Any two-qubit state can be faithfully represented by a steering ellipsoid inside the Bloch sphere, but not every ellipsoid inside the Bloch sphere corresponds to a two-qubit state. We give necessary and sufficient conditions for when the geometric data describe a physical state and investigate maximal volume ellipsoids lying on the physical-unphysical boundary. We derive monogamy relations for ...

We study the non-linear evolution of a dust ellipsoid, embedded in a Friedmann flat background universe, in order to determine the evolution of the density of the ellipsoid as the perturbation to it related detaches from general expansion and begins to collapse. We show that while the growth rate of the density contrast of a mass element is enhanced by the shear in agreement with Hoffman (1986a...

The velocity ellipsoid for 38 globular clusters with [Fe/H]≤ −1.0 is derived and shown to be significantly anisotropic with major axis directed towards low Galactic latitude. Principal axes of the spatial distribution of different groups of clusters are derived and compared with the velocity ellipsoid. The metal poor cluster spatial distribution is significantly flattened along an axis which co...

A convex body K in R has associated with it a unique circumscribed ellipsoid CE(K) with minimum volume, and a unique inscribed ellipsoid IE(K) with maximum volume. We first give a unified, modern exposition of the basic theory of these extremal ellipsoids using the semi–infinite programming approach pioneered by Fritz John in his seminal 1948 paper. We then investigate the automorphism groups o...

We present a new batch learning algorithm for text classification in the vector space of document representations. The algorithm uses ellipsoid separation [3] in the feature space which leads to a semidefinite program. An approximation of the latent semantic feature extraction approach using Gram-Schmidt orthogonalization [2] is used for the feature extraction. Preliminary results demonstrate s...

In February 1979 a note by L. G. Khachiyan indicated how an ellipsoid method for linear programming can be implemented in polynomial time. This result has caused great excitement and stimulated a flood of technical papers. Ordinarily there would be no need for a survey of work so recent, but the current circumstances are obviously exceptional. Word of Khachiyan's result has spread extraordinari...

We establish global rates of convergence for the Maximum Likelihood Estimators (MLEs) of log-concave and s-concave densities on ℝ. The main finding is that the rate of convergence of the MLE in the Hellinger metric is no worse than n-2/5 when -1 < s < ∞ where s = 0 corresponds to the log-concave case. We also show that the MLE does not exist for the classes of s-concave densities with s < -1.