Picture Fuzzy Threshold Graphs with Application in Medicine Replenishment

In this study, a novel concept of picture fuzzy threshold graph (PFTG) is introduced. It has been shown that PFTGs are free from alternating 4-cycle and it can be constructed by repeatedly adding a dominating or an isolated node. Several properties about PFTGs are discussed and obtained the results that every picture fuzzy graph (PFG) is equivalent to a PFTG under certain conditions. Also, the underlying crisp graph (UCG) of PFTG is a split graph (SG), and conversely, a given SG can be applied to constitute a PFTG. A PFTG can be decomposed in a unique way and it generates three distinct fuzzy threshold graphs (FTGs). Furthermore, two important parameters i.e., picture fuzzy (PF) threshold dimension (TD) and PF partition number (PN) of PFGs are defined. Several properties on TD and PN have also been discussed. Lastly, an application of these developed results are presented in controlling medicine resources.     

Space-Air-Ground Integrated Mobile Crowdsensing for Partially Observable Data Collection by Multi-Scale Convolutional Graph Reinforcement Learning

Mobile crowdsensing (MCS) is attracting considerable attention in the past few years as a new paradigm for large-scale information sensing. Unmanned aerial vehicles (UAVs) have played a significant role in MCS tasks and served as crucial nodes in the newly-proposed space-air-ground integrated network (SAGIN). In this paper, we incorporate SAGIN into MCS task and present a Space-Air-Ground integrated Mobile CrowdSensing (SAG-MCS) problem. Based on multi-source observations from embedded sensors and satellites, an aerial UAV swarm is required to carry out energy-efficient data collection and recharging tasks. Up to date, few studies have explored such multi-task MCS problem with the cooperation of UAV swarm and satellites. To address this multi-agent problem, we propose a novel deep reinforcement learning (DRL) based method called Multi-Scale Soft Deep Recurrent Graph Network (ms-SDRGN). Our ms-SDRGN approach incorporates a multi-scale convolutional encoder to process multi-source raw observations for better feature exploitation. We also use a graph attention mechanism to model inter-UAV communications and aggregate extra neighboring information, and utilize a gated recurrent unit for long-term performance. In addition, a stochastic policy can be learned through a maximum-entropy method with an adjustable temperature parameter. Specifically, we design a heuristic reward function to encourage the agents to achieve global cooperation under partial observability. We train the model to convergence and conduct a series of case studies. Evaluation results show statistical significance and that ms-SDRGN outperforms three state-of-the-art DRL baselines in SAG-MCS. Compared with the best-performing baseline, ms-SDRGN improves 29.0% reward and 3.8% CFE score. We also investigate the scalability and robustness of ms-SDRGN towards DRL environments with diverse observation scales or demanding communication conditions.     

Neural Networks for Financial Time Series Forecasting

Financial and economic time series forecasting has never been an easy task due to its sensibility to political, economic and social factors. For this reason, people who invest in financial markets and currency exchange are usually looking for robust models that can ensure them to maximize their profile and minimize their losses as much as possible. Fortunately, recently, various studies have speculated that a special type of Artificial Neural Networks (ANNs) called Recurrent Neural Networks (RNNs) could improve the predictive accuracy of the behavior of the financial data over time. This paper aims to forecast: (i) the closing price of eight stock market indexes; and (ii) the closing price of six currency exchange rates related to the USD, using the RNNs model and its variants: the Long Short-Term Memory (LSTM) and the Gated Recurrent Unit (GRU). The results show that the GRU gives the overall best results, especially for the univariate out-of-sample forecasting for the currency exchange rates and multivariate out-of-sample forecasting for the stock market indexes.     

Weak Graph Map Homotopy and Its Applications∗

The authors introduce a notion of a weak graph map homotopy (they call it M-homotopy), discuss its properties and applications. They prove that the weak graph map homotopy equivalence between graphs coincides with the graph homotopy equivalence defined by Yau et al in 2001. The difference between them is that the weak graph map homotopy transformation is defined in terms of maps, while the graph homotopy transformation is defined by means of combinatorial operations. They discuss its advantages over the graph homotopy transformation. As its applications, they investigate the mapping class group of a graph and the 1-order MP-homotopy group of a pointed simple graph. Moreover, they show that the 1-order MP-homotopy group of a pointed simple graph is invariant up to the weak graph map homotopy equivalence.     

基于误差理论的区间主成分分析及其应用

针对区间数样本,传统的主成分分析需进行拓展。首先讨论了区间样本数据的两种主要来源,即观测误差和符号数据分析。然后将区间数看作一个由中点和半径构成的具有一定误差的数,从误差理论出发,研究基于误差传递公式的区间主成分分析方法,并获得以区间数为表达形式的主成分。最后,结合我国2005年第四季度股票市场的数据进行了实证分析。结果表明,面对海量数据,区间PCA较传统PCA更容易从总体上把握样本的属性。     

图的{P4}-分解

一个图G的路分解是指一路集合使得G的每条边恰好出现在其中一条路上.记Pl长度为l-1的路,如果G能够分解成若干个Pl,则称G存在{Pl}—分解.关于图的给定长路分解问题主要结果有:(i)连通图G存在{P3}—分解当且仅当G有偶数条边(见[1]);(ii)连通图G存在{P3,P4}—分解当且仅当G不是C3和奇树,这里C3的长度为3的圈而奇树是所有顶点皆度数为奇数的树(见[3]).本文讨论了3正则图的{P4}—分解情况,并构造证明了边数为3k(k热∈Z且k≥2)的完全图Kn和完全二部图Kr,s存在{P4}—分解.     

巴斯卡分布参数p的置信区间

讨论了巴斯卡分布与Beta分布的联系,并通过F分布的分位点给出了参数p的置信水平为1-α的置信区间.     

高维Cotes优化积分数值算法及其余项估计

利用一维Cotes公式及高维积分Cartesian积空间上的求积法则,将Cotes公式推广到了n维空间上,并给出了简单的误差估计.该公式具有比文[4],[5],[6]相关结果更小的误差和更高的收敛阶等优点.     

Panel模型中的精确检验和置信区间

利用广义p-值和广义置信区间的概念,研究了Panel模型中未知参数的检验和置信区间问题.对于回归系数,分别考虑了单个情形和多个线性无关情形下的检验和置信区间问题,得到了精确检验和置信区间.对于方差分量,研究了其任意线性组合的检验和置信区间问题,建立了精确检验和置信区间.基于广义p-值和广义置信区间,获取精确检验和置信区间的方法具有计算方便、易应用于小样本问题的特点.最后,分别从理论和数值上研究了这些精确检验和置信区间的统计性质.     

一种基于区间过程模型的时变可靠性分析方法

本文提出了一种基于区间过程模型的时变可靠性分析方法来处理涉及区间变量和区间过程的问题.首先,定义一种基于极值响应的可靠性指标来度量区间变量和区间过程不确定性下结构的可靠性.其次,建立并求解一双层优化模型以获得可靠性指标.在内层中,使用EGO方法计算功能函数关于时间的极值响应;在外层中,对极值响应关于原始区间变量和区间过...