We look directly into multidimensional phase spaces. This is useful if little is known about suitable observables and underlying laws. The dynamical system we examine is the human body, in particular the secretion of the parathyroid hormone (PTH). tme series of PrH concentrations are transformed to multidimensional data sets. From their representations in phase

Using an algebraic analysis approach, we derive a necessary and sufficient condition so that we can parametrize all solutions of a multidimensional linear system by glueing the controllable sub-behaviour with the autonomous elements. Effective algorithms checking this condition are obtained. This result generalizes a result of 1-D linear systems for a class of multidimensional linear systems. C...

Exploiting dynamic scaling and homogeneity in the bi-limit, we developp a new class of high gain observers which incorporate a gain update law and nonlinear output error injection terms. A broader class of systems can be addressed and the observer gain is better fitted to the incremental rate of the nonlinearities. The expected improved performance is illustrated.

This chapter deals with an annotation-based decisional system. The decisional system we present is based on multidimensional databases, which are composed of facts and dimensions. The expertise of decision-makers is modelled, shared and stored through annotations. These annotations allow decision-makers to carry on active analysis and to collaborate with other decision-makers on a common analysis.

Urban systems have many heterogeneous sets and many heterogeneous relations between them. Network theory has been very successful in analysing binary relations and related dynamics and flows. Urban systems are also characterised by higher level relations between many elements, leading to a multidimensional generalisation of network theory. Many dynamic system properties are dependent on the und...

This paper introduces the notion of multidimensional fuzzy finite tree automata (MFFTA) and investigates its closure properties from the area of automata and language theory. MFFTA are a superclass of fuzzy tree automata whose behavior is generalized to adapt to multidimensional fuzzy sets. An MFFTA recognizes a multidimensional fuzzy tree language which is a regular tree language so that for e...

Through computer simulations, this paper evaluates the performance of an online multidimensional auction system with negotiation support and especially focuses on investigating the efficacy of two design features of online multidimensional auction system on its performance: sellers’ feedback and post-utility scoring method. The performance of the auction system is measured by joint gain and spe...

Low-rank approximations play an important role in systems theory and signal processing. The problems of model reduction and system identification can be posed and solved as a low-rank approximation problem for structured matrices. On the other hand, signal source separation, nonlinear system identification, and multidimensional signal processing and data analysis can be approached with powerful...