Evolutionary Approaches to Optimization Problems in Chimera Topologies

Chimera graphs define the topology of one of the first commercially available quantum computers. A variety of optimization problems have been mapped to this topology to evaluate the behavior of quantum enhanced optimization heuristics in relation to other optimizers, being able to efficiently solve problems classically to use them as benchmarks for quantum machines. In this paper we investigate for the first time the use of Evolutionary Algorithms (EAs) on Ising spin glass instances defined on the Chimera topology. Three genetic algorithms (GAs) and three estimation of distribution algorithms (EDAs) are evaluated over $1000$ hard instances of the Ising spin glass constructed from Sidon sets. We focus on determining whether the information about the topology of the graph can be used to improve the results of EAs and on identifying the characteristics of the Ising instances that influence the success rate of GAs and EDAs.Comment: 8 pages, 5 figures, 3 table

Editorial

In fact, much of the attraction of network theory initially stemmed from the fact that many networks seem to exhibit some sort of universality, as most of them belong to one of three classes: random, scale-free and small-world networks. Structural properties have been shown to translate into different important properties of a given system, including efficiency, speed of information processing, vulnerability to various forms of stress, and robustness. For example, scale-free and random topologies were shown to be..

A STUDY OF QUANTUM ANNEALING DEVICES FROM A CLASSICAL PERSPECTIVE

Spin glasses are experiencing a revival due to applications in quantum information theory. In particular, they are the archetypal native benchmark problem for quantum annealing machines. Furthermore, they find applications in fields as diverse as satisfiability, neural networks, and general combinatorial optimization problems. As such, developing and improving algorithms and methods to study these computationally complex systems is of paramount importance to many disciplines. This body of work attempts to attack the problem of solving combinatorial optimization problems by simulating spin glasses from three sides: classical algorithm development, suggestions for quantum annealing device design, and improving measurements in realistic physical systems with inherent noise. I begin with the introduction of a cluster algorithm based on Houdayer’s cluster algorithm for two-dimensional Ising spin-glasses that is applicable to any space dimension and speeds up thermalization by several orders of magnitude at low temperatures where previous algorithms have difficulty. I show improvement for the D-Wave chimera topology and the three-dimensional cubic lattice that increases with the size of the problem. One consequence of adding cluster moves is that for problems with degenerate solutions, ground-state sampling is improved. I demonstrate an ergodic algorithm to sample ground states through the use of simple Monte Carlo with parallel tempering and cluster moves. In addition, I present a non-ergodic algorithm to generate new solutions from a bank of known solutions. I compare these results against results from quantum annealing utilizing the D-Wave Inc. quantum annealing device. Finally, I present an algorithm for improving the recovery of ground-state solutions from problems with noise by using thermal fluctuations to infer the correct solution at the Nishimori temperature. While this method has been demonstrated analytically and numerically for trivial ferromagnetic and Gaussian distributions, a useful metric for more complex Gaussian distributions with added Gaussian noise is unavailable. We show improved recovery of numerical solutions on the chimera graph with a ferromagnetic distribution and added Gaussian noise. Next, I direct my focus to the design of future generations of quantum annealers. The first design is the two-dimensional square-lattice bimodal spin glass with next-nearest ferrromagnetic interactions proposed by Lemke and Campbell claimed to exhibit a finite-temperature spin-glass state for a particular relative strength of the next-nearest to nearest neighbor interactions. Our results from finite-temperature simulations show the system is in a paramagnetic state in the thermodynamic limit, thus not useful for quantum annealing device designs that would benefit from a spin-glass phase transition. The second design is the diluted next-nearest neighbor Ising spin-glass with Gaussian interactions in an attempt to improve the estimation of critical parameter with smaller system sizes by implementing averaging of observables over different graph dilutions. To date, this model has shown no improvement. Finally, I make suggestions for the choice of distributions of interactions that are robust to noise and present a method for using previously unaccessible continuous distributions. I begin with showing the best-case performance of quantum annealing devices. I show results for the resilience, the probability that the ground-state solution has changed due to inherent analog noise in the device, and present strategies for developing robust instance classes. The analog noise is also detrimental to interactions chosen from continuous distributions. Using Gaussian quadratures, I present a method for discretizing continuous distributions to reduce noise effects. Simulations on the D-Wave show that the average residual of the ground-state energy with the true ground-state energy is calculated and shown to be smaller in the case of the discrete distribution

A topological approach for protein classification

Protein function and dynamics are closely related to its sequence and structure. However prediction of protein function and dynamics from its sequence and structure is still a fundamental challenge in molecular biology. Protein classification, which is typically done through measuring the similarity be- tween proteins based on protein sequence or physical information, serves as a crucial step toward the understanding of protein function and dynamics. Persistent homology is a new branch of algebraic topology that has found its success in the topological data analysis in a variety of disciplines, including molecular biology. The present work explores the potential of using persistent homology as an indepen- dent tool for protein classification. To this end, we propose a molecular topological fingerprint based support vector machine (MTF-SVM) classifier. Specifically, we construct machine learning feature vectors solely from protein topological fingerprints, which are topological invariants generated during the filtration process. To validate the present MTF-SVM approach, we consider four types of problems. First, we study protein-drug binding by using the M2 channel protein of influenza A virus. We achieve 96% accuracy in discriminating drug bound and unbound M2 channels. Additionally, we examine the use of MTF-SVM for the classification of hemoglobin molecules in their relaxed and taut forms and obtain about 80% accuracy. The identification of all alpha, all beta, and alpha-beta protein domains is carried out in our next study using 900 proteins. We have found a 85% success in this identifica- tion. Finally, we apply the present technique to 55 classification tasks of protein superfamilies over 1357 samples. An average accuracy of 82% is attained. The present study establishes computational topology as an independent and effective alternative for protein classification

FastTree 2 – Approximately Maximum-Likelihood Trees for Large Alignments

Background: We recently described FastTree, a tool for inferring phylogenies for alignments with up to hundreds of thousands of sequences. Here, we describe improvements to FastTree that improve its accuracy without sacrificing scalability. Methodology/Principal Findings: Where FastTree 1 used nearest-neighbor interchanges (NNIs) and the minimum-evolution criterion to improve the tree, FastTree 2 adds minimum-evolution subtree-pruning-regrafting (SPRs) and maximumlikelihood NNIs. FastTree 2 uses heuristics to restrict the search for better trees and estimates a rate of evolution for each site (the ‘‘CAT’ ’ approximation). Nevertheless, for both simulated and genuine alignments, FastTree 2 is slightly more accurate than a standard implementation of maximum-likelihood NNIs (PhyML 3 with default settings). Although FastTree 2 is not quite as accurate as methods that use maximum-likelihood SPRs, most of the splits that disagree are poorly supported, and for large alignments, FastTree 2 is 100–1,000 times faster. FastTree 2 inferred a topology and likelihood-based local support values for 237,882 distinct 16S ribosomal RNAs on a desktop computer in 22 hours and 5.8 gigabytes of memory. Conclusions/Significance: FastTree 2 allows the inference of maximum-likelihood phylogenies for huge alignments

Computation in Complex Networks

Complex networks are one of the most challenging research focuses of disciplines, including physics, mathematics, biology, medicine, engineering, and computer science, among others. The interest in complex networks is increasingly growing, due to their ability to model several daily life systems, such as technology networks, the Internet, and communication, chemical, neural, social, political and financial networks. The Special Issue “Computation in Complex Networks" of Entropy offers a multidisciplinary view on how some complex systems behave, providing a collection of original and high-quality papers within the research fields of: • Community detection • Complex network modelling • Complex network analysis • Node classification • Information spreading and control • Network robustness • Social networks • Network medicin