Tematyka Prac Doktorskich, 2015 Wroclaw University of Technology

#### Tematyka Prac Doktorskich, Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Discrete Dynamical Systems In Multiple Target And Alternate Selex, 2015 Iowa State University

#### Discrete Dynamical Systems In Multiple Target And Alternate Selex, Howard A. Levine, Yeon-Jung Seo

*Mathematics Publications*

Dynamical systems are often used to model biochemical and biological processes. In Seo et al. (2010, 2014) we studied two mathematical models of the iterative biochemical procedure known as SELEX (Systematic Evolution of Ligands by EXponential Enrichment): multiple target SELEX and alternate SELEX. It is the purpose of this paper to revisit the mathematics of these processes in the language of dynamical systems on compact manifolds but for a dynamical system on a manifold with compact closure. From the experimentalist's point of view, multiple target SELEX provides a way of obtaining the best binding ligands to a pool of ...

Geometric Limits Of Julia Sets Of Maps Z^N + Exp(2Πiθ) As N → ∞, 2015 Butler University

#### Geometric Limits Of Julia Sets Of Maps Z^N + Exp(2Πiθ) As N → ∞, Scott R. Kaschner, Reaper Romero, David Simmons

*Scholarship and Professional Work - LAS*

We show that the geometric limit as n → ∞ of the Julia sets J(P_{n,c}) for the maps P_{n,c}(z) = z^{n} + c does not exist for almost every c on the unit circle. Furthermore, we show that there is always a subsequence along which the limit does exist and equals the unit circle.

Rational Maps Of Cp^2 With No Invariant Foliation, 2015 Butler University

#### Rational Maps Of Cp^2 With No Invariant Foliation, Scott R. Kaschner, Rodrigo A. Perez, Roland K.W. Roeder

*Scholarship and Professional Work - LAS*

We present simple examples of rational maps of the complex projective plane with equal first and second dynamical degrees and no invariant foliation.

Superstable Manifolds Of Invariant Circles And Codimension-One Böttcher Functions, 2015 Butler University

#### Superstable Manifolds Of Invariant Circles And Codimension-One Böttcher Functions, Scott R. Kaschner, Roland K.W. Roeder

*Scholarship and Professional Work - LAS*

Let f:X ⇢ X be a dominant meromorphic self-map, where X is a compact, connected complex manifold of dimension n>1. Suppose that there is an embedded copy of P1 that is invariant under f, with f holomorphic and transversally superattracting with degree a in some neighborhood. Suppose that f restricted to this line is given by z↦zb, with resulting invariant circle S. We prove that if a≥b, then the local stable manifold Wsloc(S) is real analytic. In fact, we state and prove a suitable localized version that can be useful in wider contexts. We then show ...

Discrete Nonlinear Planar Systems And Applications To Biological Population Models, 2015 Virginia Commonwealth University

#### Discrete Nonlinear Planar Systems And Applications To Biological Population Models, Shushan Lazaryan, Nika Lazaryan, Nika Lazaryan

*Theses and Dissertations*

We study planar systems of difference equations and applications to biological models of species populations. Central to the analysis of this study is the idea of *folding* - the method of transforming systems of difference equations into higher order scalar difference equations. Two classes of second order equations are studied: quadratic fractional and exponential.

We investigate the boundedness and persistence of solutions, the global stability of the positive fixed point and the occurrence of periodic solutions of the quadratic rational equations. These results are applied to a class of linear/rational systems that can be transformed into a quadratic fractional equation ...

Control, Stability, And Qualitative Theory Of Dynamical Systems 2014, 2015 Eastern Mediterranean University

#### Control, Stability, And Qualitative Theory Of Dynamical Systems 2014, Nazim I. Mahmudov, Mark A. Mckibben, Sakthivel Rathinasamy, Yong Ren

*Mathematics Faculty Publications*

No abstract provided.

Symbolic Neutrosophic Theory, 2015 University of New Mexico

#### Symbolic Neutrosophic Theory, Florentin Smarandache

*Mathematics and Statistics Faculty and Staff Publications*

Symbolic (or Literal) Neutrosophic Theory is referring to the use of abstract symbols (i.e. the letters *T, I, F*, or their refined indexed letters *T _{j}, I_{k}, F_{l}*) in neutrosophics.

In the first chapter we extend the dialectical triad thesis-antithesis-synthesis (dynamics of A and antiA, to get a synthesis) to the neutrosophic tetrad thesis-antithesis-neutrothesis-neutrosynthesis (dynamics of A, antiA, and neutA, in order to get a neutrosynthesis).

In the second chapter we introduce the neutrosophic system and neutrosophic dynamic system. A neutrosophic system is a quasi- or –classical system, in the sense that the neutrosophic system deals with ...

Zespół Energii Odnawialnej I Zrównoważonego Rozwoju (Eozr), 2014 Wroclaw University of Technology

#### Zespół Energii Odnawialnej I Zrównoważonego Rozwoju (Eozr), Wojciech M. Budzianowski

*Wojciech Budzianowski*

No abstract provided.

Transients In The Synchronization Of Oscillator Arrays, 2014 Portland State University

#### Transients In The Synchronization Of Oscillator Arrays, Carlos E. Cantos, J. J. P. Veerman

*Mathematics and Statistics Faculty Publications and Presentations*

The purpose of this note is threefold. First we state a few conjectures that allow us to rigorously derive a theory which is asymptotic in N (the number of agents) that describes transients in large arrays of (identical) linear damped harmonic oscillators in R with completely decentralized nearest neighbor interaction. We then use the theory to establish that in a certain range of the parameters transients grow linearly in the number of agents (and faster outside that range). Finally, in the regime where this linear growth occurs we give the constant of proportionality as a function of the signal velocities ...

Exact Tests For Singular Network Data, 2014 Portland State University

#### Exact Tests For Singular Network Data, Ian H. Dinwoodie, Kruti Pandya

*Mathematics and Statistics Faculty Publications and Presentations*

We propose methodology for exact statistical tests of hypotheses for models of network dynamics. The methodology formulates Markovian exponential families, then uses sequential importance sampling to compute expectations within basins of attraction and within level sets of a sufficient statistic for an over-dispersion model. Comparisons of hypotheses can be done conditional on basins of attraction. Examples are presented.

Mathematical Methods Of Analysis For Control And Dynamic Optimization Problems On Manifolds, 2014 Western Michigan University

#### Mathematical Methods Of Analysis For Control And Dynamic Optimization Problems On Manifolds, Robert J. Kipka

*Dissertations*

Mathematical Methods Of Analysis For Control And Dynamic Optimization Problems On Manifolds Driven by applications in fields such as robotics and satellite attitude control, as well as by a need for the theoretical development of appropriate tools for the analysis of geometric systems, problems of control of dynamical systems on manifolds have been studied intensively during the past three decades. In this dissertation we suggest new mathematical techniques for the study of control and dynamic optimization problems on manifolds. This work has several components including: an extension of the classical Chronological Calculus to control and dynamical systems which are merely ...

Vanishing Configurations In Network Dynamics With Asynchronous Updates, 2014 Portland State University

#### Vanishing Configurations In Network Dynamics With Asynchronous Updates, Ian H. Dinwoodie

*Mathematics and Statistics Faculty Publications and Presentations*

We consider Boolean dynamics for biological networks where stochasticity is introduced through asynchronous updates. An exact method is given for finding states which can reach a steady state with positive probability, and a method is given for finding states which cannot reach other steady states. These methods are based on computational commutative algebra. The algorithms are applied to dynamics of a cell survival network to determine node assignments that exclude termination in a cancerous state

High Precision Rapid Convergence Of Asian Options, 2014 Utah State University

#### High Precision Rapid Convergence Of Asian Options, Mario Y. Harper

*Mario Yuuji Harper*

We show various methods that increase the precision and convergence speed of simulated stochastic processes. We demonstrate our precision and speed by using an example from the finance world, namely that of an Asian Option. An Asian Option is a path dependent pricing mechanism that is normally priced using Monte Carlo methods, it can be thought of as a path dependent diffusion equation. We show that the precision of the simulations is increased by 70% using Control Variates (derived by approximating the true mean from an analytic closed form solution). Using sequential Monte Carlo and parallel computing across a GPU ...

Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, 2014 Marshall University

#### Stochastic Modeling Of Energy Commodity Spot Price Processes With Delay In Volatility, Olusegun Michael Otunuga, Gangaram S. Ladde

*Mathematics Faculty Research*

Employing basic economic principles, we systematically develop both deterministic and stochastic dynamic models for the log-spot price process of energy commodity. Furthermore, treating a diﬀusion coeﬃcient parameter in the non-seasonal log-spot price dynamic system as a stochastic volatility functional of log-spot price, an interconnected system of stochastic model for log-spot price, expected log-spot price and hereditary volatility process is developed. By outlining the risk-neutral dynamics and pricing, suﬃcient conditions are given to guarantee that the risk-neutral dynamic model is equivalent to the developed model. Furthermore, it is shown that the expectation of the square of volatility under the risk-neutral measure ...

Bayes, Brains & Babies: Electrophysiology And Mathematics Of Infant Holistic Processing And Selective Inhibition, 2014 University of Tennessee - Knoxville

#### Bayes, Brains & Babies: Electrophysiology And Mathematics Of Infant Holistic Processing And Selective Inhibition, Matthew Singh

*EURēCA: Exhibition of Undergraduate Research and Creative Achievement*

No abstract provided.

Dynamics Of Traveling Waves In Neural Networks In Presence Of Period Inhomogeneities, 2014 Georgia State University

#### Dynamics Of Traveling Waves In Neural Networks In Presence Of Period Inhomogeneities, Rosahn Bhattarai

*Georgia State Undergraduate Research Conference*

No abstract provided.

Basins Of Attraction For Pulse-Coupled Oscillators, 2014 College of William and Mary

#### Basins Of Attraction For Pulse-Coupled Oscillators, Ryan Gryder

*Undergraduate Honors Theses*

Basins of attraction for forward invariant sets can carve out portions of phase space where one can make predictions for asymptotic dynamics. We present com- putational algorithms for computing inner approximations of basins of attraction for discrete-time dynamical systems. The algorithms, based on subdivision tech- niques for grid construction and outer approximation of images, are adaptive and eciently allow one to identify full dimensional portions of phase space where the asymptotic dynamics may be described quantitatively. As illustration, we apply the techniques to a system of three pulse-coupled oscillators, computing an inner approximation for the basin of attraction for the ...

Euler-Poincar´E Equations For G-Strands, 2014 Imperial College London

#### Euler-Poincar´E Equations For G-Strands, Darryl Holm, Rossen Ivanov

*Conference papers*

The G-strand equations for a map R×R into a Lie group G are associated to a G-invariant Lagrangian. The Lie group manifold is also the configuration space for the Lagrangian. The G-strand itself is the map g(t,s):R×R→G, where t and s are the independent variables of the G-strand equations. The Euler-Poincar'e reduction of the variational principle leads to a formulation where the dependent variables of the G-strand equations take values in the corresponding Lie algebra g and its co-algebra, g^{∗} with respect to the pairing provided by the variational derivatives of the Lagrangian ...

Can A Falling Bullet Kill You?, 2014 California Polytechnic State University - San Luis Obispo

#### Can A Falling Bullet Kill You?, Zechariah Thurman

*Zechariah Thurman*

A terminal velocity examination of the problem of the falling bullet is investigated.