Classification of Complex Wishart Matrices with a Diffusion-Reaction System guided by Stochastic Distances

We propose a new method for PolSAR (Polarimetric Synthetic Aperture Radar) imagery classification based on stochastic distances in the space of random matrices obeying complex Wishart distributions. Given a collection of prototypes $\{Z_m\}_{m=1}^M$ and a stochastic distance $d(.,.)$, we classify any random matrix $X$ using two criteria in an iterative setup. Firstly, we associate $X$ to the class which minimizes the weighted stochastic distance $w_md(X,Z_m)$, where the positive weights $w_m$ are computed to maximize the class discrimination power. Secondly, we improve the result by embedding the classification problem into a diffusion-reaction partial differential system where the diffusion term smooths the patches within the image, and the reaction term tends to move the pixel values towards the closest class prototype. In particular, the method inherits the benefits of speckle reduction by diffusion-like methods. Results on synthetic and real PolSAR data show the performance of the method.Comment: Accepted for publication in Philosophical Transactions

Mathematics in the Baroque Period in Spain

The 17th century Spain is very advanced culturally and, in certain respects, very refined. Although Spanish culture in the reached an unprecedented peak, mathematics activity in Spain entered a period of decline and did not share in the burst of mathemathical knowledge occurring in other European countries during this century

Juan Baños de Velasco y Acevedo - Emblems in Everyday Life

A research note on a new acquisition for the Stirling Maxwell Collection of Emblem Books, held at the Special Collections department of the University of Glasgow. This was part of a round table on various other items in this recent acquisition. This research note explores different perspectives that add value to this work, namely the close association of this Spanish work with D. Juan de Austria (its dedicatee) and Portugal

The Lagrangian cobordism group of T2T^2

We compute the Lagrangian cobordism group of the standard symplectic 2-torus and prove that it is isomorphic to the Grothendieck group of its derived Fukaya category. The proofs use homological mirror symmetry for the 2-torus.Comment: 43 pages, 12 figures. V2: Result of computation of the cobordism group reformulated; further minor changes and corrections. V3: Updated such as to agree with accepted version. To appear in Selecta Mathematic

Selecting projects in a portfolio using risk and ranking

There are three dimensions in project management: time, cost and performance. Risk is a characteristic related to the previous dimensions and their relationships. A risk equation is proposed based on the nature of the uncertainty associated to each dimension as well as the relationship between the uncertainties. A ranking equation that is able to prioritise projects is proposed and discussed. The problem solved here is which projects to select in a given portfolio of projects. The model is implemented in a group decision support system (GDSS) which can guide decisionmakers in their decision process. However, the system is not intended as a substitution of the decisionmaker task, but merely as an aid. The methodology used is analysis of the equations proposed and trial and error based on examples. This paper’s main contribution is the risk equation and the ranking equation