On Wishart distribution

This paper proposes a unified approach that enables the Wishart distribution to be studied simultaneously in the real, complex, quaternion and octonion cases. In particular, the noncentral generalised Wishart distribution, the joint density of the eigenvalues and the distribution of the maximum eigenvalue are obtained for real normed division algebras.Comment: 11 page

Testing for Unit Roots: Mexico's GDP

The study presents an analysis of the stochastic nature of the gross domestic product of Mexico for the period 1900-2001. Several specifications to test for the existence of unit roots are presented. The conventional tests, Dickey Fuller, Augmented Dickey Fuller and Phillips Perron, indicate that the series is nonstationary and integrated of order 1. The result is robust to the inclusion of exogenously and endogenously determined structural breaks. Interestingly, when structural breaks are determined endogenously, a structural break in 1907 is identified. We interpret this results as suggesting that setting the date of a structural break ex-ante might not be the most efficient procedure when testing for unit roots.Unit Root tests, structural Break and gross domestic product of Mexico.

Cancer progression models and fitness landscapes: A many-to-many relationship

Motivation The identification of constraints, due to gene interactions, in the order of accumulation of mutations during cancer progression can allow us to single out therapeutic targets. Cancer progression models (CPMs) use genotype frequency data from cross-sectional samples to identify these constraints, and return Directed Acyclic Graphs (DAGs) of restrictions where arrows indicate dependencies or constraints. On the other hand, fitness landscapes, which map genotypes to fitness, contain all possible paths of tumor progression. Thus, we expect a correspondence between DAGs from CPMs and the fitness landscapes where evolution happened. But many fitness landscapes - e.g. those with reciprocal sign epistasis - cannot be represented by CPMs. Results Using simulated data under 500 fitness landscapes, I show that CPMs' performance (prediction of genotypes that can exist) degrades with reciprocal sign epistasis. There is large variability in the DAGs inferred from each landscape, which is also affected by mutation rate, detection regime and fitness landscape features, in ways that depend on CPM method. Using three cancer datasets, I show that these problems strongly affect the analysis of empirical data: fitness landscapes that are widely different from each other produce data similar to the empirically observed ones and lead to DAGs that infer very different restrictions. Because reciprocal sign epistasis can be common in cancer, these results question the use and interpretation of CPMs.This study was supported by BFU2015-67302-R (MINECO/FEDER, EU

Managing A Franchise System: A Literature Review And A Synthesis

The article reviews the line of franchising research known as managing a franchise system. The main research topics that can be found in this line of research are conflicts between franchisor and franchisee, the balance of power in the franchising system, and managing the franchisor-franchisee relationship. The author reviews some of the existing literature related to managing franchising systems and provides a synthesis and some recommendations to develop better franchising systems