Computing the period of an Ehrhart quasi-polynomial

If P is a rational polytope in R^d, then i_P(t):=#(tP\cap Z^d) is a quasi-polynomial in t, called the Ehrhart quasi-polynomial of P. A period of i_P(t) is D(P), the smallest positive integer D such that D*P has integral vertices. Often, D(P) is the minimum period of i_P(t), but, in several interesting examples, the minimum period is smaller. We prove that, for fixed d, there is a polynomial time algorithm which, given a rational polytope P in R^d and an integer n, decides whether n is a period of i_P(t). In particular, there is a polynomial time algorithm to decide whether i_P(t) is a polynomial. We conjecture that, for fixed d, there is a polynomial time algorithm to compute the minimum period of i_P(t). The tools we use are rational generating functions.Comment: 15 page

How Would You Like Your Television: With or Without Borders and With or Without Culture--a New Approach to Media Regulation in the European Union

This Essay analyzes the effectiveness of television broadcasting regulations as a means to effectuate the promotion and protection of a pan-European culture, namely, television broadcasting regulations. First, in Part I, this Essay considers the broader background developments in the audio-visual sector that led to the passing of the Directive. Part II looks at the advantages and disadvantages of the most controversial aspect of the Directive, namely, the quota provisions. Part III critiques the Directive\u27s effectiveness in realizing its dual goals of both protecting and promoting a pan-European culture. Finally, Part IV compares the goals enunciated in the Federal Communications Act ( FCC Act ) with those enunciated in the Directive. Both sets of goals reflect similar concerns and interests, although the United States takes a much broader approach in realizing its goals. This Essay concludes that the Community should, like the United States, take a more expansive approach to its audio-visual policy, similar to the approach reflected in the FCC Act, in order to strengthen and effectuate a more solid and unified European broadcast regulatory scheme that both protects and promotes a European culture

Organize to Organize: The Case of a Successful Long-Haul Campaign for Collective Bargaining Rights

After nearly four decades of campaigning, faculty and academic staff union members across the University of Wisconsin (UW) System won the right to bargain collectively in June 2009 when the Governor signed legislation that modified state labor law. In this paper, I present historical and interdisciplinary analyses of the organizational structures that were critical to the campaign’s success. While the case study should be interesting for academics across disciplines, the Wisconsin experience carries generalizable lessons for union organizing in any sector of the economy. In addition to cataloguing the tens of legislative attempts that faculty and academic staff unionists undertook to win collective bargaining rights in Wisconsin, my paper juxtaposes the legislative goals with environmental variables such as which political party controlled state government and how many faculty and academic staff were committed to the campaign at any given time as regular dues-paying members. It is clear in this light that persistence paid dividends for the campaign and that leverage created by the Local unions in relation to their state and national affiliates was necessary for the campaign’s longevity and success. Against this backdrop, I also consider the degree to which tensions between a Local union and its larger affiliates might variably impact union organizing across different international unions. The case study has relevance for discussions of minority or non-majority unions as well as strategic decisions about how unions pursue level playing fields for organizing new members

Obstructive Sleep Apnoea: a dental perspective

Obstructive sleep apnoea (OSA) is regarded as a potentially life threatening breathing disorder characterised by periodic cessation of air intake during sleep. Treatment modalities include conservative measures such as weight loss, change in sleep position and avoidance of alcohol: these may suffice in reducing airway obstruction. Pharmacotherapy has also been used with various grades of success. Nasal continuous positive airway pressure (nCPAP) helps maintain airway patency during sleep by a continuous stream of air under light pressure. Tracheostomy, by its very nature, completely bypasses any pharyngeal obstruction but is associated with a high degree of morbidity. Other surgical procedures such as uvulopalatopharyngoplasty (UPPP), orthognathic surgery, hyoid-myotomy suspension and tongue reduction have also been used. Mandibular advancement splints (MAS) are increasingly being recognised as a suitable management option for those subjects with mild to moderate OSA. A study was undertaken to ascertain the effectiveness of using mandibular advancement splints in the treatment of OSA. Mandibular protrusion using a MAS is frequently, but not invariably, associated with improvement in velo- and oro-pharyngeal airway dimensions in awake subjects.peer-reviewe