Symplectic tracking using point magnets and a reference orbit made of circular arcs and straight lines

Symplectic tracking of beam particles using point magnets is achieved using a reference orbit made of circular arcs and straight lines that join smoothly with each other. For this choice of the reference orbit, results are given for the transfer functions, transfer matrices, and the transit times of the magnets and drift spaces. These results provide a symplectic integrator, and allow the linear orbit parameters to be computed by multiplying transfer matrices. It is shown that this integrator is a second-order integrator, and that the transfer functions can be derived from a hamiltonian.Comment: 16 pages, PDF fil

Critical percolation of free product of groups

In this article we study percolation on the Cayley graph of a free product of groups. The critical probability $p_c$ of a free product $G_1*G_2*...*G_n$ of groups is found as a solution of an equation involving only the expected subcritical cluster size of factor groups $G_1,G_2,...,G_n$. For finite groups these equations are polynomial and can be explicitly written down. The expected subcritical cluster size of the free product is also found in terms of the subcritical cluster sizes of the factors. In particular, we prove that $p_c$ for the Cayley graph of the modular group $\hbox{PSL}_2(\mathbb Z)$ (with the standard generators) is $.5199...$, the unique root of the polynomial $2p^5-6p^4+2p^3+4p^2-1$ in the interval $(0,1)$. In the case when groups $G_i$ can be "well approximated" by a sequence of quotient groups, we show that the critical probabilities of the free product of these approximations converge to the critical probability of $G_1*G_2*...*G_n$ and the speed of convergence is exponential. Thus for residually finite groups, for example, one can restrict oneself to the case when each free factor is finite. We show that the critical point, introduced by Schonmann, $p_{\mathrm{exp}}$ of the free product is just the minimum of $p_{\mathrm{exp}}$ for the factors

Point-wise mutual information-based video segmentation with high temporal consistency

In this paper, we tackle the problem of temporally consistent boundary detection and hierarchical segmentation in videos. While finding the best high-level reasoning of region assignments in videos is the focus of much recent research, temporal consistency in boundary detection has so far only rarely been tackled. We argue that temporally consistent boundaries are a key component to temporally consistent region assignment. The proposed method is based on the point-wise mutual information (PMI) of spatio-temporal voxels. Temporal consistency is established by an evaluation of PMI-based point affinities in the spectral domain over space and time. Thus, the proposed method is independent of any optical flow computation or previously learned motion models. The proposed low-level video segmentation method outperforms the learning-based state of the art in terms of standard region metrics

Enabling Competing Energy Storage Technologies: Towards a Carbon-Neutral Power System

Assessment of energy storage technologies at a macro-scale for grid integration, has often focused on singular technologies and neglected competition between them, thus leaving out of the optimization the decision of which energy storage to prioritize. We present a systematic deployment analysis method that enables system-value evaluation in perfect competitive markets and demonstrate its application to 20 different energy storage technologies across 40 distinct scenarios for a representative future power system in Africa. Our results demonstrate the significant benefits of optimizing energy storage with competition compared to without (+10% cost savings) and highlight the relevance of several energy storage technologies in various scenarios. This work provides insights into the role of multi-technology energy storage in carbon-neutral power systems and informs future research and policy decisions

A kernel extension to handle missing data

An extension for univariate kernels that deals with missing values is proposed. These extended kernels are shown to be valid Mercer kernels and can adapt to many types of variables, such as categorical or continuous. The proposed kernels are tested against standard RBF kernels in a variety of benchmark problems showing different amounts of missing values and variable types. Our experimental results are very satisfactory, because they usually yield slight to much better improvements over those achieved with standard methods.Postprint (author’s final draft

A nanoflare model for active region radiance: application of artificial neural networks

Context. Nanoflares are small impulsive bursts of energy that blend with and possibly make up much of the solar background emission. Determining their frequency and energy input is central to understanding the heating of the solar corona. One method is to extrapolate the energy frequency distribution of larger individually observed flares to lower energies. Only if the power law exponent is greater than 2, is it considered possible that nanoflares contribute significantly to the energy input. Aims. Time sequences of ultraviolet line radiances observed in the corona of an active region are modelled with the aim of determining the power law exponent of the nanoflare energy distribution. Methods. A simple nanoflare model based on three key parameters (the flare rate, the flare duration time, and the power law exponent of the flare energy frequency distribution) is used to simulate emission line radiances from the ions Fe XIX, Ca XIII, and Si iii, observed by SUMER in the corona of an active region as it rotates around the east limb of the Sun. Light curve pattern recognition by an Artificial Neural Network (ANN) scheme is used to determine the values. Results. The power law exponents, alpha 2.8, 2.8, and 2.6 for Fe XIX, Ca XIII, and Si iii respectively. Conclusions. The light curve simulations imply a power law exponent greater than the critical value of 2 for all ion species. This implies that if the energy of flare-like events is extrapolated to low energies, nanoflares could provide a significant contribution to the heating of active region coronae.Comment: 4 pages, 5 figure

Weak convergence of Vervaat and Vervaat Error processes of long-range dependent sequences

Following Cs\"{o}rg\H{o}, Szyszkowicz and Wang (Ann. Statist. {\bf 34}, (2006), 1013--1044) we consider a long range dependent linear sequence. We prove weak convergence of the uniform Vervaat and the uniform Vervaat error processes, extending their results to distributions with unbounded support and removing normality assumption