The Average-Case Area of Heilbronn-Type Triangles

From among ${n \choose 3}$ triangles with vertices chosen from $n$ points in the unit square, let $T$ be the one with the smallest area, and let $A$ be the area of $T$. Heilbronn's triangle problem asks for the maximum value assumed by $A$ over all choices of $n$ points. We consider the average-case: If the $n$ points are chosen independently and at random (with a uniform distribution), then there exist positive constants $c$ and $C$ such that $c/n^3 < \mu_n < C/n^3$ for all large enough values of $n$, where $\mu_n$ is the expectation of $A$. Moreover, $c/n^3 < A < C/n^3$, with probability close to one. Our proof uses the incompressibility method based on Kolmogorov complexity; it actually determines the area of the smallest triangle for an arrangement in ``general position.''Comment: 13 pages, LaTeX, 1 figure,Popular treatment in D. Mackenzie, On a roll, {\em New Scientist}, November 6, 1999, 44--4

Is There an Energy Paradox in Fuel Economy? A Note on the Role of Consumer Heterogeneity and Sorting Bias

Previous literature finds that consumers tend to undervalue discounted future energy costs in their purchase decisions for energy-using durables. We argue that this finding could result from ignoring consumer heterogeneity in empirical analyses as opposed to true undervaluation. In the context of automobile demand, we show that, if not accounted for, consumer heterogeneity could lead to sorting, which in turn biases toward zero the estimate of marginal willingness to pay for discounted future fuel costs.energy paradox, fuel economy, consumer heterogeneity

Compound C inhibits nonsense-mediated RNA decay independently of AMPK

The nonsense mediated RNA decay (NMD) pathway safeguards the integrity of the transcriptome by targeting mRNAs with premature translation termination codons (PTCs) for degradation. It also regulates gene expression by degrading a large number of non-mutant RNAs (including mRNAs and noncoding RNAs) that bear NMD-inducing features. Consequently, NMD has been shown to influence development, cellular response to stress, and clinical outcome of many genetic diseases. Small molecules that can modulate NMD activity provide critical tools for understanding the mechanism and physiological functions of NMD, and they also offer potential means for treating certain genetic diseases and cancer. Therefore, there is an intense interest in identifying small-molecule NMD inhibitors or enhancers. It was previously reported that both inhibition of NMD and treatment with the AMPK-selective inhibitor Compound C (CC) induce autophagy in human cells, raising the possibility that CC may be capable of inhibiting NMD. Here we show that CC indeed has a NMD-inhibitory activity. Inhibition of NMD by CC is, however, independent of AMPK activity. As a competitive ATP analog, CC does not affect the kinase activity of SMG1, an essential NMD factor and the only known kinase in the NMD pathway. However, CC treatment down-regulates the protein levels of several NMD factors. The induction of autophagy by CC treatment is independent of ATF4, a NMD target that has been shown to promote autophagy in response to NMD inhibition. Our results reveal a new activity of CC as a NMD inhibitor, which has implications for its use in basic research and drug development

Birth Weight as a Risk Factor for Breast Cancer: a Meta-Analysis of 18 Epidemiologic Studies

Background: Birth weight has been identified as a birth-related factor associated with the risk of breast cancer. However, the evidence is inconsistent. Methods: To investigate the association between birth weight and breast cancer, we conducted a meta-analysis of published studies between 1996 and 2008. Eighteen studies encompassing 16,424 breast cancer cases were included in the meta-analysis. Data were combined using a fixed-effect or random-effect model depending on the heterogeneity across studies. Results: Women with their own birth weight \u3e4000 g or 8.5 lb had a higher risk for developing breast cancer than those with birth weight(OR¼1.20, 95% CI 1.08, 1.34). Findings were also consistent with a dose-response pattern effect. The summary effect estimate for breast cancer risk per 1 kg increase in birth weight was statistically significant (random effects OR¼1.07, 95% CI 1.02, 1.12). Conclusions: Although these results provided no evidence indicating whether birth weight is more strongly related to early-onset than to later-onset breast cancer, our findings suggest an association between birth weight and breast cancer. The underlying biological mechanism relating to this phenomenon needs additional study

Magnetization, crystal structure and anisotropic thermal expansion of single-crystal SrEr2O4

The magnetization, crystal structure, and thermal expansion of a nearly stoichiometric Sr$_{1.04(3)}$Er$_{2.09(6)}$O$_{4.00(1)}$ single crystal have been studied by PPMS measurements and in-house and high-resolution synchrotron X-ray powder diffraction. No evidence was detected for any structural phase transitions even up to 500 K. The average thermal expansions of lattice constants and unit-cell volume are consistent with the first-order Gr\"uneisen approximations taking into account only the phonon contributions for an insulator, displaying an anisotropic character along the crystallographic \emph{a}, \emph{b}, and \emph{c} axes. Our magnetization measurements indicate that obvious magnetic frustration appears below $\sim$15 K, and antiferromagnetic correlations may persist up to 300 K.Comment: 6 pages, 5 figure, 2 table

End-Tethered Chains Increase the Local Glass Transition Temperature of Matrix Chains by 45 K Next to Solid Substrates Independent of Chain Length

The local glass transition temperature Tg of pyrene-labeled polystyrene (PS) chains intermixed with end-tethered PS chains grafted to a neutral silica substrate was measured by fluorescence spectroscopy. To isolate the impact of the grafted chains, the films were capped with bulk neat PS layers eliminating competing effects of the free surface. Results demonstrate that end-grafted chains strongly increase the local Tg of matrix chains by $\approx$45 K relative to bulk Tg, independent of grafted chain molecular weight from Mn = 8.6 to 212 kg/mol and chemical end-group, over a wide range of grafting densities $\sigma$ = 0.003 to 0.33 chains/nm$^2$ spanning the mushroom-to-brush transition regime. The tens-of-degree increase in local Tg resulting from immobilization of the chain ends by covalent bonding in this athermal system suggests a mechanism that substantially increases the local activation energy required for cooperative rearrangements

The mechanism of the polarization dependence of the optical transmission in subwavelength metal hole arrays

We investigate the mechanism of extraordinary optical transmission in subwave-length metal hole arrays. Experimental results for the arrays consisting of square or rectangle holes are well explained about the dependence of transmission strength on the polarization direction of the incident light. This polarization dependence occurs in each single-hole. For a hole array, there is in addition an interplay between the adjacent holes which is caused by the transverse magnetic field of surface plasmon polariton on the metal film surfaces. Based on the detailed study of a single-hole and two-hole structures, a simple method to calculate the total tranmissivity of hole arrays is proposed.Comment: 34 pages, 7 figure

Anyone up for helping the Fisherman's wife? More solidarity with accidental misery than with man-made misery

We examine the willingness to donate depending on whether “misery” is random generated or self-inflicted by too high demands in bilateral negotiations. We find that randomness has a positive influence on the total amount of donation. In case of self-inflicted “misery” we observe that the subject who may have caused the unfavourable situation receives significantly less than the perceived innocent subject.altruism, bargaining experiment