Smooth bumps, a Borel theorem and partitions of smooth functions on p.c.f. fractals

We provide two methods for constructing smooth bump functions and for smoothly cutting off smooth functions on fractals, one using a probabilistic approach and sub-Gaussian estimates for the heat operator, and the other using the analytic theory for p.c.f. fractals and a fixed point argument. The heat semigroup (probabilistic) method is applicable to a more general class of metric measure spaces with Laplacian, including certain infinitely ramified fractals, however the cut off technique involves some loss in smoothness. From the analytic approach we establish a Borel theorem for p.c.f. fractals, showing that to any prescribed jet at a junction point there is a smooth function with that jet. As a consequence we prove that on p.c.f. fractals smooth functions may be cut off with no loss of smoothness, and thus can be smoothly decomposed subordinate to an open cover. The latter result provides a replacement for classical partition of unity arguments in the p.c.f. fractal setting.Comment: 26 pages. May differ slightly from published (refereed) versio

Analysis techniques for residual acceleration data

Various aspects of residual acceleration data are of interest to low-gravity experimenters. Maximum and mean values and various other statistics can be obtained from data as collected in the time domain. Additional information may be obtained through manipulation of the data. Fourier analysis is discussed as a means of obtaining information about dominant frequency components of a given data window. Transformation of data into different coordinate axes is useful in the analysis of experiments with different orientations and can be achieved by the use of a transformation matrix. Application of such analysis techniques to residual acceleration data provides additional information than what is provided in a time history and increases the effectiveness of post-flight analysis of low-gravity experiments

Decompressive Laminectomy in the Management of Spinal Epidural Metastases

In a series of 60 patients undergoing decompression laminectomy for metastatic malignancy, the median survival was 3.3 months with 11 patients (18%) living for at least one year and ambulating during part of this survival period. Forty-three per cent of the group were able to ambulate for at least some period postoperatively. If a patient could ambulate preoperatively he had a two-thirds chance of ambulating afterwards; conversely, if he could not ambulate preoperatively. he had a two-thirds chance of not ambulating postoperatively. The lymphoma group had the best prognosis. Long lesions and highly vascular tumors fared poorly. Paralysis (as defined by inability to ambulate) had developed with great rapidity in half of the patients unable to walk prior to operation. We postulate that this was caused by infarction of the spinal cord. A plea is made for early diagnosis and effective removal of these lesions before signs of cord compression are evident, and especially before the patient loses his ability to walk

Second Language Feedback Abolishes the “Hot Hand” Effect during Even-Probability Gambling

Research into language�emotion interactions has revealed intriguing cognitive inhibition effects by emotionally negative words in bilinguals. Here, we turn to the domain of human risk taking and show that the experience of positive recency in games of chance�the �hot hand� effect�is diminished when game outcomes are provided in a second language rather than the native language. We engaged late Chinese-English bilinguals with �play� or �leave� decisions upon presentation of equal-odds bets while manipulating language of feedback and outcome value. When positive game outcomes were presented in their second language, English, participants subsequently took significantly fewer gambles and responded slower compared with the trials in which equivalent feedback was provided in Chinese, their native language. Positive feedback was identified as driving the cross-language difference in preference for risk over certainty: feedback for previous winning outcomes presented in Chinese increased subsequent risk taking, whereas in the English context no such effect was observed. Complementing this behavioral effect, event-related brain potentials elicited by feedback words showed an amplified response to Chinese relative to English in the feedback-related negativity window, indicating a stronger impact in the native than in the second language. We also observed a main effect of language on P300 amplitude and found it correlated with the cross-language difference in risk selections, suggesting that the greater the difference in attention between languages, the greater the difference in risk-taking behavior. These results provide evidence that the hot hand effect is at least attenuated when an individual operates in a non-native language