A general method for finding extremal states of Hamiltonian dynamical systems, with applications to perfect fluids

In addition to the Hamiltonian functional itself, non-canonical Hamiltonian dynamical systems generally possess integral invariants known as ‘Casimir functionals’. In the case of the Euler equations for a perfect fluid, the Casimir functionals correspond to the vortex topology, whose invariance derives from the particle-relabelling symmetry of the underlying Lagrangian equations of motion. In a recent paper, Vallis, Carnevale & Young (1989) have presented algorithms for finding steady states of the Euler equations that represent extrema of energy subject to given vortex topology, and are therefore stable. The purpose of this note is to point out a very general method for modifying any Hamiltonian dynamical system into an algorithm that is analogous to those of Vallis etal. in that it will systematically increase or decrease the energy of the system while preserving all of the Casimir invariants. By incorporating momentum into the extremization procedure, the algorithm is able to find steadily-translating as well as steady stable states. The method is applied to a variety of perfect-fluid systems, including Euler flow as well as compressible and incompressible stratified flow.

Non-ergodicity of inviscid two-dimensional flow on a beta-plane and on the surface of a rotating sphere

It is shown that, for a sufficiently large value of β, two-dimensional flow on a doubly-periodic beta-plane cannot be ergodic (phase-space filling) on the phase-space surface of constant energy and enstrophy. A corresponding result holds for flow on the surface of a rotating sphere, for a sufficiently rapid rotation rate Ω. This implies that the higher-order, non-quadratic invariants are exerting a significant influence on the statistical evolution of the flow. The proof relies on the existence of a finite-amplitude Liapunov stability theorem for zonally symmetric basic states with a non-vanishing absolute-vorticity gradient. When the domain size is much larger than the size of a typical eddy, then a sufficient condition for non-ergodicity is that the wave steepness ε < 1, where ε = 2[surd radical]2Z/βU in the planar case and $\epsilon = 2^{\frac{1}{4}} a^{\frac{5}{2}}Z^{\frac{7}{4}}/\Omega U^{\frac{5}{2}}$ in the spherical case, and where Z is the enstrophy, U the r.m.s. velocity, and a the radius of the sphere. This result may help to explain why numerical simulations of unforced beta-plane turbulence (in which ε decreases in time) seem to evolve into a non-ergodic regime at large scales.

Flexibility of representational states in working memory

The relationship between working memory (WM) and attention is a highly interdependent one, with evidence that attention determines the state in which items in WM are retained. Through focusing of attention, an item might be held in a more prioritized state, commonly termed as the focus of attention (FOA). The remaining items, although still retrievable, are considered to be in a different representational state. One means to bring an item into the FOA is to use retrospective cues (‘retro-cues’) which direct attention to one of the objects retained in WM. Alternatively, an item can enter a privileged state once attention is directed towards it through bottom-up influences (e.g. recency effect) or by performing an action on one of the retained items (‘incidental’ cueing). In all these cases, the item in the FOA is recalled with better accuracy compared to the other items in WM. Far less is known about the nature of the other items in WM and whether they can be flexibly manipulated in and out of the FOA. We present data from three types of experiments as well as transcranial magnetic stimulation to early visual cortex to manipulate the item inside FOA. Taken together, our results suggest that the context in which items are retained in WM matters. When an item remains behaviourally relevant, despite not being inside the FOA, re-focusing attention upon it can increase its recall precision. This suggests that a non-FOA item can be held in a state in which it can be later retrieved. However, if an item is rendered behaviourally unimportant because it is very unlikely to be probed, it cannot be brought back into the FOA, nor recalled with high precision. Under such conditions, some information appears to be irretrievably lost from WM. These findings, obtained from several different methods, demonstrate quite considerable flexibility with which items in WM can be represented depending upon context. They have important consequences for emerging state-dependent models of WM.

Direct observation by time-resolved infrared spectroscopy of the bright and the dark excited states of the [Ru(phen)2(dppz)]2+ light-switch compound in solution and when bound to DNA

The [Ru(phen)2(dppz)]2+ complex (1) is non-emissive in water but is highly luminescent in organic solvents or when bound to DNA, making it a useful probe for DNA binding. To date, a complete mechanistic explanation for this “light-switch” effect is still lacking. With this in mind we have undertaken an ultrafast time resolved infrared (TRIR) study of 1 and directly observe marker bands between 1280–1450 cm-1, which characterise both the emissive “bright” and the non-emissive “dark” excited states of the complex, in CD3CN and D2O respectively. These characteristic spectral features are present in the [Ru(dppz)3]2+ solvent light-switch complex but absent in [Ru(phen)3]2+, which is luminescent in both solvents. DFT calculations show that the vibrational modes responsible for these characteristic bands are predominantly localised on the dppz ligand. Moreover, they reveal that certain vibrational modes of the “dark” excited state couple with vibrational modes of two coordinating water molecules, and through these to the bulk solvent, thus providing a new insight into the mechanism of the light-switch effect. We also demonstrate that the marker bands for the “bright” state are observed for both L- and D enantiomers of 1 when bound to DNA and that photo-excitation of the complex induces perturbation of the guanine and cytosine carbonyl bands. This perturbation is shown to be stronger for the L enantiomer, demonstrating the different binding site properties of the two enantiomers and the ability of this technique to determine the identity and nature of the binding site of such intercalators.

Non-genomic actions of estrogens and their interaction with genomic actions in the brain

Ligands for the nuclear receptor superfamily have at least two mechanisms of action: (a) classical transcriptional regulation of target genes (genomic mechanisms); and (b) non-genomic actions, which are initiated at the cell membrane, which could also impact transcription. Though transcriptional mechanisms are increasingly well understood, membrane-initiated actions of these ligands are incompletely understood. This has led to considerable debate over the physiological relevance of membrane-initiated actions of hormones versus genomic actions of hormones, with genomic actions predominating in the endocrine field. There is good evidence that the membrane-limited actions of hormones, particularly estrogens, involve the rapid activation of kinases and the release of calcium and that these are linked to physiologically relevant scenarios in the brain. We show evidence in this review, that membrane actions of estrogens, which activate these rapid signaling cascades, can also potentiate nuclear transcription in both the central nervous system and in non-neuronal cell lines. We present a theoretical scenario which can be used to understand this phenomenon. These signaling cascades may occur in parallel or in series but subsequently, converge at the modification of transcriptionally relevant molecules such as nuclear receptors and/or coactivators. In addition, other non-cognate hormones or neurotransmitters may also activate cascades to crosstalk with estrogen receptor-mediated transcription, though the relevance of this is less clear. The idea that coupling between membrane-initiated and genomic actions of hormones is a novel idea in neuroendocrinology and provides us with a unified view of hormone action in the central nervous system.

Membrane-initiated non-genomic signaling by estrogens in the hypothalamus: cross-talk with glucocorticoids with implications for behavior

The estrogen receptor and glucocorticoid receptor are members of the nuclear receptor superfamily that can signal using both non-genomic and genomic transcriptional modes. Though genomic modes of signaling have been well characterized and several behaviors attributed to this signaling mechanism, the physiological significance of non-genomic modes of signaling has not been well understood. This has partly been due to the controversy regarding the identity of the membrane ER (mER) or membrane GR (mGR) that may mediate rapid, non-genomic signaling and the downstream signaling cascades that may result as a consequence of steroid ligands binding the mER or the mGR. Both estrogens and glucocorticoids exert a number of actions on the hypothalamus, including feedback. This review focuses on the various candidates for the mER or mGR in the hypothalamus and the contribution of non-genomic signaling to classical hypothalamically driven behaviors and changes in neuronal morphology. It also attempts to categorize some of the possible functions of non-genomic signaling at both the cellular level and at the organismal level that are relevant for behavior, including some behaviors that are regulated by both estrogens and glucocorticoids in a potentially synergistic manner. Lastly, it attempts to show that steroid signaling via non-genomic modes may provide the organism with rapid behavioral responses to stimuli.