Hawking radiation of charged particles as tunneling from Reissner-Nordstrom-de Sitter black holes with a global monopole

Applying Parikh's semi-classical tunneling method, we consider Hawking radiation of the charged massive particles as a tunneling process from the Reissner-Nordstrom-de Sitter black hole with a global monopole. The result shows that the tunneling rate is related to the change of Bekenstein-Hawking entropy and the radiant spectrum is not a pure thermal one, but is consistent with an underlying unitary theory.Comment: 10 pages, no figure, use elsart.cls. Published version in PLB with correction

Hawking radiation as tunneling from the Kerr and Kerr-Newman black holes

Recent work, which treats the Hawking radiation as a semi-classical tunneling process at the horizon of the Schwarzschild and Reissner-Nordstrom spacetimes, indicates that the exact radiant spectrum is no longer pure thermal after considering the black hole background as dynamical and the conservation of energy. In this paper, we extend the method to investigate Hawking radiation as massless particles tunneling across the event horizon of the Kerr black hole and that of charged particles from the Kerr-Newman black hole by taking into account the energy conservation, the angular momentum conservation, and the electric charge conservation. Our results show that when self-gravitation is considered, the tunneling rate is related to the change of Bekenstein-Hawking entropy and the derived emission spectrum deviates from the pure thermal spectrum, but is consistent with an underlying unitary theory.Comment: 10 pages, no figure, Revtex4, typos removed, final version to appear in PR

Deep Cross-Modal Hashing

Due to its low storage cost and fast query speed, cross-modal hashing (CMH) has been widely used for similarity search in multimedia retrieval applications. However, almost all existing CMH methods are based on hand-crafted features which might not be optimally compatible with the hash-code learning procedure. As a result, existing CMH methods with handcrafted features may not achieve satisfactory performance. In this paper, we propose a novel cross-modal hashing method, called deep crossmodal hashing (DCMH), by integrating feature learning and hash-code learning into the same framework. DCMH is an end-to-end learning framework with deep neural networks, one for each modality, to perform feature learning from scratch. Experiments on two real datasets with text-image modalities show that DCMH can outperform other baselines to achieve the state-of-the-art performance in cross-modal retrieval applications.Comment: 12 page

Asymmetric Deep Supervised Hashing

Hashing has been widely used for large-scale approximate nearest neighbor search because of its storage and search efficiency. Recent work has found that deep supervised hashing can significantly outperform non-deep supervised hashing in many applications. However, most existing deep supervised hashing methods adopt a symmetric strategy to learn one deep hash function for both query points and database (retrieval) points. The training of these symmetric deep supervised hashing methods is typically time-consuming, which makes them hard to effectively utilize the supervised information for cases with large-scale database. In this paper, we propose a novel deep supervised hashing method, called asymmetric deep supervised hashing (ADSH), for large-scale nearest neighbor search. ADSH treats the query points and database points in an asymmetric way. More specifically, ADSH learns a deep hash function only for query points, while the hash codes for database points are directly learned. The training of ADSH is much more efficient than that of traditional symmetric deep supervised hashing methods. Experiments show that ADSH can achieve state-of-the-art performance in real applications

Homeomorphisms of 3-manifolds and the realization of Nielsen Number

The Nielsen Conjecture for Homeomorphisms asserts that any homeomorphism $f$ of a closed manifold is isotopic to a map realizing the Nielsen number of $f$, which is a lower bound for the number of fixed points among all maps homotopic to $f$. The main theorem of this paper proves this conjecture for all orientation preserving maps on geometric or Haken 3-manifolds. It will also be shown that on many manifolds all maps are isotopic to fixed point free maps. The proof is based on the understanding of homeomorphisms on 2-orbifolds and 3-manifolds. Thurston's classification of surface homeomorphisms will be generalized to 2-dimensional orbifolds, which is used to study fiber preserving maps of Seifert fiber spaces. Maps on most Seifert fiber spaces are indeed isotopic to fiber preserving maps, with the exception of four manifolds and orientation reversing maps on lens spaces or $S^3$. It will also be determined exactly which manifolds have a unique Seifert fibration up to isotopy. These informations will be used to deform a map to certain standard map on each piece of the JSJ decomposition, as well as on the neighborhood of the decomposition tori, which will make it possible to shrink each fixed point class to a single point, and remove inessential fixed point classes

Deep Discrete Supervised Hashing

Hashing has been widely used for large-scale search due to its low storage cost and fast query speed. By using supervised information, supervised hashing can significantly outperform unsupervised hashing. Recently, discrete supervised hashing and deep hashing are two representative progresses in supervised hashing. On one hand, hashing is essentially a discrete optimization problem. Hence, utilizing supervised information to directly guide discrete (binary) coding procedure can avoid sub-optimal solution and improve the accuracy. On the other hand, deep hashing, which integrates deep feature learning and hash-code learning into an end-to-end architecture, can enhance the feedback between feature learning and hash-code learning. The key in discrete supervised hashing is to adopt supervised information to directly guide the discrete coding procedure in hashing. The key in deep hashing is to adopt the supervised information to directly guide the deep feature learning procedure. However, there have not existed works which can use the supervised information to directly guide both discrete coding procedure and deep feature learning procedure in the same framework. In this paper, we propose a novel deep hashing method, called deep discrete supervised hashing (DDSH), to address this problem. DDSH is the first deep hashing method which can utilize supervised information to directly guide both discrete coding procedure and deep feature learning procedure, and thus enhance the feedback between these two important procedures. Experiments on three real datasets show that DDSH can outperform other state-of-the-art baselines, including both discrete hashing and deep hashing baselines, for image retrieval

Hawking Radiation of Charged Particles as Tunneling from Higher Dimensional Reissner-Nordstrom-de Sitter Black Holes

Recent work that treats the Hawking radiation as a semi-classical tunnelling process from the four-dimensional Schwarzschild and Reissner-Nordstrom black holes is extended to the case of higher dimensional Reissner-Nordstrom-de Sitter black holes. The result shows that the tunnelling rate is related to the change of Bekenstein-Hawking entropy and the exact radiant spectrum is no longer precisely thermal after considering the black hole background as dynamical and incorporating the self-gravitation effect of the emitted particles when the energy conservation and electric charge conservation are taken into account.Comment: 13 pages, no figure, enlarged versio

On the Evaluation Metric for Hashing

Due to its low storage cost and fast query speed, hashing has been widely used for large-scale approximate nearest neighbor (ANN) search. Bucket search, also called hash lookup, can achieve fast query speed with a sub-linear time cost based on the inverted index table constructed from hash codes. Many metrics have been adopted to evaluate hashing algorithms. However, all existing metrics are improper to evaluate the hash codes for bucket search. On one hand, all existing metrics ignore the retrieval time cost which is an important factor reflecting the performance of search. On the other hand, some of them, such as mean average precision (MAP), suffer from the uncertainty problem as the ranked list is based on integer-valued Hamming distance, and are insensitive to Hamming radius as these metrics only depend on relative Hamming distance. Other metrics, such as precision at Hamming radius R, fail to evaluate global performance as these metrics only depend on one specific Hamming radius. In this paper, we first point out the problems of existing metrics which have been ignored by the hashing community, and then propose a novel evaluation metric called radius aware mean average precision (RAMAP) to evaluate hash codes for bucket search. Furthermore, two coding strategies are also proposed to qualitatively show the problems of existing metrics. Experiments demonstrate that our proposed RAMAP can provide more proper evaluation than existing metrics

Deep Multi-Index Hashing for Person Re-Identification

Traditional person re-identification (ReID) methods typically represent person images as real-valued features, which makes ReID inefficient when the gallery set is extremely large. Recently, some hashing methods have been proposed to make ReID more efficient. However, these hashing methods will deteriorate the accuracy in general, and the efficiency of them is still not high enough. In this paper, we propose a novel hashing method, called deep multi-index hashing (DMIH), to improve both efficiency and accuracy for ReID. DMIH seamlessly integrates multi-index hashing and multi-branch based networks into the same framework. Furthermore, a novel block-wise multi-index hashing table construction approach and a search-aware multi-index (SAMI) loss are proposed in DMIH to improve the search efficiency. Experiments on three widely used datasets show that DMIH can outperform other state-of-the-art baselines, including both hashing methods and real-valued methods, in terms of both efficiency and accuracy.Comment: 10 pages, 6 figures, 2 table

Achirality of knots and links

We will develop various methods, some are of geometric nature and some are of algebraic nature, to detect the various achiralities of knots and links in $S^3$. For example, we show that the twisted Whitehead double of a knot is achiral if and only if the double is the unknot or the figure eight knot, and we show that all non-trivial links with $\leq9$ crossings are not achiral except the Borromean rings. A simple procedure for calculating the $\eta$-function is given in terms of a crossing change formula and its initial values.Comment: amstex, 28 pages with 10 figures. Results in Section 5 are substantially improve