Distortion maps for genus two curves

Distortion maps are a useful tool for pairing based cryptography. Compared with elliptic curves, the case of hyperelliptic curves of genus g > 1 is more complicated since the full torsion subgroup has rank 2g. In this paper we prove that distortion maps always exist for supersingular curves of genus g>1 and we construct distortion maps in genus 2 (for embedding degrees 4,5,6 and 12).Comment: 16 page

First CMB Constraints on the Inflationary Reheating Temperature

We present the first Bayesian constraints on the single field inflationary reheating era obtained from Cosmic Microwave Background (CMB) data. After demonstrating that this epoch can be fully characterized by the so-called reheating parameter, we show that it is constrained by the seven years Wilkinson Microwave Anisotropies Probe (WMAP7) data for all large and small field models. An interesting feature of our approach is that it yields lower bounds on the reheating temperature which can be combined with the upper bounds associated with gravitinos production. For large field models, we find the energy scale of reheating to be higher than those probed at the Large Hadron Collider, Ereh > 17.3 TeV at 95% of confidence. For small field models, we obtain the two-sigma lower limits Ereh > 890 TeV for a mean equation of state during reheating = -0.3 and Ereh > 390 GeV for = -0.2. The physical origin of these constraints is pedagogically explained by means of the slow-roll approximation. Finally, when marginalizing over all possible reheating history, the WMAP7 data push massive inflation under pressure (p < 2.2 at 95% of confidence where p is the power index of the large field potentials) while they slightly favor super-Planckian field expectation values in the small field models.Comment: 18 pages, 15 figures, uses RevTeX. References added, matches published versio

Hunting Down the Best Model of Inflation with Bayesian Evidence

We present the first calculation of the Bayesian evidence for different prototypical single field inflationary scenarios, including representative classes of small field and large field models. This approach allows us to compare inflationary models in a well-defined statistical way and to determine the current "best model of inflation". The calculation is performed numerically by interfacing the inflationary code FieldInf with MultiNest. We find that small field models are currently preferred, while large field models having a self-interacting potential of power p>4 are strongly disfavoured. The class of small field models as a whole has posterior odds of approximately 3:1 when compared with the large field class. The methodology and results presented in this article are an additional step toward the construction of a full numerical pipeline to constrain the physics of the early Universe with astrophysical observations. More accurate data (such as the Planck data) and the techniques introduced here should allow us to identify conclusively the best inflationary model.Comment: 12 pages, 2 figures, uses RevTeX. Misprint corrected, references added. Matches published versio

Why does wurtzite form in nanowires of III-V zinc-blende semiconductors?

We develop a nucleation-based model to explain the formation of the wurtzite (WZ) crystalline phase during the vapor-liquid-solid growth of free-standing nanowires of zinc-blende (ZB) semiconductors. We first show that, in nanowires, nucleation generally occurs at the outer edge of the solid/liquid interface (the triple phase line) rather than elsewhere at the solid/liquid interface. In the present case, this entails major differences between ZB and WZ nuclei. Depending on the pertinent interface energies, WZ nucleation is favored at high liquid supersaturation. This explains our systematic observation of ZB during the early stages of nanowire growth.Comment: 4 pages with 4 figures Submitted to Physical Review Letter

Analysis of OD Flows (Raw Data)

In a recent paper, Structural Analysis of Network Traffic Flows, we analyzed the set of Origin Destination traffic flows from the Sprint-Europe and Abilene backbone networks. This report presents the complete set of results from analyzing data from both networks. The results in this report are specific to the Sprint-1 and Abilene datasets studied in the above paper. The following results are presented here: 1 Rows of Principal Matrix (V) 2 1.1 Sprint-1 Dataset ................................ 2 1.2 Abilene Dataset.................................. 9 2 Set of Eigenflows 14 2.1 Sprint-1 Dataset.................................. 14 2.2 Abilene Dataset................................... 21 3 Classifying Eigenflows 26 3.1 Sprint-1 Dataset.................................. 26 3.2 Abilene Datase.................................... 44Centre National de la Recherche Scientifique (CNRS) France; Sprint Labs; Office of Naval Research (N000140310043); National Science Foundation (ANI-9986397, CCR-0325701