Constrained Molecular Dynamics Simulations of Atomic Ground-States

Constrained molecular dynamics(CoMD) model, previously introduced for nuclear dynamics, has been extended to the atomic structure and collision calculations. Quantum effects corresponding to the Pauli and Heisenberg principle are enforced by constraints, in a parameter-free way. Our calculations for small atomic system, H, He, Li, Be, F reproduce the ground-state binding energies within 3%, compared with the results of quantum mechanical Hartree-Fock calculations.Comment: 3 pages, 2 figure

Viterbi Training for PCFGs: Hardness Results and Competitiveness of Uniform Initialization

We consider the search for a maximum likelihood assignment of hidden derivations and grammar weights for a probabilistic context-free grammar, the problem approximately solved by “Viterbi training.” We show that solving and even approximating Viterbi training for PCFGs is NP-hard. We motivate the use of uniformat-random initialization for Viterbi EM as an optimal initializer in absence of further information about the correct model parameters, providing an approximate bound on the log-likelihood.

An Unusual Moving Boundary Condition Arising in Anomalous Diffusion Problems

In the context of analyzing a new model for nonlinear diffusion in polymers, an unusual condition appears at the moving interface between the glassy and rubbery phases of the polymer. This condition, which arises from the inclusion of a viscoelastic memory term in our equations, has received very little attention in the mathematical literature. Due to the unusual form of the moving-boundary condition, further study is needed as to the existence and uniqueness of solutions satisfying such a condition. The moving boundary condition which results is not solvable by similarity solutions, but can be solved by integral equation techniques. A solution process is outlined to illustrate the unusual nature of the condition; the profiles which result are characteristic of a dissolving polymer

Bifurcation of Localized Disturbances in a Model Biochemical Reaction

Asymptotic solutions are presented to the nonlinear parabolic reaction-diffusion equations describing a model biochemical reaction proposed by I. Prigogine. There is a uniform steady state which, for certain values of the adjustable parameters, may be unstable. When the uniform solution is slightly unstable, the two-timing method is used to find the bifurcation of new solutions of small amplitude. These may be either nonuniform steady states or time-periodic solutions, depending on the ratio of the diffusion coefficients. When one of the parameters is allowed to depend on space and the basic state is unstable, it is found that the nonuniform steady state which is approached may show localized spatial oscillations. The localization arises out of the presence of turning points in the linearized stability equations

Outcome Prediction for Unipolar Depression

Although effective drug and non-drug treatment for unipolar depressive illness exist, different individuals respond differently to different treatments. It is not uncommon for a given patient to lw switched several times from one treatment to another until an effective remedy for that particular patient is found. This process is costly in terms of time, money and suffering. It is thus desirable to determine at the outset the likdy response of a patient to the available treatments, so that the optimal one can be selected. Although prior attempts at outcome prediction with linear regression models have failed, recent work on this problem has indicated that the nonlinear predictive techniques of backpropagation and quadratic regression call account for a significant proportion of the variance in the data. The present research applies the nonlinear predictive technique of kernel regression to this problcrn, and employs cross-validation to test the ability of the resulting model to extract, from extremely noisy dinical data, information with predictive value. The importance of comparison with a suitable null hypothesis is illustrated.Office of Naval Research (N00014-95-1-0409