Liquid water is believed to be a transient polymer gel, with the connectivity lasting only a picosecond. The metastable extension of the phase diagram of liquid water exhibits rich features that manifest themselves in the equilibrium properties of water. For example, the maximum in the density at 4C and the minimum in the isothermal compressibility at 46C are likely manifestations of singularities in the behavior of thermodynamic quantities occurring in the supercooled region. The ``stability--limit conjecture'' suggests that thermodynamic anomalies arise from a limit of mechanical stability (spinodal line) that determines both the limit of liquid superheating at high T and of supercooling at low T. We report on an alternative hypothesis, that the observed supercooling anomalies are caused by a critical point above which two metastable amorphous phases of ice, previously shown to be separated by a line of first order transitions, become indistinguishable (1). We also report evidence from molecular dynamics simulations which support the hypothesis (1,2). Thus the two amorphous ice phases are incorporated into our understanding of the liquid state of water, so providing a more complete picture of the metastable and stable behavior
of water.

(1) See, e.g., the recent mini-review H. E. Stanley, L. Cruz, S. T. Harrington, P. H. Poole, S. Sastry, F. Sciortino, F. W. Starr, and R. Zhang, ``Cooperative Molecular Motions in Water: The Liquid-Liquid Critical Point Hypothesis'' [Proc. International Conf. on ``Complex Fluids''] Physica A {236}, 19-37 (1997), and references therein.

(2) S.~T.~Harrington, R.~Zhang, P.~H.~Poole, F,~Sciortino, and H.~E.~Stanley, ``Liquid-Liquid Phase Transition: Evidence from Simulations'' Phys. Rev. Lett. {78}, 2409-2412 (1997).

We present evidence supporting the possibility that the nucleotide sequence in noncoding DNA is power-law correlated---indeed, the identity of base pairs thousands of base pairs distant appear to statistically predictable [1]. We do not find such long-range correlation in the coding regions of the gene, so we build a ``coding sequence finder'' to locate the coding regions of an unknown DNA sequence [2]. We also discuss our finding that the long-range correlation exponent $\alpha$ (which characterizes the decay with distance of the correlation function) displays a systematic increase with evolution [3]. We then describe some recent work that systematically applies methods of statitsical linguistics to compare coding and noncoding DNA. Specifically, we adapt to DNA a form of $n$-tuple frequency analysis, and the Shannon approach to quantifying the ``redundancy'' of a linguistic text in terms of a measurable entropy function [4]. We also discuss the many subtleties and possible pitfalls of our approach [5].

[1] See, e.g., S. V. Buldyrev, A. L. Goldberger, S. Havlin, R. N. Mantegna, M. E. Matsa, C.-K. Peng, M. Simons, and H. E. Stanley, ``Long-Range Correlation Properties of Coding and Noncoding DNA Sequences: GenBank Analysis'' Phys. Rev. E {51}, 5084-5091 (1995) and references therein.

[2] S. M. Ossadnik, S. V. Buldyrev, A.~L.~Goldberger, S. Havlin, R.N. Mantegna, C.-K. Peng, M. Simons, and H. E. Stanley, ``Correlation Approach to Identify Coding Regions in DNA Sequences'' Biophysical Journal {67}, 64-70 (1994).

[3] S. V. Buldyrev, A. L. Goldberger, S. Havlin, C.-K. Peng, H. E. Stanley, M.H.R.Stanley and M. Simons, ``Fractal Landscapes and Molecular Evolution: Modeling the Myosin Heavy Chain Gene Family'' Biophysical Journal {65}, 2673-2679 (1993)

[4] R. N. Mantegna, S. V. Buldyrev, A. L. Goldberger, S. Havlin, C.-K. Peng, M. Simons, and H. E. Stanley, ``Systematic Analysis of Coding and Noncoding DNA Sequences Using Methods of Statistical Linguistics'' Phys. Rev. E {52}, 2939-2950 (1995).

[5] N. E. Israeloff et al, Phys. Rev. Lett. {76}, 1976 (1996); S. Bonhoeffer et al, Phys. Rev. Lett. {76}, 1977 (1996); R. F. Voss, Phys. Rev. Lett. {76}, 1978 (1996); R. N. Mantegna et al., Phys. Rev. Lett. {76}, 1979-1981 (1996).

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