3,281 research outputs found
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) 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
-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 QED 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 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 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 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
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