Search results for " random walk"
showing 9 items of 29 documents
Deducing self-interaction in eye movement data using sequential spatial point processes
2016
Eye movement data are outputs of an analyser tracking the gaze when a person is inspecting a scene. These kind of data are of increasing importance in scientific research as well as in applications, e.g. in marketing and man-machine interface planning. Thus the new areas of application call for advanced analysis tools. Our research objective is to suggest statistical modelling of eye movement sequences using sequential spatial point processes, which decomposes the variation in data into structural components having interpretation. We consider three elements of an eye movement sequence: heterogeneity of the target space, contextuality between subsequent movements, and time-dependent behaviou…
Juggler's exclusion process
2012
Juggler's exclusion process describes a system of particles on the positive integers where particles drift down to zero at unit speed. After a particle hits zero, it jumps into a randomly chosen unoccupied site. We model the system as a set-valued Markov process and show that the process is ergodic if the family of jump height distributions is uniformly integrable. In a special case where the particles jump according to a set-avoiding memoryless distribution, the process reaches its equilibrium in finite nonrandom time, and the equilibrium distribution can be represented as a Gibbs measure conforming to a linear gravitational potential.
Persistent random walks, variable length Markov chains and piecewise deterministic Markov processes *
2013
A classical random walk $(S_t, t\in\mathbb{N})$ is defined by $S_t:=\displaystyle\sum_{n=0}^t X_n$, where $(X_n)$ are i.i.d. When the increments $(X_n)_{n\in\mathbb{N}}$ are a one-order Markov chain, a short memory is introduced in the dynamics of $(S_t)$. This so-called "persistent" random walk is nolonger Markovian and, under suitable conditions, the rescaled process converges towards the integrated telegraph noise (ITN) as the time-scale and space-scale parameters tend to zero (see Herrmann and Vallois, 2010; Tapiero-Vallois, Tapiero-Vallois2}). The ITN process is effectively non-Markovian too. The aim is to consider persistent random walks $(S_t)$ whose increments are Markov chains with…
TESTING THE HYPOTHESIS OF AN EFFICIENT MARKET IN TERMS OF INFORMATION – THE CASE OF THE CAPITAL MARKET IN ROMANIA DURING RECESSION
2010
This paper is trying to test the hypothesis of efficient market (EMH Efficient Market Hypothesis), the case of capital market in Romania during the economic financial crisis. According to the purpose in view our research is aiming at testing the hypothesis of random walk of stock exchange indexes BET, BET-C, BET_FI of Bucharest Stock Exchange. In this respect we will enforce statistic tests to see if the capital market in Romania is efficient in a weak form during this period.
TESTING INFORMATIONAL EFFICIENCY: THE CASE OF U.E. AND BRIC EMERGENT MARKETS
2012
Empirical finance has brought together a considerable number of studies in determining the market efficiency in terms of information in the case of an emerging financial market. Conflicting results have been generated by these researches in efficient market hypothesis (EMH), so efficiency tests in the emerging financial markets are rarely definitive in reaching a conclusion about the existence of informational efficiency. This paper tests weak-form market efficiency of eight emerging markets: four U.E emerging markets: Romania, Hungary, Czech Republic, Slovakia, Estonia and BRIC emerging markets: Brazil, Russia, India and China. The random walk hypothesis of stock exchange indices is tested…
A fully automatic method for biological target volume segmentation of brain metastases
2016
Leksell Gamma Knife is a mini-invasive technique to obtain a complete destruction of cerebral lesions delivering a single high dose radiation beam. Positron Emission Tomography (PET) imaging is increasingly utilized for radiation treatment planning. Nevertheless, lesion volume delineation in PET datasets is challenging because of the low spatial resolution and high noise level of PET images. Nowadays, the biological target volume (BTV) is manually contoured on PET studies. This procedure is time expensive and operator-dependent. In this article, a fully automatic algorithm for the BTV delineation based on random walks (RW) on graphs is proposed. The results are compared with the outcomes of…
An automatic method for metabolic evaluation of gamma knife treatments
2015
Lesion volume delineation of Positron Emission Tomography images is challenging because of the low spatial resolution and high noise level. Aim of this work is the development of an operator independent segmentation method of metabolic images. For this purpose, an algorithm for the biological tumor volume delineation based on random walks on graphs has been used. Twenty-four cerebral tumors are segmented to evaluate the functional follow-up after Gamma Knife radiotherapy treatment. Experimental results show that the segmentation algorithm is accurate and has real-time performance. In addition, it can reflect metabolic changes useful to evaluate radiotherapy response in treated patients.
Random Walk and Diffusion
2014
The concept of random walk as introduced by Einstein is introduced. It is shown that a random walk on a lattice can be descrbed by a difference equation, which becomes a partial differential equation (diffusion equation) in the continuum limit. The equation is solved with the help of Fourier and Laplace transformations.
A Stochastic Algorithm Based on Fast Marching for Automatic Capacitance Extraction in Non-Manhattan Geometries
2014
WOS:000346854900026 (Nº de Acesso Web of Science) We present an algorithm for two- and three-dimensional capacitance analysis on multidielectric integrated circuits of arbitrary geometry. Our algorithm is stochastic in nature and as such fully parallelizable. It is intended to extract capacitance entries directly from a pixelized representation of the integrated circuit (IC), which can be produced from a scanning electron microscopy image. Preprocessing and monitoring of the capacitance calculation are kept to a minimum, thanks to the use of distance maps automatically generated with a fast marching technique. Numerical validation of the algorithm shows that the systematic error of the algo…