基于BDF的无约束优化方法的收敛性分析

1.介 绍 在上个世纪的七十年代末、八十年代初,基于常微分方程的优化方法或者说同伦方法是一类与拟牛顿法和共轭梯度法等我们所熟知的优化方法相竞争的重要方法[1-6,8,13,14,16].由于这类方法只是简单地利用现成的数值求解常微分方程的软件包,如CVODE[7]、LSODE[12],对同伦方程(一般是一个常微分方程的初值问题)进行计算,除了一些特殊的病态问题     

When should you sack a football manager? Results from a simple model applied to the English Premiership

What strategy should a football (soccer, in American parlance) club adopt when deciding whether to sack its manager? This paper introduces a simple model assuming that a club's objective is to maximize the number of league points that it scores per season. The club's strategy consists of three choices: the length of the honeymoon period during which it will not consider sacking a new manager, the level of the performance trapdoor below which the manager get the sack, and the weight that it will give to more recent games compared to earlier ones. Some data from the last six seasons of the English Premiership are used to calibrate the model. At this early stage of the research, the best strategy appears to have only a short honeymoon period of eight games (much less than the actual shortest period of 12 games), to set the trapdoor at 0.74 points per game, and to put 47% of the weight on the last five games. A club adopting this strategy would obtain on average 56.8 points per season, compared to a Premiership average of 51.8 points.     

On Bayes and unbiased estimators of loss

We consider estimation of loss for generalized Bayes or pseudo-Bayes estimators of a multivariate normal mean vector, θ. In 3 and higher dimensions, the MLEX is UMVUE and minimax but is inadmissible. It is dominated by the James-Stein estimator and by many others. Johnstone (1988, On inadmissibility of some unbiased estimates of loss,Statistical Decision Theory and Related Topics, IV (eds. S. S. Gupta and J. O. Berger), Vol. 1, 361–379, Springer, New York) considered the estimation of loss for the usual estimatorX and the James-Stein estimator. He found improvements over the Stein unbiased estimator of risk. In this paper, for a generalized Bayes point estimator of θ, we compare generalized Bayes estimators to unbiased estimators of loss. We find, somewhat surprisingly, that the unbiased estimator often dominates the corresponding generalized Bayes estimator of loss for priors which give minimax estimators in the original point estimation problem. In particular, we give a class of priors for which the generalized Bayes estimator of θ is admissible and minimax but for which the unbiased estimator of loss dominates the generalized Bayes estimator of loss. We also give a general inadmissibility result for a generalized Bayes estimator of loss. Research supported by NSF Grant DMS-97-04524.     

3,7-二硝基亚氨基-2,4-二氮杂双环[3,3,0]辛烷的放热分解反应动力学

在程序升温条件下 ,用DSC研究了标题化合物的放热分解反应动力学 .用线性最小二乘法、迭代法以及二分法与最小二乘法相结合的方法 ,以积分方程、微分方程和放热速率方程拟合DSC数据 .在逻辑选择建立了微分和积分机理函数的最可几一般表达式后 ,用放热速率方程得到相应的表观活化能 (Ea)、指前因子 (A)和反应级数 (n)的值 .结果表明 :该反应的微分形式的经验动力学模式函数、Ea 和A值分别为 (1-α) 0 .44、2 30 .4kJ/mol和 10 18.16s-1.借助加热速率和所得动力学参数值 ,提出了标题化合物放热分解反应的动力学方程 .该化合物的热爆炸临界温度为 30 2 .6℃ .上述动力学参数对分析、评价标题化合物的稳定性和热变化规律十分有用 .     

On effectiveness of wiretap programs in mapping social networks

Snowball sampling methods are known to be a biased toward highly connected actors and consequently produce core-periphery networks when these may not necessarily be present. This leads to a biased perception of the underlying network which can have negative policy consequences, as in the identification of terrorist networks. When snowball sampling is used, the potential overload of the information collection system is a distinct problem due to the exponential growth of the number of suspects to be monitored. In this paper, we focus on evaluating the effectiveness of a wiretapping program in terms of its ability to map the rapidly evolving networks within a covert organization. By running a series of simulation-based experiments, we are able to evaluate a broad spectrum of information gathering regimes based on a consistent set of criteria. We conclude by proposing a set of information gathering programs that achieve higher effectiveness then snowball sampling, and at a lower cost. Maksim Tsvetovat is an Assistant Professor at the Center for Social Complexity and department of Public and International Affairs at George Mason University, Fairfax, VA. He received his Ph.D. from the Computation, Organizations and Society program in the School of Computer Science, Carnegie Mellon University. His dissertation was centered on use of artificial intelligence techniques such as planning and semantic reasoning as a means of studying behavior and evolution of complex social networks, such as these of terrorist organizations. He received a Master of Science degree from University of Minnesota with a specialization in Artificial Intelligence and design of Multi-Agent Systems, and has also extensively studied organization theory and social science research methods. His research is centered on building high-fidelity simulations of social and organizational systems using concepts from distributed artificial intelligence and multi-agent systems. Other projects focus on social network analysis for mapping of internal corporate networks or study of covert and terrorist orgnaizations. Maksim’s vita and publications can be found on Kathleen M. Carley is a professor in the School of Computer Science at Carnegie Mellon University and the director of the center for Compuational Analysis of Social and Organizational Systems (CASOS) which has over 25 members, both students and research staff. Her research combines cognitive science, social networks and computer science to address complex social and organizational problems. Her specific research areas are dynamic network analysis, computational social and organization theory, adaptation and evolution, text mining, and the impact of telecommunication technologies and policy on communication, information diffusion, disease contagion and response within and among groups particularly in disaster or crisis situations. She and her lab have developed infrastructure tools for analyzing large scale dynamic networks and various multi-agent simulation systems. The infrastructure tools include ORA, a statistical toolkit for analyzing and visualizing multi-dimensional networks. ORA results are organized into reports that meet various needs such as the management report, the mental model report, and the intelligence report. Another tool is AutoMap, a text-mining systems for extracting semantic networks from texts and then cross-classifying them using an organizational ontology into the underlying social, knowledge, resource and task networks. Her simulation models meld multi-agent technology with network dynamics and empirical data. Three of the large-scale multi-agent network models she and the CASOS group have developed in the counter-terrorism area are: BioWar a city-scale dynamic-network agent-based model for understanding the spread of disease and illness due to natural epidemics, chemical spills, and weaponized biological attacks; DyNet a model of the change in covert networks, naturally and in response to attacks, under varying levels of information uncertainty; and RTE a model for examining state failure and the escalation of conflict at the city, state, nation, and international as changes occur within and among red, blue, and green forces. She is the founding co-editor with Al. Wallace of the journal Computational Organization Theory and has co-edited several books and written over 100 articles in the computational organizations and dynamic network area. Her publications can be found at: http://www.casos.cs.cmu.edu/bios/carley/publications.php     

A new stochastic method of reconstructing porous media

We present a new stochastic method of reconstructing porous medium from limited morphological information obtained from two-dimensional micro- images of real porous medium. The method is similar to simulated annealing method in the capability of reconstructing both isotropic and anisotropic structures of multi-phase but differs from the latter in that voxels for exchange are not selected completely randomly as their neighborhood will also be checked and this new method is much simpler to implement and program. We applied it to reconstruct real sandstone utilizing morphological information contained in porosity, two-point probability function and linear-path function. Good agreement of those references verifies our developed method’s powerful capability. The existing isolated regions of both pore phase and matrix phase do quite minor harm to their good connectivity. The lattice Boltzmann method (LBM) is used to compute the permeability of the reconstructed system and the results show its good isotropy and conductivity. However, due to the disadvantage of this method that the connectivity of the reconstructed system’s pore space will decrease when porosity becomes small, we suggest the porosity of the system to be reconstructed be no less than 0.2 to ensure its connectivity and conductivity.     

Existence of Pulsating Roll-Waves for the Saint Venant System

The phenomenon of roll-waves occurs when shallow water flows down open inclined channels. This flow is described by the Saint Venant’s equations with a friction term due to Chezy. In the case of a flat bottom, their existence (as entropic and periodic travelling waves) follows from a classical work due to DRESSLER [6]. The aim of this paper is to prove the existence of roll-waves when the bottom is modulated by a small periodic perturbation. Following JIN and KATSOULAKIS [15], we first compute a Burgers-type equation which possesses “pulsating” roll-waves (the wave speed oscillates around an average velocity). We prove, in a mathematically rigorous fashion, the existence of these solutions.     

Radially symmetric wave maps from (1 + 2)-dimensional Minkowski space to general targets

Extending our previous work [5] on this subject we show global existence of smooth solutions to the Cauchy problem for wave maps from the (1 + 2)-dimensional Minkowski space to an arbitrary smooth, compact Riemannian manifold without boundary, for arbitrary smooth, radially symmetric data. Received: 14 December 2001 / Accepted: 1 March 2002 / Published online: 6 August 2002