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Transcription factors (TFs) play an important role in tumors. We integrated and analyzed 13 GPL570 platform gastric cancer (GC) microarrays, identified 10 independent prognostic TFs, and constructed a GC prognostic model. Using GSE26942 as the verification set, the Kaplan-Meier curve showed that the signature distinguish the survival rate of GC patients (P < 0.01), and the AUC values are 0.746 and 0.630, respectively. Compared with the clinicopathological characteristics, the signature is an independent prognostic factor (P < 0.05). A nomogram was established based on the model, and the five-year calibration curve verified that the prediction of the nomogram was almost consistent with the actual survival rate, C-index of 0.747 indicated a moderate prognostic ability. The analysis of target genes of 10 TFs showed that they are closely related to the progression of GC. External database and rt-PCR showed that the RNA and protein expression of TFs are consistent with our analysis. • Integrating the GPL570 platform 13 gastric cancer micro-arrays to get 1027 samples. • Transcription factors differentially expressed in gastric cancer were identified. • The prognostic-related TFs were identified and a prognostic model was constructed. • The target genes of hub TFs were predicted and the molecular mechanism was analyzed. • The critical TFs have been verified by external databases and experiments. [ABSTRACT FROM AUTHOR]

In this article, we consider the Christoffel transformations for skew-orthogonal polynomials and partial-skew-orthogonal polynomials. We demonstrate that the Christoffel transformations can act as spectral problems for discrete integrable hierarchies, and therefore we derive certain integrable hierarchies from these transformations. Some reductional cases are also considered. [ABSTRACT FROM AUTHOR]

Previous works have considered the leading correction term to the scaled limit of various correlation functions and distributions for classical random matrix ensembles and their β generalisations at the hard and soft edge. It has been found that the functional form of this correction is given by a derivative operation applied to the leading term. In the present work we compute the leading correction term of the correlation kernel at the spectrum singularity for the circular Jacobi ensemble with Dyson indices β = 1 , 2 and 4, and also to the spectral density in the corresponding β -ensemble with β even. The former requires an analysis involving the Routh–Romanovski polynomials, while the latter is based on multidimensional integral formulas for generalised hypergeometric series based on Jack polynomials. In all cases this correction term is found to be related to the leading term by a derivative operation. [ABSTRACT FROM AUTHOR]

There is a two-component log-gas system with Boltzmann factor which provides an interpolation between the eigenvalue probability density function (PDF) for β = 1 and β = 4 invariant random matrix ensembles. Its solvability relies on the construction of particular skew orthogonal polynomials, with the skew inner product a linear combination of the β = 1 and β = 4 inner products, each involving weight functions. For suitably related classical weight functions, we seek to express the skew orthogonal polynomials as linear combinations of the underlying orthogonal polynomials. It is found that in each case (Gaussian, Laguerre, Jacobi and generalised Cauchy) the coefficients can be expressed in terms of hypergeometric polynomials with argument relating to the fugacity. In the Jacobi case, for example, the coefficients are Wilson polynomials. [ABSTRACT FROM AUTHOR]

Abstract The Novikov equation is an integrable analogue of the Camassa–Holm equation with a cubic (rather than quadratic) nonlinear term. Both these equations support a special family of weak solutions called multipeakon solutions. In this paper, an approach involving Pfaffians is applied to study multipeakons of the Novikov equation. First, we show that the Novikov peakon ODEs describe an isospectral flow on the manifold cut out by certain Pfaffian identities. Then, a link between the Novikov peakons and the finite Toda lattice of BKP type (B-Toda lattice) is established based on the use of Pfaffians. Finally, certain generalizations of the Novikov equation and the finite B-Toda lattice are proposed together with special solutions. To our knowledge, it is the first time that the peakon problem is interpreted in terms of Pfaffians. [ABSTRACT FROM AUTHOR]

Abstract Firstly, a formal correspondence is established between the Camassa–Holm (CH) equation and a two-component modified CH (or called SQQ) equation according to the method of moment modification for multipeakon formulae. Secondly, based on the generalized nonisospectral CH equation in Chang et al. (2014) [14] and the interlacing multipeakons of the two-component modified CH equation in Chang et al. (2016) [15] , we propose a new generalized two-component modified CH equation with two parameters, which possesses a nonisospectral Lax pair. The proposed equation still admits multipeakon solutions of explicit and closed form. Sufficient conditions for global existence of solutions are given and two concrete examples with certain interesting phenomenon are presented. Last of all, as a by-product, a generalized nonisospectral modified CH equation is deduced, together with its Lax pair. [ABSTRACT FROM AUTHOR]

[Display omitted] • Promoter plays a key role in gene transcription regulation. • We presented a database PPD, which collected the experimentally validated promoters in prokaryotes. • PPD recorded 129,148 promoters across 63 prokaryotic species. • PPD provided an online genome browser for the visualization of the resources of prokaryotic promoter. • PPD might be a novel resource for the study of prokaryotic gene transcription. As a key region, promoter plays a key role in transcription regulation. A eukaryotic promoter database called EPD has been constructed to store eukaryotic POL II promoters. Although there are some promoter databases for specific prokaryotic species or specific promoter type, such as RegulonDB for Escherichia coli K-12, DBTBS for Bacillus subtilis and Pro54DB for sigma 54 promoter, because of the diversity of prokaryotes and the development of sequencing technology, huge amounts of prokaryotic promoters are scattered in numerous published articles, which is inconvenient for researchers to explore the process of gene regulation in prokaryotes. In this study, we constructed a Prokaryotic Promoter Database (PPD), which records the experimentally validated promoters in prokaryotes, from published articles. Up to now, PPD has stored 129,148 promoters across 63 prokaryotic species manually extracted from published papers. We provided a friendly interface for users to browse, search, blast, visualize, submit and download data. The PPD will provide relatively comprehensive resources of prokaryotic promoter for the study of prokaryotic gene transcription. The PPD is freely available and easy accessed at http://lin-group.cn/database/ppd/. [ABSTRACT FROM AUTHOR]