Sharp measure contraction property for generalized H-type Carnot groups

We prove that H-type Carnot groups of rank $k$ and dimension $n$ satisfy the $\mathrm{MCP}(K,N)$ if and only if $K\leq 0$ and $N \geq k+3(n-k)$. The latter integer coincides with the geodesic dimension of the Carnot group. The same result holds true for the larger class of generalized H-type Carnot groups introduced in this paper, and for which we compute explicitly the optimal synthesis. This constitutes the largest class of Carnot groups for which the curvature exponent coincides with the geodesic dimension. We stress that generalized H-type Carnot groups have step 2, include all corank 1 groups and, in general, admit abnormal minimizing curves. As a corollary, we prove the absolute continuity of the Wasserstein geodesics for the quadratic cost on all generalized H-type Carnot groups.Comment: 18 pages. This article extends the results of arXiv:1510.05960. v2: revised and improved version. v3: final version, to appear in Commun. Contemp. Mat

Pollination of the European food-deceptive Traunsteinera globosa (Orchidaceae): the importance of nectar-producing neighbouring plants

European food-deceptive orchids generally flower early in spring and rely on naïve pollinators for their reproduction. Some species however, flower later in the summer, when many other rewarding plants species are also in bloom. In dense flowering communities, deceptive orchids may suffer from competition for pollinator resources, or might alternatively benefit from higher community attractiveness. We investigated the pollination strategy of the deceptive species Traunsteinera globosa, and more specifically whether it benefited from the presence of coflowering rewarding species. We carried out a population survey to quantify the density and reproductive success of the orchid as well as the density of all coflowering species. Our results suggest that the deceptive orchid not only benefited from the presence of coflowering species, but that interestingly the density of the species Trifolium pratense was significantly positively correlated with the orchid's reproductive success. This species might simply act as a magnet species attracting pollinators near T. globosa, or could influence the orchid reproductive fitness through a more species-specific interaction. We propose that morphological or colour similarities between the two species should be investigated in more detail to decipher this pollination facilitation effec

Experimental investigation of the effect of spatial aggregation on reproductive success in a rewardless orchid

Plant reproductive success within a patch may depend on plant aggregation through pollinator attraction. For rewardless plants that lack rewards for pollinators, reproductive success may rely strongly on the learning abilities of pollinators. These abilities depend on relative co-flowering rewarding and rewardless plant species spatial distributions. We investigated the effect of aggregation on the reproductive success of a rewardless orchid by setting up 16 arrays in a factorial design with two levels of intraspecific aggregation for both a rewardless orchid and a rewarding co-flowering species. Our results show that increasing aggregation of both species negatively influenced the reproductive success of the rewardless plants. To our knowledge, this is the first experimental study demonstrating negative effects of aggregation on reproductive success of a rewardless species due both to its own spatial aggregation and that of a co-flowering rewarding species. We argue that pollinator learning behaviour is the key driver behind this result

Do rewardless orchids show a positive relationship between phenotypic diversity and reproductive success?

Among rewardless orchids, pollinator sampling behavior has been suggested to drive a positive relationship between population phenotypic variability and absolute reproductive success, and hence population fitness. We tested this hypothesis by constructing experimental arrays using the rewardless orchid Dactylorhiza sambucina, which is dimorphic for corolla color. We found no evidence that polymorphic arrays had higher mean reproductive success than monomorphic arrays for pollinia removal, pollen deposition, or fruit set. For pollinia removal, monomorphic yellow arrays had significantly greater reproductive success, and monomorphic red the least. A tendency for yellow arrays to have higher pollen deposition was also found. We argue that differential population fitness was most likely to reflect differential numbers of pollinators attracted to arrays, through preferential long-distance attraction to arrays with yellow inflorescences. Correlative studies of absolute reproductive success in 52 populations of D. sambucina supported our experimental results. To our knowledge this is the first study to suggest that attraction of a greater number of pollinators to rewardless orchids may be of greater functional importance to population fitness, and thus ecology and conservation, than are the behavioral sequences of individual pollinators

Can remifentanil use in obstetrics be improved by optimal patient-controlled analgesia bolus timing?

Background The safety of patient-controlled i.v. analgesia (PCA) with remifentanil for obstetrical analgesia remains a matter of concern. The efficacy of remifentanil bolus application, that is, the coincidence between pain and remifentanil effect-site concentration, may be improved by forecasting contractions, but it is not known whether such a technique would also improve safety. Methods We recorded pain intensity during labour continuously using a handheld dynamometer in 43 parturients. Using these data, we compared different models in their ability to predict future contractions. In addition, we modelled remifentanil effect-site concentration using three simulated modes of bolus administration, with and without prediction of future contractions. Results The average duration of pain during contractions recorded by the dynamometer was 45 [14 standard deviation (sd)] s. The time interval between painful contractions was highly variable, with a mean of 151 (31 sd) s during the first and 154 (52 sd) s during the second recording. Using a simple algorithm (three-point moving average), the sd of the difference between predicted and observed inter-contraction intervals can be reduced from 0.95 to 0.79 min. However, the coincidence between remifentanil concentration and pain during contraction is not substantially improved when using these models to guide remifentanil bolus application. Conclusions Because of the large variability of inter-contraction intervals, the use of prediction models will not influence the mean remifentanil concentration in-between contractions. Using models predicting future contractions to improve the timing of remifentanil PCA bolus administration will not diminish the need of continuous clinical surveillance and other safety measure

Pollination of the European food-deceptive Traunsteinera globosa (Orchidaceae): the importance of nectar-producing neighbouring plants

ISSN:0378-2697ISSN:1615-611

Monge's transport problem in the Heisenberg group

We prove the existence of solutions to Monge transport problem between two compactly supported Borel probability measures in the Heisenberg group equipped with its Carnot-Caratheodory distance assuming that the initial measure is absolutely continuous with respect to the Haar measure of the group

Exact quantum jump approach to open systems in Bosonic and spin baths

A general method is developed which enables the exact treatment of the non-Markovian quantum dynamics of open systems through a Monte Carlo simulation technique. The method is based on a stochastic formulation of the von Neumann equation of the composite system and employs a pair of product states following a Markovian random jump process. The performance of the method is illustrated by means of stochastic simulations of the dynamics of open systems interacting with a Bosonic reservoir at zero temperature and with a spin bath in the strong coupling regime.Comment: 4 pages, 2 figure

Neel Order and Electron Spectral Functions in the Two-Dimensional Hubbard Model: a Spin-Charge Rotating Frame Approach

Using recently developed quantum SU(2)xU(1) rotor approach, that provides a self-consistent treatment of the antiferromagnetic state we have performed electronic spectral function calculations for the Hubbard model on the square lattice. The collective variables for charge and spin are isolated in the form of the space-time fluctuating U(1) phase field and rotating spin quantization axis governed by the SU(2) symmetry, respectively. As a result interacting electrons appear as composite objects consisting of bare fermions with attached U(1) and SU(2) gauge fields. This allows us to write the fermion Green's function in the space-time domain as the product CP^1 propagator resulting from the SU(2) gauge fields, U(1) phase propagator and the pseudo-fermion correlation function. As a result the problem of calculating the spectral line shapes now becomes one of performing the convolution of spin, charge and pseudo-fermion Green's functions. The collective spin and charge fluctuations are governed by the effective actions that are derived from the Hubbard model for any value of the Coulomb interaction. The emergence of a sharp peak in the electron spectral function in the antiferromagnetic state indicates the decay of the electron into separate spin and charge carrying particle excitations.Comment: 16 pages, 5 figures, submitted to Phys. Rev.