Semicrossed Products of Operator Algebras by Semigroups

We examine the semicrossed products of a semigroup action by $*$-endomorphisms on a C*-algebra, or more generally of an action on an arbitrary operator algebra by completely contractive endomorphisms. The choice of allowable representations affects the corresponding universal algebra. We seek quite general conditions which will allow us to show that the C*-envelope of the semicrossed product is (a full corner of) a crossed product of an auxiliary C*-algebra by a group action. Our analysis concerns a case-by-case dilation theory on covariant pairs. In the process we determine the C*-envelope for various semicrossed products of (possibly nonselfadjoint) operator algebras by spanning cones and lattice-ordered abelian semigroups. In particular, we show that the C*-envelope of the semicrossed product of C*-dynamical systems by doubly commuting representations of $\mathbb{Z}^n_+$ (by generally non-injective endomorphisms) is the full corner of a C*-crossed product. In consequence we connect the ideal structure of C*-covers to properties of the actions. In particular, when the system is classical, we show that the C*-envelope is simple if and only if the action is injective and minimal. The dilation methods that we use may be applied to non-abelian semigroups. We identify the C*-envelope for actions of the free semigroup $\mathbb{F}_+^n$ by automorphisms in a concrete way, and for injective systems in a more abstract manner. We also deal with C*-dynamical systems over Ore semigroups when the appropriate covariance relation is considered.Comment: 100 pages; comments and references update

Unified Brane Gravity: Cosmological Dark Matter from Scale Dependent Newton Constant

We analyze, within the framework of unified brane gravity, the weak-field perturbations caused by the presence of matter on a 3-brane. Although deviating from the Randall-Sundrum approach, the masslessness of the graviton is still preserved. In particular, the four-dimensional Newton force law is recovered, but serendipitously, the corresponding Newton constant is shown to be necessarily lower than the one which governs FRW cosmology. This has the potential to puzzle out cosmological dark matter. A subsequent conjecture concerning galactic dark matter follows.Comment: 6 pages, to be published in Phys. Rev.

Developmental gene regulatory network architecture across 500 million years of echinoderm evolution

Evolutionary change in morphological features must depend on architectural reorganization of developmental gene regulatory networks (GRNs), just as true conservation of morphological features must imply retention of ancestral developmental GRN features. Key elements of the provisional GRN for embryonic endomesoderm development in the sea urchin are here compared with those operating in embryos of a distantly related echinoderm, a starfish. These animals diverged from their common ancestor 520-480 million years ago. Their endomesodermal fate maps are similar, except that sea urchins generate a skeletogenic cell lineage that produces a prominent skeleton lacking entirely in starfish larvae. A relevant set of regulatory genes was isolated from the starfish Asterina miniata, their expression patterns determined, and effects on the other genes of perturbing the expression of each were demonstrated. A three-gene feedback loop that is a fundamental feature of the sea urchin GRN for endoderm specification is found in almost identical form in the starfish: a detailed element of GRN architecture has been retained since the Cambrian Period in both echinoderm lineages. The significance of this retention is highlighted by the observation of numerous specific differences in the GRN connections as well. A regulatory gene used to drive skeletogenesis in the sea urchin is used entirely differently in the starfish, where it responds to endomesodermal inputs that do not affect it in the sea urchin embryo. Evolutionary changes in the GRNs since divergence are limited sharply to certain cis-regulatory elements, whereas others have persisted unaltered

Collisional decay of a strongly driven Bose-Einstein condensate

We study the collisional decay of a strongly driven Bose-Einstein condensate oscillating between two momentum modes. The resulting products of the decay are found to strongly deviate from the usual s-wave halo. Using a stochastically seeded classical field method we simulate the collisional manifold. These results are also explained by a model of colliding Bloch states.Comment: 4 pages, 4 figure

Problems with Extraction of the Nucleon to Delta(1232) Photonic Amplitudes

We investigate the model dependence and the importance of choice of database in extracting the {\it physical} nucleon-Delta(1232) electromagnetic transition amplitudes, of interest to QCD and baryon structure, from the pion photoproduction observables. The model dependence is found to be much smaller than the range of values obtained when different datasets are fitted. In addition, some inconsistencies in the current database are discovered, and their affect on the extracted transition amplitudes is discussed.Comment: Revtex, 2 figs., submitted to PR

The eta-photon transition form factor

The eta-photon transition form factor is evaluated in a formalism based on a phenomenological description at low values of the photon virtuality, and a QCD-based description at high photon virtualities, matching at a scale $Q_{0}^{2}$. The high photon virtuality description makes use of a Distribution Amplitude calculated in the Nambu-Jona-Lasinio model with Pauli-Villars regularization at the matching scale $Q_{0}^{2}$, and QCD evolution from $Q_{0}^{2}$ to higher values of $Q^{2}$. A good description of the available data is obtained. The analysis indicates that the recent data from the BaBar collaboration on pion and eta transition form factor can be well reproduced, if a small contribution of twist three at the matching scale $Q_{0}^{2}$ is included.Comment: 14 pages, 3 figures, revised version, minor corrections, references added, conclusions unchanged. Accepted for publication in Phys. Rev.

An adult social care compendium of approaches and tools for organisational change

The purpose of this compendium is to support managers working in adult social care to be more knowledgeable about and confident in the application of different approaches and tools relevant to managing change in their organisations. In the compendium an ‘approach to change’ is used to denote an ‘overarching framework that can guide a change process’ and ‘change management tools’ as ‘techniques or templates to understand or support a specific aspect of the change process’. Examples of the latter would be stakeholder mapping exercises, organisational diagnostic methodologies, engagement processes, and direct team based interventions. The compendium does not provide detailed guidance on how to apply each approach and tool, but presents an accessible overview of what each entails, the thinking that lies behind them, and (where available) a reflection on the empirical evidence of their application in practice. Having access to this information will help to demystify the often confusing and intimidating terminology that surrounds change approaches, and in doing so will enable managers to identify the approaches most relevant to a change they are leading and explore in more depth. Understanding the method being followed will also support individuals who access services and their families to engage on a more equal playing field within a change process. This includes people who access services and their families. While potentially relevant to social care managers working at all levels of an organisation, the compendium is specifically designed for those responsible for a single service (e.g. home care team, residential care home) or team (e.g. care management team), and those who directly manage service and team managers