Numerical Schemes for Rough Parabolic Equations

This paper is devoted to the study of numerical approximation schemes for a class of parabolic equations on (0, 1) perturbed by a non-linear rough signal. It is the continuation of [8, 7], where the existence and uniqueness of a solution has been established. The approach combines rough paths methods with standard considerations on discretizing stochastic PDEs. The results apply to a geometric 2-rough path, which covers the case of the multidimensional fractional Brownian motion with Hurst index H \textgreater{} 1/3.Comment: Applied Mathematics and Optimization, 201

Mg / Ca and δ18O in living planktic foraminifers from the Caribbean, Gulf of Mexico and Florida Straits

Past ocean temperatures and salinities can be approximated from combined stable oxygen isotopes (δ18O) and Mg ∕ Ca measurements in fossil foraminiferal tests with varying success. To further refine this approach, we collected living planktic foraminifers by net sampling and pumping of sea surface water from the Caribbean Sea, the eastern Gulf of Mexico and the Florida Straits. Analyses of δ18O and Mg ∕ Ca in eight living planktic species (Globigerinoides sacculifer, Orbulina universa, Neogloboquadrina dutertrei, Pulleniatina obliquiloculata, Globorotalia menardii, Globorotalia ungulata, Globorotalia truncatulinoides and Globorotalia tumida) were compared to measured in situ properties of the ambient seawater (temperature, salinity and δ18Oseawater) and fossil tests of underlying surface sediments. “Vital effects” such as symbiont activity and test growth cause δ18O disequilibria with respect to the ambient seawater and a large scatter in foraminiferal Mg ∕ Ca. Overall, ocean temperature is the most prominent environmental influence on δ18Ocalcite and Mg ∕ Ca. Enrichment of the heavier 18O isotope in living specimens below the mixed layer and in fossil tests is clearly related to lowered in situ temperatures and gametogenic calcification. Mg ∕ Ca-based temperature estimates of G. sacculifer indicate seasonal maximum accumulation rates on the seafloor in early spring (March) at Caribbean stations and later in the year (May) in the Florida Straits, related to the respective mixed layer temperatures of ∼26 ∘C. Notably, G. sacculifer reveals a weak positive linear relationship between foraminiferal derived δ18Oseawater estimates and both measured in situ δ18Oseawater and salinity. Our results affirm the applicability of existing δ18O and Mg ∕ Ca calibrations for the reconstruction of past ocean temperatures and δ18Oseawater reflecting salinity due to the convincing accordance of proxy data in both living and fossil foraminifers, and in situ environmental parameters. Large vital effects and seasonally varying proxy signals, however, need to be taken into account

What Do MBA, MLB, and AT&T Have in Common? A Dynamic Off-Campus Application

This Application was designed for undergraduate and graduate marketing management classes. Its premise is to ensure that students receive not only sufficient grounding in theory, but also an opportunity to apply their classroom learning in a marketing rich business environment. AT&T Park, home of the San Francisco Giants, a Major League Baseball (MLB) team, provides one forum for experiencing the marketing concepts that are taught to MBA and BA marketing students. From the branded cup holders in the stadium seats, to the corporate sponsored luxury suites, to the advertisements on the Jumbotron scoreboard, the students are inundated with branding, logos, advertising, public relations, pricing schemes and countless other examples of marketing. This off-campus Application brings marketing to life in a way that cannot be accomplished through lectures, case discussions and projects. There are several goals for this Application. The first is to anchor the key marketing concepts discussed throughout the course. The second is to apply those concepts in a real world environment. The third goal is to provide the experience for students to synthesize what they have learned into a well organized and analytical deliverable in the form of a reflection and research paper. As the marketing industry continues to evolve and reinvent itself, it is important to prepare marketing students to effectively use and understand the tactics, strategies and ideas that comprise this discipline. This Application successfully provides students with an integrative experience for their Marketing Management or Principles of Marketing classes

An integral method for solving nonlinear eigenvalue problems

We propose a numerical method for computing all eigenvalues (and the corresponding eigenvectors) of a nonlinear holomorphic eigenvalue problem that lie within a given contour in the complex plane. The method uses complex integrals of the resolvent operator, applied to at least $k$ column vectors, where $k$ is the number of eigenvalues inside the contour. The theorem of Keldysh is employed to show that the original nonlinear eigenvalue problem reduces to a linear eigenvalue problem of dimension $k$. No initial approximations of eigenvalues and eigenvectors are needed. The method is particularly suitable for moderately large eigenvalue problems where $k$ is much smaller than the matrix dimension. We also give an extension of the method to the case where $k$ is larger than the matrix dimension. The quadrature errors caused by the trapezoid sum are discussed for the case of analytic closed contours. Using well known techniques it is shown that the error decays exponentially with an exponent given by the product of the number of quadrature points and the minimal distance of the eigenvalues to the contour

A Retrospective Study of the Investigation of Homicidal Childhood Asphyxial Deaths

As one of the leading causes of traumatic deaths in newborns, infants, and young children, there is no anatomic or microscopic feature that is pathognomonic for asphyxial deaths. Instead, pathologists rely on investigation information, including confessions and/or witness statements, and potential evidence at the scene. Twenty cases of homicidal newborn, infant, and young children asphyxial deaths were reviewed, which included death and police investigation reports and autopsy reports, as well as histology slides of lung sections. This series of homicidal asphyxial deaths highlight that, in a vast majority of such cases, the final cause and manner of death rulings are dependent on confession by the perpetrator. Furthermore, this series highlights the possible role of histology to help forensic pathologists better certify asphyxial deaths. Finally, this series emphasizes important investigation points and considerations at autopsy during the investigation of asphyxial deaths in newborns, infants, and young children.Peer Reviewedhttps://deepblue.lib.umich.edu/bitstream/2027.42/144651/1/jfo13666_am.pdfhttps://deepblue.lib.umich.edu/bitstream/2027.42/144651/2/jfo13666.pd

Convergence of the stochastic Euler scheme for locally Lipschitz coefficients

Stochastic differential equations are often simulated with the Monte Carlo Euler method. Convergence of this method is well understood in the case of globally Lipschitz continuous coefficients of the stochastic differential equation. The important case of superlinearly growing coefficients, however, has remained an open question. The main difficulty is that numerically weak convergence fails to hold in many cases of superlinearly growing coefficients. In this paper we overcome this difficulty and establish convergence of the Monte Carlo Euler method for a large class of one-dimensional stochastic differential equations whose drift functions have at most polynomial growth.Comment: Published at http://www.springerlink.com/content/g076w80730811vv3 in the Foundations of Computational Mathematics 201

Rapid covariance-based sampling of linear SPDE approximations in the multilevel Monte Carlo method

The efficient simulation of the mean value of a non-linear functional of the solution to a linear stochastic partial differential equation (SPDE) with additive Gaussian noise is considered. A Galerkin finite element method is employed along with an implicit Euler scheme to arrive at a fully discrete approximation of the mild solution to the equation. A scheme is presented to compute the covariance of this approximation, which allows for rapid sampling in a Monte Carlo method. This is then extended to a multilevel Monte Carlo method, for which a scheme to compute the cross-covariance between the approximations at different levels is presented. In contrast to traditional path-based methods it is not assumed that the Galerkin subspaces at these levels are nested. The computational complexities of the presented schemes are compared to traditional methods and simulations confirm that, under suitable assumptions, the costs of the new schemes are significantly lower.Comment: 18 pages, 5 figures; numerical simulations revised, implementation section added; To appear in Monte Carlo and Quasi-Monte Carlo Methods - MCQMC, Rennes, France, July 201