Approximating Multilinear Monomial Coefficients and Maximum Multilinear Monomials in Multivariate Polynomials

This paper is our third step towards developing a theory of testing monomials in multivariate polynomials and concentrates on two problems: (1) How to compute the coefficients of multilinear monomials; and (2) how to find a maximum multilinear monomial when the input is a $\Pi\Sigma\Pi$ polynomial. We first prove that the first problem is \#P-hard and then devise a $O^*(3^ns(n))$ upper bound for this problem for any polynomial represented by an arithmetic circuit of size $s(n)$. Later, this upper bound is improved to $O^*(2^n)$ for $\Pi\Sigma\Pi$ polynomials. We then design fully polynomial-time randomized approximation schemes for this problem for $\Pi\Sigma$ polynomials. On the negative side, we prove that, even for $\Pi\Sigma\Pi$ polynomials with terms of degree $\le 2$, the first problem cannot be approximated at all for any approximation factor $\ge 1$, nor {\em "weakly approximated"} in a much relaxed setting, unless P=NP. For the second problem, we first give a polynomial time $\lambda$-approximation algorithm for $\Pi\Sigma\Pi$ polynomials with terms of degrees no more a constant $\lambda \ge 2$. On the inapproximability side, we give a $n^{(1-\epsilon)/2}$ lower bound, for any $\epsilon >0,$ on the approximation factor for $\Pi\Sigma\Pi$ polynomials. When terms in these polynomials are constrained to degrees $\le 2$, we prove a $1.0476$ lower bound, assuming $P\not=NP$; and a higher $1.0604$ lower bound, assuming the Unique Games Conjecture

Low Luminosity Companions to White Dwarfs

This paper presents results of a near-infrared imaging survey for low mass stellar and substellar companions to white dwarfs. A wide field proper motion survey of 261 white dwarfs was capable of directly detecting companions at orbital separations between $\sim100$ and 5000 AU with masses as low as 0.05 $M_{\odot}$, while a deep near field search of 86 white dwarfs was capable of directly detecting companions at separations between $\sim50$ and 1100 AU with masses as low as 0.02 $M_{\odot}$. Additionally, all white dwarf targets were examined for near-infrared excess emission, a technique capable of detecting companions at arbitrarily close separations down to masses of 0.05 $M_{\odot}$. No brown dwarf candidates were detected, which implies a brown dwarf companion fraction of $<0.5$% for white dwarfs. In contrast, the stellar companion fraction of white dwarfs as measured by this survey is 22%, uncorrected for bias. Moreover, most of the known and suspected stellar companions to white dwarfs are low mass stars whose masses are only slightly greater than the masses of brown dwarfs. Twenty previously unknown stellar companions were detected, five of which are confirmed or likely white dwarfs themselves, while fifteen are confirmed or likely low mass stars. Similar to the distribution of cool field dwarfs as a function of spectral type, the number of cool unevolved dwarf companions peaks at mid-M type. Based on the present work, relative to this peak, field L dwarfs appear to be roughly 2-3 times more abundant than companion L dwarfs. Additionally, there is no evidence that the initial companion masses have been altered by post main sequence binary interactions.Comment: 149 pages, 59 figures, 11 tables, accepted to ApJ Supplement

Personality and Augmenting/Reducing (A/R) in auditory event-related potentials (ERPs) during emotional visual stimulation

An auditory augmenting/reducing ERP paradigm recorded for 5 intensity tones with emotional visual stimulation was used, for the first time, to test predictions derived from the revised Reinforcement Sensitivity Theory (rRST) of personality with respect to two major factors: behavioral inhibition system (BIS), fight/flight/freeze system (FFFS). Higher BIS and FFFS scores were negatively correlated with N1/P2 slopes at central sites (C3, Cz, C4). Conditional process analysis revealed that the BIS was a mediator of the association between the N1/P2 slope and the FFFS scores. An analysis of covariance showed that lower BIS scorers exhibited larger N1/P2 amplitudes across all tone intensities while watching negative, positive and neutral pictures. Additionally, lower FFFS scorers compared to higher FFFS scorers disclosed larger N1/P2 amplitudes to the highest tone intensities and these differences were even more pronounced while watching positive emotional pictures. Findings were explained assuming the operation of two different, but related processes: transmarginal inhibition for the BIS; the attention/emotional gating mechanism regulating cortical sensory input for the FFFS trait. These findings appear consistent with predictions derived from the rRST, which traced fear and anxiety to separate but interacting neurobehavioural systems

Optical Multicolor Photometry of Spectrophotometric Standard Stars

Photoelectric data on the Johnson-Kron-Cousins UBVRI broadband photometric system are provided for a set of stars which have been used as spectrophotometric standard stars at the Hubble Space Telescope.Comment: 76 pages, 48 figures - published version available here: http://www.journals.uchicago.edu/AJ/journal/issues/v133n3/205588/205588.html . Also see ERRATUM at: http://www.journals.uchicago.edu/AJ/journal/issues/v133n5/205838/205838.htm

Rupture of multiple parallel molecular bonds under dynamic loading

Biological adhesion often involves several pairs of specific receptor-ligand molecules. Using rate equations, we study theoretically the rupture of such multiple parallel bonds under dynamic loading assisted by thermal activation. For a simple generic type of cooperativity, both the rupture time and force exhibit several different scaling regimes. The dependence of the rupture force on the number of bonds is predicted to be either linear, like a square root or logarithmic.Comment: 8 pages, 2 figure

Formation and Interaction of Membrane Tubes

We show that the formation of membrane tubes (or membrane tethers), which is a crucial step in many biological processes, is highly non-trivial and involves first order shape transitions. The force exerted by an emerging tube is a non-monotonic function of its length. We point out that tubes attract each other, which eventually leads to their coalescence. We also show that detached tubes behave like semiflexible filaments with a rather short persistence length. We suggest that these properties play an important role in the formation and structure of tubular organelles.Comment: 4 pages, 3 figure

A spectral line survey of Orion KL in the bands 486-492 and 541-577 GHz with the Odin satellite I. The observational data

Spectral line surveys are useful since they allow identification of new molecules and new lines in uniformly calibrated data sets. Nonetheless, large portions of the sub-millimetre spectral regime remain unexplored due to severe absorptions by H2O and O2 in the terrestrial atmosphere. The purpose of the measurements presented here is to cover wavelength regions at and around 0.55 mm -- regions largely unobservable from the ground. Using the Odin astronomy/aeronomy satellite, we performed the first spectral survey of the Orion KL molecular cloud core in the bands 486--492 and 541--576 GHz with rather uniform sensitivity (22--25 mK baseline noise). Odin's 1.1 m size telescope, equipped with four cryo-cooled tuneable mixers connected to broad band spectrometers, was used in a satellite position-switching mode. Two mixers simultaneously observed different 1.1 GHz bands using frequency steps of 0.5 GHz (25 hours each). An on-source integration time of 20 hours was achieved for most bands. The entire campaign consumed ~1100 orbits, each containing one hour of serviceable astro-observation. We identified 280 spectral lines from 38 known interstellar molecules (including isotopologues) having intensities in the range 80 to 0.05 K. An additional 64 weak lines remain unidentified. Apart from the ground state rotational 1(1,0)--1(0,1) transitions of ortho-H2O, H218O and H217O, the high energy 6(2,4)--7(1,7) line of para-H2O and the HDO(2,0,2--1,1,1) line have been observed, as well as the 1,0--0,1 lines from NH3 and its rare isotopologue 15NH3. We suggest assignments for some unidentified features, notably the new interstellar molecules ND and SH-. Severe blends have been detected in the line wings of the H218O, H217O and 13CO lines changing the true linewidths of the outflow emission.Comment: 21 pages, 10 figures, 7 tables, accepeted for publication in Astronomy and Astrophysics 30 August 200

Characterizing the Chemistry of Planetary Materials Around White Dwarf Stars

Planetary systems that orbit white dwarf stars can be studied via spectroscopic observations of the stars themselves. Numerous white dwarfs are seen to have accreted mostly rocky minor planets, the remnants of which are present in the stellar photospheres. The elemental abundances in the photospheres unveil the bulk compositions of the accreted parent bodies with a precision far greater than can be attained with any other technique currently available to astronomers. The most significant discovery, overall, is that rocky extrasolar planets have bulk elemental compositions similar to those of Earth and other rocky objects in our solar system. The white dwarf studies reveal that many extrasolar minor planets (asteroids) are differentiated, possessing analogs of terrestrial crust, mantle and core; this finding has important implications for the origin of our own solar system.Comment: Updated and improved version of an invited review to appear in 'Handbook of Exoplanets,' Springer Reference Works, Juan Antonio Belmonte and Hans Deeg, Ed

Heterogeneity in Preferences towards Complexity

We analyze lottery-choice data in a way that separately estimates the effects of risk aversion and complexity aversion. Complexity is represented by the number of different outcomes in the lottery. A finite mixture random effects model is estimated which assumes that a proportion of the population are complexity-neutral. We find that around 33% of the population are complexity-neutral, around 50% complexity-averse, and the remaining 17% are complexity-loving. Subjects who do react to complexity appear to have a bias towards complexity aversion at the start of the experiment, but complexity aversion reduces with experience, to the extent that the average subject is (almost) complexity-neutral by the end of the experiment. Complexity aversion is found to increase with age and to be higher for non-UK students than for UK students. We also find some evidence that, when evaluating complex lotteries, subjects perceive probabilities in accordance with Prospective Reference Theory

Efficient Dynamic Importance Sampling of Rare Events in One Dimension

Exploiting stochastic path integral theory, we obtain \emph{by simulation} substantial gains in efficiency for the computation of reaction rates in one-dimensional, bistable, overdamped stochastic systems. Using a well-defined measure of efficiency, we compare implementations of ``Dynamic Importance Sampling'' (DIMS) methods to unbiased simulation. The best DIMS algorithms are shown to increase efficiency by factors of approximately 20 for a $5 k_B T$ barrier height and 300 for $9 k_B T$, compared to unbiased simulation. The gains result from close emulation of natural (unbiased), instanton-like crossing events with artificially decreased waiting times between events that are corrected for in rate calculations. The artificial crossing events are generated using the closed-form solution to the most probable crossing event described by the Onsager-Machlup action. While the best biasing methods require the second derivative of the potential (resulting from the ``Jacobian'' term in the action, which is discussed at length), algorithms employing solely the first derivative do nearly as well. We discuss the importance of one-dimensional models to larger systems, and suggest extensions to higher-dimensional systems.Comment: version to be published in Phys. Rev.