Production of W and Z bosons accompanied by jets at LHC startup

We report on potential for measurement of W and Z boson production accompanied by jets at the CMS experiment. Of particular interest are jet multiplicity and Pt distributions. The 10/pb to 100/pb datasets expected in the startup year of operation of LHC are likely to already provide information beyond the reach of the Tevatron collider both in jet multiplicity and Pt range. We are especially interested in understanding the ratios of W+jets to Z+jets distributions by comparing them to next-to-leading order Monte Carlo generators, as these processes present a formidable background for searches of new physics phenomena.Comment: Poster session at ICHEP08, Philadelphia, USA, July 2008. 3 pages, LaTeX, 1 jpg figure. Updated with the new latex template for ICHEP0

Exploration-exploitation tradeoffs dictate the optimal distributions of phenotypes for populations subject to fitness fluctuations

We study a minimal model for the growth of a phenotypically heterogeneous population of cells subject to a fluctuating environment in which they can replicate (by exploiting available resources) and modify their phenotype within a given landscape (thereby exploring novel configurations). The model displays an exploration-exploitation trade-off whose specifics depend on the statistics of the environment. Most notably, the phenotypic distribution corresponding to maximum population fitness (i.e. growth rate) requires a non-zero exploration rate when the magnitude of environmental fluctuations changes randomly over time, while a purely exploitative strategy turns out to be optimal in two-state environments, independently of the statistics of switching times. We obtain analytical insight into the limiting cases of very fast and very slow exploration rates by directly linking population growth to the features of the environment.Comment: 13 pages, 5 figure

Non-commutative Painleve' equations and Hermite-type matrix orthogonal polynomials

We study double integral representations of Christoffel-Darboux kernels associated with two examples of Hermite-type matrix orthogonal polynomials. We show that the Fredholm determinants connected with these kernels are related through the Its-Izergin-Korepin-Slavnov (IIKS) theory with a certain Riemann-Hilbert problem. Using this Riemann-Hilbert problem we obtain a Lax pair whose compatibility conditions lead to a non-commutative version of the Painleve' IV differential equation for each family.Comment: Final version, accepted for publication on CMP: Communications in Mathematical Physics. 24 pages, 1 figur