Local Clique Covering of Claw‐Free Graphs

A clique covering of a simple graph G is a collection of cliques of G covering all the edges of G such that each vertex is contained in at most k cliques. The smallest k for which G admits a clique covering is called the local clique cover number of G and is denoted by lcc(G). Local clique cover number can be viewed as the local counterpart of the clique cover number that is equal to the minimum total number of cliques covering all edges. In this article, several aspects of the local clique covering problem are studied and its relationships to other well‐known problems are discussed. In particular, it is proved that the local clique cover number of every claw‐free graph is at most , where Δ is the maximum degree of the graph and c is a constant. It is also shown that the bound is tight, up to a constant factor. Moreover, regarding a conjecture by Chen et al. (Clique covering the edges of a locally cobipartite graph, Discrete Math 219(1–3)(2000), 17–26), we prove that the clique cover number of every connected claw‐free graph on n vertices with the minimum degree δ, is at most , where c is a constant.     

Representations of hypergraph states with neural networks

The quantum many-body problem(QMBP) has become a hot topic in high-energy physics and condensed-matter physics. With an exponential increase in the dimensions of Hilbert space, it becomes very challenging to solve the QMBP, even with the most powerful computers. With the rapid development of machine learning, artificial neural networks provide a powerful tool that can represent or approximate quantum many-body states. In this paper, we aim to explicitly construct the neural network representations of hypergraph states. We construct the neural network representations for any k-uniform hypergraph state and any hypergraph state,respectively, without stochastic optimization of the network parameters. Our method constructively shows that all hypergraph states can be represented precisely by the appropriate neural networks introduced in [Science 355(2017) 602] and formulated in [Sci. China-Phys.Mech. Astron. 63(2020) 210312].     

Shall I Work with Them? A Knowledge Graph-Based Approach for Predicting Future Research Collaborations

We consider the prediction of future research collaborations as a link prediction problem applied on a scientific knowledge graph. To the best of our knowledge, this is the first work on the prediction of future research collaborations that combines structural and textual information of a scientific knowledge graph through a purposeful integration of graph algorithms and natural language processing techniques. Our work: (i) investigates whether the integration of unstructured textual data into a single knowledge graph affects the performance of a link prediction model, (ii) studies the effect of previously proposed graph kernels based approaches on the performance of an ML model, as far as the link prediction problem is concerned, and (iii) proposes a three-phase pipeline that enables the exploitation of structural and textual information, as well as of pre-trained word embeddings. We benchmark the proposed approach against classical link prediction algorithms using accuracy, recall, and precision as our performance metrics. Finally, we empirically test our approach through various feature combinations with respect to the link prediction problem. Our experimentations with the new COVID-19 Open Research Dataset demonstrate a significant improvement of the abovementioned performance metrics in the prediction of future research collaborations.     

Computational Abstraction

Representation and abstraction are two of the fundamental concepts of computer science. Together they enable “high-level” programming: without abstraction programming would be tied to machine code; without a machine representation, it would be a pure mathematical exercise. Representation begins with an abstract structure and seeks to find a more concrete one. Abstraction does the reverse: it starts with concrete structures and abstracts away. While formal accounts of representation are easy to find, abstraction is a different matter. In this paper, we provide an analysis of data abstraction based upon some contemporary work in the philosophy of mathematics. The paper contains a mathematical account of how Frege’s approach to abstraction may be interpreted, modified, extended and imported into type theory. We argue that representation and abstraction, while mathematical siblings, are philosophically quite different. A case of special interest concerns the abstract/physical interface which houses both the physical representation of abstract structures and the abstraction of physical systems.     

超声显微检测技术在电子封装中的应用与发展

超声显微检测技术应用于电子封装领域始于上世纪80年代,如今已是检测电子封装可靠性和完整性的重要手段,被广泛应用到了电子封装的缺陷检测和精密测量等方面。针对电子封装的超声显微检测存在回波重叠、信噪比低等问题,近年来,发展了许多时频分析方法,用于获得优于常规方法的纵向分辨率,即实现超分辨率。本文首先介绍了超声显微检测的发展历史,对其检测原理和分辨率理论进行了简述;其次,综述了超声显微检测技术在电子封装中的主要应用与发展现状;然后,对超声显微检测的超分辨率成像方法进行了综述,分别介绍了基于小波分析的反卷积、连续小波变换和稀疏表示在实现超分辨率时的原理及适用场景;最后,探讨归纳了电子封装超声显微检测的主要研究方向及难点。     

Some types and covers for quaternionic hermitian groups

We determine reducibility points for a certain family of induced representations for quaternionic hermitian and anti-hermitian groups over a p-adic field. We do this via Bushnell and Kutzko’s method of types and covers.     

A Frobenius formula for the structure coefficients of double-class algebras of Gelfand pairs

After a careful consideration of some of the well known properties of irreducible characters of finite groups to zonal spherical functions of Gelfand pairs, we were able to deduce a Frobenius formula for Gelfand pairs. For a given Gelfand pair, the structure coe?cients of its associated double-class algebra can be written in terms of zonal spherical functions. This is a generalization of the Frobenius formula which expresses the structure coe?cients of the center of a finite group algebra in terms of irreducible characters.     

Representation and approximation of convex dynamic risk measures with respect to strong–weak topologies

We provide a representation for strong-weak continuous dynamic risk measures from L^p into L^p_t spaces where these spaces are equipped respectively with strong and weak topologies and p is a finite number strictly larger than one. Conversely, we show that any such representation that admits a compact (with respect to the product of weak topologies) sub-differential generates a dynamic risk measure that is strong--weak continuous. Furthermore, we investigate sufficient conditions on the sub-differential for which the essential supremum of the representation is attained. Finally, the main purpose is to show that any convex dynamic risk measure that is strong-weak continuous can be approximated by a sequence of convex dynamic risk measures which are strong--weak continuous and admit compact sub-differentials with respect to the product of weak topologies. Throughout the arguments, no conditional translation invariance or monotonicity assumptions are applied.     

����Ԫ���������������ķ��䵹�����΢�ַ�������Ԫ�ı�ʾ����

In this paper, we establish a local representation theorem for generators of reflected backward stochastic differential equations (RBSDEs), whose generators are continuous with linear growth. It generalizes some known representation theorems for generators of backward stochastic differential equations (BSDEs). As some applications, a general converse comparison theorem for RBSDEs is obtained and some properties of RBSDEs are discussed.