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.     

Beryllium (boron) clustering quest in relativistic multifragmentation (BECQUEREL Project)

A physical program of irradiation of emulsions in beams of relativistic nuclei named the BECQUEREL Project is reviewed. It is destined to study in detail the processes of relativistic fragmentation of light radioactive and stable nuclei. The expected results would make it possible to answer some topical questions concerning the cluster structure of light nuclei. Owing to the best spatial resolution, the nuclear emulsions would enable one to obtain unique and evident results. The most important irradiations will be performed in the secondary beams of He, Be, B, C, and N radioactive nuclei formed on the basis of JINR Nuclotron beams of stable nuclei. We present results on the charged state topology of relativistic fragmentation of the ¹⁰B nucleus at low energy-momentum transfers as the first step of the research.     

Universal Models For Real Submanifolds

In previous papers by the present author, a machinery for calculating automorphisms, constructing invariants, and classifying real submanifolds of a complex manifold was developed. The main step in this machinery is the construction of a “nice” model surface. The nice model surface can be treated as an analog of the osculating paraboloid in classical differential geometry. Model surfaces suggested earlier possess a complete list of the desired properties only if some upper estimate for the codimension of the submanifold is satisfied. If this estimate fails, then the surfaces lose the universality property (that is, the ability to touch any germ in an appropriate way), which restricts their applicability. In the present paper, we get rid of this restriction: for an arbitrary type (n,K) (where n is the dimension of the complex tangent plane, and K is the real codimension), we construct a nice model surface. In particular, we solve the problem of constructing a nondegenerate germ of a real analytic submanifold of a complex manifold of arbitrary given type (n,K) with the richest possible group of holomorphic automorphisms in the given class.     

Crystallographic report: A new polymorph for bis[bis(N,N‐dibenzyldithiocarbamato)cadmium(II)]

The title compound is a centrosymmetric dimer with each cadmium in a distorted CdS₅ square pyramidal geometry. The Cd–S bond distances range from 2.5626(11) to 2.8459(11) Å. Copyright © 2004 John Wiley & Sons, Ltd.     

On the equivalence of linear equations under nonlocal transformation

Linear nth order (n?3) ordinary differential equations have been shown to possess n+1, n+2 or n+4 Lie point symmetries. Each class contains equations which are equivalent under point transformation. By taking the example of third order equations, we show that all linear equations are equivalent if the class of transformation is broadened to include nonlocal transformations and hence the representative of this class of equations is y⁽ⁿ⁾=0.     

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     

cos πρ theorems for δ-subharmonic functions

For ϕ a δ-subharmonic function, sharp results are obtained that connectA(r, ϕ), B(r, ϕ) andT(r, ϕ), whereA(r, ϕ)=inf_|z|=r ϕ(z),B(r, ϕ)=sup_|z|=r ϕ(z), andT(r, ϕ) is the Nevanlinna characteristics.     

What Oxidation State of Iron Determines the Amethyst Colour?

A colourless quartz crystal doped with ⁵⁷Fe³⁺ was obtained by hydrothermal synthesis in an NH₄F solution. The crystal was transformed into violet amethyst by gamma-irradiation. The change in colour was accompanied by changes in the Mössbauer spectrum that can be interpreted as the conversion of trivalent iron into the tetravalent state: Fe³⁺→Fe⁴⁺.