Conjugation spaces and edges of compatible torus actions

Duistermaat introduced the concept of ``real locus'' of a Hamiltonian manifold. In that and in others' subsequent works, it has been shown that many of the techniques developed in the symplectic category can be used to study real loci, so long as the coefficient ring is restricted to the integers modulo 2. It turns out that these results seem not necessarily to depend on the ambient symplectic structure, but rather to be topological in nature. This observation prompts the definition of ``conjugation space'' in a paper of the two authors with V. Puppe. Our main theorem in this paper gives a simple criterion for recognizing when a topological space is a conjugation space.Comment: 19 page

Explanation Trees for Causal Bayesian Networks

Bayesian networks can be used to extract explanations about the observed state of a subset of variables. In this paper, we ex- plicate the desiderata of an explanation and confront them with the concept of expla- nation proposed by existing methods. The necessity of taking into account causal ap- proaches when a causal graph is available is discussed. We then introduce causal expla- nation trees, based on the construction of ex- planation trees using the measure of causal information flow (Ay and Polani, 2006). This approach is compared to several other meth- ods on known networks

RNA sequencing of early round goby embryos reveals that maternal experiences can shape the maternal RNA contribution in a wild vertebrate

It has been proposed that non-genetic inheritance could promote species fitness. Non-genetic inheritance could allow offspring to benefit from the experience of their parents, and could advocate pre-adaptation to prevailing and potentially selective conditions. Indeed, adaptive parental effects have been modeled and observed, but the molecular mechanisms behind them are far from understood. In the present study, we investigated whether maternal RNA can carry information about environmental conditions experienced by the mother in a wild vertebrate. Maternal RNA directs the development of the early embryo in many non-mammalian vertebrates and invertebrates. However, it is not known whether vertebrate maternal RNA integrates information about the parental environment. We sequenced the maternal RNA contribution from a model that we expected to rely on parental effects: the invasive benthic fish species Neogobius melanostomus (Round Goby). We found that maternal RNA expression levels correlated with the water temperature experienced by the mother before oviposition, and identified temperature-responsive gene groups such as core nucleosome components or the microtubule cytoskeleton. Our findings suggest that the maternal RNA contribution may incorporate environmental information. Maternal RNA should therefore be considered a potentially relevant pathway for non-genetic inheritance. Also, the ability of a species to integrate environmental information in the maternal RNA contribution could potentially contribute to species fitness and may also play a role in extraordinary adaptive success stories of invasive species such as the round goby

Exploiting nonlinear propagation in echo sounders and sonar

The 10th European Conference on Underwater Acoustics (ECUA). 2010, Istanbul, Turkey. Mainstream sonars transmit and receive signals at the same frequency. As water is a nonlinear medium, a propagating signal generates harmonics at multiples of the transmitted frequency. For sonar applications, energy transferred to higher harmonics is seen as a disturbance. To satisfy requirements for calibration of echo sounders in fishery research, input power has to be limited to avoid energy loss to harmonics generation. Can these harmonics be used in sonar imaging? The frequency dependency of target echos, and the different spatial distribution of higher harmonics can contribute to additional information on detected targets in fish classification, ocean bathymetry, or bottom classification. Our starting point was the sonar equation adapted for the second harmonic. We have simulated nonlinear propagation of sound in water, and obtained estimates of received pressure levels of harmonics for a calibration sphere, or a fish as reflector. These pressure profiles were used in the sonar equation to compare harmonics to fundamental signal budget. Our results show that a 200 kHz thermal noise limited echo sounder, with a range of 800 m will reach around 300 m for the second harmonic. This means the second harmonic is useful in many applications

Classification and Casimir Invariants of Lie-Poisson Brackets

We classify Lie-Poisson brackets that are formed from Lie algebra extensions. The problem is relevant because many physical systems owe their Hamiltonian structure to such brackets. A classification involves reducing all brackets to a set of normal forms, and is achieved partially through the use of Lie algebra cohomology. For extensions of order less than five, the number of normal forms is small and they involve no free parameters. We derive a general method of finding Casimir invariants of Lie-Poisson bracket extensions. The Casimir invariants of all low-order brackets are explicitly computed. We treat in detail a four field model of compressible reduced magnetohydrodynamics.Comment: 59 pages, Elsevier macros. To be published in Physica