Set It and Forget It: Approximating the Set Once Strip Cover Problem

We consider the Set Once Strip Cover problem, in which n wireless sensors are deployed over a one-dimensional region. Each sensor has a fixed battery that drains in inverse proportion to a radius that can be set just once, but activated at any time. The problem is to find an assignment of radii and activation times that maximizes the length of time during which the entire region is covered. We show that this problem is NP-hard. Second, we show that RoundRobin, the algorithm in which the sensors simply take turns covering the entire region, has a tight approximation guarantee of 3/2 in both Set Once Strip Cover and the more general Strip Cover problem, in which each radius may be set finitely-many times. Moreover, we show that the more general class of duty cycle algorithms, in which groups of sensors take turns covering the entire region, can do no better. Finally, we give an optimal O(n^2 log n)-time algorithm for the related Set Radius Strip Cover problem, in which all sensors must be activated immediately.Comment: briefly announced at SPAA 201

The Interplay of Structure and Dynamics in the Raman Spectrum of Liquid Water over the Full Frequency and Temperature Range

While many vibrational Raman spectroscopy studies of liquid water have investigated the temperature dependence of the high-frequency O-H stretching region, few have analyzed the changes in the Raman spectrum as a function of temperature over the entire spectral range. Here, we obtain the Raman spectra of water from its melting to boiling point, both experimentally and from simulations using an ab initio-trained machine learning potential. We use these to assign the Raman bands and show that the entire spectrum can be well described as a combination of two temperature-independent spectra. We then assess which spectral regions exhibit strong dependence on the local tetrahedral order in the liquid. Further, this work demonstrates that changes in this structural parameter can be used to elucidate the temperature dependence of the Raman spectrum of liquid water and provides a guide to the Raman features that signal water ordering in more complex aqueous systems

Correlation of Zeno (Z = 1) line for supercritical fluids with vapor-liquid rectilinear diameters

For a wide range of substances, extending well beyond the regime of corresponding states behavior, the contour in the temperature-density plane along which the compressibility factor Z = P/{rho}kT is the same as for an ideal gas is nearly linear. This Z = 1 contour, termed the Zeno line, begins deep in the liquid region and ascends as the density decreases to the Boyle point of the supercritical fluid, specified by the temperature T{sub B} for which (dZ/d{rho}){sub T} = 0 as {rho} {r_arrow} 0; equivalent, at T{sub B} the second virial coefficient vanishes. The slope of the Z = 1 line is {minus}B{sub 3}/(dB{sub 2}/dT), in terms of the third virial coefficient and the derivative of the second, evaluated at T{sub B}. Previous work has examined the Zeno line as a means to extend corresponding states and to enhance other practical approximations. Here the authors call attention to another striking aspect, a strong correlation with the line of rectilinear diameters defined by the average of the subcritical vapor and liquid densities. This correlation is obeyed well by empirical data for many substances and computer simulations for a Lennard-jones potential; the ratios of the intercepts and slopes for the Zeno and rectilinear diameter liens are remarkably close to those predicted by the van der Waals equation, 8/9 and 16/9, respectively. Properties of the slightly imperfect fluid far above the critical point thus implicitly determine the diameter of the vapor-liquid coexistence curve below the critical point

The influence of photoperiod and light intensity on the growth and photosynthesis of Dunaliella salina (chlorophyta) CCAP 19/30

The green microalga Dunaliella salina survives in a wide range of salinities via mechanisms involving glycerol synthesis and degradation and is exploited for large amounts of nutraceutical carotenoids produced under stressed conditions. In this study, D. salina CCAP 19/30 was cultured in varying photoperiods and light intensities to study the relationship of light with different growth measurement parameters, with cellular contents of glycerol, starch and carotenoids, and with photosynthesis and respiration. Results show CCAP 19/30 regulated cell volume when growing under light/dark cycles: cell volume increased in the light and decreased in the dark, and these changes corresponded to changes in cellular glycerol content. The decrease in cell volume in the dark was independent of cell division and biological clock and was regulated by the photoperiod of the light/dark cycle. When the light intensity was increased to above 1000 μmol photons m−2 s−1, cells displayed evidence of photodamage. However, these cells also maintained the maximum level of photosynthesis efficiency and respiration possible, and the growth rate increased as light intensity increased. Significantly, the intracellular glycerol content also increased, >2-fold compared to the content in light intensity of 500 μmol photons m−2 s−1, but there was no commensurate increase in the pool size of carotenoids. These data suggest that in CCAP 19/30 glycerol stabilized the photosynthetic apparatus for maximum performance in high light intensities, a role normally attributed to carotenoids

Influence of methylene fluorination and chain length on the hydration shell structure and thermodynamics of linear diols

The interplay between the local hydration shell structure, the length of hydrophobic solutes, and their identity (perfluorinated or not) remains poorly understood. We address this issue by combining Raman–multivariate curve resolution (Raman-MCR) spectroscopy, simulation, and quantum-mechanical calculations to quantify the thermodynamics and the first principle interactions behind the formation of defects in the hydration shell of alkyl–diol and perfluoroalkyl–diol chains. The hydration shell of the fluorinated diols contains substantially more defects than that of the nonfluorinated diols; these defects are water hydroxy groups that do not donate hydrogen bonds and which either point to the solute (radial-dangling OH) or not (nonradial-dangling OH). The number of radial-dangling OH defects per carbon decreases for longer chains and toward the interior of the fluorinated diols, mainly due to less favorable electrostatics and exchange interactions; nonradial-dangling OH defects per carbon increase with chain length. In contrast, the hydration shell of the nonfluorinated diols only contains radial-dangling defects, which become more abundant toward the center of the chain and for larger chains, predominantly because of more favorable dispersion interactions. These results have implications for how the folding of macromolecules, ligand binding to biomacromolecules, and chemical reactions at water–oil interfaces could be modified through the introduction of fluorinated groups or solvents