266 research outputs found
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
Mgâ/âCa and ÎŽ18O 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 (ÎŽ18O) and MgâââCa 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 ÎŽ18O and MgâââCa 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 ÎŽ18Oseawater) and fossil tests of underlying surface sediments. âVital effectsâ such as symbiont activity and test growth cause ÎŽ18O disequilibria with respect to the ambient seawater and a large scatter in foraminiferal MgâââCa. Overall, ocean temperature is the most prominent environmental influence on ÎŽ18Ocalcite and MgâââCa. 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. MgâââCa-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 âŒ26ââC. Notably, G. sacculifer reveals a weak positive linear relationship between foraminiferal derived ÎŽ18Oseawater estimates and both measured in situ ÎŽ18Oseawater and salinity. Our results affirm the applicability of existing ÎŽ18O and MgâââCa calibrations for the reconstruction of past ocean temperatures and ÎŽ18Oseawater 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 column vectors,
where 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 .
No initial approximations of eigenvalues and eigenvectors are needed. The
method is particularly suitable for moderately large eigenvalue problems where
is much smaller than the matrix dimension. We also give an extension of the
method to the case where 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
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