The general problem of defining and determining the sample distribution in the case of continuous-parameter random fields is addressed. Defining a distribution in the case of deterministic functions is straightforward, based on measures of sublevel sets. However, the fields we consider are the sum of a deterministic component (nonrandom multidimensional function) and an i.i.d. random field; an attempt to extend the same notion to the stochastic case immediately raises some fundamental difficulties. We show that by “uniformly sampling” such random fields the difficulties may be avoided and a sample distribution may be compatibly defined and determined. Not surprisingly, the obtained result resembles the known fact that the probability distribution of the sum of two independent random variables is the convolution of their distributions. Finally, we apply the results to derive a solution to the problem of deformation estimation of one- and multidimensional signals in the presence of measurement noise.

When considering the need for an intelligent transportation mode based upon the fact that car travel is still the consumer's first choice, we decided to explore the idea of collective taxis. More precisely, we are seeking to provide an autonomous high quality door-to-door service, affordable by almost everyone, covering the entire urban area, simply by allocating in an optimal way more than one passenger to each vehicle and using the latest available information regarding traffic conditions, etc. Because this system is far less unconstrained than most public transportation systems, it has high potentialities in terms of performance and flexibility, but it is consequently very difficult to manage and to design optimally. Therefore, we present a discrete event simulation tool and show how it can be used to conceive, optimise and compare decision algorithms, achieve sound trade-off between conflicting performance indicators and assess the efficiency of the system in various contexts.

We consider the problem of registering two observations on an arbitrary object, where the two are related by a geometric affine transformation of their coordinate systems, and by a nonlinear mapping of their intensities. More generally, the framework is that of jointly estimating the geometric and radiometric deformations relating two observations on the same object. We show that the original high-dimensional, nonlinear, and nonconvex search problem of simultaneously recovering the geometric and radiometric deformations can be represented by an equivalent sequence of two linear systems. A solution of this sequence yields an exact, explicit, and efficient solution to the joint estimation problem.

This paper considers the problem of estimating the parameters of real-valued two-dimensional (2-D) sinusoidal signals observed in colored noise. This problem is a special case of the general problem of estimating the parameters of a real-valued homogeneous random field with mixed spectral distribution from a single observed realization of it. The large sample properties of the least squares (LS) estimator of the parameters of the sinusoidal components are derived, making no assumptions on the type of the probability distribution of the observed field. It is shown that if the disturbance field satisfies a combination of conditions comprised of a strong mixing condition and a condition on the order of its uniformly bounded moments, the normalized estimation error of the LS estimator is consistent asymptotically normal with zero mean and a normalized asymptotic covariance matrix for which a simple expression is derived. It is further shown that the LS estimator is asymptotically unbiased. The normalized asymptotic covariance matrix is block diagonal where each block corresponds to the parameters of a different sinusoidal component. Assuming further that the colored noise field is Gaussian, the LS estimator of the sinusoidal components is shown to be asymptotically efficient.

It is shown that a certain class of Petri nets called event graphs can be represented as linear time-invariant finite-dimensional systems using some particular algebras. This sets the ground on which a theory of these systems can be developed in a manner which is very analogous to that of conventional linear system theory. Some preliminary basic developments in that direction are shown. Several ways in which one can consider event graphs as linear systems are described. These correspond to approaches in the time domain, in the event domain, and in a two-dimensional domain. In each of these approaches, a different algebra has to be used for models to remain linear, but the common feature of these algebras is that they all fall into the axiomatic definition of 'dioids'. A unified presentation of basic algebraic results on dioids is provided.>