Geometric syzygies of elliptic normal curves and their secant varieties

We show that the linear syzygy spaces of elliptic normal curves, their secant varieties and of bielliptic canonical curves are spanned by geometric syzygies.Comment: 31 Pages; AMSlate

The quest for companions to post-common envelope binaries IV: The 2:1 mean-motion resonance of the planets orbiting NN Serpentis

We present 69 new mid-eclipse times of the young post-common envelope binary (PCEB) NN Ser, which was previously suggested to possess two circumbinary planets. We have interpreted the observed eclipse-time variations in terms of the light-travel time effect caused by two planets, exhaustively covering the multi-dimensional parameter space by fits in the two binary and ten orbital parameters. We supplemented the fits by stability calculations for all models with an acceptable chi-square. An island of secularly stable 2:1 resonant solutions exists, which coincides with the global chi-square minimum. Our best-fit stable solution yields current orbital periods P_o = 15.47 yr and P_i = 7.65 yr and eccentricities e_o = 0.14 and e_i = 0.22 for the outer (o) and inner (i) planets, respectively. The companions qualify as giant planets, with masses of 7.0 M_Jup and 1.7 M_Jup for the case of orbits coplanar with that of the binary. The two-planet model that starts from the present system parameters has a lifetime greater than 10^8 yr, which significantly exceeds the age of NN Ser of 10^6 yr as a PCEB. The resonance is characterized by libration of the resonant variable Theta_1 and circulation of omega_i-omega_o, the difference between the arguments of periapse of the two planets. No stable non-resonant solutions were found, and the possibility of a 5:2 resonance suggested previously by us is now excluded at the 99.3% confidence level.Comment: 8 pages, 8 figure

The interplay between long- and short-range temporal correlations shapes cortex dynamics across vigilance states

Increasing evidence suggests that cortical dynamics during wake exhibits long-range temporal correlations suitable to integrate inputs over extended periods of time to increase the signal-to-noise ratio in decision-making and working memory tasks. Accordingly, sleep has been suggested as a state characterized by a breakdown of long-range correlations; detailed measurements of neuronal timescales that support this view, however, have so far been lacking. Here we show that the long timescales measured at the individual neuron level in freely-behaving rats during the awake state are abrogated during non-REM (NREM) sleep. We provide evidence for the existence of two distinct states in terms of timescale dynamics in cortex: one which is characterized by long timescales which dominate during wake and REM sleep, and a second one characterized by the absence of long-range temporal correlations which characterizes NREM sleep. We observe that both timescale regimes can co-exist and, in combination, lead to an apparent gradual decline of long timescales during extended wake which is restored after sleep. Our results provide a missing link between the observed long timescales in individual neuron fluctuations during wake and the reported absence of long-term correlations during deep sleep in EEG and fMRI studies. They furthermore suggest a network-level function of sleep, to reorganize cortical networks towards states governed by slow cortex dynamics to ensure optimal function for the time awake

Alternative fungicides to control apple scab in organic apple production: results of an orchard trial in 2003

Apple scab, caused by the fungus Venturia inaequalis, is the disease that most often decreases yield and causes loss of fruit quality in organic apple production. Damage to the fruits consists of brown to black spots, but in some years and on some varieties attacks can result in small misshapen fruits, that are totally unsuitable for fresh consumption