We analyze graphs in which each vertex is assigned random coordinates in a geometric space of arbitrary dimensionality and only edges between adjacent points are present. The critical connectivity is found numerically by examining the size of the largest cluster. We derive an analytical expression for the cluster coefficient, which shows that the graphs are distinctly different from standard random graphs, even for infinite dimensionality. Insights relevant for graph bipartitioning are included.

The static cylindrically symmetric solutions of the gravitating Abelian Higgs model form a two parameter family. In this paper we give a complete classification of the string-like solutions of this system. We show that the parameter plane is composed of two different regions with the following characteristics: One region contains the standard asymptotically conic cosmic string solutions together with a second kind of solutions with Melvin-like asymptotic behavior. The other region contains two types of solutions with bounded radial extension. The border between the two regions is the curve of maximal angular deficit of 2π.

Starting from the premise that individuals within an organization are fallible, this paper advances the study of relationships between the organization's decision-making structure and its performance. We offer a general treatment that allows one to analyze the full range of organizational architectures between extreme centralized and decentralized forms (often referred to as hierarchies and polyarchies). Our approach furthermore allows designers to examine the change in the overall reliability of the organizational structure as the number of actors within the organization changes. We provide general proofs that show how decision-making structures can be constructed so they maximize reliability for a given number of agents. Our model can be used directly for a qualitative assessment of decision-making structures. It is thereby useful for assessment of the many complicated hybrid structures that we see in actual decision-making organizations, such as banks, purchasing departments, and military intelligence. An application from a bank illustrates how our framework can be used in practice.organizational architecture, organizational design, decision making, evaluation

We discuss the generalized Plateau problem in the ͑3ϩ1͒-dimensional Schwarzschild background. This represents the physical situation, which could for instance have appeared in the early universe, where a cosmic membrane ͑thin domain wall͒ is located near a black hole. Considering stationary axially symmetric membranes, three different membrane topologies are possible depending on the boundary conditions at infinity: 2ϩ1 Minkowski topology, 2ϩ1 wormhole topology, and 2ϩ1 black hole topology. Interestingly, we find that the different membrane topologies are connected via phase transitions of the form first discussed by Choptuik in investigations of scalar field collapse. More precisely, we find a first order phase transition ͑finite mass gap͒ between wormhole topology and black hole topology, the intermediate membrane being an unstable wormhole collapsing to a black hole. Moreover, we find a second order phase transition ͑no mass gap͒ between Minkowski topology and black hole topology, the intermediate membrane being a naked singularity. For the membranes of black hole topology, we find a mass scaling relation analogous to that originally found by Choptuik. However, in our case the parameter p is replaced by a 2-vector p ជ parametrizing the solutions. We find that massϰ͉p ជ Ϫp ជ * ͉ ␥ where ␥Ϸ0.66. We also find a periodic wiggle in the scaling relation. Our results show that black hole formation as a critical phenomenon is far more general than expected. ͓S0556-2821͑98͒07518-3͔PACS number͑s͒: 11.27.ϩd, 04.70.Bw, 97.60.Lf Cosmic strings and domain walls have played an important role in theoretical cosmology and astrophysics ͑for a review of topological defects, see for instance ͓1͔͒. Most of the work has been devoted to cosmic strings, while domain walls have not attracted as much attention. In fact, it has been argued that stable domain walls are cosmologically disastrous. This was already pointed out by Zeldovich, Kobzarev, and Okun ͓2͔, who considered domain wall structures in models with spontaneous breaking of CP symmetry. They argued that the energy density of the domain walls is so large that they would dominate the universe completely, violating the observed approximate isotropy and homogeneity. So if domain walls were ever formed in the early universe, they were assumed to have somehow disappeared again, for instance by collapse, evaporation, or simply by inflating away from our visible universe.Much later however, Hill, Schramm, and Fry ͓3͔ introduced the so-called ''light'' domain walls. They considered a late-time ͑post-decoupling͒ phase transition and found that light domain walls could be produced that were not necessarily in contradiction with the observed large-scale structure of the universe.Domain walls are formed in phase transitions where a discrete symmetry is broken. Already from this, one can argue that it is difficult to believe that domain walls should not have been formed sometime during the early evolution of the universe, where a number of phase transitions certainly took place. It is als...

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