Computing transition rates for the 1-D stochastic Ginzburg--Landau--Allen--Cahn equation for finite-amplitude noise with a rare event algorithm

In this paper we compute and analyse the transition rates and duration of reactive trajectories of the stochastic 1-D Allen-Cahn equations for both the Freidlin-Wentzell regime (weak noise or temperature limit) and finite-amplitude white noise, as well as for small and large domain. We demonstrate that extremely rare reactive trajectories corresponding to direct transitions between two metastable states are efficiently computed using an algorithm called adaptive multilevel splitting. This algorithm is dedicated to the computation of rare events and is able to provide ensembles of reactive trajectories in a very efficient way. In the small noise limit, our numerical results are in agreement with large-deviation predictions such as instanton-like solutions, mean first passages and escape probabilities. We show that the duration of reactive trajectories follows a Gumbel distribution like for one degree of freedom systems. Moreover, the mean duration growths logarithmically with the inverse temperature. The prefactor given by the potential curvature grows exponentially with size. The main novelty of our work is that we also perform an analysis of reactive trajectories for large noises and large domains. In this case, we show that the position of the reactive front is essentially a random walk. This time, the mean duration grows linearly with the inverse temperature and quadratically with the size. Using a phenomenological description of the system, we are able to calculate the transition rate, although the dynamics is described by neither Freidlin--Wentzell or Eyring--Kramers type of results. Numerical results confirm our analysis

Large Deviations in Fast-Slow Systems

The incidence of rare events in fast-slow systems is investigated via analysis of the large deviation principle (LDP) that characterizes the likelihood and pathway of large fluctuations of the slow variables away from their mean behavior – such fluctuations are rare on short timescales but become ubiquitous eventually. This LDP involves an Hamilton-Jacobi equation whose Hamiltonian is related to the leading eigenvalue of the generator of the fast process, and is typically non-quadratic in the momenta – in other words, the LDP for the slow variables in fast-slow systems is different in general from that of any stochastic differential equation (SDE) one would write for the slow variables alone. It is shown here that the eigenvalue problem for the Hamiltonian can be reduced to a simpler algebraic equation for this Hamiltonian for a specific class of systems in which the fast variables satisfy a linear equation whose coefficients depend nonlinearly on the slow variables, and the fast variables enter quadratically the equation for the slow variables. These results are illustrated via examples, inspired by kinetic theories of turbulent flows and plasma, in which the quasipotential characterizing the long time behavior of the system is calculated and shown again to be different from that of an SDE

Previrialization: Perturbative and N-Body Results

We present a series of N-body experiments which confirm the reality of the previrialization effect. We also use weakly nonlinear perturbative approach to study the phenomenon. These two approaches agree when the rms density contrast, $\sigma$, is small; more surprisingly, they remain in agreement when $\sigma \approx 1$. When the slope of the initial power spectrum is $n>-1$, nonlinear tidal interactions slow down the growth of density fluctuations and the magnitude of the suppression increases when $n$ (i.e. the relative amount of small scale power) is increased. For $n<-1$ we see an opposite effect: the fluctuations grow more rapidly than in linear theory. The transition occurs at $n=-1$ when the weakly nonlinear correction to $\sigma$ is close to zero and the growth rate is close to linear. Our results resolve recent controversy between two N-body studies of previrialization. Peebles (1990) assumed $n=0$ and found strong evidence in support of previrialization, while Evrard \& Crone (1992), who assumed $n=-1$, reached opposite conclusions. As we show here, the initial conditions with $n=-1$ are rather special because the nonlinear effects nearly cancel out for that particular spectrum. In addition to our calculations for scale-free initial spectra, we show results for a more realistic spectrum of Peacock \& Dodds (1994). Its slope near the scale usually adopted for normalization is close to $-1$, so $\sigma$ is close to linear. Our results retroactively justify linear normalization at 8$h^{-1}$ Mpc, while also demonstrating the danger and limitations of this practice.Comment: Significantly revised, 25 pages, uuencoded compressed postscript, figures included, to appear in Ap

CMB Polarization can constrain cosmology better than CMB temperature

We demonstrate that for a cosmic variance limited experiment, CMB E polarization alone places stronger constraints on cosmological parameters than CMB temperature. For example, we show that EE can constrain parameters better than TT by up to a factor 2.8 when a multipole range of l=30-2500 is considered. We expose the physical effects at play behind this remarkable result and study how it depends on the multipole range included in the analysis. In most relevant cases, TE or EE surpass the TT based cosmological constraints. This result is important as the small scale astrophysical foregrounds are expected to have a much reduced impact on polarization, thus opening the possibility of building cleaner and more stringent constraints of the LCDM model. This is relevant specially for proposed future CMB satellite missions, such as CORE or PRISM, that are designed to be cosmic variance limited in polarization till very large multipoles. We perform the same analysis for a Planck-like experiment, and conclude that even in this case TE alone should determine the constraint on $\Omega_ch^2$ better than TT by 15%, while determining $\Omega_bh^2$, $n_s$ and $\theta$ with comparable accuracy. Finally, we explore a few classical extensions of the LCDM model and show again that CMB polarization alone provides more stringent constraints than CMB temperature in case of a cosmic variance limited experiment.Comment: 14 pages, 16 figure

Low parathyroid hormone status induced by high dialysate calcium is an independent risk factor for cardiovascular death in hemodialysis patients

Here we studied a possible association between low parathyroid hormone (PTH) status and mortality in incident patients undergoing hemodialysis . A total of 1983 patients were included at baseline and prospectively followed for 24 months. Patients were classified according to their Kidney Disease: Improving Global Outcomes PTH status at baseline and at 12 months, and mortality evaluated at 12 to 24 months using adjusted Cox analysis. Factors potentially involved in PTH status variability between baseline and 12 months were analyzed. A decrease in serum PTH from normal or high to low values between baseline and 12 months was associated with significantly increased cardiovascular mortality at 12 to 24 months (hazard ratio, 2.03; 95% confidence interval, 1.22–3.36). For patients with high or normal baseline PTH levels, the main independent factor at 6 months for a decrease to low PTH levels at 12 months was high dialysate calcium (1.75 mmol/L), whereas prescription of non–calcium-based phosphate binders was associated with a lower risk of PTH decrease. In the high cardiovascular (CV) mortality risk subgroup of patients who acquired a low PTH status at 12 months, the main independent factor at 12 months associated with significant 12- to 24-month CV mortality was high dialysate calcium (odds ratio, 5.44; 95% CI, 2.52–11.75). Thus, patients with a serum PTH decrease to low values after 1 year of hemodialysis treatment are at high risk of short-term CV death. High dialysate calcium was an important contributor to PTH oversuppression, and continued use was associated with increased CV mortality

Direct Observation of Cosmic Strings via their Strong Gravitational Lensing Effect: II. Results from the HST/ACS Image Archive

We have searched 4.5 square degrees of archival HST/ACS images for cosmic strings, identifying close pairs of similar, faint galaxies and selecting groups whose alignment is consistent with gravitational lensing by a long, straight string. We find no evidence for cosmic strings in five large-area HST treasury surveys (covering a total of 2.22 square degrees), or in any of 346 multi-filter guest observer images (1.18 square degrees). Assuming that simulations ccurately predict the number of cosmic strings in the universe, this non-detection allows us to place upper limits on the unitless Universal cosmic string tension of G mu/c^2 < 2.3 x 10^-6, and cosmic string density of Omega_s < 2.1 x 10^-5 at the 95% confidence level (marginalising over the other parameter in each case). We find four dubious cosmic string candidates in 318 single filter guest observer images (1.08 square degrees), which we are unable to conclusively eliminate with existing data. The confirmation of any one of these candidates as cosmic strings would imply G mu/c^2 ~ 10^-6 and Omega_s ~ 10^-5. However, we estimate that there is at least a 92% chance that these string candidates are random alignments of galaxies. If we assume that these candidates are indeed false detections, our final limits on G mu/c^2 and Omega_s fall to 6.5 x 10^-7 and 7.3 x 10^-6. Due to the extensive sky coverage of the HST/ACS image archive, the above limits are universal. They are quite sensitive to the number of fields being searched, and could be further reduced by more than a factor of two using forthcoming HST data.Comment: 21 pages, 18 figure

Climate dynamics and fluid mechanics: Natural variability and related uncertainties

The purpose of this review-and-research paper is twofold: (i) to review the role played in climate dynamics by fluid-dynamical models; and (ii) to contribute to the understanding and reduction of the uncertainties in future climate-change projections. To illustrate the first point, we focus on the large-scale, wind-driven flow of the mid-latitude oceans which contribute in a crucial way to Earth's climate, and to changes therein. We study the low-frequency variability (LFV) of the wind-driven, double-gyre circulation in mid-latitude ocean basins, via the bifurcation sequence that leads from steady states through periodic solutions and on to the chaotic, irregular flows documented in the observations. This sequence involves local, pitchfork and Hopf bifurcations, as well as global, homoclinic ones. The natural climate variability induced by the LFV of the ocean circulation is but one of the causes of uncertainties in climate projections. Another major cause of such uncertainties could reside in the structural instability in the topological sense, of the equations governing climate dynamics, including but not restricted to those of atmospheric and ocean dynamics. We propose a novel approach to understand, and possibly reduce, these uncertainties, based on the concepts and methods of random dynamical systems theory. As a very first step, we study the effect of noise on the topological classes of the Arnol'd family of circle maps, a paradigmatic model of frequency locking as occurring in the nonlinear interactions between the El Nino-Southern Oscillations (ENSO) and the seasonal cycle. It is shown that the maps' fine-grained resonant landscape is smoothed by the noise, thus permitting their coarse-grained classification. This result is consistent with stabilizing effects of stochastic parametrization obtained in modeling of ENSO phenomenon via some general circulation models.Comment: Invited survey paper for Special Issue on The Euler Equations: 250 Years On, in Physica D: Nonlinear phenomen

Observing the Evolution of the Universe

How did the universe evolve? The fine angular scale (l>1000) temperature and polarization anisotropies in the CMB are a Rosetta stone for understanding the evolution of the universe. Through detailed measurements one may address everything from the physics of the birth of the universe to the history of star formation and the process by which galaxies formed. One may in addition track the evolution of the dark energy and discover the net neutrino mass. We are at the dawn of a new era in which hundreds of square degrees of sky can be mapped with arcminute resolution and sensitivities measured in microKelvin. Acquiring these data requires the use of special purpose telescopes such as the Atacama Cosmology Telescope (ACT), located in Chile, and the South Pole Telescope (SPT). These new telescopes are outfitted with a new generation of custom mm-wave kilo-pixel arrays. Additional instruments are in the planning stages.Comment: Science White Paper submitted to the US Astro2010 Decadal Survey. Full list of 177 author available at http://cmbpol.uchicago.ed

CXCL12 expression by healthy and malignant ovarian epithelial cells

<p>Abstract</p> <p>Background</p> <p>CXCL12 has been widely reported to play a biologically relevant role in tumor growth and spread. In epithelial ovarian cancer (EOC), CXCL12 enhances tumor angiogenesis and contributes to the immunosuppressive network. However, its prognostic significance remains unclear. We thus compared CXCL12 status in healthy and malignant ovaries, to assess its prognostic value.</p> <p>Methods</p> <p>Immunohistochemistry was used to analyze CXCL12 expression in the reproductive tracts, including the ovaries and fallopian tubes, of healthy women, in benign and borderline epithelial tumors, and in a series of 183 tumor specimens from patients with advanced primary EOC enrolled in a multicenter prospective clinical trial of paclitaxel/carboplatin/gemcitabine-based chemotherapy (GINECO study). Univariate COX model analysis was performed to assess the prognostic value of clinical and biological variables. Kaplan-Meier methods were used to generate progression-free and overall survival curves.</p> <p>Results</p> <p>Epithelial cells from the surface of the ovary and the fallopian tubes stained positive for CXCL12, whereas the follicles within the ovary did not. Epithelial cells in benign, borderline and malignant tumors also expressed CXCL12. In EOC specimens, CXCL12 immunoreactivity was observed mostly in epithelial tumor cells. The intensity of the signal obtained ranged from strong in 86 cases (47%) to absent in 18 cases (<10%). This uneven distribution of CXCL12 did not reflect the morphological heterogeneity of EOC. CXCL12 expression levels were not correlated with any of the clinical parameters currently used to determine EOC prognosis or with HER2 status. They also had no impact on progression-free or overall survival.</p> <p>Conclusion</p> <p>Our findings highlight the previously unappreciated constitutive expression of CXCL12 on healthy epithelia of the ovary surface and fallopian tubes, indicating that EOC may originate from either of these epithelia. We reveal that CXCL12 production by malignant epithelial cells precedes tumorigenesis and we confirm in a large cohort of patients with advanced EOC that CXCL12 expression level in EOC is not a valuable prognostic factor in itself.</p> <p>Trial Registration</p> <p>ClinicalTrials.gov: <a href="http://www.clinicaltrials.gov/ct2/show/NCT00052468">NCT00052468</a></p