Estimating the Accuracy of Spectral Learning for HMMs

Hidden Markov models (HMMs) are usually learned using the expectation maximisation algorithm which is, unfortunately, subject to local optima. Spectral learning for HMMs provides a unique, optimal solution subject to availability of a sufficient amount of data. However, with access to limited data, there is no means of estimating the accuracy of the solution of a given model. In this paper, a new spectral evaluation method has been proposed which can be used to assess whether the algorithm is converging to a stable solution on a given dataset. The proposed method is designed for real-life datasets where the true model is not available. A number of empirical experiments on synthetic as well as real datasets indicate that our criterion is an accurate proxy to measure quality of models learned using spectral learning

Comprehensive features of natural and in vitro selected GNRA tetraloop-binding receptors

Specific recognitions of GNRA tetraloops by small helical receptors are among the most widespread long-range packing interactions in large ribozymes. However, in contrast to GYRA and GAAA tetraloops, very few GNRA/receptor interactions have yet been identified to involve GGAA tetraloops in nature. A novel in vitro selection scheme based on a rigid self-assembling tectoRNA scaffold designed for isolation of intermolecular interactions with A-minor motifs has yielded new GGAA tetraloop-binding receptors with affinity in the nanomolar range. One of the selected receptors is a novel 12 nt RNA motif, (CCUGUG … AUCUGG), that recognizes GGAA tetraloop hairpin with a remarkable specificity and affinity. Its physical and chemical characteristics are comparable to those of the well-studied ‘11nt’ GAAA tetraloop receptor motif. A second less specific motif (CCCAGCCC … GAUAGGG) binds GGRA tetraloops and appears to be related to group IC3 tetraloop receptors. Mutational, thermodynamic and comparative structural analysis suggests that natural and in vitro selected GNRA receptors can essentially be grouped in two major classes of GNRA binders. New insights about the evolution, recognition and structural modularity of GNRA and A-minor RNA–RNA interactions are proposed

Attenuation of loop-receptor interactions with pseudoknot formation

RNA tetraloops can recognize receptors to mediate long-range interactions in stable natural RNAs. In vitro selected GNRA tetraloop/receptor interactions are usually more ‘G/C-rich’ than their ‘A/U-rich’ natural counterparts. They are not as widespread in nature despite comparable biophysical and chemical properties. Moreover, while AA, AC and GU dinucleotide platforms occur in natural GAAA/11 nt receptors, the AA platform is somewhat preferred to the others. The apparent preference for ‘A/U-rich’ GNRA/receptor interactions in nature might stem from an evolutionary adaptation to avoid folding traps at the level of the larger molecular context. To provide evidences in favor of this hypothesis, several riboswitches based on natural and artificial GNRA receptors were investigated in vitro for their ability to prevent inter-molecular GNRA/receptor interactions by trapping the receptor sequence into an alternative intra-molecular pseudoknot. Extent of attenuation determined by native gel-shift assays and co-transcriptional assembly is correlated to the G/C content of the GNRA receptor. Our results shed light on the structural evolution of natural long-range interactions and provide design principles for RNA-based attenuator devices to be used in synthetic biology and RNA nanobiotechnology

Promoting RNA helical stacking via A-minor junctions

RNA molecules take advantage of prevalent structural motifs to fold and assemble into well-defined 3D architectures. The A-minor junction is a class of RNA motifs that specifically controls coaxial stacking of helices in natural RNAs. A sensitive self-assembling supra-molecular system was used as an assay to compare several natural and previously unidentified A-minor junctions by native polyacrylamide gel electrophoresis and atomic force microscopy. This class of modular motifs follows a topological rule that can accommodate a variety of interchangeable A-minor interactions with distinct local structural motifs. Overall, two different types of A-minor junctions can be distinguished based on their functional self-assembling behavior: one group makes use of triloops or GNRA and GNRA-like loops assembling with helices, while the other takes advantage of more complex tertiary receptors specific for the loop to gain higher stability. This study demonstrates how different structural motifs of RNA can contribute to the formation of topologically equivalent helical stacks. It also exemplifies the need of classifying RNA motifs based on their tertiary structural features rather than secondary structural features. The A-minor junction rule can be used to facilitate tertiary structure prediction of RNAs and rational design of RNA parts for nanobiotechnology and synthetic biology

The impact of education on unemployment incidence and re-employment success: Evidence from the U.S. labour market

This study investigates the causal effects of education on individuals' transitions between employment and unemployment, with particular focus on the extent to which education improves re-employment outcomes among unemployed workers. Given that positive correlations between education and labour force transitions are likely to be confounded by the endogeneity of education, we make use of data on compulsory schooling laws and child labour laws as well as conscription risk in the Vietnam War period to create instrumental variables to identify the causal relationships. Results indicate that education significantly increases re-employment rates of the unemployed. Particularly large impacts are found in the neighborhoods of 12 and 16 years of schooling. Evidence on the impact of formal schooling on unemployment incidence is mixed

Condensation of Hard Spheres Under Gravity: Exact Results in One Dimension

We present exact results for the density profile of the one dimensional array of N hard spheres of diameter D and mass m under gravity g. For a strictly one dimensional system, the liquid-solid transition occurs at zero temperature, because the close-pakced density, $\phi_c$, is one. However, if we relax this condition slightly such that $phi_c=1-\delta$, we find a series of critical temperatures T_c^i=mgD(N+1-i)/\mu_o with \mu_o=const, at which the i-th particle undergoes the liquid-solid transition. The functional form of the onset temperature, T_c^1=mgDN/\mu_o, is consistent with the previous result [Physica A 271, 192 (1999)] obtained by the Enskog equation. We also show that the increase in the center of mass is linear in T before the transition, but it becomes quadratic in T after the transition because of the formation of solid near the bottom

The diagonalization method in quantum recursion theory

As quantum parallelism allows the effective co-representation of classical mutually exclusive states, the diagonalization method of classical recursion theory has to be modified. Quantum diagonalization involves unitary operators whose eigenvalues are different from one.Comment: 15 pages, completely rewritte

The UA_handle: a versatile submotif in stable RNA architectures†

Stable RNAs are modular and hierarchical 3D architectures taking advantage of recurrent structural motifs to form extensive non-covalent tertiary interactions. Sequence and atomic structure analysis has revealed a novel submotif involving a minimal set of five nucleotides, termed the UA_handle motif (5′XU/ANnX3′). It consists of a U:A Watson–Crick: Hoogsteen trans base pair stacked over a classic Watson–Crick base pair, and a bulge of one or more nucleotides that can act as a handle for making different types of long-range interactions. This motif is one of the most versatile building blocks identified in stable RNAs. It enters into the composition of numerous recurrent motifs of greater structural complexity such as the T-loop, the 11-nt receptor, the UAA/GAN and the G-ribo motifs. Several structural principles pertaining to RNA motifs are derived from our analysis. A limited set of basic submotifs can account for the formation of most structural motifs uncovered in ribosomal and stable RNAs. Structural motifs can act as structural scaffoldings and be functionally and topologically equivalent despite sequence and structural differences. The sequence network resulting from the structural relationships shared by these RNA motifs can be used as a proto-language for assisting prediction and rational design of RNA tertiary structures

The Dimeric Proto-Ribosome: Structural Details and Possible Implications on the Origin of Life

A symmetric pocket-like entity, composed of two L-shaped RNA units, encircles the peptide synthesis site within the contemporary ribosome. This entity was suggested to be the vestige of a dimeric proto-ribosome, which could have formed spontaneously in the prebiotic world, catalyzing non-coded peptide bond formation and elongation. This structural element, beyond offering the initial step in the evolution of translation, is hypothesized here to be linked to the origin of life. By catalyzing the production of random peptide chains, the proto-ribosome could have enabled the formation of primary enzymes, launching a process of co-evolution of the translation apparatus and the proteins, thus presenting an alternative to the RNA world hypothesis

Modeling accuracy as a function of response time with the generalised linear mixed effects model

In psycholinguistic studies using error rates as a response measure, response times (RT) are most often analyzed independently of the error rate, although it is widely recognized that they are related. In this paper we present a mixed effects logistic regression model for the error rate that uses RT as a trial-level fixed- and random-effect regression input. Production data from a translation–recall experiment are analyzed as an example. Several model comparisons reveal that RT improves the fit of the regression model for the error rate. Two simulation studies then show how the mixed effects regression model can identify individual participants for whom (a) faster responses are more accurate, (b) faster responses are less accurate, or (c) there is no relation between speed and accuracy. These results show that this type of model can serve as a useful adjunct to traditional techniques, allowing psycholinguistic researchers to examine more closely the relationship between RT and accuracy in individual subjects and better account for the variability which may be present, as well as a preliminary step to more advanced RT–accuracy modeling