Closed forms and multi-moment maps

We extend the notion of multi-moment map to geometries defined by closed forms of arbitrary degree. We give fundamental existence and uniqueness results and discuss a number of essential examples, including geometries related to special holonomy. For forms of degree four, multi-moment maps are guaranteed to exist and are unique when the symmetry group is (3,4)-trivial, meaning that the group is connected and the third and fourth Lie algebra Betti numbers vanish. We give a structural description of some classes of (3,4)-trivial algebras and provide a number of examples.Comment: 36 page

Assessing ecosystem services from multifunctional trees in pastures using Bayesian belief networks

A Bayesian belief network (BBN) was developed to assess preferred combinations of trees in live fences and on pastures in silvopastoral systems. The BBN was created with information from Rivas, Nicaragua, using local farmer knowledge on tree species, trees' costs and benefits, farmers' expressed needs and aspirations, and scientific knowledge regarding tree functional traits and their contribution to ecosystem services and benefits. The model identifies combinations of trees, which provide multiple ecosystem services from pastures, improving their productivity and contribution to farmer livelihoods. We demonstrate how the identification of portfolios of multifunctional trees can satisfy a profile of desired ecosystem services prioritized by the farmer. Diagnostics using Bayesian inference starts with an identification of farmer needs and ‘works backwards’ to identify a silvopastoral system structure. We conclude that Bayesian belief networks are a promising modeling technique for multi-criteria decisions in farm adaptation processes, where interventions must be adapted to specific contexts and farmer preferences

Influence of Salt on the Solution Dynamics of a Phosphorylcholine-Based Polyzwitterion

The diffusion of a polyzwitterion, poly(2-methacryloyloxyethyl phosphorylcholine) (PMPC), in aqueous solution containing different alkali halides was studied by fluorescence correlation spectroscopy at single molecule level. It was found that the halide anion has a greater effect on the radius of zwitterionic PMPC molecules than alkali cations, which is due to the mechanism by which PMPC molecules interact with the surrounding hydrogen bond network of water molecules and adsorbed ions. With the addition of salt, the size of PMPC remains constant while its diffusion coefficient is reduced slightly, although larger cations (e.g. K+) result in slightly increased diffusion coefficient for 1 M potassium chloride-based solutions. This enhanced diffusion coefficient is attributed to the decrease in the viscosity of the aqueous solution on the addition of salt. When the counter-ion was varied in potassium-based salts, different effects were observed for different anions, resulting a reduction in the diffusion coefficient as a function of salt concentration. This reduction was modest for KBr, but significant for KI. Overall, no discernible changes were observed as the size of the PMPC coil was varied, except in case of KI for which a significant increase was observed at higher ionic strength. Divalent cations (Ca2+ and Mg2+), produced similar effects to those found for monovalent cations. These effects are explained by the interaction of PMPC with the hydrogen bond network of water molecules and with the adsorbed ions

Live cell tracking of symmetry break in actin cytoskeleton triggered by abrupt changes in micromechanical environments

With the aid of stimulus-responsive hydrogel substrates composed of ABA triblock copolymer micelles, we monitored the morphological dynamics of myoblast (C2C12) cells in response to an abrupt change in the substrate elasticity by live cell imaging. The remodeling of actin cytoskeletons could be monitored by means of transient transfection with LifeAct-GFP. Dynamic changes in the orientational order of actin filaments were characterized by an order parameter, which enables one to generalize the mechanically induced actin cytoskeletons as a break of symmetry. The critical role that acto-myosin complexes play in the morphological transition was verified by the treatment of cells with myosin II inhibitor (blebbistatin) and the fluorescence localization of focal adhesion contacts. Such dynamically tunable hydrogels can be utilized as in vitro cellular micro-environments that can exert time-dependent stimuli to mechanically regulate target cells

On Higher Order Gravities, Their Analogy to GR, and Dimensional Dependent Version of Duff's Trace Anomaly Relation

An almost brief, though lengthy, review introduction about the long history of higher order gravities and their applications, as employed in the literature, is provided. We review the analogous procedure between higher order gravities and GR, as described in our previous works, in order to highlight its important achievements. Amongst which are presentation of an easy classification of higher order Lagrangians and its employment as a \emph{criteria} in order to distinguish correct metric theories of gravity. For example, it does not permit the inclusion of only one of the second order Lagrangians in \emph{isolation}. But, it does allow the inclusion of the cosmological term. We also discuss on the compatibility of our procedure and the Mach idea. We derive a dimensional dependent version of Duff's trace anomaly relation, which in \emph{four}-dimension is the same as the usual Duff relation. The Lanczos Lagrangian satisfies this new constraint in \emph{any} dimension. The square of the Weyl tensor identically satisfies it independent of dimension, however, this Lagrangian satisfies the previous relation only in three and four dimensions.Comment: 30 pages, added reference

Friedmann Equation and Stability of Inflationary Higher Derivative Gravity

Stability analysis on the De Sitter universe in pure gravity theory is known to be useful in many aspects. We first show how to complete the proof of an earlier argument based on a redundant field equation. It is shown further that the stability condition applies to $k \ne 0$ Friedmann-Robertson-Walker spaces based on the non-redundant Friedmann equation derived from a simple effective Lagrangian. We show how to derive this expression for the Friedmann equation of pure gravity theory. This expression is also generalized to include scalar field interactions.Comment: Revtex, 6 pages, Add two more references, some typos correcte

Libxc: a library of exchange and correlation functionals for density functional theory

The central quantity of density functional theory is the so-called exchange-correlation functional. This quantity encompasses all non-trivial many-body effects of the ground-state and has to be approximated in any practical application of the theory. For the past 50 years, hundreds of such approximations have appeared, with many successfully persisting in the electronic structure community and literature. Here, we present a library that contains routines to evaluate many of these functionals (around 180) and their derivatives.Comment: 15 page

Hamiltonian dynamics and Noether symmetries in Extended Gravity Cosmology

We discuss the Hamiltonian dynamics for cosmologies coming from Extended Theories of Gravity. In particular, minisuperspace models are taken into account searching for Noether symmetries. The existence of conserved quantities gives selection rule to recover classical behaviors in cosmic evolution according to the so called Hartle criterion, that allows to select correlated regions in the configuration space of dynamical variables. We show that such a statement works for general classes of Extended Theories of Gravity and is conformally preserved. Furthermore, the presence of Noether symmetries allows a straightforward classification of singularities that represent the points where the symmetry is broken. Examples of nonminimally coupled and higher-order models are discussed.Comment: 20 pages, Review paper to appear in EPJ