Minimum Perimeter Rectangles That Enclose Congruent Non-Overlapping Circles

We use computational experiments to find the rectangles of minimum perimeter into which a given number n of non-overlapping congruent circles can be packed. No assumption is made on the shape of the rectangles. In many of the packings found, the circles form the usual regular square-grid or hexagonal patterns or their hybrids. However, for most values of n in the tested range n =< 5000, e.g., for n = 7, 13, 17, 21, 22, 26, 31, 37, 38, 41, 43...,4997, 4998, 4999, 5000, we prove that the optimum cannot possibly be achieved by such regular arrangements. Usually, the irregularities in the best packings found for such n are small, localized modifications to regular patterns; those irregularities are usually easy to predict. Yet for some such irregular n, the best packings found show substantial, extended irregularities which we did not anticipate. In the range we explored carefully, the optimal packings were substantially irregular only for n of the form n = k(k+1)+1, k = 3, 4, 5, 6, 7, i.e., for n = 13, 21, 31, 43, and 57. Also, we prove that the height-to-width ratio of rectangles of minimum perimeter containing packings of n congruent circles tends to 1 as n tends to infinity.Comment: existence of irregular minimum perimeter packings for n not of the form (10) is conjectured; smallest such n is n=66; existence of irregular minimum area packings is conjectured, e.g. for n=453; locally optimal packings for the two minimization criteria are conjecturally the same (p.22, line 5); 27 pages, 12 figure

Random harmonic analysis program, L221 (TEV156). Volume 1: Engineering and usage

A digital computer program capable of calculating steady state solutions for linear second order differential equations due to sinusoidal forcing functions is described. The field of application of the program, the analysis of airplane response and loads due to continuous random air turbulence, is discussed. Optional capabilities including frequency dependent input matrices, feedback damping, gradual gust penetration, multiple excitation forcing functions, and a static elastic solution are described. Program usage and a description of the analysis used are presented

The NWRA Classification Infrastructure: Description and Extension to the Discriminant Analysis Flare Forecasting System (DAFFS)

A classification infrastructure built upon Discriminant Analysis has been developed at NorthWest Research Associates for examining the statistical differences between samples of two known populations. Originating to examine the physical differences between flare-quiet and flare-imminent solar active regions, we describe herein some details of the infrastructure including: parametrization of large datasets, schemes for handling "null" and "bad" data in multi-parameter analysis, application of non-parametric multi-dimensional Discriminant Analysis, an extension through Bayes' theorem to probabilistic classification, and methods invoked for evaluating classifier success. The classifier infrastructure is applicable to a wide range of scientific questions in solar physics. We demonstrate its application to the question of distinguishing flare-imminent from flare-quiet solar active regions, updating results from the original publications that were based on different data and much smaller sample sizes. Finally, as a demonstration of "Research to Operations" efforts in the space-weather forecasting context, we present the Discriminant Analysis Flare Forecasting System (DAFFS), a near-real-time operationally-running solar flare forecasting tool that was developed from the research-directed infrastructure.Comment: J. Space Weather Space Climate: Accepted / in press; access supplementary materials through journal; some figures are less than full resolution for arXi

Automated microorganism Sample Collection Module

Modified Gelman Sampler obtains representative sample of microorganism population. Proposed Sample Collection Module is based on direct inoculation of selected solid growth media encased in a cartridge at all times except during inoculation. Cartridge can be handled with no danger of contamination to sample or operator

Managing the Regulatory State: The Experience of the Bush Administration

This Article traces the history of Presidential management of the regulatory state up to the administration of President George W. Bush. It focuses on the latter\u27s implementation of smarter regulation, an approach to regulation based on unfunded mandates on the private sector implemented through the Office of Management and Budget, an organization within the Executive Office of the President. It finds cost-benefit analysis an essential, yet often neglected, tool for implementing efficient and effective regulations. It concludes the policies promoted under President Bush\u27s OMB have effectively cut costs by streamlining the rule-making process and discouraging adopting new federal rules, but cautions there is still a sea of overlapping regulations and conflict over turf among agencies causing the administrative state to steadily rise in cost

Random l-colourable structures with a pregeometry

We study finite $l$-colourable structures with an underlying pregeometry. The probability measure that is used corresponds to a process of generating such structures (with a given underlying pregeometry) by which colours are first randomly assigned to all 1-dimensional subspaces and then relationships are assigned in such a way that the colouring conditions are satisfied but apart from this in a random way. We can then ask what the probability is that the resulting structure, where we now forget the specific colouring of the generating process, has a given property. With this measure we get the following results: 1. A zero-one law. 2. The set of sentences with asymptotic probability 1 has an explicit axiomatisation which is presented. 3. There is a formula $\xi(x,y)$ (not directly speaking about colours) such that, with asymptotic probability 1, the relation "there is an $l$-colouring which assigns the same colour to $x$ and $y$" is defined by $\xi(x,y)$. 4. With asymptotic probability 1, an $l$-colourable structure has a unique $l$-colouring (up to permutation of the colours).Comment: 35 page

Manual control theory applied to air traffic controller-pilot cooperation

Reduced runway separation standards are among the means which have been proposed for increasing airport capacity. The probability of a blunder will dominate the calculation of safe separation standards. Then the determinant of safe system performance will be the system reaction time comprised of the air traffic controller's detection, decision and communication delays, and the response times of the pilot and aircraft in executing a collision avoidance manuever. Estimates of these times, based on existing data, show that the delays ascribable to the human portions of the man-machine system are comparatively unimportant. New developments in radar, computers, and data links will be required to provide any substantial improvement of the existing system, and the goal of 2500 ft of separation may not be achievable