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Starting with a skew-symmetric inner product over an elliptic curve, we propose the concept of elliptic skew-orthogonal polynomials. Inspired by the Landau–Lifshitz hierarchy and its corresponding time evolutions, we obtain the recurrence relation and the |$\tau $| -function representation for such a novel class of skew-orthogonal polynomials. Furthermore, a bilinear integral identity is derived through the so-called Cauchy–Stieljes transformation, from which we successfully establish the connection between the elliptic skew-orthogonal polynomials and an elliptic extension of the Pfaff lattice hierarchy. [ABSTRACT FROM AUTHOR]

Castleman disease is a rare and complicated disease. A case of Castleman disease (CD) in a 40⁃year⁃old woman on the neck was reported and literature review was made to understand the occurrence, clinical characteristics, diagnosis and differential diagnosis, treatment, and prognosis of Castleman disease. Because of the rarity of CD, its oc⁃ currence in the general population and the typical clinical manifestations are still lacked. There are two types of CD, namely localized CD and multicentric CD, both of them are not easy to be diagnosised. CT scans in preoperative is help⁃ ful for the clinical diagnosis, while histopathological examination and lymph node biopsy are beneficial for the early di⁃ agnosis. The treatment result is based on the histopathological examination and lymph node biopsy. The prognosis is dif⁃ ferent with the type of CD. For the localized CD, the prognosis is usually good, while for the multicentric CD is bad. Both of localized CD and multicentric CD have a certain reoccurrence rate.

Amongst the many additive manufacturing (AM) techniques, directed energy deposition (DED) is a prominent one, which can also be used for the repair of damaged components. In this paper, we provide an overview on it, with emphasis on the typical microstructures of DED alloys and discuss the processing-microstructure-mechanical property correlations. Comparison is made with those manufactured using the conventional techniques and those obtained with laser beam powder bed fusion (LB-PBF). The characteristic solidification rates and thermal histories in DED result in distinct micro- and meso-structural features and mechanical performance, which are succinctly summarized. The potential of DED for manufacturing graded materials and for component repair is elaborated while highlighting the key-associated challenges and possible solutions. Modelling and simulation studies that facilitate an in-depth understanding of the DED technique are summarized. Finally, some critical issues and research directions that would help develop DED further and extend its application potential are identified. [ABSTRACT FROM AUTHOR]

Metal–organic frameworks (MOFs) as types of proton conductive materials have attracted much attention. Here, an acylamide-functionalized 3D MOF, [Ni3(TPBTC)2(stp)2(H2O)4]·2DMA·32H2O, has been successfully constructed via combining Ni(NO3)2, TPBTC (TPBTC = benzene-1,3,5-tricarboxylic acid tris-pyridin-4-ylamide) and 2-H2stp (2-H2stp = 2-sulfoterephthalic acid monosodium salt) under solvothermal conditions. Single-crystal X-ray diffraction revealed that there are uncoordinated guest DMA molecules in the pores of the compound. On removal of guest DMA molecules, the proton conductivity of the compound increased to 2.25 × 10−3 S cm−1 at 80 °C and 98% RH which is about 110 times that of the original material. It is hoped that this work can provide essential insight for designing and obtaining improved crystalline-state proton conducting materials by considering the influences of guest molecules on proton conduction properties of porous materials. [ABSTRACT FROM AUTHOR]

This paper focuses on different reductions of the two-dimensional (2d)-Toda hierarchy. Symmetric and skew-symmetric moment matrices are first considered, resulting in differential relations between symmetric/skew-symmetric tau functions and 2d-Toda’s tau functions, respectively. Furthermore, motivated by the Cauchy two-matrix model and Bures ensemble from random matrix theory, we study the rank-one shift condition in the symmetric case and rank-two shift condition in the skew-symmetric case, from which the C-Toda and B-Toda hierarchies are determined, together with their special Lax matrices and integrable structures. [ABSTRACT FROM AUTHOR]

Objective: To investigate the effects of home‐based telerehabilitation based on the Internet‐based rehabilitation management system on hip function, activities of daily living and somatic integrative ability of elderly postoperative hip fracture patients. Methods: From June 2020 to November 2020, we recruited 58 elderly postoperative hip fracture patients and randomly assigned them to the telephone group (n = 29) and the telerehabilitation group (n = 29). Both groups received routine discharge instructions, and the former received telephone follow‐up after discharge, while the latter received remote rehabilitation based on the Internet‐based rehabilitation management system. The Harris hip score (HHS), functional independence measure (FIM), timed up‐and‐go test (TUG), and short physical performance battery (SPPB) were used to evaluate the patients' hip function, activities of daily living, and overall somatic ability. Results: There was no significant difference between the baseline data of the two groups before the intervention (P > 0.05); no matter after hip replacement or internal fixation, the HHS score and FIM score of both groups increased gradually with the postoperative time, and the scores in the telerehabilitation group were higher than those in the telephone group at 1 and 3 months after the intervention, and the difference was significant (P < 0.05); for patients after hip replacement, the TUG and SPPB scores in the telerehabilitation group were better than those in the telephone group at 3 months after the intervention, and the difference was significant (P < 0.05). Conclusions: The Internet‐based rehabilitation management system applied to postoperative home rehabilitation of elderly hip fracture patients can improve the functional recovery of the hip joint and enhance the ability to perform activities of daily living and somatic integration to a certain extent. This seems to provide an effective option for conducting home rehabilitation. [ABSTRACT FROM AUTHOR]

The theory of Pólya ensembles of positive definite random matrices provides structural formulas for the corresponding biorthogonal pair, and correlation kernel, which are well suited to computing the hard edge large N asymptotics. Such an analysis is carried out for products of Laguerre ensembles, the Laguerre Muttalib–Borodin ensemble, and products of Laguerre ensembles and their inverses. The latter includes, as a special case, the Jacobi unitary ensemble. In each case, the hard edge scaled kernel permits an expansion in powers of 1/N, with the leading term given in a structured form involving the hard-edge scaling of the biorthogonal pair. The Laguerre and Jacobi ensembles have the special feature that their hard edge scaled kernel – the Bessel kernel – is symmetric and this leads to there being a choice of hard edge scaling variables for which the rate of convergence of the correlation functions is O (1 / N 2). [ABSTRACT FROM AUTHOR]

This study explores the role of the long noncoding RNA (LncRNA) CRNDE in cisplatin (CDDP) resistance of gastric cancer (GC) cells. Here, we show that LncRNA CRNDE is upregulated in carcinoma tissues and tumor‐associated macrophages (TAMs) of GC patients. In vitro experiments show that CRNDE is enriched in M2‐polarized macrophage‐derived exosomes (M2‐exo) and is transferred from M2 macrophages to GC cells via exosomes. Silencing CRNDE in M2‐exo reverses the promotional effect of M2‐exo on cell proliferation in CDDP‐treated GC cells and homograft tumor growth in CDDP‐treated nude mice. Mechanistically, CRNDE facilitates neural precursor cell expressed developmentally downregulated protein 4‐1 (NEDD4‐1)‐mediated phosphatase and tensin homolog (PTEN) ubiquitination. Silencing CRNDE in M2‐exo enhances the CDDP sensitivity of GC cells treated with M2‐exo, which is reduced by PTEN knockdown. Collectively, these data reveal a vital role for CRNDE in CDDP resistance of GC cells and suggest that the upregulation of CRNDE in GC cells may be attributed to the transfer of TAM‐derived exosomes. SYNOPSIS: LncRNA CRNDE is transferred from M2‐polarized macrophages to GC cells via exosomes, suppressing PTEN expression in GC cells. The latter leads to a reduced sensitivity of GC cells to cisplatin. LncRNA CRNDE is enriched in TAMs of GC patients.LncRNA CRNDE is transferred from M2‐polarized macrophages to GC cells via exosomes in vitro.CRNDE facilitates NEDD4‐1‐mediated PTEN ubiquitination in GC cells.Exosomal transfer of LncRNA CRNDE is linked to cisplatin resistance in GC cells caused by reduced PTEN levels. [ABSTRACT FROM AUTHOR]

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 paper, an orthogonal polynomials-based (OPs-based) approach to generate discrete moving frames and invariants is developed. It is shown that OPs can provide explicit expressions for the discrete moving frame as well as the associated difference invariants, and this approach enables one to obtain the corresponding discrete invariant curve flows simultaneously. Several examples in the cases of centro-affine plane, pseudo-Euclidean plane, and high-dimensional centro-affine space are presented. [ABSTRACT FROM AUTHOR]

A |$\theta $| -deformation of the Laguerre weighted Cauchy two-matrix model, and the Bures ensemble, is introduced. Such a deformation is familiar from the Muttalib–Borodin ensemble. The |$\theta $| -deformed Cauchy–Laguerre two-matrix model is a two-component determinantal point process. It is shown that the correlation kernel, and its hard edge scaled limit, can be written in terms of particular Fox H-functions, generalising the Meijer G-function class known from the study of the case |$\theta = 1$|⁠. In the |$\theta =1$| case, it is shown that the Laguerre–Bures ensemble is related to the Laguerre–Cauchy two-matrix model, notwithstanding the Bures ensemble corresponding to a Pfaffian point process. This carries over to the |$\theta $| -deformed case, allowing explicit expressions involving Fox H-functions for the correlation kernel, and its hard edge scaling limit, to also be obtained for the |$\theta $| -deformed Laguerre–Bures ensemble. The hard edge scaling limit is in the Raney class |$(\theta /2+1,1/2)$|⁠. [ABSTRACT FROM AUTHOR]

5-Methylcytosine (m5C) plays an extremely important role in the basic biochemical process. With the great increase of identified m5C sites in a wide variety of organisms, their epigenetic roles become largely unknown. Hence, accurate identification of m5C site is a key step in understanding its biological functions. Over the past several years, more attentions have been paid on the identification of m5C sites in multiple species. In this work, we firstly summarized the current progresses in computational prediction of m5C sites and then constructed a more powerful and reliable model for identifying m5C sites. To train the model, we collected experimentally confirmed m5C data from Homo sapiens , Mus musculus , Saccharomyces cerevisiae and Arabidopsis thaliana , and compared the performances of different feature extraction methods and classification algorithms for optimizing prediction model. Based on the optimal model, a novel predictor called iRNA-m5C was developed for the recognition of m5C sites. Finally, we critically evaluated the performance of iRNA-m5C and compared it with existing methods. The result showed that iRNA-m5C could produce the best prediction performance. We hope that this paper could provide a guide on the computational identification of m5C site and also anticipate that the proposed iRNA-m5C will become a powerful tool for large scale identification of m5C sites. [ABSTRACT FROM AUTHOR]

Cancer stem cells are undifferentiated cancer cells that have self‐renewal ability, a high tumorigenic activity, and a multilineage differentiation potential. MicroRNAs play a critical role in regulating gene expression during carcinogenesis. Here, we investigated the role of miR‐7 and the mechanism by which it is dysregulated in gastric cancer stem cells (GCSCs). The stem cell marker, CD44, was used to sort GCSCs by fluorescence‐activated cell sorting. We found that CD44 (+) cells have higher invasiveness and form more number of sphere colonies than CD44 (−) cells. Quantitative real‐time polymerase chain reaction (PCR) revealed that the miR‐7‐5p expression was remarkably downregulated in GCSCs but was significantly increased in the methionine‐deprived medium. The downregulation of miR‐7‐5p results from the increased DNA methylation in the promoter region using the methylation‐specific PCR. Overexpression of miR‐7‐5p reduced the formation of colony and decreased the invasion of GCSCs through targeting Smo and Hes1 and subsequent repressing Notch and Hedgehog signaling pathways in vitro. Notably, upregulating miR‐7‐5p inhibited the growth of tumor in the xenograft model. Hence, these data demonstrated that miR‐7‐5p represses GCSC invasion through inhibition of Smo and Hes1, which provides a potential therapeutic target of gastric cancer treatment. [ABSTRACT FROM AUTHOR]