Temporal and spatial distribution and abundance of flathead sole (Hippoglossoides elassodon) eggs and larvae in the western Gulf of Alaska

Data from ichthyoplankton surveys conducted in 1972 and from 1977 to 1999 (no data were collected in 1980) by the Alaska Fisheries Science Center (NOAA, NMFS) in the western Gulf of Alaska were used to examine the timing of spawning, geographic distribution and abundance, and the vertical distribution of eggs and larvae of flathead sole (Hippoglossoides elassodon). In the western Gulf of Alaska, flathead sole spawning began in early April and peaked from early to mid-May on the continental shelf. It progressed in a southwesterly direction along the Alaska Peninsula where three main areas of flathead sole spawning were indentified: near the Kenai Peninsula, in Shelikof Strait, and between the Shumagin Islands and Unimak Island. Flathead sole eggs are pelagic, and their depth distribution may be a function of their developmental stage. Data from MOCNESS tows indicated that eggs sink near time of hatching and the larvae rise to the surface to feed. The geographic distribution of larvae followed a pattern similar to the distribution of eggs, only it shifted about one month later. Larval abundance peaked from early to mid-June in the southern portion of Shelikof Strait. Biological and environmental factors may help to retain flathead sole larvae on the continental shelf near their juvenile nursery areas

Conformal Parametrisation of Loxodromes by Triples of Circles

We provide a parametrisation of a loxodrome by three specially arranged cycles. The parametrisation is covariant under fractional linear transformations of the complex plane and naturally encodes conformal properties of loxodromes. Selected geometrical examples illustrate the usage of parametrisation. Our work extends the set of objects in Lie sphere geometry---circle, lines and points---to the natural maximal conformally-invariant family, which also includes loxodromes.Comment: 14 pages. 9 PDF in four figures, AMS-LaTe

Frequency-based brain networks: From a multiplex framework to a full multilayer description

We explore how to study dynamical interactions between brain regions using functional multilayer networks whose layers represent the different frequency bands at which a brain operates. Specifically, we investigate the consequences of considering the brain as a multilayer network in which all brain regions can interact with each other at different frequency bands, instead of as a multiplex network, in which interactions between different frequency bands are only allowed within each brain region and not between them. We study the second smallest eigenvalue of the combinatorial supra-Laplacian matrix of the multilayer network in detail, and we thereby show that the heterogeneity of interlayer edges and, especially, the fraction of missing edges crucially modify the spectral properties of the multilayer network. We illustrate our results with both synthetic network models and real data sets obtained from resting state magnetoencephalography. Our work demonstrates an important issue in the construction of frequency-based multilayer brain networks.Comment: 13 pages, 8 figure