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In this paper, we show that each element in the convex hull of the rotation set of a compact invariant chain transitive set is realized by a Birkhoff solution, which is an improvement of the fundamental lemma of T. Zhou and W.-X. Qin [Pseudo solutions, rotation sets, and shadowing rotations for monotone recurrence relations. Math. Z. 297 (2021), 1673–1692] in the study of rotation sets for monotone recurrence relations. We then investigate the properties of rotation sets assuming the system has zero topological entropy. The rotation set for a Birkhoff recurrence class is a singleton and the forward and backward rotation numbers are identical for each solution in the same Birkhoff recurrence class. We also show the continuity of rotation numbers on the set of non-wandering points. If the rotation set is upper-stable, then we show that each boundary point is a rational number, and we also obtain a result of bounded deviation.

To investigate the antitumor effects of probiotics Clostridium butyricum and Bacillus subtilis on colorectal cancer (CRC) progression. The effects of C. butyricum and B. subtilis on CRC cells were studied. Male C57BL/6 mice with 1,2-dimethylhydrazine dihydrochloride (DMH)-induced CRC were intervened by these two probiotics and the antitumor effects were examined by comparing the tumor incidence and detecting the inflammatory and immune-related markers. C. butyricum and B. subtilis inhibited the proliferation of CRC cells, caused cell cycle arrest and promoted apoptosis. In vivo, these two probiotics inhibited the development of DMH-induced CRC. The molecular mechanism involved reduced inflammation and improved immune homeostasis. This work establishes a basis for the protective role of probiotics B. subtilis and C. butyricum in intestinal tumorigenesis.

Background: Dickkopf-1 (DKK1), a secreted protein, is known as a negative regulator of the Wnt signaling pathway, which has been implicated in the development of several types of cancers. Clinical significance of serum DKK1 in lung cancer remains to be determined. Methods: A novel time-resolved immunofluorometric assay was developed. By use of this method, we investigated the serum concentrations of DKK1 in 592 patients with malignancies, 72 patients with benign lung disease, and 120 healthy controls. Serum cytokeratin 19 fragment and neuron-specific enolase values were obtained. Results: Serum DKK1 concentrations were significantly higher in patients with lung cancer than in patients with other malignant tumors or benign lung diseases and healthy controls. Serum concentrations of DKK1 were decreased significantly in groups of patients with gastric cancer, colorectal cancer, ovarian cancer, and cervical adenocarcinoma compared with healthy controls. Application of both DKK1 and cytokeratin 19 fragment increased sensitivity, correctly identifying 89.6% of the non–small cell lung cancer patients as positive. The use of both DKK1 and neuron-specific enolase increased sensitivity to detect small cell lung cancer to 86.2%. DKK1 concentrations increased with stage, tumor class, and presence of lymph node and distant metastases, regardless of histology and patient age and sex. Patients with a DKK1 concentration of 22.6 μg/L or higher had a statistically significantly diminished survival compared with patients whose DKK1 values were lower. Conclusions: DKK1 was preferentially expressed in lung cancer. Increasing concentrations of DKK1were significantly associated with tumor progression and decreased survival in patients with lung cancer. .

We associate the existence or non-existence of rotational invariant circles of an area-preserving twist map on the cylinder with a physically motivated quantity, the depinning force, which is a critical value in the depinning transition. Assume that $H:\\mathbb{R}^{2}\\mapsto \\mathbb{R}$ is a $C^{2}$ generating function of an exact area-preserving twist map $\\bar{\\unicode[STIX]{x1D711}}$ and consider the tilted Frenkel–Kontorova (FK) model: $$\\begin{eqnarray}{\\dot{x}}_{n}=-D_{1}H(x_{n},x_{n+1})-D_{2}H(x_{n-1},x_{n})+F,\\quad n\\in \\mathbb{Z},\\end{eqnarray}$$ where $F\\geq 0$ is the driving force. The depinning force is the critical value $F_{d}(\\unicode[STIX]{x1D714})$ depending on the mean spacing $\\unicode[STIX]{x1D714}$ of particles, above which the tilted FK model is sliding, and below which the particles are pinned. We prove that there exists an invariant circle with irrational rotation number $\\unicode[STIX]{x1D714}$ for $\\bar{\\unicode[STIX]{x1D711}}$ if and only if $F_{d}(\\unicode[STIX]{x1D714})=0$ . For rational $\\unicode[STIX]{x1D714}$ , $F_{d}(\\unicode[STIX]{x1D714})=0$ is equivalent to the existence of an invariant circle on which $\\bar{\\unicode[STIX]{x1D711}}$ is topologically conjugate to the rational rotation with rotation number $\\unicode[STIX]{x1D714}$ . Such conclusions were claimed much earlier by Aubry et al. We also show that the depinning force $F_{d}(\\unicode[STIX]{x1D714})$ is continuous at irrational $\\unicode[STIX]{x1D714}$ .

Background A remolded microenvironment in hepatocellular carcinoma (HCC) caused by abnormally expressed matricellular proteins could promote HCC progression. The cell-matrix interactions mediated by integrins play an important role in tumor microenvironment. Epidermal Growth Factor-like repeats and Discoidin I-Like Domains 3 (EDIL3), an extracellular matrix (ECM) protein with angiogenic and anti-inflammatory effects, is abnormally highly expressed in HCC. Here we aim to analyze its expression in liver and HCC tissues, investigate the underlined mechanisms accounted for HCC progression. Methods EDIL3 expression level is examined in normal liver, cirrhotic liver and HCC at both mRNA and protein level. The association between EDIL3 and clinical outcomes is analyzed. The pattern of EDIL3 expression and location is examined using Immunofluorescence and ELISA. Overexpression or knock-down of EDIL3 in a panel of cell lines are subjected to assays related to proliferation, invasion, and anoikis to investigate the mechanisms of this matrix protein in HCC progression. Recombinant EDIL3 treatment is applied to confirm the results. Results Compared with normal liver and cirrhotic liver, EDIL3 is elevated in HCC. High level of EDIL3 protein is much more commonly in patients with larger tumor or portal vein tumor thrombus (PVTT) formation, associated with poor prognosis. EDIL3 is abundantly expressed in HCC cells and secreted by cancer cells. In vitro and in vivo studies indicate that EDIL3, probably in an autocrine manner, inhibits anoikis and promotes anchorage-independent growth of HCC cells. Further mechanistic studies suggest integrin ligation by EDIL3 and thus that the sustained activation of the FAK-Src-AKT signal is responsible for the anoikis resistance and anchorage independence. Both the administration of cilengitide, a RGD-containing integrin antagonist, and silencing of integrin αV, an important RGD-binding integrin, results in the blockade of anoikis-resistance induced by EDIL3. Conclusion Our study suggests that high levels of autocrine EDIL3 may contribute to a receptive microenvironment for the survival of detached HCC cells and may involve in cancer cell spreading. We also highlight the importance of interaction between EDIL3 and integrin αV and suggest disrupting the ligation of EDIL3 to integrins via RGD-blocking in selected patients may bear potential therapeutic value.

We associate the topological entropy of monotone recurrence relations with the Aubry–Mather theory. If there exists an interval $[{\\it\\rho}_{0},{\\it\\rho}_{1}]$ such that, for each ${\\it\\omega}\\in ({\\it\\rho}_{0},{\\it\\rho}_{1})$, all Birkhoff minimizers with rotation number ${\\it\\omega}$ do not form a foliation, then the diffeomorphism on the high-dimensional cylinder defined via the monotone recurrence relation has positive topological entropy.

Employing the monotonicity approach and the theory of orientation preserving circle homeomorphisms, we provide a rigorous analysis on the IV characteristics of the coupled Josephson junctions including an interference term in a specified parameters region. In particular, when the system is driven by a dc-current, we show that there exist either globally stable single-wave-form solutions if and only if the average voltage is nonzero, or equilibria if and only if the average voltage vanishes.

Via the monotonicity approach, we prove that the single-wave-form solution for the underdamped Frenkel-Kontorova model with dc-driving and periodic boundary conditions is globally stable, provided the driving force is large enough.

ABSTRACT CT120, a novel membrane-associated gene implicated in lung carcinogenesis, was previously identified from chromosome 17p13.3 locus, a hot mutation spot involved in human malignancies. In the present study, we further determined that CT120 ectopic expression could promote cell proliferation activity of NIH3T3 cells using MTS assay, and monitored the downstream effects of CT120 in NIH3T3 cells with Atlas mouse cDNA expression arrays. Among 588 known genes, 133 genes were found to be upregulated or downregulated by CT120 . Two major signaling pathways involved in cell proliferation, cell survival and anti-apoptosis were overexpressed and activated in response to CT120: One is the Raf/MEK/Erk signal cascades and the other is the PI3K/Akt signal cascades, suggesting that CT120 might contribute, at least in part, to the constitutively activation of Erk and Akt in human lung caner cells. In addition, some tumor metastasis associated genes cathepsin B, cathepsin D, cathepsin L, MMP-2/TIMP-2 were also upregulated by CT120, upon which CT120 might be involved in tumor invasiveness and metastasis. In addition, CT120 might play an important role in tumor progression through modulating the expression of some candidate “Lung Tumor Progression” genes including B-Raf, Rab-2, BAX, BAG-1, YB-1 , and Cdc42 .

Background： Regenerative techniques help promote the formation of new attachment and bone filling in periodontal detects. However, the dimensions of intraosseous defects are a key determinant of periodontal regeneration outcomes. In this study, we evaluated the efficacy of use of anorganic bovine bone （ABB） graft in combination with collagen membrane （CM）, to facilitate healing ofnoncontained （1-wall） and contained （3-wall） critical size periodontal defects. Methods： The study began on March 2013, and was completed on May 2014. One-wall （7 mm × 4 mm） and 3-wall （5 mm × 4 mm） intrabony periodontal defects were surgically created bilaterally in the mandibular third premolars and first molars in eight beagles. The defects were treated with ABB in combination with CM （ABB ＋ CM group） or open flap debridement （OFD group）. The animals were euthanized at 8-week postsurgery for histological analysis. Two independent Student＇s t-tests （1-wall [ABB ＋ CM] vs. 1-wall [OFD] and 3-wall [ABB ＋ CM] vs. 3-wall [OFD]） were used to assess between-group differences. Results： The mean new bone height in both 1- and 3-wall intrabony defects in the ABB ＋ CM group was significantly greater than that in the OFD group （1-wall： 4.99± 0.70 mm vs. 3.01 ± 0.37 mm, P 〈 0.05; 3-wall： 3.11±0.59 mm vs. 2.08± 0.24 mm, P 〈 0.05）. The mean new cementum in 1-wall intrabony defects in the ABB ＋ CM group was significantly greater than that in their counterparts in the OFD group （5.08 ±0.68 mm vs. 1.16 ± 0.38 mm; P 〈 0.05）. Likewise, only the 1-wall intrabony defect model showed a significant difference with respect to junctional epithelium between ABB ＋ CM and OFD groups （0.67 ±0.23 mm vs. 1.12 ± 0.28 mm, P 〈 0.05）. Conclusions： One-wall intrabony defects treated with ABB and CM did not show less periodontal regeneration than that in 3-wall intrabony defect. The noncontained l-wall intrabony defect might be a more discriminative defect model for further research into periodontal regeneration.