Non-Analyticity and the van der Waals Limit

We study the analyticity properties of the free energy f_\ga(m) of the Kac model at points of first order phase transition, in the van der Waals limit \ga\searrow 0. We show that there exists an inverse temperature $\beta_0$ and \ga_0>0 such that for all $\beta\geq \beta_0$ and for all \ga\in(0,\ga_0), f_\ga(m) has no analytic continuation along the path $m\searrow m^*$ ($m^*$ denotes spontaneous magnetization). The proof consists in studying high order derivatives of the pressure p_\ga(h), which is related to the free energy f_\ga(m) by a Legendre transform

HITECH Revisited

Assesses the 2009 Health Information Technology for Economic and Clinical Health Act, which offers incentives to adopt and meaningfully use electronic health records. Recommendations include revised criteria, incremental approaches, and targeted policies

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

Geochemical and lithium isotope characterization of Ogallala aquifer and Permian Basin carbonate reservoir waters at an enhanced oil recovery site, northwest Texas, USA

Geochemical and lithium isotope compositions (δ7Li) of Permian Basin produced waters and groundwater from overlying aquifers at an enhanced oil recovery (EOR) site in Gaines County, northwest Texas were determined to evaluate the effects of brine-groundwater-rock interactions, identify sources of dissolved solids, and characterize fluid migration and mixing processes. δ7Li values for produced waters from dolostones of the Permian Basin San Andres Formation ranged from +11 to +16 per mil (‰) and fall within the range of formation waters from Gulf of Mexico and Appalachian basin oil and gas reservoir rocks. The chemical composition and TDS content (800 to 2,200 mg L-1) of water from five Tertiary Ogallala Formation groundwater wells in the study area is comparable to other groundwaters from the Southern High Plains aquifer. Groundwaters from the Triassic Dockum Group Santa Rosa (δ7Li range of +21 to +23) are isotopically distinct from waters from the San Andres and Ogallala Formations. In addition to tracking groundwater-brine mixing and water-rock interaction, temporal changes in the δ7Li composition of deep groundwater in the study area has potential use in the early detection of upward or injection-induced brine migration, prior to its incursion into the sensitive overlying Ogallala aquifer

Bright tripartite entanglement in triply concurrent parametric oscillation

We show that a novel optical parametric oscillator, based on concurrent $\chi^{(2)}$ nonlinearities, can produce, above threshold, bright output beams of macroscopic intensities which exhibit strong tripartite continuous-variable entanglement. We also show that there are {\em two} ways that the system can exhibit a new three-mode form of the Einstein-Podolsky-Rosen paradox, and calculate the extra-cavity fluctuation spectra that may be measured to verify our predictions.Comment: title change, expanded intro and discussion of experimental aspects, 1 new figure. Conclusions unaltere