Internal Diffusion-Limited Aggregation: Parallel Algorithms and Complexity

The computational complexity of internal diffusion-limited aggregation (DLA) is examined from both a theoretical and a practical point of view. We show that for two or more dimensions, the problem of predicting the cluster from a given set of paths is complete for the complexity class CC, the subset of P characterized by circuits composed of comparator gates. CC-completeness is believed to imply that, in the worst case, growing a cluster of size n requires polynomial time in n even on a parallel computer. A parallel relaxation algorithm is presented that uses the fact that clusters are nearly spherical to guess the cluster from a given set of paths, and then corrects defects in the guessed cluster through a non-local annihilation process. The parallel running time of the relaxation algorithm for two-dimensional internal DLA is studied by simulating it on a serial computer. The numerical results are compatible with a running time that is either polylogarithmic in n or a small power of n. Thus the computational resources needed to grow large clusters are significantly less on average than the worst-case analysis would suggest. For a parallel machine with k processors, we show that random clusters in d dimensions can be generated in O((n/k + log k) n^{2/d}) steps. This is a significant speedup over explicit sequential simulation, which takes O(n^{1+2/d}) time on average. Finally, we show that in one dimension internal DLA can be predicted in O(log n) parallel time, and so is in the complexity class NC

Rich States, Poor States: ALEC-Laffer State Economic Competitiveness Index

Ranks states' business climates based on income, population growth, and employment and outlook based on current tax policies; analyzes their fiscal conditions; reviews 2010 fiscal reform initiatives; and recommends policies to spur economic growth

Peace-Building in an Inseparable World

Our world is increasingly divided between the haves and the have nots, and the gap between these two is growing. Despite this, with all of its riches, the United States remains disconnected. A poor country in the aftermath of war is a microcosm of the world at large. Given the prodigious problems of the failed and failing nations discussed here -- Afghanistan, Cambodia, East Timor, Haiti, Iraq, Kosovo, Mozambique, Rwanda, Sri Lanka, Somalia -- the tendency is to deny the enormity of the task and to treat the problem superficially and peremptorily rather than to attack its root causes. The United Nations, flawed institution that it is, is at the core of peace-building. It has the experience, the expertise, and the mandate to help countries move from war to peace, but it must be strengthened. There are no certain prescriptions here, there are many sorrowful tales, some noble efforts, there are some elemental principles to guide us, and, finally, there is the necessity to keep trying, and to try harder

Plasma Impedance: "The end of the line?"

This report accompanies the research performed during the first three terms of a one-year MPhil program into RP-generated, capacitively-coupled gas discharge plasmas and methods of electrical diagnostics. Gas discharge plasmas are often used for surface processing in the semiconductor fabrication industry and a discharge’s electrical properties (power and impedance) are often required to be related to its physical and chemical mechanisms. Typical R.F supplies do not incorporate accurate enough power monitors with even fewer indicating impedance. Even so, it is required to measure power and impedance actually at the driven electrode and not prior to a lossy matching network and chamber feed. The design and calibration of an accurate voltage and current probe are proposed (to be placed at a point between the matching network and the discharge chamber) together with a procedure to fully characterise the transmission line that remains between the probe and electrode. Finally, a software routine is presented to indicate power and impedance together with distortion of the 2nd and 3rd harmonic, feed efficiency and various equivalent circuits. Results show that the proposed probe is of reasonably high accuracy and that measurements taken of typical plasma discharges relate to theory in the main

A rank based social norms model of how people judge their levels of drunkenness whilst intoxicated

Background: A rank based social norms model predicts that drinkers’ judgements about their drinking will be based on the rank of their breath alcohol level amongst that of others in the immediate environment, rather than their actual breath alcohol level, with lower relative rank associated with greater feelings of safety. This study tested this hypothesis and examined how people judge their levels of drunkenness and the health consequences of their drinking whilst they are intoxicated in social drinking environments. Methods: Breath alcohol testing of 1,862 people (mean age = 26.96 years; 61.86 % male) in drinking environments. A subset (N = 400) also answered four questions asking about their perceptions of their drunkenness and the health consequences of their drinking (plus background measures). Results: Perceptions of drunkenness and the health consequences of drinking were regressed on: (a) breath alcohol level, (b) the rank of the breath alcohol level amongst that of others in the same environment, and (c) covariates. Only rank of breath alcohol level predicted perceptions: How drunk they felt (b 3.78, 95 % CI 1.69 5.87), how extreme they regarded their drinking that night (b 3.7, 95 % CI 1.3 6.20), how at risk their long-term health was due to their current level of drinking (b 4.1, 95 % CI 0.2 8.0) and how likely they felt they would experience liver cirrhosis (b 4.8. 95 % CI 0.7 8.8). People were more influenced by more sober others than by more drunk others. Conclusion: Whilst intoxicated and in drinking environments, people base judgements regarding their drinking on how their level of intoxication ranks relative to that of others of the same gender around them, not on their actual levels of intoxication. Thus, when in the company of others who are intoxicated, drinkers were found to be more likely to underestimate their own level of drinking, drunkenness and associated risks. The implications of these results, for example that increasing the numbers of sober people in night time environments could improve subjective assessments of drunkenness, are discussed