The Jacobian Conjecture 2n implies the Dixmier Problem n

The aim of the paper is to describe some ideas, approaches, comments, etc. regarding the Dixmier Conjecture, its generalizations and analogues

Normal subgroups in the Cremona group (long version)

Let k be an algebraically closed field. We show that the Cremona group of all birational transformations of the projective plane P^2 over k is not a simple group. The strategy makes use of hyperbolic geometry, geometric group theory, and algebraic geometry to produce elements in the Cremona group that generate non trivial normal subgroups.Comment: With an appendix by Yves de Cornulier. Numerous but minors corrections were made, regarding proofs, references and terminology. This long version contains detailled proofs of several technical lemmas about hyperbolic space

ISR meets SAR outside: Additive action of the endophyte Bacillus pumilus INR7 and the chemical inducer, benzothiadiazole, on induced resistance against bacterial spot in field-grown pepper

Induced resistance has been recognised as an attractive tool for plant disease management in modern agriculture. During the last two decades, studies on chemically- and biologically-elicited induced resistance have revealed previously unknown features of the plant defence response including defence priming. As a biological trigger for induced resistance, plant growth-promoting rhizobacteria (PGPR) are a group of root-associated bacteria that can reduce plant disease severity and incidence, and augment plant growth and yield under greenhouse and field conditions. We evaluated the potential of an endophytic PGPR, Bacillus pumilus INR7, to induce systemic resistance against bacterial spot caused by Xanthomonas axonopodis pv. vesicatoria in pepper. Trials in the greenhouse showed significantly less symptom development in pepper plants inoculated with strain INR7 compared to a water treatment. Furthermore, a single dipping treatment with INR7 before transplantation of pepper plants into the field elicited an induced systemic resistance (ISR) response against bacterial spot caused by artificially infiltration of X. axonopodis pv. vesicatoria and even against naturally occurring bacterial spot disease. We identified an additiveeffect on induced resistance after administration of a combination treatment composed of strain INR7 with a chemical inducer, benzothiadiazole (BTH) in the field. The combination treatment stimulated expression of pepper defence marker genes CaPR1, CaTin1, and CaPR4 to a greater extent than did treatment with either agent alone. Similar experiments conducted with tobacco revealed no additive effects under field conditions. Interestingly, co-application of plants with INR7 lifted the growth repressing effect of BTH. Application of benzothiadiazole onto pepper and tobacco did not affect rhizosphere colonisation but supported a higher population density inside plant roots when compared to water-treated control plants. Our results indicate that PGPR ca

Long Noncoding RNA E2F4as Promotes Progression and Predicts Patient Prognosis in Human Ovarian Cancer

(1) Background: LncRNAs could be a promising biomarker to predict the prognosis of various cancers. The significance of E2F4antisense lncRNA remains unclear in cancer. In this study, we examined the expression level of E2F4as in the serum of ovarian cancer patients and the functional role of E2F4as. (2) Methods: Serum samples were obtained from 108 OC patients and 32 normal patients to measure the expression of E2F4as in the serum. Ovarian cancer cells were used to investigate the role of E2F4as in cell proliferation, invasion, migration and apoptosis, and the expression of E2F4as was knocked down using RNA interference. In addition, E2F4as knockdown cell lines were used in in vivo experiments. (3) Results: The expression of E2F4as was significantly higher in the serum of OC patients than in that of control patients (p < 0.05). The knockdown of E2F4as in ovarian cancer cells led to a decrease in cell proliferation, invasion and migration and an increase in apoptosis. E2F4as knockdown also reduced the expression of epithelium–mesenchymal metastasis (EMT) genes. (4) Conclusion: These findings highlight the clinical significance of E2F4as in predicting the prognosis of OC patients and suggest its potential in promoting tumour aggressiveness by the regulation of EMT-related mechanisms

LncRNA SNHG4 Modulates EMT Signal and Antitumor Effects in Endometrial Cancer through Transcription Factor SP-1

Long non-coding RNAs (lncRNAs) are implicated in the initiation and progression of a variety of tumors, including endometrial cancer. However, the mechanisms of lncRNA in endometrial cancer formation and progression remain largely unknown. In this study, we confirmed that the lncRNA SNHG4 is upregulated in endometrial cancer and correlates with lower survival rates in endometrial cancer patients. Knock-down of SNHG4 significantly reduced cell proliferation, colonization, migration, and invasion in vitro, as well as modulating the cell cycle and reduced tumor growth of endometrial cancer in vivo. In addition, the effect of SNHG4 by the transcription factor SP-1 was confirmed in vitro. We found in this study that SNHG4/SP-1 plays an important role in endometrial cancer progression and may be used as a potential therapeutic and prognostic biomarker for endometrial cancer