Equilibrium and dynamic methods when comparing an English text and its Esperanto translation

A comparison of two English texts written by Lewis Carroll, one (Alice in Wonderland), also translated into Esperanto, the other (Through the Looking Glass) are discussed in order to observe whether natural and artificial languages significantly differ from each other. One dimensional time series like signals are constructed using only word frequencies (FTS) or word lengths (LTS). The data is studied through (i) a Zipf method for sorting out correlations in the FTS and (ii) a Grassberger-Procaccia (GP) technique based method for finding correlations in LTS. The methods correspond to an equilibrium and a dynamic approach respectively to human texts features. There are quantitative statistical differences between the original English text and its Esperanto translation, but the qualitative differences are very minutes. However different power laws are observed with characteristic exponents for the ranking properties, and the phase space attractor dimensionality. The Zipf exponent can take values much less than unity (∼0.50 or 0.30) depending on how a sentence is defined. This variety in exponents can be conjectured to be an intrinsic measure of the book style or purpose, rather than the language or author vocabulary richness, since a similar exponent is obtained whatever the text. Moreover the attractor dimension r is a simple function of the so called phase space dimension n, i.e., r=n^λ, with λ=0.79. Such an exponent could also be conjectured to be a measure of the author style versatility, — here well preserved in the translation.     

FFT-based homogenization on periodic anisotropic translation invariant spaces

In this paper we derive a discretisation of the equation of quasi-static elasticity in homogenization in form of a variational formulation and the so-called Lippmann–Schwinger equation, in anisotropic spaces of translates of periodic functions. We unify and extend the truncated Fourier series approach, the constant finite element ansatz and the anisotropic lattice derivation. The resulting formulation of the Lippmann–Schwinger equation in anisotropic translation invariant spaces unifies and analyses for the first time both the Fourier methods and finite element approaches in a common mathematical framework. We further define and characterize the resulting periodised Green operator. This operator coincides in case of a Dirichlet kernel corresponding to a diagonal matrix with the operator derived for the Galerkin projection stemming from the truncated Fourier series approach and to the anisotropic lattice derivation for all other Dirichlet kernels. Additionally, we proof the boundedness of the periodised Green operator. The operator further constitutes a projection if and only if the space of translates is generated by a Dirichlet kernel. Numerical examples for both de la Vallée Poussin means and Box splines illustrate the flexibility of this framework.     

Attractors for non-autonomous wave equations with a new class of external forces

We introduce a new concept Condition (C*), and denote the set of all functions satisfying Condition (C*) by , which are translation bounded but not translation compact in , and we show that there are many functions satisfying Condition (C*); then, in application, we obtain the existence of uniform attractors in for non-autonomous wave equations involving mixed differential quotient terms with this new class of time dependent external forces .     

Ribosome kinetics and aa-tRNA competition determine rate and fidelity of peptide synthesis

It is generally accepted that the translation rate depends on the availability of cognate aa-tRNAs. In this study it is shown that the key factor that determines translation rate is the competition between near-cognate and cognate aa-tRNAs. The transport mechanism in the cytoplasm is diffusion, thus the competition between cognate, near-cognate and non-cognate aa-tRNAs to bind to the ribosome is a stochastic process. Two competition measures are introduced; C(i) and R(i) (i = 1, 64) are quotients of the arrival frequencies of near-cognates vs. cognates and non-cognates vs. cognates, respectively. Furthermore, the reaction rates of bound cognates differ from those of bound near-cognates. If a near-cognate aa-tRNA binds to the A site of the ribosome, it may be rejected at the anti-codon recognition step or proofreading step or it may be accepted. Regardless of its fate, the near-cognates and non-cognates have caused delays of varying duration to the observed rate of translation. Rate constants have been measured at a temperature of 20 °C by (Gromadski, K.B., Rodnina, M.V., 2004. Kinetic determinants of high-fidelity tRNA discrimination on the ribosome. Mol. Cell 13, 191–200). These rate constants have been re-evaluated at 37 °C, using experimental data at 24.5 °C and 37 °C (Varenne, S., et al., 1984. Translation in a non-uniform process: effect of tRNA availability on the rate of elongation of nascent polypeptide chains. J. Mol. Biol. 180, 549–576). The key results of the study are: (i) the average time (at 37 °C) to add an amino acid, as defined by the ith codon, to the nascent peptide chain is: τ(i) = 9.06 + 1.445 × [10.48C(i) + 0.5R(i)] (in ms); (ii) the misreading frequency is directly proportional to the near-cognate competition, E(i) = 0.0009C(i); (iii) the competition from near-cognates, and not the availability of cognate aa-tRNAs, is the most important factor that determines the translation rate – the four codons with highest near-cognate competition (in the case of E. coli) are [GCC] > [CGG] > [AGG] > [GGA], which overlap only partially with the rarest codons: [AGG] < [CCA] < [GCC] < [CAC]; (iv) based on the kinetic rates at 37 °C, the average time to insert a cognate amino acid is 9.06 ms and the average delay to process a near-cognate aa-tRNA is 10.45 ms and (vii) the model also provides estimates of the vacancy times of the A site of the ribosome – an important factor in frameshifting.     

In Situ Self-Assembly of Fluorogenic RNA Nanozipper Enables Real-Time Imaging of Single Viral mRNA Translation

Real-time visualization of individual viral mRNA translation activities in live cells is essential to obtain critical details of viral mRNA dynamics and to detect its transient responses to environmental stress. Fluorogenic RNA aptamers are powerful tools for real-time imaging of mRNA in live cells, but monitoring the translation activity of individual mRNAs remains a challenge due to their intrinsic photophysical properties. Here, we develop a genetically encoded turn-on 3,5-difluoro-4-hydroxybenzylidene imidazolinone (DFHBI)-binding RNA nanozipper with superior brightness and high photostability by in situ self-assembly of multiple nanozippers along single mRNAs. The nanozipper enables real-time imaging of the mobility and dynamic translation of individual viral mRNAs in live cells, providing information on the spatial dynamics and translational elongation rate of viral mRNAs.     

小波基按平移性的分类及非调和小波基

本文研究小波子空间与一般整平移空间可平移点集 Ｓ的结构,证明了 Ｓ＝Ｒ或者 Ｓ＝１／ｑＺ（ｑ ∈ Ｎ）．给出了可平移性的谱刻画与泛函刻画,最后讨论了非调和小波基．     

一类平面n+2次系统的定性分析

本文对一类具有实际意义的平面ｎ＋２次系统进行定性分析,得到了其极限环存在性、唯一性的较完整的大范围分析结果。