Abundance and American democracy: a test of dire predictions

The American political system was severely tested in the 1970s and it is not yet obvious that the system's response to those tests was adequate. Some scholars have argued that the confusion we witnessed in energy, environmental and economic policies was symptomatic of even worse situations to come. Their consensus is that our style of democratic politics is incapable of dealing with the problems we increasingly face. Consequently, they predict that democracy's days are numbered. Furthermore, many Americans sense that the "joy ride" may be over, and that our economy may be hard pressed to maintain standards, much less continue its historic growth. One poll showed a 34 percent increase, since 1977, in respondents who believe, "The United States is in deep and serious trouble," and a well known economist, employing the terminology of game theory, has suggested that ours has become a "Zero-Sum society.

Irredundant Triangular Decomposition

Triangular decomposition is a classic, widely used and well-developed way to represent algebraic varieties with many applications. In particular, there exist sharp degree bounds for a single triangular set in terms of intrinsic data of the variety it represents, and powerful randomized algorithms for computing triangular decompositions using Hensel lifting in the zero-dimensional case and for irreducible varieties. However, in the general case, most of the algorithms computing triangular decompositions produce embedded components, which makes it impossible to directly apply the intrinsic degree bounds. This, in turn, is an obstacle for efficiently applying Hensel lifting due to the higher degrees of the output polynomials and the lower probability of success. In this paper, we give an algorithm to compute an irredundant triangular decomposition of an arbitrary algebraic set $W$ defined by a set of polynomials in C[x_1, x_2, ..., x_n]. Using this irredundant triangular decomposition, we were able to give intrinsic degree bounds for the polynomials appearing in the triangular sets and apply Hensel lifting techniques. Our decomposition algorithm is randomized, and we analyze the probability of success

Permutable entire functions and multiply connected wandering domains

Let f and g be permutable transcendental entire functions. We use a recent analysis of the dynamical behaviour in multiply connected wandering domains to make progress on the long standing conjecture that the Julia sets of f and g are equal; in particular, we show that J(f)=J(g) provided that neither f nor g has a simply connected wandering domain in the fast escaping set

Understanding Sample Generation Strategies for Learning Heuristic Functions in Classical Planning

We study the problem of learning good heuristic functions for classical planning tasks with neural networks based on samples that are states with their cost-to-goal estimates. It is well known that the learned model quality depends on the training data quality. Our main goal is to understand better the influence of sample generation strategies on the performance of a greedy best-first heuristic search guided by a learned heuristic function. In a set of controlled experiments, we find that two main factors determine the quality of the learned heuristic: the regions of the state space included in the samples and the quality of the cost-to-goal estimates. Also, these two factors are interdependent: having perfect estimates of cost-to-goal is insufficient if an unrepresentative part of the state space is included in the sample set. Additionally, we study the effects of restricting samples to only include states that could be evaluated when solving a given task and the effects of adding samples with high-value estimates. Based on our findings, we propose practical strategies to improve the quality of learned heuristics: three strategies that aim to generate more representative states and two strategies that improve the cost-to-goal estimates. Our resulting neural network heuristic has higher coverage than a basic satisficing heuristic. Also, compared to a baseline learned heuristic, our best neural network heuristic almost doubles the mean coverage and can increase it for some domains by more than six times.Comment: 27 page

Bose-Einstein Condensation in a CO_2-laser Optical Dipole Trap

We report on the achieving of Bose-Einstein condensation of a dilute atomic gas based on trapping atoms in tightly confining CO_2-laser dipole potentials. Quantum degeneracy of rubidium atoms is reached by direct evaporative cooling in both crossed and single beam trapping geometries. At the heart of these all-optical condensation experiments is the ability to obtain high initial atomic densities in quasistatic dipole traps by laser cooling techniques. Finally, we demonstrate the formation of a condensate in a field insensitive m_F=0 spin projection only. This suppresses fluctuations of the chemical potential from stray magnetic fields.Comment: 8 pages, 5 figure

Quartz Cherenkov Counters for Fast Timing: QUARTIC

We have developed particle detectors based on fused silica (quartz) Cherenkov radiators read out with micro-channel plate photomultipliers (MCP-PMTs) or silicon photomultipliers (SiPMs) for high precision timing (Sigma(t) about 10-15 ps). One application is to measure the times of small angle protons from exclusive reactions, e.g. p + p - p + H + p, at the Large Hadron Collider, LHC. They may also be used to measure directional particle fluxes close to external or stored beams. The detectors have small areas (square cm), but need to be active very close (a few mm) to the intense LHC beam, and so must be radiation hard and nearly edgeless. We present results of tests of detectors with quartz bars inclined at the Cherenkov angle, and with bars in the form of an "L" (with a 90 degree corner). We also describe a possible design for a fast timing hodoscope with elements of a few square mm.Comment: 24 pages, 14 figure