Symmetrized models of last passage percolation and non-intersecting lattice paths

It has been shown that the last passage time in certain symmetrized models of directed percolation can be written in terms of averages over random matrices from the classical groups $U(l)$, $Sp(2l)$ and $O(l)$. We present a theory of such results based on non-intersecting lattice paths, and integration techniques familiar from the theory of random matrices. Detailed derivations of probabilities relating to two further symmetrizations are also given.Comment: 21 pages, 5 figure

Distillation of continuous-variable entanglement with optical means

We present an event-ready procedure that is capable of distilling Gaussian two-mode entangled states from a supply of weakly entangled states that have become mixed in a decoherence process. This procedure relies on passive optical elements and photon detectors distinguishing the presence and the absence of photons, but does not make use of photon counters. We identify fixed points of the iteration map, and discuss in detail its convergence properties. Necessary and sufficient criteria for the convergence to two-mode Gaussian states are presented. On the basis of various examples we discuss the performance of the procedure as far as the increase of the degree of entanglement and two-mode squeezing is concerned. Finally, we consider imperfect operations and outline the robustness of the scheme under non-unit detection efficiencies of the detectors. This analysis implies that the proposed protocol can be implemented with currently available technology and detector efficiencies.Comment: 14 pages, 12 figure

Response of Acala Cotton to Nitrogen Rates in the San Joaquin Valley of California

The responses of Acala cotton (Gossypium hirsutum L.) in California to a range of applied nitrogen (N) treatments were investigated in a 5-year, multisite experiment. The experiment’s goals were to identify crop growth and yield responses to applied N and provide information to better assess the utility of soil residual N estimates in improving fertilizer management. Baseline fertilizer application rates for the lowest applied N treatments were based on residual soil nitrate-N (NO3-N) levels determined on soil samples from the upper 0.6 m of the soil collected prior to spring N fertilization and within 1 week postplanting each year. Results have shown positive cotton lint yield responses to increases in applied N across the 56 to 224 kg N/ha range in only 41% (16 out of 39) of test sites. Soil NO3-N monitoring to a depth of 2.4 m in the spring (after planting) and fall (postharvest) indicate most changes in soil NO3- occur within the upper 1.2 m of soil. However, some sites (those most prone to leaching losses of soluble nutrients) also exhibited net increases in soil NO3-N in the 1.2- to 2.4-m depth zone when comparing planting time vs. postharvest data. The lack of yield responses and soil NO3-N accumulations at some sites indicate that more efforts should be put into identifying the amount of plant N requirements that can be met from residual soil N, rather than solely from fertilizer N applications