一类分数阶微积分的中值定理及应用

Riemann-Liouville分数阶微积分算子是一类带有一个函数的分数阶微积分算子的特殊情形，以Riemann-Liouville分数阶微积分算子的积分中值定理和微分中值定理为基础，我们得到了一类带有一个函数的分数阶微积分算子的积分中值定理和微分中值定理，并给出其在计算方面的一些应用。     

Learn decision trees with deep visual primitives

In this paper, we strive to propose a self-interpretable framework, termed PrimitiveTree, that incorporates deep visual primitives condensed from deep features with a conventional decision tree, bridging the gap between deep features extracted from deep neural networks (DNNs) and trees’ transparent decision-making processes. Specifically, we utilize a codebook, which embeds the continuous deep features into a finite discrete space (deep visual primitives) to distill the most common semantic information. The decision tree adopts the spatial location information and the mapped primitives to present the decision-making process of the deep features in a tree hierarchy. Moreover, the trained interpretable PrimitiveTree can inversely explain the constituents of the deep features, highlighting the most critical and semantic-rich image patches attributing to the final predictions of the given DNN. Extensive experiments and visualization results validate the effectiveness and interpretability of our method.     

A general framework to study the price‐color relationship in paintings with an application to Mark Rothko rectangular series

We propose a general framework to study the relationship between the price of a painting and its color‐related attributes. To this end we focus on four key aspects: dominant colors, features of the color palette, color harmony, and color emotions. We demonstrate the usefulness of this approach with an example based on Mark Rothko's post‐1950 paintings (the “rectangular” series), and auction data from the 1994 to 2018 period. We identify two distinct price‐color regimes in Rothko's market: (a) [1994‐2005], a period in which prices are explained mainly by the growing popularity of the artist regardless of the color attributes of the paintings sold; and (b) [2006‐2018], a period in which color‐related attributes explain most of the prices. Furthermore, we find that in this second period, the dominant colors and the diversity of the color palette, are by far the most relevant attributes that influence the price; color harmony and color emotions hold almost no explanatory power during this period. Finally, we propose a new metric based on the Herfindahl Index to describe color diversity; this metric seems to be promising at characterizing the effect of the color palette on the price of a painting.     

The Photomontage Activity of Postmodernism

For decades now, Douglas Crimp’s landmark 1980 essay ‘The Photographic Activity of Postmodernism’ has shaped our understanding of modernism’s aftermath, at least as it unfolded in North America and Western Europe. Less remembered, however, is the degree to which the procedures of disjunction, copying, appropriation, and outright theft that he highlighted were epitomised not just by contemporary photography, but by photomontage in particular. This article recovers the debates that led critics such as Crimp, Abigail Solomon-Godeau, Christopher Phillips, Benjamin Buchloh and others to turn to photomontage as one of their principal objects of concern in what became known as the postmodern critique of photography. Why was montage tasked to perform this critical function, particularly by people around the journal October who had not otherwise devoted the balance of their writing to photography’s history? The article suggests that these men and women, along with the contemporary artists they foregrounded, manifested what Mary Anne Doane has called a ‘desire for signification’, a reaction in the late 1970s against the mute theatricality of minimalist and conceptual art. Photomontage reintroduced representation to contemporary art and to the canon of art history. But unlike the reemerging illusionism in painting that also manifested this desire, montage guarded against an uncomplicated realism by highlighting and critiquing operations of representation in a manner that painting no longer could.     

Study of planar structure applying reciprocity technique combined with MGEC and analysis of discontinuity

The 3D structure electromagnetic computation presents several difficulties related to the volume mesh. In fact, the entire volume space must be taken into account even the smallest details. In this article, we propose a formulation based on the reciprocity theorem combined with the generalized equivalent circuit method to model a planar 3D structure with both coaxial and planar excitation. The major advantage of this formulation is the fact to reduce the computational volume into 2D ones in the discontinuity plane. In addition, we focused on the calculation of the discontinuity between the excitation source and the planar structure to determine the exact behavior of the electric coaxial excitation model. The obtained current density, electric field distributions, and the input impedance are presented and discussed in the following sections. An approximately good agreement of input impedance with those obtained by the simulator and measurement is shown.     

基于查询的新闻多文档自动摘要技术研究

针对新闻文本领域,该文提出一种基于查询的自动文本摘要技术,更加有针对性地满足用户信息需求。根据句子的TF-IDF、与查询句的相似度等要素,计算句子权重,并根据句子指示的时间给定不同的时序权重系数,使得最近发生的新闻内容具有更高的权重,最后使用最大边界相关的方法选择摘要句。通过与基于TF-IDF、Text-Rank、LDA等六种方法的对比,该摘要方法ROUGE评测指标上优于其他方法。从结合评测结果及摘要示例可以看出,该文提出的方法可以有效地从新闻文档集中摘取核心信息,满足用户查询内容的信息需求。     

Weighted preliminary-summation-based principal component analysis for non-Gaussian processes

For industrial chemical process, preliminary-summation-based principal component analysis (PS-PCA), an amended PCA method was recently provided for coping with both Gaussian and non-Gaussian characteristics. By summing the training and monitoring data respectively, PS-PCA is capable of resolving the issue of non-Gaussian processes and achieves higher fault detection rate than the traditional PCA. However, in the PS-PCA summation operation, all data samples are regarded as the same weight, which results in the fault information of newly-samples may be diluted, leading to significant detection delays. To address this challenge, in this paper, we propose a novel weighted PS-PCA (WPS-PCA) method that employs an exponential weighting scheme to put more emphasis on recent information. Subsequently, a mathematical argument demonstrates that when the number of variables is enough plentiful, the obtained summation combined with the generalized central limit theorem conforms to approximately a Gaussian distribution. The kurtosis relationships indicate this conversion will bring out well-pleasing feasibility for conventional PCA. Ultimately, the proposed technique verifies detection performance using the Tennessee Eastman process, which is compared with the existing PCA and PS-PCA schemes, in terms of the fault detection time and fault detection rate. The simulation studies reveal that the proposed method is efficient and superior.