Search results for "Random"

The Homogeneous Poisson Point Process

2008

Modal analysis for random response of MDOF systems

1990

The usefulness of the mode-superposition method of multidegrees of freedom systems excited by stochastic vector processes is here presented. The differential equations of moments of every order are written in compact form by means of the Kronecker algebra; then the method for integration of these equations is presented for both classically and non-classically damped systems, showing that the fundamental operator available for evaluating the response in the deterministic analysis is also useful for evaluating the response in the stochastic analysis.

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.

Convergence of Measures

2020

One focus of probability theory is distributions that are the result of an interplay of a large number of random impacts. Often a useful approximation can be obtained by taking a limit of such distributions, for example, a limit where the number of impacts goes to infinity. With the Poisson distribution, we have encountered such a limit distribution that occurs as the number of very rare events when the number of possibilities goes to infinity (see Theorem 3.7). In many cases, it is necessary to rescale the original distributions in order to capture the behavior of the essential fluctuations, e.g., in the central limit theorem. While these theorems work with real random variables, we will a…

Stochastic linearization for the response of MDOF systems subjected to external and parametric Gaussian excitations

1991

The stochastic linearization approach is examined for the most general case of non zero-mean response of non-linear MDOF systems subjected to parametric and external Gaussian white excitations. It is shown that, for these systems too, stochastic linearization and Gaussian closure are two equivalent approaches if the former is applied to the coefficients of the Ito differential rule. Moreover, an extension of the Atalik-Utku approach to non zero-mean response systems allows to obtain simple formulations for the linearized drift coefficients. Some applications show the good accuracy of the method.

Application of Periodic Frames to Image Restoration

2014

In this chapter, we present examples of image restoration using periodic frames. Images to be restored were degraded by blurring, aggravated by random noise and random loss of significant number of pixels. The images are transformed by periodic frames designed in Sects. 17.2 and 17.4, which are extended to the 2D setting in a standard tensor product way. In the presented experiments, performances of different tight and semi-tight frames are compared between each other in identical conditions.

A new approach for estimating a nonlinear growth component in multilevel modeling

2011

This study presents a new approach to estimation of a nonlinear growth curve component with fixed and random effects in multilevel modeling. This approach can be used to estimate change in longitudinal data, such as day-of-the-week fluctuation. The motivation of the new approach is to avoid spurious estimates in a random coefficient regression model due to the synchronized periodical effect (e.g., day-of-the-week fluctuation) appearing both in independent and dependent variables. First, the new approach is introduced. Second, a Monte Carlo simulation study is carried out to examine the functioning of the proposed new approach in the case of small sample sizes. Third, the use of the approac…

Anomaly Detection Algorithms for the Sleeping Cell Detection in LTE Networks

2015

The Sleeping Cell problem is a particular type of cell degradation in Long-Term Evolution (LTE) networks. In practice such cell outage leads to the lack of network service and sometimes it can be revealed only after multiple user complains by an operator. In this study a cell becomes sleeping because of a Random Access Channel (RACH) failure, which may happen due to software or hardware problems. For the detection of malfunctioning cells, we introduce a data mining based framework. In its core is the analysis of event sequences reported by a User Equipment (UE) to a serving Base Station (BS). The crucial element of the developed framework is an anomaly detection algorithm. We compare perfor…

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…

A Serendipity-Oriented Greedy Algorithm for Recommendations

2017

Most recommender systems suggest items to a user that are popular among all users and similar to items the user usually consumes. As a result, a user receives recommendations that she/he is already familiar with or would find anyway, leading to low satisfaction. To overcome this problem, a recommender system should suggest novel, relevant and unexpected, i.e. serendipitous items. In this paper, we propose a serendipity-oriented algorithm, which improves serendipity through feature diversification and helps overcome the overspecialization problem. To evaluate our algorithm and compare it with others, we employ a serendipity metric that captures each component of serendipity, unlike the most …