In this paper, we describe ongoing research conducted in our Laboratory concerning activity analysis of elderly or frail people with non-intrusive sensors. Activity is evaluated regarding autonomous mobility inferred from indoor tracking of many people. Non-intrusive photoelectric beam barrier sensors have been installed in our lab, in a nursing home and a medical care and research unit for respectively more than one year and 6 months. Incremental design, sensor fusion, data processing and acceptance concerns are discussed in the paper.

In this paper, we analyze Nash equilibria between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity production. We set out a clear Nash equilibrium on the power market that can be used to compute equilibrium prices on both markets as well as the related electricity produced and CO2 emissions released.

In this note, we present an existence result of a Nash equilibrium between electricity producers selling their production on an electricity market and buying CO2 emission allowances on an auction carbon market. The producers' strategies integrate the coupling of the two markets via the cost functions of the electricity production. We set out a clear Nash equilibrium that can be used to compute equilibrium prices on both markets as well as the related electricity produced and CO2 emissions covered.

In their seminal paper [1], Orda, Rom and Shimkin have already studied fully symmetric routing games, i.e. games in which all players have the same sources, destinations, demands and costs. They established the uniqueness of an equilibrium in these games. We extend their result to weaker forms of symmetry, which does not require a common source or destination. Considering routing games, we provide conditions under which whenever there is some symmetry between some players, then any equilibrium necessarily has these symmetry property as well. We then extend the symmetry result to general games.

Interval-based methods can approximate all the real solutions of a system of equations and inequalities. The Box interval constraint propagation algorithm enforces Box consistency. Itsmain procedure BoxNarrow handles one function f corresponding to the revised constraint, and one variable x, replacing the other variables of f by their current intervals. This paper proposes an improved BoxNarrow procedure for narrowing the domain of x when f respects certain conditions. In particular, these conditions are fulfilled when f is polynomial. f is first symbolically rewritten into a new form g. A narrowing step is then run on the non-interval extremal functions that enclose the interval function g. The corresponding algorithm is described and validated on several numerical constraint systems.

The carbon market was launched in the European Union in 2005 as part of the EU's initiative to reduce its greenhouse gas (GHG) emissions. This means that industrial players must now include their GHG emissions in their production costs. We aim to model the behaviour of an industrial agent who faces market uncertainties, and we compare the expected value of an optimal production strategy when buying (or not buying) supplementary emission allowances. This allows us to compute the agent's carbon indifference price which defines its market behaviour (buyer or not). We aim to use the resulting indifference price to study the sensitivity of the carbon market to the shape of the penalty and the emission allowances allocation.

Consider the situation where, in a single network or system, several different types of atomic and nonatomic users coexist and have attained their own optima unilaterally. We call the combination of the optima a ldquomixed optimumrdquo. For a distributed system with identical nodes each having identical arrivals, we obtain the analytic expression of the unique mixed optimum, where mutual job forwarding among nodes may occur for some atomic users, resulting in paradoxical performance degradation.

Finding the zeros of polynomials is a problem that arises in many field of applied mathematics. For example stability system analysis, molecular configuration and so on. In general the coefficients of the polynomials to be studied are based upon physical values that are approximated with finite accuracy through measures or estimations, and only approximations of the “real” polynomials are available. Very often probabilistic representation is used for modelling problems with uncertainty. Nevertheless, this approach may not be suitable is many cases. For some cases it is somewhat artificial to stick some probability distribution on some parameters, and the determination of the parameters of this distribution is highly arbitrary. Furthermore, the use of probabilistic approach leads to results in terms of expectation, witch in not acceptable in many cases. For example one may not be satisfied with results insuring that a medical robot or a robot used in some nuclear power will do the prescribed job with probability 0.99. Instead one may need certified results, i.e. on may need to be certain that the solution of the problem belong to some set whatever the real value of the parameters are.

In recent years there has been a growing interest in mathematical models for routing in networks in which the decisions are taken in a non-cooperative way. Instead of a single decision maker (that may represent the network) that chooses the paths so as to maximize a global utility, one considers a number of decision makers having each its own utility to maximize by routing its own flow. This gives rise to the use of non-cooperative game theory and the Nash equilibrium concept for optimality. In the special case in which each decision maker wishes to find a minimal path for each routed object (e.g. a packet) then the solution concept is the Wardrop equilibrium. It is well known that equilibria may exhibit inefficiencies and paradoxical behavior, such as the famous Braess paradox (in which the addition of a link to a network results in worse performance to all users). This raises the challenge for the network administrator of how to upgrade the network so that it indeed results in improved performance. We present in this paper some guidelines for that.

We consider a model of an electricity market in which S suppliers offer electricity: each supplier Si offers a maximum quantity qi at a fixed price pi. The response of the market to these offers is the quantities bought from the suppliers. The objective of the market is to satisfy its demand at minimal price. We investigate two cases. In the first case, each of the suppliers strives to maximize its market share on the market; in the second case each supplier strives to maximize its profit. We show that in both cases some Nash equilibrium exists. Nevertheless a close analysis of the equilibrium for profit maximization shows that it is not realistic. This raises the difficulty to predict the behavior of a market where the suppliers are known to be mainly interested by profit maximization.