Production of non-Abelian tensor gauge bosons. Tree amplitudes in generalized Yang-Mills theory and BCFW recursion relation

The BCFW recursion relation allows to calculate tree-level scattering amplitudes in generalized Yang-Mills theory and, in particular, four-particle amplitudes for the production rate of non-Abelian tensor gauge bosons of arbitrary high spin in the fusion of two gluons. The consistency of the calculations in different kinematical channels is fulfilled when all dimensionless cubic coupling constants between vector bosons (gluons) and high spin non-Abelian tensor gauge bosons are equal to the Yang-Mills coupling constant. There are no high derivative cubic vertices in the generalized Yang-Mills theory. The amplitudes vanish as complex deformation parameter tends to infinity, so that there is no contribution from the contour at infinity. We derive a generalization of the Parke-Taylor formula in the case of production of two tensor gauge bosons of spin-s and N gluons (jets). The expression is holomorhic in the spinor variables of the scattered particles, exactly as the MHV gluon amplitude is, and reduces to the gluonic MHV amplitude when s=1. In generalized Yang-Mills theory the tree level n-particle scattering amplitudes with all positive helicities vanish, but tree amplitudes with one negative helicity particle are already nonzero.Comment: 19 pages, LaTex fil

Colocation and role of polyphosphates and alkaline phosphatase in apatite biomineralization of elasmobranch tesserae

AbstractElasmobranchs (e.g. sharks and rays), like all fishes, grow continuously throughout life. Unlike other vertebrates, their skeletons are primarily cartilaginous, comprising a hyaline cartilage-like core, stiffened by a thin outer array of mineralized, abutting and interconnected tiles called tesserae. Tesserae bear active mineralization fronts at all margins and the tesseral layer is thin enough to section without decalcifying, making this a tractable but largely unexamined system for investigating controlled apatite mineralization, while also offering a potential analog for endochondral ossification. The chemical mechanism for tesserae mineralization has not been described, but has been previously attributed to spherical precursors, and alkaline phosphatase (ALP) activity. Here, we use a variety of techniques to elucidate the involvement of phosphorus-containing precursors in the formation of tesserae at their mineralization fronts. Using Raman spectroscopy, fluorescence microscopy and histological methods, we demonstrate that ALP activity is located with inorganic phosphate polymers (polyP) at the tessera–uncalcified cartilage interface, suggesting a potential mechanism for regulated mineralization: inorganic phosphate (Pi) can be cleaved from polyP by ALP, thus making Pi locally available for apatite biomineralization. The application of exogenous ALP to tissue cross-sections resulted in the disappearance of polyP and the appearance of Pi in uncalcified cartilage adjacent to mineralization fronts. We propose that elasmobranch skeletal cells control apatite biomineralization by biochemically controlling polyP and ALP production, placement and activity. Previous identification of polyP and ALP shown previously in mammalian calcifying cartilage supports the hypothesis that this mechanism may be a general regulating feature in the mineralization of vertebrate skeletons

Six-Quark Amplitudes from Fermionic MHV Vertices

The fermionic extension of the CSW approach to perturbative gauge theory coupled with fermions is used to compute the six-quark QCD amplitudes. We find complete agreement with the results obtained by using the usual Feynman rules.Comment: Latex file, 16 pages, 4 figure

A direct proof of the CSW rules

Using recursion methods similar to those of Britto, Cachazo, Feng and Witten (BCFW) a direct proof of the CSW rules for computing tree-level gluon amplitudes is given.Comment: 11 pages, uses axodraw.st

Influence of boundary conditions on quantum escape

It has recently been established that quantum statistics can play a crucial role in quantum escape. Here we demonstrate that boundary conditions can be equally important - moreover, in certain cases, may lead to a complete suppression of the escape. Our results are exact and hold for arbitrarily many particles.Comment: 6 pages, 3 figures, 1 tabl

Emotion perception and electrophysiological correlates in Huntington\u27s disease

Objective This study aimed to characterise, emotion perception deficits in symptomatic Huntington\u27s disease (HD) via the use of event-related potentials (ERPs). Methods ERP data were recorded during a computerised facial expression task in 11 HD participants and 11 matched controls. Expression (scrambled, neutral, happy, angry, disgust) classification accuracy and intensity were assessed. Relationships between ERP indices and clinical disease characteristics were also examined. Results Accuracy was significantly lower for HD relative to controls, due to reduced performance for neutral, angry and disgust (but not happy) faces. Intensity ratings did not differ between groups. HD participants displayed significantly reduced visual processing amplitudes extending across pre-face (P100) and face-specific (N170) processing periods, whereas subsequent emotion processing amplitudes (N250) were similar across groups. Face-specific and emotion-specific derivations of the N170 and N250 (\u27neutral minus scrambled\u27 and \u27each emotion minus neutral\u27, respectively) did not differ between groups. Conclusions Our data suggest that the facial emotion recognition performance deficits in HD are primarily related to neural degeneration underlying \u27generalised\u27 visual processing, rather than face or emotional specific processing. Significance ERPs are a useful tool to separate functionally discreet impairments in HD, and provide an important avenue for biomarker application that could more-selectively track disease progression

Processor Allocation for Optimistic Parallelization of Irregular Programs

Optimistic parallelization is a promising approach for the parallelization of irregular algorithms: potentially interfering tasks are launched dynamically, and the runtime system detects conflicts between concurrent activities, aborting and rolling back conflicting tasks. However, parallelism in irregular algorithms is very complex. In a regular algorithm like dense matrix multiplication, the amount of parallelism can usually be expressed as a function of the problem size, so it is reasonably straightforward to determine how many processors should be allocated to execute a regular algorithm of a certain size (this is called the processor allocation problem). In contrast, parallelism in irregular algorithms can be a function of input parameters, and the amount of parallelism can vary dramatically during the execution of the irregular algorithm. Therefore, the processor allocation problem for irregular algorithms is very difficult. In this paper, we describe the first systematic strategy for addressing this problem. Our approach is based on a construct called the conflict graph, which (i) provides insight into the amount of parallelism that can be extracted from an irregular algorithm, and (ii) can be used to address the processor allocation problem for irregular algorithms. We show that this problem is related to a generalization of the unfriendly seating problem and, by extending Tur\'an's theorem, we obtain a worst-case class of problems for optimistic parallelization, which we use to derive a lower bound on the exploitable parallelism. Finally, using some theoretically derived properties and some experimental facts, we design a quick and stable control strategy for solving the processor allocation problem heuristically.Comment: 12 pages, 3 figures, extended version of SPAA 2011 brief announcemen

Loops in Twistor Space

We elucidate the one-loop twistor-space structure corresponding to momentum-space MHV diagrams. We also discuss the infrared divergences, and argue that only a limited set of MHV diagrams contain them. We show how to introduce a twistor-space regulator corresponding to dimensional regularization for the infrared-divergent diagrams. We also evaluate explicitly the `holomorphic anomaly' pointed out by Cachazo, Svrcek, and Witten, and use the result to define modified differential operators which can be used to probe the twistor-space structure of one-loop amplitudes.Comment: 21 pages, TeX. v3. missing citations added. v4. subtlety with the i \epsilon prescription clarifie

Spectral statistics of random geometric graphs

We use random matrix theory to study the spectrum of random geometric graphs, a fundamental model of spatial networks. Considering ensembles of random geometric graphs we look at short range correlations in the level spacings of the spectrum via the nearest neighbour and next nearest neighbour spacing distribution and long range correlations via the spectral rigidity Delta_3 statistic. These correlations in the level spacings give information about localisation of eigenvectors, level of community structure and the level of randomness within the networks. We find a parameter dependent transition between Poisson and Gaussian orthogonal ensemble statistics. That is the spectral statistics of spatial random geometric graphs fits the universality of random matrix theory found in other models such as Erdos-Renyi, Barabasi-Albert and Watts-Strogatz random graph.Comment: 19 pages, 6 figures. Substantially updated from previous versio

MHV Lagrangian for N=4 Super Yang-Mills

Here we formulate two field redefinitions for N=4 Super Yang-Mills in light cone superspace that generates only MHV vertices in the new Lagrangian. After careful consideration of the S-matrix equivalence theorem, we see that only the canonical transformation gives the MHV Lagrangian that would correspond to the CSW expansion. Being in superspace, it is easier to analyse the equivalence theorem at loop level. We calculate the on shell amplitude for 4pt $(\bar{\Lambda}\bar{{\rm A}}\Lambda {\rm A})$ MHV in the new lagrangian and show that it reproduces the previously known form. We also briefly discuss the relationship with the off-shell continuation prescription of CSW.Comment: 17 pages 4 figures, 2 sections and several references added typo correcte