Controllability on infinite-dimensional manifolds

Following the unified approach of A. Kriegl and P.W. Michor (1997) for a treatment of global analysis on a class of locally convex spaces known as convenient, we give a generalization of Rashevsky-Chow's theorem for control systems in regular connected manifolds modelled on convenient (infinite-dimensional) locally convex spaces which are not necessarily normable.Comment: 19 pages, 1 figur

Strong Chaos without Butterfly Effect in Dynamical Systems with Feedback

We discuss the predictability of a conservative system that drives a chaotic system with positive maximum Lyapunov exponent $\lambda_0$, such as the erratic motion of an asteroid in the gravitational field of two bodies of much larger mass. We consider the case where in absence of feedback (restricted model), the driving system is regular and completely predictable. A small feedback of strength $\epsilon$ still allows a good forecasting in the driving system up to a very long time $T_p \sim \epsilon^{-\alpha}$, where $\alpha$ depends on the details of the system. The most interesting situation happens when the Lyapunov exponent of the total system is strongly chaotic with $\lambda_{tot} \approx \lambda_0$ , practically independent of $\epsilon$. Therefore an exponential amplification of a small incertitude on the initial conditions in the driving system for any $\epsilon \neq 0$ coexists with very long predictability times. The paradox stems from saturation effects in the evolution for the growth of the incertitude as illustrated in a simple model of coupled maps and in a system of three point vortices in a disk.Comment: uuencoded gzipped .tar file with 9 pages of .ps file and 2 .ps figure

Set shifting and reversal learning in patients with bipolar disorder or schizophrenia

Background. Bipolar disorder and schizophrenia have both been associated with deficits in extra-dimensional set shifting (EDS). Deficits in reversal learning (RL) have also been shown in schizophrenia but not in bipolar disorder. This study sought to assess the specificity of these findings in a direct comparison of clinically stable patients with each disorder. Method. The intra-dimensional/extra-dimensional (IDED) set-shifting task, part of the Cambridge Neuropsychological Test Automated Battery (CANTAB), was administered to 30 patients with schizophrenia, 47 with bipolar disorder and a group of 44 unaffected controls. EDS and RL errors were compared between the groups and related to measures of current and past psychiatric symptoms and medication. Results. Both groups of patients with schizophrenia or bipolar disorder made more EDS and RL errors than controls. Neither measure separated the two disorders, even when the analysis was restricted to euthymic patients. No relationship was found with prescribed medication. Conclusions. Patients with bipolar disorder or schizophrenia show common deficits in EDS and RL. These deficits do not seem to be attributable to current symptoms and are consistent with disrupted networks involving the ventral prefrontal cortex

A new method to detect long term trends of methane (CH₄) and nitrous oxide (N₂O) total columns measured within the NDACC ground-based high resolution solar FTIR network

Total columns measured with the ground-based solar FTIR technique are highly variable in time due to atmospheric chemistry and dynamics in the atmosphere above the measurement station. In this paper, a multiple regression model with anomalies of air pressure, total columns of hydrogen fluoride (HF) and carbon monoxide (CO) and tropopause height are used to reduce the variability in the methane (CH4) and nitrous oxide (N2O) total columns to estimate reliable linear trends with as small uncertainties as possible. The method is developed at the Harestua station (60°N, 11°E, 600ma.s.l.) and used on three other European FTIR stations, i.e. Jungfraujoch (47°N, 8°E, 3600ma.s.l.), Zugspitze (47°N, 11°E, 3000ma.s.l.), and Kiruna (68°N, 20°E, 400ma.s.l.). Linear CH4 trends between 0.13±0.01-0.25±0.02%yr−1 were estimated for all stations in the 1996-2009 period. A piecewise model with three separate linear trends, connected at change points, was used to estimate the short term fluctuations in the CH4 total columns. This model shows a growth in 1996–1999 followed by a period of steady state until 2007. From 2007 until 2009 the atmospheric CH4 amount increases between 0.57±0.22–1.15±0.17%yr−1. Linear N2O trends between 0.19±0.01–0.40±0.02%yr−1 were estimated for all stations in the 1996-2007 period, here with the strongest trend at Harestua and Kiruna and the lowest at the Alp stations. From the N2O total columns crude tropospheric and stratospheric partial columns were derived, indicating that the observed difference in the N2O trends between the FTIR sites is of stratospheric origin. This agrees well with the N2O measurements by the SMR instrument onboard the Odin satellite showing the highest trends at Harestua, 0.98±0.28%yr−1, and considerably smaller trends at lower latitudes, 0.27±0.25%yr−1. The multiple regression model was compared with two other trend methods, the ordinary linear regression and a Bootstrap algorithm. The multiple regression model estimated CH4 and N2O trends that differed up to 31% compared to the other two methods and had uncertainties that were up to 300% lower. Since the multiple regression method were carefully validated this stresses the importance to account for variability in the total columns when estimating trend from solar FTIR data

Cohomological tautness for Riemannian foliations

In this paper we present some new results on the tautness of Riemannian foliations in their historical context. The first part of the paper gives a short history of the problem. For a closed manifold, the tautness of a Riemannian foliation can be characterized cohomologically. We extend this cohomological characterization to a class of foliations which includes the foliated strata of any singular Riemannian foliation of a closed manifold

Carbon monoxide (CO) and ethane (C₂H₆) trends from ground-based solar FTIR measurements at six European stations, comparison and sensitivity analysis with the EMEP model

Trends in the CO and C2H6 partial columns (~0–15 km) have been estimated from four European groundbasedsolar FTIR (Fourier Transform InfraRed) stations for the 1996–2006 time period. The CO trends from the four stations Jungfraujoch, Zugspitze, Harestua and Kiruna have been estimated to −0.45±0.16%yr−1, −1.00 ± 0.24%yr−1, −0.62±0.19%yr−1 and −0.61±0.16%yr−1, respectively. The corresponding trends for C2H6 are−1.51±0.23%yr−1, −2.11±0.30%yr−1, −1.09±0.25%yr−1 and −1.14±0.18%yr−1. All trends are presented with their 2-σ confidence intervals. To find possible reasons for the CO trends, the global-scale EMEP MSC-W chemical transport model has been used in a series of sensitivity scenarios. It is shown that the trends are consistent with the combination of a 20% decrease in the anthropogenic CO emissions seen in Europe and North America during the 1996–2006 period and a 20% increase in the anthropogenic CO emissions in East Asia, during the same time period. The possible impacts of CH4 and biogenic volatile organic compounds (BVOCs) are also considered. The European and global-scale EMEP models have been evaluated against the measured CO and C2H6 partial columns from Jungfraujoch, Zugspitze, Bremen, Harestua, Kiruna and Ny-Ålesund. The European model reproduces, on average the measurements at the different sites fairly well and within 10–22% deviation for CO and 14–31% deviation for C2H6. Their seasonal amplitude is captured within 6–35% and 9–124% for CO and C2H6, respectively. However, 61–98% of the CO and C2H6 partial columns in the European model are shown to arise from the boundary conditions, making the globalscale model a more suitable alternative when modeling these two species. In the evaluation of the global model the average partial columns for 2006 are shown to be within 1–9% and 37–50% of the measurements for CO and C2H6, respectively. The global model sensitivity for assumptions made in this paper is also analyzed

Field propagation-induced directionality of carrier-envelope phase-controlled photoemission from nanospheres

Near-fields of non-resonantly laser-excited nanostructures enable strong localization of ultrashort light fields and have opened novel routes to fundamentally modify and control electronic strong-field processes. Harnessing spatiotemporally tunable near-fields for the steering of sub-cycle electron dynamics may enable ultrafast optoelectronic devices and unprecedented control in the generation of attosecond electron and photon pulses. Here we utilize unsupported sub-wavelength dielectric nanospheres to generate near-fields with adjustable structure and study the resulting strong-field dynamics via photoelectron imaging. We demonstrate field propagation-induced tunability of the emission direction of fast recollision electrons up to a regime, where nonlinear charge interaction effects become dominant in the acceleration process. Our analysis supports that the timing of the recollision process remains controllable with attosecond resolution by the carrier-envelope phase, indicating the possibility to expand near-field-mediated control far into the realm of high-field phenomena.112926Ysciescopu

Technical Note: Latitude-time variations of atmospheric column-average dry air mole fractions of CO_2, CH_4 and N_2O

We present a comparison of an atmospheric general circulation model (AGCM)-based chemistry-transport model (ACTM) simulation with total column measurements of CO_2, CH_4 and N_2O from the Total Carbon Column Observing Network (TCCON). The model is able to capture observed trends, seasonal cycles and inter hemispheric gradients at most sampled locations for all three species. The model-observation agreements are best for CO_2, because the simulation uses fossil fuel inventories and an inverse model estimate of non-fossil fuel fluxes. The ACTM captures much of the observed seasonal variability in CO_2 and N_2O total columns (~81 % variance, R>0.9 between ACTM and TCCON for 19 out of 22 cases). These results suggest that the transport processes in troposphere and stratosphere are well represented in ACTM. Thus the poor correlation between simulated and observed CH4 total columns, particularly at tropical and extra-tropical sites, have been attributed to the uncertainties in surface emissions and loss by hydroxyl radicals. While the upward-looking total column measurements of CO_2 contains surface flux signals at various spatial and temporal scales, the N_2O measurements are strongly affected by the concentration variations in the upper troposphere and stratosphere

The rolling problem: overview and challenges

In the present paper we give a historical account -ranging from classical to modern results- of the problem of rolling two Riemannian manifolds one on the other, with the restrictions that they cannot instantaneously slip or spin one with respect to the other. On the way we show how this problem has profited from the development of intrinsic Riemannian geometry, from geometric control theory and sub-Riemannian geometry. We also mention how other areas -such as robotics and interpolation theory- have employed the rolling model.Comment: 20 page