Statistical Mechanics for Unstable States in Gel'fand Triplets and Investigations of Parabolic Potential Barriers

Free energies and other thermodynamical quantities are investigated in canonical and grand canonical ensembles of statistical mechanics involving unstable states which are described by the generalized eigenstates with complex energy eigenvalues in the conjugate space of Gel'fand triplet. The theory is applied to the systems containing parabolic potential barriers (PPB's). The entropy and energy productions from PPB systems are studied. An equilibrium for a chemical process described by reactions $A+CB\rightleftarrows AC+B$ is also discussed.Comment: 14 pages, AmS-LaTeX, no figur

The Alliance AMBUSH Trial: Rationale and Design

Unlike medulloblastoma (MB) in children, robust prospective trials have not taken place for older patients due to the low incidence of MB in adults and adolescent and young adults (AYA). Current MB treatment paradigms for older patients have been extrapolated from the pediatric experience even though questions exist about the applicability of these approaches. Clinical and molecular classification of MB now provides better prognostication and is being incorporated in pediatric therapeutic trials. It has been established that genomic alterations leading to activation of the sonic hedgehog (SHH) pathway occur in approximately 60% of MB in patients over the age of 16 years. Within this cohort, protein patched homolog (PTCH) and smoothened (SMO) mutations are commonly found. Among patients whose tumors harbor the SHH molecular signature, it is estimated that over 80% of patients could respond to SHH pathway inhibitors. Given the advances in the understanding of molecular subgroups and the lack of robust clinical data for adult/AYA MB, the Alliance for Clinical Trial in Oncology group developed the AMBUSH trial: Comprehensive Management of AYA and Adult Patients with Medulloblastoma or Pineal Embryonal Tumors with a Randomized Placebo Controlled Phase II Focusing on Sonic Hedgehog Pathway Inhibition in SHH Subgroup Patients (Adult & Adolescent MedulloBlastoma Using Sonic Hedgehog Trial). This trial will enroll patients 18 years of age or older with MB (any molecular subgroup and risk stratification) or pineal embryonal tumor. Patients will be assigned to one of three cohorts: (1) average risk non-SHH-MB, (2) average risk SHH-MB, and (3) high risk MB or pineal embryonal tumors. All patients will receive protocol-directed comprehensive treatment with radiation therapy and chemotherapy. Patients with SHH-MB in cohort 1 will be randomized to a smoothened inhibitor or placebo as maintenance therapy for one year