Complete Equivalence Between Gluon Tree Amplitudes in Twistor String Theory and in Gauge Theory

The gluon tree amplitudes of open twistor string theory, defined as contour integrals over the ACCK link variables, are shown to satisfy the BCFW relations, thus confirming that they coincide with the corresponding amplitudes in gauge field theory. In this approach, the integration contours are specified as encircling the zeros of certain constraint functions that force the appropriate relation between the link variables and the twistor string world-sheet variables. To do this, methods for calculating the tree amplitudes using link variables are developed further including diagrammatic methods for organizing and performing the calculations.Comment: 38 page

Dual conformal constraints and infrared equations from global residue theorems in N=4 SYM theory

Infrared equations and dual conformal constraints arise as consistency conditions on loop amplitudes in N=4 super Yang-Mills theory. These conditions are linear relations between leading singularities, which can be computed in the Grassmannian formulation of N=4 super Yang-Mills theory proposed recently. Examples for infrared equations have been shown to be implied by global residue theorems in the Grassmannian picture. Both dual conformal constraints and infrared equations are mapped explicitly to global residue theorems for one-loop next-to-maximally-helicity-violating amplitudes. In addition, the identity relating the BCFW and its parity-conjugated form of tree-level amplitudes, is shown to emerge from a particular combination of global residue theorems.Comment: 21 page

The S-Matrix in Twistor Space

The simplicity and hidden symmetries of (Super) Yang-Mills and (Super)Gravity scattering amplitudes suggest the existence of a "weak-weak" dual formulation in which these structures are made manifest at the expense of manifest locality. We suggest that this dual description lives in (2,2) signature and is naturally formulated in twistor space. We recast the BCFW recursion relations in an on-shell form that begs to be transformed into twistor space. Our twistor transformation is inspired by Witten's, but differs in treating twistor and dual twistor variables more equally. In these variables the three and four-point amplitudes are amazingly simple; the BCFW relations are represented by diagrammatic rules that precisely define the "twistor diagrams" of Andrew Hodges. The "Hodges diagrams" for Yang-Mills theory are disks and not trees; they reveal striking connections between amplitudes and suggest a new form for them in momentum space. We also obtain a twistorial formulation of gravity. All tree amplitudes can be combined into an "S-Matrix" functional which is the natural holographic observable in asymptotically flat space; the BCFW formula turns into a quadratic equation for this "S-Matrix", providing a holographic description of N=4 SYM and N=8 Supergravity at tree level. We explore loop amplitudes in (2,2) signature and twistor space, beginning with a discussion of IR behavior. We find that the natural pole prescription renders the amplitudes well-defined and free of IR divergences. Loop amplitudes vanish for generic momenta, and in twistor space are even simpler than their tree-level counterparts! This further supports the idea that there exists a sharply defined object corresponding to the S-Matrix in (2,2) signature, computed by a dual theory naturally living in twistor space.Comment: V1: 46 pages + 23 figures. Less telegraphic abstract in the body of the paper. V2: 49 pages + 24 figures. Largely expanded set of references included. Some diagrammatic clarifications added, minor typo fixe

Making Associativity Operational

The purpose of this paper is to propose an operational idea for developing algebraic thinking in the absence of alphanumeric symbols. The paper reports on a design experiment encouraging preschool children to use the associative property algebraically. We describe the theoretical basis of the design, the tasks used, and examples of algebraic thinking in 5–6-year-old children. Theoretically, the paper makes a critical distinction between operational and structural meanings of the notion of equality. We argue that mathematical thinking involving equality among young learners can comprise both an operational and a structural conception and that the operational conception has a side that is productively linked to the structural conception. Using carefully designed hands-on tasks, the crux of the paper is the realization of algebraic thinking (in verbal mathematics) as operationally experienced in the ability to transform one number structure, with a quantity that is subject to change, into another through equality-preserving transformations

Gravito-electromagnetic analogies

We reexamine and further develop different gravito-electromagnetic (GEM) analogies found in the literature, and clarify the connection between them. Special emphasis is placed in two exact physical analogies: the analogy based on inertial fields from the so-called "1+3 formalism", and the analogy based on tidal tensors. Both are reformulated, extended and generalized. We write in both formalisms the Maxwell and the full exact Einstein field equations with sources, plus the algebraic Bianchi identities, which are cast as the source-free equations for the gravitational field. New results within each approach are unveiled. The well known analogy between linearized gravity and electromagnetism in Lorentz frames is obtained as a limiting case of the exact ones. The formal analogies between the Maxwell and Weyl tensors are also discussed, and, together with insight from the other approaches, used to physically interpret gravitational radiation. The precise conditions under which a similarity between gravity and electromagnetism occurs are discussed, and we conclude by summarizing the main outcome of each approach.Comment: 60 pages, 2 figures. Improved version (compared to v2) with some re-write, notation improvements and a new figure that match the published version; expanded compared to the published version to include Secs. 2.3 and

Family Planning Decisions, Perceptions and Gender Dynamics among Couples in Mwanza, Tanzania: A Qualitative Study.

Contraceptive use is low in developing countries which are still largely driven by male dominated culture and patriarchal values. This study explored family planning (FP) decisions, perceptions and gender dynamics among couples in Mwanza region of Tanzania. Twelve focus group discussions and six in-depth interviews were used to collect information from married or cohabiting males and females aged 18-49. The participants were purposively selected. Qualitative methods were used to explore family planning decisions, perceptions and gender dynamics among couples. A guide with questions related to family planning perceptions, decisions and gender dynamics was used. The discussions and interviews were tape-recorded, transcribed verbatim and analyzed manually and subjected to content analysis. Four themes emerged during the study. First, "risks and costs" which refer to the side effects of FP methods and the treatment of side -effects as well as the costs inherit in being labeled as an unfaithful spouse. Second, "male involvement" as men showed little interest in participating in family planning issues. However, the same men were mentioned as key decision-makers even on the number of children a couple should have and the child spacing of these children. Third, "gender relations and communication" as participants indicated that few women participated in decision-making on family planning and the number of children to have. Fourth, "urban-rural differences", life in rural favoring having more children than urban areas therefore, the value of children depended on the place of residence. Family Planning programs should adapt the promotion of communication as well as joint decision-making on FP among couples as a strategy aimed at enhancing FP use

Activity profiles of elite wheelchair rugby players during competition

To quantify the activity profiles of elite wheelchair rugby and establish classification-specific arbitrary speed zones. Additionally, indicators of fatigue during full matches were explored. Methods: Seventy-five elite wheelchair rugby players from eleven national teams were monitored using a radio-frequency based, indoor tracking system across two international tournaments. Players who participated in complete quarters (n = 75) and full matches (n = 25) were included and grouped by their International Wheelchair Rugby Federation functional classification: group I (0-0.5), II (1.0-1.5), III (2.0-2.5) and IV (3.0-3.5). Results: During a typical quarter, significant increases in total distance (m), relative distance (m·minˉ¹), and mean speed (m·sˉ¹) were associated with an increase in classification group (P < 0.001), with the exception of group III and IV. However, group IV players achieved significantly higher peak speeds (3.82 ± 0.31 m·sˉ¹) than groups I (2.99 ± 0.28 m·sˉ¹), II (3.44 ± 0.26 m·sˉ¹) and III (3.67 ± 0.32 m·sˉ¹). Groups I and II differed significantly in match intensity during very low/low speed zones and the number of high-intensity activities in comparison with groups III and IV (P < 0.001). Full match analysis revealed that activity profiles did not differ significantly between quarters. Conclusions: Notable differences in the volume of activity were displayed across the functional classification groups. However, the specific on-court requirements of defensive (I and II) and offensive (III and IV) match roles appeared to influence the intensity of match activities and consequently training prescription should be structured accordingly

Protective role of vitamin B6 (PLP) against DNA damage in Drosophila models of type 2 diabetes

Growing evidence shows that improper intake of vitamin B6 increases cancer risk and several studies indicate that diabetic patients have a higher risk of developing tumors. We previously demonstrated that in Drosophila the deficiency of Pyridoxal 5' phosphate (PLP), the active form of vitamin B6, causes chromosome aberrations (CABs), one of cancer prerequisites, and increases hemolymph glucose content. Starting from these data we asked if it was possible to provide a link between the aforementioned studies. Thus, we tested the effect of low PLP levels on DNA integrity in diabetic cells. To this aim we generated two Drosophila models of type 2 diabetes, the first by impairing insulin signaling and the second by rearing flies in high sugar diet. We showed that glucose treatment induced CABs in diabetic individuals but not in controls. More interestingly, PLP deficiency caused high frequencies of CABs in both diabetic models demonstrating that hyperglycemia, combined to reduced PLP level, impairs DNA integrity. PLP-depleted diabetic cells accumulated Advanced Glycation End products (AGEs) that largely contribute to CABs as α-lipoic acid, an AGE inhibitor, rescued not only AGEs but also CABs. These data, extrapolated to humans, indicate that low PLP levels, impacting on DNA integrity, may be considered one of the possible links between diabetes and cancer

Elevation and cholera: an epidemiological spatial analysis of the cholera epidemic in Harare, Zimbabwe, 2008-2009

BACKGROUND: In highly populated African urban areas where access to clean water is a challenge, water source contamination is one of the most cited risk factors in a cholera epidemic. During the rainy season, where there is either no sewage disposal or working sewer system, runoff of rains follows the slopes and gets into the lower parts of towns where shallow wells could easily become contaminated by excretes. In cholera endemic areas, spatial information about topographical elevation could help to guide preventive interventions. This study aims to analyze the association between topographic elevation and the distribution of cholera cases in Harare during the cholera epidemic in 2008 and 2009. METHODS: We developed an ecological study using secondary data. First, we described attack rates by suburb and then calculated rate ratios using whole Harare as reference. We illustrated the average elevation and cholera cases by suburbs using geographical information. Finally, we estimated a generalized linear mixed model (under the assumption of a Poisson distribution) with an Empirical Bayesian approach to model the relation between the risk of cholera and the elevation in meters in Harare. We used a random intercept to allow for spatial correlation of neighboring suburbs. RESULTS: This study identifies a spatial pattern of the distribution of cholera cases in the Harare epidemic, characterized by a lower cholera risk in the highest elevation suburbs of Harare. The generalized linear mixed model showed that for each 100 meters of increase in the topographical elevation, the cholera risk was 30% lower with a rate ratio of 0.70 (95% confidence interval=0.66-0.76). Sensitivity analysis confirmed the risk reduction with an overall estimate of the rate ratio between 20% and 40%. CONCLUSION: This study highlights the importance of considering topographical elevation as a geographical and environmental risk factor in order to plan cholera preventive activities linked with water and sanitation in endemic areas. Furthermore, elevation information, among other risk factors, could help to spatially orientate cholera control interventions during an epidemic

Analytic result for the two-loop six-point NMHV amplitude in N=4 super Yang-Mills theory

We provide a simple analytic formula for the two-loop six-point ratio function of planar N = 4 super Yang-Mills theory. This result extends the analytic knowledge of multi-loop six-point amplitudes beyond those with maximal helicity violation. We make a natural ansatz for the symbols of the relevant functions appearing in the two-loop amplitude, and impose various consistency conditions, including symmetry, the absence of spurious poles, the correct collinear behaviour, and agreement with the operator product expansion for light-like (super) Wilson loops. This information reduces the ansatz to a small number of relatively simple functions. In order to fix these parameters uniquely, we utilize an explicit representation of the amplitude in terms of loop integrals that can be evaluated analytically in various kinematic limits. The final compact analytic result is expressed in terms of classical polylogarithms, whose arguments are rational functions of the dual conformal cross-ratios, plus precisely two functions that are not of this type. One of the functions, the loop integral \Omega^{(2)}, also plays a key role in a new representation of the remainder function R_6^{(2)} in the maximally helicity violating sector. Another interesting feature at two loops is the appearance of a new (parity odd) \times (parity odd) sector of the amplitude, which is absent at one loop, and which is uniquely determined in a natural way in terms of the more familiar (parity even) \times (parity even) part. The second non-polylogarithmic function, the loop integral \tilde{\Omega}^{(2)}, characterizes this sector. Both \Omega^{(2)} and tilde{\Omega}^{(2)} can be expressed as one-dimensional integrals over classical polylogarithms with rational arguments.Comment: 51 pages, 4 figures, one auxiliary file with symbols; v2 minor typo correction