New analyticity constraints on the high energy behavior of hadron-hadron cross sections

We here comment on a series of recent papers by Igi and Ishida[K. Igi and M. Ishida, Phys. Lett B 622, 286 (2005)] and Block and Halzen[M. M. Block and F. Halzen, Phys. Rev D 72, 036006 (2005)] that fit high energy $pp$ and $\bar pp$ cross section and $\rho$-value data, where $\rho$ is the ratio of the real to the imaginary portion of the forward scattering amplitude. These authors used Finite Energy Sum Rules and analyticity consistency conditions, respectively, to constrain the asymptotic behavior of hadron cross sections by anchoring their high energy asymptotic amplitudes--even under crossing--to low energy experimental data. Using analyticity, we here show that i) the two apparently very different approaches are in fact equivalent, ii) that these analyticity constraints can be extended to give new constraints, and iii) that these constraints can be extended to crossing odd amplitudes. We also apply these extensions to photoproduction. A new interpretation of duality is given.Comment: 9 pages, 1 postscript figure; redone for clarity, removal of typos, changing reference; figure replace

Localization and synthesis of prenylquinones in isolated outer and inner envelope membranes from spinach chloroplasts

The prenylquinone content and biosynthetic capabilities of membrane fractions enriched in outer and inner envelope membranes from spinach chloroplasts were analyzed. Both envelope membranes contain prenylquinones, and in almost similar amounts (on a protein basis). However, the outer envelope membrane contains more -tocopherol than the inner one although this prenylquinone is the major one in both fractions. On the contrary, plastoquinone-9 is present in higher amounts in the inner envelope membrane than in the outer one. In addition, it has been demonstrated that all the enzymes involved in the last steps of -tocopherol and plastoquinone-9 biosynthesis i.e., homogentisate decarboxylase polyprenyltransferase, S-adenosyl-methionine: methyl-6-phytylquinol methyltransferase, S-adenosyl-methionine: -tocopherol methyltransferase, homogentisate decarboxylase solanesyltransferase, S-adenosyl-methionine:methyl-6-solanesylquinol methyltransferase, and possibly 2,3-dimethylphytylquinol cyclase, are localized on the inner envelope membrane. These results demonstrate that the inner membrane of the chloroplast envelope plays a key role in chloroplast biogenesis, and especially for the synthesis of the two major plastid prenylquinones

Computing Node Polynomials for Plane Curves

According to the G\"ottsche conjecture (now a theorem), the degree N^{d, delta} of the Severi variety of plane curves of degree d with delta nodes is given by a polynomial in d, provided d is large enough. These "node polynomials" N_delta(d) were determined by Vainsencher and Kleiman-Piene for delta <= 6 and delta <= 8, respectively. Building on ideas of Fomin and Mikhalkin, we develop an explicit algorithm for computing all node polynomials, and use it to compute N_delta(d) for delta <= 14. Furthermore, we improve the threshold of polynomiality and verify G\"ottsche's conjecture on the optimal threshold up to delta <= 14. We also determine the first 9 coefficients of N_delta(d), for general delta, settling and extending a 1994 conjecture of Di Francesco and Itzykson.Comment: 23 pages; to appear in Mathematical Research Letter

What Is Wrong with the No-Report Paradigm and How to Fix It

Is consciousness based in prefrontal circuits involved in cognitive processes like thought, reasoning, and memory or, alternatively, is it based in sensory areas in the back of the neocortex? The no-report paradigm has been crucial to this debate because it aims to separate the neural basis of the cognitive processes underlying post-perceptual decision and report from the neural basis of conscious perception itself. However, the no-report paradigm is problematic because, even in the absence of report, subjects might engage in post-perceptual cognitive processing. Therefore, to isolate the neural basis of consciousness, a no-cognition paradigm is needed. Here, I describe a no-cognition approach to binocular rivalry and outline how this approach can help resolve debates about the neural basis of consciousness

Decoupling the coupled DGLAP evolution equations: an analytic solution to pQCD

Using Laplace transform techniques, along with newly-developed accurate numerical inverse Laplace transform algorithms, we decouple the solutions for the singlet structure function $F_s(x,Q^2)$ and $G(x,Q^2)$ of the two leading-order coupled singlet DGLAP equations, allowing us to write fully decoupled solutions: F_s(x,Q^2)={\cal F}_s(F_{s0}(x), G_0(x)), G(x,Q^2)={\cal G}(F_{s0}(x), G_0(x)). Here ${\cal F}_s$ and $\cal G$ are known functions---found using the DGLAP splitting functions---of the functions $F_{s0}(x) \equiv F_s(x,Q_0^2)$ and $G_{0}(x) \equiv G(x,Q_0^2)$, the chosen starting functions at the virtuality $Q_0^2$. As a proof of method, we compare our numerical results from the above equations with the published MSTW LO gluon and singlet $F_s$ distributions, starting from their initial values at $Q_0^2=1 GeV^2$. Our method completely decouples the two LO distributions, at the same time guaranteeing that both distributions satisfy the singlet coupled DGLAP equations. It furnishes us with a new tool for readily obtaining the effects of the starting functions (independently) on the gluon and singlet structure functions, as functions of both $Q^2$ and $Q_0^2$. In addition, it can also be used for non-singlet distributions, thus allowing one to solve analytically for individual quark and gluon distributions values at a given $x$ and $Q^2$, with typical numerical accuracies of about 1 part in $10^5$, rather than having to evolve numerically coupled integral-differential equations on a two-dimensional grid in $x, Q^2$, as is currently done.Comment: 6 pages, 2 figure