Applications in random matrix theory of a PIII’ τ-function sequence from Okamoto’s Hamiltonian formulation

We consider the singular linear statistic of the Laguerre unitary ensemble (LUE) consisting of the sum of the reciprocal of the eigenvalues. It is observed that the exponential generating function for this statistic can be written as a Toeplitz determinant with entries given in terms of particular [Formula: see text] Bessel functions. Earlier studies have identified the same determinant, but with the [Formula: see text] Bessel functions replaced by [Formula: see text] Bessel functions, as relating to the hard edge scaling limit of a generalized gap probability for the LUE, in the case of non-negative integer Laguerre parameter. We show that the Toeplitz determinant formed from an arbitrary linear combination of these two Bessel functions occurs as a [Formula: see text]-function sequence in Okamoto’s Hamiltonian formulation of Painlevé III[Formula: see text], and consequently the logarithmic derivative of both Toeplitz determinants satisfies the same [Formula: see text]-form Painlevé III[Formula: see text] differential equation, giving an explanation of a fact which can be observed from earlier results. In addition, some insights into the relationship between this characterization of the generating function, and its characterization in the [Formula: see text] limit, both with the Laguerre parameter [Formula: see text] fixed, and with [Formula: see text] (this latter circumstance being relevant to an application to the distribution of the Wigner time delay statistic), are given.

Knock-Down of a Novel snoRNA in Tetrahymena Reveals a Dual Role in 5.8S rRNA Processing and Generation of a 26S rRNA Fragment

In eukaryotes, 18S, 5.8S, and 28S rRNAs are transcribed as precursor molecules that undergo extensive modification and nucleolytic processing to form the mature rRNA species. Central in the process are the small nucleolar RNAs (snoRNAs). The majority of snoRNAs guide site specific chemical modifications but a few are involved in defining pre-rRNA cleavages. Here, we describe an unusual snoRNA (TtnuCD32) belonging to the box C/D subgroup from the ciliate Tetrahymena thermophila. We show that TtnuCD32 is unlikely to function as a modification guide snoRNA and that it is critical for cell viability. Cell lines with genetic knock-down of TtnuCD32 were impaired in growth and displayed two novel and apparently unrelated phenotypes. The most prominent phenotype is the accumulation of processing intermediates of 5.8S rRNA. The second phenotype is the decrease in abundance of a ~100 nt 26S rRNA fragment of unknown function. Sequence analysis demonstrated that TtnuCD32 share features with the essential snoRNA U14 but an alternative candidate (TtnuCD25) was more closely related to other U14 sequences. This, together with the fact that the observed rRNA processing phenotypes were not similar to what has been observed in U14 depleted cells, suggests that TtnuCD32 is a U14 homolog that has gained novel functions.

Fe oxidation by a fused cytochrome-porin common to diverse Fe-oxidizing bacteria

SummaryFe oxidation is one of Earth’s major biogeochemical processes, key to weathering, soil formation, water quality, and corrosion. However, our ability to track the contributions of Fe-oxidizing microbes is limited by our relatively incomplete knowledge of microbial Fe oxidation mechanisms, particularly in neutrophilic Fe-oxidizers. The genomes of many Fe-oxidizers encode homologs to an outer-membrane cytochrome (Cyc2) that has been shown to oxidize Fe in two acidophiles. Here, we demonstrate the Fe oxidase function of a heterologously expressed Cyc2 homolog derived from a neutrophilic Fe oxidizer. Phylogenetic analyses show that Cyc2 from neutrophiles cluster together, suggesting a common function. Sequence analysis and modeling reveal the entire Cyc2 family is defined by a unique structure, a fused cytochromeporin, consistent with Fe oxidation on the outer membrane, preventing internal Fe oxide encrustation. Metatranscriptomes from Fe-oxidizing environments show exceptionally high expression of cyc2, supporting its environmental role in Fe oxidation. Together, these results provide evidence that cyc2 encodes Fe oxidases in diverse Fe-oxidizers and therefore can be used to recognize microbial Fe oxidation. The presence of cyc2 in 897 genomes suggests that microbial Fe oxidation may be a widespread metabolism.

Load Identification of Aircraft Airfoil

According to the structure of the airfoil, cantilever plate is made to substitute airfoil. The function of load is fit by using the primary function sequence. The load identification is transformed into solution of the fitting coefficients; numerical simulation shows the method is effective. Finally, the factors of effecting precision are studied.