Numerical algorithm and complexity analysis for diagonalization of multivariate homogeneous polynomials

We study the computational complexity of a criterion and an algorithm for diagonalization of multivariate homogeneous polynomials, that is, expressing them as sums of powers of independent linear forms. They are based on Harrison's center theory and only require solving linear and quadratic systems of equations. Detailed descriptions and computational complexity of each step of the algorithm are provided. The complexity analysis focuses on the impacts of problem sizes, including the number of variables and the degree of given polynomials. We show that this algorithm runs in polynomial time and validate it through numerical experiments. Other diagonalization algorithms are reviewed and compared in terms of complexity

Characterizing Urban Household Waste Generation and Metabolism Considering Community Stratification in a Rapid Urbanizing Area of China

The relationship between social stratification and municipal solid waste generation remains uncertain under current rapid urbanization. Based on a multi-object spatial sampling technique, we selected 191 households in a rapidly urbanizing area of Xiamen, China. The selected communities were classified into three types: work-unit, transitional, and commercial communities in the context of housing policy reform in China. Field survey data were used to characterize household waste generation patterns considering community stratification. Our results revealed a disparity in waste generation profiles among different households. The three community types differed with respect to family income, living area, religious affiliation, and homeowner occupation. Income, family structure, and lifestyle caused significant differences in waste generation among work-unit, transitional, and commercial communities, respectively. Urban waste generation patterns are expected to evolve due to accelerating urbanization and associated community transition. A multi-scale integrated analysis of societal and ecosystem metabolism approach was applied to waste metabolism linking it to particular socioeconomic conditions that influence material flows and their evolution. Waste metabolism, both pace and density, was highest for family structure driven patterns, followed by lifestyle and income driven. The results will guide community-specific management policies in rapidly urbanizing areas

Nontrivial Solutions for Periodic Schrödinger Equations with Sign-Changing Nonlinearities

We prove a new infinite-dimensional linking theorem. Using this theorem, we obtain nontrivial solutions for strongly indefinite periodic Schrödinger equations with sign-changing nonlinearities

Results on entire solutions for a degenerate critical elliptic equation with anisotropic coefficients

In this paper, we study the following degenerate critical elliptic equations with anisotropic coefficients $$-div(|x_{N}|^{2\alpha}\nabla u)=K(x)|x_{N}|^{\alpha\cdot 2^{*}(s)-s}|u|^{2^{*}(s)-2}u {in} \mathbb{R}^{N}$$ where $x=(x_{1},...,x_{N})\in\mathbb{R}^{N},$ $N\geq 3,$ $\alpha>1/2,$ $0\leq s\leq 2$ and $2^{*}(s)=2(N-s)/(N-2).$ Some basic properties of the degenerate elliptic operator $-div(|x_{N}|^{2\alpha}\nabla u)$ are investigated and some regularity, symmetry and uniqueness results for entire solutions of this equation are obtained. We also get some variational identities for solutions of this equation. As a consequence, we obtain some nonexistence results for solutions of this equation.Comment: 29 page

Yao medicine Amydrium hainanense suppresses hepatic fibrosis by repressing hepatic stellate cell activation via STAT3 signaling

Ethnopharmacological relevance: Hepatic fibrosis (HF) occurs in response to chronic liver injury and may easily develop into irreversible liver cirrhosis or even liver cancer. Amydrium hainanense water extract (AHWE) is a water-soluble component extracted from the Yao medicine Amydrium hainanense (H.Li, Y.Shiao & S.L.Tseng) H.Li, which is commonly used for treating inflammatory diseases in folk. Previous evidence suggested that AHWE significantly inhibited hepatic stellate cell activation. However, little is known regarding the therapeutic effect of AHWE in HF and its underlying action mechanism.Objective: Investigation of the therapeutic effect of AHWE in HF and its underlying mechanism.Methods: The therapeutic effect of AHWE was tested in vivo using an HF mouse model via an intraperitoneal injection of carbon tetrachloride (CCl4). Histological evaluation of liver injury and fibrosis were tested by H&E staining and Masson’s trichrome staining. Serum levels of ALT, AST, collagen type I (Col I), and hydroxyproline (HYP) were measured. The mRNA expression of liver fibrotic and inflammatory genes were tested, and the protein levels of alpha smooth muscle actin (α-SMA) and signal transducers and activators of transcription 3 (STAT3) were analyzed. The in vitro experiments were conducted using HSC-T6 and RAW264.7 cell lines.Results: Treatment with AHWE significantly reversed histopathological liver damage and liver function abnormalities in CCl4 mouse model. Also, the serum levels of ALT, AST, Col I, and HYP in CCl4-induced HF mice were improved in AHWE treatment. Further, AHWE showed a remarkable inhibitory effect on the expression of fibrosis markers (Acta2, Col1a1, and Col3a1) and inflammatory factors (Stat3, Tnfa, Il6, and Il1b) induced by CCl4. The results of in vitro experiments were consistent with those obtained in vivo. In addition, it is shown that STAT3 signaling was involved in the anti-fibrotic effects of AHWE as evidenced by STAT3 overexpression.Conclusion: The present study proposed a novel ethnomedicine for HF and suggested the underlying role of STAT3 signaling pathway regulation in this anti-fibrotic effect of the proposed medicine. These findings would serve as solid scientific evidence in support of the development of AHWE as a novel alternative or complementary therapy for HF prevention and treatment

hDOT1L Links Histone Methylation to Leukemogenesis

SummaryEpigenetic modifications play an important role in human cancer. One such modification, histone methylation, contributes to human cancer through deregulation of cancer-relevant genes. The yeast Dot1 and its human counterpart, hDOT1L, methylate lysine 79 located within the globular domain of histone H3. Here we report that hDOT1L interacts with AF10, an MLL (mixed lineage leukemia) fusion partner involved in acute myeloid leukemia, through the OM-LZ region of AF10 required for MLL-AF10-mediated leukemogenesis. We demonstrate that direct fusion of hDOT1L to MLL results in leukemic transformation in an hDOT1L methyltransferase activity-dependent manner. Transformation by MLL-hDOT1L and MLL-AF10 results in upregulation of a number of leukemia-relevant genes, such as Hoxa9, concomitant with hypermethylation of H3-K79. Our studies thus establish that mistargeting of hDOT1L to Hoxa9 plays an important role in MLL-AF10-mediated leukemogenesis and suggests that the enzymatic activity of hDOT1L may provide a potential target for therapeutic intervention