Relative Well-Posedness of Constrained Systems with Applications to Variational Inequalities

The paper concerns foundations of sensitivity and stability analysis, being primarily addressed constrained systems. We consider general models, which are described by multifunctions between Banach spaces and concentrate on characterizing their well-posedness properties that revolve around Lipschitz stability and metric regularity relative to sets. The enhanced relative well-posedness concepts allow us, in contrast to their standard counterparts, encompassing various classes of constrained systems. Invoking tools of variational analysis and generalized differentiation, we introduce new robust notions of relative coderivatives. The novel machinery of variational analysis leads us to establishing complete characterizations of the relative well-posedness properties with further applications to stability of affine variational inequalities. Most of the obtained results valid in general infinite-dimensional settings are also new in finite dimensions.Comment: 25 page

An inexact regularized proximal Newton method for nonconvex and nonsmooth optimization

This paper focuses on the minimization of a sum of a twice continuously differentiable function $f$ and a nonsmooth convex function. We propose an inexact regularized proximal Newton method by an approximation of the Hessian $\nabla^2\!f(x)$ involving the $\varrho$th power of the KKT residual. For $\varrho=0$, we demonstrate the global convergence of the iterate sequence for the KL objective function and its $R$-linear convergence rate for the KL objective function of exponent $1/2$. For $\varrho\in(0,1)$, we establish the global convergence of the iterate sequence and its superlinear convergence rate of order $q(1\!+\!\varrho)$ under an assumption that cluster points satisfy a local H\"{o}lderian local error bound of order $q\in(\max(\varrho,\frac{1}{1+\varrho}),1]$ on the strong stationary point set; and when cluster points satisfy a local error bound of order $q>1+\varrho$ on the common stationary point set, we also obtain the global convergence of the iterate sequence, and its superlinear convergence rate of order $\frac{(q-\varrho)^2}{q}$ if $q>\frac{2\varrho+1+\sqrt{4\varrho+1}}{2}$. A dual semismooth Newton augmented Lagrangian method is developed for seeking an inexact minimizer of subproblem. Numerical comparisons with two state-of-the-art methods on $\ell_1$-regularized Student's $t$-regression, group penalized Student's $t$-regression, and nonconvex image restoration confirm the efficiency of the proposed method

Online Combinatorial Auctions for Resource Allocation with Supply Costs and Capacity Limits

We study a general online combinatorial auction problem in algorithmic mechanism design. A provider allocates multiple types of capacity-limited resources to customers that arrive in a sequential and arbitrary manner. Each customer has a private valuation function on bundles of resources that she can purchase (e.g., a combination of different resources such as CPU and RAM in cloud computing). The provider charges payment from customers who purchase a bundle of resources and incurs an increasing supply cost with respect to the totality of resources allocated. The goal is to maximize the social welfare, namely, the total valuation of customers for their purchased bundles, minus the total supply cost of the provider for all the resources that have been allocated. We adopt the competitive analysis framework and provide posted-price mechanisms with optimal competitive ratios. Our pricing mechanism is optimal in the sense that no other online algorithms can achieve a better competitive ratio. We validate the theoretic results via empirical studies of online resource allocation in cloud computing. Our numerical results demonstrate that the proposed pricing mechanism is competitive and robust against system uncertainties and outperforms existing benchmarks.Comment: arXiv admin note: text overlap with arXiv:2004.0964

Exploring the curriculum development in content and language integrated learning: A systematic review

Content and language integrated learning (CLIL) is a booming innovation pervading many educational settings. The global spread of CLIL is being practiced in classrooms the world over. Nevertheless, there is still a lack of systematic curricula for CLIL, despite its widespread adoption. Furthermore, the majority of teachers are implementing CLIL without the support of suitable published materials or resource banks. To explore and explain the curriculum development in CLIL, 281 studies from 2009 to 2019 were reviewed systematically, focusing on peer-reviewed English-language journals. We identified studies through using 'Content and Language Integrated Learning' and CLIL as the search terms in the ProQuest Research Library and EBSCOhost databases. Selected articles were organized into five inquiry areas and analyzed thematically, inspired by the curriculum development model proposed by Pawlas and Oliva: 1) CLIL philosophy; 2) CLIL goals; 3) CLIL plan; 4) CLIL implementation; and 5) CLIL evaluation. Based on these themes, Boyer's scholarship of integration was introduced to propose a holistic model for CLIL curriculum development

Revision of the orb-weaver spider genus Gea C.L. Koch, 1843 (Araneae, Araneidae) from China

The orb-weaver spider genus Gea C.L. Koch, 1843 from China is revised, and three species including one new species, are recognized: Gea jingdong Mi, Wang & Gan, sp. nov. (♂♀) from Yunnan; Gea spinipes C.L. Koch, 1843 (♂♀) from Guangdong, Guangxi, Guizhou, Hainan, Taiwan, and Yunnan; and Gea subarmata Thorell, 1890 (♂♀) from Guangxi and Hainan. Gea subarmata is newly recorded in China

Maize microrna166 inactivation confers plant development and abiotic stress resistance

MicroRNAs are important regulators in plant developmental processes and stress responses. In this study, we generated a series of maize STTM166 transgenic plants. Knock-down of miR166 resulted in various morphological changes, including rolled leaves, enhanced abiotic stress resistance, inferior yield-related traits, vascular pattern and epidermis structures, tassel architecture, as well as abscisic acid (ABA) level elevation and indole acetic acid (IAA) level reduction in maize. To profile miR166 regulated genes, we performed RNA-seq and qRT-PCR analysis. A total of 178 differentially expressed genes (DEGs) were identified, including 118 up-regulated and 60 down-regulated genes. These DEGs were strongly enriched in cell and intercellular components, cell membrane system components, oxidoreductase activity, single organism metabolic process, carbohydrate metabolic process, and oxidation reduction process. These results indicated that miR166 plays important roles in auxin and ABA interaction in monocots, yet the specific mechanism may differ from dicots. The enhanced abiotic stress resistance is partly caused via rolling leaves, high ABA content, modulated vascular structure, and the potential changes of cell membrane structure. The inferior yield-related traits and late flowering are partly controlled by the decreased IAA content, the interplay of miR166 with other miRNAs and AGOs. Taken together, the present study uncovered novel functions of miR166 in maize, and provide insights on applying short tandem target mimics (STTM) technology in plant breeding

Human EVI2B acts as a Janus-faced oncogene/antioncogene by differently affecting as per cancer type neoplastic cells growth and immune infiltration

Objectives: The EVI2B (Ecotropic Viral Integration Site 2B) gene encodes a transmembrane glycoprotein pivotal in immunocytes maturation. Recent evidence implicated EV12B’s expression with human colon cancer progression. However, EVI2B’s downstream pathways affecting tumor growth and tumor-infiltrating cells remain unclear. Methods: We first studied the diagnostic and prognostic value of EVI2B in pan-cancers by utilizing a series of in silico tools and clinical samples. Then we identified the modulated transcriptional expression and DNA methylation in high EVI2B’s expression groups of the same three cancers. We verified via RT-PCR the effect of stable EVI2B knock-down on the expression of JAK/STAT-related genes in two immune cell lines and the acceleration of proliferation in four cancer cell lines. Finally, the regulation of leukocyte infiltration was studied using TIMER. Results: In SKCM and LUAD a heightened EVI2B’s expression promoted a better prognosis. Conversely, in LGG EVI2B’s upregulation concurred with a worse prognosis. EVI2B silencing enhanced the proliferation of the tumor cell lines. The hypermethylated genome strengthened EVI2B’s Janus-like effect in high EVI2B expressing SKCM and LUAD tumors. While the total DNA methylation was lower in high EVI2B expressing LGG. Further analysis revealed that multiple EVI2B-involved down-stream JAK-STAT genes also exhibited the Janus-like feature in SKCM, LUAD and LGG progression. Correspondingly, anti-tumor leukocytes infiltrated EVI2B high expressing SKCM and LUAD while more pro-tumor ones penetrated into EVI2B heightened LGG. Conclusions: EVI2B acts as a Janus-faced oncogene/antioncogene by differently affecting neoplastic cell proliferation rates and tumor-promoting or tumor-hindering immunocytes’ infiltration