Graph edit distance from spectral seriation

This paper is concerned with computing graph edit distance. One of the criticisms that can be leveled at existing methods for computing graph edit distance is that they lack some of the formality and rigor of the computation of string edit distance. Hence, our aim is to convert graphs to string sequences so that string matching techniques can be used. To do this, we use a graph spectral seriation method to convert the adjacency matrix into a string or sequence order. We show how the serial ordering can be established using the leading eigenvector of the graph adjacency matrix. We pose the problem of graph-matching as a maximum a posteriori probability (MAP) alignment of the seriation sequences for pairs of graphs. This treatment leads to an expression in which the edit cost is the negative logarithm of the a posteriori sequence alignment probability. We compute the edit distance by finding the sequence of string edit operations which minimizes the cost of the path traversing the edit lattice. The edit costs are determined by the components of the leading eigenvectors of the adjacency matrix and by the edge densities of the graphs being matched. We demonstrate the utility of the edit distance on a number of graph clustering problems

Typification and economic analysis of beef-producing farms in Spain

In spite of different economic agents’ interests, as well as the Administration’s effort in promoting extensive beef-producing systems over the last years, this kind of activity still hasn’t reached the desirable levels, being necessary that farmers perceive an appropriate benefit which supports their activity. In this sense, this paper, using the data obtained by a statistical survey representing all the extensive beef-producing farms existing in Castile and Leon (Spain), aims to analyze the economical results of extensive beef-producing farms, previously classified in representative groups according a quantitative method. The study is a preliminary research which intends to generate additional knowledge about the role of the different variables which make part of the economic results, and takes part of a research project financed by Castile and Leon Regional Governments, Education and Culture Council, through the annual program to support research projects (Order EDU/1143/2004).Cluster Analysis, extensive beef producing systems, economic accounts, Livestock Production/Industries,

A graph-spectral approach to shape-from-shading

In this paper, we explore how graph-spectral methods can be used to develop a new shape-from-shading algorithm. We characterize the field of surface normals using a weight matrix whose elements are computed from the sectional curvature between different image locations and penalize large changes in surface normal direction. Modeling the blocks of the weight matrix as distinct surface patches, we use a graph seriation method to find a surface integration path that maximizes the sum of curvature-dependent weights and that can be used for the purposes of height reconstruction. To smooth the reconstructed surface, we fit quadrics to the height data for each patch. The smoothed surface normal directions are updated ensuring compliance with Lambert's law. The processes of height recovery and surface normal adjustment are interleaved and iterated until a stable surface is obtained. We provide results on synthetic and real-world imagery

The Einstein-Boltzmann Relation for Thermodynamic and Hydrodynamic Fluctuations

When making the connection between the thermodynamics of irreversible processes and the theory of stochastic processes through the fluctuation-dissipation theorem, it is necessary to invoke a postulate of the Einstein-Boltzmann type. For convective processes hydrodynamic fluctuations must be included, the velocity is a dynamical variable and although the entropy cannot depend directly on the velocity, $\delta^{2} S$ will depend on velocity variations. Some authors do not include velocity variations in $\delta^{2} S$, and so have to introduce a non-thermodynamic function which replaces the entropy and does depend on the velocity. At first sight, it seems that the introduction of such a function requires a generalisation of the Einstein-Boltzmann relation to be invoked. We review the reason why it is not necessary to introduce such a function, and therefore why there is no need to generalise the Einstein-Boltzmann relation in this way. We then obtain the fluctuation-dissipation theorem which shows some differences as compared with the non-convective case. We also show that $\delta^{2} S$ is a Liapunov function when it includes velocity fluctuations.Comment: 13 Page

Equation of state of a seven-dimensional hard-sphere fluid. Percus-Yevick theory and molecular dynamics simulations

Following the work of Leutheusser [Physica A 127, 667 (1984)], the solution to the Percus-Yevick equation for a seven-dimensional hard-sphere fluid is explicitly found. This allows the derivation of the equation of state for the fluid taking both the virial and the compressibility routes. An analysis of the virial coefficients and the determination of the radius of convergence of the virial series are carried out. Molecular dynamics simulations of the same system are also performed and a comparison between the simulation results for the compressibility factor and theoretical expressions for the same quantity is presented.Comment: 12 pages, 4 figures; v3: Equation (A.19) corrected (see http://dx.doi.org/10.1063/1.2390712

Dual contribution to amplification in the mammalian inner ear

The inner ear achieves a wide dynamic range of responsiveness by mechanically amplifying weak sounds. The enormous mechanical gain reported for the mammalian cochlea, which exceeds a factor of 4,000, poses a challenge for theory. Here we show how such a large gain can result from an interaction between amplification by low-gain hair bundles and a pressure wave: hair bundles can amplify both their displacement per locally applied pressure and the pressure wave itself. A recently proposed ratchet mechanism, in which hair-bundle forces do not feed back on the pressure wave, delineates the two effects. Our analytical calculations with a WKB approximation agree with numerical solutions.Comment: 4 pages, 4 figure