On Chern-Simons theory with an inhomogeneous gauge group and BF theory knot invariants

We study the Chern-Simons topological quantum field theory with an inhomogeneous gauge group, a non-semi-simple group obtained from a semi-simple one by taking its semi-direct product with its Lie algebra. We find that the standard knot observables (i.e. traces of holonomies along knots) essentially vanish, but yet, the non-semi-simplicity of our gauge group allows us to consider a class of un-orthodox observables which breaks gauge invariance at one point and which lead to a non-trivial theory on long knots in $\mathbb{R}^3$. We have two main morals : 1. In the non-semi-simple case, there is more to observe in Chern-Simons theory! There might be other interesting non semi-simple gauge groups to study in this context beyond our example. 2. In our case of an inhomogeneous gauge group, we find that Chern-Simons theory with the un-orthodox observable is actually the same as 3D BF theory with the Cattaneo-Cotta-Ramusino-Martellini knot observable. This leads to a simplification of their results and enables us to generalize and solve a problem they posed regarding the relation between BF theory and the Alexander-Conway polynomial. Our result is that the most general knot invariant coming from pure BF topological quantum field theory is in the algebra generated by the coefficients of the Alexander-Conway polynomial.Comment: To appear in Journal of Mathematical Physics vol.46 issue 12. Available on http://link.aip.org/link/jmapaq/v46/i1

The chromatographic identification of some biologically important phosphate esters

the objective of the present work was to provide a means for separating and indentifying phosphate esters involved in glycolysis in higher plants. Paper chromatography of phosphate esters has been employed by several workers, most notably Benson et al. (1) and Hanes and Isherwood (2). Benson's procedures were not primarily designed for identification of phosphate esters and gave low Rr values for the phosphate compounds of particular interest to us. The unidimensional methods of Hanes and Isherwood do not result in adequate resolution of the complex mixtures such as are obtained from our plant materials. The present procedure is based on two-dimensional chromatography with successive development in an acid and in a basic solvent. The solvents finally selected gave the best over-all resolution of the intermediates involved in plant glycolysis. Undoubtedly the resolution of certain pairs of compounds may be improved by suitable modifications. We have in addition made certain improvements in the procedure for locating the chromatographed materials

Consistent 3D Quantum Gravity on Lens Spaces

We study non-perturbative quantization of 3d gravity with positive cosmological constant (de Sitter space being the prototype vacuum solution, whose Euclideanization of course gives the three sphere) on the background topology of lens space, which is a three spheres modulo a discrete group. Instead of the strategy followed by a recent work \cite{Castro:2011xb}, which compares results in the second and first order formulations of gravity, we concentrate on the later solely. We note, as a striking feature, that the quantization, that relies heavily on the axiomatics of topological quantum field theory (TQFT) can only be consistently carried by augmenting the conventional theory by an additional topological term coupled through a dimensionless parameter. More importantly the introduction of this additional parameter renders the theory finite.Comment: New section and references added. Accepted in Phys. Rev. D for publicatio

Geometric Prequantization of the Moduli Space of the Vortex equations on a Riemann surface

The moduli space of solutions to the vortex equations on a Riemann surface are well known to have a symplectic (in fact K\"{a}hler) structure. We show this symplectic structure explictly and proceed to show a family of symplectic (in fact, K\"{a}hler) structures $\Omega_{\Psi_0}$ on the moduli space, parametrised by $\Psi_0$, a section of a line bundle on the Riemann surface. Next we show that corresponding to these there is a family of prequantum line bundles ${\mathcal P}_{\Psi_0}$on the moduli space whose curvature is proportional to the symplectic forms $\Omega_{\Psi_0}$.Comment: 8 page

Emotional Strategies as Catalysts for Cooperation in Signed Networks

The evolution of unconditional cooperation is one of the fundamental problems in science. A new solution is proposed to solve this puzzle. We treat this issue with an evolutionary model in which agents play the Prisoner's Dilemma on signed networks. The topology is allowed to co-evolve with relational signs as well as with agent strategies. We introduce a strategy that is conditional on the emotional content embedded in network signs. We show that this strategy acts as a catalyst and creates favorable conditions for the spread of unconditional cooperation. In line with the literature, we found evidence that the evolution of cooperation most likely occurs in networks with relatively high chances of rewiring and with low likelihood of strategy adoption. While a low likelihood of rewiring enhances cooperation, a very high likelihood seems to limit its diffusion. Furthermore, unlike in non-signed networks, cooperation becomes more prevalent in denser topologies.Comment: 24 pages, Accepted for publication in Advances in Complex System

Ear to the Battleground: NEw Books on Hearing What is Lost

Of the five senses, vision tends to get the glory. We hail great innovators as visionary, praise writers for their insight, and thank friends for offering perspective. We call prophets seers, but also admire daily perspicacity and seek to avoid myopia and blind spots. Just consider the words spectacles and spectacular, and you catch a glimpse—not a whisper, a glimpse—of the divergence between vision in the optometrist’s office and vision in our cultural construction of it. But while vision gets the glory, hearing has our trust. We want justice to be blind during court hearings. In times of crisis, more than to the insightful friend, we turn to the good listener. Perhaps this is because hearing is our most social sense, the sense we have the least control over, the sense that is the most democratic. It’s easy enough on the subway to look away from someone, but it’s almost impossible to hear away, to filter out one particular voice

Critical behavior in an evolutionary Ultimatum Game

Experimental studies have shown the ubiquity of altruistic behavior in human societies. The social structure is a fundamental ingredient to understand the degree of altruism displayed by the members of a society, in contrast to individual-based features, like for example age or gender, which have been shown not to be relevant to determine the level of altruistic behavior. We explore an evolutionary model aiming to delve how altruistic behavior is affected by social structure. We investigate the dynamics of interacting individuals playing the Ultimatum Game with their neighbors given by a social network of interaction. We show that a population self-organizes in a critical state where the degree of altruism depends on the topology characterizing the social structure. In general, individuals offering large shares but in turn accepting large shares, are removed from the population. In heterogeneous social networks, individuals offering intermediate shares are strongly selected in contrast to random homogeneous networks where a broad range of offers, below a critical one, is similarly present in the population.Comment: 13 pages, 7 figure

Algebraic Characterization of Vector Supersymmetry in Topological Field Theories

An algebraic cohomological characterization of a class of linearly broken Ward identities is provided. The examples of the topological vector supersymmetry and of the Landau ghost equation are discussed in detail. The existence of such a linearly broken Ward identities turns out to be related to BRST exact antifield dependent cocycles with negative ghost number.Comment: 30 pages, latex2e file, subm. to Journ. of Math. Phy