Search results for " Random walk"
showing 10 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…
Avoiding Boundary Effects in Wang-Landau Sampling
2003
A simple modification of the ``Wang-Landau sampling'' algorithm removes the systematic error that occurs at the boundary of the range of energy over which the random walk takes place in the original algorithm.
On fractional diffusion and continuous time random walks
2003
Abstract A continuous time random walk model is presented with long-tailed waiting time density that approaches a Gaussian distribution in the continuum limit. This example shows that continuous time random walks with long time tails and diffusion equations with a fractional time derivative are in general not asymptotically equivalent.
Quadratic speedup for finding marked vertices by quantum walks
2020
A quantum walk algorithm can detect the presence of a marked vertex on a graph quadratically faster than the corresponding random walk algorithm (Szegedy, FOCS 2004). However, quantum algorithms that actually find a marked element quadratically faster than a classical random walk were only known for the special case when the marked set consists of just a single vertex, or in the case of some specific graphs. We present a new quantum algorithm for finding a marked vertex in any graph, with any set of marked vertices, that is (up to a log factor) quadratically faster than the corresponding classical random walk.
A fully automatic approach for multimodal PET and MR image segmentation in gamma knife treatment planning
2017
The aim of this study is to combine Biological Target Volume (BTV) segmentation and Gross Target Volume (GTV) segmentation in stereotactic neurosurgery.Our goal is to enhance Clinical Target Volume (CTV) definition, including metabolic and morphologic information, for treatment planning and patient follow-up.We propose a fully automatic approach for multimodal PET and MR image segmentation. This method is based on the Random Walker (RW) and Fuzzy C-Means clustering (FCM) algorithms. A total of 19 brain metastatic tumors, undergone stereotactic neuro-radiosurgery, were retrospectively analyzed. A framework for the evaluation of multimodal PET/MRI segmentation is presented, considering volume…
Quantum Search with Multiple Walk Steps per Oracle Query
2015
We identify a key difference between quantum search by discrete- and continuous-time quantum walks: a discrete-time walk typically performs one walk step per oracle query, whereas a continuous-time walk can effectively perform multiple walk steps per query while only counting query time. As a result, we show that continuous-time quantum walks can outperform their discrete-time counterparts, even though both achieve quadratic speedups over their corresponding classical random walks. To provide greater equity, we allow the discrete-time quantum walk to also take multiple walk steps per oracle query while only counting queries. Then it matches the continuous-time algorithm's runtime, but such …
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 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…
Donsker-Type Theorem for BSDEs: Rate of Convergence
2019
In this paper, we study in the Markovian case the rate of convergence in Wasserstein distance when the solution to a BSDE is approximated by a solution to a BSDE driven by a scaled random walk as introduced in Briand, Delyon and Mémin (Electron. Commun. Probab. 6 (2001) Art. ID 1). This is related to the approximation of solutions to semilinear second order parabolic PDEs by solutions to their associated finite difference schemes and the speed of convergence. peerReviewed
One-dimensional random walks with self-blocking immigration
2017
We consider a system of independent one-dimensional random walkers where new particles are added at the origin at fixed rate whenever there is no older particle present at the origin. A Poisson ansatz leads to a semi-linear lattice heat equation and predicts that starting from the empty configuration the total number of particles grows as $c \sqrt{t} \log t$. We confirm this prediction and also describe the asymptotic macroscopic profile of the particle configuration.