Realignment in the NHL, MLB, the NFL, and the NBA

Sports leagues consist of conferences subdivided into divisions. Teams play a number of games within their divisions and fewer games against teams in different divisions and conferences. Usually, a league structure remains stable from one season to the next. However, structures change when growth or contraction occurs, and realignment of the four major professional sports leagues in North America has occurred more than twenty-five times since 1967. In this paper, we describe a method for realigning sports leagues that is flexible, adaptive, and that enables construction of schedules that minimize travel while satisfying other criteria. We do not build schedules; we develop league structures which support the subsequent construction of efficient schedules. Our initial focus is the NHL, which has an urgent need for realignment following the recent move of the Atlanta Thrashers to Winnipeg, but our methods can be adapted to virtually any situation. We examine a variety of scenarios for the NHL, and apply our methods to the NBA, MLB, and NFL. We find the biggest improvements for MLB and the NFL, where adopting the best solutions would reduce league travel by about 20%.Comment: 20 figures, 1 tabl

A Simple Algorithm for Local Conversion of Pure States

We describe an algorithm for converting one bipartite quantum state into another using only local operations and classical communication, which is much simpler than the original algorithm given by Nielsen [Phys. Rev. Lett. 83, 436 (1999)]. Our algorithm uses only a single measurement by one of the parties, followed by local unitary operations which are permutations in the local Schmidt bases.Comment: 5 pages, LaTeX, reference adde

Exact arborescences, matchings and cycles

AbstractSuppose we are given a graph in which edge has an integral weight. An ‘exact’ problem is to determine whether a desired structure exists for which the sum of the edge weights is exactly k for some prescribed k.We consider the special case of the problem in which all costs are zero or one for arborescences and show that a ‘continuity’ property is prossessed similar to that possessed by matroids. This enables us to determine in polynomial time the complete set of values of k for which a solution exists. We also give a minmax theorem for the maximum possible value of k, in terms of a packing of certain directed cuts in the graph.We also show how enumerative techniques can be used to solve the general exact problem for arborescences (implying spanning trees), perfect matchings in planar graphs and sets of disjoint cycles in a class of planar directed graphs which includes those of degree three. For these problems, we thereby obtain polynomial algorithms provided that the weights are bounded by a constant or encoded in unary

Emergent phonology

To what extent do complex phonological patterns require the postulation of universal mechanisms specific to language? In this volume, we explore the Emergent Hypothesis, that the innate language-specific faculty driving the shape of adult grammars is minimal, with grammar development relying instead on cognitive capacities of a general nature. Generalisations about sounds, and about the way sounds are organised into meaningful units, are constructed in a bottom-up fashion: As such, phonology is emergent. We present arguments for considering the Emergent Hypothesis, both conceptually and by working through an extended example in order to demonstrate how an adult grammar might emerge from the input encountered by a learner. Developing a concrete, data-driven approach, we argue that the conventional, abstract notion of unique underlying representations is unmotivated; such underlying representations would require some innate principle to ensure their postulation by a learner. We review the history of the concept and show that such postulated forms result in undesirable phonological consequences. We work through several case studies to illustrate how various types of phonological patterns might be accounted for in the proposed framework. The case studies illustrate patterns of allophony, of productive and unproductive patterns of alternation, and cases where the surface manifestation of a feature does not seem to correspond to its morphological source. We consider cases where a phonetic distinction that is binary seems to manifest itself in a way that is morphologically ternary, and we consider cases where underlying representations of considerable abstractness have been posited in previous frameworks. We also consider cases of opacity, where observed phonological properties do not neatly map onto the phonological generalisations governing patterns of alternation

Analysis of oxygenated polycyclic aromatic hydrocarbons in contaminated soil and water systems to Inform remediation strategy and risk assessment

Polycyclic aromatic hydrocarbons (PAH) have been regulated as priority pollutants since the 1970’s. Since then, there has been increasing recognition that oxygenated PAH transformation products may present a greater risk than parent PAH. This is a concern for soil remediation sites where formation of oxygenated PAH can be accelerated. Currently, routine monitoring is challenged due to a lack of standard analytical protocols. This thesis applies new analytical methods to investigate the formation and distribution of oxygenated PAH in contaminated soil-water systems under different remediation scenarios. High performance liquid chromatography and gas chromatography - mass spectrometry were used to investigate the effect of lignin phenol amendments on PAH transformation processes in a simulated soil-water system. Samples with highest PAH attenuation were characterised by increased utilisation of lignin phenols and distinct patterns of oxygenated PAH removal/formation, suggesting a potential approach to enhance PAH biodegradation. Challenges for analysing soilbound oxygenated PAH were addressed through the development of a novel aminopropylsilica solid phase extraction method. Strong recoveries of ketone- and hydroxyl-modified PAH were obtained, and the method also supported limited qualitative analysis for acid and aldehyde products. In addition, contamination level and clay content were shown to influence recovery of targeted compounds from different soils. Combining analytical methods for total extractable, leachate, and readily available soil fractions, the distribution of oxygenated PAH in gasworks soils undergoing remediation was monitored over a six-month period. Biochar, compost, and no amendment treatments were compared for effects on contaminant degradation/formation, and contaminant lability. It was shown that the biochar amendment was most likely to increase, and compost amendment most likely to decrease, risks associated with oxygenated PAH in these soils. Together, these studies show how new analytical techniques for the detection of oxygenated PAH can be used to enhance remediation science and support decision making at remediation sites

Harmony Drivers: No Disagreement Allowed

'Harmony' is a widely attested pattern in natural language, a configuration where within some domain all eligible anchors for some feature bear the same feature value. Typically, a harmony system exhibits a choice between two feature values. Either all anchors within some domain D bear the feature value F or all anchors within D bear the opposite value G. Depending on the theory of features and harmony, both harmonic values may be overtly specified or one may be indicated by the absence of featural specification. In exploring here the option of deriving harmony by prohibiting feature disharmony, the functional motivation is that the resetting of articulatory targets costs the grammar