Short expressions of permutations as products and cryptanalysis of the Algebraic Eraser

On March 2004, Anshel, Anshel, Goldfeld, and Lemieux introduced the \emph{Algebraic Eraser} scheme for key agreement over an insecure channel, using a novel hybrid of infinite and finite noncommutative groups. They also introduced the \emph{Colored Burau Key Agreement Protocol (CBKAP)}, a concrete realization of this scheme. We present general, efficient heuristic algorithms, which extract the shared key out of the public information provided by CBKAP. These algorithms are, according to heuristic reasoning and according to massive experiments, successful for all sizes of the security parameters, assuming that the keys are chosen with standard distributions. Our methods come from probabilistic group theory (permutation group actions and expander graphs). In particular, we provide a simple algorithm for finding short expressions of permutations in $S_n$, as products of given random permutations. Heuristically, our algorithm gives expressions of length $O(n^2\log n)$, in time and space $O(n^3)$. Moreover, this is provable from \emph{the Minimal Cycle Conjecture}, a simply stated hypothesis concerning the uniform distribution on $S_n$. Experiments show that the constants in these estimations are small. This is the first practical algorithm for this problem for $n\ge 256$. Remark: \emph{Algebraic Eraser} is a trademark of SecureRF. The variant of CBKAP actually implemented by SecureRF uses proprietary distributions, and thus our results do not imply its vulnerability. See also arXiv:abs/12020598Comment: Final version, accepted to Advances in Applied Mathematics. Title slightly change

Higher Order Couplings from Heterotic Orbifold Theory

We calculate couplings of arbitrary order from correlation functions among twisted strings, using conformal field theory. Twisted strings arise in heterotic string compactified on orbifolds yielding matter fields in the low energy limit. We calculate completely the classical and the quantum amplitude including normalization, up to a contribution from Kahler potential. The classical action has saddle points which are interpreted as worldsheet instantons described by metastable untwisted strings, formed by twisted strings distributed at certain fixed points. This understanding generalizes the area rule, in the case that the locations of twisted strings do not form a polygon, and provides a general rule for calculating these kinds of instanton corrections. An interpretation of couplings involving linearly combined states is given, which commonly appear in non-prime order orbifolds. The quantum part of the amplitude is given by ratios of gamma functions with order one arguments.Comment: 32+1 pages, 5 figure

Quark masses and mixing angles in heterotic orbifold models

We study systematically the possibility for realizing realistic values of quark mass ratios $m_c/m_t$ and $m_s/m_b$ and the mixing angle $V_{cb}$ by using only renormalizable Yukawa couplings derived from heterotic orbifold models. We assume one pair of up and down sector Higgs fields. We show realistic examples including hierarchical and democratic forms of Yukawa matrices.Comment: 16 pages, late

Factors associated with statin treatment for the primary prevention of cardiovascular disease in people within 2 years following diagnosis of diabetes in Scotland, 2006-2008

© 2014 The Authors. Diabetic Medicine published by John Wiley & Sons Ltd on behalf of Diabetes UK. Funded by Scottish Health Informatics Programme. Grant Number: WT086113 Scottish Government Scottish Diabetes Research NetworkPeer reviewedPublisher PD

Yukawa Coupling Structure in Intersecting D-brane Models

The structure of Yukawa coupling matrices is investigated in type IIA T^6/(Z_2 x Z_2) orientifold models with intersecting D-branes. Yukawa coupling matrices are difficult to be realistic in the conventional models in which the generation structure emerges by the multiple intersection of D-branes in the factorized T^6 = T^2 x T^2 x T^2. We study the new type of flavor structure, where Yukawa couplings are dynamically generated, and show this type of models lead to nontrivial structures of Yukawa coupling matrices, which can be realistic.Comment: 9 pages, 2 figure

Searching for realistic 4d string models with a Pati-Salam symmetry -- Orbifold grand unified theories from heterotic string compactification on a Z6 orbifold

Motivated by orbifold grand unified theories, we construct a class of three-family Pati-Salam models in a Z6 abelian symmetric orbifold with two discrete Wilson lines. These models have marked differences from previously-constructed three-family models in prime-order orbifolds. In the limit where one of the six compactified dimensions (which lies in a Z2 sub-orbifold) is large compared to the string length scale, our models reproduce the supersymmetry and gauge symmetry breaking pattern of 5d orbifold grand unified theories on an S1/Z2 orbicircle. We find a horizontal 2+1 splitting in the chiral matter spectra -- 2 families of matter are localized on the Z2 orbifold fixed points, and 1 family propagates in the 5d bulk -- and identify them as the first-two and third families. Remarkably, the first two families enjoy a non-abelian dihedral D4 family symmetry, due to the geometric setup of the compactified space. In all our models there are always some color triplets, i.e. (6,1,1) representations of the Pati-Salam group, survive orbifold projections. They could be utilized to spontaneously break the Pati-Salam symmetry to that of the Standard Model. One model, with a 5d E6 symmetry, may give rise to interesting low energy phenomenology. We study gauge coupling unification, allowed Yukawa couplings and some of their phenomenological consequences. The E6 model has a renormalizable Yukawa coupling only for the third family. It predicts a gauge-Yukawa unification relation at the 5d compactification scale, and is capable of generating reasonable quark/lepton masses and mixings. Potential problems are also addressed, they may point to the direction for refining our models.Comment: 58 pages, 5 figures, 4 tables, revtex4 with ams fonts. Version to appear in NP

Vector boson pair production at the LHC

We present phenomenological results for vector boson pair production at the LHC, obtained using the parton-level next-to-leading order program MCFM. We include the implementation of a new process in the code, pp -> \gamma\gamma, and important updates to existing processes. We incorporate fragmentation contributions in order to allow for the experimental isolation of photons in \gamma\gamma, W\gamma, and Z\gamma production and also account for gluon-gluon initial state contributions for all relevant processes. We present results for a variety of phenomenological scenarios, at the current operating energy of \sqrt{s} = 7 TeV and for the ultimate machine goal, \sqrt{s} = 14 TeV. We investigate the impact of our predictions on several important distributions that enter into searches for new physics at the LHC.Comment: 35 pages, 14 figure

A Z2xZ2 standard model

We present a Z_2 x Z_2 orbifold compactification of the E_8 x E_8 heterotic string which gives rise to the exact chiral MSSM spectrum. The GUT breaking SU(5) to SU(3)_C x SU(2)_L x U(1)_Y is realized by modding out a freely acting symmetry. This ensures precision gauge coupling unification. Further, it allows us to break the GUT group without switching on flux in hypercharge direction, such that the standard model gauge bosons can remain massless when the orbifold singularities are blown up. The model has vacuum configurations with matter parity, a large top Yukawa coupling and other phenomenologically appealing features.Comment: 16 page

The impact of unhealthy food sponsorship vs. pro-health sponsorship models on young adults' food preferences: A randomised controlled trial

Background: Unhealthy foods are promoted heavily, through food company sponsorship of elite sport, resulting in extensive exposure among young adults who are avid sport spectators. This study explores the effects of sponsorship of an elite sporting event by: (A) non-food brands (control), (B) unhealthy food brands, (C) healthier food brands, or (D) an obesity prevention public health campaign on young adults' brand awareness, attitudes, image perceptions, event-sponsor fit perceptions, and preference for food sponsors' products. Methods: A between-subjects web-based experiment was conducted, consisting of four sponsorship conditions (A through D) featuring three product categories within each condition. Australian adults (N = 1132) aged 18-24 years were recruited via a national online panel. Participants viewed promotional videos and news stories about an upcoming international, multi-sport event (with sponsor content edited to reflect each condition), completed a distractor task, and then answered questions assessing the response variables. Regression analyses were conducted to test for differences by sponsorship condition on the respective outcome measures. Results: Compared to the control condition, unhealthy food sponsorship promoted higher awareness of, and more favourable attitudes towards, unhealthy food sponsor brands. Unhealthy food sponsorship also led to greater perceived event-sponsor fit and transfer of perceptions of the sporting event to the unhealthy food sponsor brands, relative to the control group. Exposure to sponsorship for healthier foods produced similar sponsorship effects for healthier food sponsor brands, as well as prompting a significant increase in the proportion of young adults showing a preference for these products. Obesity prevention campaign sponsorship promoted higher campaign awareness and perceived event-sponsor fit, but did not impact food attitudes or preference for unhealthy versus healthier foods. Conclusion: Findings suggest that restricting elite sport sponsorship to healthier food brands that meet set nutritional criteria could help promote healthier eating among young adults. Sporting organisations should be encouraged to seek sponsorship from companies who produce healthier food brands and government-funded social marketing campaigns. Clinical trial registration: Australian New Zealand Clinical Trials Registry (ANZCTR) registration number ACTRN12618000368235. Retrospectively registered 12 March 2018

A search for line intensity enhancements in the far-UV spectra of active late-type stars arising from opacity

Radiative transfer calculations have predicted intensity enhancements for optically thick emission lines, as opposed to the normal intensity reductions, for astrophysical plasmas under certain conditions. In particular, the results are predicted to be dependent both on the geometry of the emitting plasma and the orientation of the observer. Hence in principle the detection of intensity enhancement may provide a way of determining the geometry of an unresolved astronomical source. To investigate such enhancements we have analyzed a sample of active late-type stars observed in the far ultraviolet spectral region. Emission lines of O VI in the FUSE satellite spectra of epsilon Eri, II Peg and Prox Cen were searched for intensity enhancements due to opacity. We have found strong evidence for line intensity enhancements due to opacity during active or flare-like activity for all three stars. The O VI 1032/1038 line intensity ratios, predicted to have a value of 2.0 in the optically thin case, are found to be up to ~30% larger during several orbital phases. Our measurements, combined with radiative transfer models, allow us to constrain both the geometry of the O VI emitting regions in our stellar sources and the orientation of the observer. A spherical emitting plasma can be ruled out, as this would lead to no intensity enhancement. In addition, the theory tells us that the line-of-sight to the plasma must be close to perpendicular to its surface, as observations at small angles to the surface lead to either no intensity enhancement or the usual line intensity decrease over the optically thin value. For the future, we outline a laboratory experiment, that could be undertaken with current facilities, which would provide an unequivocal test of predictions of line intensity enhancement due to opacity, in particular the dependence on plasma geometry.Comment: 10 Pages, 8 Figures, and 2 Tables; Accepted in A&