Eigenvector localization in the heavy-tailed random conductance model

We generalize our former localization result about the principal Dirichlet eigenvector of the i.i.d. heavy-tailed random conductance Laplacian to the first $k$ eigenvectors. We overcome the complication that the higher eigenvectors have fluctuating signs by invoking the Bauer-Fike theorem to show that the $k$th eigenvector is close to the principal eigenvector of an auxiliary spectral problem.Comment: 14 pages. Generalizes the results of article arXiv:1608.02415 to higher order eigenvectors. For better readability, we have copied the main definition

The fractional p-Laplacian emerging from homogenization of the random conductance model with degenerate ergodic weights and unbounded-range jumps

We study a general class of discrete $p$-Laplace operators in the random conductance model with long-range jumps and ergodic weights. Using a variational formulation of the problem, we show that under the assumption of bounded first moments and a suitable lower moment condition on the weights, the homogenized limit operator is a fractional $p$-Laplace operator. Under strengthened lower moment conditions, we can apply our insights also to the spectral homogenization of the discrete Laplace operator to the continuous fractional Laplace operator

Dynamical localization and eigenstate localization in trap models

The one-dimensional random trap model with a power-law distribution of mean sojourn times exhibits a phenomenon of dynamical localization in the case where diffusion is anomalous: The probability to find two independent walkers at the same site, as given by the participation ratio, stays constant and high in a broad domain of intermediate times. This phenomenon is absent in dimensions two and higher. In finite lattices of all dimensions the participation ratio finally equilibrates to a different final value. We numerically investigate two-particle properties in a random trap model in one and in three dimensions, using a method based on spectral decomposition of the transition rate matrix. The method delivers a very effective computational scheme producing numerically exact results for the averages over thermal histories and initial conditions in a given landscape realization. Only a single averaging procedure over disorder realizations is necessary. The behavior of the participation ratio is compared to other measures of localization, as for example to the states' gyration radius, according to which the dynamically localized states are extended. This means that although the particles are found at the same site with a high probability, the typical distance between them grows. Moreover the final equilibrium state is extended both with respect to its gyration radius and to its Lyapunov exponent. In addition, we show that the phenomenon of dynamical localization is only marginally connected with the spectrum of the transition rate matrix, and is dominated by the properties of its eigenfunctions which differ significantly in dimensions one and three.Comment: 10 pages, 10 figures, submitted to EPJ

Localization of the principal Dirichlet eigenvector in the heavy-tailed random conductance model

We study the asymptotic behavior of the principal eigenvector and eigenvalue of the random conductance Laplacian in a large domain of Zd (d ≥ 2) with zero Dirichlet condition. We assume that the conductances w are positive i.i.d.\ random variables, which fulfill certain regularity assumptions near zero. If γ = \sup \{ q ≥ 0; \E [w^{-q}]<∞ \}<¼, then we show that for almost every environment the principal Dirichlet eigenvector asymptotically concentrates in a single site and the corresponding eigenvalue scales subdiffusively. The threshold γ{\rm c} = ¼ is sharp. Indeed, other recent results imply that for γ>¼ the top of the Dirichlet spectrum homogenizes. Our proofs are based on a spatial extreme value analysis of the local speed measure, Borel-Cantelli arguments, the Rayleigh-Ritz formula, results from percolation theory, and path arguments

Violation of Women's Reproductive Rights : The Doctrine, Laws, and Habits that Create the Foundation of Our Sexist Culture

The purpose of this written report of my thesis is to discuss the visual element presented as partial fulfillment of the Master of Fine Arts degree. My creative work proposes a dialogue about the violation of women's reproductive rights in our culture. I am focusing on the inequalities set in place for all women through the interweaving of religion, politics, and visual culture.  The extended scope of the church's belief system is fueled by the media and threads itself throughout our politics affecting all women in our culture. My visual work specifically addresses the church's intrusion into women's reproductive rights. In my creative work, I juxtapose iconic symbols of the Catholic Church with contraceptives, not only to show the violation of women but also, the way in which power is abused.  M.F.A

Hypothesis for heritable, anti-viral immunity in crustaceans and insects

Correction to Flegel, TW: Hypothesis for heritable, anti-viral immunity in crustaceans and insects. Biology Direct 2009, 4:32

Smart Grant Writing Project

“The estimated cost burden to the Minnesota K-12 system due to children entering kindergarten unprepared for school success is about $113 million annually” (Chase, Coffee-Borden, Anton, Morre, and Valorose, 2008, pg. 1). These delays in school readiness can lead to continued achievement gaps throughout a child’s academic career (Gonzali-Lee and Mueller, 2010). One way to decrease that achievement gap is through offering innovative early intervention programming to increase readiness skills before kindergarten. Hand in Hand Preschool, located in Northfield, MN is a preschool that is continuously looking for ways to increase all students’ readiness skills. One such program that increases student readiness skills is Stimulating Maturity Through Accelerated Readiness Training (SMART). This program is a multi-sensory based curriculum designed to increase readiness skills through utilizing movement to stimulate the brain. Implementation of this program has the potential to help all children including those who have special needs and those who are typically developing. The barrier to the implementation of SMART in Hand in Hand Preschool is funding for training of teachers in SMART and equipment needed. This problem led the author to research and develop a grant proposal for Hand in Hand Preschool teachers to attend the training and obtain equipment for the initiation of the SMART program. The research of this scholarly project includes the background and basis of the SMART program along with the processes involved with developing a grant proposal. The activities/methodology includes the actions that were taken to write a grant proposal for the SMART program. The product of this project is a grant proposal that was submitted for full funding of the SMART program for Hand in Hand Preschool

Fraud Detection from a Business Perspective: Future Directions and Challenges

This contribution summarizes the state of the art of fraud detection in practice and shows the relations between the technology for fraud detection and intrusion detection. We identify prospective directions for further investigation and imminent challenges