Biplots of compositional data

The singular value decomposition and its interpretation as a linear biplot has proved to be a powerful tool for analysing many forms of multivariate data. Here we adapt biplot methodology to the speciffic case of compositional data consisting of positive vectors each of which is constrained to have unit sum. These relative variation biplots have properties relating to special features of compositional data: the study of ratios, subcompositions and models of compositional relationships. The methodology is demonstrated on a data set consisting of six-part colour compositions in 22 abstract paintings, showing how the singular value decomposition can achieve an accurate biplot of the colour ratios and how possible models interrelating the colours can be diagnosed.Logratio transformation, principal component analysis, relative variation biplot, singular value decomposition, subcomposition

Finite Temperature Time-Dependent Effective Theory For The Goldstone Field In A BCS-Type Superfluid

We extend to finite temperature the time-dependent effective theory for the Goldstone field (the phase of the pair field) $\theta$ which is appropriate for a superfluid containing one species of fermions with s-wave interactions, described by the BCS Lagrangian. We show that, when Landau damping is neglected, the effective theory can be written as a local time-dependent non-linear Schr\"{o}dinger Lagrangian (TDNLSL) which preserves the Galilean invariance of the zero temperature effective theory and is identified with the superfluid component. We then calculate the relevant Landau terms which are non-local and which destroy the Galilean invariance. We show that the retarded $\theta$-propagator (in momentum space) can be well represented by two poles in the lower-half frequency plane, describing damping with a predicted temperature, frequency and momentum dependence. It is argued that the real parts of the Landau terms can be approximately interpreted as contributing to the normal fluid component.Comment: 25 pages, 5 figures, references added, Introduction rewritte

The Pioneer anomaly: the measure of a topological phase defect of light in cosmology

It is shown that a wave vector representing a light pulse in an adiabatically evolving expanding space should develop, after a round trip (back and forth to the emitter) a geometric phase for helicity states at a given fixed position coordinate of this expanding space.In a section of the Hopf fibration of the Poincare sphere that identifies a projection to the physically allowed states, the evolution defines a parallel transported state that can be joined continuously with the initial state by means of the associated Berry-Pancharatnam connection. The connection allows to compute an anomaly in the frequency for the vector modes in terms of the scale factor of the space-time background being identical to the reported Pioneer Anomaly.Comment: 10 pages, some minor notation changes have been made. Some additional remarks were writte

Infrared divergence in QED3_3 at finite temperature

We consider various ways of treating the infrared divergence which appears in the dynamically generated fermion mass, when the transverse part of the photon propagator in N flavour $QED_{3}$ at finite temperature is included in the Matsubara formalism. This divergence is likely to be an artefact of taking into account only the leading order term in the $1 \over N$ expansion when we calculate the photon propagator and is handled here phenomenologically by means of an infrared cutoff. Inserting both the longitudinal and the transverse part of the photon propagator in the Schwinger-Dyson equation we find the dependence of the dynamically generated fermion mass on the temperature and the cutoff parameters. It turns out that consistency with certain statistical physics arguments imposes conditions on the cutoff parameters. For parameters in the allowed range of values we find that the ratio $r=2*Mass(T=0)/critical temperature$ is approximately 6, consistently with previous calculations which neglected the transverse photon contribution.Comment: 37 pages, 12 figures, typos corrected, references added, Introduction rewritte

Death with Raindrops

My story is about the final hours in the life of the Brazilian social activist and rubber, Chico Mendes, before he was assassinated on December 22, 1988. Even before I moved to Brazil in 1992–and got married and started a tour business there–I was hugely interested in the Amazon and its history and exploration. And what student of Amazonian culture hasn’t heard of Chico Mendes? He was what really inspired me to start traveling to the Amazon to see what I could perhaps do to help save the rainforest. My story is an humble effort to show the strength of the forces affecting Chico Mendes in the last days of his life, principally the push-pull between his love for life and his reassignment to dying for the cause he so strongly believed in, that being the need to preserve and sustain the Amazon Rainforest. Chico Mendes IS the Martin Luther King Jr. of my generation and his life and work deserve to be studied by all with an interest in conservation and social justice