Relative Periodic Solutions of the Complex Ginzburg-Landau Equation

A method of finding relative periodic orbits for differential equations with continuous symmetries is described and its utility demonstrated by computing relative periodic solutions for the one-dimensional complex Ginzburg-Landau equation (CGLE) with periodic boundary conditions. A relative periodic solution is a solution that is periodic in time, up to a transformation by an element of the equation's symmetry group. With the method used, relative periodic solutions are represented by a space-time Fourier series modified to include the symmetry group element and are sought as solutions to a system of nonlinear algebraic equations for the Fourier coefficients, group element, and time period. The 77 relative periodic solutions found for the CGLE exhibit a wide variety of temporal dynamics, with the sum of their positive Lyapunov exponents varying from 5.19 to 60.35 and their unstable dimensions from 3 to 8. Preliminary work indicates that weighted averages over the collection of relative periodic solutions accurately approximate the value of several functionals on typical trajectories.Comment: 32 pages, 12 figure

A phase field method for tomographic reconstruction from limited data.

Classical tomographic reconstruction methods fail for problems in which there is extreme temporal and spatial sparsity in the measured data. Reconstruction of coronal mass ejections (CMEs), a space weather phenomenon with potential negative effects on the Earth, is one such problem. However, the topological complexity of CMEs renders recent limited data reconstruction methods inapplicable. We propose an energy function, based on a phase field level set framework, for the joint segmentation and tomographic reconstruction of CMEs from measurements acquired by coronagraphs, a type of solar telescope. Our phase field model deals easily with complex topologies, and is more robust than classical methods when the data are very sparse. We use a fast variational algorithm that combines the finite element method with a trust region variant of Newton’s method to minimize the energy. We compare the results obtained with our model to classical regularized tomography for synthetic CME-like images

Using Motion-Activated Trail Cameras to Study Diet and Productivity of Cliff-Nesting Golden Eagles

Studies of cliff-nesting raptors can be challenging because direct observations of nest contents are difficult. Our goals were to develop a protocol for installing motion-activated trail cameras at Golden Eagle (Aquila chrysaetos) nests to record diet information and productivity, and to estimate prey detection probability using different diet study methods. In 2014 and 2015, we installed cameras at 12 Golden Eagle nests with 18–42-d-old nestlings. Following installation, we monitored adult behavior using direct observation and post-installation image review. At two nests, adult eagles did not return to nests or exhibited behaviors suggesting avoidance of the cameras, but returned to the nests after cameras were removed. We visited the 10 remaining nests every 4 d to collect prey remains and pellets to generate prey-specific detection estimates for both images, and prey remains and pellets. Compared to inspection of prey remains and pellets, cameras recorded twice the number of prey (622 vs. 316), were more likely to detect the smallest and largest prey, and cost half as much. Cameras recorded productivity, fledging dates, and in one case, a nestling death. Trail cameras may be a reliable and cost-effective option to address clearly defined research goals and obtain required information about eagle behavior and nest contents. However, cameras should be used judiciously because installation creates a persistent manipulation at the nest. Camera appearance should be minimized, and post-installation monitoring that allows for timely responses to nest-avoidance behavior by adult eagles is important to prevent adverse effects on nesting success

Abundance of Planktonic Virus-Like Particles in Lake Erie Subsurface Waters

Author Institution: Department of Biological Sciences, Kent State University - Trumbull Campus ; Department of Biological Sciences and Water Resources Research Institute, Kent State UniversityAbundance of virus-like particles (VLP) was determined in Lake Erie subsurface water. The relationship between VLP and the bacterial and phytoplankton communities were investigated. Viral and bacterial numbers were determined using nucleic acid stains and epifluorescent microscopy. Phytoplankton abundance was estimated by chlorophylls extraction. Viral abundance averaged 1.05 x 106 VLP/ml and the ratio of viral to bacterial number was less than 1.0 across most sampling sites and dates. Viral abundance was not correlated with either bacterial abundance or chlorophyll a concentration. Viral abundance was found to be most similar to other Great Lakes and marine systems and dissimilar to other freshwater systems

The utility of twins in developmental cognitive neuroscience research: How twins strengthen the ABCD research design

The ABCD twin study will elucidate the genetic and environmental contributions to a wide range of mental and physical health outcomes in children, including substance use, brain and behavioral development, and their interrelationship. Comparisons within and between monozygotic and dizygotic twin pairs, further powered by multiple assessments, provide information about genetic and environmental contributions to developmental associations, and enable stronger tests of causal hypotheses, than do comparisons involving unrelated children. Thus a sub-study of 800 pairs of same-sex twins was embedded within the overall Adolescent Brain and Cognitive Development (ABCD) design. The ABCD Twin Hub comprises four leading centers for twin research in Minnesota, Colorado, Virginia, and Missouri. Each site is enrolling 200 twin pairs, as well as singletons. The twins are recruited from registries of all twin births in each State during 2006–2008. Singletons at each site are recruited following the same school-based procedures as the rest of the ABCD study. This paper describes the background and rationale for the ABCD twin study, the ascertainment of twin pairs and implementation strategy at each site, and the details of the proposed analytic strategies to quantify genetic and environmental influences and test hypotheses critical to the aims of the ABCD study. Keywords: Twins, Heritability, Environment, Substance use, Brain structure, Brain functio

Pricing European Options with a Log Student's t-Distribution: a Gosset Formula

The distribution of the returns for a stock are not well described by a normal probability density function (pdf). Student's t-distributions, which have fat tails, are known to fit the distributions of the returns. We present pricing of European call or put options using a log Student's t-distribution, which we call a Gosset approach in honour of W.S. Gosset, the author behind the nom de plume Student. The approach that we present can be used to price European options using other distributions and yields the Black-Scholes formula for returns described by a normal pdf.Comment: 12 journal pages, 9 figures and 3 tables (Submitted to Physica A

A phase field method for tomographic reconstruction from limited data

Classical tomographic reconstruction methods fail for problems in which there is extreme temporal and spatial sparsity in the measured data. Reconstruction of coronal mass ejections (CMEs), a space weather phenomenon with potential negative effects on the Earth, is one such problem. However, the topological complexity of CMEs renders recent limited data reconstruction methods inapplicable. We propose an energy function, based on a phase field level set framework, for the joint segmentation and tomographic reconstruction of CMEs from measurements acquired by coronagraphs, a type of solar telescope. Our phase field model deals easily with complex topologies, and is more robust than classical methods when the data are very sparse. We use a fast variational algorithm that combines the finite element method with a trust region variant of Newton’s method to minimize the energy. We compare the results obtained with our model to classical regularized tomography for synthetic CME-like images