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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]

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]

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]

In this paper, we plan to show an eigenvalue algorithm for block Hessenberg matrices by using the idea of non-commutative integrable systems and matrix-valued orthogonal polynomials. We introduce adjacent families of matrix-valued θ\documentclass[12pt]{minimal}\usepackage{amsmath}\usepackage{wasysym}\usepackage{amsfonts}\usepackage{amssymb}\usepackage{amsbsy}\usepackage{mathrsfs}\usepackage{upgreek}\setlength{\oddsidemargin}{-69pt}\begin{document}$$\theta $$\end{document}-deformed bi-orthogonal polynomials, and derive corresponding discrete non-commutative hungry Toda lattice from discrete spectral transformations for polynomials. It is shown that this discrete system can be used as a pre-precessing algorithm for block Hessenberg matrices. Besides, some convergence analysis and numerical examples of this algorithm are presented. [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]

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]

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]

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]