The quantum states which satisfy the equality in the generalised uncertainty relation are called intelligent states. We prove the existence of intelligent states for the Anandan-Aharonov uncertainty relation based on the geometry of the quantum state space for arbitrary parametric evolutions of quantum states when the initial and final states are non-orthogonal. email:[email protected] I...

A number of machine learning algorithms are using a metric, or a distance, in order to compare individuals. The Euclidean distance is usually employed, but it may be more efficient to learn a parametric distance such as Mahalanobis metric. Learning such a metric is a hot topic since more than ten years now, and a number of methods have been proposed to efficiently learn it. However, the nature ...

Kernel regression is a popular non-parametric fitting technique. It aims at learning a function which estimates the targets for test inputs as precise as possible. Generally, the function value for a test input is estimated by a weighted average of the surrounding training examples. The weights are typically computed by a distancebased kernel function and they strongly depend on the distances b...

Under new assumptions, we provide suffcient conditions for the upper and lower semicontinuity and continuity of the solution mappings to a class of generalized parametric set-valued Ky Fan inequality problems in linear metric space. These results extend and improve some known results in the literature e.g., Gong, 2008; Gong and Yoa, 2008; Chen and Gong, 2010; Li and Fang, 2010 . Some examples a...

Image parsing is vital for many high-level image understanding tasks. Although both parametric and non-parametric approaches have achieved remarkable success, many technical challenges still prevail for images containing things/objects with broad-coverage and high-variability, because it still lacks versatile and effective strategies to seamlessly integrate local–global features selection, cont...

In the learning and recognition methods we introduced till now, we have not made strong assumptions about the data: Nearest neighbor, SVM, distance metric learning, normalization and decision trees do not explicitly assuming distributional properties of the data; PCA and FLD are optimal solutions under certain data assumptions, but they work well in many other situations too; parametric probabi...

The paper studies large deviations of maximum likelihood and related estimates in the case of i.i.d. observations with distribution determined by a parameter θ taking values in a general metric space. The main theorems provide sufficient conditions under which an approximate sieve maximum likelihood estimate is an asymptotically locally optimal estimate of g(θ) in the sense of Bahadur, for virt...