Shine-Dalgarno (SD) signal has long been viewed as the dominant translation initiation signal in prokaryotes. Recently, leaderless genes, which lack 5'-untranslated regions (5'-UTR) on their mRNAs, have been shown abundant in archaea. However, current large-scale in silico analyses on initiation mechanisms in bacteria are mainly based on the SD-led initiation way, other than the leaderless one. The study of leaderless genes in bacteria remains open, which causes uncertain understanding of translation initiation mechanisms for prokaryotes.

First-principle-based prediction of mean-flow quantities of wall-bounded turbulent flows (channel, pipe and turbulent boundary layer (TBL)) is of great importance from both physics and engineering standpoints. Here we present a symmetry-based approach which yields analytical expressions for the mean-velocity profile (MVP) from a Lie-group analysis. After verifying the dilatation-group invariance of the Reynolds averaged Navier–Stokes (RANS) equation in the presence of a wall, we depart from previous Lie-group studies of wall turbulence by selecting a stress length function as a similarity variable. We argue that this stress length function characterizes the symmetry property of wall flows having a simple dilatation-invariant form. Three kinds of (local) invariant forms of the length function are postulated, a combination of which yields a multi-layer formula giving its distribution in the entire flow region normal to the wall and hence also the MVP, using the mean-momentum equation. In particular, based on this multi-layer formula, we obtain analytical expressions for the (universal) wall function and separate wake functions for pipe and channel, which are validated by data from direct numerical simulations (DNS). In conclusion, an analytical expression for the entire MVP of wall turbulence, beyond the log law or power law, is developed in this paper and the theory can be used to describe the mean turbulent kinetic-energy distribution, as well as a variety of boundary conditions such as pressure gradient, wall roughness, buoyancy, etc. where the dilatation-group invariance is valid in the wall-normal direction.

Background: Protein secondary structure prediction method based on probabilistic models such as hidden Markov model (HMM) appeals to many because it provides meaningful information relevant to sequence-structure relationship. However, at present, the prediction accuracy of pure HMM-type methods is much lower than that of machine learning-based methods such as neural networks (NN) or support vector machines (SVM). Results: In this paper, we report a new method of probabilistic nature for protein secondary structure prediction, based on dynamic Bayesian networks (DBN). The new method models the PSI-BLAST profile of a protein sequence using a multivariate Gaussian distribution, and simultaneously takes into account the dependency between the profile and secondary structure and the dependency between profiles of neighboring residues. In addition, a segment length distribution is introduced for each secondary structure state. Tests show that the DBN method has made a significant improvement in the accuracy compared to other pure HMM-type methods. Further improvement is achieved by combining the DBN with an NN, a method called DBNN, which shows better Q ₃ accuracy than many popular methods and is competitive to the current state-of-the-arts. The most interesting feature of DBN/DBNN is that a significant improvement in the prediction accuracy is achieved when combined with other methods by a simple consensus. Conclusion: The DBN method using a Gaussian distribution for the PSI-BLAST profile and a high-ordered dependency between profiles of neighboring residues produces significantly better prediction accuracy than other HMM-type probabilistic methods. Owing to their different nature, the DBN and NN combine to form a more accurate method DBNN. Future improvement may be achieved by combining DBNN with a method of SVM type.

Despite dedicated effort for many decades, statistical description of highly technologically important wall turbulence remains a great challenge. Current models are unfortunately incomplete, or empirical, or qualitative. After a review of the existing theories of wall turbulence, we present a new framework, called the structure ensemble dynamics (SED), which aims at integrating the turbulence dynamics into a quantitative description of the mean flow. The SED theory naturally evolves from a statistical physics understanding of non-equilibrium open systems, such as fluid turbulence, for which mean quantities are intimately coupled with the fluctuation dynamics. Starting from the ensemble-averaged Navier–Stokes (EANS) equations, the theory postulates the existence of a finite number of statistical states yielding a multi-layer picture for wall turbulence. Then, it uses order functions (ratios of terms in the mean momentum as well as energy equations) to characterize the states and transitions between states. Application of the SED analysis to an incompressible channel flow and a compressible turbulent boundary layer shows that the order functions successfully reveal the multi-layer structure for wall-bounded turbulence, which arises as a quantitative extension of the traditional view in terms of sub-layer, buffer layer, log layer and wake. Furthermore, an idea of using a set of hyperbolic functions for modeling transitions between layers is proposed for a quantitative model of order functions across the entire flow domain. We conclude that the SED provides a theoretical framework for expressing the yet-unknown effects of fluctuation structures on the mean quantities, and offers new methods to analyze experimental and simulation data. Combined with asymptotic analysis, it also offers a way to evaluate convergence of simulations. The SED approach successfully describes the dynamics at both momentum and energy levels, in contrast with all prevalent approaches describing the mean velocity profile only. Moreover, the SED theoretical framework is general, independent of the flow system to study, while the actual functional form of the order functions may vary from flow to flow. We assert that as the knowledge of order functions is accumulated and as more flows are analyzed, new principles (such as hierarchy, symmetry, group invariance, etc.) governing the role of turbulent structures in the mean flow properties will be clarified and a viable theory of turbulence might emerge.

We present new scaling expressions, including high-Reynolds-number ( $Re$ ) predictions, for all Reynolds stress components in the entire flow domain of turbulent channel and pipe flows. In Part 1 (She et al., J. Fluid Mech., vol. 827, 2017, pp. 322–356), based on the dilation symmetry of the mean Navier–Stokes equation a four-layer formula of the Reynolds shear stress length $\ell _{12}$ – and hence also the entire mean velocity profile (MVP) – was obtained. Here, random dilations on the second-order balance equations for all the Reynolds stresses (shear stress $-\overline{u^{\prime }v^{\prime }}$ , and normal stresses $\overline{u^{\prime }u^{\prime }}$ , $\overline{v^{\prime }v^{\prime }}$ , $\overline{w^{\prime }w^{\prime }}$ ) are analysed layer by layer, and similar four-layer formulae of the corresponding stress length functions $\ell _{11}$ , $\ell _{22}$ , $\ell _{33}$ (hence the three turbulence intensities) are obtained for turbulent channel and pipe flows. In particular, direct numerical simulation (DNS) data are shown to agree well with the four-layer formulae for $\ell _{12}$ and $\ell _{22}$ – which have the celebrated linear scalings in the logarithmic layer, i.e. $\ell _{12}\approx \unicode[STIX]{x1D705}y$ and $\ell _{22}\approx \unicode[STIX]{x1D705}_{22}y$ . However, data show an invariant peak location for $\overline{w^{\prime }w^{\prime }}$ , which theoretically leads to an anomalous scaling in $\ell _{33}$ in the log layer only, namely $\ell _{33}\propto y^{1-\unicode[STIX]{x1D6FE}}$ with $\unicode[STIX]{x1D6FE}\approx 0.07$ . Furthermore, another mesolayer modification of $\ell _{11}$ yields the experimentally observed location and magnitude of the outer peak of $\overline{u^{\prime }u^{\prime }}$ . The resulting $-\overline{u^{\prime }v^{\prime }}$ , $\overline{u^{\prime }u^{\prime }}$ , $\overline{v^{\prime }v^{\prime }}$ and $\overline{w^{\prime }w^{\prime }}$ are all in good agreement with DNS and experimental data in the entire flow domain. Our additional results include: (1) the maximum turbulent production is located at $y^{+}\approx 12$ ; (2) the location of peak value $-\overline{u^{\prime }v^{\prime }}_{p}$ has a scaling transition from $5.7Re_{\unicode[STIX]{x1D70F}}^{1/3}$ to $1.5Re_{\unicode[STIX]{x1D70F}}^{1/2}$ at $Re_{\unicode[STIX]{x1D70F}}\approx 3000$ , with a $1+\overline{u^{\prime }v^{\prime }}_{p}^{+}$ scaling transition from $8.5Re_{\unicode[STIX]{x1D70F}}^{-2/3}$ to $3.0Re_{\unicode[STIX]{x1D70F}}^{-1/2}$ ( $Re_{\unicode[STIX]{x1D70F}}$ the friction Reynolds number); (3) the peak value $\overline{w^{\prime }w^{\prime }}_{p}^{+}\approx 0.84Re_{\unicode[STIX]{x1D70F}}^{0.14}(1-48/Re_{\unicode[STIX]{x1D70F}})$ ; (4) the outer peak of $\overline{u^{\prime }u^{\prime }}$ emerges above $Re_{\unicode[STIX]{x1D70F}}\approx 10^{4}$ with its location scaling as $1.1Re_{\unicode[STIX]{x1D70F}}^{1/2}$ and its magnitude scaling as $2.8Re_{\unicode[STIX]{x1D70F}}^{0.09}$ ; (5) an alternative derivation of the log law of Townsend (1976, The Structure of Turbulent Shear Flow, Cambridge University Press), namely, $\overline{u^{\prime }u^{\prime }}^{+}\approx -1.25\ln y+1.63$ and $\overline{w^{\prime }w^{\prime }}^{+}\approx -0.41\ln y+1.00$ in the bulk.

Despite persistent efforts over the last century, a theory for predicting the effects of surface roughness on the mean flow is still missing. Here, we extend a recently proposed multi-state theory to incorporate roughness effects. A formula for the roughness function is constructed by applying the Lie-group invariance theory, giving excellent agreement with the fully collapsed data of both the Nikuradze sand-coated and Princeton honed pipes. A major advantage of the theory is its ability to successfully describe the non-universality—either inflectional or monotonic variations—in a transitionally rough regime with a single sharpness parameter. This model then yields an analytic prediction for the friction factor and mean velocity profiles in rough pipes, agreeing with the empirical data. Consistent with classical understanding (e.g. Townsend's similarity hypothesis), our results confirm the multi-layer theory of wall turbulence, regardless of smooth or rough surfaces.