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

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

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