The Sylvester equation and integrable equations: I. The Korteweg-de Vries system and sine-Gordon equation

The paper is to reveal the direct links between the well known Sylvester equation in matrix theory and some integrable systems. Using the Sylvester equation $\boldsymbol{K} \boldsymbol{M}+\boldsymbol{M} \boldsymbol{K}=\boldsymbol{r}\, \boldsymbol{s}^{T}$ we introduce a scalar function $S^{(i,j)}=\boldsymbol{s}^{T}\, \boldsymbol{K}^j(\boldsymbol{I}+\boldsymbol{M})^{-1}\boldsymbol{K}^i\boldsymbol{r}$ which is defined as same as in discrete case. $S^{(i,j)}$ satisfy some recurrence relations which can be viewed as discrete equations and play indispensable roles in deriving continuous integrable equations. By imposing dispersion relations on $\boldsymbol{r}$ and $\boldsymbol{s}$, we find the Korteweg-de Vries equation, modified Korteweg-de Vries equation, Schwarzian Korteweg-de Vries equation and sine-Gordon equation can be expressed by some discrete equations of $S^{(i,j)}$ defined on certain points. Some special matrices are used to solve the Sylvester equation and prove symmetry property $S^{(i,j)}=S^{(i,j)}$. The solution $\boldsymbol{M}$ provides $\tau$ function by $\tau=|\boldsymbol{I}+\boldsymbol{M}|$. We hope our results can not only unify the Cauchy matrix approach in both continuous and discrete cases, but also bring more links for integrable systems and variety of areas where the Sylvester equation appears frequently.Comment: 23 page

A Deep Learning Prediction Model Based on Extreme-Point Symmetric Mode Decomposition and Cluster Analysis

Aiming at the irregularity of nonlinear signal and its predicting difficulty, a deep learning prediction model based on extreme-point symmetric mode decomposition (ESMD) and clustering analysis is proposed. Firstly, the original data is decomposed by ESMD to obtain the finite number of intrinsic mode functions (IMFs) and residuals. Secondly, the fuzzy c-means is used to cluster the decomposed components, and then the deep belief network (DBN) is used to predict it. Finally, the reconstructed IMFs and residuals are the final prediction results. Six kinds of prediction models are compared, which are DBN prediction model, EMD-DBN prediction model, EEMD-DBN prediction model, CEEMD-DBN prediction model, ESMD-DBN prediction model, and the proposed model in this paper. The same sunspots time series are predicted with six kinds of prediction models. The experimental results show that the proposed model has better prediction accuracy and smaller error

Earnings Management for Second-time IPOs: Evidence from China

In China’s IPO market, firms that fail in their first IPO application make considerable adjustments before making their second IPO application. Examining firms that applied for IPOs during 2004-2018, we find that failed IPO applicant firms “package” themselves to obtain approval of the China Securities Regulatory Commission (CSRC) by reducing accrual earnings management and increasing real earnings management. In addition, after a successful second IPO application, these firms relax their vigilance vis-à-vis the CSRC and increase both accrual and real earnings management. This pre-IPO “packaging” behavior deceives investors, leading to higher IPO prices and higher post-IPO returns

TENSILE: A Tensor granularity dynamic GPU memory scheduling method towards multiple dynamic workloads system

Recently, deep learning has been an area of intense research. However, as a kind of computing-intensive task, deep learning highly relies on the scale of GPU memory, which is usually prohibitive and scarce. Although there are some extensive works have been proposed for dynamic GPU memory management, they are hard to be applied to systems with multiple dynamic workloads, such as in-database machine learning systems. In this paper, we demonstrated TENSILE, a method of managing GPU memory in tensor granularity to reduce the GPU memory peak, considering the multiple dynamic workloads. TENSILE tackled the cold-starting and across-iteration scheduling problem existing in previous works. We implement TENSILE on a deep learning framework built by ourselves and evaluated its performance. The experiment results show that TENSILE can save more GPU memory with less extra time overhead than prior works in both single and multiple dynamic workloads scenarios

Genetically predicted serum testosterone and risk of gynecological disorders: a Mendelian randomization study

BackgroundTestosterone plays a key role in women, but the associations of serum testosterone level with gynecological disorders risk are inconclusive in observational studies.MethodsWe leveraged public genome-wide association studies to analyze the effects of four testosterone related exposure factors on nine gynecological diseases. Causal estimates were calculated by inverse variance–weighted (IVW), MR–Egger and weighted median methods. The heterogeneity test was performed on the obtained data through Cochrane’s Q value, and the horizontal pleiotropy test was performed on the data through MR–Egger intercept and MR-PRESSO methods. “mRnd” online analysis tool was used to evaluate the statistical power of MR estimates.ResultsThe results showed that total testosterone and bioavailable testosterone were protective factors for ovarian cancer (odds ratio (OR) = 0.885, P = 0.012; OR = 0.871, P = 0.005) and endometriosis (OR = 0.805, P = 0.020; OR = 0.842, P = 0.028) but were risk factors for endometrial cancer (OR = 1.549, P < 0.001; OR = 1.499, P < 0.001) and polycystic ovary syndrome (PCOS) (OR = 1.606, P = 0.019; OR = 1.637, P = 0.017). dehydroepiandrosterone sulfate (DHEAS) is a protective factor against endometriosis (OR = 0.840, P = 0.016) and premature ovarian failure (POF) (OR = 0.461, P = 0.046) and a risk factor for endometrial cancer (OR= 1.788, P < 0.001) and PCOS (OR= 1.970, P = 0.014). sex hormone-binding globulin (SHBG) is a protective factor against endometrial cancer (OR = 0.823, P < 0.001) and PCOS (OR = 0.715, P = 0.031).ConclusionOur analysis suggested causal associations between serum testosterone level and ovarian cancer, endometrial cancer, endometriosis, PCOS, POF

Tumor-Like Stem Cells Derived from Human Keloid Are Governed by the Inflammatory Niche Driven by IL-17/IL-6 Axis

Background: Alterations in the stem cell niche are likely to contribute to tumorigenesis; however, the concept of niche promoted benign tumor growth remains to be explored. Here we use keloid, an exuberant fibroproliferative dermal growth unique to human skin, as a model to characterize benign tumor-like stem cells and delineate the role of their pathological niche in the development of the benign tumor. Methods and Findings: Subclonal assay, flow cytometric and multipotent differentiation analyses demonstrate that keloid contains a new population of stem cells, named keloid derived precursor cells (KPCs), which exhibit clonogenicity, self-renewal, distinct embryonic and mesenchymal stem cell surface markers, and multipotent differentiation. KPCs display elevated telomerase activity and an inherently upregulated proliferation capability as compared to their peripheral normal skin counterparts. A robust elevation of IL-6 and IL-17 expression in keloid is confirmed by cytokine array, western blot and ELISA analyses. The altered biological functions are tightly regulated by the inflammatory niche mediated by an autocrine/paracrine cytokine IL-17/IL-6 axis. Utilizing KPCs transplanted subcutaneously in immunocompromised mice we generate for the first time a human keloid-like tumor model that is driven by the in vivo inflammatory niche and allows testing of the anti-tumor therapeutic effect of antibodies targeting distinct niche components, specifically IL-6 and IL-17. Conclusions/Significance: These findings support our hypothesis that the altered niche in keloids, predominantly inflammatory, contributes to the acquirement of a benign tumor-like stem cell phenotype of KPCs characterized by the uncontrolled self-renewal and increased proliferation, supporting the rationale for in vivo modification of the pathological stem cell niche as a novel therapy for keloid and other mesenchymal benign tumors. © 2009 Zhang et al

Long noncoding RNA DANCR, working as a competitive endogenous RNA, promotes ROCK1-mediated proliferation and metastasis via decoying of miR-335-5p and miR-1972 in osteosarcoma

Background: Accumulating evidences indicate that non-coding RNAs (ncRNAs) including long non-coding RNAs (lncRNAs) and microRNAs (miRNAs) acting as crucial regulators in osteosarcoma (OS). Previously, we reported that Rho associated coiled-coil containing protein kinase 1 (ROCK1), a metastatic-related gene was negatively regulated by microRNA-335-5p (miR-335-5p) and work as an oncogene in osteosarcoma. Whether any long non-coding RNAs participate in the upstream of miR-335-5p/ROCK1 axial remains unclear. Methods: Expression of differentiation antagonizing non-protein coding RNA (DANCR) and miR-335-5p/miR-1972 in osteosarcoma tissues were determined by a qRT-PCR assay and an ISH assay. Osteosarcoma cells' proliferation and migration/invasion ability changes were measured by a CCK-8/EDU assay and a transwell assay respectively. ROCK1 expression changes were checked by a qRT-PCR assay and a western blot assay. Targeted binding effects between miR-335-5p/miR-1972 and ROCK1 or DANCR were verified by a dual luciferase reporter assay and a RIP assay. In vivo experiments including a nude formation assay as well as a CT scan were applied to detect tumor growth and metastasis changes in animal level. Results: In the present study, an elevated DNACR was found in osteosarcoma tissue specimens and in osteosarcoma cell lines, and the elevated DNACR was closely correlated with poor prognosis in clinical patients. Functional experiments illustrated that a depression of DANCR suppressed ROCK1-mediated proliferation and metastasis in osteosarcoma cells. The results of western blot assays and qRT-PCR assays revealed that DANCR regulated ROCK1 via crosstalk with miR-335-5p and miR-1972. Further cellular behavioral experiments demonstrated that DNACR promoted ROCK1-meidated proliferation and metastasis through decoying both miR-335-5p and miR-1972. Finally, the outcomes of in vivo animal models showed that DANCR promoted tumor growth and lung metastasis of osteosarcoma. Conclusions: LncRNA DANCR work as an oncogene and promoted ROCK1-mediated proliferation and metastasis through acting as a competing endogenous RNA (ceRNA) in osteosarcoma