Usage simulation methods for education

The paper deals with usage of computer simulation methods for education at Department of Electrical and Electronic Engineering and Signaling in Transport, Jan Perner Transport Faculty, University of Pardubice. Current situation of railway technics is very complicated and sophisticated both from viewpoint of railway infrastructure and from viewpoint of transport means. The particular parts of system are necessary to be analyzed from viewpoint of their behaviour and from viewpoint of influence to surrounding parts of the whole system. Therefore students as future railway experts must be trained for ability of problem identification and suitable design of problem solution. This readiness of experts for real operation of these devices is one of the main goals of lecturers from the mentioned department

On the Structure of General Mean-Variance Hedging Strategies

We provide a new characterization of mean-variance hedging strategies in a general semimartingale market. The key point is the introduction of a new probability measure $P^{\star}$ which turns the dynamic asset allocation problem into a myopic one. The minimal martingale measure relative to $P^{\star}$ coincides with the variance-optimal martingale measure relative to the original probability measure $P$.Comment: Published at http://dx.doi.org/10.1214/009117906000000872 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

Road charging in the Czech Republic and EU and external costs of transport

In the paper the Czech toll system and its future are presented. E-toll Czech project: Facts and Figures (today) are included and the next steps in the process of developing microwave infrastructure are mentioned. In the event of possible system extension of the roads of the 1st, 2nd and 3rd class (ca 55,000 km), the satellite technology will be used. The feasibility of such a combination of these two technologies, microwave and satellite, is subject to the compatibility of both systems in terms of the control equipment. For the microwave toll system, economic analyses according to EU directives were prepared for the Czech Ministry of Transport. Special attention is paid to the problems of traffic congestion, noise and damage to the environment, on the basis of the "user pays" and "polluter pays" according to the Eurovignette Directive principles. A complete survey of the EU toll system is included in the list of information sources

Scaling limit for trap models on Zd\mathbb{Z}^d

We give the ``quenched'' scaling limit of Bouchaud's trap model in ${d\ge 2}$. This scaling limit is the fractional-kinetics process, that is the time change of a $d$-dimensional Brownian motion by the inverse of an independent $\alpha$-stable subordinator.Comment: Published in at http://dx.doi.org/10.1214/009117907000000024 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

The algorithm by Ferson et al. is surprisingly fast: An NP-hard optimization problem solvable in almost linear time with high probability

We start with the algorithm of Ferson et al. (\emph{Reliable computing} {\bf 11}(3), p.~207--233, 2005), designed for solving a certain NP-hard problem motivated by robust statistics. First, we propose an efficient implementation of the algorithm and improve its complexity bound to $O(n \log n+n\cdot 2^\omega)$, where $\omega$ is the clique number in a certain intersection graph. Then we treat input data as random variables (as it is usual in statistics) and introduce a natural probabilistic data generating model. On average, we get $2^\omega = O(n^{1/\log\log n})$ and $\omega = O(\log n / \log\log n)$. This results in average computing time $O(n^{1+\epsilon})$ for $\epsilon > 0$ arbitrarily small, which may be considered as ``surprisingly good'' average time complexity for solving an NP-hard problem. Moreover, we prove the following tail bound on the distribution of computation time: ``hard'' instances, forcing the algorithm to compute in time $2^{\Omega(n)}$, occur rarely, with probability tending to zero faster than exponentially with $n \rightarrow \infty$