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

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

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

Theory of hyperbolic stratified nanostructures for surface enhanced Raman scattering

We theoretically investigate the enhancement of surface enhanced Raman spectroscopy (SERS) using hyperbolic stratified nanostructures and compare to metal nanoresonators. The photon Green function of each nanostructure within its environment is first obtained from a semi-analytical modal theory, which is used in a quantum optics formalism of the molecule-nanostructure interaction to model the SERS spectrum. An intuitive methodology is presented for calculating the single molecule enhancement factor (SMEF), which is also able to predict known experimental SERS enhancement factors of an example gold nano-dimer. We elucidate the important figures-of-merit of the enhancement and explore these for different designs. We find that the use of hyperbolic stratified materials can enhance the photonic local density of states (LDOS) by close to 2 times in comparison to pure metal nanostructures, when both designed to work at the same operating wavelengths. However, the increased LDOS is accompanied by higher electric field concentration within the lossy hyperbolic material, which leads to increased quenching that serves to reduce the overall detected SERS enhancement in the far field. For nanoresonators with resonant localized surface plasmon wavelengths in the near-infrared, the SMEF for the hyperbolic stratified nanostructure is approximately an order of magnitude lower than the pure metal counterpart. Conversely, we show that by detecting the Raman signal using a near-field probe, hyperbolic materials can provide an improvement in SERS enhancement compared to using pure metal nanostructures when the probe is sufficiently close (<50 nm) to the Raman active molecule at the plasmonic hotspot.Comment: 18 pages, 9 figure

From simplicial Chern-Simons theory to the shadow invariant II

This is the second of a series of papers in which we introduce and study a rigorous "simplicial" realization of the non-Abelian Chern-Simons path integral for manifolds M of the form M = Sigma x S1 and arbitrary simply-connected compact structure groups G. More precisely, we introduce, for general links L in M, a rigorous simplicial version WLO_{rig}(L) of the corresponding Wilson loop observable WLO(L) in the so-called "torus gauge" by Blau and Thompson (Nucl. Phys. B408(2):345-390, 1993). For a simple class of links L we then evaluate WLO_{rig}(L) explicitly in a non-perturbative way, finding agreement with Turaev's shadow invariant |L|.Comment: 53 pages, 1 figure. Some minor changes and corrections have been mad

Einstein Radii from Binary Lensing Events

We show that the Einstein ring radius and transverse speed of a lens projected on the source plane, $\hat{r}_{\rm e}$ and $\hat{v}$, can be determined from the light curve of a binary-source event, followed by the spectroscopic determination of the orbital elements of the source stars. The determination makes use of the same principle that allows one to measure the Einstein ring radii from finite-source effects. For the case when the orbital period of the source stars is much longer than the Einstein time scale, $P\gg t_{\rm e}$, there exists a single two-fold degeneracy in determining $\hat{r}_{\rm e}$. However, when $P \lesssim t_{\rm e}$ the degeneracy can often be broken by making use of the binary-source system's orbital motion. %Once $\hat{r}_{\rm e}$, and thus $\hat{v}$ are determined, one can %distinguish self-lensing events in the Large Magellanic Cloud %from Galactic halo events. For an identifiable 8\% of all lensing events seen toward the Large Magellanic Cloud (LMC), one can unambiguously determine whether the lenses are Galactic, or whether they lie in the LMC itself. The required observations can be made after the event is over and could be carried out for the $\sim 8$ events seen by Alcock et al.\ and Aubourg et al.. In addition, we propose to include eclipsing binaries as sources for gravitational lensing experiments.Comment: 18 pages, revised version, submitted to Ap

Freezing and Slow Evolution in a Constrained Opinion Dynamics Model

We study opinion formation in a population that consists of leftists, centrists, and rightist. In an interaction between neighboring agents, a centrist and a leftist can become both centrists or leftists (and similarly for a centrist and a rightist). In contrast, leftists and rightists do not affect each other. The initial density of centrists rho_0 controls the evolution. With probability rho_0 the system reaches a centrist consensus, while with probability 1-rho_0 a frozen population of leftists and rightists results. In one dimension, we determine this frozen state and the opinion dynamics by mapping the system onto a spin-1 Ising model with zero-temperature Glauber kinetics. In the frozen state, the length distribution of single-opinion domains has an algebraic small-size tail x^{-2(1-psi)} and the average domain size grows as L^{2*psi}, where L is the system length. The approach to this frozen state is governed by a t^{-psi} long-time tail with psi-->2*rho_0/pi as rho_0-->0.Comment: 4 pages, 6 figures, 2-column revtex4 format, for submission to J. Phys. A. Revision contains lots of stylistic changes and 1 new result; the main conclusions are the sam