Kullback–Leibler relative-entropy has unique properties in cases involving distributions resulting from relative-entropy minimization. Tsallis relative-entropy is a one-parameter generalization of Kullback–Leibler relative-entropy in the nonextensive thermostatistics. In this paper, we present the properties of Tsallis relative-entropy minimization and present some differences with the classica...

Automatic facial recognition has many potential applications in different areas of humancomputer interaction. However, they are not yet fully realized due to the lack of an effectivefacial feature descriptor. In this paper, we present a new appearance based feature descriptor,the local directional pattern (LDP), to represent facial geometry and analyze its performance inrecognition. An LDP feat...

We prove that for the relative entropy of faithful normal states φ and ω on the von Neumann algebra M the formula S(φ,ω) = sup{ω(Λ)-logφ(/): h = h*eM] holds. In general von Neumann algebras the relative entropy was defined and investigated by Araki [1, 3]. After Lieb had proved the joint convexity of the relative entropy in the type / case [10] several proofs appeared in the literature and they...

Generalizing the notion of relative entropy, the difference between a priori and a posteriori relative entropy for quantum systems is drawn. The former, known as quantum relative entropy, is associated with quantum states recognition. The latter—a posteriori relative quantum entropy is introduced and shown to be related with state reconstruction due to the following property: given a density op...

automatic facial recognition has many potential applications in different areas of humancomputer interaction. however, they are not yet fully realized due to the lack of an effectivefacial feature descriptor. in this paper, we present a new appearance based feature descriptor,the local directional pattern (ldp), to represent facial geometry and analyze its performance inrecognition. an ldp feat...

For two gaussian states with given correlation matrices, in order that relative entropy between them is practically calculable, I in this paper describe the ways of transforming the correlation matrix to matrix in the exponential density operator. Gaussian relative entropy of entanglement is proposed as the minimal relative entropy of the gaussian state with respect to separable gaussian state ...

Fundamental properties for the Tsallis relative entropy in both classical and quantum systems are studied. As one of our main results, we give the parametric extension of the trace inequality between the quantum relative entropy and the minus of the trace of the relative operator entropy given by Hiai and Petz. The monotonicity of the quantum Tsallis relative entropy for the trace preserving co...

Recently there has been an extensive study on Relative Semi-Dynamical Systems (RSD-Systems). In this paper, we explore some topological properties of RSD-systems. Here, in particular, minimal RSD-systems are characterized and transitive homeomorphisms are investigated. Moreover, α-level relative topological entropy is extended to RSD-systems. Finally, as a computational example, we develop an R...