Class and rank of differential modules

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a substitute for the length of a free complex--and on the rank of a differential module in terms of invariants of its homology. These results specialize to basic theorems in commutative algebra and algebraic topology. One instance is a common generalization of the equicharacteristic case of the New Intersection Theorem of Hochster, Peskine, P. Roberts, and Szpiro, concerning complexes over noetherian commutative rings, and of a theorem of G. Carlsson on differential graded modules over graded polynomial rings.Comment: 27 pages. Minor changes; mainly stylistic. To appear in Inventiones Mathematica

Differential Forms on Log Canonical Spaces

The present paper is concerned with differential forms on log canonical varieties. It is shown that any p-form defined on the smooth locus of a variety with canonical or klt singularities extends regularly to any resolution of singularities. In fact, a much more general theorem for log canonical pairs is established. The proof relies on vanishing theorems for log canonical varieties and on methods of the minimal model program. In addition, a theory of differential forms on dlt pairs is developed. It is shown that many of the fundamental theorems and techniques known for sheaves of logarithmic differentials on smooth varieties also hold in the dlt setting. Immediate applications include the existence of a pull-back map for reflexive differentials, generalisations of Bogomolov-Sommese type vanishing results, and a positive answer to the Lipman-Zariski conjecture for klt spaces.Comment: 72 pages, 6 figures. A shortened version of this paper has appeared in Publications math\'ematiques de l'IH\'ES. The final publication is available at http://www.springerlink.co

Economic evaluation of rituximab plus cyclophosphamide, vincristine and prednisolone for advanced follicular lymphoma

The addition of rituximab to cyclophosphamide, vincristine and prednisolone (CVP) for advanced follicular lymphoma increases median time to progression by 17 months. A US societal cost-effectiveness of R-CVP versus CVP is estimated for a representative 50-year-old patient. Progression-free survival (PFS) and overall survival are based on a randomized Phase III trial. Costs are estimated using Medicare reimbursement rates and published drug price data, and include drug and administration costs, adverse events, treatment of relapses, and end-of-life care. Utility estimates are derived from the literature and a 3% discount rate is employed. Mean overall survival is projected to be 1.51 years longer for patients assigned to R-CVP versus CVP. The cost per quality-adjusted year of life gained is $28,565. The utility associated with stable or progressive disease and the unit drug cost of rituximab most influence the findings. The cost-effectiveness ratio of R-CVP compared with CVP is projected to be cost-effective in the United States under a range of sensitivity analyses

Phase III Prospective Randomized Comparison Trial of Depot Octreotide Plus Interferon Alfa-2b Versus Depot Octreotide Plus Bevacizumab in Patients With Advanced Carcinoid Tumors: SWOG S0518

Purpose Treatment options for neuroendocrine tumors (NETs) remain limited. This trial assessed the progression-free survival (PFS) of bevacizumab or interferon alfa-2b (IFN-α-2b) added to octreotide among patients with advanced NETs. Patients and Methods Southwest Oncology Group (SWOG) S0518, a phase III study conducted in a US cooperative group system, enrolled patients with advanced grades 1 and 2 NETs with progressive disease or other poor prognostic features. Patients were randomly assigned to treatment with octreotide LAR 20 mg every 21 days with either bevacizumab 15 mg/kg every 21 days or 5 million units of IFN-α-2b three times per week. The primary end point was centrally assessed PFS. This trial is registered with ClinicalTrials.gov as NCT00569127. Results A total of 427 patients was enrolled, of whom 214 were allocated to bevacizumab and 213 to IFN-α-2b. The median PFS by central review was 16.6 months (95% CI, 12.9 to 19.6 months) in the bevacizumab arm and was 15.4 months (95% CI, 9.6 to 18.6 months) in the IFN arm (hazard ratio [HR], 0.93; 95% CI, 0.73 to 1.18; P = .55). By site review, the median PFS times were 15.4 months (95% CI, 12.6 to 17.2 months) for bevacizumab and 10.6 months (95% CI, 8.5 to 14.4 months) for interferon (HR, 0.90; 95% CI, 0.72 to 1.12; P = .33). Time to treatment failure was longer with bevacizumab than with IFN (HR, 0.72; 95% CI, 0.58 to 0.89; P = .003). Confirmed radiologic response rates were 12% (95% CI, 8% to 18%) for bevacizumab and 4% (95% CI, 2% to 8%) for IFN. Common adverse events with bevacizumab and octreotide included hypertension (32%), proteinuria (9%), and fatigue (7%); with IFN and octreotide, they included fatigue (27%), neutropenia (12%), and nausea (6%). Conclusion No significant differences in PFS were observed between the bevacizumab and IFN arms, which suggests that these agents have similar antitumor activity among patients with advanced NETs

Few smooth d-polytopes with n lattice points

We prove that, for fixed n there exist only finitely many embeddings of Q-factorial toric varieties X into P^n that are induced by a complete linear system. The proof is based on a combinatorial result that for fixed nonnegative integers d and n, there are only finitely many smooth d-polytopes with n lattice points. We also enumerate all smooth 3-polytopes with at most 12 lattice points. In fact, it is sufficient to bound the singularities and the number of lattice points on edges to prove finiteness.Comment: 20+2 pages; major revision: new author, new structure, new result

Unimodality Problems in Ehrhart Theory

Ehrhart theory is the study of sequences recording the number of integer points in non-negative integral dilates of rational polytopes. For a given lattice polytope, this sequence is encoded in a finite vector called the Ehrhart $h^*$-vector. Ehrhart $h^*$-vectors have connections to many areas of mathematics, including commutative algebra and enumerative combinatorics. In this survey we discuss what is known about unimodality for Ehrhart $h^*$-vectors and highlight open questions and problems.Comment: Published in Recent Trends in Combinatorics, Beveridge, A., et al. (eds), Springer, 2016, pp 687-711, doi 10.1007/978-3-319-24298-9_27. This version updated October 2017 to correct an error in the original versio

MRD response in relapsed/refractory FL after obinutuzumab plus bendamustine or bendamustine alone in the GADOLIN trial

We report assessment of minimal residual disease (MRD) status and its association with outcome in rituximab-refractory follicular lymphoma (FL) in the randomized GADOLIN trial (NCT01059630). Patients received obinutuzumab (G) plus bendamustine (Benda) induction followed by G maintenance, or Benda induction alone. Patients with a clonal marker (t[14;18] translocation and/or immunoglobulin heavy or light chain rearrangement) detected at study screening were assessed for MRD at mid-induction (MI), end of induction (EOI), and every 6-24 months post-EOI/discontinuation by real-time quantitative PCR. At MI, 41/52 (79%) patients receiving G-Benda were MRD-negative vs. 17/36 (47%) patients receiving Benda alone (p = 0.0029). At EOI, 54/63 (86%) patients receiving G-Benda were MRD-negative vs. 30/55 (55%) receiving Benda alone (p = 0.0002). MRD-negative patients at EOI had improved progression-free survival (HR, 0.33, 95% CI, 0.19-0.56, p \u3c 0.0001) and overall survival (HR, 0.39, 95% CI, 0.19-0.78, p = 0.008) vs. MRD-positive patients, and maintained their MRD-negative status for longer if they received G maintenance than if they did not. These results suggest that the addition of G to Benda-based treatment during induction can significantly contribute to the speed and depth of response, and G maintenance in MRD-negative patients potentially delays lymphoma regrowth

Identification of a Genomic Region Between SLC29A1 and HSP90AB1 Associated With Risk of Bevacizumab-Induced Hypertension: CALGB 80405 (Alliance)

Purpose: Bevacizumab is a VEGF-specific angiogenesis inhibitor indicated as an adjunct to chemotherapy for the treatment of multiple cancers. Hypertension is commonly observed during bevacizumab treatment, and high-grade toxicity can limit therapy or lead to cardiovascular complications. The factors that contribute to interindividual variability in blood pressure rise during bevacizumab treatment are not well understood.Experimental Design: To identify genomic regions associated with bevacizumab-induced hypertension risk, sequencing of candidate genes and flanking regulatory regions was performed on 61 patients treated with bevacizumab (19 cases developed early-onset grade 3 hypertension and 42 controls had no reported hypertension in the first six cycles of treatment). SNP-based tests for common variant associations and gene-based tests for rare variant associations were performed in 174 candidate genes.Results: Four common variants in independent linkage disequilibrium blocks between SLC29A1 and HSP90AB1 were among the top associations. Validation in larger bevacizumab-treated cohorts supported association between rs9381299 with early grade 3+ hypertension (P = 0.01; OR, 2.4) and systolic blood pressure >180 mm Hg (P = 0.02; OR, 2.1). rs834576 was associated with early grade 3+ hypertension in CALGB 40502 (P = 0.03; OR, 2.9). These SNP regions are enriched for regulatory elements that may potentially increase gene expression. In vitro overexpression of SLC29A1 in human endothelial cells disrupted adenosine signaling and reduced nitric oxide levels that were further lowered upon bevacizumab exposure.Conclusions: The genomic region between SLC29A1 and HSP90AB1 and its role in regulating adenosine signaling are key targets for further investigation into the pathogenesis of bevacizumab-induced hypertension

Identification of a Genomic Region between SLC29A1 and HSP90AB1 Associated with Risk of Bevacizumab-Induced Hypertension: CALGB 80405 (Alliance).

Purpose: Bevacizumab is a VEGF-specific angiogenesis inhibitor indicated as an adjunct to chemotherapy for the treatment of multiple cancers. Hypertension is commonly observed during bevacizumab treatment, and high-grade toxicity can limit therapy or lead to cardiovascular complications. The factors that contribute to interindividual variability in blood pressure rise during bevacizumab treatment are not well understood.Experimental Design: To identify genomic regions associated with bevacizumab-induced hypertension risk, sequencing of candidate genes and flanking regulatory regions was performed on 61 patients treated with bevacizumab (19 cases developed early-onset grade 3 hypertension and 42 controls had no reported hypertension in the first six cycles of treatment). SNP-based tests for common variant associations and gene-based tests for rare variant associations were performed in 174 candidate genes.Results: Four common variants in independent linkage disequilibrium blocks between SLC29A1 and HSP90AB1 were among the top associations. Validation in larger bevacizumab-treated cohorts supported association between rs9381299 with early grade 3+ hypertension (P = 0.01; OR, 2.4) and systolic blood pressure >180 mm Hg (P = 0.02; OR, 2.1). rs834576 was associated with early grade 3+ hypertension in CALGB 40502 (P = 0.03; OR, 2.9). These SNP regions are enriched for regulatory elements that may potentially increase gene expression. In vitro overexpression of SLC29A1 in human endothelial cells disrupted adenosine signaling and reduced nitric oxide levels that were further lowered upon bevacizumab exposure.Conclusions: The genomic region between SLC29A1 and HSP90AB1 and its role in regulating adenosine signaling are key targets for further investigation into the pathogenesis of bevacizumab-induced hypertension. Clin Cancer Res; 24(19); 4734-44. ©2018 AACR

Rituximab in B-Cell Hematologic Malignancies: A Review of 20 Years of Clinical Experience

Rituximab is a human/murine, chimeric anti-CD20 monoclonal antibody with established efficacy, and a favorable and well-defined safety profile in patients with various CD20-expressing lymphoid malignancies, including indolent and aggressive forms of B-cell non-Hodgkin lymphoma. Since its first approval 20 years ago, intravenously administered rituximab has revolutionized the treatment of B-cell malignancies and has become a standard component of care for follicular lymphoma, diffuse large B-cell lymphoma, chronic lymphocytic leukemia, and mantle cell lymphoma. For all of these diseases, clinical trials have demonstrated that rituximab not only prolongs the time to disease progression but also extends overall survival. Efficacy benefits have also been shown in patients with marginal zone lymphoma and in more aggressive diseases such as Burkitt lymphoma. Although the proven clinical efficacy and success of rituximab has led to the development of other anti-CD20 monoclonal antibodies in recent years (e.g., obinutuzumab, ofatumumab, veltuzumab, and ocrelizumab), rituximab is likely to maintain a position within the therapeutic armamentarium because it is well established with a long history of successful clinical use. Furthermore, a subcutaneous formulation of the drug has been approved both in the EU and in the USA for the treatment of B-cell malignancies. Using the wealth of data published on rituximab during the last two decades, we review the preclinical development of rituximab and the clinical experience gained in the treatment of hematologic B-cell malignancies, with a focus on the well-established intravenous route of administration. This article is a companion paper to A. Davies, et al., which is also published in this issue