Functional equations from generating functions: a novel approach to deriving identities for the Bernstein basis functions

The main aim of this paper is to provide a novel approach to deriving identities for the Bernstein polynomials using functional equations. We derive various functional equations and differential equations using generating functions. Applying these equations, we give new proofs for some standard identities for the Bernstein basis functions, including formulas for sums, alternating sums, recursion, subdivision, degree raising, differentiation and a formula for the monomials in terms of the Bernstein basis functions. We also derive many new identities for the Bernstein basis functions based on this approach. Moreover, by applying the Laplace transform to the generating functions for the Bernstein basis functions, we obtain some interesting series representations for the Bernstein basis functions.Comment: 1

A new conceptual approach for systematic error correction in CNC machine tools minimizing worst case prediction error

A new artifact-based method to identify the systematic errors in multi-axis CNC machine tools minimizing the worst case prediction error is presented. The closed loop volumetric error is identified by simultaneously moving the axes of the machine tool. The physical artifact is manufactured on the machine tool and later measured on a coordinate measuring machine. The artifact consists of a set of holes in the machine tool workspace at locations that minimize the worst case prediction error for a given bounded measurement error. The number of holes to be drilled depends on the degree of the polynomials used to model the systematic error and the number of axes of the machine tool. The prediction error is also function of the number and location of the holes. The feasibility of the method is first investigated for a two-axis machine to find the best experimental setting. Finally based on the two-axis case study, we extend the results to machine tools with any number of axes. The obtained results are very promising and require only a short time to produce the artifac

ATM variants 7271T>G and IVS10-6T>G among women with unilateral and bilateral breast cancer

Recent reports suggest that two ATM gene mutations, 7271T>G and IVS10-6T>G, are associated with a high risk of breast cancer among multiple-case families. To assess the importance of these two mutations in another 'high-risk' group, young women (under age 51) with multiple primaries, we screened a large population-based series of young women with bilateral breast cancer and compared the frequency of these mutations among similar women diagnosed with unilateral breast cancer. The 1149 women included were enrolled in an ongoing population-based case-control study of the genetic factors that contribute to bilateral breast cancer; they were not selected on the basis of family history of cancer. Screening for 7271T>G and IVS10-6T>G ATM gene mutations was conducted using DHPLC followed by direct sequencing. The 7271T>G mutation was detected in one out of 638 (0.2%) women with unilateral breast cancer and in none of the bilateral cases, and the IVS10-6T>G mutation in one out of 511 (0.2%) bilateral and in eight out of 638 (1.3%) unilateral breast cancer cases. Carriers of either mutation were not limited to women with a family history. Given the likelihood that young women with bilateral breast cancer have a genetic predisposition, the observed mutation distribution is contrary to that expected if these two mutations were to play an important role in breast carcinogenesis among individuals at high risk

Dusty Planetary Systems

Extensive photometric stellar surveys show that many main sequence stars show emission at infrared and longer wavelengths that is in excess of the stellar photosphere; this emission is thought to arise from circumstellar dust. The presence of dust disks is confirmed by spatially resolved imaging at infrared to millimeter wavelengths (tracing the dust thermal emission), and at optical to near infrared wavelengths (tracing the dust scattered light). Because the expected lifetime of these dust particles is much shorter than the age of the stars (>10 Myr), it is inferred that this solid material not primordial, i.e. the remaining from the placental cloud of gas and dust where the star was born, but instead is replenished by dust-producing planetesimals. These planetesimals are analogous to the asteroids, comets and Kuiper Belt objects (KBOs) in our Solar system that produce the interplanetary dust that gives rise to the zodiacal light (tracing the inner component of the Solar system debris disk). The presence of these "debris disks" around stars with a wide range of masses, luminosities, and metallicities, with and without binary companions, is evidence that planetesimal formation is a robust process that can take place under a wide range of conditions. This chapter is divided in two parts. Part I discusses how the study of the Solar system debris disk and the study of debris disks around other stars can help us learn about the formation, evolution and diversity of planetary systems by shedding light on the frequency and timing of planetesimal formation, the location and physical properties of the planetesimals, the presence of long-period planets, and the dynamical and collisional evolution of the system. Part II reviews the physical processes that affect dust particles in the gas-free environment of a debris disk and their effect on the dust particle size and spatial distribution.Comment: 68 pages, 25 figures. To be published in "Solar and Planetary Systems" (P. Kalas and L. French, Eds.), Volume 3 of the series "Planets, Stars and Stellar Systems" (T.D. Oswalt, Editor-in-chief), Springer 201

Age at first childbirth and oral contraceptive use are associated with risk of androgen receptor-negative breast cancer: the Malmö Diet and Cancer Cohort.

Risk factors for breast cancer vary according to breast cancer subtype. This study analyzes the impact of potential risk factors in breast cancer by androgen receptor (AR) status

Essential Functions of the Histone Demethylase Lid

Drosophila Little imaginal discs (Lid) is a recently described member of the JmjC domain class of histone demethylases that specifically targets trimethylated histone H3 lysine 4 (H3K4me3). To understand its biological function, we have utilized a series of Lid deletions and point mutations to assess the role that each domain plays in histone demethylation, in animal viability, and in cell growth mediated by the transcription factor dMyc. Strikingly, we find that lid mutants are rescued to adulthood by either wildtype or enzymatically inactive Lid expressed under the control of its endogenous promoter, demonstrating that Lid's demethylase activity is not essential for development. In contrast, ubiquitous expression of UAS-Lid transgenes lacking its JmjN, C-terminal PHD domain, and C5HC2 zinc finger were unable to rescue lid homozygous mutants, indicating that these domains carry out Lid's essential developmental functions. Although Lid-dependent demethylase activity is not essential, dynamic removal of H3K4me3 may still be an important component of development, as we have observed a genetic interaction between lid and another H3K4me3 demethylase, dKDM2. We also show that Lid's essential C-terminal PHD finger binds specifically to di- and trimethylated H3K4 and that this activity is required for Lid to function in dMyc-induced cell growth. Taken together, our findings highlight the importance of Lid function in the regulated removal and recognition of H3K4me3 during development

Common ataxia telangiectasia mutated haplotypes and risk of breast cancer: a nested case–control study

INTRODUCTION: The ataxia telangiectasia mutated (ATM) gene is a tumor suppressor gene with functions in cell cycle arrest, apoptosis, and repair of DNA double-strand breaks. Based on family studies, women heterozygous for mutations in the ATM gene are reported to have a fourfold to fivefold increased risk of breast cancer compared with noncarriers of the mutations, although not all studies have confirmed this association. Haplotype analysis has been suggested as an efficient method for investigating the role of common variation in the ATM gene and breast cancer. Five biallelic haplotype tagging single nucleotide polymorphisms are estimated to capture 99% of the haplotype diversity in Caucasian populations. METHODS: We conducted a nested case–control study of breast cancer within the Nurses' Health Study cohort to address the role of common ATM haplotypes and breast cancer. Cases and controls were genotyped for five haplotype tagging single nucleotide polymorphisms. Haplotypes were predicted for 1309 cases and 1761 controls for which genotype information was available. RESULTS: Six unique haplotypes were predicted in this study, five of which occur at a frequency of 5% or greater. The overall distribution of haplotypes was not significantly different between cases and controls (χ(2 )= 3.43, five degrees of freedom, P = 0.63). CONCLUSION: There was no evidence that common haplotypes of ATM are associated with breast cancer risk. Extensive single nucleotide polymorphism detection using the entire genomic sequence of ATM will be necessary to rule out less common variation in ATM and sporadic breast cancer risk