Characterisation of large changes in wind power for the day-ahead market using a fuzzy logic approach

Wind power has become one of the renewable resources with a major growth in the electricity market. However, due to its inherent variability, forecasting techniques are necessary for the optimum scheduling of the electric grid, specially during ramp events. These large changes in wind power may not be captured by wind power point forecasts even with very high resolution Numerical Weather Prediction (NWP) models. In this paper, a fuzzy approach for wind power ramp characterisation is presented. The main benefit of this technique is that it avoids the binary definition of ramp event, allowing to identify changes in power out- put that can potentially turn into ramp events when the total percentage of change to be considered a ramp event is not met. To study the application of this technique, wind power forecasts were obtained and their corresponding error estimated using Genetic Programming (GP) and Quantile Regression Forests. The error distributions were incorporated into the characterisation process, which according to the results, improve significantly the ramp capture. Results are presented using colour maps, which provide a useful way to interpret the characteristics of the ramp events

Relationship between physiological measures of excitability and levels of glutamate and GABA in the human motor cortex

Magnetic resonance spectroscopy (MRS) allows measurement of neurotransmitter concentrations within a region of interest in the brain. Inter-individual variation in MRS-measured GABA levels have been related to variation in task performance in a number of regions. However, it is not clear how MRS-assessed measures of GABA relate to cortical excitability or GABAergic synaptic activity. We therefore performed two studies investigating the relationship between neurotransmitter levels as assessed by MRS and transcranial magnetic stimulation (TMS) measures of cortical excitability and GABA synaptic activity in the primary motor cortex. We present uncorrected correlations, where the P value should therefore be considered with caution. We demonstrated a correlation between cortical excitability, as assessed by the slope of the TMS input-output curve and MRS-assessed glutamate levels (r = 0.803, P = 0.015) but no clear relationship between MRS-assessed GABA levels and TMS-assessed synaptic GABA(A) activity (2.5 ms inter-stimulus interval (ISI) short-interval intracortical inhibition (SICI); Experiment 1: r = 0.33, P = 0.31; Experiment 2: r = -0.23, P = 0.46) or GABA(B) activity (long-interval intracortical inhibition (LICI); Experiment 1: r = -0.47, P = 0.51; Experiment 2: r = 0.23, P = 0.47). We demonstrated a significant correlation between MRS-assessed GABA levels and an inhibitory TMS protocol (1 ms ISI SICI) with distinct physiological underpinnings from the 2.5 ms ISI SICI (r = -0.79, P = 0.018). Interpretation of this finding is challenging as the mechanisms of 1 ms ISI SICI are not well understood, but we speculate that our results support the possibility that 1 ms ISI SICI reflects a distinct GABAergic inhibitory process, possibly that of extrasynaptic GABA tone

Darboux Transformations for a Lax Integrable System in 2n2n-Dimensions

A $2n$-dimensional Lax integrable system is proposed by a set of specific spectral problems. It contains Takasaki equations, the self-dual Yang-Mills equations and its integrable hierarchy as examples. An explicit formulation of Darboux transformations is established for this Lax integrable system. The Vandermonde and generalized Cauchy determinant formulas lead to a description for deriving explicit solutions and thus some rational and analytic solutions are obtained.Comment: Latex, 14 pages, to be published in Lett. Math. Phy

Resummation of mass terms in perturbative massless quantum field theory

The neutral massless scalar quantum field $\Phi$ in four-dimensional space-time is considered, which is subject to a simple bilinear self-interaction. Is is well-known from renormalization theory that adding a term of the form $-\frac{m^2}{2} \Phi^2$ to the Lagrangean has the formal effect of shifting the particle mass from the original zero value to m after resummation of all two-leg insertions in the Feynman graphs appearing in the perturbative expansion of the S-matrix. However, this resummation is accompanied by some subtleties if done in a proper mathematical manner. Although the model seems to be almost trivial, is shows many interesting features which are useful for the understanding of the convergence behavior of perturbation theory in general. Some important facts in connection with the basic principles of quantum field theory and distribution theory are highlighted, and a remark is made on possible generalizations of the distribution spaces used in local quantum field theory. A short discussion how one can view the spontaneous breakdown of gauge symmetry in massive gauge theories within a massless framework is presented.Comment: 15 pages, LaTeX (style files included), one section adde

Monotonicity conditions for multirate and partitioned explicit Runge-Kutta schemes

Multirate schemes for conservation laws or convection-dominated problems seem to come in two ¿avors: schemes that are locally inconsistent, and schemes that lack mass-conservation. In this paper these two defects are discussed for one-dimensional conservation laws. Particular attention will be given to monotonicity properties of the multirate schemes, such as maximum principles and the total variation diminishing (TVD) property. The study of these properties will be done within the framework of partitioned Runge-Kutta methods. It will also be seen that the incompatibility of consistency and mass-conservation holds for ‘genuine’ multirate schemes, but not for general partitioned methods