Arithmetic based fractals associated with Pascal's triangle

Our goal is to study Pascal-Sierpinski gaskets, which are certain fractal sets defined in terms of divisibility of entries in Pascal's triangle. The principal tool is a "carry rule" for the addition of the base-q representation of coordinates of points in the unit square. In the case that q = p is prime, we connect the carry rule to the power of p appearing in the prime factorization of binomialcoefficients. We use the carry rule to define a family of fractal subsets Bqr of the unit square, and we show that when q = p is prime, Bqr coincides with the Pascal-Sierpinski gasket corresponding to N = pr . We go on to describe Bqr as the limit of an iterated function system of "partial similarities", and we determine its Hausdorff dimension. We consider also the corresponding fractal sets in higher-dimensional Euclidean space

Cluster values of analytic functions on a Banach space

We investigate uniform algebras of bounded analytic functions on the unit ball of a complex Banach space. We prove several cluster value theorems, relating cluster sets of a function to its range on the fibers of the spectrum of the algebra. These lead to weak versions of the corona theorem for the open unit balls of c0 and ℓ2, in which all but one of the functions comprising the corona data extend to be weak-star continuous on the closed unit ball.Fil: Aron, Richard Martin. Kent State University; Estados UnidosFil: Carando, Daniel Germán. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Gamelin, T. W.. University of California at Los Angeles; Estados UnidosFil: Lassalle, Silvia Beatriz. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; ArgentinaFil: Maestre, Manuel. Universidad de Valencia; Españ

On badly approximable functions

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/21738/1/0000131.pd

Survey of oxaliplatin-associated neurotoxicity using an interview-based questionnaire in patients with metastatic colorectal cancer

BACKGROUND: New chemotherapy regimens for patients with colorectal cancer have improved survival, but at the cost of clinical toxicity. Oxaliplatin, an agent used in first-line therapy for metastatic colorectal cancer, causes acute and chronic neurotoxicity. This study was performed to carefully assess the incidence, type and duration of oxaliplatin neurotoxicity. METHODS: A detailed questionnaire was completed after each chemotherapy cycle for patients with metastatic colorectal cancer enrolled in a phase I trial of oxaliplatin and capecitabine. An oxaliplatin specific neurotoxicity scale was used to grade toxicity. RESULTS: Eighty-six adult patients with colorectal cancer were evaluated. Acute neuropathy symptoms included voice changes, visual alterations, pharyngo-laryngeal dysesthesia (lack of awareness of breathing); peri-oral or oral numbness, pain and symptoms due to muscle contraction (spasm, cramps, tremors). When the worst neurotoxicity per patient was considered, grade 1/2/3/4 dysesthesias and paresthesias were seen in 71/12/5/0 and 66/20/7/1 percent of patients. By cycles 3, 6, 9, and 12, oxaliplatin dose reduction or discontinuation was needed in 2.7%, 20%, 37.5% and 62.5% of patients. CONCLUSION: Oxaliplatin-associated acute neuropathy causes a variety of distressing, but transient, symptoms due to peripheral sensory and motor nerve hyperexcitability. Chronic neuropathy may be debilitating and often necessitates dose reductions or discontinuation of oxaliplatin. Patients should be warned of the possible spectrum of symptoms and re-assured about the transient nature of acute neurotoxicity. Ongoing studies are addressing the treatment and prophylaxis of oxaliplatin neurotoxicity

Single-crystalline, wormlike hematite photoanodes for efficient solar water splitting

A hematite photoanode showing a stable, record-breaking performance of 4.32 mA/cm(2) photoelectrochemical water oxidation current at 1.23 V vs. RHE under simulated 1-sun (100 mW/cm(2)) irradiation is reported. This photocurrent corresponds to ca. 34% of the maximum theoretical limit expected for hematite with a band gap of 2.1 V. The photoanode produced stoichiometric hydrogen and oxygen gases in amounts close to the expected values from the photocurrent. The hematitle has a unique single-crystalline "wormlike" morphology produced by in-situ two-step annealing at 550 degrees C and 800 degrees C of beta-FeOOH nanorods grown directly on a transparent conducting oxide glass via an all-solution method. In addition, it is modified by platinum doping to improve the charge transfer characteristics of hematite and an oxygen-evolving co-catalyst on the surface.open2

Optical Drug Monitoring: Photoacoustic Imaging of Nanosensors to Monitor Therapeutic Lithium in Vivo

Personalized medicine could revolutionize how primary care physicians treat chronic disease and how researchers study fundamental biological questions. To realize this goal, we need to develop more robust, modular tools and imaging approaches for in vivo monitoring of analytes. In this report, we demonstrate that synthetic nanosensors can measure physiologic parameters with photoacoustic contrast, and we apply that platform to continuously track lithium levels in vivo. Photoacoustic imaging achieves imaging depths that are unattainable with fluorescence or multiphoton microscopy. We validated the photoacoustic results that illustrate the superior imaging depth and quality of photoacoustic imaging with optical measurements. This powerful combination of techniques will unlock the ability to measure analyte changes in deep tissue and will open up photoacoustic imaging as a diagnostic tool for continuous physiological tracking of a wide range of analytes

Analysis of Polymorphisms and Haplotype Structure of the Human Thymidylate Synthase Genetic Region: A Tool for Pharmacogenetic Studies

5-fluorouracil (5FU), a widely used chemotherapeutic drug, inhibits the DNA replicative enzyme, thymidylate synthase (Tyms). Prior studies implicated a VNTR (variable numbers of tandem repeats) polymorphism in the 5′-untranslated region (5′-UTR) of the TYMS gene as a determinant of Tyms expression in tumors and normal tissues and proposed that these VNTR genotypes could help decide fluoropyrimidine dosing. Clinical associations between 5FU-related toxicity and the TYMS VNTR were reported, however, results were inconsistent, suggesting that additional genetic variation in the TYMS gene might influence Tyms expression. We thus conducted a detailed genetic analysis of this region, defining new polymorphisms in this gene including mononucleotide (poly A:T) repeats and novel single nucleotide polymorphisms (SNPs) flanking the VNTR in the TYMS genetic region. Our haplotype analysis of this region used data from both established and novel genetic variants and found nine SNP haplotypes accounting for more than 90% of the studied population. We observed non-exclusive relationships between the VNTR and adjacent SNP haplotypes, such that each type of VNTR commonly occurred on several haplotype backgrounds. Our results confirmed the expectation that the VNTR alleles exhibit homoplasy and lack the common ancestry required for a reliable marker of a linked adjacent locus that might govern toxicity. We propose that it may be necessary in a clinical trial to assay multiple types of genetic polymorphisms in the TYMS region to meaningfully model linkage of genetic markers to 5FU-related toxicity. The presence of multiple long (up to 26 nt), polymorphic monothymidine repeats in the promoter region of the sole human thymidylate synthetic enzyme is intriguing

Predictors of survival and toxicity in patients on adjuvant therapy with 5-fluorouracil for colorectal cancer

The present study aimed at investigating whether the simultaneous evaluation of pharmacokinetic, pharmacogenetic and demographic factors could improve prediction on toxicity and survival in colorectal cancer patients treated with adjuvant 5-fluorouracil (5FU)/leucovorin therapy. One hundred and thirty consecutive, B2 and C Duke's stage colorectal cancer patients were prospectively enrolled. 5FU pharmacokinetics was evaluated at the first cycle. Thymidylate synthase (TYMS) 5′UTR and 3′UTR polymorphisms and methylenetetrahydrofolate reductase (MTHFR) C677T and A1298C polymorphisms were assessed in peripheral leukocytes. Univariate and multivariate analyses were applied to evaluate which variables could predict chemotherapy-induced toxicity, disease-free survival (DFS) and overall survival (OS). Multivariate analysis showed that: (a) low 5FU clearance was an independent predictive factor for severe toxicity (OR=7.32; P<0.0001); (b) high-5FU clearance predicted poorer DFS (HR=1.96; P=0.041) and OS (HR=3.37; P=0.011); (c) advanced age was associated with shorter DFS (HR=3.34; P=0.0008) and OS (HR=2.66; P=0.024); (d) the C/C genotype of the MTHFR C677T polymorphism was protective against grade 3–4 toxicity (P=0.040); (e) none of the TYMS polymorphisms could explain 5FU toxicity or clinical outcome