Chip-Firing Games on Directed Graphs

We consider the following (solitary) game: each node of a directed graph contains a pile of chips. A move consists of selecting a node with at least as many chips as its outdegree, and sending one chip along each outgoing edge to its neighbors. We extend to directed graphs several results on the undirected version obtained earlier by the authors, P. Shor, and G. Tardos, and we discuss some new topics such as periodicity, reachability, and probabilistic aspects.Among the new results specifically concerning digraphs, we relate the length of the shortest period of an infinite game to the length of the longest terminating game, and also to the access time of random walks on the same graph. These questions involve a study of the Laplace operator for directed graphs. We show that for many graphs, in particular for undirected graphs, the problem whether a given position of the chips can be reached from the initial position is polynomial time solvable.Finally, we show how the basic properties of the probabilistic abacus can be derived from our results.     

A Sharp Condition for the Ground State of Difference Equation

This note is concerned with a novel inequality condition for the existence of ground states of partial difference systems. Our result is potentially applicable to the estimation of eigenvalues of the loaded strings and nets.     

Two coordination polymers based on 2,2′-biimidazoles and d10 metal ions: syntheses,structures, and luminescence

Two d¹⁰ metal coordination polymers, [Zn(µ-Me₂biim)Cl₂] _n (1) and [Cd₃(MeHbiim)₂(1,4-BDC)₃] _n (2) (Me₂biim?=?N,N′-dimethyl-2,2′-biimidazole, MeHbiim?=?N-methyl-2,2′-biimidazole, 1,4-BDC?=?1,4-benzenedicarboxylate), were synthesized under hydrothermal conditions and characterized by elemental analysis, infrared spectroscopy, thermogravimetric analysis, and single-crystal X-ray crystallography. Complex 1 features an infinite neutral zigzag 1-D chain. Interchain hydrogen-bonding interactions further extend the 1-D arrangement to generate a 2-D supramolecular architecture. Complex 2 features a 3-D coordination polymer with α-Po net topology, based on linear trinuclear {Cd₃O₁₄N₄} clusters. Both complexes have high thermal stability and exhibit strong luminescence at room temperature.     

Analytical modeling of Transmission Control Protocol NewReno using Generalized Stochastic Petri Nets

This paper presents a novel analytical model of Transmission Control Protocol (TCP) using a generalized stochastic Petri net (GSPN). Extensive simulation work has been done for the performance evaluation of TCP NewReno protocol. In view of the limitations of the simulation technique, we present an analytical approach using GSPN. A GSPN is a useful mathematical tool that solves continuous time Markov chains for complex systems and evaluates the stationary behavior. In this paper, we analyze the slow‐but‐steady variant of TCP NewReno. The model captures the behavioral aspects of the slow start and the congestion avoidance phase together with the fast retransmit and recovery capabilities of TCP NewReno. Performance metrics such as throughput, goodput, and task completion time of the system are obtained. The effect of variation in the model parameters on the performance is studied. The results are validated using the network simulator, and their accuracy is verified by evaluating the confidence interval. The performance of the proposed model is compared with that of TCP Reno. The performance of the proposed model is also compared with one of the previous models. The numerical illustrations and comparison of the proposed technique with simulation validates the accuracy, efficiency, and competence of the GSPN technique. While GSPN modeling for TCP is investigated in depth for the TCP NewReno and TCP Reno variant in this paper, other protocols could be also analyzed similarly. Copyright © 2013 John Wiley & Sons, Ltd.     

Comment on “Extending Hirshfeld‐I to bulk and periodic materials”

In recent years, several methods have been developed that partition the electron density among atoms using spherically symmetric atomic weights. D. E. P. Vanpoucke, P. Bultinck, and I. Van Driessche (J. Comput. Chem. 2012, doi: 10.1002/jcc.23088) recently reported a periodic implementation of the Hirshfeld‐I method that uses a combination of Becke‐style and uniform integration grids and modified atomic reference densities to compute net atomic charges in periodic materials. Herein, this method is discussed in the context of earlier periodic implementations of the Hirshfeld‐I method, the Iterated Stockholder Atoms method, and the density derived electrostatic and chemical method.     

Metal ions Directed Self-assembly based on Mixed Ligands: From 2D hcb Net to 3D cds Framework

Two coordination polymers (CPs), namely, [Zn(BPDC)(3-bpdb)_0.5(H₂O)₂]_n ( 1 ), and [Ni(BPDC)(3-bpdb)(H₂O)₂]_n ( 2 ) (where H₂BPDC = 4,4'-biphenyldicarboxylic acid, 3-bpdb = 1,4-bis(3-pyridyl)-2,3-diaza-1,3-butadiene) have been solvothermally synthesized and characterized by single-crystal X-ray diffraction, IR, elemental analyses, PXRD, and SEM. CP 1 possesses a 2D 3-connected hcb net, and weak hydrogen bonding and π ··· π stacking contacts further link the 2D networks to form 3D supramolecular structure. The structure of 2 presents a 4-connected threefold interpenetrated cds framework. Through structural analysis, it is found that the coordination geometry of metal ions significantly affects the binding behaviors of the ligands and the resultant extended networks of the CPs. Besides, the Hirshfeld surface analyses detailed the surface characteristics of the two CPs. In addition, the thermal stabilities and photoluminescent properties were also investigated.     

基于条件生成式对抗网络的油藏单井产量预测模型

为克服机器学习方法在油藏单井产量预测中的过拟合问题,提高油田生产中的产量预测精度,提出一种基于条件生成式对抗网络(CGAN)的油藏单井产量预测模型。该模型使用长短期记忆、全连接等基础神经网络,构建生成和判别网络模型。生成网络模型以产量影响因素为条件输入,生成预测产量数据,利用对数损失函数评价预测数据与真实数据之间的偏差,通过条件生成式对抗网络的博弈训练,并结合贝叶斯超参数优化算法,优化模型结构,综合提高模型的泛化能力。基于Eclipse数值模拟软件建立同一井网条件下不同地质和生产条件下的油藏单井产量数据库,以地质与生产条件等产量影响因素作为模型的条件输入,进行油藏单井产量预测。结果表明：与全连接神经网络(FCNN)、随机森林(RF)以及长短期记忆神经网络(LSTM)模型的预测结果相比,CGAN模型在测试集上的平均绝对百分比误差分别提升了2.59%、 0.81%以及1.72%,并且过拟合比最小(1.027)。说明CGAN降低了机器学习产量预测模型的过拟合程度,提高了模型的泛化能力与预测精度,验证了所提算法的优越性,对指导油田高效开发和保障我国能源战略安全具有重要意义。     

一种价格时间Petri网的状态空间计算

价格时间Petri网是对web服务过程和工作流模型等进行时间和成本分析的一种新工具.而价格时间自动机则是一种相对成熟的工具.提出一种状态空间计算方法,可以将价格时间Petri网的状态空间构造为一个价格时间自动机.该方法的核心思想是在扩展状态类中增加价格参数.进一步证明了构造出的价格时间自动机和初始的价格时间Petri网是双相似的.     

光缆接入网的建设

介绍了光缆接入网建设的重要性,然后重点介绍光缆接入网的建设原则,最后提出光缆线路保护方式、资源利用方法和要求.     

电阻网络在集成电路电子音量调节中的应用

提出了一种新颖的电阻网络设计方法,该方法设计误差小、音量调节精度高、版图容易实现。该设计方法是在串联电阻网络的基础上进行了改进,提出了串并联电阻网络结构,误差降到0．6％以内。实现了串联电阻网络无法实现的大衰减,可达99dB,调节步进为1dB．