137,461 research outputs found
Are the String and Einstein Frames Equivalent
The low energy physics as predicted by strings can be expressed in two
(conformally related) different variables, usually called {\em frames}. The
problem is raised as to whether it is physically possible in some situations to
tell one from the other.Comment: 12 pages, LaTe
A Monte Carlo Approach to the Fluctuation Problem in Optimal Alignments of Random Strings
The problem of determining the correct order of fluctuation of the optimal alignment score of two random strings of length has been open for several decades. It is known [12] that the biased expected effect of a random letter-change on the optimal score implies an order of fluctuation linear in â. However, in many situations where such a biased effect is observed empirically, it has been impossible to prove analytically. The main result of this paper shows that when the rescaled-limit of the optimal alignment score increases in a certain direction, then the biased effect exists. On the basis of this result one can quantify a confidence level for the existence of such a biased effect and hence of an order â fluctuation based on simulation of optimal alignments scores. This is an important step forward, as the correct order of fluctuation was previously known only for certain special distributions [12],[13],[5],[10]. To illustrate the usefulness of our new methodology, we apply it to optimal alignments of strings written in the DNA-alphabet. As scoring function, we use the BLASTZ default-substitution matrix together with a realistic gap penalty. BLASTZ is one of the most widely used sequence alignment methodologies in bioinformatics. For this DNA-setting, we show that with a high level of confidence, the fluctuation of the optimal alignment score is of order Î(â). An important special case of optimal alignment score is the Longest Common Subsequence (LCS) of random strings. For binary sequences with equiprobably symbols the question of the fluctuation of the LCS remains open. The symmetry in that case does not allow for our method. On the other hand, in real-life DNA sequences, it is not the case that all letters occur with the same frequency. So, for many real life situations, our method allows to determine the order of the fluctuation up to a high confidence level
Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions
We analyse the Weak Gravity Conjecture for chiral four-dimensional F-theory
compactifications with N=1 supersymmetry. Extending our previous work on nearly
tensionless heterotic strings in six dimensions, we show that under certain
assumptions a tower of asymptotically massless states arises in the limit of
vanishing coupling of a U(1) gauge symmetry coupled to gravity. This tower
contains super-extremal states whose charge-to-mass ratios are larger than
those of certain extremal dilatonic Reissner-Nordstrom black holes, precisely
as required by the Weak Gravity Conjecture. Unlike in six dimensions, the tower
of super-extremal states does not always populate a charge sub-lattice. The
main tool for our analysis is the elliptic genus of the emergent heterotic
string in the chiral N=1 supersymmetric effective theories. This also governs
situations where the heterotic string is non-perturbative. We show how it can
be computed in terms of BPS invariants on elliptic four-folds, by making use of
various dualities and mirror symmetry. Compared to six dimensions, the geometry
of the relevant elliptically fibered four-folds is substantially richer than
that of the three-folds, and we classify the possibilities for obtaining
critical, nearly tensionless heterotic strings. We find that the
(quasi-)modular properties of the elliptic genus crucially depend on the choice
of flux background. Our general results are illustrated in a detailed example.Comment: 72 pages, 2 figure
Optimal shapes of compact strings
Optimal geometrical arrangements, such as the stacking of atoms, are of
relevance in diverse disciplines. A classic problem is the determination of the
optimal arrangement of spheres in three dimensions in order to achieve the
highest packing fraction; only recently has it been proved that the answer for
infinite systems is a face-centred-cubic lattice. This simply stated problem
has had a profound impact in many areas, ranging from the crystallization and
melting of atomic systems, to optimal packing of objects and subdivision of
space. Here we study an analogous problem--that of determining the optimal
shapes of closely packed compact strings. This problem is a mathematical
idealization of situations commonly encountered in biology, chemistry and
physics, involving the optimal structure of folded polymeric chains. We find
that, in cases where boundary effects are not dominant, helices with a
particular pitch-radius ratio are selected. Interestingly, the same geometry is
observed in helices in naturally-occurring proteins.Comment: 8 pages, 3 composite ps figure
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