Integrable Supersymmetry Breaking Perturbations of N=1,2 Superconformal Minimal Models

We display a new integrable perturbation for both N=1 and N=2 superconformal minimal models. These perturbations break supersymmetry explicitly. Their existence was expected on the basis of the classification of integrable perturbations of conformal field theories in terms of distinct classical KdV type hierarchies sharing a common second Hamiltonian structure.Comment: 10 pages (harvmac), LAVAL PHY-20-9

TREEWIDTH and PATHWIDTH parameterized by vertex cover

After the number of vertices, Vertex Cover is the largest of the classical graph parameters and has more and more frequently been used as a separate parameter in parameterized problems, including problems that are not directly related to the Vertex Cover. Here we consider the TREEWIDTH and PATHWIDTH problems parameterized by k, the size of a minimum vertex cover of the input graph. We show that the PATHWIDTH and TREEWIDTH can be computed in O*(3^k) time. This complements recent polynomial kernel results for TREEWIDTH and PATHWIDTH parameterized by the Vertex Cover

Carne--Varopoulos bounds for centered random walks

We extend the Carne--Varopoulos upper bound on the probability transitions of a Markov chain to a certain class of nonreversible processes by introducing the definition of a ``centering measure.'' In the case of random walks on a group, we study the connections between different notions of centering.Comment: Published at http://dx.doi.org/10.1214/009117906000000052 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

On Integration Methods Based on Scrambled Nets of Arbitrary Size

We consider the problem of evaluating $I(\varphi):=\int_{[0,1)^s}\varphi(x) dx$ for a function $\varphi \in L^2[0,1)^{s}$. In situations where $I(\varphi)$ can be approximated by an estimate of the form $N^{-1}\sum_{n=0}^{N-1}\varphi(x^n)$, with $\{x^n\}_{n=0}^{N-1}$ a point set in $[0,1)^s$, it is now well known that the $O_P(N^{-1/2})$ Monte Carlo convergence rate can be improved by taking for $\{x^n\}_{n=0}^{N-1}$ the first $N=\lambda b^m$ points, $\lambda\in\{1,\dots,b-1\}$, of a scrambled $(t,s)$-sequence in base $b\geq 2$. In this paper we derive a bound for the variance of scrambled net quadrature rules which is of order $o(N^{-1})$ without any restriction on $N$. As a corollary, this bound allows us to provide simple conditions to get, for any pattern of $N$, an integration error of size $o_P(N^{-1/2})$ for functions that depend on the quadrature size $N$. Notably, we establish that sequential quasi-Monte Carlo (M. Gerber and N. Chopin, 2015, \emph{J. R. Statist. Soc. B, to appear.}) reaches the $o_P(N^{-1/2})$ convergence rate for any values of $N$. In a numerical study, we show that for scrambled net quadrature rules we can relax the constraint on $N$ without any loss of efficiency when the integrand $\varphi$ is a discontinuous function while, for sequential quasi-Monte Carlo, taking $N=\lambda b^m$ may only provide moderate gains.Comment: 27 pages, 2 figures (final version, to appear in The Journal of Complexity

Parameters influencing calcium phosphate precipitation in granular sludge sequencing batch reactor

Parameters influencing calcium phosphate precipitation in Calcium phosphate precipitation inside microbial granules cultivated in a granular sequenced batch reactor (GSBR) has been demonstrated to contribute to phosphorus removal during wastewater treatment. Whereas hydroxyapatite (HAP) is proven to accumulate in the granule, the main calcium phosphate precursors that form prior to HAP are here investigated. A separate batch reactor was used to distinguish reactions involving biological phosphate removal from physicochemical reactions involving phosphateprecipitation in order to establish the kinetics and stoichiometry of calcium phosphate formation. Experiments and simulations with PHREEQC and AQUASIM software support the assumption that amorphous calciumphosphate (ACP) is the intermediary in HAP crystallization. The results provide the kinetic rate constants and thermodynamic constants of ACP. The formation of bioliths inside biological aggregates as well as the main parameters that drive their formations are discussed here. Finally, the influence of pH and calcium and phosphate concentrations in the influent was also assessed, in order to determine the contribution of precipitation in the different operating conditions