Showing 1 - 10 of 94 Items
Tree-based language complexity of Thompson's group F
Date: 2015-11-01
Creator: Jennifer Taback, Sharif Younes
Access: Open access
- The definition of graph automatic groups by Kharlampovich, Khoussainov and Miasnikov and its extension to C-graph automatic by Elder and the first author raise the question of whether Thompson's group F is graph automatic. We define a language of normal forms based on the combinatorial "caret types", which arise when elements of F are considered as pairs of finite rooted binary trees. The language is accepted by a finite state machine with two counters, and forms the basis of a 3-counter graph automatic structure for the group.
On the sign representations for the complex reflection groups G(r, p, n)
Date: 2016-11-01
Creator: Aba Mbirika, Thomas Pietraho, William Silver
Access: Open access
- We present a formula for the values of the sign representations of a complex reflection group G(r, p, n) in terms of its image under a generalized Robinson–Schensted algorithm.
Dark breathers in granular crystals
Date: 2013-04-08
Creator: C. Chong, P. G. Kevrekidis, G. Theocharis, Chiara Daraio
Access: Open access
- We present a study of the existence, stability, and bifurcation structure of families of dark breathers in a one-dimensional uniform chain of spherical beads under static load. A defocusing nonlinear Schrödinger equation (NLS) is derived for frequencies that are close to the edge of the phonon band and is used to construct targeted initial conditions for numerical computations. Salient features of the system include the existence of large amplitude solutions that emerge from the small amplitude solutions described by the NLS equation, and the presence of a nonlinear instability that, to the best of the authors' knowledge, has not been observed in classical Fermi-Pasta-Ulam lattices. Finally, it is also demonstrated that these dark breathers can be detected in a physically realistic experimental settings by merely actuating the ends of an initially at rest chain of beads and inducing destructive interference between their signals. © 2013 American Physical Society.
Multistable solitons in the cubic-quintic discrete nonlinear Schrödinger equation
Date: 2006-04-01
Creator: R. Carretero-González, J. D. Talley, C. Chong, B. A. Malomed
Access: Open access
- We analyze the existence and stability of localized solutions in the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with a combination of competing self-focusing cubic and defocusing quintic onsite nonlinearities. We produce a stability diagram for different families of soliton solutions that suggests the (co)existence of infinitely many branches of stable localized solutions. Bifurcations that occur with an increase in the coupling constant are studied in a numerical form. A variational approximation is developed for accurate prediction of the most fundamental and next-order solitons, together with their bifurcations. Salient properties of the model, which distinguish it from the well-known cubic DNLS equation, are the existence of two different types of symmetric solitons and stable asymmetric soliton solutions that are found in narrow regions of the parameter space. The asymmetric solutions appear from and disappear back into the symmetric ones via loops of forward and backward pitchfork bifurcations. © 2006 Elsevier Ltd. All rights reserved.
A relation for domino robinson-schensted algorithms
Date: 2010-01-01
Creator: Thomas Pietraho
Access: Open access
- We describe a map relating hyperoctahedral Robinson-Schensted algorithms on standard domino tableaux of unequal rank. Iteration of this map relates the algorithms defined by Garfinkle and Stanton-White and when restricted to involutions, this construction answers a question posed by van Leeuwen. The principal technique is derived from operations defined on standard domino tableaux by Garfinkle which must be extended to this more general setting. © Birkhäuser Verlag Basel/Switzerland 2009.
The Current Support Theorem in Context
Date: 2023-01-01
Creator: Ethan Winters
Access: Open access
- This work builds up the theory surrounding a recent result of Erlandsson, Leininger, and Sadanand: the Current Support Theorem. This theorem states precisely when a hyperbolic cone metric on a surface is determined by the support of its Liouville current. To provide background for this theorem, we will cover hyperbolic geometry and hyperbolic surfaces more generally, cone surfaces, covering spaces of surfaces, the notion of an orbifold, and geodesic currents. A corollary to this theorem found in the original paper is discussed which asserts that a surface with more than $32(g-1)$ cone points must be rigid. We extend this result to the case that there are more than $3(g-1)$ cone points. An infinite family of cone surfaces which are not rigid and which have precisely $3(g-1)$ cone points is also provided, hence demonstrating tightness.
Dispersive Shock Waves in Granular Chains This record is embargoed.
- Embargo End Date: 2026-05-18
Date: 2023-01-01
Creator: Ari Geisler
Access: Embargoed
A Comprehensive Survey on Functional Approximation
Date: 2022-01-01
Creator: Yucheng Hua
Access: Open access
- The theory of functional approximation has numerous applications in sciences and industry. This thesis focuses on the possible approaches to approximate a continuous function on a compact subset of R2 using a variety of constructions. The results are presented from the following four general topics: polynomials, Fourier series, wavelets, and neural networks. Approximation with polynomials on subsets of R leads to the discussion of the Stone-Weierstrass theorem. Convergence of Fourier series is characterized on the unit circle. Wavelets are introduced following the Fourier transform, and their construction as well as ability to approximate functions in L2(R) is discussed. At the end, the universal approximation theorem for artificial neural networks is presented, and the function representation and approximation with single- and multilayer neural networks on R2 is constructed.
Extreme Value Theory and Backtest Overfitting in Finance
Date: 2015-05-01
Creator: Daniel C Byrnes
Access: Open access
- In order to identify potentially profitable investment strategies, hedge funds and asset managers can use historical market data to simulate a strategy's performance, a process known as backtesting. While the abundance of historical stock price data and powerful computing technologies has made it feasible to run millions of simulations in a short period of time, this process may produce statistically insignificant results in the form of false positives. As the number of configurations of a strategy increases, it becomes more likely that some of the configurations will perform well by chance alone. The phenomenon of backtest overfitting occurs when a model interprets market idiosyncrasies as signal rather than noise, and is often not taken into account in the strategy selection process. As a result, the finance industry and academic literature are rife with skill-less strategies that have no capability of beating the market. This paper explores the development of a minimum criterion that managers and investors can use during the backtesting process in order to increase confidence that a strategy's performance is not the result of pure chance. To do this we will use extreme value theory to determine the probability of observing a specific result, or something more extreme than this result, given that multiple configurations of a strategy were tested.
A Bayesian hierarchical mixture model with continuous-time Markov chains to capture bumblebee foraging behavior
Date: 2021-01-01
Creator: Max Thrush Hukill
Access: Open access
- The standard statistical methodology for analyzing complex case-control studies in ethology is often limited by approaches that force researchers to model distinct aspects of biological processes in a piecemeal, disjointed fashion. By developing a hierarchical Bayesian model, this work demonstrates that statistical inference in this context can be done using a single coherent framework. To do this, we construct a continuous-time Markov chain (CTMC) to model bumblebee foraging behavior. To connect the experimental design with the CTMC, we employ a mixture model controlled by a logistic regression on the two-factor design matrix. We then show how to infer these model parameters from experimental data using Markov chain Monte Carlo and interpret the results from a motivating experiment.