Noisy Monte Carlo: Convergence of Markov chains with approximate transition kernels

Monte Carlo algorithms often aim to draw from a distribution $\pi$ by simulating a Markov chain with transition kernel $P$ such that $\pi$ is invariant under $P$. However, there are many situations for which it is impractical or impossible to draw from the transition kernel $P$. For instance, this is the case with massive datasets, where is it prohibitively expensive to calculate the likelihood and is also the case for intractable likelihood models arising from, for example, Gibbs random fields, such as those found in spatial statistics and network analysis. A natural approach in these cases is to replace $P$ by an approximation $\hat{P}$. Using theory from the stability of Markov chains we explore a variety of situations where it is possible to quantify how 'close' the chain given by the transition kernel $\hat{P}$ is to the chain given by $P$. We apply these results to several examples from spatial statistics and network analysis.Comment: This version: results extended to non-uniformly ergodic Markov chain

A Protein Aggregation Based Test for Screening of the Agents Affecting Thermostability of Proteins

To search for agents affecting thermal stability of proteins, a test based on the registration of protein aggregation in the regime of heating with a constant rate was used. The initial parts of the dependences of the light scattering intensity (I) on temperature (T) were analyzed using the following empiric equation: I = Kagg(T−T0)2, where Kagg is the parameter characterizing the initial rate of aggregation and T0 is a temperature at which the initial increase in the light scattering intensity is registered. The aggregation data are interpreted in the frame of the model assuming the formation of the start aggregates at the initial stages of the aggregation process. Parameter T0 corresponds to the moment of the origination of the start aggregates. The applicability of the proposed approach was demonstrated on the examples of thermal aggregation of glycogen phosphorylase b from rabbit skeletal muscles and bovine liver glutamate dehydrogenase studied in the presence of agents of different chemical nature. The elaborated approach to the study of protein aggregation may be used for rapid identification of small molecules that interact with protein targets

QCD and strongly coupled gauge theories : challenges and perspectives

We highlight the progress, current status, and open challenges of QCD-driven physics, in theory and in experiment. We discuss how the strong interaction is intimately connected to a broad sweep of physical problems, in settings ranging from astrophysics and cosmology to strongly coupled, complex systems in particle and condensed-matter physics, as well as to searches for physics beyond the Standard Model. We also discuss how success in describing the strong interaction impacts other fields, and, in turn, how such subjects can impact studies of the strong interaction. In the course of the work we offer a perspective on the many research streams which flow into and out of QCD, as well as a vision for future developments.Peer reviewe

EFFECT OF ALPHA-CRYSTALLIN ON THERMAL DENATURATION AND AGGREGATION OF RABBIT MUSCLE GLYCERALDEHYDE-3-PHOSPHATE DEHYDROGENASE.

The study of thermal denaturation of rabbit muscle glyceraldehyde-3-phosphate dehydrogenase (GAPDH) in the presence of alpha-crystallin by differential scanning calorimetry (DSC) showed that the position of the maximum on the DSC profile (T(max)) was shifted toward lower temperatures with increasing alpha-crystallin concentration. The diminishing GAPDH stability in the presence of alpha-crystallin has been explained assuming that heating of GAPDH induces dissociation of the tetrameric form of the enzyme into dimers interacting with alpha-crystallin. The dissociation of the enzyme tetramer was shown by sedimentation velocity at 45 degrees C. Suppression of thermal aggregation of GAPDH by alpha-crystallin was studied by dynamic light scattering under the conditions wherein temperature was elevated at a constant rate. The construction of the light scattering intensity versus the hydrodynamic radius (R(h)) plots enabled estimating the hydrodynamic radius of the start aggregates (R(h,0)). When aggregation of GAPDH was studied in the presence of alpha-crystallin, the start aggregates of lesser size were observed