Root to Kellerer

We revisit Kellerer's Theorem, that is, we show that for a family of real probability distributions $(\mu_t)_{t\in [0,1]}$ which increases in convex order there exists a Markov martingale $(S_t)_{t\in[0,1]}$ s.t.\ $S_t\sim \mu_t$. To establish the result, we observe that the set of martingale measures with given marginals carries a natural compact Polish topology. Based on a particular property of the martingale coupling associated to Root's embedding this allows for a relatively concise proof of Kellerer's theorem. We emphasize that many of our arguments are borrowed from Kellerer \cite{Ke72}, Lowther \cite{Lo07}, and Hirsch-Roynette-Profeta-Yor \cite{HiPr11,HiRo12}.Comment: 8 pages, 1 figur

Multi-field Inflation with a Random Potential

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian motion with a drift in the D-dimensional field space. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, leads to rich phenomenologies, such as primordial fluctuations in the power spectrum on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and can be detected or falsified with more data coming in the future. The tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, but can possibly be enhanced by resonant effects or arise from the entropic perturbations during the onset of (p)reheating. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.Comment: More clarifications and references adde

Multi-field Inflation with a Random Potential

Motivated by the possibility of inflation in the cosmic landscape, which may be approximated by a complicated potential, we study the density perturbations in multi-field inflation with a random potential. The random potential causes the inflaton to undergo a Brownian motion with a drift in the D-dimensional field space. To quantify such an effect, we employ a stochastic approach to evaluate the two-point and three-point functions of primordial perturbations. We find that in the weakly random scenario the resulting power spectrum resembles that of the single field slow-roll case, with up to 2% more red tilt. The strongly random scenario, leads to rich phenomenologies, such as primordial fluctuations in the power spectrum on all angular scales. Such features may already be hiding in the error bars of observed CMB TT (as well as TE and EE) power spectrum and can be detected or falsified with more data coming in the future. The tensor power spectrum itself is free of fluctuations and the tensor to scalar ratio is enhanced. In addition a large negative running of the power spectral index is possible. Non-Gaussianity is generically suppressed by the growth of adiabatic perturbations on super-horizon scales, but can possibly be enhanced by resonant effects or arise from the entropic perturbations during the onset of (p)reheating. The formalism developed in this paper can be applied to a wide class of multi-field inflation models including, e.g. the N-flation scenario.Comment: More clarifications and references adde

New quinoxaline derivatives as potential MT₁ and MT₂ receptor ligands.

Ever since the idea arose that melatonin might promote sleep and resynchronize circadian rhythms, many research groups have centered their efforts on obtaining new melatonin receptor ligands whose pharmacophores include an aliphatic chain of variable length united to an N-alkylamide and a methoxy group (or a bioisostere), linked to a central ring. Substitution of the indole ring found in melatonin with a naphthalene or quinoline ring leads to compounds of similar affinity. The next step in this structural approximation is to introduce a quinoxaline ring (a bioisostere of the quinoline and naphthalene rings) as the central nucleus of future melatoninergic ligand

The Trispectrum in the Multi-brid Inflation

The trispectrum is at least as important as the bispectrum and its size can be characterized by two parameters $\tau_{NL}$ and $g_{NL}$. In this short paper, we focus on the Multi-brid inflation, in particular the two-brid inflation model in arXiv.0805.0974, and find that $\tau_{NL}$ is always positive and roughly equals to $({6\over 5}f_{NL})^2$ for the low scale inflation, but $g_{NL}$ can be negative or positive and its order of magnitude can be the same as that of $\tau_{NL}$ or even largerComment: 12 pages; minor correction, refs added; further refs added, version for publication in JCA

Primordial Trispectrum from Entropy Perturbations in Multifield DBI Model

We investigate the primordial trispectra of the general multifield DBI inflationary model. In contrast with the single field model, the entropic modes can source the curvature perturbations on the super horizon scales, so we calculate the contributions from the interaction of four entropic modes mediating one adiabatic mode to the trispectra, at the large transfer limit ($T_{RS}\gg1$). We obtained the general form of the 4-point correlation functions, plotted the shape diagrams in two specific momenta configurations, "equilateral configuration" and "specialized configuration". Our figures showed that we can easily distinguish the two different momenta configurations.Comment: 17pages, 7 figures, version to appear in JCA

An Inflationary Scenario in Intersecting Brane Models

We propose a new scenario for D-term inflation which appears quite straightforwardly in the open string sector of intersecting brane models. We take the inflaton to be a chiral field in a bifundamental representation of the hidden sector and we argue that a sufficiently flat potential can be brane engineered. This type of model generically predicts a near gaussian red spectrum with negligible tensor modes. We note that this model can very naturally generate a baryon asymmetry at the end of inflation via the recently proposed hidden sector baryogenesis mechanism. We also discuss the possibility that Majorana masses for the neutrinos can be simultaneously generated by the tachyon condensation which ends inflation. Our proposed scenario is viable for both high and low scale supersymmetry breaking.Comment: 30 pages, 2 figures; v2 references and comments adde

Effect of denosumab versus zoledronic acid in preventing skeletal-related events in patients with bone metastases by baseline characteristics

Background: Analyses of phase III trials showed that denosumab was superior to zoledronic acid (ZA) in preventing skeletal-related events (SREs) irrespective of age, history of SREs, or baseline pain status. This analysis assessed the risk of SREs across additional baseline characteristics. Patients and Methods: Patients (N Z 5543) from three phase III trials who had breast cancer, prostate cancer, or other solid tumours and one or more bone metastasis were included. Superiority of denosumab versus ZA in reducing risk of first SRE and first and subsequent SREs was assessed in subgroups defined by the Eastern Cooperative Oncology Group performance status (ECOG PS), bone metastasis location, bone metastasis number, visceral metastasis presence/absence, and urinary N-telopeptide (uNTx) level using Cox proportional hazards and AndersoneGill models. Subgroups except bone metastasis location were also assessed for each solid tumour type. Results: Compared with ZA, denosumab significantly reduced the risk of first SRE across all subgroups (hazard ratio [HR] ranges: ECOG PS, 0.79e0.84; bone metastasis location, 0.78e0.83; bone metastasis number, 0.78e0.84; visceral metastasis presence/absence, 0.80e0.82; uNTx level, 0.73e0.86) and reduced the risk of first and subsequent SREs in all subgroups (HR ranges: ECOG PS, 0.76e0.83; bone metastasis location, 0.78e0.84; bone metastasis number, 0.79e0.81; visceral metastasis presence/absence, 0.79e0.81; uNTx level, 0.74e0.83). Similar results were observed in subgroups across tumour types. Conclusion: Denosumab was superior to ZA in preventing SREs in patients with bone metastases from advanced cancer, regardless of ECOG PS, bone metastasis number, baseline visceral metastasis presence/absence, and uNTx leve

Cherenkov radiation emitted by ultrafast laser pulses and the generation of coherent polaritons

We report on the generation of coherent phonon polaritons in ZnTe, GaP and LiTaO$_{3}$ using ultrafast optical pulses. These polaritons are coupled modes consisting of mostly far-infrared radiation and a small phonon component, which are excited through nonlinear optical processes involving the Raman and the second-order susceptibilities (difference frequency generation). We probe their associated hybrid vibrational-electric field, in the THz range, by electro-optic sampling methods. The measured field patterns agree very well with calculations for the field due to a distribution of dipoles that follows the shape and moves with the group velocity of the optical pulses. For a tightly focused pulse, the pattern is identical to that of classical Cherenkov radiation by a moving dipole. Results for other shapes and, in particular, for the planar and transient-grating geometries, are accounted for by a convolution of the Cherenkov field due to a point dipole with the function describing the slowly-varying intensity of the pulse. Hence, polariton fields resulting from pulses of arbitrary shape can be described quantitatively in terms of expressions for the Cherenkov radiation emitted by an extended source. Using the Cherenkov approach, we recover the phase-matching conditions that lead to the selection of specific polariton wavevectors in the planar and transient grating geometry as well as the Cherenkov angle itself. The formalism can be easily extended to media exhibiting dispersion in the THz range. Calculations and experimental data for point-like and planar sources reveal significant differences between the so-called superluminal and subluminal cases where the group velocity of the optical pulses is, respectively, above and below the highest phase velocity in the infrared.Comment: 13 pages, 11 figure

Lectures on inflation and cosmological perturbations

The purpose of these lectures is to give a pedagogical introduction to inflation and the production of primordial perturbations, as well as a review of some of the latest developments in this domain. After a short introduction, we review the main principles of the Hot Big Bang model, as well as its limitations. This motivates the study of cosmological inflation induced by a slow-rolling scalar field. We then turn to the analysis of cosmological perturbations, and explain how the vacuum quantum fluctuations are amplified during an inflationary phase. The next step consists in relating the perturbations generated during inflation to the perturbations of the cosmological fluid in the radiation dominated phase. The final part of these lectures gives a review of more general models of inflation, involving multiple fields or non standard kinetic terms. Although more complicated, these models are usually motivated by high energy physics and they can lead to specific signatures that are not expected in the simplest models of inflation. After introducing a very general formalism to describe perturbations in multi-field models with arbitrary kinetic terms, several interesting cases are presented. We also stress the role of entropy perturbations in the context of multi-field models. Finally, we discuss in detail the non-Gaussianities of the primordial perturbations and some models that could produce a detectable level of non-Gaussianities.Comment: 56 pages, 5 figures; Lectures given at the Second TRR33 Winter School on cosmology, Passo del Tonale (Italy), December 200