The study of higher-dimensional black holes is a subject which has recently attracted vast interest. Perhaps one of the most surprising discoveries is a realization that the properties of ...higher-dimensional black holes with the spherical horizon topology and described by the Kerr–NUT–(A)dS metrics are very similar to the properties of the well known four-dimensional Kerr metric. This remarkable result stems from the existence of a single object called the principal tensor. In our review we discuss explicit and hidden symmetries of higher-dimensional Kerr–NUT–(A)dS black hole spacetimes. We start with discussion of the Killing and Killing–Yano objects representing explicit and hidden symmetries. We demonstrate that the principal tensor can be used as a “seed object” which generates all these symmetries. It determines the form of the geometry, as well as guarantees its remarkable properties, such as special algebraic type of the spacetime, complete integrability of geodesic motion, and separability of the Hamilton–Jacobi, Klein–Gordon, and Dirac equations. The review also contains a discussion of different applications of the developed formalism and its possible generalizations.
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DOBA, IZUM, KILJ, NUK, PILJ, PNG, SAZU, UILJ, UKNU, UL, UM, UPUK
This paper revisits blind source separation of instantaneously mixed quasi-stationary sources (BSS-QSS), motivated by the observation that in certain applications (e.g., speech) there exist time ...frames during which only one source is active, or locally dominant. Combined with nonnegativity of source powers, this endows the problem with a nice convex geometry that enables elegant and efficient BSS solutions. Local dominance is tantamount to the so-called pure pixel/separability assumption in hyperspectral unmixing/nonnegative matrix factorization, respectively. Building on this link, a very simple algorithm called successive projection algorithm (SPA) is considered for estimating the mixing system in closed form. To complement SPA in the specific BSS-QSS context, an algebraic preprocessing procedure is proposed to suppress short-term source cross-correlation interference. The proposed procedure is simple, effective, and supported by theoretical analysis. Solutions based on volume minimization (VolMin) are also considered. By theoretical analysis, it is shown that VolMin guarantees perfect mixing system identifiability under an assumption more relaxed than (exact) local dominance - which means wider applicability in practice. Exploiting the specific structure of BSS-QSS, a fast VolMin algorithm is proposed for the overdetermined case. Careful simulations using real speech sources showcase the simplicity, efficiency, and accuracy of the proposed algorithms.
Image steganalysis has witnessed significant development but still encounters challenges in detection speed and accuracy. Based on this consideration, this paper proposes a simple yet efficient ...dominant feature selection method. First, a separability measurement is designed utilizing the principles of “intraclass aggregation and interclass dispersion” and “maximum interclass disparity”, by which the contribution of each feature is better evaluated. Second, a separability measurement is presented considering the “holistic interclass disparity”, and thus dominant features are directly determined. Moreover, a compensation strategy is proposed to reduce the possibility of missing dominant features, thereby further enhancing the accuracy of the selected features. The effectiveness of the proposed method is empirically verified. Extensive experiments are conducted on the BOSSbase 1.01 and ALASKA2 datasets. The results show that, compared to some state-of-the-art works, the proposed method achieves better performance in terms of computational cost, feature dimension, and detection accuracy. In particular, the computational cost of the proposed method is extremely low.
•A fast feature selection with compensation for image steganalysis is presented.•The proposed separability measurement improves computational efficiency.•A feature compensation strategy is proposed to increase the feature diversity.•Compared to the state-of-the-art works, our method achieves better performance.
Soft topology studies a structure on the collection of all soft sets on a given set of alternatives (the relevant attributes being fixed). It is directly inspired by the axioms of a topological ...space. This paper contributes to the theoretical bases of soft topology in various ways. We extend a general construction of soft topologies from topologies on the set of alternatives in two different directions. An extensive discussion with criteria about what a soft counterpart of “topological separability” should satisfy is also given. The interactions of the properties that arise with separability, and of second-countability and its soft counterpart, are studied under the general mechanisms that generate soft topological spaces. The first non-trivial examples of soft second-countable soft topological spaces are produced as a consequence.
The present study with 248 German teachers examined the conceptual separability of six dimensions of teachers’ self-concept (pedagogical skills, subject content knowledge, consulting, innovation, ...media use, diagnostics) and three emotions (enjoyment, anger, anxiety) as well as relations of these constructs. Results showed that all self-concepts and emotions were clearly separable from each other. All six self-concepts were positively related to enjoyment and negatively related to anxiety and anger. However, regression analysis revealed that only self-concept of pedagogical skills was positively linked to enjoyment and negatively linked to anger, while only self-concept of subject content knowledge was negatively linked to anxiety.
•Teachers' self-concepts are multifaceted.•Teachers' self-concepts are differentially related to specific emotions.•Only self-concept of pedagogical skills is positively linked to enjoyment.•Only self-concept of pedagogical skills is negatively linked to anger.•Only self-concept of subject content knowledge is negatively linked to anxiety.
The concentrations of measure phenomena were discovered as the mathematical background to statistical mechanics at the end of the nineteenth/beginning of the twentieth century and have been explored ...in mathematics ever since. At the beginning of the twenty-first century, it became clear that the proper utilization of these phenomena in machine learning might transform the curse of dimensionality into the blessing of dimensionality. This paper summarizes recently discovered phenomena of measure concentration which drastically simplify some machine learning problems in high dimension, and allow us to correct legacy artificial intelligence systems. The classical concentration of measure theorems state that i.i.d. random points are concentrated in a thin layer near a surface (a sphere or equators of a sphere, an average or median-level set of energy or another Lipschitz function, etc.). The new stochastic separation theorems describe the thin structure of these thin layers: the random points are not only concentrated in a thin layer but are all linearly separable from the rest of the set, even for exponentially large random sets. The linear functionals for separation of points can be selected in the form of the linear Fisher's discriminant. All artificial intelligence systems make errors. Non-destructive correction requires separation of the situations (samples) with errors from the samples corresponding to correct behaviour by a simple and robust classifier. The stochastic separation theorems provide us with such classifiers and determine a non-iterative (one-shot) procedure for their construction.
This article is part of the theme issue 'Hilbert's sixth problem'.
In this paper we introduce and investigate the notion of semiseparable functor. One of its first features is that it allows a novel description of separable and naturally full functors in terms of ...faithful and full functors, respectively. To any semiseparable functor we attach an invariant, given by an idempotent natural transformation, which controls when the functor is separable and yields a characterization of separable functors in terms of (dual) Maschke and conservative functors. We prove that any semiseparable functor admits a canonical factorization as a naturally full functor followed by a separable functor. Here the main tool is the construction of the coidentifier category attached to the associated idempotent natural transformation. Then we move our attention to the semiseparability of functors that have an adjoint. First we obtain a Rafael-type Theorem. Next we characterize the semiseparability of adjoint functors in terms of the (co)separability of the associated (co)monads and the natural fullness of the corresponding (co)comparison functor. We also focus on functors that are part of an adjoint triple. In particular, we describe bireflections as semiseparable (co)reflections, or equivalently, as either Frobenius or naturally full (co)reflections. As an application of our results, we study the semiseparability of functors traditionally attached to ring homomorphisms, coalgebra maps, corings and bimodules, introducing the notions of semicosplit coring and semiseparability relative to a bimodule which extend those of cosplit coring and Sugano's separability relative to a bimodule, respectively.
•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.
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