Circular Jacobi Ensembles and deformed Verblunsky coefficients

Using the spectral theory of unitary operators and the theory of orthogonal polynomials on the unit circle, we propose a simple matrix model for the following circular analogue of the Jacobi ensemble: c_{\delta,\beta}^{(n)} \prod_{1\leq k with $\Re \delta > -1/2$. If $e$ is a cyclic vector for a unitary $n\times n$ matrix $U$, the spectral measure of the pair $(U,e)$ is well parameterized by its Verblunsky coefficients $(\alpha_0, ..., \alpha_{n-1})$. We introduce here a deformation $(\gamma_0, >..., \gamma_{n-1})$ of these coefficients so that the associated Hessenberg matrix (called GGT) can be decomposed into a product $r(\gamma_0)... r(\gamma_{n-1})$ of elementary reflections parameterized by these coefficients. If $\gamma_0, ..., \gamma_{n-1}$ are independent random variables with some remarkable distributions, then the eigenvalues of the GGT matrix follow the circular Jacobi distribution above. These deformed Verblunsky coefficients also allow to prove that, in the regime $\delta = \delta(n)$ with \delta(n)/n \to \dd, the spectral measure and the empirical spectral distribution weakly converge to an explicit nontrivial probability measure supported by an arc of the unit circle. We also prove the large deviations for the empirical spectral distribution.Comment: New section on large deviations for the empirical spectral distribution, Corrected value for the limiting free energ

Operator-valued spectral measures and large deviations

International audienceWe study large deviation properties of random matricial spectral measures

Modelling of amorphous polymer surfaces in computer simulation

We study surface effects in amorphous polymer systems by means of computer simulation. In the framework of molecular dynamics, we present two different methods to prepare such surfaces. {\em Free} surfaces are stabilized solely by van--der--Waals interactions whereas {\em confined} surfaces emerge in the presence of repelling plates. The two models are compared in various computer simulations. For free surfaces, we analyze the migration of end--monomers to the surface. The buildup of density and pressure profiles from zero to their bulk values depends on the surface preparation method. In the case of confined surfaces, we find density and pressure oszillations next to the repelling plates. We investigate the influence of surfaces on the coordination number, on the orientation of single bonds, and on polymer end--to--end vectors. Furthermore, different statistical methods to determine location and width of the surface region for systems of various chain lengths are discussed and applied. We introduce a ``height function'' and show that this method allows to determine average surface profiles only by scanning the outermost layer of monomers.Comment: 23 pages, 12 figure

A fast Monte Carlo algorithm for studying bottle-brush polymers

Obtaining reliable estimates of the statistical properties of complex macromolecules by computer simulation is a task that requires high computational effort as well as the development of highly efficient simulation algorithms. We present here an algorithm combining local moves, the pivot algorithm, and an adjustable simulation lattice box for simulating dilute systems of bottle-brush polymers with a flexible backbone and flexible side chains under good solvent conditions. Applying this algorithm to the bond fluctuation model, very precise estimates of the mean square end-to-end distances and gyration radii of the backbone and side chains are obtained, and the conformational properties of such a complex macromolecule are studied. Varying the backbone length (from $N_b=67$ to $N_b=1027$), side chain length (from N=0 to N=24 or 48), the scaling predictions for the backbone behavior as well as the side chain behavior are checked. We are also able to give a direct comparison of the structure factor between experimental data and the simulation results.Comment: 9 pages, 10 figure

Reactions at polymer interfaces: A Monte Carlo Simulation

Reactions at a strongly segregated interface of a symmetric binary polymer blend are investigated via Monte Carlo simulations. End functionalized homopolymers of different species interact at the interface instantaneously and irreversibly to form diblock copolymers. The simulations, in the framework of the bond fluctuation model, determine the time dependence of the copolymer production in the initial and intermediate time regime for small reactant concentration $\rho_0 R_g^3=0.163 ... 0.0406$. The results are compared to recent theories and simulation data of a simple reaction diffusion model. For the reactant concentration accessible in the simulation, no linear growth of the copolymer density is found in the initial regime, and a $\sqrt{t}$-law is observed in the intermediate stage.Comment: to appear in Macromolecule

Scale-free static and dynamical correlations in melts of monodisperse and Flory-distributed homopolymers: A review of recent bond-fluctuation model studies

It has been assumed until very recently that all long-range correlations are screened in three-dimensional melts of linear homopolymers on distances beyond the correlation length $\xi$ characterizing the decay of the density fluctuations. Summarizing simulation results obtained by means of a variant of the bond-fluctuation model with finite monomer excluded volume interactions and topology violating local and global Monte Carlo moves, we show that due to an interplay of the chain connectivity and the incompressibility constraint, both static and dynamical correlations arise on distances $r \gg \xi$. These correlations are scale-free and, surprisingly, do not depend explicitly on the compressibility of the solution. Both monodisperse and (essentially) Flory-distributed equilibrium polymers are considered.Comment: 60 pages, 49 figure

Predicting the seasonal evolution of southern African summer precipitation in the DePreSys3 prediction system

We assess the ability of the DePreSys3 prediction system to predict austral summer precipitation (DJF) over southern Africa, defined as the African continent south of 15°S. DePresys3 is a high resolution prediction system (at a horizontal resolution of ~ 60 km in the atmosphere in mid-latitudes and of the quarter degree in the Ocean) and spans the long period 1959–2016. We find skill in predicting interannual precipitation variability, relative to a long-term trend; the anomaly correlation skill score over southern Africa is greater than 0.45 for the first summer (i.e. lead month 2–4), and 0.37 over Mozambique, Zimbabwe and Zambia for the second summer (i.e. lead month 14–16). The skill is related to the successful prediction of the El-Nino Southern Oscillation (ENSO), and the successful simulation of ENSO teleconnections to southern Africa. However, overall skill is sensitive to the inclusion of strong La-Nina events and also appears to change with forecast epoch. For example, the skill in predicting precipitation over Mozambique is significantly larger for the first summer in the 1990–2016 period, compared to the 1959–1985 period. The difference in skill in predicting interannual precipitation variability over southern Africa in different epochs is consistent with a change in the strength of the observed teleconnections of ENSO. After 1990, and consistent with the increased skill, the observed impact of ENSO appears to strengthen over west Mozambique, in association with changes in ENSO related atmospheric convergence anomalies. However, these apparent changes in teleconnections are not captured by the ensemble-mean predictions using DePreSys3. The changes in the ENSO teleconnection are consistent with a warming over the Indian Ocean and modulation of ENSO properties between the different epochs, but may also be associated with unpredictable atmospheric variability

Evidence of a causal and modifiable relationship between kidney function and circulating trimethylamine N-oxide

The host-microbiota co-metabolite trimethylamine N-oxide (TMAO) is linked to increased cardiovascular risk but how its circulating levels are regulated remains unclear. We applied "explainable" machine learning, univariate, multivariate and mediation analyses of fasting plasma TMAO concentration and a multitude of phenotypes in 1,741 adult Europeans of the MetaCardis study. Here we show that next to age, kidney function is the primary variable predicting circulating TMAO, with microbiota composition and diet playing minor, albeit significant, roles. Mediation analysis suggests a causal relationship between TMAO and kidney function that we corroborate in preclinical models where TMAO exposure increases kidney scarring. Consistent with our findings, patients receiving glucose-lowering drugs with reno-protective properties have significantly lower circulating TMAO when compared to propensity-score matched control individuals. Our analyses uncover a bidirectional relationship between kidney function and TMAO that can potentially be modified by reno-protective anti-diabetic drugs and suggest a clinically actionable intervention for decreasing TMAO-associated excess cardiovascular risk

Imidazole propionate is increased in diabetes and associated with dietary patterns and altered microbial ecology

Microbiota-host-diet interactions contribute to the development of metabolic diseases. Imidazole propionate is a novel microbially produced metabolite from histidine, which impairs glucose metabolism. Here, we show that subjects with prediabetes and diabetes in the MetaCardis cohort from three European countries have elevated serum imidazole propionate levels. Furthermore, imidazole propionate levels were increased in subjects with low bacterial gene richness and Bacteroides 2 enterotype, which have previously been associated with obesity. The Bacteroides 2 enterotype was also associated with increased abundance of the genes involved in imidazole propionate biosynthesis from dietary histidine. Since patients and controls did not differ in their histidine dietary intake, the elevated levels of imidazole propionate in type 2 diabetes likely reflects altered microbial metabolism of histidine, rather than histidine intake per se. Thus the microbiota may contribute to type 2 diabetes by generating imidazole propionate that can modulate host inflammation and metabolism