Varieties Connected by Chains of Lines

In this paper we give for any integer l > 2 a numerical criterion ensuring the existence of a chain of length l of lines through two general points of an irreducible variety X in P^N, involving the degrees and the number of homogeneous polynomials defining X. We show that our criterion is sharp.Comment: 8 page

Modelling approach to simulate reductions in LDL cholesterol levels after combined intake of statins and phytosterols/-stanols in humans

<p>Abstract</p> <p>Background</p> <p>To examine the effects on LDL cholesterol of the combined use of statins and phytosterols/-stanols, in vivo studies and clinical trials are necessary. However, for a better interpretation of the experimental data as well as to possibly predict cholesterol levels given a certain dosing regimen of statins and phytosterols/-stanols a more theoretically based approach is helpful. This study aims to construct a mathematical model to simulate reductions in low-density lipoprotein (LDL) cholesterol in persons who combine the use of statins with a high intake of phytosterols/-stanols, e.g. by the use of functional foods.</p> <p>Methods and Results</p> <p>The proposed model includes the cholesterol pool size in the liver and serum levels of very low-density lipoprotein (VLDL) cholesterol. Both an additional and a multiplicative effect of phytosterol/-stanol intake on LDL cholesterol reduction were predicted from the model. The additional effect relates to the decrease of dietary cholesterol uptake reduction, the multiplicative effect relates to the decrease in enterohepatic recycling efficiency, causing increased cholesterol elimination through bile. From the model, it was demonstrated that a daily intake of 2 g phytosterols/-stanols reduces LDL cholesterol level by about 8% to 9% on top of the reduction resulting from statin use. The additional decrease in LDL cholesterol caused by phytosterol/-stanol use at the recommended level of 2 g/d appeared to be similar or even greater than the decrease achieved by doubling the statin dose.</p> <p>Conclusion</p> <p>We proposed a simplified mathematical model to simulate the reduction in LDL cholesterol after separate and combined intake of statins and functional foods acting on intestinal (re)absorption of cholesterol or bile acids in humans. In future work, this model can be extended to include more complex (regulatory) mechanisms.</p

Higher Spins in AdS and Twistorial Holography

In this paper we simplify and extend previous work on three-point functions in Vasiliev's higher spin gauge theory in AdS4. We work in a gauge in which the space-time dependence of Vasiliev's master fields is gauged away completely, leaving only the internal twistor-like variables. The correlation functions of boundary operators can be easily computed in this gauge. We find complete agreement of the tree level three point functions of higher spin currents in Vasiliev's theory with the conjectured dual free O(N) vector theory.Comment: 23 pages. v3: minor errors fixed, added comments and reference

Non-global logarithms and jet algorithms in high-pT jet shapes

We consider jet-shape observables of the type proposed recently, where the shapes of one or more high-pT jets, produced in a multi-jet event with definite jet multiplicity, may be measured leaving other jets in the event unmeasured. We point out the structure of the full next-to-leading logarithmic resummation specifically including resummation of non-global logarithms in the leading-Nc limit and emphasising their properties. We also point out differences between jet algorithms in the context of soft gluon resummation for such observables.Comment: 22 pages, 4 figures. Title and a few words changed. Several typos corrected. Version accepted by JHE

Comment on Higgs Inflation and Naturalness

We rebut the recent claim (arXiv:0912.5463) that Einstein-frame scattering in the Higgs inflation model is unitary above the cut-off energy Lambda ~ Mp/xi. We show explicitly how unitarity problems arise in both the Einstein and Jordan frames of the theory. In a covariant gauge they arise from non-minimal Higgs self-couplings, which cannot be removed by field redefinitions because the target space is not flat. In unitary gauge, where there is only a single scalar which can be redefined to achieve canonical kinetic terms, the unitarity problems arise through non-minimal Higgs-gauge couplings.Comment: 5 pages, 1 figure V3: Journal Versio