Uncovering the Properties of Energy-Weighted Conformation Space Networks with a Hydrophobic-Hydrophilic Model

The conformation spaces generated by short hydrophobic-hydrophilic (HP) lattice chains are mapped to conformation space networks (CSNs). The vertices (nodes) of the network are the conformations and the links are the transitions between them. It has been found that these networks have “small-world” properties without considering the interaction energy of the monomers in the chain, i. e. the hydrophobic or hydrophilic amino acids inside the chain. When the weight based on the interaction energy of the monomers in the chain is added to the CSNs, it is found that the weighted networks show the “scale-free” characteristic. In addition, it reveals that there is a connection between the scale-free property of the weighted CSN and the folding dynamics of the chain by investigating the relationship between the scale-free structure of the weighted CSN and the noted parameter Z score. Moreover, the modular (community) structure of weighted CSNs is also studied. These results are helpful to understand the topological properties of the CSN and the underlying free-energy landscapes

Free energy score spaces: using generative information in discriminative classifiers

A score function induced by a generative model of the data can provide a feature vector of a fixed dimension for eachdata sample. Data samples themselves may be of differing lengths (e.g., speech segments, or other sequential data), but as ascore function is based on the properties of the data generation process, it produces a fixed-length vector in a highly informativespace, typically referred to as \u201cscore space\u201d. Discriminative classifiers have been shown to achieve higher performances inappropriately chosen score spaces with respect to what is achievable by either the corresponding generative likelihood-basedclassifiers, or the discriminative classifiers using standard feature extractors. In this paper, we present a novel score space thatexploits the free energy associated with a generative model. The resulting free energy score space (FESS) takes into accountthe latent structure of the data at various levels, and can be shown to lead to classification performance that at least matchesthe performance of the free energy classifier based on the same generative model, and the same factorization of the posterior.We also show that in several typical computer vision and computational biology applications the classifiers optimized in FESSoutperform the corresponding pure generative approaches, as well as a number of previous approaches combining discriminatingand generative models

A Seeded Genetic Algorithm for RNA Secondary Structural Prediction with Pseudoknots

This work explores a new approach in using genetic algorithm to predict RNA secondary structures with pseudoknots. Since only a small portion of most RNA structures is comprised of pseudoknots, the majority of structural elements from an optimal pseudoknot-free structure are likely to be part of the true structure. Thus seeding the genetic algorithm with optimal pseudoknot-free structures will more likely lead it to the true structure than a randomly generated population. The genetic algorithm uses the known energy models with an additional augmentation to allow complex pseudoknots. The nearest-neighbor energy model is used in conjunction with Turner’s thermodynamic parameters for pseudoknot-free structures, and the H-type pseudoknot energy estimation for simple pseudoknots. Testing with known pseudoknot sequences from PseudoBase shows that it out performs some of the current popular algorithms

Clustering in Hilbert space of a quantum optimization problem

The solution space of many classical optimization problems breaks up into clusters which are extensively distant from one another in the Hamming metric. Here, we show that an analogous quantum clustering phenomenon takes place in the ground state subspace of a certain quantum optimization problem. This involves extending the notion of clustering to Hilbert space, where the classical Hamming distance is not immediately useful. Quantum clusters correspond to macroscopically distinct subspaces of the full quantum ground state space which grow with the system size. We explicitly demonstrate that such clusters arise in the solution space of random quantum satisfiability (3-QSAT) at its satisfiability transition. We estimate both the number of these clusters and their internal entropy. The former are given by the number of hardcore dimer coverings of the core of the interaction graph, while the latter is related to the underconstrained degrees of freedom not touched by the dimers. We additionally provide new numerical evidence suggesting that the 3-QSAT satisfiability transition may coincide with the product satisfiability transition, which would imply the absence of an intermediate entangled satisfiable phase.Comment: 11 pages, 6 figure

Variational Hamiltonian Monte Carlo via Score Matching

Traditionally, the field of computational Bayesian statistics has been divided into two main subfields: variational methods and Markov chain Monte Carlo (MCMC). In recent years, however, several methods have been proposed based on combining variational Bayesian inference and MCMC simulation in order to improve their overall accuracy and computational efficiency. This marriage of fast evaluation and flexible approximation provides a promising means of designing scalable Bayesian inference methods. In this paper, we explore the possibility of incorporating variational approximation into a state-of-the-art MCMC method, Hamiltonian Monte Carlo (HMC), to reduce the required gradient computation in the simulation of Hamiltonian flow, which is the bottleneck for many applications of HMC in big data problems. To this end, we use a {\it free-form} approximation induced by a fast and flexible surrogate function based on single-hidden layer feedforward neural networks. The surrogate provides sufficiently accurate approximation while allowing for fast exploration of parameter space, resulting in an efficient approximate inference algorithm. We demonstrate the advantages of our method on both synthetic and real data problems

Building Water Models, A Different Approach

Simplified, classical models of water are an integral part of atomistic molecular simulations, especially in biology and chemistry where hydration effects are critical. Yet, despite several decades of effort, these models are still far from perfect. Presented here is an alternative approach to constructing point charge water models - currently, the most commonly used type. In contrast to the conventional approach, we do not impose any geometry constraints on the model other than symmetry. Instead, we optimize the distribution of point charges to best describe the "electrostatics" of the water molecule, which is key to many unusual properties of liquid water. The search for the optimal charge distribution is performed in 2D parameter space of key lowest multipole moments of the model, to find best fit to a small set of bulk water properties at room temperature. A virtually exhaustive search is enabled via analytical equations that relate the charge distribution to the multipole moments. The resulting "optimal" 3-charge, 4-point rigid water model (OPC) reproduces a comprehensive set of bulk water properties significantly more accurately than commonly used rigid models: average error relative to experiment is 0.76%. Close agreement with experiment holds over a wide range of temperatures, well outside the ambient conditions at which the fit to experiment was performed. The improvements in the proposed water model extend beyond bulk properties: compared to the common rigid models, predicted hydration free energies of small molecules in OPC water are uniformly closer to experiment, root-mean-square error < 1kcal/mol