Recurrence and winding number for a revolving random walk

We consider simple random walks on two partially directed square lattices. One common feature of these walks is that they are bound to revolve clockwise; however they exhibit different recurrence/transience behaviors. Our main result is indeed a proof of recurrence for one of the graphs, solving a conjecture of Menshikov et al. ('17). For the other one, we analyze the asymptotics of the return probabilities, providing a new proof of its transience. Furthermore, we study the limiting laws of the winding number around the origin for these walks.Comment: 23 page

Research Hotspots and Trends of Microrna in Periodontology and Dental Implantology: a Bibliometric analysis

BACKGROUND: Periodontal disease is a leading cause of tooth loss, and microRNA (miRNA) has been shown to regulate various biological processes. This study aimed to quantitatively analyze the literature related to miRNA in periodontology and dental implantology and summarize the research hotspots and trends in this field. METHODS: Literature records from 1985 to 2020 were obtained from the Web of Science Core Collection database. After manual selection, the data was used for cooperative network analysis, keyword co-occurrence analysis, and reference co-citation analysis and visualized by CiteSpace. RESULTS: A total of 287 papers were analyzed between 2007 and 2020, and more than 95% of them were published in the past decade. The largest number of publications were from China, followed by the USA and Japan. The direct cooperation among the productive institutions was not close. At present, most of the research belongs to the discipline of dentistry, oral surgery, cell biology, and molecular biology. Literature clusters generated by reference co-citation analysis and keyword co-occurrence network showed that previous studies mainly focused on four hotspots: periodontal ligament stem cells (PDLSCs), the pathological process of periodontitis, osteogenic differentiation/bone regeneration, and the competing endogenous RNA (ceRNA) network. CONCLUSIONS: The therapeutic potential of miRNA in promoting bone formation and how the ceRNA network contributes to miRNA regulation at a deeper level have become the two main research trends of this field

Progressive IRP Models for Power Resources Including EPP

In the view of optimizing regional power supply and demand, the paper makes effective planning scheduling of supply and demand side resources including energy efficiency power plant (EPP), to achieve the target of benefit, cost, and environmental constraints. In order to highlight the characteristics of different supply and demand resources in economic, environmental, and carbon constraints, three planning models with progressive constraints are constructed. Results of three models by the same example show that the best solutions to different models are different. The planning model including EPP has obvious advantages considering pollutant and carbon emission constraints, which confirms the advantages of low cost and emissions of EPP. The construction of progressive IRP models for power resources considering EPP has a certain reference value for guiding the planning and layout of EPP within other power resources and achieving cost and environmental objectives

FGF Receptor-Mediated Gene Delivery Using Ligands Coupled to PEI-β-CyD

A novel vector with high gene delivery efficiency and special cell-targeting ability was developed using a good strategy that utilized low-molecular-weight polyethylenimine (PEI; molecular weight: 600 KDa [PEI600]) crosslinked to β-cyclodextrin (β-CyD) via a facile synthetic route. Fibroblast growth factor receptors (FGFRs) are highly expressed in a variety of human cancer cells and are potential targets for cancer therapy. In this paper, CY11 peptides, which have been proven to combine especially with FGFRs on cell membranes were coupled to PEI-β-CyD using N-succinimidyl-3-(2-pyridyldithio) propionate as a linker. The ratios of PEI600, β-CyD, and peptide were calculated based on proton integral values obtained from the 1H-NMR spectra of the resulting products. Electron microscope observations showed that CY11-PEI-β-CyD can efficiently condense plasmid DNA (pDNA) into nanoparticles of about 200 nm, and MTT assays suggested the decreased toxicity of the polymer. Experiments on gene delivery efficiency in vitro showed that CY11-PEI-β-CyD/pDNA polyplexes had significantly greater transgene activities than PEI-β-CyD/pDNA in the COS-7 and HepG2 cells, which positively expressed FGFR, whereas no such effect was observed in the PC-3 cells, which negatively expressed FGFR. Our current research indicated that the synthesized nonviral vector shows improved gene delivery efficiency and targeting specificity in FGFR-positive cells