Mixing times of lozenge tiling and card shuffling Markov chains

We show how to combine Fourier analysis with coupling arguments to bound the mixing times of a variety of Markov chains. The mixing time is the number of steps a Markov chain takes to approach its equilibrium distribution. One application is to a class of Markov chains introduced by Luby, Randall, and Sinclair to generate random tilings of regions by lozenges. For an L X L region we bound the mixing time by O(L^4 log L), which improves on the previous bound of O(L^7), and we show the new bound to be essentially tight. In another application we resolve a few questions raised by Diaconis and Saloff-Coste, by lower bounding the mixing time of various card-shuffling Markov chains. Our lower bounds are within a constant factor of their upper bounds. When we use our methods to modify a path-coupling analysis of Bubley and Dyer, we obtain an O(n^3 log n) upper bound on the mixing time of the Karzanov-Khachiyan Markov chain for linear extensions.Comment: 39 pages, 8 figure

Mixing Time of the Rudvalis Shuffle

We extend a technique for lower-bounding the mixing time of card-shuffling Markov chains, and use it to bound the mixing time of the Rudvalis Markov chain, as well as two variants considered by Diaconis and Saloff-Coste. We show that in each case Theta(n^3 log n) shuffles are required for the permutation to randomize, which matches (up to constants) previously known upper bounds. In contrast, for the two variants, the mixing time of an individual card is only Theta(n^2) shuffles.Comment: 9 page

Gambling with communities

In this chapter we draw attention to spoken and unspoken aspects of government policy found in the disadvantaging of community forms of gambling. Much of the rhetoric presented by government claims to be about protecting communities from gambling, but we argue that this language is at odds with the realities of policy and of practice. Such rhetoric foreshadowed the recent Review of Gaming, but the outcomes to date are not designed to redress the balance. These outcomes include a moratorium on casino licences securing the existing monopoly, increased surveillance on gaming machines run by clubs and pubs by the Department of Internal Affairs, and a bizarre effort to check Internet-based gambling in New Zealand

Everyday gambling in New Zealand

There is a sizeable body of statistics on gambling in New Zealand which points albeit unintentionally - to the everyday status of this activity. Max Abbott and Rachel Volberg, two leading figures in the rapidly growing discipline of gambling studies, note that in 15 short years there have been no less than seven surveys on gambling in New Zealand (not including a large number of university theses). These include three assessments of people's participation in gambling by the Department of Internal Affairs, plus two surveys funded by the department focusing on problem gambling. To these can be added one conducted by a regional health authority, North Health, under contract to the Committee on Problem Gambling Management and one conducted on behalf of the Casino Control Authority. This much research on gambling should suggest to the reader that there is something about gambling that piques the interest of government bureaucrats and agencies. Here the frequency of the phrase `problem gambling' is the giveaway. In this section we will review some of the findings of this research and cover its more pathological rationale later

New Measures of Port Efficiency Using International Trade Data

As the clearinghouses for a major portion of the world's rapidly increasing international trade flows, ocean ports and the efficiency with which they process cargo have become an ever more important topic. Yet, there exist very little data that allows one to compare port efficiency measures of any kind across ports and, especially, over time. This paper provides a new statistical method of uncovering port efficiency measures using U.S. Census data on imports into U.S. ports. Unlike previous measures, this study's methodology can provide such estimates for a much broader sample of countries and years with little cost. Thus, such data can be used by future researchers to examine a myriad of new issues, including the evolution of port efficiencies over time and its effects on international trade flows and country-level growth.

Contracting for Canola in the Great Plains States

Canola has become an important crop in the last decade in the U.S. Production of canola is risky and competes with other crops which have a range of risk reduction mechanisms. Alternative contracting strategies were evaluated by comparing returns to labor and management for growers and gross margins for processors. Alternative contracting strategies included no contract, fixed price with and without act of god provisions, and an oil premium contract. Grower returns and processor gross margins were simulated and resulting distributions were evaluated using stochastic efficiency with respect to a function. We estimated certainty equivalents and ranked contract preferences for both growers and processors by region in North Dakota. Grower and processor risk preferences varied by region. Producers and processors preferences differed for contract alternatives in the Northwest, Northeast and Eastcentral regions and were in agreement in the Northcentral region. This suggests that development of a single contract that would be widely adopted across the state would likely have to be altered by region to be acceptable to growers and processors.Canola, Grower, Processor, Contracting, Risk, Stochastic Efficiency (SERF)., Agricultural Finance, Crop Production/Industries,

PROCUREMENT RISKS AND STRATEGIES TO IMPROVE QUALITY CONSISTENCY IN WHEAT SHIPMENTS

Consistency of functional characteristics in wheat is a concern confronting buyers and sellers. This research analyzes the cost and risk of different procurement strategies for importers. A stochastic simulation model is used to determine the probability of a functional characteristic being satisfied subject to quality targets and costs for alternative purchase strategies (purchase by protein only, variety, location, variety by location, or functional tests). Joint probabilities of meeting specifications and costs were determined for the alternative purchase strategies. Stochastic dominance was used to determine which purchase strategies dominate others, and stochastic efficiency was utilized to determine the degree of preference. Results indicate that, as more specific characteristics are incorporated into a contract, the probabilities of meeting end-use requirements increase. Requirements of specific characteristics come with a higher cost, due to increased testing costs related to identity preservation. Risk premiums for alternative strategies were derived.Buying Strategies, Location, Variety, Functional Characteristic Tests, Costs, Risks, Simulation, Stochastic Dominance, Crop Production/Industries, Risk and Uncertainty,

Dynamic Changes in Market Structure and Competition in the Corn and Soybean Seed Sector

The purpose of this paper is to analyze the dynamics of R&D investments, and the structure of the seed distribution sector using novel data sets that have not been used before to describe competition in these industries. The results describe four sets of issues of particular importance. One is that while all agbiotechology firms have increased their R&D expenditures, there have been sharp differences in the scope of this spending. Most important is that this has spawned the growth in what is now referred as “seeds and traits.” Second, a large number of future traits will be commercialized in the coming years. A third set of results indicates that one firm grew its market share by 14% and a portion of this growth has been through acquisition. The other three majors lost market share, but the ISC (independent seed companies) grew by 10%. At the crop reporting district level, the industry concentration ratios for the four largest firms (CR4) in most regions are .5‐.7. Finally, farmers purchased corn and soybean seed from 4‐7 different companies in most crop reporting districts (CRD) and up to 20 or more companies in the larger producing regions.Agbiotechnology, grain seeds, competition, Agribusiness, Crop Production/Industries, Demand and Price Analysis,

MARKETING OF WHEAT ON A CONSTANT AND NIL MOISTURE BASIS

This study examined moisture specification practices in the United States and for major exporters and assessed impacts of changes to a nil or constant moisture basis on prices and revenue. These were examined under scenarios where information on moisture in current prices is limited and under a scenario where current prices reflect Full Knowledge of moisture advantages. Results indicate that changing to a nil moisture basis (which requires a subsequent adjustment in volumes to reflect the subtraction of moisture) would increase reported prices from 42 to 70 c/bu for the wheat classes, while changing to a 12 percent constant moisture basis would have limited impacts on reported prices. Effects on relative prices/revenue depend on whether knowledge of moisture advantages are reflected in current prices. If current prices reflect moisture advantages (Full Knowledge), then relative effects on prices/revenues are minimal. If current prices do not reflect moisture advantages (Limited Knowledge), then prices/revenue in drier production regions would increase.moisture, specifications, pricing, wheat, constant moisture, nil moisture, Crop Production/Industries,

EFFECT OF HARD RED SPRING WHEAT CONSISTENCY ON MILLING VALUE

Increased concerns over the quality of wheat in domestic and export markets has focused attention on the consistency of wheat quality. This study utilized three measures to examine the effect of variability in characteristics on the milling value of wheat. Distributions and correlations for wheat quality characteristics were estimated from U.S. wheat export data from 1985-1997. Effects of variability of wheat characteristics on the value of wheat to the miller for each of the three measures were estimated using a simulation model. U.S. No. 1 exports of Hard Red Spring (HRS) had higher value to millers on each of the three measures (net wheat, millable wheat index, and value added in milling) than did exports of No. 2 or better (OB). However, the value to millers of No. 1 HRS was more variable than for No. 2 OB HRS, likely due to a larger negative correlation between the levels of moisture and shrunken and broken kernels in exports of No. 2 OB HRS than No. 1 HRS. Further, the value of wheat to millers for each of the three measures varied substantially by importing country. Sensitivity analysis indicated that increases in the consistency of moisture would provide the greatest reduction in the variability of value to millers, while increases in the consistency of foreign material, shrunken and broken kernels, and dockage had lesser impacts. This suggests that millers looking to increase the value of wheat lots used in milling may want to consider adding restrictions/incentives on moisture to limit the variability from lot to lot. However for dockage, shrunken and broken kernels, and foreign material, the focus should be on actual levels within lots rather than variability between lots.quality consistency, wheat, net wheat, millable wheat value index, milling value, HRS, HRW, Marketing,