Reduced projection method for quasiperiodic Schr\"{o}dinger eigenvalue problems

This paper presents a reduced algorithm to the classical projection method for the solution of $d$-dimensional quasiperiodic problems, particularly Schr\"{o}dinger eigenvalue problems. Using the properties of the Schr\"{o}dinger operator in higher-dimensional space via a projection matrix of size $d\times n$, we rigorously prove that the generalized Fourier coefficients of the eigenfunctions decay exponentially along a fixed direction associated with the projection matrix. An efficient reduction strategy of the basis space is then proposed to reduce the degrees of freedom from $O(N^{n})$ to $O(N^{n-d}D^d)$, where $N$ is the number of Fourier grids in one dimension and the truncation coefficient $D$ is much less than $N$. Correspondingly, the computational complexity of the proposed algorithm for solving the first $k$ eigenpairs using the Krylov subspace method decreases from $O(kN^{2n})$ to $O(kN^{2(n-d)}D^{2d})$. Rigorous error estimates of the proposed reduced projection method are provided, indicating that a small $D$ is sufficient to achieve the same level of accuracy as the classical projection method. We present numerical examples of quasiperiodic Schr\"{o}dinger eigenvalue problems in one and two dimensions to demonstrate the accuracy and efficiency of our proposed method.Comment: 20 pages, 9 figure

Unipolar Resistance Switching in Amorphous High-k dielectrics Based on Correlated Barrier Hopping Theory

We have proposed a kind of nonvolatile resistive switching memory based on amorphous LaLuO3, which has already been established as a promising candidate of high-k gate dielectric employed in transistors. Well-developed unipolar switching behaviors in amorphous LaLuO3 make it suited for not only logic but memory applications using the conventional semiconductor or the emerging nano/CMOS architectures. The conduction transition between high- and low- resistance states is attributed to the change in the separation between oxygen vacancy sites in the light of the correlated barrier hopping theory. The mean migration distances of vacancies responsible for the resistive switching are demonstrated in nanoscale, which could account for the ultrafast programming speed of 6 ns. The origin of the distributions in switching parameters in oxides can be well understood according to the switching principle. Furthermore, an approach has also been developed to make the operation voltages predictable for the practical applications of resistive memories.Comment: 18 pages, 6 figure

Pythagoras Superposition Principle for Localized Eigenstates of 2D Moir\'e Lattices

Moir\'e lattices are aperiodic systems formed by a superposition of two periodic lattices with a relative rotational angle. In optics, the photonic moir\'e lattice has many promising mysteries such as its ability to localize light, thus attracting much attention to exploring features of such a structure. One fundamental research area for photonic moir\'e lattices is the properties of eigenstates, particularly the existence of localized eigenstates and the localization-to-delocalization transition in the energy band structure. Here we propose an accurate algorithm for the eigenproblems of aperiodic systems by combining plane wave discretization and spectral indicator validation under the higher-dimensional projection, allowing us to explore energy bands of fully aperiodic systems. A localization-delocalization transition regarding the intensity of the aperiodic potential is observed and a novel Pythagoras superposition principle for localized eigenstates of 2D moir\'e lattices is revealed by analyzing the relationship between the aperiodic and its corresponding periodic eigenstates. This principle sheds light on exploring the physics of localizations for moir\'e lattice.Comment: 7 pages, 3 figure

M2-Polarized tumor-associated macrophages are associated with poor prognoses resulting from accelerated lymphangiogenesis in lung adenocarcinoma

OBJECTIVES: Tumor-associated macrophages have been implicated in promoting tumor growth, progression and metastasis. However, the activated phenotype (M1 or M2) of tumor-associated macrophages remains unknown in solid tumors. Therefore, this study examined the density and prognostic significance of M2-polarized tumor-associated macrophages in lung adenocarcinoma. METHODS: Tumor specimens from 65 lung adenocarcinoma patients were assessed by ELISA for Th1/Th2 cytokine concentrations. The activated phenotype (M1 or M2) of tumor-associated macrophages was determined utilizing immunofluorescence staining. Additionally, to evaluate lymphangiogenesis, peritumoral lymphatic microvessel density was measured using D2-40. The correlation between tumor-associated macrophage subtype and overall patient survival was analyzed using the Kaplan-Meier method and compared using the log-rank test. RESULTS: A shift toward Th2 cytokine expression was detected within lung adenocarcinoma microenvironments. Approximately 79.71±16.27% of tumor-associated macrophages were M2 polarized; the remaining 20.35±5.31% were M1 polarized. The infiltration of M2-polarized macrophages was significantly associated with P-TNM staging and lymph node metastasis. The peritumoral lymphatic microvessel density was significantly higher in the high M2-polarized tumor-associated macrophage group than in the low M2-polarized tumor-associated macrophage group. A significant difference in overall patient survival was detected not only between patients with tumors with high and low macrophage counts but also between patients with tumors with high and low counts of M2-polarized macrophages. CONCLUSION: Tumor-associated macrophages in lung adenocarcinoma have an M2-polarized subtype and are associated with poor prognoses, perhaps resulting from accelerated lymphangiogenesis and lymph node metastasis

M2-polarized macrophages promote metastatic behavior of Lewis lung carcinoma cells by inducing vascular endothelial growth factor-C expression

OBJECTIVES: Tumor-associated macrophages that generally exhibit an alternatively activated (M2) phenotype have been linked to tumor progression and metastasis. However, the role of M2-polarized macrophages in the growth and metastasis of lung adenocarcinoma remains enigmatic. The aim of this study was to explore the effect of M2 macrophages on the proliferation and migration of mouse Lewis lung carcinoma cells and tumor-induced lymphangiogenesis. METHODS: Trypan blue staining and the Transwell migration assay were performed to evaluate the effects of activated (M1 or M2) macrophages on the proliferation and migration of Lewis cells. Furthermore, vascular endothelial growth factor-C expression in Lewis cells and nitric oxide secretion from activated macrophages were detected during the co-culture assay. Following treatment with activated macrophages, lymphatic endothelial cells differentiated into capillary-like structures, and the induction of Lewis cell migration was assessed using a twodimensional Matrigel-based assay. RESULTS: In the co-culture Transwell system, the proliferation and migration of Lewis cells were promoted by M2 macrophages. Moreover, the co-culture significantly increased the expression of vascular endothelial growth factor-C by Lewis cells and reduced the secretion of nitric oxide from M2 macrophages, which subsequently led to the capillary morphogenesis of lymphatic endothelial cells. Interestingly, following co-culture with Lewis cells, the function of RAW264.7 cells was polarized toward that of the M2 macrophage phenotype. CONCLUSION: M2-polarized macrophages promoted the metastatic behavior of Lewis cells by inducing vascular endothelial growth factor-C expression. Thus, the interruption of signaling between M2 macrophages and Lewis cells may be considered to be a new therapeutic strategy

A Novel Temperature Model of Regions Formed during the Preheating Stage of Belt Heating in Incremental Sheet Forming

The temperature of a forming region has a gradient distribution characteristic in the belt heating incremental sheet forming process, in which the relation between the heating power and the temperature distribution is ambiguous in the pre-heating stage. The setup of the heating power is therefore challenging, and the whole forming efficiency might decrease due to the above issue. Therefore, this paper proposes a belt heating method for electric conduction heating and presents a temperature calculation model for the forming region of the plate in the preheating state based on the heat conduction model. The calculated accuracy of the model is analysed through physical experiments, and the thermal transfer efficiency of heating tubes is analysed in detail. Based on the result, the thermal transfer efficiency value for heating tubes is determined to improve the accuracy of the suggested model. In addition, the effect of the model slope on the calculated result is further analysed, and the setting method of the slope value for the model is proposed according to different accuracy requirements