Rapid Computation of Thermodynamic Properties Over Multidimensional Nonbonded Parameter Spaces using Adaptive Multistate Reweighting

We show how thermodynamic properties of molecular models can be computed over a large, multidimensional parameter space by combining multistate reweighting analysis with a linear basis function approach. This approach reduces the computational cost to estimate thermodynamic properties from molecular simulations for over 130,000 tested parameter combinations from over a thousand CPU years to tens of CPU days. This speed increase is achieved primarily by computing the potential energy as a linear combination of basis functions, computed from either modified simulation code or as the difference of energy between two reference states, which can be done without any simulation code modification. The thermodynamic properties are then estimated with the Multistate Bennett Acceptance Ratio (MBAR) as a function of multiple model parameters without the need to define a priori how the states are connected by a pathway. Instead, we adaptively sample a set of points in parameter space to create mutual configuration space overlap. The existence of regions of poor configuration space overlap are detected by analyzing the eigenvalues of the sampled states' overlap matrix. The configuration space overlap to sampled states is monitored alongside the mean and maximum uncertainty to determine convergence, as neither the uncertainty or the configuration space overlap alone is a sufficient metric of convergence. This adaptive sampling scheme is demonstrated by estimating with high precision the solvation free energies of charged particles of Lennard-Jones plus Coulomb functional form. We also compute entropy, enthalpy, and radial distribution functions of unsampled parameter combinations using only the data from these sampled states and use the free energies estimates to examine the deviation of simulations from the Born approximation to the solvation free energy

Symmetries of differential-difference dynamical systems in a two-dimensional lattice

Classification of differential-difference equation of the form $\ddot{u}_{nm}=F_{nm}\big(t, \{u_{pq}\}|_{(p,q)\in \Gamma}\big)$ are considered according to their Lie point symmetry groups. The set $\Gamma$ represents the point $(n,m)$ and its six nearest neighbors in a two-dimensional triangular lattice. It is shown that the symmetry group can be at most 12-dimensional for abelian symmetry algebras and 13-dimensional for nonsolvable symmetry algebras.Comment: 24 pages, 1 figur

Quantum Gravity at the Planck Length

I describe our understanding of physics near the Planck length, in particular the great progress in the last four years in string theory. These are lectures presented at the 1998 SLAC Summer Institute.Comment: 33 pages, LaTeX, 11 epsf figure

Classification of five-point differential-difference equations

Using the generalized symmetry method, we carry out, up to autonomous point transformations, the classification of integrable equations of a subclass of the autonomous five-point differential-difference equations. This subclass includes such well-known examples as the Itoh-Narita-Bogoyavlensky and the discrete Sawada-Kotera equations. The resulting list contains 17 equations some of which seem to be new. We have found non-point transformations relating most of the resulting equations among themselves and their generalized symmetries.Comment: 29 page

Expanding perfect fluid generalizations of the C-metric

We reexamine Petrov type D gravitational fields generated by a perfect fluid with spatially homogeneous energy density and in which the flow lines form a timelike non-shearing and non-rotating congruence. It is shown that the anisotropic such spacetimes, which comprise the vacuum C-metric as a limit case, can have \emph{non-zero} expansion, contrary to the conclusion in the original investigation by Barnes (Gen. Rel. Grav. 4, 105 (1973)). This class consists of cosmological models with generically one and at most two Killing vectors. We construct their line element and discuss some important properties. The methods used in this investigation incite to deduce testable criteria regarding shearfree normality and staticity op Petrov type $D$ spacetimes in general, which we add in an appendix.Comment: 16 pages, extended and amended versio

Automated Identification of Unhealthy Drinking Using Routinely Collected Data: A Machine Learning Approach

Background: Unhealthy drinking is prevalent in the United States and can lead to serious health and social consequences, yet it is under-diagnosed and under-treated. Identifying unhealthy drinkers can be time-consuming for primary care providers. An automated tool for identification would allow attention to be focused on patients most likely to need care and therefore increase efficiency and effectiveness. Objectives: To build a clinical prediction tool for unhealthy drinking based solely on routinely collected demographic and laboratory data. Methods: We obtained demographic and laboratory data on 89,325 adults seen at the University of Vermont Medical Center from 2011-2017. Logistic regression, support vector machines (SVM), k-nearest neighbor, and random forests were each used to build clinical prediction models. The model with the largest area under the receiver operator curve (AUC) was selected. Results: SVM with polynomials of degree 3 produced the largest AUC. The most influential predictors were alkaline phosphatase, gender, glucose, and serum bicarbonate. The optimum operating point had sensitivity 31.1%, specificity 91.2%, positive predictive value 50.4%, and negative predictive value 82.1%. Application of the tool increased the prevalence of unhealthy drinking from 18.3% to 32.4%, while reducing the target population by 22%. Limitations: Universal screening was not used during the time data was collected. The prevalence of unhealthy drinking among those screened was 60% suggesting the AUDIT-C was administered to confirm rather than screen for unhealthy drinking. Conclusion: An automated tool, using commonly available data, can identify a subset of patients who appear to warrant clinical attention for unhealthy drinking

Introduction: What is Meaning in a Legal Text? A First Dialogue for Law and Linguistics

This Article begins by describing the development of interest within linguistics over the last two decades in the language of legal processes, continues by tracing the evolution of the conference from a 1993 collaborative research project carried out by one law professor and three linguists, and concludes with some personal observations of the author on the benefits that linguists like herself stand to gain from further interdisciplinary efforts in this domain

Reparametrization-Invariant Path Integral in GR and "Big Bang" of Quantum Universe

The reparametrization-invariant generating functional for the unitary and causal perturbation theory in general relativity in a finite space-time is obtained. The region of validity of the Faddeev-Popov-DeWitt functional is studied. It is shown that the invariant content of general relativity as a constrained system can be covered by two "equivalent" unconstrained systems: the "dynamic" (with "dynamic" evolution parameter as the metric scale factor) and "geometric" (given by the Levi-Civita type canonical transformation to the action-angle variables where the energy constraint converts into a new momentum). "Big Bang", the Hubble evolution, and creation of matter fields by the "geometric" vacuum are described by the inverted Levi-Civita (LC) transformation of the geomeric system into the dynamic one. The particular case of the LC transformations are the Bogoliubov ones of the particle variables (diagonalizing the dynamic Hamiltonian) to the quasiparticles (diagonalizing the equations of motion). The choice of initial conditions for the "Big Bang" in the form of the Bogoliubov (squeezed) vacuum reproduces all stages of the evolution of the Friedmann-Robertson-Walker Universe in their conformal (Hoyle-Narlikar) versions.Comment: 21 pages, latex, 4 figures in postscrip