Disaggregating Input-Output Tables by the Multidimensional RAS Method

An unknown input-output table can be estimated by the RAS method when only its row and column sums are known and some initial structure is assumed. The RAS approach can also be utilized for disaggregation of an annual national table to more detailed tables such as regional, quarterly and domestic/imported tables. However, the regular RAS method does not ensure that the sums of disaggregated tables are equal to the total table. For this problem, we propose to use the multidimensional RAS method which besides input and output totals also ensures regional, quarterly and domestic/imported totals. Our analysis of the Czech industry shows that the multidimensional RAS method increases the accuracy of table estimation as well as accuracy of input-output applications such as the Leontief inverse, the regional Isard's model and the quarterly value added

A Numerical Method to solve Optimal Transport Problems with Coulomb Cost

In this paper, we present a numerical method, based on iterative Bregman projections, to solve the optimal transport problem with Coulomb cost. This is related to the strong interaction limit of Density Functional Theory. The first idea is to introduce an entropic regularization of the Kantorovich formulation of the Optimal Transport problem. The regularized problem then corresponds to the projection of a vector on the intersection of the constraints with respect to the Kullback-Leibler distance. Iterative Bregman projections on each marginal constraint are explicit which enables us to approximate the optimal transport plan. We validate the numerical method against analytical test cases

Approximating a similarity matrix by a latent class model: A reappraisal of additive fuzzy clustering

Let Q be a given n×n square symmetric matrix of nonnegative elements between 0 and 1, similarities. Fuzzy clustering results in fuzzy assignment of individuals to K clusters. In additive fuzzy clustering, the n×K fuzzy memberships matrix P is found by least-squares approximation of the off-diagonal elements of Q by inner products of rows of P. By contrast, kernelized fuzzy c-means is not least-squares and requires an additional fuzziness parameter. The aim is to popularize additive fuzzy clustering by interpreting it as a latent class model, whereby the elements of Q are modeled as the probability that two individuals share the same class on the basis of the assignment probability matrix P. Two new algorithms are provided, a brute force genetic algorithm (differential evolution) and an iterative row-wise quadratic programming algorithm of which the latter is the more effective. Simulations showed that (1) the method usually has a unique solution, except in special cases, (2) both algorithms reached this solution from random restarts and (3) the number of clusters can be well estimated by AIC. Additive fuzzy clustering is computationally efficient and combines attractive features of both the vector model and the cluster mode

Inferring the Coronal Density Irregularity from EUV Spectra

Understanding the density structure of the solar corona is important for modeling both coronal heating and the solar wind. Direct measurements are difficult because of line-of-sight integration and possible unresolved structures. We present a new method for quantifying such structure using density-sensitive EUV line intensities to derive a density irregularity parameter, a relative measure of the amount of structure along the line of sight. We also present a simple model to relate the inferred irregularities to physical quantities, such as the filling factor and density contrast. For quiet Sun regions and interplume regions of coronal holes, we find a density contrast of at least a factor of three to ten and corresponding filling factors of about 10-20%. Our results are in rough agreement with other estimates of the density structures in these regions. The irregularity diagnostic provides a useful relative measure of unresolved structure in various regions of the corona.Comment: Submitted to the Astrophysical Journa