Integral representation and estimation of harmonic functions in the quaternionic half space

In this article, we discuss the integral representation of quaternionic harmonic functions in the half space with the general boundary condition. Next, we derive a lower bound from an upper one for quaternionic harmonic functions. These results generalize some of the classic results from the case of plane to the case of noncommutative quaterninionic half space. Copyright © 2017 John Wiley & Sons, Ltd.     

Convergent sequences of sparse graphs: A large deviations approach

Models based on sparse graphs are of interest to many communities: they appear as basic models in combinatorics, probability theory, optimization, statistical physics, information theory, and more applied fields of social sciences and economics. Different notions of similarity (and hence convergence) of sparse graphs are of interest in different communities. In probability theory and combinatorics, the notion of Benjamini‐Schramm convergence, also known as left‐convergence, is used quite frequently. Statistical physicists are interested in the the existence of the thermodynamic limit of free energies, which leads naturally to the notion of right‐convergence. Combinatorial optimization problems naturally lead to so‐called partition convergence, which relates to the convergence of optimal values of a variety of constraint satisfaction problems. The relationship between these different notions of similarity and convergence is, however, poorly understood. In this paper we introduce a new notion of convergence of sparse graphs, which we call Large Deviations or LD‐convergence, and which is based on the theory of large deviations. The notion is introduced by “decorating” the nodes of the graph with random uniform i.i.d. weights and constructing corresponding random measures on and . A graph sequence is defined to be converging if the corresponding sequence of random measures satisfies the Large Deviations Principle with respect to the topology of weak convergence on bounded measures on . The corresponding large deviations rate function can be interpreted as the limit object of the sparse graph sequence. In particular, we can express the limiting free energies in terms of this limit object. We then establish that LD‐convergence implies the other three notions of convergence discussed above, and at the same time establish several previously unknown relationships between the other notions of convergence. In particular, we show that partition‐convergence does not imply left‐ or right‐convergence, and that right‐convergence does not imply partition‐convergence. © 2016 Wiley Periodicals, Inc. Random Struct. Alg., 51, 52–89, 2017     

Constructing near spanning trees with few local inspections

Constructing a spanning tree of a graph is one of the most basic tasks in graph theory. Motivated by several recent studies of local graph algorithms, we consider the following variant of this problem. Let G be a connected bounded‐degree graph. Given an edge e in G we would like to decide whether e belongs to a connected subgraph consisting of edges (for a prespecified constant ), where the decision for different edges should be consistent with the same subgraph . Can this task be performed by inspecting only a constant number of edges in G ? Our main results are:

• We show that if every t‐vertex subgraph of G has expansion then one can (deterministically) construct a sparse spanning subgraph of G using few inspections. To this end we analyze a “local” version of a famous minimum‐weight spanning tree algorithm.
• We show that the above expansion requirement is sharp even when allowing randomization. To this end we construct a family of 3‐regular graphs of high girth, in which every t‐vertex subgraph has expansion . We prove that for this family of graphs, any local algorithm for the sparse spanning graph problem requires inspecting a number of edges which is proportional to the girth.

© 2016 Wiley Periodicals, Inc. Random Struct. Alg., 50, 183–200, 2017     

An Electrocardiogram Signal Classification Algorithm Based on Improved Deep Residual Shrinkage Networks北大核心CSCD

心电信号分类是医疗保健领域的重要研究内容.针对大多数方法不能很好地降低样本数量少的类别漏诊率,以及降低预处理操作的复杂性问题,提出了一种基于改进深度残差收缩网络(IDRSN)的心电信号分类算法(即DRSL算法).首先,使用合成少数类过采样技术(SMOTE)扩充数量少的类别样本,从而解决了类不平衡问题;其次,利用改进深度残差收缩网络提取空间特征,其残差模块可以避免网络层加深造成的过拟合,压缩激励和软阈值化子网络可以提取重要局部特征并自动去除噪声;然后,通过长短期记忆网络(LSTM)提取时间特征;最后,利用全连接网络输出分类结果.在MIT-BIH心律失常数据集上的实验结果表明,该算法的分类性能优于IDRSN、DRSN、GAN+2DCNN、CNN+LSTM_ATTENTION、SE-CNN-LSTM分类算法.     

Reconstruction of Sparse Polynomials via Quasi-Orthogonal Matching Pursuit Method

In this paper, we propose a Quasi-Orthogonal Matching Pursuit (QOMP) algorithm for constructing a sparse approximation of functions in terms of expansion by orthonormal polynomials. For the two kinds of sampled data, data with noises and without noises, we apply the mutual coherence of measurement matrix to establish the convergence of the QOMP algorithm which can reconstruct $s$-sparse Legendre polynomials, Chebyshev polynomials and trigonometric polynomials in $s$ step iterations. The results are also extended to general bounded orthogonal system including tensor product of these three univariate orthogonal polynomials. Finally, numerical experiments will be presented to verify the effectiveness of the QOMP method.     

Synthesis,Aromaticity, and Application of peri-Pentacenopentacene: Localized Representation of Benzenoid Aromatic Compounds

We report the synthesis and optoelectronic properties of TIPS-peri-pentacenopentacene ( TIPS-PPP ), a vertical extension of TIPS-pentacene ( TIPS-PEN ) and a low-band-gap material with remarkable stability. We found the synthetic conditions to avoid the competition between 1,2- and 1,4-addition of lithium acetylide on the large aromatic dione. The high stability of TIPS-PPP is due to the peri-fusion which increases the aromaticity by generating two localized aromatic sextets that are flanked with 2 diene fragments, similar to two fused-anthracenes. Like TIPS-PEN , TIPS-PPP shows the archetypal 2D brickwall motif in crystals with a larger transfer integral and smaller reorganization energy. The high mobility of up to 1 cm² V^?1 s^?1 was obtained in an organic field-effect transistor fabricated by a wet process. Also, TIPS-PPP was used as a near-infrared (NIR) emitter for NIR organic-light-emitting-diode devices resulting in a high external quantum efficiency at 800 nm.     

The Mechanism of Biochemical NO-Sensing: Insights from Computational Chemistry

The binding of small gas molecules such as NO and CO plays a major role in the signaling routes of the human body. The sole NO-receptor in humans is soluble guanylyl cyclase (sGC) – a histidine-ligated heme protein, which, upon NO binding, activates a downstream signaling cascade. Impairment of NO-signaling is linked, among others, to cardiovascular and inflammatory diseases. In the present work, we use a combination of theoretical tools such as MD simulations, high-level quantum chemical calculations and hybrid QM/MM methods to address various aspects of NO binding and to elucidate the most likely reaction paths and the potential intermediates of the reaction. As a model system, the H-NOX protein from Shewanella oneidensis (So H-NOX) homologous to the NO-binding domain of sGC is used. The signaling route is predicted to involve NO binding to form a six-coordinate intermediate heme-NO complex, followed by relatively facile His decoordination yielding a five-coordinate adduct with NO on the distal side with possible isomerization to the proximal side through binding of a second NO and release of the first one. MD simulations show that the His sidechain can quite easily rotate outward into solvent, with this motion being accompanied in our simulations by shifts in helix positions that are consistent with this decoordination leading to significant conformational change in the protein.     

基于虚拟响应信号的结构参数时域辨识研究

在充分考虑线性动力系统的时域响应特性以及小波包分析的频率空间剖分特性的基础上,提出了一种基于虚拟响应信息提取的信号去噪新方法.虚拟响应虽然没有在结构动力检测过程中真实发生,但却是在某种激励下可以实现的一个响应,因此,根据虚拟响应信息同样可以进行结构系统的动力识别.数值研究表明,对于地脉动响应这种有效信号频带与噪声频带相互覆盖的低信噪比信号而言,小波阈值去噪法已无能为力,而基于虚拟响应信息提取的信号去噪方法则有较好的去噪效果.     

PRINCIPAL AXIS INTRINSIC METHOD AND THE HIGH DIMENSIONAL TENSOR EQUATION AX－XA＝C

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