The complexity of cutting complexes

This paper investigates the combinatorial and computational aspects of certain extremal geometric problems in two and three dimensions. Specifically, we examine the problem of intersecting a convex subdivision with a line in order to maximize the number of intersections. A similar problem is to maximize the number of intersected facets in a cross-section of a three-dimensional convex polytope. Related problems concern maximum chains in certain families of posets defined over the regions of a convex subdivision. In most cases we are able to prove sharp bounds on the asymptotic behavior of the corresponding extremal functions. We also describe polynomial algorithms for all the problems discussed.Bernard Chazelle wishes to acknowledge the National Science Foundation for supporting this research in part under Grant No. MCS83-03925. Herbert Edelsbrunner is pleased to acknowledge the support of Amoco Fnd. Fac. Dev. Comput. Sci. 1-6-44862.     

Reply to Nathan: How to reconstruct the causal argument

Nicholas Nathan tries to resist the current version of the causal argument for sense-data in two ways. First he suggests that, on what he considers to be the correct re-construction of the argument, it equivocates on the sense of proximate cause. Second he defends a form of disjunctivism, by claiming that there might be an extra mechanism involved in producing veridical hallucination, that is not present in perception. I argue that Nathan’s reconstruction of the argument is not the appropriate one, and that, properly interpreted, the argument does not equivocate on proximate cause. Furthermore, I claim that his postulation of a modified mechanism for hallucinations is implausibly ad hoc.     

Collaborative distributed decision making for large scale disaster relief operations: Drawing analogies from robust natural systems

One of the most ignored, but urgent and vital challenges confronting society today is the vulnerability of urban areas to extreme events. Current organization of response systems, predominantly based on a command and control model, limits their effectiveness and efficiency. Particularly, in decision‐making processes where a large number of actors may be involved. In this article, a new distributed collaborative decision‐making model is proposed to overcome command and control limitations encountered in stressful, hostile, chaotic, and large‐scale settings. This model was derived by borrowing concepts from the collective decision making of honeybees foraging, a successful process in solving complex tasks within complex settings. The model introduced in this article was evaluated through differential equations, i.e., continuous analysis, and difference equations, i.e., discrete analysis. The most important result found is that the best available option in any large‐scale decision‐making problem can be configured as an attractor, in a distributed and timely manner. We suggest that the proposed model has the potential to facilitate decision‐making processes in large‐scale settings. © 2005 Wiley Periodicals, Inc. Complexity 11:28–38, 2005     

Rotating Charge Coupled to the Maxwell Field: Scattering Theory and Adiabatic Limit

We consider a spinning charge coupled to the Maxwell field. Through the appropriate symmetry in the initial conditions the charge remains at rest. We establish that any time-dependent finite energy solution converges to a sum of a soliton wave and an outgoing free wave. The convergence holds in global energy norm. Under a small constant external magnetic field the soliton manifold is stable in local energy seminorms and the evolution of the angular velocity is guided by an effective finite-dimensional dynamics. The proof uses a non-autonomous integral inequality method.     

Variational conditions with smooth constraints: structure and analysis

 This is an expository paper about the analysis of variational conditions over sets defined in finite-dimensional spaces by fairly smooth functions satisfying a constraint qualification. The primary focus is on results that can provide quantitative and computable sensitivity information for particular instances of the problems under study, and our objective is to give a personal view of the state of current knowledge in this area and of gaps in that knowledge that require future work. The writing style is informal, in keeping with the objective of focusing the reader's attention on the basic concepts and the relationships between them, rather than on details of the particular results themselves. Received: December 1, 2002 / Accepted: April 25, 2003 Published online: May 28, 2003 Key words. variational condition – variational inequality – complementarity – sensitivity – stability – nondegeneracy Mathematics Subject Classification (2000): Primary: 90C31. Secondary: 47J20, 49J40, 49J53, 90C33     

Local adsorption sites and bondlength changes in Ni(1 0 0)/H/CO and Ni(1 0 0)/CO

The local adsorption geometry of CO adsorbed in different states on Ni(1 0 0) and on Ni(1 0 0) precovered with atomic hydrogen has been determined by C 1s (and O 1s) scanned-energy mode photoelectron diffraction, using the photoelectron binding energy changes to characterise the different states. The results confirm previous spectroscopic assignments of local atop and bridge sites both with and without coadsorbed hydrogen. The measured Ni–C bondlengths for the Ni(1 0 0)/CO states show an increase of 0.16 ± 0.04 Å in going from atop to bridge sites, while comparison with similar results for Ni(1 1 1)/CO for threefold coordinated adsorption sites show a further lengthening of the bond by 0.05 ± 0.04 Å. These changes in the Ni–CO chemisorption bondlength with bond order (for approximately constant adsorption energy) are consistent with the standard Pauling rules. However, comparison of CO adsorbed in the atop geometry with and without coadsorbed hydrogen shows that the coadsorption increases the Ni–C bondlength by only 0.06 ± 0.04 Å, despite the decrease in adsorption energy of a factor of 2 or more. This result is also reproduced by density functional theory slab calculations. The results of both the experiments and the density functional theory calculations show that CO adsorption onto the Ni(1 0 0)/H surface is accompanied by significant structural modification; the low desorption energy may then be attributed to the energy cost of this restructuring rather than weak local bonding.