On the non-convergence of the Wang-Landau algorithms with multiple random walkers

This paper discusses some convergence properties in the entropic sampling Monte Carlo methods with multiple random walkers, particularly in the Wang-Landau (WL) and $1/t$ algorithms. The classical algorithms are modified by the use of $m$ independent random walkers in the energy landscape to calculate the density of states (DOS). The Ising model is used to show the convergence properties in the calculation of the DOS, as well as the critical temperature, while the calculation of the number $\pi$ by multiple dimensional integration is used in the continuum approximation. In each case, the error is obtained separately for each walker at a fixed time, $t$; then, the average over $m$ walkers is performed. It is observed that the error goes as $1/\sqrt{m}$. However, if the number of walkers increases above a certain critical value $m>m_x$, the error reaches a constant value (i.e. it saturates). This occurs for both algorithms; however, it is shown that for a given system, the $1/t$ algorithm is more efficient and accurate than the similar version of the WL algorithm. It follows that it makes no sense to increase the number of walkers above a critical value $m_x$, since it does not reduces the error in the calculation. Therefore, the number of walkers does not guarantee convergence.Comment: 10 pages, 12 figures, Regular Articl

Verification of Hierarchical Artifact Systems

Data-driven workflows, of which IBM's Business Artifacts are a prime exponent, have been successfully deployed in practice, adopted in industrial standards, and have spawned a rich body of research in academia, focused primarily on static analysis. The present work represents a significant advance on the problem of artifact verification, by considering a much richer and more realistic model than in previous work, incorporating core elements of IBM's successful Guard-Stage-Milestone model. In particular, the model features task hierarchy, concurrency, and richer artifact data. It also allows database key and foreign key dependencies, as well as arithmetic constraints. The results show decidability of verification and establish its complexity, making use of novel techniques including a hierarchy of Vector Addition Systems and a variant of quantifier elimination tailored to our context.Comment: Full version of the accepted PODS pape

Analysis of the convergence of the 1/t and Wang-Landau algorithms in the calculation of multidimensional integrals

In this communication, the convergence of the 1/t and Wang - Landau algorithms in the calculation of multidimensional numerical integrals is analyzed. Both simulation methods are applied to a wide variety of integrals without restrictions in one, two and higher dimensions. The errors between the exact and the calculated values of the integral are obtained and the efficiency and accuracy of the methods are determined by their dynamical behavior. The comparison between both methods and the simple sampling Monte Carlo method is also reported. It is observed that the time dependence of the errors calculated with 1/t algorithm goes as N^{-1/2} (with N the MC trials) in quantitative agreement with the simple sampling Monte Carlo method. It is also showed that the error for the Wang - Landau algorithm saturates in time evidencing the non-convergence of the methods. The sources for the error are also determined.Comment: 8 pages, 5 figure

Active role of elongation factor G in maintaining the mRNA reading frame during translation.

During translation, the ribosome moves along the mRNA one codon at a time with the help of elongation factor G (EF-G). Spontaneous changes in the translational reading frame are extremely rare, yet how the precise triplet-wise step is maintained is not clear. Here, we show that the ribosome is prone to spontaneous frameshifting on mRNA slippery sequences, whereas EF-G restricts frameshifting. EF-G helps to maintain the mRNA reading frame by guiding the A-site transfer RNA during translocation due to specific interactions with the tip of EF-G domain 4. Furthermore, EF-G accelerates ribosome rearrangements that restore the ribosome's control over the codon-anticodon interaction at the end of the movement. Our data explain how the mRNA reading frame is maintained during translation

Wang-Landau Algorithm: a Theoretical Analysis of the Saturation of the Error

In this work we present a theoretical analysis of the convergence of the Wang-Landau algorithm [Phys. Rev. Lett. 86, 2050 (2001)] which was introduced years ago to calculate the density of states in statistical models. We study the dynamical behavior of the error in the calculation of the density of states.We conclude that the source of the saturation of the error is due to the decreasing variations of the refinement parameter. To overcome this limitation, we present an analytical treatment in which the refinement parameter is scaled down as a power law instead of exponentially. An extension of the analysis to the N-fold way variation of the method is also discussed.Comment: 7 pages, 5 figure

Non-canonical binding site for bacterial initiation factor 3 on the large ribosomal subunit.

Canonical translation initiation in bacteria entails the assembly of the 30S initiation complex (IC), which binds the 50S subunit to form a 70S IC. IF3, a key initiation factor, is recruited to the 30S subunit at an early stage and is displaced from its primary binding site upon subunit joining. We employed four different FRET pairs to monitor IF3 relocation after 50S joining. IF3 moves away from the 30S subunit, IF1 and IF2, but can remain bound to the mature 70S IC. The secondary binding site is located on the 50S subunit in the vicinity of ribosomal protein L33. The interaction between IF3 and the 50S subunit is largely electrostatic with very high rates of IF3 binding and dissociation. The existence of the non-canonical binding site may help explain how IF3 participates in alternative initiation modes performed directly by the 70S ribosomes, such as initiation on leaderless mRNAs or re-initiation

Perturbation of ribosomal subunit dynamics by inhibitors of tRNA translocation

Many antibiotics that bind to the ribosome inhibit translation by blocking the movement of tRNAs and mRNA or interfering with ribosome dynamics, which impairs the formation of essential translocation intermediates. Here we show how translocation inhibitors viomycin (Vio), neomycin (Neo), paromomycin (Par), kanamycin (Kan), spectinomycin (Spc), hygromycin B (HygB), and streptomycin (Str, an antibiotic that does not inhibit tRNA movement), affect principal motions of the small ribosomal subunits (SSU) during EF-G-promoted translocation. Using ensemble kinetics, we studied the SSU body domain rotation and SSU head domain swiveling in real time. We show that although antibiotics binding to the ribosome can favor a particular ribosome conformation in the absence of EF-G, their kinetic effect on the EF-G-induced transition to the rotated/swiveled state of the SSU is moderate. The antibiotics mostly inhibit backward movements of the SSU body and/or the head domains. Vio, Spc, and high concentrations of Neo completely inhibit the backward movements of the SSU body and head domain. Kan, Par, HygB, and low concentrations of Neo slow down both movements, but their sequence and coordination are retained. Finally, Str has very little effect on the backward rotation of the SSU body domain, but retards the SSU head movement. The data underscore the importance of ribosome dynamics for tRNA-mRNA translocation and provide new insights into the mechanism of antibiotic action

Programmed –1 frameshifting by kinetic partitioning during impeded translocation.

Programmed –1 ribosomal frameshifting (−1PRF) is an mRNA recoding event utilized by cells to enhance the information content of the genome and to regulate gene expression. The mechanism of –1PRF and its timing during translation elongation are unclear. Here, we identified the steps that govern –1PRF by following the stepwise movement of the ribosome through the frameshifting site of a model mRNA derived from the IBV 1a/1b gene in a reconstituted in vitro translation system from Escherichia coli. Frameshifting occurs at a late stage of translocation when the two tRNAs are bound to adjacent slippery sequence codons of the mRNA. The downstream pseudoknot in the mRNA impairs the closing movement of the 30S subunit head, the dissociation of EF-G, and the release of tRNA from the ribosome. The slippage of the ribosome into the –1 frame accelerates the completion of translocation, thereby further favoring translation in the new reading frame