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A connection between matrix orthogonal polynomials and non-abelian integrable lattices is investigated in this paper. The normalization factors of matrix orthogonal polynomials expressed using quasi-determinants are shown to be the solutions to the non-abelian Toda lattice in semi-discrete and full-discrete cases. Moreover, with a moment modification method, we demonstrate that the Bäcklund transformation of the non-abelian Toda lattice given by Popowicz (1983) is equivalent to the non-abelian Volterra lattice, whose solutions can be expressed using quasi-determinants as well. [ABSTRACT FROM AUTHOR]

In this paper, we introduce multiple skew-orthogonal polynomials and investigate their connections with classical integrable systems. By using Pfaffian techniques, we show that multiple skew-orthogonal polynomials can be expressed by multi-component Pfaffian tau-functions upon appropriate deformations. Moreover, a two-component Pfaff lattice hierarchy, which is equivalent to the Pfaff–Toda hierarchy studied by Takasaki, is obtained by considering the recurrence relations and Cauchy transforms of multiple skew-orthogonal polynomials. [ABSTRACT FROM AUTHOR]

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]

Integral imaging (II) display, one of the most critical true-3D display technologies, has received increasing research recently. Significantly, an achromatic metalens array has realized a broadband metalens-array-based II (meta-II). However, the past micro-scale metalens arrays were incompatible with commercial micro-displays; furthermore, the elemental image array (EIA) rendering is always slow. The two hinders in device and algorithm prevent meta-II from being used for practical video-rate near-eye displays (NEDs). This research demonstrates a meta-II NED combining a commercial micro-display and a metalens array. The large-area nanoimprint technology fabricates the metalens array, and a novel real-time rendering algorithm is proposed to generate the EIA. The hardware and software efforts solve the bottlenecks of video-rate meta-II displays. We also build a see-through prototype based on our meta-II NED, demonstrating the feasibility of augmented reality. Our work explores the potential of video-rate meta-II displays, which we expect can be valuable for future virtual and augmented reality. [ABSTRACT FROM AUTHOR]

A framework to study the eigenvalue probability density function for products of unitary random matrices with an invariance property is developed. This involves isolating a class of invariant unitary matrices, to be referred to as cyclic Pólya ensembles, and examining their properties with respect to the spherical transform on U (N) . Included in the cyclic Pólya ensemble class are Haar invariant unitary matrices, the circular Jacobi ensemble, known in relation to the Fisher-Hartwig singularity in the theory of Toeplitz determinants, as well as the heat kernel for Brownian motion on the unitary group. We define cyclic Pólya frequency functions and show their relation to the cyclic Pólya ensembles, and give a uniqueness statement for the corresponding weights. The natural appearance of bilateral hypergeometric series is highlighted, with this special function playing the role of the Meijer G-function in the transform theory of unitary invariant product of positive definite matrices. We construct a family of functions forming bi-orthonormal pairs which underly the correlation kernel of the corresponding determinantal point processes, and furthermore obtain an integral formula for the correlation kernel involving just two of these functions. [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]

The generalisation of continuous orthogonal polynomial ensembles from random matrix theory to the q-lattice setting is considered. We take up the task of initiating a systematic study of the corresponding moments of the density from two complementary viewpoints. The first requires knowledge of the ensemble average with respect to a general Schur polynomial, from which the spectral moments follow as a corollary. In the case of little q-Laguerre weight, a particular 3 ϕ 2 basic hypergeometric polynomial is used to express density moments. The second approach is to study the q-Laplace transform of the un-normalised measure. Using integrability properties associated with the q-Pearson equation for the q-classical weights, a fourth-order q-difference equation is obtained, generalising a result of Ledoux in the continuous classical cases. [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]

Background: To avoid the inconvenience of triangulation among various rigid operating instruments in mediastinoscopy-assisted esophagectomy, we invented a new technique: used a flexible endoscope to mobilize thoracic esophagus and dissected mediastinal lymph nodes through the left cervical incision. This technology has not been reported so far. In this study, we introduce our long-term experience and demonstrate this new technique. Methods: Twenty-nine patients with early esophageal cancer underwent mediastinoscopy-assisted esophagectomy in our hospital from June 2018 to September 2020. Among them, 12 patients used flexible mediastinoscopy, and 17 patients used conventional rigid mediastinoscopy and instruments to observe their therapeutic effect. Results: There were no significant differences between the two groups in gender, average age, body mass index, incidence of adverse reactions, bleeding volume, and postoperative hospital stay. The operation time of flexible mediastinoscopy group was significantly shorter than that of rigid mediastinoscopy group (192.9 ± 13.0 vs 246.8 ± 6.9 min, p < 0.01). The number of lymph nodes removed by flexible endoscopy was significantly more than that of rigid endoscopy (8.5 ± 0.6 vs 6.0 ± 0.3, P < 0.01). Postoperative follow-up was completed for all patients, and the average follow-up time was 11.6 ± 7.2 months. During the follow-up period, no recurrence or death was observed. Conclusions: Mediastinoscopy-assisted esophagectomy is an effective way to treat early esophageal cancer. The application of flexible mediastinoscopy provides more convenience and better stability. It can facilitate the operation of the surgeon and lymph node dissection, which proved to be a feasible technology. [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]

Background: Catamenial pneumothorax is characterized by spontaneous recurring pneumothorax during menstruation, which is a common clinical manifestation of thoracic endometriosis syndrome. There are still controversies about its pathogenesis.Case Presentation: A 43-year-old woman with a history of endometriosis came to our hospital due to recurring pneumothorax during menstruation. Uniportal Video-assisted Thoracoscopic Surgery (VATS) exploration was performed on the eve of menstruating. We thoroughly explored the diaphragm, visceral and parietal pleura: The lung surface was scattered with yellowish-brown implants; no bullae were found; multiple diaphragmatic defects were found on the dome. And surprisingly, we caught a fascinating phenomenon: Bubbles were slipping into pleural cavity through diaphragmatic defects. We excised the diaphragmatic lesions and wedge resected the right upper lung lesion; cleared the deposits and flushed the thoracic cavity with pure iodophor. Diaphragmatic lesions confirmed the presence of endometriosis, and interestingly enough, microscopically, endometrial cells were shedding with impending menses. After a series of intraoperative operations and postoperative endocrine therapy, the disease did not recur after a period of follow-up.Conclusion: We have witnessed the typical signs of catamenial pneumothorax at the accurate timing: Not only observed the process of gas migration macroscopically, but also obtained pathological evidence of diaphragmatic periodic perforation microscopically, which is especially precious and confirms the existing theory that retrograde menstruation leads to diaphragmatic endometriosis, and the diaphragmatic fenestration is obtained due to the periodic activities of ectopic endometrium. [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]

In this article, we consider the generalised two-parameter Cauchy two-matrix model and the corresponding integrable lattice equation. It is shown that with parameters chosen as 1 / k i , k i ∈ Z > 0 ( i = 1 , 2 ), the average characteristic polynomials admit (k 1 + k 2 + 2) -term recurrence relations, which can be interpreted as spectral problems for integrable lattices. The tau function is then given by the partition function of the generalised Cauchy two-matrix model as well as Gram determinant. The simplest solvable example is given. [ABSTRACT FROM AUTHOR]

Background/Aims: Targeted drug delivery vehicles with low immunogenicity and toxicity are needed for cancer therapy. Here, we prepare an active targeting drug carrier of low immunogenicity and toxicity for targeted therapy. Methods: Immature dendritic cells (imDCs) from BALB/c mice were used as donor cells of exosomes (Exos) that were transfected with the plasmids expressing fusion proteins of a tumor-targeting peptide known as internalizing RGD (iRGD) to construct a type of tumor-targeting iRGD-Exos and observe the interaction between these iRGD-Exos. Also, recombinant methioninase (rMETase) was loaded into the iRGD-Exos by electroporation to construct iRGD-Exos-rMETase and to assess the tumor-targeting function of the iRGD-Exos-rMETase. Finally, 30 BALB/c were randomly divided into five groups (n = 6), to observe tumor growth in vivo. Results: The iRGD-Exos-rMETase was 99.58 nm in diameter and presented a unique "goblet" structure under transmission electron microscopy (TEM), with the encapsulation efficiency (EE) of 19.05%. iRGD-Exos-rMETase group has the strongest tumor suppressive effect. Compared to the iRGD-Exos-rMETase group, rMETase group and the blank-Exos-rMETase group were less effective, while the PBS group and the iRGD-Exos group showed no inhibitory effect on tumor growth. After treatment, the iRGD-Exos-rMETase group had gastric tumors significantly smaller and lighter than the other groups (P < 0.05). Conclusion: The iRGD-Exos-rMETase is an effective antitumor therapy that delivers rMETase to tumor tissue using the iRGD-Exos. With its favorable inhibitory effect and tumor-targeting function, the iRGD-Exos-rMETase shows excellent potential value and exciting prospects in clinical applications. [ABSTRACT FROM AUTHOR]

Straw returning usually gives rise to greenhouse gas (GHG) emissions from the soil, and thus negatively affects carbon footprint (CF) of crop production. Numerous studies reported the effects of straw returning on the CF from single crop production. However, little is known about the integrated effects of different levels of straw returning on the CF and net ecosystem economic benefits (NEEB) from rice-wheat rotation. Here, we investigated the effects of different amounts of straw returning on soil CH4 and N2O emissions, GHG emissions from agricultural inputs (AIGHG), CF, and NEEB from a 2-year cycle of rice-wheat rotation. The CF was determined based on the total GHG emissions associated with crop production inputs and services. Overall, straw returning significantly increased annual CH4 emissions by 5.4–72.2% and reduced annual N2O emissions by 3.3–31.4% compared with straw removal. Straw returning remarkably increased rice grain yields by 8.1–9.9% and wheat grain yields by 10.2–21.1% compared with straw removal. The average annual AIGHG from rice-wheat rotation ranged from 3579 to 4987 kg CO2-eq ha–1. Diesel consumption played a dominant role in the AIGHG. The annual CF ranged from 0.96 to 1.31 kg CO2-eq kg–1 and increased with increasing straw returning amounts. The NEEB, which ranged from 14161 to 17413 CNY ha–1, was significantly affected by the levels of straw returning. The treatment with returning of 1/3 of preceding crop straw to the field (2.19–2.47 kg ha−1 year−1 of rice straw in the wheat season and 1.38–1.68 kg ha−1 year−1 of wheat straw in the rice season) resulted in relatively higher grain yield, the lowest CF, and the highest NEEB among all treatments, and thus can reduce CF, and increase grain yields and NEEB, and thus can be recommended as a sustainable approach to mitigate GHG emissions and increase economic benefits from rice-wheat rotation. [ABSTRACT FROM AUTHOR]

This study focused on the role of methionine (MET) in the autophagy of gastric cancer stem cells (GCSCs) and aims to elaborate its regulatory mechanism. In the present study, the GCSCs were isolated from human gastric cancer cell lines using an anti-CD44 antibody, and then cultured in MET+ homocysteine (HCY)− or MET−HCY+ medium. In MET+HCY–treated GCSCs, autophagy was suppressed, the methylation and phosphorylation of RAB37 were elevated, and miR-200b expression was down-regulated. Lentiviral vector (LV-) carrying methionine-γ lyase (an enzyme that could specifically lyse MET; Metase) promoted autophagy, reduced the methylation and phosphorylation of RAB37, and up-regulated miR-200b expression in MET+HCY–-treated GCSCs. Then, we found that miR-200b suppressed the expression of protein kinase C α (PKCα), a protein that could inactivate RAB37 through promoting its phosphorylation. LV-Metase down-regulated RAB37 phosphorylation via miR-200b/PKCα, thus promoting the RAB37-mediated autophagy and suppressing cell viability in MET+HCY–treated GCSCs. Finally, the in vivo study proved that LV-Metase treatment inhibited tumor growth through up-regulating RAB37 expression. In conclusion, MET suppressed RAB37 expression via enhancing its methylation and suppressed RAB37 activity via miR-200b/PKCα axis, thus repressing RAB37-mediated autophagy in GCSCs. The supplementation of Metase lysed MET, thus inducing the autophagy of GCSCs and inhibiting tumor growth. [ABSTRACT FROM AUTHOR]

As one of the major irradiation defects, helium bubbles have a marked influence on the microstructures and mechanical properties of metals. In recent decades, many experiments and simulations have focused on helium bubbles to reveal their nucleation and growth mechanisms, dynamic evolution under stimulations, and their effects on mechanical properties. With the quick development of various in situ techniques, the abundant dynamic features of helium bubbles have been revealed. In this review, we briefly explore the related researches on the dynamic evolution of helium bubbles under simulated service conditions, such as at high temperatures, under irradiation, and upon mechanical loading. We also discuss the challenges and opportunities in revealing the dynamics of helium bubbles using in situ technologies. This short review intends to advance our understanding of the failure mechanisms of helium-irradiated metals and the basic properties of irradiation-induced helium bubbles. [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]

The eigenvalue probability density function for symplectic invariant random matrix ensembles can be generalized to discrete settings involving either a linear or an exponential lattice. The corresponding correlation functions can be expressed in terms of certain discrete and q skew orthogonal polynomials, respectively. We give a theory of both of these classes of polynomials, and the correlation kernels determining the correlation functions, in the cases in which the weights for the corresponding discrete unitary ensembles are classical. Crucial for this are certain difference operators which relate the relevant symmetric inner products to the skew symmetric ones, and have a tridiagonal action on the corresponding (discrete or q) orthogonal polynomials. [ABSTRACT FROM AUTHOR]

Background: Autophagy plays an important role in regulating cisplatin (CDDP) resistance in gastric cancer cells. However, the underlying mechanism of methioninase (METase) in the regulation of autophagy and CDDP resistance of gastric cancer cells is still not clear. Materials and methods: Western blot was used to detect the levels of autophagy-related proteins, multidrug-resistant 1 (MDR-1), and FoxM1 protein. LncRNA HULC was detected by qRT-PCR. Cell viability was detected using CCK-8 assay. The interaction between lncRNA HULC and FoxM1 was confirmed by RNA pull-down and RIP assay. Results: Lentiviral vector carrying METase (LV-METase) suppressed autophagy and CDDP resistance of drug-resistant gastric cancer cells. LncRNA HULC was significantly downregulated in drug-resistant gastric cancer cells transfected with LV-METase. Besides, we found that lncRNA HULC interacted with FoxM1. In addition, METase suppressed autophagy to reduce CDDP resistance of drug-resistant gastric cancer cells through regulating HULC/FoxM1, and interfering HULC suppressed autophagy to reduce CDDP resistance of drug-resistant gastric cancer cells through regulating FoxM1. Finally, interfering HULC inhibited tumor growth in vivo. Conclusion: METase suppressed autophagy to reduce CDDP resistance of drug-resistant gastric cancer cells through regulating HULC/FoxM1 pathway. [ABSTRACT FROM AUTHOR]

Background: The aim of this study was to investigate the value of a smartphone‐compatible thermal imaging camera in the mapping of the peroneal artery perforators. Methods: Twelve consecutive patients scheduled for fibular flap reconstruction were enrolled. The lower limbs were first studied using smartphone‐based dynamic infrared thermography (DIRT). During the rewarming, the hotspots were marked, small rubber markers were taped to the registered sites, and then the patients were sent for a CT scan. The diagnostic performance of smartphone‐based DIRT was evaluated by comparing the DIRT findings with CT angiography and intraoperative findings. Results: DIRT detected 42 of the 57 dominant perforators in 24 limbs and resulted in a sensitivity of 73.7% and a positive predictive value of 65.6%. Conclusions: The sensitivity and positive predictive value of the smartphone‐based DIRT are low. Currently, it should be used as an adjunctive tool together with the established imaging techniques. [ABSTRACT FROM AUTHOR]

This paper mainly talks about the Cauchy two-matrix model and its corresponding integrable hierarchy with the help of orthogonal polynomial theory and Toda-type equations. Starting from the symmetric reduction in Cauchy biorthogonal polynomials, we derive the Toda equation of CKP type (or the C-Toda lattice) as well as its Lax pair by introducing time flows. Then, matrix integral solutions to the C-Toda lattice are extended to give solutions to the CKP hierarchy which reveals the time-dependent partition function of the Cauchy two-matrix model is nothing but the τ-function of the CKP hierarchy. At last, the connection between the Cauchy two-matrix model and Bures ensemble is established from the point of view of integrable systems. [ABSTRACT FROM AUTHOR]

Skew-orthogonal polynomials (SOPs) arise in the study of the n-point distribution function for orthogonal and symplectic random matrix ensembles. Motivated by the average of characteristic polynomials of the Bures random matrix ensemble studied in Forrester and Kieburg (Commun Math Phys 342(1):151-187, 2016), we propose the concept of partial-skew-orthogonal polynomials (PSOPs) as a modification of the SOPs, and then the PSOPs with a variety of special skew-symmetric kernels and weight functions are addressed. By considering appropriate deformations of the weight functions, we derive nine integrable lattices in different dimensions. As a consequence, the tau-functions for these systems are shown to be expressed in terms of Pfaffians and the wave vectors PSOPs. In fact, the tau-functions also admit the multiple integral representations. Among these integrable lattices, some of them are known, while the others are novel to the best of our knowledge. In particular, one integrable lattice is related to the partition function of the Bures ensemble. Besides, we derive a discrete integrable lattice which can be used to compute certain vector Padé approximants. This yields the first example regarding the connection between integrable lattices and generalised inverse vector-valued Padé approximants, about which Hietarinta, Joshi, and Nijhoff pointed out that, “This field remains largely to be explored”, in the recent monograph (Hietarinta et al. in Discrete systems and integrability, vol 54. Cambridge University Press, Cambridge, 2016, [Section 4.4]). [ABSTRACT FROM AUTHOR]

In the literature, most known sequence transformations can be written as a ratio of two determinants. But, it is not always this case. One exception is that the sequence transformation proposed by Brezinski, Durbin, and Redivo-Zaglia cannot be expressed as a ratio of two determinants. Motivated by this, we will introduce a new algebraic tool—pfaffians, instead of determinants in the paper. It turns out that Brezinski-Durbin-Redivo-Zaglia’s transformation can be expressed as a ratio of two pfaffians. To the best of our knowledge, this is the first time to introduce pfaffians in the expressions of sequence transformations. Furthermore, an extended transformation of high order is presented in terms of pfaffians and a new convergence acceleration algorithm for implementing the transformation is constructed. Then, the Lax pair of the recursive algorithm is obtained which implies that the algorithm is integrable. Numerical examples with applications of the algorithm are also presented. [ABSTRACT FROM AUTHOR]

Helium (He) bubbles are typical radiation defects in structural materials in nuclear reactors after high dose energetic particle irradiation. In the past decades, extensive studies have been conducted to explore the dynamic evolution of He bubbles under various conditions and to investigate He-induced hardening and embrittlement. In this review, we summarize the current understanding of the behavior of He bubbles in metals; overview the mechanisms of He bubble nucleation, growth, and coarsening; introduce the latest methods of He control by using interfaces in nanocrystalline metals and metallic multilayers; analyze the effects of He bubbles on strength and ductility of metals; and point out some remaining questions related to He bubbles that are crucial for design of advanced radiation-tolerant materials. [ABSTRACT FROM AUTHOR]