Dimensions and singular traces for spectral triples, with applications to fractals

Given a spectral triple (A,D,H), the functionals on A of the form a -> tau_omega(a|D|^(-t)) are studied, where tau_omega is a singular trace, and omega is a generalised limit. When tau_omega is the Dixmier trace, the unique exponent d giving rise possibly to a non-trivial functional is called Hausdorff dimension, and the corresponding functional the (d-dimensional) Hausdorff functional. It is shown that the Hausdorff dimension d coincides with the abscissa of convergence of the zeta function of |D|^(-1), and that the set of t's for which there exists a singular trace tau_omega giving rise to a non-trivial functional is an interval containing d. Moreover, the endpoints of such traceability interval have a dimensional interpretation. The corresponding functionals are called Hausdorff-Besicovitch functionals. These definitions are tested on fractals in R, by computing the mentioned quantities and showing in many cases their correspondence with classical objects. In particular, for self-similar fractals the traceability interval consists only of the Hausdorff dimension, and the corresponding Hausdorff-Besicovitch functional gives rise to the Hausdorff measure. More generally, for any limit fractal, the described functionals do not depend on the generalized limit omega.Comment: latex, 36 pages, no figures, to appear on Journ. Funct. Analysi

A Phase 1 Study of Intravenous Busulfan as a Conditioning Regimen for Multiple Myeloma

The efficacy of melphalan (MEL) 140 mg/m 2 pre-transplant conditioning versus MEL 200 mg/m 2 for the elderly is still debated. We hypothesized that single-agent intravenous busulfan (BU) would show significant anti-myeloma efficacy and be better tolerated by elderly patients. A prospective 3+3 dose escalation study enrolled symptomatic multiple myeloma (MM) patients 65 years or older with SWOG performance 0–2 for treatment with intravenous BU pre-transplant at different administration levels. The primary objective was to determine the maximum tolerated dose (MTD) of BU that could be safely given over the least number of days. All patients, except one, received maintenance treatment post-transplant, mostly for 2 years. We enrolled 13 patients, mean age of 73 years (range 68–80). Pharmacokinetic analysis showed no greater than 2% accumulation in the 13 patients, confirming a lack of accumulation in the multi-dose regimen. No deaths occurred in the peri-transplant period. Grade 3/4 adverse effects were hematological, no dose-limiting toxicity was observed and MTD was not reached. Three patients developed grade 3 mucositis but none developed veno-occlusive disease. Ten (77%) patients achieved a complete remission (CR) post-transplant with a remarkably long average time to best response of 6.7 months (range: 6–14 m), and two attained a partial response. Median overall survival was 84 months (95% CI, 21–104) and the median progression-free survival was 60 months (95% CI, 9–93). Our results suggest that IV BU could be an alternative conditioning regimen to MEL 140 in elderly patients with MM, and supports future randomized trials

Alkaline phosphatase variation during carfilzomib treatment is associated with best response in multiple myeloma patients

The ubiquitin–proteasome pathway regulates bone formation through osteoblast differentiation. We analyzed variation alkaline phosphatase (ALP) during carfilzomib treatment. Data from 38 patients enrolled in the PX‐171‐003 and 29 patients in PX‐171‐004 studies, for patients with relapsed/refractory myeloma, were analyzed. All patients received 20 mg/m 2 of carfilzomib on Days 1, 2, 8, 9, 15, and 16 of a 28‐day cycle. Sixty‐seven patients from ALP data were evaluable. In PX‐171‐003, the ORR (>PR) was 18% and the clinical benefit response (CBR; >MR) was 26%, while in PX‐171‐004, the ORR was 35.5% overall and 57% in bortezomib‐naive patients. ALP increment from baseline was statistically different in patients who achieved ≥VGPR compared with all others on Days 1 ( P  = 0.0049) and 8 ( P  = 0.006) of Cycle 2. In patients achieving a VGPR or better, ALP increased more than 15 units per liter at Cycle 2 Day 1 over baseline. An ALP increase over the same period of time was seen in 26%, 13% and 11% of patients achieving PR, MR, and SD, respectively. This retrospective analysis of patients with relapsed or refractory myeloma treated with single‐agent carfilzomib indicates that early elevation in ALP is associated with subsequent myeloma response.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/86807/1/j.1600-0609.2011.01602.x.pd

A Meta-analysis of Multiple Myeloma Risk Regions in African and European Ancestry Populations Identifies Putatively Functional Loci

Genome-wide association studies (GWAS) in European populations have identified genetic risk variants associated with multiple myeloma (MM)

Thrombophilia

Thrombophilia or hypercoagulable state is a clinical condition characterized by a tendency to develop venous (less frequently arterial) thrombosis. The development of a venous thromboembolic episode (VTE) is the result of environmental risk factors such as age, male sex, obesity, the exposure to “risk periods” of immobilization, trauma, cancer, pregnancy or the use of exogenous hormones or antineoplastic medications often on a background of a congenital procoagulant state. Table 1 summarizes the most frequently inherited and acquired thrombophilic conditions in a population of patients with a first episode of VTE.In patients with venous thrombosis before the early nineties a biologic cause of thrombophilia was detectable in only 5% to 15% of cases and was confined to deficiencies of antithrombin, protein C, and protein S. The discovery of two prothrombotic mutations prevalent in white populations, the factor V-Arg506Gln mutation (factor V Leiden) and the prothrombin G20210A mutation has significantly increased the number of patients with recognizable hereditary risk factor. The antiphospholipid antibody syndrome and elevated plasma homocysteine levels are also frequently identifiable risk factors in patients presenting with venous as well as arterial thrombosis

Toxoplasma Encephalitis following Tandem Autologous Hematopoietic Stem Cell Transplantation: A Case Report and Review of the Literature

Infection with Toxoplasma gondii is a rare but often fatal complication in hematopoietic stem cell transplantation (HSCT) recipients. Most cases have been reported in allogeneic (allo-) HSCT recipients, with only narrative reports following autologous HSCT (ASCT). We report the case of a 58-year-old Caucasian male presenting with toxoplasma encephalitis following tandem ASCT for myeloma and successfully treated with diagnosis by polymerase chain reaction analysis of cerebrospinal fluid. He was treated with sulfadiazine and pyrimethamine (with leucovorin) followed by pyrimethamine and atovaquone as secondary prophylaxis while receiving subsequent therapy for progressive multiple myeloma. Toxoplasmosis is a potential complication in allo-HSCT as well as ASCT recipients and should be considered in any post-HSCT patient with neurological dysfunction. Rapid diagnosis and immediate antimicrobial treatment are essential to avoid morbidity and mortality