Variational cross-validation of slow dynamical modes in molecular kinetics

Markov state models (MSMs) are a widely used method for approximating the eigenspectrum of the molecular dynamics propagator, yielding insight into the long-timescale statistical kinetics and slow dynamical modes of biomolecular systems. However, the lack of a unified theoretical framework for choosing between alternative models has hampered progress, especially for non-experts applying these methods to novel biological systems. Here, we consider cross-validation with a new objective function for estimators of these slow dynamical modes, a generalized matrix Rayleigh quotient (GMRQ), which measures the ability of a rank-$m$ projection operator to capture the slow subspace of the system. It is shown that a variational theorem bounds the GMRQ from above by the sum of the first $m$ eigenvalues of the system's propagator, but that this bound can be violated when the requisite matrix elements are estimated subject to statistical uncertainty. This overfitting can be detected and avoided through cross-validation. These result make it possible to construct Markov state models for protein dynamics in a way that appropriately captures the tradeoff between systematic and statistical errors

Measuring consensus as the midpoint of the central tendency

Federal Open Market Committee ; Forecasting

FOMC consensus forecasts

In November 2007, the Federal Open Market Committee (FOMC) announced a change in the way it communicates its view of the economic outlook: It increased the frequency of its forecasts from two to four times per year, and it increased the length of the forecasting horizon from two to three years. The FOMC does not release the individual members' forecasts or standard measures of consensus such as the mean or median. Rather, it continues to release the forecast information as a range of forecasts, both the full range between the high and the low and a central tendency that omits the extreme values. This paper uses individual forecaster data from the Survey of Professional Forecasters (SPF) to mimic the FOMC's method for creating their central tendency. The authors show that the midpoint of the central tendency of the SPF is a reliable measure of the consensus, suggesting that the FOMC reporting method is also a reliable measure of consensus. For the dates when both are available, the authors also compare the relative forecast accuracy of the FOMC and SPF consensus forecasts for output growth and inflation. Overall, the differences in forecast accuracy are too small to be statistically significant.Federal Open Market Committee ; Monetary policy

Freezing Transition of Random Heteropolymers Consisting of an Arbitrary Set of Monomers

Mean field replica theory is employed to analyze the freezing transition of random heteropolymers comprised of an arbitrary number ($q$) of types of monomers. Our formalism assumes that interactions are short range and heterogeneity comes only from pairwise interactions, which are defined by an arbitrary $q \times q$ matrix. We show that, in general, there exists a freezing transition from a random globule, in which the thermodynamic equilibrium is comprised of an essentially infinite number polymer conformations, to a frozen globule, in which equilibrium ensemble is dominated by one or very few conformations. We also examine some special cases of interaction matrices to analyze the relationship between the freezing transition and the nature of interactions involved.Comment: 30 pages, 1 postscript figur

FORMULATION AND STABILITY INDICATING ANALYSIS OF ORODISPERSIBLE TABLET OF PIROXICAM

The main object of this research work is to develop and studying the stability analysis of orodispersible tablet of piroxicam. Five formulationsof orodispersible tablets of piroxicam (F1-F4) were prepared using two different superdisintegrants namely crospovidone and sodiumstarch glycolate with two concentrations and a control F5 (without superdisintegrant) by direct term stability studies for the formulationsshowed no significant changes in disintegration compression method. The precompression and post compression study of piroxicam andexcipient were carried out. The short time, drug content and percentage of drug released when stored at 4°C±2°C, 27°C ±2°C, and 45°C±2°Cfor 15 days.Keywords: Orodispersible, Stability, Piroxicam, Anti-inflammatory, Direct compression, Superdisintegrant