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Pages
 Title
 Analytical Results on the Role of Flexibility in Flapping Propulsion.
 Creator

Moore, Nicholas
 Abstract/Description

Wing or fin flexibility can dramatically affect the performance of flying and swimming animals. Both laboratory experiments and numerical simulations have been used to study these effects, but analytical results are notably lacking. Here, we develop smallamplitude theory to model a flapping wing that pitches passively due to a combination of wing compliance, inertia and fluid forces. Remarkably, we obtain a class of exact solutions describing the wing's emergent pitching motions, along with...
Show moreWing or fin flexibility can dramatically affect the performance of flying and swimming animals. Both laboratory experiments and numerical simulations have been used to study these effects, but analytical results are notably lacking. Here, we develop smallamplitude theory to model a flapping wing that pitches passively due to a combination of wing compliance, inertia and fluid forces. Remarkably, we obtain a class of exact solutions describing the wing's emergent pitching motions, along with expressions for how thrust and efficiency are modified by compliance. The solutions recover a range of realistic behaviours and shed new light on how flexibility can aid performance, the importance of resonance, and the separate roles played by wing and fluid inertia. The simple robust estimates afforded by our theory may prove valuable even in situations where details of the flapping motion and wing geometry differ.
Show less  Date Issued
 2014
 Identifier
 FSU_migr_math_faculty_publications0002, 10.1017/jfm.2014.533
 Format
 Citation
 Title
 Acknowledging the Religious Beliefs Students Bring into the Science Classroom: Using the Bounded Nature of Science.
 Creator

Southerland, Sherry A., Scharmann, Lawrence Conrad
 Abstract/Description

Scientific knowledge often appears to contradict many students' religious beliefs. Indeed, the assumptions of science appear contradictory to the metaphysical claims of many religions. This conflict is most evident in discussions of biological evolution. Teachers, in attempts to limit the controversy, often avoid this topic or teach it superficially. Recently, there has been a political effort to "teach to the controversy" – which some see as a way of introducing religious explanations for...
Show moreScientific knowledge often appears to contradict many students' religious beliefs. Indeed, the assumptions of science appear contradictory to the metaphysical claims of many religions. This conflict is most evident in discussions of biological evolution. Teachers, in attempts to limit the controversy, often avoid this topic or teach it superficially. Recently, there has been a political effort to "teach to the controversy" – which some see as a way of introducing religious explanations for biological diversity into science classrooms. Many science educators reject this approach, insisting that we limit classroom discussions to science alone. This "science only" approach leaves the negotiation of alternative knowledge frameworks to students, who are often illprepared for such epistemological comparisons. To support students' understanding of science while maintaining their religious commitments, this article explores the utility of emphasizing the boundaries of scientific knowledge and the need to support students in their comparison of contradictory knowledge frameworks.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_ste_faculty_publications0013, 10.1080/07351690.2013.743778
 Format
 Citation
 Title
 The Influence of RET's on Elementary and Secondary Teachers' Views of Scientific Inquiry.
 Creator

Bahbah, Sibel, Golden, Barry W. (Barry Wade), Roseler, Katrina, Enderle, Patrick, Saka, Yavuz, Southerland, Sherry A.
 Abstract/Description

This study explores inservice elementary and secondary science teachers' conceptions of the Nature of Scientific Inquiry and the influence participation in two different Research Experience for Teacher (RET) had on these conceptions. Participant teachers attended one of two six week RET programs in which they worked with scientists to engage in scientific inquiry. Before and after the RETs, teachers completed the Views of Scientific Inquiry (VOSI) questionnaire. Teachers' answers were...
Show moreThis study explores inservice elementary and secondary science teachers' conceptions of the Nature of Scientific Inquiry and the influence participation in two different Research Experience for Teacher (RET) had on these conceptions. Participant teachers attended one of two six week RET programs in which they worked with scientists to engage in scientific inquiry. Before and after the RETs, teachers completed the Views of Scientific Inquiry (VOSI) questionnaire. Teachers' answers were analyzed to determine the degree of sophistication of their understanding of five facets of scientific inquiry. Both elementary and secondary teacher participants showed improvement in their understanding of nature of scientific inquiry as a result of program participation, and both programs were successful in supporting the development of inquiry conceptions, although secondary science teachers started and finished the RET's with a more sophisticated understandings of scientific inquiry. Areas of improvement for elementary teachers included the role of questions in science and the role subjectivity and creativity play in the processes of science, and for secondary teachers growth was seen in the role of questions, the relationship of data and evidence, the distinction of experiments and other means of investigations, and the varied methods of science. Implications of these results are discussed.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_ste_faculty_publications0014, 10.5539/ies.v6n1p117
 Format
 Citation
 Title
 Exponential Convergence Fourier Method and Its Application to Option Pricing with Lévy Processes.
 Creator

Gu, Fangxi, Nolder, Craig, Huffer, Fred W. (Fred William), Kercheval, Alec N., Nichols, Warren D., Ökten, Giray, Florida State University, College of Arts and Sciences,...
Show moreGu, Fangxi, Nolder, Craig, Huffer, Fred W. (Fred William), Kercheval, Alec N., Nichols, Warren D., Ökten, Giray, Florida State University, College of Arts and Sciences, Department of Mathematics
Show less  Abstract/Description

Option pricing by the Fourier method has been popular for the past decade, many of its applications to Lévy processes has been applied especially for European options. This thesis focuses on exponential convergence Fourier method and its application to discrete monitoring options and Bermudan options. An alternative payoff truncating method is derived to compare the benchmark Hilbert transform. A general error control framework is derived to keep the Fourier method out of an overflow problem....
Show moreOption pricing by the Fourier method has been popular for the past decade, many of its applications to Lévy processes has been applied especially for European options. This thesis focuses on exponential convergence Fourier method and its application to discrete monitoring options and Bermudan options. An alternative payoff truncating method is derived to compare the benchmark Hilbert transform. A general error control framework is derived to keep the Fourier method out of an overflow problem. Numerical results verify that the alternative payoff truncating sinc method performs better than the benchmark Hilbert transform method under the error control framework.
Show less  Date Issued
 2016
 Identifier
 FSU_FA2016_Gu_fsu_0071E_13579
 Format
 Thesis
 Title
 Understanding the Induction of a Science Teacher: The Interaction of Identity and Context.
 Creator

Saka, Yavuz, Southerland, Sherry A., Kittleson, Julie, Hunter, Todd
 Abstract/Description

The demanding first years of teaching are a time when many teachers leave the teaching profession or discard the reformminded practice emphasized in teacher preparation. If we are to lessen teacher attrition and more effectively support teachers during their development, a better understanding of what occurs during their induction into the profession is needed. The question that drove this research was what factors influence how a beginning science teacher negotiates entry into teaching?...
Show moreThe demanding first years of teaching are a time when many teachers leave the teaching profession or discard the reformminded practice emphasized in teacher preparation. If we are to lessen teacher attrition and more effectively support teachers during their development, a better understanding of what occurs during their induction into the profession is needed. The question that drove this research was what factors influence how a beginning science teacher negotiates entry into teaching? Specifically, we sought to understand how a beginning science teacher's identities interact with the teaching context, how this interactions shapes his use of reform minded teaching practice, and how the negotiation of identity, context and practice influence a novice teacher's employment decisions. The study involved two years of data collection; data included classroom and school observations, questionnaires, interviews, and teaching artifacts (such as lesson plans and assessments). The results demonstrate how conflicts in identities, institutional expectations, and personal dispositions of this novice influenced his transition in becoming a member of his school community. Implications of these interactions for teacher preparation and support are provided.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_ste_faculty_publications0012, 10.1007/s1116501293105
 Format
 Citation
 Title
 A longitudinal study on predictors of early calculation development among young children at risk for learning difficulties.
 Creator

Peng, Peng, Namkung, Jessica M, Fuchs, Douglas, Fuchs, Lynn S, Patton, Samuel, Yen, Loulee, Compton, Donald L, Zhang, Wenjuan, Miller, Amanda, Hamlett, Carol
 Abstract/Description

The purpose of this study was to explore domaingeneral cognitive skills, domainspecific academic skills, and demographic characteristics that are associated with calculation development from first grade to third grade among young children with learning difficulties. Participants were 176 children identified with reading and mathematics difficulties at the beginning of first grade. Data were collected on working memory, language, nonverbal reasoning, processing speed, decoding, numerical...
Show moreThe purpose of this study was to explore domaingeneral cognitive skills, domainspecific academic skills, and demographic characteristics that are associated with calculation development from first grade to third grade among young children with learning difficulties. Participants were 176 children identified with reading and mathematics difficulties at the beginning of first grade. Data were collected on working memory, language, nonverbal reasoning, processing speed, decoding, numerical competence, incoming calculations, socioeconomic status, and gender at the beginning of first grade and on calculation performance at four time points: the beginning of first grade, the end of first grade, the end of second grade, and the end of third grade. Latent growth modeling analysis showed that numerical competence, incoming calculation, processing speed, and decoding skills significantly explained the variance in calculation performance at the beginning of first grade. Numerical competence and processing speed significantly explained the variance in calculation performance at the end of third grade. However, numerical competence was the only significant predictor of calculation development from the beginning of first grade to the end of third grade. Implications of these findings for early calculation instructions among young atrisk children are discussed.
Show less  Date Issued
 20161201
 Identifier
 FSU_pmch_27572520, 10.1016/j.jecp.2016.07.017, PMC5052117, 27572520, 27572520, S00220965(16)301059
 Format
 Citation
 Title
 On Elliptic Fibrations and FTheory Compactifications of String Vacua.
 Creator

Fullwood, James, Aluﬃ, Paolo, Reina, Laura, Van Hoeij, Mark, Aldrovandi, Ettore, Hironaka, Eriko, Department of Mathematics, Florida State University
 Abstract/Description

We investigate some algebrogeometric aspects of several families of elliptic fibrations relevant for Ftheory model building along with some physical applications. In particular, we compute topological invariants of elliptic fibrations via `SethiVafaWitten formulas', which relate the given invariant of the total space of the fibration to invariants of the base. We find that these invariants can often be computed in a baseindependent manner, and moreover, can be computed for all possible...
Show moreWe investigate some algebrogeometric aspects of several families of elliptic fibrations relevant for Ftheory model building along with some physical applications. In particular, we compute topological invariants of elliptic fibrations via `SethiVafaWitten formulas', which relate the given invariant of the total space of the fibration to invariants of the base. We find that these invariants can often be computed in a baseindependent manner, and moreover, can be computed for all possible dimensions of a base at once. As such, we construct generating series $f(t)$ corresponding to each invariant such that the coefficient of $t^k$ encodes the invariant of the elliptic fibration over a base of dimension $k$, solely in terms of invariants of the base. From the Ftheory perspective, we highlight aspects of elliptic fibrations other than Weierstrass models, and construct a new orientifold limit of Ftheory associated with $D_5$ fibrations, i.e., elliptic fibrations whose elliptic fiber is realized via a complete intersection of two quadrics in $\mathbb{P}^3$. We verify tadpole relations as predicted by the (conjectural) equivalence between Ftheory and typeIIB, as well as `universal tadpole relations', which are mathematical generalizations of the tadpole relations predicted by the physics of Ftheory. We also simplify formulas for invariants of CalabiYau fourfolds, and suggest that all Hodge numbers of CalabiYau fourfolds depend linearly on $c_1(B)^3$, where $B$ is the base of the fibration.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4848
 Format
 Thesis
 Title
 Modeling Order Book Dynamics Using Queues and Point Processes.
 Creator

Huang, He, Kercheval, Alec, Marquis, Milton, Nolder, Craig, Okten, Giray, Ewald, Brian, Department of Mathematics, Florida State University
 Abstract/Description

The objective of this dissertation is to study the queuing and point process models that try to capture as many features as possible of the highfrequency data of a limit order book. First, we use a generalized birthdeath stochastic process to model the highfrequency dynamics of the limit order book, and illustrate it using parameters estimated from Level II data for a stock on the London Stock Exchange. A new feature of this model is that limit orders are allowed to arrive in multiple...
Show moreThe objective of this dissertation is to study the queuing and point process models that try to capture as many features as possible of the highfrequency data of a limit order book. First, we use a generalized birthdeath stochastic process to model the highfrequency dynamics of the limit order book, and illustrate it using parameters estimated from Level II data for a stock on the London Stock Exchange. A new feature of this model is that limit orders are allowed to arrive in multiple sizes, an important empirical feature of the order book. We can compute various quantities of interest without resorting to simulation, conditional on the state of the order book, such as the probability that the next move of the midprice will be upward, or the probability, as a function of order size, that a limit ask order will be executed before a downward move in the midprice. Furthermore, univariatebivariate Hawkes' processes are developed and calibrated to capture the ``clustering'' and "mutually exciting'' features of the order arrivals in a limit order book. Although due to technical reasons, probabilities of interest such as those of prices going up for the next move are not shown for this model, a Monte Carlo simulation algorithm of point processes called emph{thinning algorithm} is successfully modified to derive the cumulative distribution functions of some firstpassage times in the order book.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4919
 Format
 Thesis
 Title
 Learning Shape Metrics for Inferring the Nature of Allometry and Shape Classification.
 Creator

Fan, Yu, Mio, Washington, Kumar, Piyush, Quine, Jack, Hurdal, Monica, Cogan, Nick, Department of Mathematics, Florida State University
 Abstract/Description

We extend the classical Procrustes metric to a new family of shape metrics and introduce a generalized Procrustes shape model. Furthermore, we propose learning models and numerical algorithms for learning metrics by using, guided by the suggestion from biologists that the spreads of landmarks should be concentrated in relatively small regions, optimization of some measurements of sparseness to select the appropriate shape metric for gene data. We apply the generalized Procrustes shape model...
Show moreWe extend the classical Procrustes metric to a new family of shape metrics and introduce a generalized Procrustes shape model. Furthermore, we propose learning models and numerical algorithms for learning metrics by using, guided by the suggestion from biologists that the spreads of landmarks should be concentrated in relatively small regions, optimization of some measurements of sparseness to select the appropriate shape metric for gene data. We apply the generalized Procrustes shape model to the shape classification problem as well and propose a selection criterion to pick out the most qualified metric for distinguishing different shape species. The experiment results illustrate the power of our shape framework.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4821
 Format
 Thesis
 Title
 Algorithms for Computing Congruences Between Modular Forms.
 Creator

Heaton, Randy, Agashe, Amod, Van Hoeij, Mark, Capstick, Simon, Aldrovandi, Ettore, Department of Mathematics, Florida State University
 Abstract/Description

Let $N$ be a positive integer. We first discuss a method for computing intersection numbers between subspaces of $S_{2}(Gamma_{0}(N),C)$. Then we present a new method for computing a basis of qexpansions for $S_{2}(Gamma_{0}(N),Q)$, describe an algorithm for saturating such a basis in $S_{2}(Gamma_{0}(N),Z)$, and show how these results have applications to computing congruence primes and studying cancellations in the conjectural Birch and SwinnertonDyer formula.
 Date Issued
 2012
 Identifier
 FSU_migr_etd4904
 Format
 Thesis
 Title
 An Analytic Approach to Estimating the Required Surplus, Benchmark Profit, and Optimal Reinsurance Retention for an Insurance Enterprise.
 Creator

Boor, Joseph A. (Joseph Allen), Born, Patricia, Case, Bettye Anne, Tang, Qihe, Rogachev, Grigory, Okten, Giray, Aldrovandi, Ettore, Paris, Steve, Department of Mathematics,...
Show moreBoor, Joseph A. (Joseph Allen), Born, Patricia, Case, Bettye Anne, Tang, Qihe, Rogachev, Grigory, Okten, Giray, Aldrovandi, Ettore, Paris, Steve, Department of Mathematics, Florida State University
Show less  Abstract/Description

This paper presents an analysis of the capital needs, needed return on capital, and optimum reinsurance retention for insurance companies, all in the context where claims are either paid out or known with certainty within or soon after the policy period. Rather than focusing on how to estimate such values using Monte Carlo simulation, it focuses on closed form expressions and approximations for key quantities that are needed for such an analysis. Most of the analysis is also done using a...
Show moreThis paper presents an analysis of the capital needs, needed return on capital, and optimum reinsurance retention for insurance companies, all in the context where claims are either paid out or known with certainty within or soon after the policy period. Rather than focusing on how to estimate such values using Monte Carlo simulation, it focuses on closed form expressions and approximations for key quantities that are needed for such an analysis. Most of the analysis is also done using a distributionfree approach with respect to the loss severity distribution, so minimal or no assumptions surrounding the specific distribution are needed when analyzing the results. However, one key parameter, that is treated via an exhaustion of cases, involves the degree of parameter uncertainty, the number of separate lines of business involved. This is done for the no parameter uncertainty monoline compound Poisson distribution as well as situations involving (lognormal) severity parameter uncertainty, (gamma/negative binomial) count parameter uncertainty, the multiline compound Poisson case, and the compound Poisson scenario with parameter uncertainty, and especially parameter uncertainty correlated across the lines of business. It shows how the risk of extreme aggregate losses that is inherent in insurance operations may be understood (and, implicitly, managed) by performing various calculations using the loss severity distribution, and, where appropriate, key parameters driving the parameter uncertainty distributions. Formulas are developed that estimate the capital and surplus needs of a company(using the VaR approach), and therefore the profit needs of a company that involve tractable calculations. As part of that the process the benchmark loading for profit, reflecting both the needed financial support for the amount of capital to adequately secure to a given one year survival probability, and the amount needed to recompense investors for diversifiable risk is discussed. An analysis of whether or not the loading for diversifiable risk is needed is performed. Approximations to the needed values are performed using the moments of the capped severity distribution and analytic formulas from the frequency distribution as inputs into method of moments normal and lognormal approximations to the percentiles of the aggregate loss distribution. An analysis of the optimum reinsurance retention/policy limit is performed as well, with capped loss distribution/frequency distribution equations resulting from the relationship that the marginal profit (with respect to the loss cap) should be equal to the marginal expense and profit dollar loading with respect to the loss cap. Analytical expressions are developed for the optimum reinsurance retention. Approximations to the optimum retention based on the normal distribution were developed and their error analyzed in great detail. The results indicate that in the vast majority of practical scenarios, the normal distribution approximation to the optimum retention is acceptable. Also included in the paper is a brief comparison of the VaR (survival probability) and expected policyholder deficit (EPD) and TVaR approaches to surplus adequacy (which conclude that the VaR approach is superior for most property/casualty companies); a mathematical analysis of the propriety of insuring the upper limits of the loss distribution, which concludes that, even if unlimited funds were available to secure losses in capital and reinsurance, it would not be in the insured's best interest to do so. Further inclusions to date include a illustrative derivation of the generalized collective risk equation and a method for interpolating ``along'' a mathematical curve rather than directly using the values on the curve. As a prelude to a portion of the analysis, a theorem was proven indicating that in most practical situations, the n1st order derivatives of a suitable probability mass function at values L, when divided by the product of L and the nth order derivative, generate a quotient with a limit at infinity that is less than 1/n.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4726
 Format
 Thesis
 Title
 Chern Classes of Sheaves of Logarithmic Vector Fields for Free Divisors.
 Creator

Liao, Xia, Aluﬃ, Paolo, Reina, Laura, Klassen, Eric P., Aldrovandi, Ettore, Petersen, Kathleen, Department of Mathematics, Florida State University
 Abstract/Description

The thesis work we present here focuses on solving a conjecture raised by Aluffi about ChernSchwartzMacPherson classes. Let $X$ be a nonsingular variety defined over an algebraically closed field $k$ of characteristic $0$, $D$ a reduced effective divisor on $X$, and $U = X smallsetminus D$ the open complement of $D$ in $X$. The conjecture states that $c_{textup{SM}}(1_U) = c(textup{Der}_X(log D)) cap [X]$ in $A_{*}(X)$ for any locally quasihomogeneous free divisor $D$. We prove a stronger...
Show moreThe thesis work we present here focuses on solving a conjecture raised by Aluffi about ChernSchwartzMacPherson classes. Let $X$ be a nonsingular variety defined over an algebraically closed field $k$ of characteristic $0$, $D$ a reduced effective divisor on $X$, and $U = X smallsetminus D$ the open complement of $D$ in $X$. The conjecture states that $c_{textup{SM}}(1_U) = c(textup{Der}_X(log D)) cap [X]$ in $A_{*}(X)$ for any locally quasihomogeneous free divisor $D$. We prove a stronger version of this conjecture. We also report on work aimed at studying the Grothedieck class of hypersurfaces of low degree. In this work, we verified the Geometric ChevalleyWarning conjecture in several low dimensional cases.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7467
 Format
 Thesis
 Title
 Modeling Cortical Folding Patterns of the Brain Using a Growing Domain.
 Creator

Toole, Gregory, Hurdal, Monica K., Steinbock, Oliver, Bertram, Richard, Cogan, Nick, Ewald, Brian, Department of Mathematics, Florida State University
 Abstract/Description

The brain is one of nature's greatest mysteries. The mechanism by which the folds of the brain's cerebral cortex, called gyri (hills) and sulci (valleys), are formed remains unknown. Existing biological hypotheses that attempt to explain the underlying mechanism of cortical folding conflict. Some hypotheses, such as the Intermediate Progenitor Model, emphasize genetic chemical factor control. Others, such as the Axonal Tension Hypothesis, emphasize the influence of physical tension due to...
Show moreThe brain is one of nature's greatest mysteries. The mechanism by which the folds of the brain's cerebral cortex, called gyri (hills) and sulci (valleys), are formed remains unknown. Existing biological hypotheses that attempt to explain the underlying mechanism of cortical folding conflict. Some hypotheses, such as the Intermediate Progenitor Model, emphasize genetic chemical factor control. Others, such as the Axonal Tension Hypothesis, emphasize the influence of physical tension due to axonal connections. To bring mathematics into this debate, this dissertation presents two biomathematical models of cortical folding that utilize a Turing reactiondiffusion system on an exponentially or logistically growing prolate spheroidal domain. These models are used to investigate the validity of the Intermediate Progenitor Model, thereby investigating the role of genetic chemical factor control of the development of cortical folding patterns. We observe that the presence of domain growth drives the patterns generated by our growing prolate spheroidal Turing systems to become transient. An exponentially growing prolate spheroidal domain generates a pattern that continually evolves, while a logistically growing prolate spheroidal domain generates a pattern that evolves while the domain is growing but then converges to a final pattern once the domain growth asymptotically stops. Patterns generated by the model systems represent genetic chemical prepatterns for selfamplification of intermediate progenitor cells, which may be correlated to cortical folding patterns according to the Intermediate Progenitor Model. By altering system parameters, we are able to model diseases of cortical folding such as polymicrogyria where the cortex possesses too many folds as well as diseases where the cortex has too few cortical folds such as NormanRoberts Syndrome (microcephalic lissencephaly) and normocephalic lissencephaly. Our ability to model such a variety of diseases lends support to the role of genetic control of cortical folding pattern development and therefore to the Intermediate Progenitor Model.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7631
 Format
 Thesis
 Title
 Discrete Frenet Frame with Application to Structural Biology and Kinematics.
 Creator

Lu, Yuanting, Quine, John R., Huffer, Fred W., Bertram, Richard, Cross, Timothy A., Cogan, Nick, Department of Mathematics, Florida State University
 Abstract/Description

The classical Frenet frame is a moving frame on a smooth curve. Connecting a sequence of points in space by line segments makes a discrete curve. The reference frame consisting of tangent, normal and binormal vectors at each point is defined as discrete Frenet frame (DFF). The DFF is useful in studying shapes of long molecules such as proteins. In this dissertation, we provide a solid mathematics foundation for DFF by showing the limit of the Frenet formula for DFF is the classical Frenet...
Show moreThe classical Frenet frame is a moving frame on a smooth curve. Connecting a sequence of points in space by line segments makes a discrete curve. The reference frame consisting of tangent, normal and binormal vectors at each point is defined as discrete Frenet frame (DFF). The DFF is useful in studying shapes of long molecules such as proteins. In this dissertation, we provide a solid mathematics foundation for DFF by showing the limit of the Frenet formula for DFF is the classical Frenet formula. As part of a survey of various ways to compute rigid body motion, we show the DenavitHartenberg (DH) conventions in robotics are a special case of the DFFs. Finally, we apply DFF to solve the kink angle problem in protein alpha helical structure using data from NMR experiments.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7477
 Format
 Thesis
 Title
 Stochastic Modeling of Financial Derivatives.
 Creator

Huang, Wanwan, Okten, Giray, Ewald, Brian, Huffer, Fred, Kercheval, Alec, Tang, Qihe, Kim, Kyounghee, Department of Mathematics, Florida State University
 Abstract/Description

The Coupled Additive Multiplicative Noises (CAM) model is introduced as a stochastic volatility process to extend the classical BlackScholes model. The fast Fourier transform (FFT) method is used to compute the values of the probability density function of the underlying assets under the CAM model, as well as the price of European call options. We discuss four dierent discretization schemes for the CAM model: the Euler scheme, the simplied weak Euler scheme, the order 2 weak Taylor scheme...
Show moreThe Coupled Additive Multiplicative Noises (CAM) model is introduced as a stochastic volatility process to extend the classical BlackScholes model. The fast Fourier transform (FFT) method is used to compute the values of the probability density function of the underlying assets under the CAM model, as well as the price of European call options. We discuss four dierent discretization schemes for the CAM model: the Euler scheme, the simplied weak Euler scheme, the order 2 weak Taylor scheme and the stochastic AdamsBashforth scheme. A martingale control variate method for pricing European call options is developed, and its advantages in terms of variance reduction are investigated numerically. We also develop Monte Carlo methods for estimating the sensitivities of the European call options under the CAM model.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7429
 Format
 Thesis
 Title
 Probabilistic Uncertainty Analysis and Its Applications in Option Models.
 Creator

Namihira, Motoi J., Kopriva, David A., Srivastava, Anuj, Ewald, Brian, Hussaini, M. Yousuﬀ, Nichols, Warren, Okten, Giray, Department of Mathematics, Florida State University
 Abstract/Description

In this work we quantify the effect of uncertainty in volatility in the prices and Deltas of an American and European put using probabilistic uncertainty analysis. We review the current methods of uncertainty analysis including worst case or scenario analysis, Monte Carlo, and provide an in depth review of Polynomial Chaos in both one and multiple dimensions. We develop a numerically stable method of generating orthogonal polynomials that is used in the practical construction of the...
Show moreIn this work we quantify the effect of uncertainty in volatility in the prices and Deltas of an American and European put using probabilistic uncertainty analysis. We review the current methods of uncertainty analysis including worst case or scenario analysis, Monte Carlo, and provide an in depth review of Polynomial Chaos in both one and multiple dimensions. We develop a numerically stable method of generating orthogonal polynomials that is used in the practical construction of the Polynomial Chaos basis functions. We also develop a semi analytic density transform method that is 200 times faster and 1000 times more accurate than the Monte Carlo based kernel density method. Finally, we analyze the European and American put option models assuming a distribution for the volatility that is historically observed. We find that the sensitivity to uncertainty in volatility is greatest for the price of ATM puts, and tapers as one moves away from the strike. The Delta, however, exhibits the least sensitivity when ATM and is most sensitive when moderately ITM. The price uncertainty for ITM American puts is less than the price uncertainty of equivalent European puts. For OTM options, the price uncertainty is similar between American and European puts. The uncertainty in the Delta of ITM American puts is greater than the uncertainty of equivalent European puts. For OTM puts, the uncertainty in Delta is similar between American and European puts. For the American put, uncertainty in volatility introduces uncertainty in the location of the optimal exercise boundary, thereby making optimal exercise decisions more difficult.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7525
 Format
 Thesis
 Title
 Nonlinear Dynamics Underlying Fast Bursting in Pituitary Cells.
 Creator

Teka, Wondimu Woubante, Bertram, Richard, Trombley, Paul Q., Tabak, Jöel, Cogan, Nick G., Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

Neurons and endocrine cells display various patterns of electrical activity, including periodic bursting. Bursting oscillations are characterized by the alternation between periods of fast spiking (the active phase) and quiescent periods (the silent phase), and are accompanied by slow variations in one or more slowly changing variables. Bursts are often more efficient than periodic spiking in evoking the release of neurotransmitter or hormone. The technique of twofast/oneslow analysis,...
Show moreNeurons and endocrine cells display various patterns of electrical activity, including periodic bursting. Bursting oscillations are characterized by the alternation between periods of fast spiking (the active phase) and quiescent periods (the silent phase), and are accompanied by slow variations in one or more slowly changing variables. Bursts are often more efficient than periodic spiking in evoking the release of neurotransmitter or hormone. The technique of twofast/oneslow analysis, which takes advantage of time scale differences, is typically used to analyze the dynamics of bursting in mathematical models. Two classes of bursting oscillations that have been identified with this technique, plateau and pseudoplateau bursting, are often observed in neurons and endocrine cells, respectively. These two types of bursting have very different properties and likely serve different functions. This latter point is supported by the divergent expression of the bursting patterns into different cell types, and raises the question of whether it is even possible for a model for one type of cell to produce bursting of the type seen in the other type without large changes to the model. Using fast/slow analysis, we show here that this is possible, and we provide a procedure for achieving this transition. This suggests that the mechanisms for bursting in endocrine cells are just quantitative variations of those for bursting in neurons. The twofast/oneslow analysis used to make the transition between plateau and pseudoplateau bursting, and to understand the dynamics of plateau bursting is of limited use for pseudoplateau bursting. Using a onefast/twoslow analysis technique, we show that pseudoplateau bursting is a canardinduced mixed mode oscillation. Using this technique, it is possible to determine the region of parameter space where bursting occurs as well as salient properties of the burst such as the number of spikes in the burst. Finally we show the relationship between the twofast/oneslow analysis and onefast/twoslow analysis techniques.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5219
 Format
 Thesis
 Title
 Risk Forecasting and Portfolio Optimization with GARCH, Skewed t Distributions and Multiple Timescales.
 Creator

Liu, Yang, Kercheval, Alec N., Schlagenhauf, Don E., Kim, Kyounghee, Nolder, Craig, Department of Mathematics, Florida State University
 Abstract/Description

It is wellestablished that distributions of financial returns are heavytailed and exhibit skewness and other nonGaussian characteristics. As time series, return data have volatilities that vary over time and show profound serial correlation (or crosscorrelation in the multivariate case). To address these issues, time series models such as GARCH (generalized autoregressive conditionally heteroskedastic) processes and nonGaussian distributions such as generalized hyperbolic (GH)...
Show moreIt is wellestablished that distributions of financial returns are heavytailed and exhibit skewness and other nonGaussian characteristics. As time series, return data have volatilities that vary over time and show profound serial correlation (or crosscorrelation in the multivariate case). To address these issues, time series models such as GARCH (generalized autoregressive conditionally heteroskedastic) processes and nonGaussian distributions such as generalized hyperbolic (GH) distributions have been introduced into financial modeling. A typical procedure featuring GARCH and nonGaussian distributions involves the following steps. First, filter data with GARCH to get residuals that are approximately i.i.d. Second, calibrate parameters of a nonGaussian distribution to those residuals. Finally, forecast various quantities based on knowledge of the calibrated distribution. Existing implementations of this procedure are fixedfrequency in nature. That is, all three steps are carried out on the same timescale. Reliable filtering and calibration requires a sufficient amount of historical data. As the forecast horizon grows, the model demands an increasingly long price history and may become infeasible if data are too scarce. To reduce the model's dependence on data availability, we propose a mixedfrequency method. Filtering and calibration are done on a relatively small timescale where data are more abundant. We then shift to a longer time horizon and make forecasts through aggregating GARCH processes and Monte Carlo simulation. We first apply this mixedfrequency approach to forecasting univariate valueatrisk (VaR) for stock index returns. Backtesting conducted on a variety of timescales shows that the method is indeed viable. Moreover, compared with the fixedfrequency method, our new method is able to produce VaR forecasts that respond more quickly to volatility changes. Therefore, even if data availability is not an issue, the mixedfrequency method is still a valuable alternative for risk managers. Portfolio optimization, a multivariate problem, is tackled next. We enhance traditional Markowitz optimization with expected shortfall (ES), which measures tail risks better than standard deviation, and skewed t distributions, a promising subfamily of GH distributions. The mixedfrequency idea is incorporated as well. Factors that affect the efficient frontier and optimal portfolio compositions are thoroughly discussed. Last but not least, we implement investment strategies based on GARCHskewed tES portfolio optimization and evaluate their performance, both in terms of return and risk.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4998
 Format
 Thesis
 Title
 Sequences of PseudoAnosov Mapping Classes with Asymptotically Small Dilatation.
 Creator

Valdivia, Aaron David, Hironaka, Eriko, Reina, Laura, Heil, Wolfgang, Klassen, Eric, Department of Mathematics, Florida State University
 Abstract/Description

We construct sequences of pseudoAnosov examples which we use to bound the minimal dilatation on arbitrary surfaces. We show that these bounds give the asymptotic behavior of the minimal dilatations for certain sequences. Further we show that the mapping classes for a given sequence from our construction can be realized as fibrations of a single 3manifold.
 Date Issued
 2011
 Identifier
 FSU_migr_etd5242
 Format
 Thesis
 Title
 From Songs to Synapses, Ion Channels and Mathematical Modeling.
 Creator

Daou, Arij, Bertram, Richard, Ryan, Pamela, Johnson, Frank, Hyson, Richard, Wu, Wei, Okten, Giray, Department of Mathematics, Florida State University
 Abstract/Description

Since the scientific study of birdsong began in the late 1950s, songbirds have emerged as impressive neurobiological models for aspects of human verbal communication because they learn to sequence their song elements, analogous, in many ways, to how humans learn to produce spoken sequences with syntactic structure. Thus, determining how spoken language evolved is more likely to become clearer with concerted efforts in researching songbirds. Some of the most fundamental questions in...
Show moreSince the scientific study of birdsong began in the late 1950s, songbirds have emerged as impressive neurobiological models for aspects of human verbal communication because they learn to sequence their song elements, analogous, in many ways, to how humans learn to produce spoken sequences with syntactic structure. Thus, determining how spoken language evolved is more likely to become clearer with concerted efforts in researching songbirds. Some of the most fundamental questions in neuroscience are pursued through the study of songbirds. How does the brain generate complex sequential behaviors? How do we learn to speak? How do humans learn various behaviors by observing and imitating others? Where are the "prime movers" that control behavior? Which circuits in the brain control the order in which motor gestures of a learned behavior are generated? Among all these questions, of particular interest to us is the question of sequential behavior. Understanding the neural mechanisms that underlie sequential behavior and imitative learning is the holy grail of the field. The birdsong provided us with a uniquely powerful model for tackling this question in a system where the brain structures responsible for its generation are well known. We pursued the study of sequential neural activity in songbirds on three levels: behavioral, cellular and network. On the behavioral level, we developed a computational tool for automated, quantitative syllablelevel analysis of bird song syntax. This tool aids songbird researchers and fanciers in comparing and quantifying the syntactic structure of songs produced by a bird prior to and after a manipulation such as ablation of brain region or infusion of pharmacological agents, in addition to several other purposes. As we will discuss later, this syntactic structure is highly stereotyped in songbirds and driven by neurons firing in sequential order in particular regions of the songbird's brain. On the cellular level, the telencephalic nucleus HVC (proper name) within the songbird analogue of the mammalian premotor cortex is situated at a critical point in the patterngenerating premotor brain circuitry of oscine songbirds. This nucleus is of extreme importance to the songbird and produces stereotyped instructions through the motor pathway leading to precise, learned vocalization by songbirds. HVC contains three populations of neurons that are interconnected, with specific patterns of excitatory and inhibitory connectivity. Characterizing the neurons in HVC is a very important requirement for decoding the neural code of the birdsong. We performed wholecell current clamp recordings on HVC neurons within brain slices to examine their intrinsic firing properties and determine which ionic currents are responsible for their characteristic firing patterns. We also developed conductancebased models for the different neurons and calibrated the models using data from our brain slice work. These models were then used to generate predictions about the makeup of the ionic currents that are responsible for the different responses to stimuli. These predictions were then tested and verified in the slice using pharmacological manipulations. Our results are an improved characterization of the HVC neurons responsible for song production in the songbird which are the key ingredients in understanding the HVC network. We then developed prototype neural architectures of the HVC that can produce the patterns of sequential neural activity exhibited by the three types of HVC neurons during singing. Our networks consist of microcircuits of interconnected neurons which are active during different syllables of the song. The various networks that we consider assign different roles to each of the HVC neurons types in the production of the sequential activity pattern, and show great flexibility in the connectivity patterns among the neuron types. The model networks developed provide key insights into how the different types of HVC neurons can be used for sequence generation. The significance of the work presented in this dissertation is that it helps elucidate the neural mechanisms behind HVC activity. The in vitro studies we performed in brain slices and the models we developed provide critical pieces to the puzzle of sequential behavior.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7347
 Format
 Thesis
 Title
 Calibration of Local Volatility Models and Proper Orthogonal Decomposition Reduced Order Modeling for Stochastic Volatility Models.
 Creator

Geng, Jian, Navon, Ionel Michael, Case, Bettye Anne, Contreras, Rob, Okten, Giray, Kercheval, Alec N., Ewald, Brian, Department of Mathematics, Florida State University
 Abstract/Description

There are two themes in this thesis: local volatility models and their calibration, and Proper Orthogonal Decomposition (POD) reduced order modeling with application in stochastic volatility models, which has a potential in the calibration of stochastic volatility models. In the first part of this thesis (chapters IIIII), the local volatility models are introduced first and then calibrated for European options across all strikes and maturities of the same underlying. There is no...
Show moreThere are two themes in this thesis: local volatility models and their calibration, and Proper Orthogonal Decomposition (POD) reduced order modeling with application in stochastic volatility models, which has a potential in the calibration of stochastic volatility models. In the first part of this thesis (chapters IIIII), the local volatility models are introduced first and then calibrated for European options across all strikes and maturities of the same underlying. There is no interpolation or extrapolation of either the option prices or the volatility surface. We do not make any assumption regarding the shape of the volatility surface except to assume that it is smooth. Due to the smoothness assumption, we apply a second order Tikhonov regularization. We choose the Tikhonov regularization parameter as one of the singular values of the Jacobian matrix of the Dupire model. Finally we perform extensive numerical tests to assess and verify the aforementioned techniques for both local volatility models with known analytical solutions of European option prices and real market option data. In the second part of this thesis (chapters IVV), stochastic volatility models, POD reduced order modeling are introduced first respectively. Then POD reduced order modeling is applied to the Heston stochastic volatility model for the pricing of European options. Finally, chapter VI summaries the thesis and points out future research areas.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7388
 Format
 Thesis
 Title
 Spectral Methods for Morphometry.
 Creator

Bates, Jonathan R., Mio, Washington, Patrangenaru, Victor, Bertram, Richard, Liu, Xiuwen, Quine, Jack, Department of Mathematics, Florida State University
 Abstract/Description

Methods from shape analysis are used in morphometry, which is the quantitative analysis of macroscopic anatomical features. We assume that anatomy is flexible, and this brings us to the first problem of resolving how ``shape'' should be represented if it is allowed to bend. We are motivated to use representations of intrinsic geometry, which, for example, does not distinguish a flat sheet of paper from a rolled sheet. The spectral embedding (``heat kernel representation'') as a representation...
Show moreMethods from shape analysis are used in morphometry, which is the quantitative analysis of macroscopic anatomical features. We assume that anatomy is flexible, and this brings us to the first problem of resolving how ``shape'' should be represented if it is allowed to bend. We are motivated to use representations of intrinsic geometry, which, for example, does not distinguish a flat sheet of paper from a rolled sheet. The spectral embedding (``heat kernel representation'') as a representation of intrinsic geometry has many desirable features for computational anatomy and other areas of shape and data analysis. Several breakthroughs are made toward understanding and applying this representation. A novel shape representation is also considered and used for classification of control vs. affected groups. One goal of morphometry is to make statistically objective comparisons. Hence, once a suitable representation of shape is chosen, the second problem is to compare shapes. Shape comparison may occur at many levels of scale. The simplest comparisons are made with global features: volume, length, etc. Finer comparisons may occur at regional levels. A finest level of comparison can be made after matching all homologous points, that is, after finding a oneone correspondence between points on shapes. A point correspondence is found by a registration algorithm. A method for unsupervised shape registration is presented and applied to localize differences between control and affected groups. We focus on the 3D case, where imaging has made anatomical surface data readily available, yet the analysis challenging. Structural MRI of living persons is currently used to study the macroscopic effects on anatomy by neurodegenerative disease (e.g. Alzheimer's). In the earliest stages of Alzheimer's disease (AD), certain brain structures have been observed to have reduced volume, in autopsy and in vivo, including the hippocampus, putamen, and thalamus. Our methods will be applied to these surfaces.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7291
 Format
 Thesis
 Title
 Jump Dependence and Multidimensional Default Risk: A New Class of Structural Models with Stochastic Intensities.
 Creator

Garreau, Pierre, Kercheval, Alec N., Marquis, Milton H., Beaumont, Paul M., Kopriva, David A., Okten, Giray, Department of Mathematics, Florida State University
 Abstract/Description

This thesis presents a new structural framework for multidimensional default risk. The time of default is the first jump of the logreturns of the stock price of a firm below a stochastic default level. When the stock price is an exponential Levy process, this new formulation is equivalent to a default model with stochastic intensity where the intensity process is parametrized by a Levy measure. This framework calibrates well to various term structures of credit default swaps. Furthermore,...
Show moreThis thesis presents a new structural framework for multidimensional default risk. The time of default is the first jump of the logreturns of the stock price of a firm below a stochastic default level. When the stock price is an exponential Levy process, this new formulation is equivalent to a default model with stochastic intensity where the intensity process is parametrized by a Levy measure. This framework calibrates well to various term structures of credit default swaps. Furthermore, the dependence between the default times of firms within a basket of credit securities is the result of the jump dependence of their respective stock prices: this class of models makes the link between the Equity and Credit markets. As an application, we show the valuation of a firsttodefault swaps. To motivate this new framework, we compute the default probability in a traditional structural model of default where the firm value follows a general Levy processes. This is made possible via the resolution of a partial integrodifferential equation (PIDE). We solve this equation numerically using a spectral element method based on the approximation of the solution with high order polynomials described in (Garreau & Korpiva, 2013). This method is able to handle the sharp kernels in the integral term. It is faster than the competing numerical Laplace transform methods used for first passage time problems, and can be used to compute the price of exotic options with barriers. This PIDE approach does not however extend well in higher dimensions. To understand the joint default of our new framework, we investigate the dependence structures of Levy processes. We show that for two one dimensional Levy processes to form a two dimensional Levy process, their joint survival times need to satisfy a two dimensional version of the memoryless property. We make the link with bivariate exponential random variables and the MarshallOlkin copula. This result yields a necessary construction of dependent Levy processes, a characterization theorem for Poisson random measures and has important ramification for default models with jointly conditionally Poisson processes.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8555
 Format
 Thesis
 Title
 Uncertainty Quantification and Data Fusion Based on DempsterShafer Theory.
 Creator

He, Yanyan, Hussaini, M. Yousuff, Oates, William S., Kopriva, David A., Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

Quantifying uncertainty in modeling and simulation is crucial since the parameters of the physical system are inherently nondeterministic and knowledge of the system embodied in the model is incomplete or inadequate. The most welldeveloped nonadditivemeasure theory  the DempsterShafer theory of evidence  is explored for uncertainty quantification and propagation. For ''uncertainty quantification," we propose the MinMax method to construct belief functions to represent uncertainty in...
Show moreQuantifying uncertainty in modeling and simulation is crucial since the parameters of the physical system are inherently nondeterministic and knowledge of the system embodied in the model is incomplete or inadequate. The most welldeveloped nonadditivemeasure theory  the DempsterShafer theory of evidence  is explored for uncertainty quantification and propagation. For ''uncertainty quantification," we propose the MinMax method to construct belief functions to represent uncertainty in the information (data set) involving the inseparably mixed type of uncertainties. Using the principle of minimum uncertainty and the concepts of entropy and specificity, the MinMax method specifies a partition of a finite interval on the real line and assigns belief masses to the uniform subintervals. The method is illustrated in a simple example and applied to the total uncertainty quantification in flight plan of two actual flights. For ''uncertainty propagation," we construct belief/probability density functions for the output or the statistics of the output given the belief/probability density functions for the uncertain input variables. Different approaches are introduced for aleatory uncertainty propagation, epistemic uncertainty propagation, and mixed type of uncertainty propagation. The impact of the uncertain input parameters on the model output is studied using these approaches in a simple example of aerodynamic flow: quasionedimensional nozzle flow. In the situation that multiple models are available for the same quantity of interest, the combination rules in the DempsterShafer theory can be utilized to integrate the predictions from the different models. In the present work, we propose a robust and comprehensive procedure to combine multiple bodies of evidence. It is robust in that it can combine multiple bodies of evidence, consistent or otherwise. It is comprehensive in the sense that it examines the bodies of evidence strongly conflicted with others, reconstructs the basic belief mass functions by discounting, and then fuses all the bodies of evidence using an optimally parametrized combination rule. The proposed combination procedure is applied to radiotherapy dose response outcome analysis.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8563
 Format
 Thesis
 Title
 Numerical Methods for Multiphase Systems with Applications to Biology.
 Creator

Whidden, Mark E., Cogan, Nicholas, Wang, Xiaoqiang, Bertram, Richard, Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

This dissertation is comprised of a variety of efforts towards the development of fast numerical methods and their applications, particularly in the context of simulating biological systems. Scientific computing of these problems requires many considerations bridging gaps between computer science, applied mathematics, and the biology of the specific application. This dissertation spans these fields, with the formulation of heterogeneous mixture descriptions in one chapter, the study and...
Show moreThis dissertation is comprised of a variety of efforts towards the development of fast numerical methods and their applications, particularly in the context of simulating biological systems. Scientific computing of these problems requires many considerations bridging gaps between computer science, applied mathematics, and the biology of the specific application. This dissertation spans these fields, with the formulation of heterogeneous mixture descriptions in one chapter, the study and implementation of efficient and robust numerical techniques in the next, and the application of this modeling framework and computational procedure to specific biological problems in the remaining chapters. The first of these efforts is the construction of multiphase models for macroscopic descriptions of biophysical problems. The second is the development of fast and flexible methods for simulating models derived from this modeling framework. The third is the revelation of this modeling framework to exhibit spatiotemporal patterns that can be initiated by localized perturbations in space. The fourth is the simulation of a fourphase model of biofilm formation implicated in Pierce's Disease.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8661
 Format
 Thesis
 Title
 Shape Analysis of Curves in Higher Dimensions.
 Creator

Wells, Linda Crystal, Klassen, Eric, Chicken, Eric, Srivastava, Anuj, Mio, Washington, Nichols, Warren, Department of Mathematics, Florida State University
 Abstract/Description

In this dissertation we will discuss geodesics between open curves and also between closed curves in Rn where n ≥ 2. In order to calculate these geodesics, we will form a Riemannian metric on a space of smooth curves with nonvanishing derivative. The metric will be invariant with respect to scaling, translation, rotation, and reparametrization. Using this metric we will define a distance between two curves invariant to the above mentioned transformations. This distance function will be...
Show moreIn this dissertation we will discuss geodesics between open curves and also between closed curves in Rn where n ≥ 2. In order to calculate these geodesics, we will form a Riemannian metric on a space of smooth curves with nonvanishing derivative. The metric will be invariant with respect to scaling, translation, rotation, and reparametrization. Using this metric we will define a distance between two curves invariant to the above mentioned transformations. This distance function will be defined utilizing the existence of isometries which allow our curves to map into a subspace of L2 where we already have geodesics defined and then map that geodesic back to the space of curves we are working in. Then we apply our metric to the geodesic to define the distance between the two initial curves. Some of our applications are 2D open curves, 3D open curves, and 3D closed curves including facial curves being categorized. The case of curves in R2 was studies by Laurent Younes, Peter W. Michor, Jayant Shah and David Mumford.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7658
 Format
 Thesis
 Title
 The Evolution of Deception in Signaling Systems.
 Creator

Ohm, Candace, MestertonGibbons, Mike, Isaac, Mark, Kercheval, Alec, Nichols, Warren, Department of Mathematics, Florida State University
 Abstract/Description

In this dissertation, we create a dynamical learning model that helps to explain the evolution of deception in signaling systems. In our model, the signaler may choose to signal either of two possible states. We apply this model to Batesian mimicry and to deceptive signaling of fighting ability, or resource holding potential. We show how to expand this model to allow for multiple receivers as well as multiple possible states.
 Date Issued
 2013
 Identifier
 FSU_migr_etd8616
 Format
 Thesis
 Title
 Periods and Motives: Applications in Mathematical Physics.
 Creator

Li, Dan, Marcolli, Matilde, Reina, Laura, Aluﬃ, Paolo, Agashe, Amod, Aldrovandi, Ettore, Department of Mathematics, Florida State University
 Abstract/Description

The study of periods arose in number theory and algebraic geometry, periods are interesting transcendental numbers like multiple zeta values, on the other hand periods are integrals of algebraic differential forms over domains described by algebraic relations. Viewed as abstract periods, we also consider their relations with motives. In this work, we consider two problems in mathematical physics as applications of the ideas and tools from periods and motives. We first consider the algebro...
Show moreThe study of periods arose in number theory and algebraic geometry, periods are interesting transcendental numbers like multiple zeta values, on the other hand periods are integrals of algebraic differential forms over domains described by algebraic relations. Viewed as abstract periods, we also consider their relations with motives. In this work, we consider two problems in mathematical physics as applications of the ideas and tools from periods and motives. We first consider the algebrogeometric approach to the spectral theory of Harper operators in solid state physics. When the parameters are irrational, the compactification of its Bloch variety is an indprovariety, which is a Cantorlike geometric space and it is compatible with the picture of Hofstadter butterfly. On each approximating component the density of states of the electronic model can be expressed in terms of period integrals over Fermi curves, which can be explicitly computed as elliptic integrals or periods of elliptic curves. The above density of states satisfies a PicardFuchs equation, whose solutions are generally given by hypergeometric functions. We use the idea of mirror maps as in mirror symmetry of elliptic curves to derive a qexpansion for the energy level based on the PicardFuchs equation. In addition, formal spectral functions such as the partition function are derived as new period integrals. Secondly, we consider generalized Feynman diagram evaluations of an effective noncommutative field theory of the PonzanoRegge model coupled with matter in loop quantum gravity. We present a parametric representation in a linear kapproximation of the effective field theory derived from a kdeformation of the PonzanoRegge model and define a generalized Kirchhoff polynomial with kcorrection terms. Setting k equal to 1, we verify that the number of points of the corresponding hypersurface of the tetrahedron over finite fields does not fit polynomials with integer coefficients by computer calculations. We then conclude that the hypersurface of the tetrahedron is not polynomially countable, which possibly implies that the hypersurface of the tetrahedron as a motive is not mixed Tate.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5390
 Format
 Thesis
 Title
 Applications of Quantum Dots in Gene Therapy.
 Creator

Barnes, Laura F., Strouse, Geoffrey, Logan, Timothy, Miller, Brian, Department of Chemistry and Biochemistry, Florida State University
 Abstract/Description

Gene therapy is a rising field and requires multifunctional delivery platforms in order to overcome the cellular barriers. Quantum dots (QDs) provide a optically fluorescent and biocompatible surface to act as a multifunctional delivery platform for gene therapy. The objective of this research is to manipulate the surface of quantum dots for use in gene therapy. The first goal was to make the QDs water soluble and therefore biocompatible. The second goal was to functionalize the surface of...
Show moreGene therapy is a rising field and requires multifunctional delivery platforms in order to overcome the cellular barriers. Quantum dots (QDs) provide a optically fluorescent and biocompatible surface to act as a multifunctional delivery platform for gene therapy. The objective of this research is to manipulate the surface of quantum dots for use in gene therapy. The first goal was to make the QDs water soluble and therefore biocompatible. The second goal was to functionalize the surface of the QDs with plasmid DNA for direct use in gene therapy. This approach uses chemoselective coupling chemistry between an InP/ZnS quantum dot (QD) and linker DNA (DNAlinker) to control the timing of protein expression. Linear DNA (lDNA), containing the CMV promoter and DsRedExpress gene, was condensed on the surface of the QDDNAlinker. Optical and flow cytometry analysis of the DsRedExpress expression after transfection of the QDlDNA into CHO cells shows a delayed protein expression for both coupling chemistries compared to naked lDNA. It is also clear that the protein expression form the QDSlDNA turns on quicker than the QDNHlDNA. We believe the protein expression delay is due to the site of coupling between the QD and DNAlinker and its affect on the lDNA packing strength. The SDNAlinker is believed to couple by direct exchange at the vertices of the QD whereas the NHDNAlinker couples through a condensation reaction to the facets. The delay in protein expression reflects the delayed exchange rate at the facets over the vertices. The ability to control the coupling chemistry and timing of release from the QD surface suggests a mechanism for dose control in transient gene therapeutics, and show QD delivery approaches are ideal candidates for multifunctional, targeted, drug carrying platforms that can simultaneously control dosing. The third goal of this research was to functionalize the surface of the QDs with the HIV cell penetrating peptide, TAT, and study its affects on QD internalization as well as toxicological affects within the cells. Tracking of the cellular uptake of these QDs by optical microscopy shows rapid, diffuse accumulation of both 10 % TAT and 100 % TAT passivated QDs throughout the cytosol of the cells. Toxicity studies were conducted by flow cytometry to investigate the effects of these materials on apoptosis, necrosis, and metabolic damage in Chinese Hamster Ovary (CHO) cells. These studies suggest toxic effects of the cell penetrating QDs are dependent on the amount of CAAKATAT used on the surface of the QD as well as the concentration of QD added. These observations aid in the use of QDs as self transfecting, nano delivery scaffolds for drug or gene therapy.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd5467
 Format
 Thesis
 Title
 Solving Linear Differential Equations in Terms of Hypergeometric Functions by ₂Descent.
 Creator

Fang, Tingting, Van Hoeij, Mark, Van Engelen, Robert A., Agashe, Amod, Aldrovandi, Ettore, Aluﬃ, Paolo, Department of Mathematics, Florida State University
 Abstract/Description

Let L be a linear ordinary differential equation with coefficients in C(x). This thesis presents algorithms to solve L in closed form. The key part of this thesis is 2descent method, which is used to reduce L to an equation that is easier to solve. The starting point is an irreducible L, and the goal of 2descent is to decide if L is projectively equivalent to another equation $\tilde{L}$ that is defined over a subfield C(f) of C(x). Although part of the mathematics for 2descent has already...
Show moreLet L be a linear ordinary differential equation with coefficients in C(x). This thesis presents algorithms to solve L in closed form. The key part of this thesis is 2descent method, which is used to reduce L to an equation that is easier to solve. The starting point is an irreducible L, and the goal of 2descent is to decide if L is projectively equivalent to another equation $\tilde{L}$ that is defined over a subfield C(f) of C(x). Although part of the mathematics for 2descent has already been treated before, a complete implementation could not be given because it involved a step for which we do not have a complete implementation. Our key novelty is to give an approach that is fully implementable. We describe and implement the algorithm for order 2, and show by examples that the same also work for higher order. By doing 2descent for L, the number of true singularities drops to at most n/2 + 2 (n is the number of true singularities of L). This provides us ways to solve L in closed form(e.g.in terms of hypergeometric funtions).
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5350
 Format
 Thesis
 Title
 Finding All Bessel Type Solutions for Linear Differential Equations with Rational Function Coefficients.
 Creator

Yuan, Quan, Van Hoeij, Mark, Van Engelen, Robert A., Agashe, Amod, Aldrovandi, Ettore, Aluﬃ, Paolo, Department of Mathematics, Florida State University
 Abstract/Description

A linear differential equation with rational function coefficients has a Bessel type solution when it is solvable in terms of Bessel functions, change of variables, algebraic operations and exponential integrals. For second order equations with rational function coefficients, the function f of change of variables must be a rational function or the square root of a rational function. An algorithm was given by Debeerst, van Hoeij, and Koepf, that can compute Bessel type solutions if and only if...
Show moreA linear differential equation with rational function coefficients has a Bessel type solution when it is solvable in terms of Bessel functions, change of variables, algebraic operations and exponential integrals. For second order equations with rational function coefficients, the function f of change of variables must be a rational function or the square root of a rational function. An algorithm was given by Debeerst, van Hoeij, and Koepf, that can compute Bessel type solutions if and only if change of variables is a rational function. In this thesis we extend this work to the square root case, resulting in a complete algorithm to find all Bessel type solutions. This algorithm can be easily extended to a Whittaker/Kummer solver. Combine the two algorithms, we can get a complete algorithm for all 0F1 and 1F1 type solutions. We also use our algorithm to analyze the relation between Bessel functions and Heun functions.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5296
 Format
 Thesis
 Title
 Dirac Operators, Multipliers and H[superscript P] Spaces of Monogenic Functions.
 Creator

Wang, Guanghou, Nolder, Craig, Hawkes, Lois, Case, Bettye, Hironaka, Eriko, Quine, Jack, Seppälä, Mika, Department of Mathematics, Florida State University
 Abstract/Description

We have done a few things under Clifford algebra settings. Firstly, one Caccioppoli type estimate is derived for solutions of $A$Dirac equations in the form $DA(x,Du) = 0$, where $D$ is the Dirac operator. This kind of $A$Dirac equations are generalizations of elliptic equations of $A$harmonic type, i.e. div$A(x,\nabla u)=0.$ Secondly, the multiplier theory from Fourier analysis is generalized to Clifford analysis. After the multipliers of operators $\mathcal{D}$, $T$ and $ \Pi$ are...
Show moreWe have done a few things under Clifford algebra settings. Firstly, one Caccioppoli type estimate is derived for solutions of $A$Dirac equations in the form $DA(x,Du) = 0$, where $D$ is the Dirac operator. This kind of $A$Dirac equations are generalizations of elliptic equations of $A$harmonic type, i.e. div$A(x,\nabla u)=0.$ Secondly, the multiplier theory from Fourier analysis is generalized to Clifford analysis. After the multipliers of operators $\mathcal{D}$, $T$ and $ \Pi$ are identified, some related properties will be very easy to achieve, including two integral representation theorems, also the iterations of operators $\mathcal{D}$ and $\Delta$ are also discussed. Thirdly, one Carleson measure theorem is achieved for monogenic Hardy spaces on the unit ball in $R^{n+1}$, as well as one Clifford Riesz representation theorem. Furthermore, one bounded theorem about certain inhomogeneous Dirac equations is established with the help of spherical monogenic functions theory.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5259
 Format
 Thesis
 Title
 Slow Variable Dominance in Pancreatic βCell Models.
 Creator

Watts, Margaret A., Bertram, Richard, Steinbock, Oliver, Quine, Jack, Cogan, Nick, Tabak, Joel, Department of Mathematics, Florida State University
 Abstract/Description

Like nerve and many other endocrine cells, pancreatic betacells are electrically excitable and produce electrical impulses in response to elevations in glucose. These electrical impulses typically come in the form of bursting. One type of bursting model with two or more slow variables has been called 'phantom bursting' since the burst period is a blend of the time constants of the slow variables. In this dissertation, the relative contributions that slow variables make to the bursting...
Show moreLike nerve and many other endocrine cells, pancreatic betacells are electrically excitable and produce electrical impulses in response to elevations in glucose. These electrical impulses typically come in the form of bursting. One type of bursting model with two or more slow variables has been called 'phantom bursting' since the burst period is a blend of the time constants of the slow variables. In this dissertation, the relative contributions that slow variables make to the bursting produced by two different phantom bursting models are quantified using a measure called the 'dominance factor'. Using this quantification, it is demonstrated that the control of different phases of the burst can be shifted from one slow variable to another by changing a model parameter. It is also demonstrated that the contributions that the slow processes make to bursting can be nonobvious. One application of the dominance factor is in making predictions about the resetting properties of the model cells. This application is demonstrated using a general phantom bursting model.
Show less  Date Issued
 2011
 Identifier
 FSU_migr_etd5264
 Format
 Thesis
 Title
 Functional Data Analysis and Partial Shape Matching in the Square Root Velocity Framework.
 Creator

Robinson, Daniel T., Klassen, Eric, Reina, Laura, Bellenot, Steven, Mio, Washington, Srivastava, Anuj, Department of Mathematics, Florida State University
 Abstract/Description

We investigate two problems in elastic curve shape analysis, working within the context of the square root velocity (SRV) framework. The first of these is to develop specialized algorithms for the analysis of onedimensional curves, which are just realvalued functions. In this particularly simple case, the elastic matching problem can be stated as a finite combinatorial problem in which the optimal solution can be found exactly. We also develop a method for groupwise alignment, and use it to...
Show moreWe investigate two problems in elastic curve shape analysis, working within the context of the square root velocity (SRV) framework. The first of these is to develop specialized algorithms for the analysis of onedimensional curves, which are just realvalued functions. In this particularly simple case, the elastic matching problem can be stated as a finite combinatorial problem in which the optimal solution can be found exactly. We also develop a method for groupwise alignment, and use it to compute Karcher means of collections of functions. Second, we consider the problem of finding optimal partial matches between curves in Euclidean space within the SRV framework, and present algorithms and heuristics to solve this problem. Finally, we give a brief overview of libsrvf, an opensource software library providing implementations of the algorithms developed in the course of this work.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd5424
 Format
 Thesis
 Title
 Partial Differential Equation Methods to Price Options in the Energy Market.
 Creator

Yan, Jinhua, Kopriva, David, Huﬀer, Fred, Case, Bettye Anne, Nolder, Craig, Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

We develop partial differential equation methods with wellposed boundary conditions to price average strike options and swing options in the energy market. We use the energy method to develop boundary conditions that make a two space variable model of Asian options wellposed on a finite domain. To test the performance of wellposed boundary conditions, we price an average strike call. We also derive new boundary conditions for the average strike option from the putcall parity. Numerical...
Show moreWe develop partial differential equation methods with wellposed boundary conditions to price average strike options and swing options in the energy market. We use the energy method to develop boundary conditions that make a two space variable model of Asian options wellposed on a finite domain. To test the performance of wellposed boundary conditions, we price an average strike call. We also derive new boundary conditions for the average strike option from the putcall parity. Numerical results show that wellposed boundary conditions are working appropriately and solutions with new boundary conditions match the similarity solution significantly better than those provided in the existing literature. To price swing options, we develop a finite element penalty method on a one factor mean reverting diffusion model. We use the energy method to find wellposed boundary conditions on a finite domain, derive formulas to estimate the size of the numerical domain, develop a priori error estimates for both Dirichlet boundary conditions and Neumann boundary conditions. We verify the results through numerical experiments. Since the optimal exercise price is unknown in advance, which makes the swing option valuation challenging, we use a penalty method to resolve the difficulty caused by the early exercise feature. Numerical results show that the finite element penalty method is thousands times faster than the Binomial tree method at the same level of accuracy. Furthermore, we price a multiple right swing option with different strike prices. We find that a jump discontinuity can occur in the initial condition of a swing right since the exercise of another swing right may force its optimal exercise region to shrink. We develop an algorithm to identify the optimal exercise boundary at each time level, which allows us to record the optimal exercise time. Numerical results are accurate to one cent comparing with the benchmark solutions computed by a Binomial tree method. We extend applications to multiple right swing options with a waiting period restriction. A waiting period exists between two swing rights to be exercised successively, so we cannot exercise the latter right when we see an optimal exercise opportunity within the waiting period, but have to wait for the first optimal exercise opportunity after the waiting period. Therefore, we keep track of the optimal exercise time when pricing each swing right. We also verify an extreme case numerically. When the waiting time decreases, the value of M right swing option price increases to the value of M times an American option price as expected.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7673
 Format
 Thesis
 Title
 3Manifolds of S1Category Three.
 Creator

Wang, Dongxu, Heil, Wolfgang, Niu, Xufeng, Klassen, Eric P., Hironaka, Eriko, Nichols, Warren D., Department of Mathematics, Florida State University
 Abstract/Description

I study 3manifold theory, which is a fascinating research area in topology. Many new ideas and techniques were introduced during these years, which makes it an active and fast developing subject. It is one of the most fruitful branches of today's mathematics and with the solution of the Poincare conjecture, it is getting more attention. This dissertation is motivated by results about categorical properties for 3manifolds. This can be rephrased as the study of 3manifolds which can be...
Show moreI study 3manifold theory, which is a fascinating research area in topology. Many new ideas and techniques were introduced during these years, which makes it an active and fast developing subject. It is one of the most fruitful branches of today's mathematics and with the solution of the Poincare conjecture, it is getting more attention. This dissertation is motivated by results about categorical properties for 3manifolds. This can be rephrased as the study of 3manifolds which can be covered by certain sets satisfying some homotopy properties. A special case is the problem of classifying 3manifolds that can be covered by three simple S1contractible subsets. S1contractible subsets are subsets of a 3manifold M3 that can be deformed into a circle in M3. In this thesis, I consider more geometric subsets with this property, namely subsets are homeomorphic to 3balls, solid tori and solid Klein bottles. The main result is a classication of all closed 3manifolds that can be obtained as a union of three solid Klein bottles.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd7650
 Format
 Thesis
 Title
 Alternative Models for Stochastic Volatility Corrections for Equity and Interest Rate Derivatives.
 Creator

Liang, Tianyu, Kercheval, Alec N., Wang, Xiaoming, Liu, Ewald, Brian, Nichols, Warren D., Department of Mathematics, Florida State University
 Abstract/Description

A lot of attention has been paid to the stochastic volatility model where the volatility is randomly fluctuating driven by an additional Brownian motion. In our work, we change the mean level in the meanreverting process from a constant to a function of the underlying process. We apply our models to the pricing of both equity and interest rate derivatives. Throughout the thesis, a singular perturbation method is employed to derive closedform formulas up to first order asymptotic solutions....
Show moreA lot of attention has been paid to the stochastic volatility model where the volatility is randomly fluctuating driven by an additional Brownian motion. In our work, we change the mean level in the meanreverting process from a constant to a function of the underlying process. We apply our models to the pricing of both equity and interest rate derivatives. Throughout the thesis, a singular perturbation method is employed to derive closedform formulas up to first order asymptotic solutions. We also implement multiplicative noise to arithmetic OrnsteinUhlenbeck process to produce a wider variety of effects. Calibration and Monte Carlo simulation results show that the proposed model outperform Fouque's original stochastic volatility model during some particular window in history. A more efficient numerical scheme, the heterogeneous multiscale method (HMM), is introduced to simulate the multiscale differential equations discussed over the chapters.
Show less  Date Issued
 2012
 Identifier
 FSU_migr_etd4990
 Format
 Thesis
 Title
 Modeling HighFrequency Order Book Dynamics with Support Vector Machines.
 Creator

Zhang, Yuan, Kercheval, Alec N., Niu, Xufeng, Nichols, Warren, Kim, Kyounghee, Department of Mathematics, Florida State University
 Abstract/Description

A machine learning based framework is proposed in this paper to capture the dynamics of highfrequency limit order books in financial markets and automate the prediction process in realtime on metrics characterizing the dynamics such as midprice and price spread crossing. By representing each entry in a limit order book with a vector of features including price and volume at different levels as well as statistic features derived from limit order book, the proposed framework builds a...
Show moreA machine learning based framework is proposed in this paper to capture the dynamics of highfrequency limit order books in financial markets and automate the prediction process in realtime on metrics characterizing the dynamics such as midprice and price spread crossing. By representing each entry in a limit order book with a vector of features including price and volume at different levels as well as statistic features derived from limit order book, the proposed framework builds a learning model for each metric with the help of multiclass support vector machines (SVMs) to predict the directions of market movement. Experiments with real data as well as synthetic data establish that features selected by the proposed framework have highly differentiating capability, models built are effective and efficient in predictions on price movements, and trading strategies based on resulting models can achieve profitable returns with low risk.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8670
 Format
 Thesis
 Title
 NonIntrusive Methods for Probablistic Uncertainty Quantification and Global Sensitivity Analysis in Nonlinea Stochastic Phenomena.
 Creator

Liu, Yaning, Hussaini, M. Yousuff, Okten, Giray, Srivastava, Anuj, Sussman, Mark, Department of Mathematics, Florida State University
 Abstract/Description

The objective of this work is to quantify uncertainty and perform global sensitivity analysis for nonlinear models with a moderate or large number of stochastic parameters. We implement nonintrusive methods that do not require modification of the programming code of the underlying deterministic model. To avoid the curse of dimensionality, two methods, namely sampling methods and high dimensional model representation are employed to propagate uncertainty and compute global sensitivity indices...
Show moreThe objective of this work is to quantify uncertainty and perform global sensitivity analysis for nonlinear models with a moderate or large number of stochastic parameters. We implement nonintrusive methods that do not require modification of the programming code of the underlying deterministic model. To avoid the curse of dimensionality, two methods, namely sampling methods and high dimensional model representation are employed to propagate uncertainty and compute global sensitivity indices. Variancebased global sensitivity analysis identifies significant and insignificant model parameters. It also provides basis for reducing a model's stochastic dimension by freezing identified insignificant model parameters at their nominal values. The dimensionreduced model can then be analyzed efficiently. We use uncertainty quantification and global sensitivity analysis in three applications. The first application is to the Rothermel wildland surface fire spread model, which consists of around 80 nonlinear algebraic equations and 24 parameters. We find the reduced models for the selected model outputs and apply efficient sampling methods to quantify the uncertainty. High dimensional model representation is also applied for the Rothermel model for comparison. The second application is to a recently developed biological model that describes inflammatory host response to a bacterial infection. The model involves four nonlinear coupled ordinary differential equations and the dimension of the stochastic space is 16. We compute global sensitivity indices for all parameters and build a dimensionreduced model. The sensitivity results, combined with experiments, can improve the validity of the model. The third application quantifies the uncertainty of weather derivative models and investigates model robustness based on global sensitivity analysis. Three commonly used weather derivative models for the daily average temperature are considered. The one which is least influenced by an increase of parametric uncertainty level is identified as robust. In summary, the following contributions are made in this dissertation: 1. The optimization of sensitivity derivative enhanced sampling that guarantees variance reduction and improved estimation of stochastic moments. 2. The combination of optimized sensitivity derivative enhanced sampling with randomized quasiMonte Carlo sampling, and adaptive Monte Carlo sampling, to achieve higher convergence rates. 3. The construction of cutHDMR component functions based on Gauss quadrature points which results in a more accurate surrogate model, derivation of an integral form of low order partial variances based on cutHDMR, and efficient computation of global sensitivity analysis based on cutHDMR. 4. The application of efficient sampling methods, RSHDMR and cutHDMR for the quantification of Rothermel's wildland fire surface spread model. 5. The uncertainty quantification and global sensitivity analysis of a newly developed immune response model with parametric uncertainty. 6. The uncertainty quantification of weather derivative models and the analysis of model robustness based on global sensitivity analysis.
Show less  Date Issued
 2013
 Identifier
 FSU_migr_etd8681
 Format
 Thesis
 Title
 ON THE RAUTOMORPHISMS OF R(X).
 Creator

DOWLEN, MARY MARGARET., Florida State University
 Abstract/Description

Throughout, R is a commutative ring with identity and X is an indeterminate over R. We consider R{X}, the polynomial ring in one indeterminate over R, and G(R), the group of Rautomorphisms of R{X}. In particular, we consider the subring of R{X} left fixed by the group G(R), denoted by R{X}('G(R)). Let B(R) be the subgroup of G(R) such that (sigma) (ELEM) B(R) if and only if (sigma)(X) = a + bX, b a unit of R. If R is reduced, then G(R) = B(R); otherwise, B(R) (LHOOK) G(R). We prove in...
Show moreThroughout, R is a commutative ring with identity and X is an indeterminate over R. We consider R{X}, the polynomial ring in one indeterminate over R, and G(R), the group of Rautomorphisms of R{X}. In particular, we consider the subring of R{X} left fixed by the group G(R), denoted by R{X}('G(R)). Let B(R) be the subgroup of G(R) such that (sigma) (ELEM) B(R) if and only if (sigma)(X) = a + bX, b a unit of R. If R is reduced, then G(R) = B(R); otherwise, B(R) (LHOOK) G(R). We prove in Chapter I that R{X}('G(R)) = R{X}('B(R))., In Chapter I we also prove that for R to be properly contained in R{X}('G(R)), it is necessary that R/M is a finite field for some maximal ideal M of R. Hence, if R is a quasilocal ring with maximal ideal M and R/M is infinite, then R{X}('G(R)) = R., Let R be a quasilocal ring with maximal ideal M such that R/M is isomorphic to the Galois field with p('s) elements, where p is a prime integer and s (ELEM) Z('+). In Chapter II, we show that, (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI), where, (DIAGRAM, TABLE OR GRAPHIC OMITTED...PLEASE SEE DAI), In particular, we determine Z(,n){X}('G(Zn)) for n (ELEM) Z('+). Moreover, we prove that R{X}('G(R)) contains a nonconstant monic polynomial if and only if R is a 0dimensional SFTring., In Chapter III, we investigate R{X}('G(R)) for a von Neumann regular ring R. We obtain equivalent conditions for R{X}('G(R)) to contain a nonconstant monic polynomial; one of these is that {card(R/M)} is bounded for all maximal ideals M of R. Moreover, we prove that R is properly contained in R{X}('G(R)) if and only if R has a direct summand S such that S{X}('G(S)) contains a nonconstant monic polynomial. Finally, in Chapter III we construct a von Neumann regular ring B such that B/M is finite for infinitely many maximal ideals M of B, but B{X}('G(B)) = B., In Chapter IV, we show that for any commutative ring R with identity, R{X}('G(R)) contains a nonconstant monic polynomial if and only if R is 0dimensional, card(R/M) < N for some N (ELEM) Z('+) and for all maximal ideals M of R, and nilpotent elements have bounded order of nilpotency.
Show less  Date Issued
 1982, 1982
 Identifier
 AAI8218637, 3085307, FSDT3085307, fsu:74802
 Format
 Document (PDF)
 Title
 A Spectral Element Method to Price Single and MultiAsset European Options.
 Creator

Zhu, Wuming, Kopriva, David A., Huﬀer, Fred, Case, Bettye Anne, Kercheval, Alec N., Okten, Giray, Wang, Xiaoming, Department of Mathematics, Florida State University
 Abstract/Description

We develop a spectral element method to price European options under the BlackScholes model, Merton's jump diffusion model, and Heston's stochastic volatility model with one or two assets. The method uses piecewise high order Legendre polynomial expansions to approximate the option price represented pointwise on a GaussLobatto mesh within each element. This piecewise polynomial approximation allows an exact representation of the nonsmooth initial condition. For options with one asset under...
Show moreWe develop a spectral element method to price European options under the BlackScholes model, Merton's jump diffusion model, and Heston's stochastic volatility model with one or two assets. The method uses piecewise high order Legendre polynomial expansions to approximate the option price represented pointwise on a GaussLobatto mesh within each element. This piecewise polynomial approximation allows an exact representation of the nonsmooth initial condition. For options with one asset under the jump diffusion model, the convolution integral is approximated by high order GaussLobatto quadratures. A second order implicit/explicit (IMEX) approximation is used to integrate in time, with the convolution integral integrated explicitly. The use of the IMEX approximation in time means that only a block diagonal, rather than full, system of equations needs to be solved at each time step. For options with two variables, i.e., two assets under the BlackScholes model or one asset under the stochastic volatility model, the domain is subdivided into quadrilateral elements. Within each element, the expansion basis functions are chosen to be tensor products of the Legendre polynomials. Three iterative methods are investigated to solve the system of equations at each time step with the corresponding second order time integration schemes, i.e., IMEX and CrankNicholson. Also, the boundary conditions are carefully studied for the stochastic volatility model. The method is spectrally accurate (exponentially convergent) in space and second order accurate in time for European options under all the three models. Spectral accuracy is observed in not only the solution, but also in the Greeks.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd0513
 Format
 Thesis
 Title
 Modeling the Folding Pattern of the Cerebral Cortex.
 Creator

Striegel, Deborah A., Hurdal, Monica K., Steinbock, Oliver, Quine, Jack, Sumners, DeWitt, Bertram, Richard, Department of Mathematics, Florida State University
 Abstract/Description

The mechanism for cortical folding pattern formation is not fully understood. Current models represent scenarios that describe pattern formation through local interactions and one recent model is the intermediate progenitor model. The intermediate progenitor (IP) model describes a local chemicallydriven scenario, where an increase in intermediate progenitor cells in the subventricular zone (an area surrounding the lateral ventricles) correlates to gyral formation. This dissertation presents...
Show moreThe mechanism for cortical folding pattern formation is not fully understood. Current models represent scenarios that describe pattern formation through local interactions and one recent model is the intermediate progenitor model. The intermediate progenitor (IP) model describes a local chemicallydriven scenario, where an increase in intermediate progenitor cells in the subventricular zone (an area surrounding the lateral ventricles) correlates to gyral formation. This dissertation presents the Global Intermediate Progenitor (GIP) model, a theoretical biological model that uses features of the IP model and further captures global characteristics of cortical pattern formation. To illustrate how global features can effect the development of certain patterns, a mathematical model that incorporates a Turing system is used to examine pattern formation on a prolate spheroidal surface. Pattern formation in a biological system can be studied with a Turing reactiondiffusion system which utilizes characteristics of domain size and shape to predict which pattern will form. The GIP model approximates the shape of the lateral ventricle with a prolate spheroid. This representation allows the capture of a key shape feature, lateral ventricular eccentricity, in terms of the focal distance of the prolate spheroid. A formula relating domain scale and focal distance of a prolate spheroidal surface to specific prolate spheroidal harmonics is developed. This formula allows the prediction of pattern formation with solutions in the form of prolate spheroidal harmonics based on the size and shape of the prolate spheroidal surface. By utilizing this formula a direct correlation between the size and shape of the lateral ventricle, which drives the shape of the ventricular zone, and cerebral cortical folding pattern formation is found. This correlation is illustrated in two different applications: (i) how the location and directionality of the initial cortical folds change with respect to evolutionary development and (ii) how the initial folds change with respect to certain diseases, such as Microcephalia Vera and Megalencephaly Polymicrogyria Polydactyly with Hydrocephalus. The significance of the model, presented in this dissertation, is that it elucidates the consistency of cortical patterns among healthy individuals within a species and addresses interspecies variability based on global characteristics. This model provides a critical piece to the puzzle of cortical pattern formation.
Show less  Date Issued
 2009
 Identifier
 FSU_migr_etd0394
 Format
 Thesis
 Title
 Peridynamic Multiscale Models for the Mechanics of Materials: Constitutive Relations, Upscaling from Atomistic Systems, and Interface Problems.
 Creator

Seleson, Pablo D, Gunzburger, Max, Rikvold, Per Arne, ElAzab, Anter, Peterson, Janet, Shanbhag, Sachin, Lehoucq, Richard B., Parks, Michael L., Department of Scientific...
Show moreSeleson, Pablo D, Gunzburger, Max, Rikvold, Per Arne, ElAzab, Anter, Peterson, Janet, Shanbhag, Sachin, Lehoucq, Richard B., Parks, Michael L., Department of Scientific Computing, Florida State University
Show less  Abstract/Description

This dissertation focuses on the non local continuum peridynamics model for the mechanics of materials, related constitutive models, its connections to molecular dynamics and classical elasticity, and its multiscale and multimodel capabilities. A more generalized role is defined for influence functions in the statebased peridynamic model which allows for the strength of non local interactions to be modulated. This enables the connection between different peridynamic constitutive models,...
Show moreThis dissertation focuses on the non local continuum peridynamics model for the mechanics of materials, related constitutive models, its connections to molecular dynamics and classical elasticity, and its multiscale and multimodel capabilities. A more generalized role is defined for influence functions in the statebased peridynamic model which allows for the strength of non local interactions to be modulated. This enables the connection between different peridynamic constitutive models, establishing a hierarchy that reveals that some models are special cases of others. Furthermore, this allows for the modulation of the strength of non local interactions, even for a fixed radius of interactions between material points in the peridynamics model. The multiscale aspect of peridynamics is demonstrated through its connections to molecular dynamics. Using higherorder gradient models, it is shown that peridynamics can be viewed as an upscaling of molecular dynamics, preserving the relevant dynamics under appropriate choices of length scales. The statebased peridynamic model is shown to be appropriate for the description of multiscale and multimodel systems. A formulation for nonlocal interface problems involving scalar fields is presented, and derivations of non local transmission conditions are derived. Specializations that describe local, non local, and local/non local transmission conditions are considered. Moreover, the convergence of the non local transmission conditions to their classical local counterparts is shown. In all cases, results are illustrated by numerical experiments.
Show less  Date Issued
 2010
 Identifier
 FSU_migr_etd0273
 Format
 Thesis
 Title
 QuasiMonte Carlo and Genetic Algorithms with Applications to Endogenous Mortgage Rate Computation.
 Creator

Shah, Manan, Okten, Giray, Goncharov, Yevgeny, Srinivasan, Ashok, Bellenot, Steve, Case, Bettye Anne, Kercheval, Alec, Kopriva, David, Nichols, Warren, Department of Mathematics...
Show moreShah, Manan, Okten, Giray, Goncharov, Yevgeny, Srinivasan, Ashok, Bellenot, Steve, Case, Bettye Anne, Kercheval, Alec, Kopriva, David, Nichols, Warren, Department of Mathematics, Florida State University
Show less  Abstract/Description

In this dissertation, we introduce a genetic algorithm approach to estimate the star discrepancy of a point set. This algorithm allows for the estimation of the star discrepancy in dimensions larger than seven, something that could not be done adequately by other existing methods. Then, we introduce a class of random digitpermutations for the Halton sequence and show that these permutations yield comparable or better results than their deterministic counterparts in any number of dimensions...
Show moreIn this dissertation, we introduce a genetic algorithm approach to estimate the star discrepancy of a point set. This algorithm allows for the estimation of the star discrepancy in dimensions larger than seven, something that could not be done adequately by other existing methods. Then, we introduce a class of random digitpermutations for the Halton sequence and show that these permutations yield comparable or better results than their deterministic counterparts in any number of dimensions for the test problems considered. Next, we use randomized quasiMonte Carlo methods to numerically solve a onefactor mortgage model expressed as a stochastic fixedpoint problem. Finally, we show that this mortgage model coincides with and is computationally faster than Citigroup's MOATS model, which is based on a binomial tree approach.
Show less  Date Issued
 2008
 Identifier
 FSU_migr_etd0297
 Format
 Thesis
 Title
 A computational study of turbulent jet flows and their instability waves.
 Creator

Thies, Andrew Timothy., Florida State University
 Abstract/Description

The nature of turbulent jet flows is considered. First, the effects of nozzle geometry are examined. A boundary element formulation, which may be used to analyze the stability of vortexsheet jets of arbitrary geometry, is developed. This formulation is applied to rectangular jets. It is found that rectangular jets support four linearly independent families of instability waves. Within each family there are infinitely many modes. A way to classify these modes according to the characteristics...
Show moreThe nature of turbulent jet flows is considered. First, the effects of nozzle geometry are examined. A boundary element formulation, which may be used to analyze the stability of vortexsheet jets of arbitrary geometry, is developed. This formulation is applied to rectangular jets. It is found that rectangular jets support four linearly independent families of instability waves. Within each family there are infinitely many modes. A way to classify these modes according to the characteristics of their eigenfunctions is proposed. It is found that the first and third modes of each family are corner modes. The fluctuations associated with these waves are localized near the corners of the jet. The second mode in each family, however, is a center mode with maximum fluctuations concentrated near the central portions of the jet. The center modes have the largest spatial growth rates. It is anticipated that as the instability waves propagate downstream the center modes would emerge as the dominant instabilities of the jet. Second, a K$\varepsilon$ turbulence model, which incorporates Pope's nonplaner correction and Sarkar's high convective Mach number correction, is proposed for the computation of timeaveraged turbulent jet flows. It is demonstrated that this model does contain the essential ingredients of turbulence physics for adequate jet mean flow prediction. However, the empirical constants that are generally used are found to be inappropriate for jets. A highorder parabolized approach to computing ideally expanded jet flows is presented. A new set of empirical constants is chosen, which better correlates the computations with measurements for a set of jets representative of a variety of nozzle configurations. It is demonstrated that, when the standard constants are replaced by the new ones, the model can offer good mean flow predictions for axisymmetric,, rectangular and elliptic jets with Mach numbers ranging from 0.4 to 2.0 and jet total temperature to ambient temperature ratios ranging from 1.0 to 4.0. Together, the two efforts lay much of the groundwork for a complete study of the effects of nozzle geometry on the mixing and noise generation in highspeed jet flows.
Show less  Date Issued
 1995, 1995
 Identifier
 AAI9526498, 3088592, FSDT3088592, fsu:77394
 Format
 Document (PDF)
 Title
 On the motion of a rigid cylinder parallel to its axis in a rotating electrically conducting fluid.
 Creator

Ruan, Kezhi., Florida State University
 Abstract/Description

In an effort to understand better the flow in the core of the Earth, we investigate the steady rise of an infinitely long vertical rigid cylinder parallel to its axis in a rotating electrically conducting fluid in the presence of uniform prescribed transverse magnetic field. The rotation and magneticfield vectors have arbitrary orientation. We suppose the circular cylinder is forced to rise with a constant speed and investigate the structure of the flow and calculate the drag on the cylinder...
Show moreIn an effort to understand better the flow in the core of the Earth, we investigate the steady rise of an infinitely long vertical rigid cylinder parallel to its axis in a rotating electrically conducting fluid in the presence of uniform prescribed transverse magnetic field. The rotation and magneticfield vectors have arbitrary orientation. We suppose the circular cylinder is forced to rise with a constant speed and investigate the structure of the flow and calculate the drag on the cylinder. The flow structure is found by solving a twodimensional (independent of the axial coordinate) mixed boundary value problem. Approximate analytic solutions for velocity field and perturbed magnetic field are obtained. The buoyancy driven rise speed of the cylinder is calculated. The results are consistent with the those derived from Moore and Saffman (1969) and given by Hasimoto (1960) as limiting cases. The numerical value of dimensional rise speed obtained is in good agreement with the typically quoted rise speed in geophysics.
Show less  Date Issued
 1995, 1995
 Identifier
 AAI9525925, 3088642, FSDT3088642, fsu:77444
 Format
 Document (PDF)
 Title
 An analysis of mushchimney structure.
 Creator

Yang, YoungKyun., Florida State University
 Abstract/Description

When a multicomponent liquid is cooled and solidified, commonly, the solid phase advances from the cold boundary into the liquid as a branching forest of dendritic crystals. This creates a region of mixed solid and liquid phases, referred to as a mushy zone, in which the solid forms a rigidly connected framework with the liquid occurring in the intercrystalline gaps. When the fluid seeps through the dendrites, further freezing occurs which fills in pores of the matrix and reduces its...
Show moreWhen a multicomponent liquid is cooled and solidified, commonly, the solid phase advances from the cold boundary into the liquid as a branching forest of dendritic crystals. This creates a region of mixed solid and liquid phases, referred to as a mushy zone, in which the solid forms a rigidly connected framework with the liquid occurring in the intercrystalline gaps. When the fluid seeps through the dendrites, further freezing occurs which fills in pores of the matrix and reduces its permeability to the liquid flow. In particular, if a binary alloy (for example, NH$\sb4$ClH$\sb2$O solution) is cooled at bottom and a dense component (for example, NH$\sb4$Cl) is solidified, buoyant material released during freezing in the pores returns to the melt only through thin, vertical, but widely separated, 'chimneys', the flow through the matrix between them being organized to supply these chimneys., We presented photos of a mushchimney system obtained from the ammonium chloride experiment, and we studied how convection with horizontal divergence affects the structure and flow of the mushchimney system. We use a simple ODE system in the mush derived by assuming that the temperature depends on vertical coordinate only. We find that the mass fraction of solid increases and the depth of a mush decreases when the strength of convection increases., We present an axisymmetric model containing only one chimney to analyze the structure of the mushchimney system. We find solutions of the temperature, the solid fraction, and the pressure in the chimney wall. In particular, the pressure expression shows that the fluid flow needs a huge pressure in order to pass through the chimney wall if its permeability is very small., We assume that a ratio of composition is large, which allows us to neglect the pressure contribution of the chimney wall. We use the knowledge of the variables in the mush, evaluated on the chimney wall, to find the fluid flow in the chimney and the radius of chimney. Our procedure employs the von KarmanPohlhausen technique for determining chimney flow (Roberts & Loper, 1983) and makes use of the fact that the radius of the chimney is much less than the thickness of the mush. We find a relation between a parameter measuring the ratio of viscous and buoyancy forces in the chimney and the vertical velocity component on the top of the mush, and estimate numerically the value of this velocity measuring the strength of convection. The results obtained show reasonably good agreement with theoretical and experimental works (Roberts & Loper (1983), Chen & Chen (1991), Tait & Jaupart (1992), Hellawell etc. (1993), Worster (1991)).
Show less  Date Issued
 1995, 1995
 Identifier
 AAI9540067, 3088707, FSDT3088707, fsu:77509
 Format
 Document (PDF)
 Title
 An analytical approach to the thermal residual stress problem in fiberreinforced composites.
 Creator

Xie, Zhiyun., Florida State University
 Abstract/Description

A pair of two new tensors called Generalized Plane Strain (GPS) tensors S and D is proposed for the concentric cylindrical inclusion problem. GPS tensors take the fiber volume fraction explicitly into account. When the cylindrical matrix is of infinite radius, tensor S reduces to the appropriate Eshelby's tensor. The GPS tensors provide a convenient form of solution to a class of problems involving eigenstrain, e.g., strain due to thermal expansion, phase transformation, plastic and misfit...
Show moreA pair of two new tensors called Generalized Plane Strain (GPS) tensors S and D is proposed for the concentric cylindrical inclusion problem. GPS tensors take the fiber volume fraction explicitly into account. When the cylindrical matrix is of infinite radius, tensor S reduces to the appropriate Eshelby's tensor. The GPS tensors provide a convenient form of solution to a class of problems involving eigenstrain, e.g., strain due to thermal expansion, phase transformation, plastic and misfit strain. Explicit expressions to evaluate thermal residual stresses in the matrix and the fiber using GPS tensors are developed for metallic/intermetallic matrix composites. Results are compared with Eshelby's infinite domain solution and Finite Element solution for SCS6/Ti24Al11Nb composite. The method of superposition using GPS tensor is proposed for evaluating thermal residual stress distribution in a fiber reinforced composite with periodic arrays. The results compare very favorably with Finite Element solution. GPS tensors are also used in the evaluation of the effective material properties. We demonstrated the approach by studying two fiber reinforced composites, Graphite/Epoxy and Glass/Epoxy composites. A good agreement between analytical results using GPS tensor and experimental data was found. We also compared the results of using GPS tensor along with the original Eshelby's tensor and found that GPS tensor provides a better match with experimental data.
Show less  Date Issued
 1995, 1995
 Identifier
 AAI9526758, 3088646, FSDT3088646, fsu:77448
 Format
 Document (PDF)
 Title
 Doublynullcobordant links.
 Creator

Sun, Biansheng., Florida State University
 Abstract/Description

Throughout, we work in the smooth category. We consider a special class of links and knots in $S\sp3$ which are transverse crosssections of trivial 2spheres in $S\sp4.$ They are called DoublyNullCobordant (DNC) links and DNC knots respectively. Closely related concepts are those of NullCobordant (NC) links and NC knots., We are interested in obtaining necessary conditions satisfied by DNC (NC) links and knots, and in constructing nontrivial links and knots which satisfy these conditions....
Show moreThroughout, we work in the smooth category. We consider a special class of links and knots in $S\sp3$ which are transverse crosssections of trivial 2spheres in $S\sp4.$ They are called DoublyNullCobordant (DNC) links and DNC knots respectively. Closely related concepts are those of NullCobordant (NC) links and NC knots., We are interested in obtaining necessary conditions satisfied by DNC (NC) links and knots, and in constructing nontrivial links and knots which satisfy these conditions., Based on analysis of various linking patterns of NC links, we are able to prove that any Hopf link of $\mu$ components is NC if and only if $\mu$ is odd. Another result obtained in this work is that there exists at least one pair of components of an NC link of an even number of components such that the linking number between these two components is zero. Various methods are employed in the geometric realizations of DNC links of a given number of components; we construct DNC links for any given number of components., The 2fold branched cyclic cover of $S\sp3$ branched along any link plays a fundamental role in detecting whether a given link is DNC or not since the cyclic branched cover embeds in $S\sp4$ if the given link is DNC. Considering the embedding problem of the cyclic branched cover leads to the hyperbolicity problem of the associated linking pairing on the homology of the cyclic branched cover. By investigating the torsion part of the first homology of the rfold cyclic branched cover of the 3sphere branched along a link, we are able to produce infinitely many NC links, none of which are DNC links. When specialized to knots, we also discover infinitely many NC knots, none of which are DNC., We also consider higher dimensional DNC links. We obtain a necessary condition for a higher dimensional link being DNC. Specifically, we prove that if L is a DNC (2m $$ 1)link of $\mu$ components with $m >$ 1, then L has a DNC Seifert matrix for any connected Seifert manifold of L.
Show less  Date Issued
 1995, 1995
 Identifier
 AAI9527942, 3088652, FSDT3088652, fsu:77454
 Format
 Document (PDF)