A criterion to locate tricritical points in phase diagrams is proposed. The criterion is formulated in the framework of the Elementary Catastrophe Theory and encompasses all the existing criteria in that it applies to systems described by a generally non symmetric free energy which can depend on one or more order parameters. We show that a tricritical point is given whenever the free energy is ...

This paper proposes an automated system for recognizing plant species based on leaf images. Plant leaf images corresponding to three plant types, are analyzed using three different shape modelling techniques, the first two based on the Moments-Invariant (M-I) model and the Centroid-Radii (C-R) model and the third based on a proposed technique of Binary-Superposition (B-S). For the M-I model the...

We study large scale collective dynamics of isoscalar type and examine the in-uence of interactions residual to independent particle motion. It is argued that for excitations which commonly are present in experimental situations such interactions must not be neglected. They even help to justify better the assumption of locality, both in time as well as in phase space, which is necessary not onl...

It is shown that Bell’s proof of violation of local realism in phase space is incorrect. Using Bell’s approach, a violation can be derived also for nonnegative Wigner distributions. The error is found to lie in the use of an unnormalizable Wigner function.

Recent experimental measurements of atomic intensity correlations through atom shot noise suggest that atomic quadrature phase correlations may soon be measured with a similar precision. We propose a test of local realism with mesoscopic numbers of massive particles based on such measurements. Using dissociation of a Bose-Einstein condensate of diatomic molecules into bosonic atoms, we demonstr...

Semiclassical delocalization in phase space constitutes a manifestation of the Uncertainty Principle, one indispensable part of the present understanding of Nature and the Wehrl entropy is widely regarded as the foremost localization-indicator. We readdress the matter here within the framework of the celebrated semiclassical Husimi distributions and their associated Wehrl entropies, suitably κ−...

We study large scale collective dynamics of isoscalar type and examine the influence of interactions residual to independent particle motion. It is argued that for excitations which commonly are present in experimental situations such interactions must not be neglected. They even help to justify better the assumption of locality, both in time as well as in phase space, which is necessary not on...

Let X be an n× p matrix whose rows are iid random vectors Xi· with mean μ ∈ R and covariance Σ ∈ Sp+— for example, they might be (Xi·) iid ∼ No(μ,Σ). For many problems (such as multivariate regression of some Y on X) we might wish to reduce the dimension p of these rows. For example, if we have a vector of p = 1000 possible explanatory variables about each individual, we may hope that a small s...

We introduce Localized Components Analysis (LoCA) for describing surface shape variation in an ensemble of biomedical objects using a linear subspace of spatially localized shape components. In contrast to earlier methods, LoCA optimizes explicitly for localized components and allows a flexible trade-off between localized and concise representations. Experiments comparing LoCA to a variety of c...

In this paper we propose a novel method for learning a Mahalanobis distance measure to be used in the KNN classification algorithm. The algorithm directly maximizes a stochastic variant of the leave-one-out KNN score on the training set. It can also learn a low-dimensional linear embedding of labeled data that can be used for data visualization and fast classification. Unlike other methods, our...