The Kauffman bracket and the Jones polynomial in quantum gravity

An analysis of the action of the Hamiltonian constraint of quantum gravity on the Kauffman bracket and Jones knot polynomials is proposed. It is explicitely shown that the Kauffman bracket is a formal solution of the Hamiltonian constraint with cosmological constant ($\Lambda$) to third order in $\Lambda$. The calculation is performed in the extended loop representation of quantum gravity. The analysis makes use of the analytical expressions of the knot invariants in terms of the two and three point propagators of the Chern-Simons theory. Some particularities of the extended loop calculus are considered and the implications of the results to the case of the conventional loop representation are discussed.Comment: 21 page

Educating Maltese journalists

The media institutions of a country can be studied as a system in which a set of input-output relationships bind its constituent elements in a network of mutual dependences. Significant variation in the activity of one component will be associated with significant variation of all other components. A system's approach to the Maltese media would show that they are "essentially secondary bodies; entirely dependent on others for the news and opinions they pass on; and highly constrained in their operation by a number of political, economic, cultural and technological factors".peer-reviewe

Connectivity by geodesics on a class of globally hyperbolic spacetimes

During the past years there has been a considerable amount of research related to the problem of geodesic connectedness of Lorentzian manifolds. This topic has wide applications in Physics, but for mathematicians its interest is essentially due to the peculiar di culty of this natural problem, which makes it challenging from both an analytical and a geometrical point of view. In this talk I discuss the geodesic connectedness problem on globally hyper- bolic spacetimes endowed with a complete, timelike or lightlike, Killing vector eld and a complete Cauchy hypersurface. Then I introduce the notion of open subset with convex boundary and present some applications of previous results.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

On plane sextics with double singular points

We compute the fundamental groups of five maximizing sextics with double singular points only; in four cases, the groups are as expected. The approach used would apply to other sextics as well, given their equations.Comment: A few explanations and references adde

The psychology of errors

One of the lasting contributions to psychology by Sigmund Freud and Jean Piaget has been their focus on human errors as keys to the workings of the mind. Freud dedicated two of his first lectures of A general introduction to psychoanalysis (1935) to "The Psychology of Errors". He considered slips of the tongue, misreading and the forgetting of resolutions as related to unconscious mental processes. Hence the expression "a Freudian slip". Similarly Piaget did not follow the developers of intelligence tests who focused on those tasks which most children could solve at progressive ages, but turned his attention instead to those tasks which most children at any given age invariably failed to solve. He based his theory of stages in children's intellectual development on their errors in dealing with problems that required a level of thinking beyond their particular level of development (see e.g. Piaget, 1954).peer-reviewe

The Gauss Constraint in the Extended Loop Representation

The Gauss constraint in the extended loop representation for quantum gravity is studied. It is shown that there exists a sector of the state space that is rigorously gauge invariant without the generic convergence issues of the extended holonomies.Comment: 8 pages, latex, no figure

Nutrition in childhood

Childhood is the stage in a human’s life associated with growth and development. Growth proceeds rapidly in early life, slows down in middle childhood and accelerates at puberty before linear growth ceases. With increasing age there is also physical and psychomotor maturation, which influences activity, body composition, feeding skills and food choices (Geissler, 2011). Adequate nutrition is essential for growth, health and development of children. Poor nutrition increases the risk of illness, and is responsible directly or indirectly for one third of the estimated 9.5 million deaths that occurred in 2006 in children less than 5 years of age. Inappropriate nutrition can also lead to childhood obesity. (WHO, 2009a).peer-reviewe

Gauge-Invariant Temperature Anisotropies and Primordial Non-Gaussianity

We provide the gauge-invariant expression for large-scale cosmic microwave background temperature fluctuations at second-order in perturbation theory. It enables to unambiguously define the nonlinearity parameter f_NL which is used by experimental collaborations to pin down the level of Non-Gaussianity in the temperature fluctuations. Furthermore, it contains a primordial term encoding all the information about the Non-Gaussianity generated at primordial epochs and about the mechanism which gave rise to cosmological perturbations, thus neatly disentangling the primordial contribution to Non-Gaussianity from the one caused by the post-inflationary evolution.Comment: 4 pages, LaTeX file. Revised to match the version to appear in Phys. Rev. Let

Flowing active liquids in a pipe: Hysteretic response of polar flocks to external fields

We investigate the response of colloidal flocks to external fields. We first show that individual colloidal rollers align with external flows as would a classical spin with magnetic fields. Assembling polar active liquids from colloidal rollers, we experimentally demonstrate their hysteretic response: confined colloidal flocks can proceed against external flows. We theoretically explain this collective robustness, using an active hydrodynamic description, and show how orientational elasticity and confinement protect the direction of collective motion. Finally, we exploit the intrinsic bistability of confined active flows to devise self-sustained microfluidic oscillators.Comment: 12 pages, 7 figure; accepted for publication in Physical Review

On classical set-compatibility

In this paper, I generalise the logical concept of compatibility into a broader set-theoretical one. The basic idea is that two sets are incompatible if they produce at least one pair of opposite objects under some operation. I formalise opposition as an operation ′ ∶ E → E, where E is the set of opposable elements of our universe U, and I propose some models. From this, I define a relation ℘U × ℘U × ℘U^℘U, which has (mutual) logical compatibility as its more natural interpretation