Prediction of RNA pseudoknots by Monte Carlo simulations

In this paper we consider the problem of RNA folding with pseudoknots. We use a graphical representation in which the secondary structures are described by planar diagrams. Pseudoknots are identified as non-planar diagrams. We analyze the non-planar topologies of RNA structures and propose a classification of RNA pseudoknots according to the minimal genus of the surface on which the RNA structure can be embedded. This classification provides a simple and natural way to tackle the problem of RNA folding prediction in presence of pseudoknots. Based on that approach, we describe a Monte Carlo algorithm for the prediction of pseudoknots in an RNA molecule.Comment: 22 pages, 14 figure

A very simple safe-Bayesian random forest

Random forests works by averaging several predictions of de-correlated trees. We show a conceptually radical approach to generate a random forest: random sampling of many trees from a prior distribution, and subsequently performing a weighted ensemble of predictive probabilities. Our approach uses priors that allow sampling of decision trees even before looking at the data, and a power likelihood that explores the space spanned by combination of decision trees. While each tree performs Bayesian inference to compute its predictions, our aggregation procedure uses the power likelihood rather than the likelihood and is therefore strictly speaking not Bayesian. Nonetheless, we refer to it as a Bayesian random forest but with a built-in safety. The safeness comes as it has good predictive performance even if the underlying probabilistic model is wrong. We demonstrate empirically that our Safe-Bayesian random forest outperforms MCMC or SMC based Bayesian decision trees in term of speed and accuracy, and achieves competitive performance to entropy or Gini optimised random forest, yet is very simple to construct

Projected single-spin flip dynamics in the Ising Model

We study transition matrices for projected dynamics in the energy-magnetization space, magnetization space and energy space. Several single spin flip dynamics are considered such as the Glauber and Metropolis canonical ensemble dynamics and the Metropolis dynamics for three multicanonical ensembles: the flat energy-magnetization histogram, the flat energy histogram and the flat magnetization histogram. From the numerical diagonalization of the matrices for the projected dynamics we obtain the sub-dominant eigenvalue and the largest relaxation times for systems of varying size. Although, the projected dynamics is an approximation to the full state space dynamics comparison with some available results, obtained by other authors, shows that projection in the magnetization space is a reasonably accurate method to study the scaling of relaxation times with system size. The transition matrices for arbitrary single-spin flip dynamics are obtained from a single Monte-Carlo estimate of the infinite temperature transition-matrix, for each system size, which makes the method an efficient tool to evaluate the relative performance of any arbitrary local spin-flip dynamics. We also present new results for appropriately defined average tunnelling times of magnetization and compute their finite-size scaling exponents that we compare with results of energy tunnelling exponents available for the flat energy histogram multicanonical ensemble.Comment: 23 pages and 6 figure

Remote sensing of sediment characteristics by optimized echo-envelope matching

A sediment geoacoustic parameter estimation technique is described which compares bottom returns, measured by a calibrated monostatic sonar oriented within 15° of vertical and having a 10°–21° beamwidth, with an echo envelope model based on high-frequency (10–100 kHz) incoherent backscattertheory and sediment properties such as: mean grain size, strength, and exponent of the power law characterizing the interface roughness energy density spectrum, and volume scattering coefficient. An average echo envelope matching procedure iterates on the reflection coefficient to match the peak echo amplitude and separate coarse from fine-grain sediments, followed by a global optimization using a combination of simulated annealing and downhill simplex searches over mean grain size, interface roughness spectral strength, and sediment volume scattering coefficient. Error analyses using Monte Carlo simulations validate this optimization procedure. Moderate frequencies (33 kHz) and orientations normal with the interface are best suited for this application. Distinction between sands and fine-grain sediments is demonstrated based on acoustic estimation of mean grain size alone. The creation of feature vectors from estimates of mean grain size and interface roughness spectral strength shows promise for intraclass separation of silt and clay. The correlation between estimated parameters is consistent with what is observed in situ