Preferences on Intervals: a general framework

I present a general framework for the comparison of alternatives to which (possibly) an interval of values is associated. Some representation theorems for the existence of the intervals are discussed as well the possibility ot explicitly take into account situations of hesitation. Some appropriate logical formalisms are discussed for such a purpose

Metric propositional neighborhood logic with an equivalence relation

The propositional interval logic of temporal neighborhood (PNL for short) features two modalities that make it possible to access intervals adjacent to the right (modality \u27e8 A\u27e9) and to the left (modality \u27e8 A\uaf \u27e9) of the current interval. PNL stands at a central position in the realm of interval temporal logics, as it is expressive enough to encode meaningful temporal conditions and decidable (undecidability rules over interval temporal logics, while PNL is NEXPTIME-complete). Moreover, it is expressively complete with respect to the two-variable fragment of first-order logic extended with a linear order FO 2[<]. Various extensions of PNL have been studied in the literature, including metric, hybrid, and first-order ones. Here, we study the effects of the addition of an equivalence relation 3c to Metric PNL (MPNL 3c). We first show that the finite satisfiability problem for PNL extended with 3c is still NEXPTIME-complete. Then, we prove that the same problem for MPNL 3c can be reduced to the decidable 0\u20130 reachability problem for vector addition systems and vice versa (EXPSPACE-hardness immediately follows)

Preference Modelling

This paper provides the reader with a presentation of preference modelling fundamental notions as well as some recent results in this field. Preference modelling is an inevitable step in a variety of fields: economy, sociology, psychology, mathematical programming, even medicine, archaeology, and obviously decision analysis. Our notation and some basic definitions, such as those of binary relation, properties and ordered sets, are presented at the beginning of the paper. We start by discussing different reasons for constructing a model or preference. We then go through a number of issues that influence the construction of preference models. Different formalisations besides classical logic such as fuzzy sets and non-classical logics become necessary. We then present different types of preference structures reflecting the behavior of a decision-maker: classical, extended and valued ones. It is relevant to have a numerical representation of preferences: functional representations, value functions. The concepts of thresholds and minimal representation are also introduced in this section. In section 7, we briefly explore the concept of deontic logic (logic of preference) and other formalisms associated with "compact representation of preferences" introduced for special purpoes. We end the paper with some concluding remarks

Observations of Detailed Structure in the Solar Wind at 1 AU with STEREO/HI-2

Heliospheric imagers offer the promise of remote sensing of large-scale structures present in the solar wind. The STEREO/HI-2 imagers, in particular, offer high resolution, very low noise observations of the inner heliosphere but have not yet been exploited to their full potential. This is in part because the signal of interest, Thomson scattered sunlight from free electrons, is ~1000 times fainter than the background visual field in the images, making background subtraction challenging. We have developed a procedure for separating the Thomson-scattered signal from the other background/foreground sources in the HI-2 data. Using only the Level 1 data from STEREO/HI-2, we are able to generate calibrated imaging data of the solar wind with sensitivity of a few times 1e-17 Bsun, compared to the background signal of a few times 1e-13 Bsun. These images reveal detailed spatial structure in CMEs and the solar wind at projected solar distances in excess of 1 AU, at the instrumental motion-blur resolution limit of 1-3 degree. CME features visible in the newly reprocessed data from December 2008 include leading-edge pileup, interior voids, filamentary structure, and rear cusps. "Quiet" solar wind features include V shaped structure centered on the heliospheric current sheet, plasmoids, and "puffs" that correspond to the density fluctuations observed in-situ. We compare many of these structures with in-situ features detected near 1 AU. The reprocessed data demonstrate that it is possible to perform detailed structural analyses of heliospheric features with visible light imagery, at distances from the Sun of at least 1 AU.Comment: Accepted by Astrophysical Journa

Critical properties in long-range hopping Hamiltonians

Some properties of $d$-dimensional disordered models with long-range random hopping amplitudes are investigated numerically at criticality. We concentrate on the correlation dimension $d_2$ (for $d=2$) and the nearest level spacing distribution $P_c(s)$ (for $d=3$) in both the weak ($b^d \gg 1$) and the strong ($b^d \ll 1$) coupling regime, where the parameter $b^{-d}$ plays the role of the coupling constant of the model. It is found that (i) the extrapolated values of $d_2$ are of the form $d_2=c_db^d$ in the strong coupling limit and $d_2=d-a_d/b^d$ in the case of weak coupling, and (ii) $P_ (s)$ has the asymptotic form $P_c(s)\sim\exp (-A_ds^{\alpha})$ for $s\gg$, with the critical exponent $\alpha=2-a_d/b^d$ for $b^d \gg 1$ and $\alpha=1+c_d b^d$ for $b^d \ll 1$. In these cases the numerical coefficients $A_d$, $a_d$ and $c_d$ depend only on the dimensionality.Comment: 9 pages, 6 .eps figures, contribution to the Festschrift for Michael Schreiber's 50th birthda

Strategic interaction between futures and spot markets.

There is a literature (e.g., Allaz and Vila, 1992 and Hughes and Kao, 1997) showing that in an oligopolistic context, the presence of a futures market induces firms to use it in order to increase its market share. The consequence of this behavior is that the total quantity supplied by the industry increases, thus making the oligopolistic outcome closer to the competitive equilibrium. In the present work, we propose a model to study the interaction of spot and futures markets that does not imply this pro-competitive effect. The model is the same as in Allaz and Vila in the sense that firms have infinitely many moments to trade in the futures market before the spot market takes place. We analyze the equilibria in the infinite case directly and show that many equilibria emerge in a kind of folk-theorem result (but ours is not a repeated game). The equilibrium in which firms do not use the forward market is particularly robust as it satisfies the most demanding definition of renegotiation-proofuess. Furthermore, if firms are allowed to buy in the futures market, they can sustain the monopolistic outcome in a renegotiation-proof equilibrium (notice that there is only one period in the spot market). We also study the role of information in the model and argue that our results fit better stylized facts of some industries like the power market in the U.K.Futures markets; Cournot competition; Collusion;

Universal features of fluctuations

Universal scaling laws of fluctuations (the $\Delta$-scaling laws) can be derived for equilibrium and off-equilibrium systems when combined with the finite-size scaling analysis. In any system in which the second-order critical behavior can be identified, the relation between order parameter, criticality and scaling law of fluctuations has been established and the relation between the scaling function and the critical exponents has been found.Comment: 10 pages; TORINO 2000, New Frontiers in Soft Physics and Correlations on the Threshold of the Third Milleniu

Discriminating thresholds as a tool to cope with imperfect knowledge in multiple criteria decision aiding: Theoretical results and practical issues

International audienceThis article deals with preference modeling. It concerns the concepts of discriminating thresholdsas a tool cope with the imperfect nature of knowledge in decision aiding. Such imperfect knowledgeis related with the definition of each criterion as well as with the data we have to take into account.On the one hand, we shall present a useful theoretical synthesis for the analyst in his/her decisionaiding activity, and, on the other hand, we shall provide some practical instructions concerning theapproach to follow for assigning the values to these discriminating thresholds.Cet article traite du concept de seuils de discrimination en tant qu’outils permettant de prendre encompte en aide multicritère à la décision le caractère imparfait (incertain, ambigu, mal déterminé)des connaissances. Ce caractère imparfait des connaissances affecte aussi bien la définition descritères que les données qu’ils doivent prendre en compte. On présente d’une part une synthèsedes résultats théoriques utiles à l’analyste dans son travail de modélisation et d’autre part desindications pratiques concernant la démarche à suivre pour attribuer des valeurs à ces seuils