When two or more degrees of freedom become coupled in a physical system, a number of observables of the latter cannot be represented by mathematical expressions separable with respect to the ...different degrees of freedom. In recent years it appeared clear that these expressions may display the same mathematical structures exhibited by multiparty entangled states in quantum mechanics. In this work, we investigate the occurrence of such structures in optical beams, a phenomenon that is often referred to as 'classical entanglement'. We present a unified theory for different kinds of light beams exhibiting classical entanglement and we indicate several possible extensions of the concept. Our results clarify and shed new light upon the physics underlying this intriguing aspect of classical optics.
In this work, the separability, locally separability, weakly separability and locally weakly separability of the space of probability measures of an infinite compact space are studied. It is proved ...that an infinite compact space
is a separable (locally separable), if and only if the space
is a separable (locally separable). It was also proved that, if a space
is a weakly separable (locally weakly separable), then the space
is a weakly separable (locally weakly separable).
How can one prove that a given quantum state is entangled? In this paper we review different methods that have been proposed for entanglement detection. We first explain the basic elements of ...entanglement theory for two or more particles and then entanglement verification procedures such as Bell inequalities, entanglement witnesses, the determination of nonlinear properties of a quantum state via measurements on several copies, and spin squeezing inequalities. An emphasis is given to the theory and application of entanglement witnesses. We also discuss several experiments, where some of the presented methods have been implemented.
We investigate four finiteness conditions related to residual finiteness: complete separability, strong subsemigroup separability, weak subsemigroup separability and monogenic subsemigroup ...separability. For each of these properties we examine under which conditions the property is preserved under direct products. We also consider if any of the properties are inherited by the factors in a direct product. We give necessary and sufficient conditions for finite semigroups to preserve the properties of strong subsemigroup separability and monogenic subsemigroup separability in a direct product.
In this paper we propose a novel method combining graph embedding and difference criterion techniques for image feature extraction, namely two-dimensional maximum embedding difference (2DMED). This ...method directly extracts the optimal projective vectors from 2D image matrices by simultaneously considering characteristic that is the intra-class compactness graph, the margin graph and inter-class separability graph, respectively. In this method, it is not necessary to convert the image matrix into high-dimensional image vector so that much computational time would be saved. In addition, the proposed method preserves the manifold reconstruction relationships in the low-dimensional subspace. Experimental results on the ORL, Yale face and USPS database show the effectiveness of the proposed method.
•Proposed a new texture feature extraction method.•This method comprehensively considers spatial continuity and gray diversity.•It could effectively distinguish ground objects with different ...fragmentation degrees.•It could contribute to achieving the fine recognition of ground objects.•Its performance advantages are more obvious with the decrease of spatial resolution.
Texture features play an important role in the field of remote sensing classification. However, most existing methods lack a comprehensive consideration of spatial continuity, which makes them either destroy the spatial integrity of regular ground objects or fail to quantify the fragmentation degrees of irregular ground objects. These problems weak the ability of existing methods to distinguish ground objects with different fragmentation degrees. Therefore, this study proposed a new texture feature extraction method considering spatial continuity and gray diversity (SCGD). SCGD first connected all pixels in a neighborhood in series from end to end according to the row and column directions, and the diversities of the spatial continuity encoding in different directions were calculated by the Shannon index. Then, the Shannon index was used to calculate the gray diversity. Finally, SCGD calculated the weighted average of spatial continuity diversity and gray diversity to obtain the final texture feature values. Validation results indicated that SCGD can effectively distinguish ground objects with different fragmentation degrees, and its performance is better than that of traditional methods. As the spatial resolution decreases, its performance advantage becomes more obvious. Moreover, SCGD has great application potential in the field of ground object classification, and combining it with deep learning models will contribute to achieving the fine recognition of ground objects.
PDF
