A note on path kernels and partitions

AbstractThe detour order of a graph G, denoted by τ(G), is the order of a longest path in G. A subset S of V(G) is called a Pn-kernel of G if τ(G[S])≤n−1 and every vertex v∈V(G)−S is adjacent to an end-vertex of a path of order n−1 in G[S]. A partition of the vertex set of G into two sets, A and B, such that τ(G[A])≤a and τ(G[B])≤b is called an (a,b)-partition of G. In this paper we show that any graph with girth g has a Pn+1-kernel for every n<3g2−1. Furthermore, if τ(G)=a+b, 1≤a≤b, and G has girth greater than 23(a+1), then G has an (a,b)-partition

System calibration method for Fourier ptychographic microscopy

Fourier ptychographic microscopy (FPM) is a recently proposed quantitative phase imaging technique with high resolution and wide field-of-view (FOV). In current FPM imaging platforms, systematic error sources come from the aberrations, LED intensity fluctuation, parameter imperfections and noise, which will severely corrupt the reconstruction results with artifacts. Although these problems have been researched and some special methods have been proposed respectively, there is no method to solve all of them. However, the systematic error is a mixture of various sources in the real situation. It is difficult to distinguish a kind of error source from another due to the similar artifacts. To this end, we report a system calibration procedure, termed SC-FPM, based on the simulated annealing (SA) algorithm, LED intensity correction and adaptive step-size strategy, which involves the evaluation of an error matric at each iteration step, followed by the re-estimation of accurate parameters. The great performance has been achieved both in simulation and experiments. The reported system calibration scheme improves the robustness of FPM and relaxes the experiment conditions, which makes the FPM more pragmatic.Comment: 18 pages, 9 figure

Electron Density Dependence of in-plane Spin Relaxation Anisotropy in GaAs/AlGaAs Two-Dimensional Electron Gas

We investigated the spin dynamics of two-dimensional electrons in (001) GaAs/AlGaAs heterostructure using the time resolved Kerr rotation technique under a transverse magnetic field. The in-plane spin lifetime is found to be anisotropic below 150k due to the interference of Rashba and Dresselhaus spin-orbit coupling and D'yakonov-Perel' spin relaxation. The ratio of in-plane spin lifetimes is measured directly as a function of temperature and pump power, showing that the electron density in 2DEG channel strongly affects the Rashba spin-orbit coupling.Comment: 3 pages, 2 figure

Coupling of carbon and silicon geochemical cycles in rivers and lakes

Carbon (C) and silicon (Si) biogeochemical cycles are important factors in the regulation of atmospheric CO2 concentrations and hence climate change. Theoretically, these elements are linked by chemical weathering and organism stoichiometry, but this coupling has not been investigated in freshwaters. Here we compiled data from global rivers and lakes in the United States of America and the United Kingdom, in order to characterize the stoichiometry between the biogeochemical cycles of C and Si. In rivers this coupling is confirmed by a significant relationship between HCO3-/Na+ and DSi/Na+, and DSi:HCO3- ratio can reflect the mineral source of chemical weathering. In lakes, however, these characteristic ratios of chemical weathering are altered by algal activity. The lacustrine Si:C atomic ratio is negative feedback regulation by phytoplankton, which may result in this ratio in algal assemblages similar to that in water column. And this regulation suggests lacustrine photosynthetic C fixation in this equilibrium state is quantitative and depends on the DSi concentration. These findings provide new insights into the role of freshwaters in global C and Si biogeochemical cycles

Dexmedetomidine Versus Propofol Sedation Improves Sublingual Microcirculation After Cardiac Surgery: A Randomized Controlled Trial

ObjectivesTo compare the effects of dexmedetomidine and propofol on sublingual microcirculation in patients after cardiac surgery.DesignA prospective, randomized, single-blind study.SettingUniversity hospital.ParticipantsAdult patients undergoing elective valve surgery with cardiopulmonary bypass.InterventionsOn arrival in the intensive care unit (ICU), patients were assigned randomly to receive either dexmedetomidine (0.2-1.5 μg/kg/h) or propofol (5-50 μg/kg/min) with open-label titration to a target Richmond Agitation-Sedation Scale of 0 to –3.Measurements and Main ResultsSublingual microcirculation was recorded using sidestream dark-field imaging at ICU admission (baseline [T1]) and 4 hours (T2) and 24 hours after ICU admission (T3). At T2, median changes in perfused small-vessel density and the De Backer score from baseline were significantly greater in the dexmedetomidine group (n = 29) than in the propofol group (n = 32) (1.3 v 0 mm/mm2, p = 0.025; 0.9 v –0.1/mm, p = 0.005, respectively); median changes in small-vessel density and the proportion of perfused small vessels from baseline also tended to be higher in the dexmedetomidine group compared with the propofol group (1.0 v –0.1 mm/mm2, p = 0.050; 2.1% v 0.5%, p = 0.062, respectively). At T3, there still was a trend toward greater improvements in the small vessel density, proportion of perfused small-vessels, perfused small-vessel density, and De Backer score from baseline in the dexmedetomidine group than in the propofol group.ConclusionsThis trial demonstrated that dexmedetomidine sedation may be better able to improve microcirculation in cardiac surgery patients during the early postoperative period compared with propofol

Effects of dams on riverine biogeochemical cycling and ecology

Currently, dam construction is a main and growing global anthropogenic disturbance on rivers. Dams have major effects on the physics, chemistry, and biology of the original river, including altering water circulation and retention time, sedimentation, nutrient biogeochemical cycling (especially greenhouse gas emissions), and the amount and composition of the organisms present. Among those, the effect of dams on the riverine material cycle and ecology is especially concerning because of its close relationship with current global environmental problems such as climate change and ecological deterioration. This review thus mainly focuses on nutrient cycling and ecological changes in a regulated river. In the future, research on reservoir–river systems should focus on (1) processes and mechanisms of nutrient biogeochemical cycles, (2) interaction between these processes and ecological change such as phytoplankton succession, and (3) developing mathematical functions and models to describe and forecast these processes and their future interactions