Spectral identification of networks using sparse measurements

We propose a new method to recover global information about a network of interconnected dynamical systems based on observations made at a small number (possibly one) of its nodes. In contrast to classical identification of full graph topology, we focus on the identification of the spectral graph-theoretic properties of the network, a framework that we call spectral network identification. The main theoretical results connect the spectral properties of the network to the spectral properties of the dynamics, which are well-defined in the context of the so-called Koopman operator and can be extracted from data through the Dynamic Mode Decomposition algorithm. These results are obtained for networks of diffusively-coupled units that admit a stable equilibrium state. For large networks, a statistical approach is considered, which focuses on spectral moments of the network and is well-suited to the case of heterogeneous populations. Our framework provides efficient numerical methods to infer global information on the network from sparse local measurements at a few nodes. Numerical simulations show for instance the possibility of detecting the mean number of connections or the addition of a new vertex using measurements made at one single node, that need not be representative of the other nodes' properties.Comment: 3

Fall Back Equilibrium

Fall back equilibrium is a refinement of the Nash equilibrium concept. In the underly- ing thought experiment each player faces the possibility that, after all players decided on their action, his chosen action turns out to be blocked. Therefore, each player has to decide beforehand on a back-up action, which he plays in case he is unable to play his primary action. In this paper we introduce the concept of fall back equilibrium and show that the set of fall back equilibria is a non-empty and closed subset of the set of Nash equilibria. We discuss the relations with other equilibrium concepts, and among other results it is shown that each robust equilibrium is fall back and for bimatrix games also each proper equilibrium is a fall back equilibrium. Furthermore, we show that for bimatrix games the set of fall back equilibria is the union of finitely many polytopes, and that the notions of fall back equilibrium and strictly fall back equilibrium coincide. Finally, we allow multiple actions to be blocked, resulting in the notion of complete fall back equilibrium. We show that the set of complete fall back equilibria is a non-empty and closed subset of the set of proper equilibria.strategic game;equilibrium refinement;blocked action;fall back equilibrium

Paired Comparisons Analysis: An Axiomatic Approach to Rankings in Tournaments

In this paper we present an axiomatic analysis of several ranking methods for tournaments. We find that two of them exhibit a very good behaviour with respect to the set of properties under consideration. One of them is the maximum likelihood ranking, the most common method in statistics and psychology. The other one is a new ranking method introduced in this paper: recursive Buchholz. One of the most widely studied methods in social choice, the fair bets ranking, also performs quite well, but fails to satisfy some arguably important properties.Tournament;ranking;paired comparisons;fair bets;maximum likelihood

A Geometric Characterisation of the Compromise Value

In this paper, we characterise the compromise value of a game as the barycentre of the edges of its core cover.For this, we introduce the value, which extends the adjusted proportional rule for bankruptcy situations and coincides with the compromise value on a large class of games.geometry;games;bankruptcy;core

Compromise Solutions for Bankruptcy Situations with References

This paper deals with bankruptcy situations in which in addition to the claims, an exogenously given reference point for the allocation of the estate is present.We introduce and analyse two types of compromise solutions and show that they coincide with the T value of two corresponding TU games.We apply our solutions to a real-life case of allocating university money to degree courses.bankruptcy;allocation;t-value;games

Thermal inactivation kinetics of suspensions of bacillus amyloliquefaciens a-amylase in hydrophobic organic solvents

The thermal inactivation of suspensions of á-amylase from Bacillus amyloliquefaciens equilibrated at three low moisture contents and with added hydrophobic organic solvents of different hydrophobicity (dodecane, octane and 1-octanol) was systematically studied at temperatures between 135 to 150°C. The inactivation kinetics showed a first order decay in all cases. The enzyme is much more thermostable and less temperature sensitive than in aqueous solution. The behaviour was compared to inactivation in dry atmospheres, at similar water contents, without solvents. The organic solvents caused a larger influence of the water content and some environments caused significant changes in the rate constants, but the activation energy was not significantly affected. The solvent showing a higher impact on the kinetic parameters was 1-octanol