and conducting electricity as quickly as its hardware allows. These physics enable new forms of information processing that are faster and more complex than clocked digital circuitry. However, modern electronic design tools often fail to measure or predict the properties of large recurrent networks, and their presence can disrupt other clocked architectures. In this thesis, I study and apply the physics of complex networks of self-interacting logic gates at sub-ns timescales. At a high level, my unique contributions are: 1. I derive a general theory of network dynamics and develop open-source simulation libraries and experimental circuit designs to re-create this work; 2. I invent a best-in-class digital measurement system to experimentally analyze signals at the trillionth-of-a-second (ps) timescale; 3. I introduce a network computing architecture based on chaotic fractal dynamics, creating the first `physically unclonable function' with near-infinite entropy. In practice, I use a digital computer to reconfigure a tabletop electronic device containing millions of logic gates (a field-programmable gate array; FPGA) into a network of Boolean functions (a hybrid Boolean network; HBN). From within the FPGA, I release the HBN from initial conditions and measure the resulting state of the network over time. These data are transferred to an external computer and used to study the system experimentally and via a mathematical model. Existing mathematical theories and FPGA simulation tools produce in (open full item for complete abstract)

Committee: Daniel Gauthier (Advisor); Emre Koksal (Committee Member); Gregory Lafyatis (Committee Member); Antonio Boveia (Committee Member) Subjects: Applied Mathematics; Computer Engineering; Computer Science; Condensed Matter Physics; Electrical Engineering; Electromagnetics; Electromagnetism; Engineering; Experiments; High Temperature Physics; Information Science; Information Systems; Information Technology; Low Temperature Physics; Materials Science; Mathematics; Medical Imaging; Nanotechnology; Particle Physics; Physics; Quantum Physics; Scientific Imaging; Solid State Physics; Systems Design; Technology; Theoretical Physics

Doctor of Education, University of Toledo, 2022, Curriculum and Instruction

This exploratory Q methodological study uses Complex-Dynamical Systems (CDS) theory to frame pre-service teacher (PST) role identity development. There is a twofold purpose: to contribute to the emerging CDS literature by examining CDS structures and processes; and, to assess the suitability of Q methodology to study and facilitate PST development. For this single case study, a novel Q sort was developed using the Dynamic Systems Model of Role Identity (DSMRI), which also guided post-facto data interpretation. Using Cultural-Historical Activity Theory (CHAT) to operationalize complex-dynamical systems in educational spaces, the study revealed contradictions, tensions, and harmonies PSTs experience and are expected to negotiate, as well as multiple dimensions of role identity that influence one's professional role identity development. Qualitative and quantitative data from Mike's story highlight the dangers of the gaps between theory and practice that continue to plague teacher education and educational research. The study concludes that Q methodology is uniquely adept at exploratory studies of identity, and potential harmonies between Q methodology and CDS research has exciting implications for future research and practice.

Committee: Mark Templin (Committee Chair); Dale Snauwaert (Committee Member); Revathy Kumar (Committee Member); Leigh Chiarelott (Committee Member) Subjects: Teacher Education

Master of Sciences, Case Western Reserve University, 2020, Applied Mathematics

An animal's survival depends on its ability to adapt to a constantly shifting environment. Mathematical models of rhythmic motor patterns typically incorporate a central pattern generator (CPG) circuit, driving motor output in the body. In this thesis, we study Shaw and Lyttle's model for the feeding system of the marine mollusk Aplysia californica, which eats seaweed. The CPG has a heteroclinic channel architecture with three metastable fixed points. Using mean rate of seaweed ingestion as an objective function, we studied the system's sensitivity to parameters representing (i) the force with which seaweed opposes swallowing, and (ii) threshold and weighting parameters controlling when the feeding apparatus (grasper) opens or closes on the seaweed. We found eight motor "strategies," corresponding to whether the grasper was open or closed near each of the CPG's fixed points. In addition, we studied how rhythmic movements break down when challenged by excessively large resisting forces.

Committee: Peter Thomas (Advisor); Hillel Chiel (Committee Member); Wanda Strychalski (Committee Member); Somersalo Erkki (Committee Member) Subjects: Applied Mathematics

Doctor of Philosophy, The Ohio State University, 2019, Electrical and Computer Engineering

This research presents a novel framework for generating system equations from the input-output data of unknown discrete dynamical systems. The two-step process consists of system identification followed by a black box input-output analysis in the likes of Monte Carlo sample-based global sensitivity analysis. System identification is performed using temporal convolutional networks trained with only input-output data. A structured approach to network design and training is detailed for yielding accurate identification models and a benchmark is performed using a publicly available dataset known as the Silverbox. The trained identification model serves as a system emulator that can be excited at low computational cost, allowing for detailed sample-based sensitivity analysis. The key to the analysis is an imagined decomposition of the the model into a sum of less complex constituent functions of all input combinations. A method for sampling the constituent functions is presented to not only determine relevant constituents, but to estimate them as well. The sum of relevant constituent functions is equal to the original model, which parallels the source system of the original input-output data. The imagined decomposition of the identification model allows for a potentially complex estimation problem to be broken down into many smaller and less complex problems. The analysis resultant is a human comprehensible mathematical model for the discrete dynamical system, where comprehensibility implies that the equation gives insight into system operation. The presented framework helps to shed light on black box identification models, and the system equation extracted from the identification model can be used as a transparent replacement for the original model. This aids in a myriad of practical applications such as control, stability analysis, and software verification. The framework is fully implemented and made publicly available. A number of synthetic examples are presented (open full item for complete abstract)

Committee: Ümit Özgüner (Advisor); Keith Redmill (Advisor); Yingbin Liang (Committee Member) Subjects: Computer Engineering; Computer Science; Electrical Engineering

Doctor of Philosophy, The Ohio State University, 2019, Physics

There is currently great interest in applying artificial neural networks to a host of commercial and industrial tasks. Such networks with a layered, feedforward structure are currently deployed in technologies ranging from facial recognition software to self-driving cars. They are favored by a large portion of machine learning experts for a number of reasons. Namely: they possess a documented ability to generalize to unseen data and handle large data sets; there exists a number of well-understood training algorithms and integrated software packages for implementing them; and they have rigorously proven expressive power making them capable of approximating any bounded, static map arbitrarily well. Within the last couple of decades, reservoir computing has emerged as a method for training a different type of artificial neural network known as a recurrent neural network. Unlike layered, feedforward neural networks, recurrent neural networks are non-trivial dynamical systems that exhibit time-dependence and dynamical memory. In addition to being more biologically plausible, they more naturally handle time-dependent tasks such as predicting the load on an electrical grid or efficiently controlling a complicated industrial process. Fully-trained recurrent neural networks have high expressive power and are capable of emulating broad classes of dynamical systems. However, despite many recent insights, reservoir computing remains relatively young as a field. It remains unclear what fundamental properties yield a well-performing reservoir computer. In practice, this results in their design being left to domain experts, despite the actual training process being remarkably simple to implement. In this thesis, I describe a number of numerical and experimental results that expand the understanding and application of reservoir computing techniques. I develop an algorithm for controlling unknown dynamical systems with layers of reservoir computers. I demonstrate this algori (open full item for complete abstract)

Committee: Daniel Gauthier (Advisor); Gregory Lafyatis (Committee Member); Dick Furnstahl (Committee Member); Mikhail Belkin (Committee Member); Christopher Zirkle (Committee Member) Subjects: Physics

Doctor of Philosophy (PhD), Ohio University, 2018, Mathematics (Arts and Sciences)

Dynamical systems as models of complex biological systems are powerful tools that have been used to study problems in biology. This dissertation first discusses a problem in the theory of dynamical systems on the definition of topological entropy. Then dynamical systems are applied in two different fields of biology: proliferation of monolayer epithelia and the spread of infections and information. The notion of topological entropy is a measure of the complexity of a dynamical system. It can be conceptualized in terms of the number of forward trajectories that are distinguishable at resolution ε within T time units. It can then be formally defined as a limit of a limit superior that involves either covering numbers, or separation numbers, or spanning numbers. If covering numbers are used, the limit superior reduces to a limit. While it has been generally believed that the latter may not necessarily be the case when the definition is based on separation or spanning numbers, no actual counterexamples appear to have been previously known. Here we fill this gap in the literature by constructing such counterexamples. We then use dynamical systems to study the proliferation of epithelia. Epithelia are sheets of tightly adherent cells that line both internal and external surfaces in metazoans (multicellular animals). Mathematically, a cell in an epithelial tissue can be modeled as a k-sided polygon. Empirically studied distributions of the proportions of k-sided cells in epithelia show remarkable similarities in a wide range of evolutionarily distant organisms. Multiple types of mathematical models have been proposed to explain this phenomenon. Among the most parsimonious of such models are topological ones that take into account only the number of sides of a given cell and the neighborhood relation between cells. The model studied here is a refinement of a previously published such model (Patel et al., PLoS Comput. Biol., 2009). While using the same modeling framew (open full item for complete abstract)

Committee: Winfried Just (Advisor); Todd Young (Committee Member); Martin Mohlenkamp (Committee Member); Alexander Neiman (Committee Member) Subjects: Applied Mathematics; Mathematics

Doctor of Philosophy, Case Western Reserve University, 2017, EMC - Mechanical Engineering

The objective of this research is to advance the state of predictive science by integrating physics-based stochastic modeling methods with data analytic techniques to improve the accuracy and reliability of probabilistic prediction of event occurrence in dynamical systems, such as manufacturing machines or processes. To accomplish the above described objective, a hybrid modeling method is developed in this research, which integrates physical models for system performance degradation with stochastic modeling (realized by Bayesian inference) and data analytics (e.g. deep learning), to enable non-linear and non-Gaussian system modeling. The research addresses four fundamental questions : 1) how to quantify the accuracy and confidence in system tracking and performance variation prediction, given the limited observability; 2) how to incorporate uncertainty arising from varying operating conditions and environmental disturbance into prognostic models, 3) how to effectively fuse different data analytic techniques into one prognostic model, in order to take advantage of the strength of each of the techniques; and 4) how to improve the computational efficiency of the modeling and prediction process by leveraging emerging infrastructure enabled by cloud computing, for on-line, real-time, and remote prognosis. Specific research tasks include: 1) deriving system health indicators as a function of operating conditions measured by sensors through machine learning techniques (e.g. deep leaning); 2) developing stochastic models of system degradation based on multi-mode particle filter with adaptive resampling capability, to track variations in health indicators for prediction of performance deterioration with time-varying degradation rates and/or modes; 3) developing an optimization method to detect transient changes in health indicators due to abrupt fault occurrence; and 4) improving computational efficiency of particle filtering by modifying the sampling and resampling (open full item for complete abstract)

Committee: Robert Gao (Advisor); Roger Quinn (Committee Member); Bo Li (Committee Member); Wojbor Woyczynski (Committee Member) Subjects: Mechanical Engineering

PhD, University of Cincinnati, 2016, Arts and Sciences: Psychology

Recent work investigating the dynamics of coupled physical systems with uni-directional slave-master coupling dynamics has demonstrated that the incorporation of delayed feedback within the slave system allows it to achieve anticipation of chaotic master system behavior. This counterintuitive phenomenon of self-organized anticipatory synchronization has been observed for a variety of systems including coupled electrical circuits, laser semi-conductors, and neurons. Most recently research has shown that human individuals are capable of exhibiting the same kind of aperiodic anticipation in the context of interpersonal interaction following the introduction of perceptual-motor feedback delays. Understanding such human behavior as defined by the same universal dynamical laws as other physical systems provides a more parsimonious explanation for how humans are able to maintain complex coordination given the existence of inherent neural and perceptual-motor delays than previously proposed accounts, which depend on the existence of internal models and neural simulation processes. This perspective also provides a novel opportunity to inform the advancement of human robotic interaction; through an in-depth understanding of anticipatory synchronization in humans and other physical systems it should be possible to develop adaptive artificial agents defined by systems of low-dimensional dynamical equations capable of coordinating with complex human behavior in real time. The goal of the current project was to gain further information about human anticipatory synchronization in order to facilitate the design, development and testing of an artificial agent intended to exhibit self-organized anticipation during interaction with a human co-actor. In each of three initial studies, a participant was asked to coordinate with the continuous arm movements of a robot avatar seen via a virtual reality headset. The participant's own virtual arm movements reflected the behavioral outcomes o (open full item for complete abstract)

Committee: Michael Richardson Ph.D. (Committee Chair); Rachel Kallen Ph.D. (Committee Member); Kevin Shockley Ph.D. (Committee Member) Subjects: Psychology

PhD, University of Cincinnati, 2016, Arts and Sciences: Mathematical Sciences

A circadian rhythm is a fundamental biological process observed in many organisms. Circadian oscillations play a vital role in maintaining the daily activities of approximately 24 hours. Dysfunctions of this process can be dangerous to an organism, and even life threatening. In this research, analysis is performed on mathematical models of the circadian clock in order to reveal unknown features of the clock, in particular, its response to external stimuli. Both simulations and experiments are performed for cross-validation using the model organism, Neurospora crassa. A novel approach of this project is the use of the phase response curve to identify chemical reactions responding to external inputs such as light administration. The results found in this study may provide useful information for potential treatments for circadian related diseases such as sleep disorders.

Committee: Sookkyung Lim Ph.D. (Committee Chair); Donald French Ph.D. (Committee Member); Christian Hong Ph.D. (Committee Member); Benjamin Vaughan Ph.D. (Committee Member) Subjects: Mathematics

PhD, University of Cincinnati, 2015, Arts and Sciences: Psychology

Healthy development leads to a fluid integration of competing constraints. A marker of such fluid behavior is hysteresis, reflecting a multi-stable system that takes into account its immediate history. The current study investigates patterns of hysteresis in typically developing children and those diagnosed with autism spectrum disorder (ASD). The task was to grasp and lift an object. I manipulated the social context of the task, given that ASD is characterized by abnormal development in social domains. Results of the grasping task were also compared to a standardized clinical measure of mental flexibility: a computerized version of the Wisconsin Card Sorting Test, due to evidence that children with ASD have a tendency to demonstrate perseveration and rigid thought patterns. For the grasping task, a series of differently sized objects were designed that they could be picked up with one hand or two, marking a range of bi-stable behavior. Results of the grasping task show hysteresis in typically developing children, whether or not the task was situated in the social context. Analyses indicated a similar pattern for the children with ASD. However, there was a suggestive trend in the data that they may not have demonstrated hysteresis in the social context. For both diagnostic groups, perseveration on the Wisconsin Card Sorting Test did not correlate to the degree of hysteresis, regardless of the presence or absence of social cues. Results provide support to the idea that the analysis of behavior dynamics provides a unique window into typical and atypical development.

Committee: Adelheid Kloos Ph.D. (Committee Chair); Michael Richardson Ph.D. (Committee Member); Paula Shear Ph.D. (Committee Member) Subjects: Clinical Psychology

Doctor of Philosophy (PhD), Ohio University, 2015, Mathematics (Arts and Sciences)

This thesis is devoted to using the techniques of dynamical systems to studying clustering in the cell division cycle of yeast through the medium of a feedback model in which cells in one part of the cell division cycle influence the rate of cells in a different part of the cell division cycle. In Chapter 1, we introduce the model and see that it causes clustering under both positive and negative feedback. In Chapter 2 we pass to a clustered submanifold. We factorize a Poincare map and use this factorization to prove that asymptotically stable cyclic solutions exist under negative feedback. We partition parameter space in a way that allows us to quickly investigate stability of solutions under a wide range of parameter values. In Chapter 3 we prove many of the observations of Chapter 2, in particular that positive feedback gives rise to unstable solutions. We also prove that asymptotic stability in the clustered submanifold implies asymptotic stability in the full phase space. In Chapter 4, we contrast the effect of adding biologically motivated bounded noise against the effect of zero-mean Gaussian white noise, and see that the various noise models act essentially similarly under a variety of metrics. In Chapter 5, we consider a modification of the system wherein certain previously disjoint intervals are allowed to overlap. We observe that in the clustered subspace, the dynamics of this system are similar to those of the original system. However, we observe complicated behavior in the full phase space, where solutions that are asymptotically stable in the clustered space are merely stable, or even unstable, in the full phase space.

Committee: Todd Young Ph.D. (Advisor); Winfried Just Ph.D. (Committee Member); Alexander Neiman Ph.D. (Committee Member); Sergiu Aizicovici Ph.D. (Committee Member) Subjects: Applied Mathematics; Cellular Biology; Mathematics

BA, Oberlin College, 2015, Mathematics

We study a family of discrete-time recurrent neural network models in which the synaptic connectivity changes slowly with respect to the neuronal dynamics. The fast (neuronal) dynamics of these models display a wealth of behaviors ranging from simple convergence and oscillation to chaos, and the addition of slow (synaptic) dynamics which mimic the biological mechanisms of learning and memory induces complex multiscale dynamics which render rigorous analysis quite difficult. Nevertheless, we prove a general result on the interplay of these two dynamical timescales, demarcating a regime of parameter space within which a gradual dampening of chaotic neuronal behavior is induced by a broad class of learning rules.

Committee: Jim Walsh (Advisor) Subjects: Mathematics; Neurosciences

PhD, University of Cincinnati, 2015, Arts and Sciences: Philosophy

Mechanistic frameworks of investigation and explanation dominate the cognitive, neural, and psychological sciences. In this dissertation, I argue that mechanistic frameworks cannot, in principle, explain some kinds of cognition. In its place, I argue that complexity science has methods and theories more appropriate for investigating and explaining some cognitive phenomena. I begin with an examination of the term `cognition.' I defend the idea that “cognition” has been a moving target of investigation in the relevant sciences. As such it is not historically true that there has been a thoroughly entrenched and agreed upon conception of “cognition.” Next, I take up mechanistic frameworks. Although `mechanism' is an umbrella term for a set of loosely related characteristics, there are common features: linearity, localization, and component dominance. I then describe complexity science, with emphasis on its utilization of dynamical systems modeling. Next, I discuss two phenomena that typically fall under the purview of complexity science: nonlinearity and interaction dominance. A complexity science framework guided by the theory of self-organized criticality and utilizing the methods of dynamical systems modeling can surmount a number of challenges that face mechanistic frameworks when investigating some kinds of cognition. The first challenge is epistemic and concerns the inadequacy of mechanistic frameworks to facilitate the comprehensibility of massive amounts of data across various scales and areas of inquiry. I argue that complexity science is more appropriate for making big data comprehensible when investigating cognition, particularly across disciplines. I demonstrate this via an approach called nested dynamical modeling (NDM). NDM can facilitate comprehensibility of large amounts of data obtained from various scales of investigation by eliminating irrelevant degrees of freedom of that system as relates to the target of investigation. The second shortcomi (open full item for complete abstract)

Committee: Anthony Chemero Ph.D. (Committee Chair); Rick Dale Ph.D. (Committee Member); Valerie Hardcastle Ph.D. (Committee Member); Robert Richardson Ph.D. (Committee Member) Subjects: Philosophy

MA, University of Cincinnati, 2014, Arts and Sciences: Psychology

Many of our daily behaviors provide evidence that people are capable of coordinating in an effortless manner, even when faced with highly variable, often unpredictable behavioral events. While a substantial amount of research on joint-action has focused on the coordination that occurs between simple stereotyped or periodic movements, a larger proportion of everyday social and interpersonal interaction requires that individuals coordinate complex, aperiodic actions. In fact, many of the actions performed by individuals in an interactive context likely exhibit characteristics synonymous with chaos (i.e., are unpredictable yet deterministic). Although counterintuitive, recent research in physics and human movement science indicates that small temporal feedback delays may actually enhance an individual's ability to synchronize with chaotic environmental events. The current study was designed to determine whether a similar phenomenon might be at work in the interpersonal coordination of aperiodic behaviors and, if so, to examine the underlying anticipatory processes. In order to evaluate the effect of small perceptual feedback delays on aperiodic interpersonal coordination, three experiments were conducted. Since the phenomenon of anticipatory synchronization had only previously been observed for a single actor coordinating with a computer-generated chaotic stimulus, these experiments were performed in a progressive manner, transitioning from an actor-environment context to an interpersonal, bi-directionally coupled context involving two co-actors. In each experiment, a participant was asked to coordinate their arm movements with another continuous movement sequence displayed to them as a moving dot on a large HD monitor. Perceptual feedback was available to participants via the display of their own movements as a different colored dot. This dot either reflected the behavioral outcomes of a participant's actions in real time, or at one of three short (open full item for complete abstract)

Committee: Michael Richardson Ph.D. (Committee Chair); Rachel Kallen Ph.D. (Committee Member); Kevin Shockley Ph.D. (Committee Member) Subjects: Psychology

Doctor of Philosophy (PhD), Ohio University, 2014, Mathematics (Arts and Sciences)

Mathematical models are used to study two biological systems: pulmonary innate immunity and autonomous oscillation in yeast. In order to better understand the dynamics of an early infection of the lungs, we construct a predator-prey ODE model of pulmonary innate immunity which describes several observed properties of the pulmonary innate immune system. Under reasonable biological assumptions, the model predicts a single nontrivial equilibrium point with a stable and unstable manifold. Trajectories to one side of the stable manifold are asymptotic to the disease-free equilibrium and on the other side are unbounded in the size of the infection. The model also reproduces a phenomenon observed by Ben-David et al whereby the innate response to an infectious challenge reduces the ability of further infections to take hold. The model may be useful in analyzing and understanding time series data obtained by new methods in pathogen detection in ventilated patients. We also examine several models of autonomous oscillation in yeast (YAO), called the Immediate, Gap, and Mediated models. These models are based on a new concept of Response / Signaling (RS) coupled oscillator models, where feedback signaling and response are phase-dependent. In all three models, clustering of the type seen in YAO is a robust and generic phenomenon. The Gap and Mediated models add a dynamical delay, the latter by modeling a signaling agent present in the culture. For dense populations the Mediated model approximates the Immediate model, but the Mediated model includes dynamical quorum sensing where clustered solutions become stable through density-dependent bifurcations. A partial differential equations model is also examined, and we demonstrate existence and uniqueness of solutions for most parameter values.

Committee: Todd Young (Advisor); Winfried Just (Committee Member); Alexander Neiman (Committee Member); Tatiana Savin (Committee Member) Subjects: Applied Mathematics; Cellular Biology; Immunology