Towards the computation of the convex hull of a configuration from its corresponding separating matrix

In this paper, we cope with the following problem: compute the size of the convex hull of a configuration C, where the given data is the number of separating lines between any two points of the configuration (where the lines are generated by pairs of other points of the configuration). We give an algorithm for the case that the convex hull is of size 3, and a partial algorithm and some directions for the case that the convex hull is of size bigger than 3.Comment: 10 pages, 3 figures; To appear in the Australasian Journal of Combinatoric

Military Recruitment on High School and College Campuses: A Policy and Legal Analysis

[Excerpt] In recent years, many academic institutions have enacted rules that protect individuals who are gay from discrimination on campus. As a result, some high schools and institutions of higher education have sought to bar military recruiters from their campuses and/or to eliminate Reserve Officer Training Corps (ROTC) programs on campus in response to the military\u27s Don\u27t Ask, Don\u27t Tell (DADT) policy, which prohibits homosexual conduct by members of the armed services. These efforts, however, have largely been thwarted due to several laws that bar giving federal funds to campuses that block access for military recruiters. These laws include the No Child Left Behind (NCLB) Act of 2001, which amended the Elementary and Secondary Education Act (ESEA) by requiring high schools that receive federal funds to provide certain student contact information to military recruiters upon request and to allow recruiters to have the same access to students as employers and colleges. This provision is different from similar Department of Defense (DOD) provisions that allow DOD to compile directory information on high school students for military recruitment purposes and that require colleges and universities that receive federal funds to give military recruiters the same access to students and campuses that is provided to other employers. Known as the Solomon Amendment, the latter provision was upheld as constitutional by the Supreme Court in the 2006 case Rumsfeld v. Forum for Academic and Institutional Rights (FAIR). This report describes the various laws regarding military recruitment on high school and college campuses, as well as discusses the policy and legal issues that they may raise. Meanwhile, several bills that would amend these military recruitment provisions have been introduced in the 111th Congress, including H.R. 1026, H.R. 1091, and S. 87

Homosexuals and the U.S. Military: Current Issues

[Excerpt] In 1993, new laws and regulations pertaining to homosexuals and U.S. military service came into effect reflecting a compromise in policy. This compromise, colloquially referred to as “don’t ask, don’t tell,” holds that the presence in the armed forces of persons who demonstrate a propensity or intent to engage in homosexual acts would create an unacceptable risk to the high standards of morale, good order and discipline, and unit cohesion which are the essence of military capability. Service members are not to be asked about nor allowed to discuss their homosexuality. This compromise notwithstanding, the issue has remained politically contentious. Prior to the 1993 compromise, the number of individuals discharged for homosexuality was generally declining. Since that time, the number of discharges for homosexual conduct has generally increased until recently. Constitutional challenges to the former and current military policies regarding homosexuals followed in the wake of the new 1993 laws and regulations. Based on the U.S. Supreme Court ruling in Bowers v. Hardwick that there is no fundamental right to engage in consensual homosexual sodomy, the courts have uniformly held that the military may discharge a service member for overt homosexual conduct. However, the legal picture was complicated by the Court’s 2003 decision in Lawrence v. Texas which overruled Bowers by declaring unconstitutional a Texas law that prohibited sexual acts between same sex couples. In addition, unsettled legal questions remain as to whether a discharge based solely on a statement that a service member is homosexual transgresses constitutional limits. Meanwhile, efforts to allow individuals of the same sex to marry legally appear unlikely to affect the DOD policy in the near term, since such individuals are barred from serving in the military, although court challenges are possible. In recent years, many academic institutions have enacted rules that protect homosexuals from discrimination on campus. As a result, colleges, universities, and even high schools have sought to bar military recruiters from their campuses and/or to eliminate Reserve Officer Training Corps (ROTC) programs on campus because of the DOD policy on homosexuals in the military. At the same time, legislation has been enacted that bars giving federal funds to campuses that block access for military recruiters. On March 6, 2006, the Supreme Court reversed a federal appeals court ruling in Rumsfeld v. Forum for Academic and Institutional Rights (FAIR), and upheld the constitutionality of the Solomon Amendment, which prohibits certain federal funding to higher educational institutions that deny access by military recruiters to their students equal to that provided to other employers. On November 14, 2006, the San Francisco school board voted 4-2 to phase out Junior ROTC over two years. That phase-out was later delayed by an additional year. This report will be updated as events warrant

Gaussian potentials facilitate access to quantum Hall states in rotating Bose gases

Through exact numerical diagonalization for small numbers of atoms, we show that it is possible to access quantum Hall states in harmonically confined Bose gases at rotation frequencies well below the centrifugal limit by applying a repulsive Gaussian potential at the trap center. The main idea is to reduce or eliminate the effective trapping frequency in regions where the particle density is appreciable. The critical rotation frequency required to obtain the bosonic Laughlin state can be fixed at an experimentally accessible value by choosing an applied Gaussian whose amplitude increases linearly with the number of atoms while its width increases as the square root.Comment: 4 pages, 4 figure

The Orchard crossing number of an abstract graph

We introduce the Orchard crossing number, which is defined in a similar way to the well-known rectilinear crossing number. We compute the Orchard crossing number for some simple families of graphs. We also prove some properties of this crossing number. Moreover, we define a variant of this crossing number which is tightly connected to the rectilinear crossing number, and compute it for some simple families of graphs.Comment: 17 pages, 10 figures. Totally revised, new material added. Submitte