Scaled-Particle Theory and the Length-scales Involved in Hydrophobic Hydration of Aqueous Biomolecular Assemblies

Hydrophobic hydration plays a crucial role in self-assembly processes over multiple length-scales, but the extrapolation of molecular-scale models to larger length-scale hydration phenomena is sometimes not warranted. Scaled-particle theories are based upon an interpolative view of that issue. We revisit the scaled-particle theory proposed thirty years ago by Stillinger, adopt a practical generalization, and consider the implications for hydrophobic hydration in light of our current understanding. The generalization is based upon identifying a molecular length, implicit in previous applications of scaled-particle models, that provides an effective radius for joining microscopic and macroscopic descriptions. We demonstrate that the generalized theory correctly reproduces many of the anomalous thermodynamic properties of hydrophobic hydration for molecularly sized solutes, including solubility minima and entropy convergence, successfully interpolates between the microscopic and macroscopic extremes, and provides new insights into the underlying molecular mechanisms. The results are discussed in terms of length-scales associated with component phenomena; in particular we first discuss the micro-macroscopic joining radius identified by the theory, then we discuss in turn the Tolman length that leads to an analogous length describing curvature corrections of a surface area model of hydrophobic hydration free energies, and the length-scales on which entropy convergence of hydration free energies are expected.Comment: 19 pages, 14 figures, one figure added, submitted to Rev. Mod. Phy

A Rate-Distortion Exponent Approach to Multiple Decoding Attempts for Reed-Solomon Codes

Algorithms based on multiple decoding attempts of Reed-Solomon (RS) codes have recently attracted new attention. Choosing decoding candidates based on rate-distortion (R-D) theory, as proposed previously by the authors, currently provides the best performance-versus-complexity trade-off. In this paper, an analysis based on the rate-distortion exponent (RDE) is used to directly minimize the exponential decay rate of the error probability. This enables rigorous bounds on the error probability for finite-length RS codes and leads to modest performance gains. As a byproduct, a numerical method is derived that computes the rate-distortion exponent for independent non-identical sources. Analytical results are given for errors/erasures decoding.Comment: accepted for presentation at 2010 IEEE International Symposium on Information Theory (ISIT 2010), Austin TX, US

On Multiple Decoding Attempts for Reed-Solomon Codes: A Rate-Distortion Approach

One popular approach to soft-decision decoding of Reed-Solomon (RS) codes is based on using multiple trials of a simple RS decoding algorithm in combination with erasing or flipping a set of symbols or bits in each trial. This paper presents a framework based on rate-distortion (RD) theory to analyze these multiple-decoding algorithms. By defining an appropriate distortion measure between an error pattern and an erasure pattern, the successful decoding condition, for a single errors-and-erasures decoding trial, becomes equivalent to distortion being less than a fixed threshold. Finding the best set of erasure patterns also turns into a covering problem which can be solved asymptotically by rate-distortion theory. Thus, the proposed approach can be used to understand the asymptotic performance-versus-complexity trade-off of multiple errors-and-erasures decoding of RS codes. This initial result is also extended a few directions. The rate-distortion exponent (RDE) is computed to give more precise results for moderate blocklengths. Multiple trials of algebraic soft-decision (ASD) decoding are analyzed using this framework. Analytical and numerical computations of the RD and RDE functions are also presented. Finally, simulation results show that sets of erasure patterns designed using the proposed methods outperform other algorithms with the same number of decoding trials.Comment: to appear in the IEEE Transactions on Information Theory (Special Issue on Facets of Coding Theory: from Algorithms to Networks

Peter Piper

Illustration of young boy ressed up in yellow, black, and white suit holding string attached to card of young girl and large yellow ball with titlehttps://scholarsjunction.msstate.edu/cht-sheet-music/7874/thumbnail.jp

A Super-Earth Orbiting the Nearby Sun-like Star HD 1461

We present precision radial velocity data that reveal a Super-Earth mass planet and two probable additional planets orbiting the bright nearby G0V star HD 1461. Our 12.8 years of Keck HIRES precision radial velocities indicate the presence of a 7.4M_Earth planet on a 5.77-day orbit. The data also suggest, but cannot yet confirm, the presence of outer planets on low-eccentricity orbits with periods of 446.1 and 5017 days, and projected masses (M sin i) of 27.9 and 87.1M_Earth, respectively. Test integrations of systems consistent with the radial velocity data suggest that the configuration is dynamically stable. We present a 12.2-year time series of photometric observations of HD 1461, which comprise 799 individual measurements, and indicate that it has excellent long-term photometric stability. However, there are small amplitude variations with periods comparable to those of the suspected 2nd and 3rd signals in the radial velocities near 5000 and 446 days, thus casting some suspicion on those periodicities as Keplerian signals. If the 5.77-day companion has a Neptune-like composition, then its expected transit depth is of order ~0.5 millimags. The geometric a priori probability of transits is ~8%. Phase-folding of the ground-based photometry shows no indication that transits of the 5.77-day companion are occurring, but high-precision follow-up of HD 1461 during upcoming transit phase windows will be required to definitively rule out or confirm transits. This new system joins a growing list of solar-type stars in the immediate galactic neighborhood that are accompanied by at least one Neptune- (or lower) mass planets having orbital periods of 50 days or less.Comment: 33 pages, 7 figure