We introduce a new construction algorithm for digital nets for integration in certain weighted tensor product Hilbert spaces. The first weighted Hilbert space we consider is based on Walsh functions. Dick and Pillichshammer calculated the worst-case error for integration using digital nets for this space. Here we extend this result to a special construction method for digital nets based on polynomials over finite fields. This result allows us to find polynomials which yield a small worst-case error by computer search. We prove an upper bound on the worst-case error for digital nets obtained by such a search algorithm which shows that the convergence rate is best possible and that strong tractability holds under some condition on the weights.
We extend the results for the weighted Hilbert space based on Walsh functions to weighted Sobolev spaces. In this case we use randomly digitally shifted digital nets. The construction principle is the same as before, only the worst-case error is slightly different. Again digital nets obtained from our search algorithm yield a worst-case error achieving the optimal rate of convergence and as before strong tractability holds under some condition on the weights. These results show that such a construction of digital nets yields the until now best known results of this kind and that our construction methods are comparable to the construction methods known for lattice rules.
We conclude the article with numerical results comparing the expected worst-case error for randomly digitally shifted digital nets with those for randomly shifted lattice rules.
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 相似文献
This paper is devoted to the analysis of function spaces modeled on Besov spaces and their applications to non-linear partial differential equations, with emphasis on the incompressible, isotropic Navier-Stokes system and semi-linear heat equations. Specifically, we consider the class, introduced by Hideo Kozono and Masao Yamazaki, of Besov spaces based on Morrey spaces, which we call Besov-Morrey or BM spaces. We obtain equivalent representations in terms of the Weierstrass semigroup and wavelets, and various embeddings in classical spaces. We then establish pseudo-differential and para-differential estimates. Our results cover non-regular and exotic symbols. Although the heat semigroup is not strongly continuous on Morrey spaces, we show that its action defines an equivalent norm. In particular, homogeneous BM spaces belong to a larger class constructed by Grzegorz Karch to analyze scaling in parabolic equations. We compare Karch's results with those of Kozono and Yamazaki and generalize them by obtaining short-time existence and uniqueness of solutions for arbitrary data with subcritical regularity. We exploit pseudo-differential calculus to extend the analysis to compact, smooth, boundaryless, Riemannian manifolds. BM spaces are defined by means of partitions of unity and coordinate patches, and intrinsically in terms of functions of the Laplace operator.
Summary Characteristics of optimal solutions under nonlinear buckling constraints are investigated by using a bar-spring model. It is demonstrated that optimization under buckling constraints of a symmetric system often leads to a structure with hill-top branching, where a limit point and bifurcation points coincide. A general formulation is derived for imperfection sensitivity of the critical load factor corresponding to a hill-top branching point. It is shown that the critical load is not imperfection-sensitive even for the case where an asymmetric bifurcation point exists at the limit point. 相似文献
We use qualitative analysis and numerical simulation to study peaked traveling wave solutions of CH-γ and CH equations. General expressions of peakon and periodic cusp wave solutions are obtained. Some previous results become our special cases. 相似文献