Robust permanence for interacting structured populations

The dynamics of interacting structured populations can be modeled by $\frac{dx_i}{dt}= A_i (x)x_i$ where $x_i\in \R^{n_i}$, $x=(x_1,\dots,x_k)$, and $A_i(x)$ are matrices with non-negative off-diagonal entries. These models are permanent if there exists a positive global attractor and are robustly permanent if they remain permanent following perturbations of $A_i(x)$. Necessary and sufficient conditions for robust permanence are derived using dominant Lyapunov exponents $\lambda_i(\mu)$ of the $A_i(x)$ with respect to invariant measures $\mu$. The necessary condition requires $\max_i \lambda_i(\mu)>0$ for all ergodic measures with support in the boundary of the non-negative cone. The sufficient condition requires that the boundary admits a Morse decomposition such that $\max_i \lambda_i(\mu)>0$ for all invariant measures $\mu$ supported by a component of the Morse decomposition. When the Morse components are Axiom A, uniquely ergodic, or support all but one population, the necessary and sufficient conditions are equivalent. Applications to spatial ecology, epidemiology, and gene networks are given

Correlation of total cholesterol and protein in urine in patients with the nephrotic syndrome

The excretion of protein and cholesterol in 24 h urine was measured in 42 patients with the nephrotic syndrome. The finding of a positive correlation (r=0.76,p<0.01) between urinary cholesterol and urinary protein would be compatible with an enhanced glomerular filtration of plasma lipoproteins as the cause of lipiduria in the nephrotic syndrome

Optimal extension to Sobolev rough paths

We show that every $\mathbb{R}^d$-valued Sobolev path with regularity $\alpha$ and integrability $p$ can be lifted to a Sobolev rough path in the sense of T. Lyons provided $\alpha >1/p>0$. Moreover, we prove the existence of unique rough path lifts which are optimal w.r.t. strictly convex functionals among all possible rough path lifts given a Sobolev path. As examples, we consider the rough path lift with minimal Sobolev norm and characterize the Stratonovich rough path lift of a Brownian motion as optimal lift w.r.t. to a suitable convex functional. Generalizations of the results to Besov spaces are briefly discussed.Comment: Typos fixed. To appear in Potential Analysi

Sovereign bond risk premiums

Credit risk has become an important factor driving government bond returns. We therefore introduce an asset pricing model which exploits information contained in both forward interest rates and forward CDS spreads. Our empirical analysis covers euro-zone countries with German government bonds as credit risk-free assets. We construct a market factor from the first three principal components of the German forward curve as well as a common and a country-specific credit factor from the principal components of the forward CDS curves. We find that predictability of risk premiums of sovereign euro-zone bonds improves substantially if the market factor is augmented by a common and an orthogonal country-specific credit factor. While the common credit factor is significant for most countries in the sample, the country-specific factor is significant mainly for peripheral euro-zone countries. Finally, we find that during the current crisis period, market and credit risk premiums of government bonds are negative over long subintervals, a finding that we attribute to the presence of financial repression in euro-zone countries

A Multivariate Fast Discrete Walsh Transform with an Application to Function Interpolation

For high dimensional problems, such as approximation and integration, one cannot afford to sample on a grid because of the curse of dimensionality. An attractive alternative is to sample on a low discrepancy set, such as an integration lattice or a digital net. This article introduces a multivariate fast discrete Walsh transform for data sampled on a digital net that requires only $O(N \log N)$ operations, where $N$ is the number of data points. This algorithm and its inverse are digital analogs of multivariate fast Fourier transforms. This fast discrete Walsh transform and its inverse may be used to approximate the Walsh coefficients of a function and then construct a spline interpolant of the function. This interpolant may then be used to estimate the function's effective dimension, an important concept in the theory of numerical multivariate integration. Numerical results for various functions are presented

Ring opening polymerization of lactides and lactones by multimetallic alkyl zinc complexes derived from the acids Ph₂C(X)CO₂2H (X = OH, NH₂ )

The reaction of the dialkylzinc reagents R₂Zn with the acids 2,2-Ph₂C(X)(CO₂H), where X = NH₂, OH, i.e. 2,2′-diphenylglycine (dpgH) or benzilic acid (benzH2), in toluene at reflux temperature afforded the tetra-nuclear ring complexes [RZn(dpg)]₄, where R = Me (1), Et (2), 2-CF₃C₆H₄ (3), and 2,4,6-F₃C₆H₂ (4); complex 2 has been previously reported. The crystal structures of 1·(2MeCN), 3 and 4·(4(C₇H₈)·1.59(H₂O)) are reported, along with that of the intermediate compound (2-CF₃C₆H₄)3B·MeCN and the known compound [ZnCl₂(NCMe)₂]. Complexes 1–4, together with the known complex [(ZnEt)₃(ZnL)₃(benz)₃] (5; L = MeCN), have been screened, in the absence of benzyl alcohol, for their potential to act as catalysts for the ring opening polymerization (ROP) of ε-caprolactone (ε-CL), δ-valerolactone (δ-VL) and rac-lactide (rac-LA); the co-polymerization of ε-CL with rac-LA was also studied. Complexes 3 and 4 bearing fluorinated aryls at zinc were found to afford the highest activities