Multicenter Phase II of CD26 Using Sitagliptin for Engraftment After UBC Transplant

Inclusion Criteria: * Patients must have one of the following disease types: * Acute myeloid leukemia (AML) with disease features as described in the protocol. * Acute lymphoblastic leukemia (ALL) with disease features as described in the protocol. * Myelodysplasia with disease features as described in the protocol. * Chronic myelogenous leukemia (CML) with disease features as described in the protocol. * Patients with aggressive non-Hodgkin's lymphoma (NHL), including diffuse large cell lymphoma, mediastinal B-cell lymphoma, transformed lymphoma, mantle cell lymphoma, and peripheral T cell lymphoma, who also have one of the disease features as described in the protocol. * At least 35 days following start of preceding leukemia induction cytotoxic chemotherapy. * For patients in remission, there should be no readily available consenting HLA-matched related donor who is either matched fully matched or mismatched at only one locus of HLA-A, -B, and DRB1. * No availability of a readily available HLA-matched volunteer unrelated donor (8 of 8 allele match at HLA-A, -B, -C and -DRB1). * Patients must have a matched or partially matched UCB unit with \>/= 2.5 x10\^7 nucleated cells/kg of recipient weight at the time of cryopreservation. * No current uncontrolled bacterial, viral or fungal infection (defined as currently taking medication and progression of clinical symptoms). * No HIV disease. * Non pregnant and non-nursing. * Required baseline laboratory values as descri…