Expert Conceptualizations of the Convergence of Taylor Series Yesterday, Today, and Tomorrow

Taylor series is a topic briefly covered in most university calculus sequences. In many cases it constitutes only one or two sections of a calculus textbook. With this limited exposure, what do calculus students really understand about the convergence of Taylor series? Do they think of Taylor series convergence as a sequence of converging polynomials? Do they think of convergence as a remainder going to zero? Do they think the Taylor series for sine really "equals" sine, or is it merely a good estimation for sine? Furthermore, how might experts respond to these questions?This study reported qualitative research methods which utilized multiple phases of data collection consisting of questionnaires and interviews from expert and novice (undergraduate student) participant groups. In addition, this study utilized multiple layers of analysis incorporating methods such as Strauss and Corbin's open coding and Sfard's discourse analysis. Using Tall and Vinner's notion of concept images, I analyzed and described the different ways in which both experts and novices conceptualized the convergence of Taylor series. In so doing, commonalities and differences amongst the expert and novice participant groups emerged.The main result from this study was found in the descriptions of thirteen different concept images that experts and novices employed concerning the convergence of Taylor series. Some of these images were used more than others by the different participant groups, and some images appeared to date back to the early years of calculus. Even though both groups employed a variety of images, on an individual level, experts were more prone to use a wider range of images that they efficiently and effectively employed as different situations prompted. The most notable difference between experts and novices was found in their graphical images of Taylor series convergence. Experts demonstrated little to no difficulties interpreting graphs of Taylor series, but the vast majority of novices were unable to correctly produce graphs related to Taylor series convergence. In several cases, novices appeared to be incorrectly applying previous knowledge of graphical properties of translating functions in an attempt to build their conceptions of Taylor polynomial graphs. This finding has implications for future research into the effects of graphical images, both dynamic and static, on student conceptions of the convergence of Taylor series

Activation of p73 and induction of Noxa by DNA damage requires NF-kappa B

Although the transcription factor NF-κB is most clearly linked to the inhibition of extrinsic apoptotic signals such as TNFα by upregulating known anti-apoptotic genes, NF-κB has also been proposed to be required for p53-induced apoptosis in transformed cells. However, the involvement of NF-κB in this process is poorly understood. Here we investigate this mechanism and show that in transformed MEFs lacking NF-κB (p65-null cells) genotoxin-induced cytochrome c release is compromised. To further address how NF-κB contributes to apoptosis, gene profiling by microarray analysis of MEFs was performed, revealing that NF-κB is required for expression of Noxa, a pro-apoptotic BH3-only protein that is induced by genotoxins and that triggers cytochrome c release. Moreover, we find that in the absence of NF-κB, genotoxin treatment cannot induce Noxa mRNA expression. Noxa expression had been shown to be regulated directly by genes of the p53 family, like p73 and p63, following genotoxin treatment. Here we show that p73 is activated after genotoxin treatment only in the presence of NF-κB and that p73 induces Noxa gene expression through the p53 element in the promoter. Together our data provides an explanation for how loss of NF-κB abrogates genotoxin-induced apoptosis

Delusions in frontotemporal lobar degeneration

We assessed the significance and nature of delusions in frontotemporal lobar degeneration (FTLD), an important cause of young-onset dementia with prominent neuropsychiatric features that remain incompletely characterised. The case notes of all patients meeting diagnostic criteria for FTLD attending a tertiary level cognitive disorders clinic over a three year period were retrospectively reviewed and eight patients with a history of delusions were identified. All patients underwent detailed clinical and neuropsychological evaluation and brain MRI. The diagnosis was confirmed pathologically in two cases. The estimated prevalence of delusions was 14 %. Delusions were an early, prominent and persistent feature. They were phenomenologically diverse; however paranoid and somatic delusions were prominent. Behavioural variant FTLD was the most frequently associated clinical subtype and cerebral atrophy was bilateral or predominantly right-sided in most cases. We conclude that delusions may be a clinical issue in FTLD, and this should be explored further in future work

Estimating sea-ice coverage, draft, and velocity in Marguerite Bay (Antarctica) using a subsurface moored upward-looking acoustic Doppler current profiler (ADCP)

Author Posting. © Elsevier B.V., 2007. This is the author's version of the work. It is posted here by permission of Elsevier B.V. for personal use, not for redistribution. The definitive version was published in Deep Sea Research Part II: Topical Studies in Oceanography 55 (2008): 351-364, doi:10.1016/j.dsr2.2007.11.004.A technique for the analysis of data from a subsurface moored upward-looking acoustic Doppler current profiler (ADCP) to determine ice coverage, draft and velocity is presented and applied to data collected in Marguerite Bay on the western Antarctic Peninsula shelf. This method provides sea ice information when no dedicated upward-looking sonar (ULS) data is available. Ice detection is accomplished using windowed variances of ADCP vertical velocity, vertical error velocity, and surface horizontal speed. ADCP signal correlation and backscatter intensity were poor indicators of the presence of ice at this site. Ice draft is estimated using a combination of ADCP backscatter data, atmospheric and oceanic pressure data, and information about the thermal stratification. This estimate requires corrections to the ADCP-derived range for instrument tilt and sound speed profile. Uncertainties of ± 0.20 m during midwinter and ± 0.40 m when the base of the surface mixed layer is above the ADCP for ice draft are estimated based on (a) a Monte Carlo simulation, (b) uncertainty in the sound speed correction, and (c) performance of the zero-draft estimate during times of known open water. Ice velocity is taken as the ADCP horizontal velocity in the depth bin specified by the range estimate.This work was supported by the NSF Office of Polar Programs through U.S. Southern Ocean GLOBEC grants OPP 99-10092 and OPP 06-23223, the WHOI Smith Chair in Coastal Oceanography, and the WHOI Education Office

Validation of Kepler's Multiple Planet Candidates. III: Light Curve Analysis & Announcement of Hundreds of New Multi-planet Systems

The Kepler mission has discovered over 2500 exoplanet candidates in the first two years of spacecraft data, with approximately 40% of them in candidate multi-planet systems. The high rate of multiplicity combined with the low rate of identified false-positives indicates that the multiplanet systems contain very few false-positive signals due to other systems not gravitationally bound to the target star (Lissauer, J. J., et al., 2012, ApJ 750, 131). False positives in the multi- planet systems are identified and removed, leaving behind a residual population of candidate multi-planet transiting systems expected to have a false-positive rate less than 1%. We present a sample of 340 planetary systems that contain 851 planets that are validated to substantially better than the 99% confidence level; the vast majority of these have not been previously verified as planets. We expect ~2 unidentified false-positives making our sample of planet very reliable. We present fundamental planetary properties of our sample based on a comprehensive analysis of Kepler light curves and ground-based spectroscopy and high-resolution imaging. Since we do not require spectroscopy or high-resolution imaging for validation, some of our derived parameters for a planetary system may be systematically incorrect due to dilution from light due to additional stars in the photometric aperture. None the less, our result nearly doubles the number of verified exoplanets.Comment: 138 pages, 8 Figures, 5 Tables. Accepted for publications in the Astrophysical Journa

Capillary Density of Skeletal Muscle: A Contributing Mechanism for Exercise Intolerance in Class II–III Chronic Heart Failure Independent of Other Peripheral Alterations

AbstractOBJECTIVESThe study was conducted to determine if the capillary density of skeletal muscle is a potential contributor to exercise intolerance in class II–III chronic heart failure (CHF).BACKGROUNDPrevious studies suggest that abnormalities in skeletal muscle histology, contractile protein content and enzymology contribute to exercise intolerance in CHF.METHODSThe present study examined skeletal muscle biopsies from 22 male patients with CHF compared with 10 age-matched normal male control patients. Aerobic capacities, myosin heavy chain (MHC) isoforms, enzymes, and capillary density were measured.RESULTSThe patients with CHF demonstrated a reduced peak oxygen consumption when compared to controls (15.0 ± 2.5 vs. 19.8 ± 5.0 ml·kg−1·min−1, p <0.05). Using cell-specific antibodies to directly assess vascular density, there was a reduction in capillary density in CHF measured as the number of endothelial cells/fiber (1.42 ± 0.28 vs. 1.74 ± 0.35, p = 0.02). In CHF, capillary density was inversely related to maximal oxygen consumption (r = 0.479, p = 0.02). The MHC IIx isoform was found to be higher in patients with CHF versus normal subjects (28.5 ± 13.6 vs. 19.5 ± 9.4, p <0.05).CONCLUSIONSThere was a significant reduction in microvascular density in patients with CHF compared with the control group, without major differences in other usual histologic and biochemical aerobic markers. The inverse relationship with peak oxygen consumption seen in the CHF group suggests that a reduction in microvascular density of skeletal muscle may precede other skeletal muscle alterations and play a critical role in the exercise intolerance characteristic of patients with CHF

Patient‐reported outcomes after 3‐dimensional conformal, intensity‐modulated, or proton beam radiotherapy for localized prostate cancer

BACKGROUND: Recent studies have suggested differing toxicity patterns for patients with prostate cancer who receive treatment with 3‐dimensional conformal radiotherapy (3DCRT), intensity‐modulated radiotherapy (IMRT), or proton beam therapy (PBT). METHODS: The authors reviewed patient‐reported outcomes data collected prospectively using validated instruments that assessed bowel and urinary quality of life (QOL) for patients with localized prostate cancer who received 3DCRT (n = 123), IMRT (n = 153) or PBT (n = 95). Clinically meaningful differences in mean QOL scores were defined as those exceeding half the standard deviation of the baseline mean value. Changes from baseline were compared within groups at the first post‐treatment follow‐up (2‐3 months from the start of treatment) and at 12 months and 24 months. RESULTS: At the first post‐treatment follow‐up, patients who received 3DCRT and IMRT, but not those who received PBT, reported a clinically meaningful decrement in bowel QOL. At 12 months and 24 months, all 3 cohorts reported clinically meaningful decrements in bowel QOL. Patients who received IMRT reported clinically meaningful decrements in the domains of urinary irritation/obstruction and incontinence at the first post‐treatment follow‐up. At 12 months, patients who received PBT, but not those who received IMRT or 3DCRT, reported a clinically meaningful decrement in the urinary irritation/obstruction domain. At 24 months, none of the 3 cohorts reported clinically meaningful changes in urinary QOL. CONCLUSIONS: Patients who received 3DCRT, IMRT, or PBT reported distinct patterns of treatment‐related QOL. Although the timing of toxicity varied between the cohorts, patients reported similar modest QOL decrements in the bowel domain and minimal QOL decrements in the urinary domains at 24 months. Prospective randomized trials are needed to further examine these differences. Cancer 2013. © 2013 American Cancer Society. Prostate cancer patients who receive 3‐dimensional conformal radiotherapy, intensity‐modulated radiotherapy, or proton beam therapy report distinct patterns of treatment‐related quality of life. Although the timing of toxicity varies between cohorts, patients report similar modest quality‐of‐life decrements in the bowel domain and minimal QOL decrements in the urinary domains at 24 months.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/97476/1/27956_ftp.pd

Planet Occurrence within 0.25 AU of Solar-type Stars from Kepler

We report the distribution of planets as a function of planet radius (R_p), orbital period (P), and stellar effective temperature (Teff) for P < 50 day orbits around GK stars. These results are based on the 1,235 planets (formally "planet candidates") from the Kepler mission that include a nearly complete set of detected planets as small as 2 Earth radii (Re). For each of the 156,000 target stars we assess the detectability of planets as a function of R_p and P. We also correct for the geometric probability of transit, R*/a. We consider first stars within the "solar subset" having Teff = 4100-6100 K, logg = 4.0-4.9, and Kepler magnitude Kp < 15 mag. We include only those stars having noise low enough to permit detection of planets down to 2 Re. We count planets in small domains of R_p and P and divide by the included target stars to calculate planet occurrence in each domain. Occurrence of planets varies by more than three orders of magnitude and increases substantially down to the smallest radius (2 Re) and out to the longest orbital period (50 days, ~0.25 AU) in our study. For P < 50 days, the radius distribution is given by a power law, df/dlogR= k R^\alpha. This rapid increase in planet occurrence with decreasing planet size agrees with core-accretion, but disagrees with population synthesis models. We fit occurrence as a function of P to a power law model with an exponential cutoff below a critical period P_0. For smaller planets, P_0 has larger values, suggesting that the "parking distance" for migrating planets moves outward with decreasing planet size. We also measured planet occurrence over Teff = 3600-7100 K, spanning M0 to F2 dwarfs. The occurrence of 2-4 Re planets in the Kepler field increases with decreasing Teff, making these small planets seven times more abundant around cool stars than the hottest stars in our sample. [abridged]Comment: Submitted to ApJ, 22 pages, 10 figure