The triangulations of the 3-sphere with up to 8 vertices

AbstractThe different combinatorial types of triangulations of the 3-sphere with up to 8 vertices are determined. Using similar methods we show that one cannot always preassign the shape of a facet of a 4-polytope

Establishment Clause: State Aid to Non-Public School Children Upheld in Part

Wolman v. Walter, 433 U.S. 229 (1977). On June 24, 1977, the Supreme Court of the United States in Wolman v. Walter affirmed in part and reversed in part a lower court ruling which upheld the constitutionality of an Ohio statute providing certain services to private school students at public expense. With this decision the Court further delineated the permissible limits to which a state may go in providing support for private secondary and primary education. But in doing so the Court revealed a house divided on the method of analyzing establishment clause cases and a basic conflict within the Court as to the permissible limits of state aid. Wolman represents the farthest limits that the Supreme Court has allowed a state to go in aiding nonpublic education. Beginning in 1947 with Everson v. Board of Education the Supreme Court upheld the reimbursement of parents for the cost of transportation to private, non-profit schools. In 1968 the Court, in Board of Education v. Allen, approved the loan of textbooks to all children, including those in private schools. In 1971 the Court struck down Rhode Island and Pennsylvania statutes which provided a subsidy for private school teachers in Lemon v. Kurtzman. Two 1973 New York cases, Levitt v. Committee for Public Education and Committee for Public Education v. Nyquist, declared invalid statutes providing reimbursement for testing and scoring along with maintenance and repair subsidies and tuition rebates. Finally, in 1975 the forerunner of the Wolman case, Meek v. Pittenger, struck down all but the textbook provisions of a Pennsylvania statute which provided counseling, testing, psychological, speech, hearing, and related diagnostic and therapeutic services to nonpublic school children. The Ohio legislature, aware of this chain of decisions and its own ten year conflict in finding a constitutional method of aiding private education, responded with legislation building upon these prior cases

Acceleration techniques for dependability simulation

As computer systems increase in complexity, the need to project system performance from the earliest design and development stages increases. We have to employ simulation for detailed dependability studies of large systems. However, as the complexity of the simulation model increases, the time required to obtain statistically significant results also increases. This paper discusses an approach that is application independent and can be readily applied to any process-based simulation model. Topics include background on classical discrete event simulation and techniques for random variate generation and statistics gathering to support simulation

Irreducible Triangulations are Small

A triangulation of a surface is \emph{irreducible} if there is no edge whose contraction produces another triangulation of the surface. We prove that every irreducible triangulation of a surface with Euler genus $g\geq1$ has at most $13g-4$ vertices. The best previous bound was $171g-72$.Comment: v2: Referees' comments incorporate

Acceleration Techniques for Dependability Simulation

Coordinated Science Laboratory was formerly known as Control Systems LaboratoryOffice of Naval ResearchComp. Sci. Corp.National Aeronautics and Space AdministrationU of I OnlyRestricted to UIUC communit

The maximum number of cliques in a graph embedded in a surface

This paper studies the following question: Given a surface $\Sigma$ and an integer $n$, what is the maximum number of cliques in an $n$-vertex graph embeddable in $\Sigma$? We characterise the extremal graphs for this question, and prove that the answer is between $8(n-\omega)+2^{\omega}$ and $8n+{3/2} 2^{\omega}+o(2^{\omega})$, where $\omega$ is the maximum integer such that the complete graph $K_\omega$ embeds in $\Sigma$. For the surfaces $\mathbb{S}_0$, $\mathbb{S}_1$, $\mathbb{S}_2$, $\mathbb{N}_1$, $\mathbb{N}_2$, $\mathbb{N}_3$ and $\mathbb{N}_4$ we establish an exact answer

A new scale to measure family members' perception of community health care services for persons with Huntington disease

Huntington Disease (HD) is a progressive genetic brain disease leading to disruptive cognitive, behavioral, and physical impairments. Persons with the condition and their caregivers need appropriate and accessible health care services to help them manage the disease adequately. The purpose of this study was to evaluate the psychometric properties of a new scale that measures family members' perception of community health care services (CHCS) for persons with HD

Phagocytosis by an HIV antibody is associated with reduced viremia irrespective of enhanced complement lysis

Increasingly, antibodies are being used to treat and prevent viral infections. In the context of HIV, efficacy is primarily attributed to dose-dependent neutralization potency and to a lesser extent Fc-mediated effector functions. It remains unclear whether augmenting effector functions of broadly neutralizing antibodies (bNAbs) may improve their clinical potential. Here, we use bNAb 10E8v4 targeting the membrane external proximal region (MPER) to examine the role of antibody-mediated effector and complement (C’) activity when administered prophylactically against SHIV challenge in rhesus macaques. With sub-protective dosing, we find a 78–88% reduction in post-acute viremia that is associated with 10E8v4-mediated phagocytosis acting at the time of challenge. Neither plasma nor tissue viremic outcomes in vivo is improved with an Fc-modified variant of 10E8v4 enhanced for C’ functions as determined in vitro. These results suggest that effector functions inherent to unmodified 10E8v4 contribute to efficacy against SHIVSF162P3 in the absence of plasma neutralizing titers, while C’ functions are dispensable in this setting, informing design of bNAb modifications for improving protective efficacy