We examine nonstationary inverse problems in which the time evolution of the unknown quantity is modelled by a stochastic partial differential equation. We consider the problem as a state estimation problem. The time discrete state evolution equation is exact since the solution is given by an analytic semigroup. For the practical reasons the space discretization of the time discrete state estim...

This paper presents several results on the weighted region optimal path problem. An often-used approach to approximately solve this problem is to apply a discrete search algorithm to a graph G2 generated by a discretization of the problem; this graph guarantees to contain an 2-approximation of an optimal path between given source and destination points. We first provide a discretization scheme ...

One of the main strengths of connectionist systems also known as neural networks is their massive parallelism However most neural networks are simulated on serial computers where the advantage of massive parallelism is lost For large and real world applications parallel hardware implementations are therefore essential Since a discretization or quantization of the neural network parameters is of...

One of the main strengths of connectionist systems, also known as neural networks, is their massive parallelism. However, most neural networks are simulated on serial computers where the advantage of massive parallelism is lost. For large and real-world applications, parallel hardware implementations are therefore essential. Since a discretization or quantization of the neural network parameter...

The effect on the MRI signal of water diffusion in biological tissues in the presence of applied magnetic field gradient pulses can be modelled by a multiple compartment Bloch-Torrey partial differential equation. We present a method for the numerical solution of this equation by coupling a standard Cartesian spatial discretization with an adaptive time discretization. The time discretization i...

The stationary monochromatic radiative transfer equation is a partial differential transport equation stated on a five-dimensional phase space. To obtain a well-posed problem, inflow boundary conditions have to be prescribed. The sparse tensor product discretization has been successfully applied to finite element methods in radiative transfer with wavelet discretization of the angular domain (W...

Many classification algorithms require that training examples contain only discrete values. In order to use these algorithms when some attributes have continuous numeric values, the numeric attributes must be converted into discrete ones. This paper describes a new way of discretizing numeric values using information theory. The amount of information each interval gives to the target attribute ...

In this work, popular discretization techniques for continuous features in data sets are surveyed, and a new one based on equal width binning and error minimization is introduced. This discretization technique is implemented for the UCI Machine Learning Repository [7] dataset, Adult database and tested on two classifiers from WEKA tool [6], NaiveBayes and J48. Relative performance changes for t...

The performance of many machine learning algorithms can be substantially improved with a proper discretization scheme. In this paper we describe a theoretically rigorous approach to discretization of continuous attribute values, based on a Bayesian clustering framework. The method produces a probabilistic scoring metric for diierent discretizations, and it can be combined with various types of ...

Discretization is used in click-based graphical passwords so that approximately correct entries can be accepted by the system. We show that the existing discretization scheme of Birget et al.(2006) allows for false accepts and false rejects because the tolerance region is not guaranteed to be centered on the original click-point, causing usability and security concerns. Using empirical data fro...