Non-Reversible Parallel Tempering: a Scalable Highly Parallel MCMC Scheme

Parallel tempering (PT) methods are a popular class of Markov chain Monte Carlo schemes used to sample complex high-dimensional probability distributions. They rely on a collection of $N$ interacting auxiliary chains targeting tempered versions of the target distribution to improve the exploration of the state-space. We provide here a new perspective on these highly parallel algorithms and their tuning by identifying and formalizing a sharp divide in the behaviour and performance of reversible versus non-reversible PT schemes. We show theoretically and empirically that a class of non-reversible PT methods dominates its reversible counterparts and identify distinct scaling limits for the non-reversible and reversible schemes, the former being a piecewise-deterministic Markov process and the latter a diffusion. These results are exploited to identify the optimal annealing schedule for non-reversible PT and to develop an iterative scheme approximating this schedule. We provide a wide range of numerical examples supporting our theoretical and methodological contributions. The proposed methodology is applicable to sample from a distribution $\pi$ with a density $L$ with respect to a reference distribution $\pi_0$ and compute the normalizing constant. A typical use case is when $\pi_0$ is a prior distribution, $L$ a likelihood function and $\pi$ the corresponding posterior.Comment: 74 pages, 30 figures. The method is implemented in an open source probabilistic programming available at https://github.com/UBC-Stat-ML/blangSD

Multiscale Simulations of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) lack stable secondary and/or tertiary structures under physiological conditions. The have now been recognized to play important roles in numerous biological processes, particularly cellular signaling and regulation. Mutation of IDPs are frequently associated with human diseases, such as cancers and neuron degenerative diseases. Therefore, it is important to understand the structure, dynamics, and interactions of IDPs, so as to establish the mechanistic basis of how intrinsic disorder mediates versatile functions and how such mechanisms may fail in human diseases. However, the heterogeneous structural ensembles of IDPs are not amenable to high resolution characterization solely through experimental measurements, and molecular modelling and simulation are required to study IDP structures, dynamics, and interactions at the atomistic levels. Here, we first applied the state-of-the-art explicit solvent atomistic simulations to an anti-apoptotic protein Bcl-xL and demonstrated how inherent structural disorder may provide a physical basis of protein regulated unfolding in signaling transduction. We have also constructed a series of efficient coarse-grained models to directly simulate the interactions between IDPs and unveiled how the preexisting structural elements accelerate binding of ACTR to NCBD by promoting efficient folding upon encounter. These studies shed important light on how IDPs perform functions in the cellular regulatory network, but also reveal the necessity of new sampling techniques for more efficient simulations of IDPs. We have thus developed a novel sampling technique, called multiscale enhanced sampling (MSES). MSES couples the atomistic model with coarse-grained ones, to accelerate the sampling of atomistic conformational space. Bias from coupling to a coarse-grained model can be removed using Hamiltonian replica exchange. To achieve the best possible efficiency of MSES simulations, we have developed a new hybrid resolution protein model that could capture the essential features of IDP structures, so as to generate local and long-range fluctuations that are largely consistent with those at the atomistic level. We have also developed an advanced replica exchange protocol, to allow the fast conformational transitions observed in the coupled conditions to be rapidly exchanged to the unbiased limit. Application of these strategies to characterize the structural ensembles of a few non-trivial IDPs shows that faster convergence rate can be achieved, demonstrating the great potential of MSES for atomistic simulations of larger and more complex IDPs

Tomographic observations of deep convection and the thermal evolution of the Greenland Sea Gyre, 1988-1989

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution February 1994The thermal evolution of the Greenland Sea Gyre is investigated using both historical data and tomographic results from the 1988-89 Greenland Sea Tomography Experiment. Thermal evolution of the gyre center divides naturally into three periods: a preconditioning phase (November-January), during which surface salinity is increased by brine rejection from ice formation and by entrainment but in which the mixed-layer deepens only slowly to a depth of some 150-200m, a deep mixing phase (February-March) during which the surface mixed-layer deepens rapidly to approximately 1500m in the gyre center purely under the influence of local surface cooling, and a restratification phase during which the products of deep mixing are replaced by inflowing Arctic Intermediate Water (AIW). The onset of the deep mixing phase occurs after ice formation in the gyre center stops, resulting in an area of open water where large heat fluxes can occur. In surrounding regions, including the odden region to the south, ice is still being formed, and the mixed layer does not deepen significantly. To the north and west, closer to the steep topography of the continental shelf, the inverse results show significant variability due to advection, and large temperature and heat content fluctuations with a period of about 50 days are seen. The effects of advection are deduced from heat and salt budgets, and appear to be important only during the restratification phase for intermediate depths, and only during the summer for the surface waters. Comparison of the tomographic results with point measurements indicates that deep mixing occurs in a field of small plumes in which dense water sinks downwards, surrounded by larger regions of upwelling. The plume geometry is consistent with that predicted by numerical and laboratory models. Dynamical processes for bringing the AIW to the surface in order to form deep water are not needed in this scenario, rather the surface waters are modified until they match the density of the AIW after which surface cooling drives convection

Determination of losing and gaining reaches in Arid and Semi-Arid environments of NSW

During the last decade, surface groundwater connectivity has become a major issue for water resources management in NSW. Consequently, as part of this PhD study, I have applied heat an environmental tracer to study infiltration/exfiltration in two contrasting hydro-geomorphological environments in NSW, Australia (Peel, Cockburn and Gunnedah sites in the Namoi Catchment, and Baldry and Sloans sites in the Central West Catchment). In the context of this thesis, the hydrological processes targeted of relevance to water resources management are grouped into three main issues listed below: 1. Delineation gaining and losing reaches within the study area using heat as an environmental tracer; 2. Inference of the dynamic nature of stream bed conductance from a thermal stream bed data; 3. Importance the issue of scale in surface/groundwater connectivity studies

Molecular Dynamics Simulation

Condensed matter systems, ranging from simple fluids and solids to complex multicomponent materials and even biological matter, are governed by well understood laws of physics, within the formal theoretical framework of quantum theory and statistical mechanics. On the relevant scales of length and time, the appropriate ‘first-principles’ description needs only the Schroedinger equation together with Gibbs averaging over the relevant statistical ensemble. However, this program cannot be carried out straightforwardly—dealing with electron correlations is still a challenge for the methods of quantum chemistry. Similarly, standard statistical mechanics makes precise explicit statements only on the properties of systems for which the many-body problem can be effectively reduced to one of independent particles or quasi-particles. [...

Abstracts of manuscripts submitted in 1993 for publication

This volume contains the abstracts of manuscripts submitted for publication during calendar year 1993 by the staff and students of the Woods Hole Oceanographic Institution. We identify the journal of those manuscripts which are in press or have been published. The volume is intended to be informative, but not a bibliography. The abstracts are listed by title in the Table of Contents and ar grouped into one of our five departents, Marine Policy Center, Coastal Research Center, or the student category. An author index is presented in the back to facilitate locating specific papers