Uniformities for the convergence in law and in probability

The convergence (X _n, Y_n)0 is investigated and characterized for probability metrics which metrize convergence in distribution or in probability. Some related metrics are also considered.     

Deep Multilabel Multilingual Document Learning for Cross-Lingual Document Retrieval

Cross-lingual document retrieval, which aims to take a query in one language to retrieve relevant documents in another, has attracted strong research interest in the last decades. Most studies on this task start with cross-lingual comparisons at the word level and then represent documents via word embeddings, which leads to insufficient structure information. In this work, the cross-lingual comparison at the document level is achieved through the cross-lingual semantic space. Our method, MDL (deep multilabel multilingual document learning), leverages a six-layer fully connected network to project cross-lingual documents into a shared semantic space. The semantic distances can be calculated when the cross-lingual documents are transformed into embeddings in semantic space. The supervision signals are automatically extracted from the data and then used to construct the semantic space via a linear classifier. The ambiguity of manual labels could be avoided and the multilabel supervision signals can be acquired instead of a single label. The representation of the semantic space is enriched by multilabel supervision signals, which improves the discriminative ability of the embeddings. The MDL is easy to extend to other fields since it does not depend on specific data. Furthermore, MDL is more efficient than the models training all languages jointly, since each language is trained individually. Experiments on Wikipedia data showed that the proposed method outperforms the state-of-the-art cross-lingual document retrieval methods.     

Separability Criteria Based on the Weyl Operators

Entanglement as a vital resource for information processing can be described by special properties of the quantum state. Using the well-known Weyl basis we propose a new Bloch decomposition of the quantum state and study its separability problem. This decomposition enables us to find an alternative characterization of the separability based on the correlation matrix. We show that the criterion is effective in detecting entanglement for the isotropic states, Bell-diagonal states and some PPT entangled states. We also use the Weyl operators to construct an detecting operator for quantum teleportation.     

伪辛空间的生成及其表现形式

通过对辛空间的深入分析和研究,从空间中的度量与向量的迷向性问题入手并展开较为详细的讨论,定义"伪辛"的概念,阐述"辛"概念的演变、扩充与伪辛空间生成的事实,进而揭示伪辛空间的本质属性及其与辛空间的内在联系与区别.论述过程同时给出了伪辛空间关于辛空间的内蕴和外延表示式.     

Recasting the (Synchrosqueezed) Short-Time Fourier Transform as an Instantaneous Spectrum

In a previous work, we proposed a time-frequency analysis called instantaneous spectral analysis (ISA), which generalizes the notion of the Fourier spectrum and in which instantaneous frequency is utilized to the fullest extent. In this paper, we recast both the Fourier transform (FT) and filterbank (FB) interpretations of the short-time Fourier transform (STFT) as instantaneous spectra. We show that to recast the FB interpretation of STFT as an instantaneous spectrum with valid structure, frequency reassignment is a fundamental necessity, thus demonstrating that this IS is closely related to the synchrosqueezed STFT. This result provides a new theoretical motivation for the synchrosqueezed STFT. Finally, we illustrate through example the instantaneous spectra corresponding to the FT and FB interpretations of STFT using two closed-form examples.     

奇偶对相干态的维格纳函数和层析图函数

利用纠缠态η〉表象下的维格纳算符,重构了奇偶对相干态的维格纳函数.根据维格纳函数在相空间中随变量ρ和γ的变化规律,讨论了奇偶对相干态的非经典性质和量子干涉效应.研究发现,奇偶对相干态总呈现非经典性质,并且当q取奇数时,奇偶对相干态更容易出现非经典性质.奇偶对相干态的量子干涉效应的显著程度与q取值有关,但对于q的同一取值,奇对相干态的量子干涉效应更为显著.利用纠缠态η〉表象下的维格纳算符Δ1,2(ρ,γ)和纠缠态η,τ1,τ2〉的投影算符之间满足的拉东变换,获得了奇偶对相干态的量子层析图函数.     

Three‐unit semicircles curve: A compact 3D graphical representation of DNA sequences based on classifications of nucleotides

A new three‐dimensional graphical representation of DNA sequences, three‐unit semicircles (TUS)‐curve, which maps a given sequence into a dot sequences embedded in three‐unit semicircles, is proposed based on three biclassifications of nucleotides. TUS‐curve has the merit of compactness and could avoid the degeneracy and loss of information. The geometrical center of the curve, which indicates the distribution of base frequencies of the corresponding DNA sequence, is extracted and applied to analyze the similarity of various species. Phylogenetic tree of 11 species based on their first exons of β‐globin genes showed that the TUS‐curve is a powerful tool to get valuable biological information. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2011