INF Type Research Articles

Asymptotic symmetry and local behavior of solutions of higher order conformally invariant equations with isolated singularities

We prove sharp blow up rates of solutions of higher order conformally invariant equations in a bounded domain with an isolated singularity, and show the asymptotic radial symmetry of the solutions near the singularity. This is an extension of the celebrated theorem of Caffarelli-Gidas-Spruck for the second order Yamabe equation with isolated singularities to higher order equations. Our approach uses blow up analysis for local integral equations, and is unified for all critical elliptic equations of order smaller than the dimension. We also prove the existence of Fowler solutions to the global equations, and establish a sup ⁎ inf type Harnack inequality of Schoen for integral equations.

Tumor infiltrative growth pattern correlates with the immune microenvironment and is an independent factor for lymph node metastasis and prognosis in stage T1 esophageal squamous cell carcinoma.

In this retrospective study, we analyzed the association between the tumor infiltrative growth pattern (INF) and tumor immune environment and its predictive value for lymph node metastasis and overall survival (OS) in stage T1 esophageal squamous cell carcinoma (ESCC). In total, 593 patients with a diagnosis of stage T1 ESCC who underwent esophagectomy and regional lymphadenectomy between 2009 and 2018 were included. The INF type and elements of the tumor immune microenvironment, including tumor infiltrative lymphocytes (TILs) and tertiary lymphoid structures (TLSs), were microscopically evaluated within the tumor invasive margin with hematoxylin and eosin (HE)-stained slices. The infiltrative-type INF (INFc) was associated with low-grade TILs and the absence of TLSs, deep tumor invasion, poorly differentiated phenotype. Multivariate logistic regression identified INFc as one of the independent risk factors for lymph node metastasis. INFc and low-grade TILs were independent inferior predictive factors for OS. A novel histologic risk stratification model was classified as INFa/b and high-grade TILs, INFa/b and low-grade TILs, INFc and high-grade TILs, and INFc and low-grade TILs. The Kaplan-Meier curves showed that INFa/b and high-grade TILs were associated with the best prognosis, and INFc and low-grade TILs were associated with the worst prognosis, and there was significant difference between groups. In conclusion, INFc is an independent risk factor for lymph node metastasis and an independent inferior prognostic factor for stage T1 ESCC. Furthermore, INFc is associated with immunosuppression, and the combination of the INF and TILs is useful for the risk stratification of prognosis.

Small deviations for admixture additive & multiplicative processes

Define the admixture additive processes \t\t\tXγ,H,αa1,a2,a3,a4(t)≜a1B(t1)+a2Wγ(t2)+a3BH(t3)+a4Sα(t4)∈R,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\mathbb{X}^{a_{1}, a_{2}, a_{3}, a_{4}}_{\\gamma,H,\\alpha}(\\mathrm{t})\\triangleq a_{1}B(t_{1})+a_{2}W_{\\gamma}(t_{2})+a_{3}B_{H}(t_{3})+a_{4}S_{\\alpha}(t_{4}) \\in\\mathbb{R}, $$\\end{document} and the admixture multiplicative processes \t\t\tYγ,H,α(t)≜B(t1)⋅Wγ(t2)⋅BH(t3)⋅Sα(t4)∈R,\\documentclass[12pt]{minimal}\t\t\t\t\\usepackage{amsmath}\t\t\t\t\\usepackage{wasysym}\t\t\t\t\\usepackage{amsfonts}\t\t\t\t\\usepackage{amssymb}\t\t\t\t\\usepackage{amsbsy}\t\t\t\t\\usepackage{mathrsfs}\t\t\t\t\\usepackage{upgreek}\t\t\t\t\\setlength{\\oddsidemargin}{-69pt}\t\t\t\t\\begin{document}$$\\mathbb{Y}_{\\gamma,H,\\alpha}(\\mathrm{t})\\triangleq B(t_{1})\\cdot W_{\\gamma}(t_{2})\\cdot B_{H}(t_{3})\\cdot S_{\\alpha}(t_{4})\\in\\mathbb{R}, $$\\end{document} where mathrm{t}=(t_{1},t_{2},t_{3},t_{4})inmathbb{R}_{+}^{mathrm{4}},a_{1},a_{2},a_{3},a_{4} are finite constants, B(t_{1}) is the standard Brownian motion, W_{gamma}(t_{2}) is the fractional integrated Brownian motion with index parameter gamma>-1/2, B_{H}(t_{3}) is the fractional Brownian motion with Hurst parameter Hin(0,1), S_{alpha}(t_{4}) is the stable process with index alphain(0,2], and they are independent of each other. The small deviation for mathbb{X}^{a_{1}, a_{2}, a_{3}, a_{4}}_{gamma,H,alpha}(mathrm{t}) and the lower bound of small deviation for mathbb{Y}_{gamma,H,alpha}(mathrm{t}) are obtained. As an application, limit inf type LIL is given for mathbb{X}^{a_{1}, a_{2}, a_{3}, a_{4}}_{gamma,H,alpha}(mathrm{t}).

MiR-29b negatively regulates MMP2 to impact gastric cancer development by suppress gastric cancer cell migration and tumor growth.

MicroRNAs (miRNAs) are important regulators and associated with the development of many different types of cancer, including gastric cancer. However, their pathophysiologic role and their relevance to tumorigenesis, invasion and metastasis are still unknown. In our current study, we performed microRNA array and found that 28 of miRNAs were differentially expressed in INF type of gastric cancer. Among 28 miRNAs, miR-29b was one of the most significantly down-regulated miRNA. Further bioinformatics analysis showed that MMP2 was a potential target of miR-29b. Interestingly, luciferase analysis showed that miR-29b negatively regulates MMP2 by binding with the miRNA response element (MRE) on the 3'UTR of MMP2. In addition, overexpression of miR-29b significantly decreased the mRNA and protein level of MMP2 and the activity of MMP2 to suppress gastric cancer cell migration. Moreover, lentivirus mediated overexpression of miR-29b dramatically suppressed the ability of BGC823 cells to form colonies in vitro and their ability to develop tumor in vivo in nude mice. Finally, our qPCR and western blot analysis showed that miR-29b was significantly reduced in clinical gastric cancer tissue, whereas MMP2 protein was significantly up-regulated, suggesting that this aberrant down-regulation of miR-29b might be associated with the abnormal regulation of MMP2 and the development of gastric cancer. Significant apparent was also found between miR-29b expression and TNM staging, lymph node status, tumor differentiation and Ming classification. Together, our data suggest an important regulatory role of miR-29b in the development of gastric cancer. Thus, miR-29b and MMP2 might be important diagnostic or therapeutic targets for human tumor diseases.

A classification of solutions of a fourth order semi-linear elliptic equation in $\mathbb R^n$

In this paper, we classify all regular sign changing~solutions~of $$ \Delta ^2 u=u_+^{p} \,\,\,\mbox {in}\, \, \mathbb R^n\ \ \,\,u_+^{p}\in L^1(\mathbb R^n), $$ where $\Delta ^2$ denotes the biharmonic operator in $\mathbb R^n$, $1 < p\leq \frac{n}{n-4}$ and $n\geq 5$. We prove by using the procedure of moving parallel planes that such solutions are radially symmetric about some point in $\mathbb R^n$. We also present a sup+inf type inequality for regular solutions of the following equation: $$ (-\Delta )^m u=u_+^{p}\,\,\,\mbox{in}\,\,\, \Omega, $$ where $\Omega$ is a bounded domain in $\mathbb R^n$, $m\geq1$, $n\geq 2m+1$ and $p\in (1,(n+2m)/(n-2m) )$.

Tumor infiltrative pattern predicts sites of recurrence after curative gastrectomy for gastric cancer.

38 Background: In East Asia, the tumor infiltrative pattern (INF) has been routinely evaluated by hematoxylin and eosin-stained sections as a pathologic characteristic of surgically resected specimens. Methods: The infiltrative pattern of gastric cancer (GC) has been histopathologically classified as INFa (expansive growth), INFb (intermediate type) and INFc (infiltrative growth) according to the Japanese Classification of Gastric Carcinoma. The prognostic value and characteristics of the disease recurrence pattern for each INF type were assessed in 785 patients with various stages of GC and also in 243 patients with stages 2 and 3 GC. Results: Comparison of the overall survival experienced by patients independently of stage showed that INF was significantly associated with prognosis. Specifically, peritoneal metastasis was present in 91 % of stage 4 patients in the INFc group, whereas hepatic metastasis was present in 39 % of stage 4 patients in the INFa and INFb group. After curative gastrectomy of patients with stages 2 or 3 GC, INF was not significantly associated with survival. The prevalence of peritoneal recurrence was significantly higher in the INFc group than in the INFa and INFb group, whereas the prevalence of hepatic recurrence was significantly higher in the INFa and INFb group than in the INFc group. Multivariate analysis identified INFc as an independent risk factor for peritoneal recurrence after curative gastrectomy. The association of the INF type with the incidence of peritoneal recurrence was observed with all disease stages regardless whether the patient was given adjuvant chemotherapy or not. Conclusions: Evaluation of the INF type shows promise for its role as a predictor of postoperative recurrence sites in patients with GC.

Tumor Infiltrative Pattern Predicts Sites of Recurrence After Curative Gastrectomy for Stages 2 and 3 Gastric Cancer.

In East Asia, the tumor infiltrative pattern (INF) has been routinely evaluated by hematoxylin and eosin-stained sections as a pathologic characteristic of surgically resected specimens. The infiltrative pattern of gastric cancer (GC) has been histopathologically classified as INFa (expansive growth), INFb (intermediate type) and INFc (infiltrative growth) according to the Japanese Classification of Gastric Carcinoma. The prognostic value and characteristics of the disease recurrence pattern for each INF type were assessed in 785 patients with various stages of GC and also in 243 patients with stages 2 and 3 GC. Comparison of the overall survival experienced by patients independently of stage showed that INF was significantly associated with prognosis. Specifically, peritoneal metastasis was present in 91% of stage 4 patients in the INFc group, whereas hepatic metastasis was present in 39% of stage 4 patients in the INFa and INFb group. After curative gastrectomy of patients with stages 2 or 3 GC, INF was not significantly associated with survival. The prevalence of peritoneal recurrence was significantly higher in the INFc group than in the INFa and INFb group, whereas the prevalence of hepatic recurrence was significantly higher in the INFa and INFb group than in the INFc group. Multivariate analysis identified INFc as an independent risk factor for peritoneal recurrence after curative gastrectomy. The association of the INF type with the incidence of peritoneal recurrence was observed with all disease stages regardless whether the patient was given adjuvant chemotherapy or not. Evaluation of the INF type shows promise for its role as a predictor of postoperative recurrence sites in patients with GC.

Mode of infiltrative growth of colorectal liver metastases is a useful predictor of recurrence after hepatic resection.

Many studies have been conducted to determine prognosis on the basis of the characteristics of metastatic liver tumor from colorectal cancer. The present study was carried out to determine whether the pathological mode of infiltrative growth (INF) of a metastatic liver nodule is useful in predicting recurrence in the remnant liver after hepatic resection. A total of 42 curative hepatic resections were performed for 37 patients with isolated liver metastases from colorectal cancer. Multivariate analysis (n = 42) showed that number, INF type, and size of liver metastases were statistically significant as independent risk factors. Of these, 28 resected liver metastases (smaller than 6 cm in size or containing fewer than 4 nodules) were classified pathologically into INF alpha or beta types (INF a b; n = 14) and gamma type (INFg; n = 14). Disease-free survival at 5 years was 64% for patients with INF a b type, and 14% for those with the INF g type of liver metastases. Of these, recurrent disease of the liver after hepatic resection was found in 2 (14%) and 11 (79%) patients with INF a b and INF g types, respectively. From these observations, we concluded that pathological infiltrative growth of liver metastases is an informative predictor of disease-free survival and especially of recurrence in the remnant liver.

Longest runs in a sequence ofm-dependent random variables

Let {X i ,i≧1} be a sequence of random 0's and 1's. We define the lengthR n of the longest head run as follows: $$R_n = \max \left\{ {k \leqq n:\mathop {\max }\limits_{0 \leqq i \leqq n - k} 1\{ X_{i + 1} = \cdots = X_{i + k} = 1\} = 1} \right\}$$ The limit law for the distribution ofR n asn→∞ was found in 1943. The rate of convergence in that limit theorem remained unknown until recently even for Bernoulli independent trials. Supposing that {X i ,i≧1} is a stationary sequence ofm-dependent r.v.'s, we given an estimate on the rate of convergence in that limit theorem. This estimate provides the unimprovable raten −1(lnn) for the independent case. A result of lim inf type is obtained too.

Reflex control of extrinsic tongue muscle activities by lingual mechanoreceptors.

An attempt has been made to clarify the exteroceptive control mechanism of extrinsic tongue muscles in cats. For this purpose, excitatory and inhibitory receptive fields of extrinsic tongue muscle motor units on the tongue surface have been investigated in urethanechloralose anesthetized or decerebrate cats.1. Styloglossal motor units responded with spike discharges to gentle stroking of the anterior part of the tongue dorsum. The receptive field of this reflex response has been classified into 5 types; ipsilateral filiform type (iF type), ipsilateral nonfiliform type (iNF type), bilateral nonfilifbrm ype (bNF type), ipsilateral filifbrm plus ipsilateral nonfliform type (iF+iNF type) and ipsilateral filifbrm plus bilateral nonfiliform type (iF+bNF type). The majority of styloglossal motor units were of the bNF type in urethane-chloralose anesthetized cats. On the other hand, motor units of the iF type dominated in decerebrate cats.2. Hyoglossal motor units were divided into two groups; ventral and dorsal. Ventral hyoglossal motor units responded with spike discharges to gentle stroking of the ipsilateral posterior part of the tongue dorsum, while dorsal hyoglossal motor units to that of the ipsilateral filiform area of the anterior tongue dorsum.3. Only a minority of genioglossal motor units responded with spike discharges to tactile stimulation of the filiform area of the anterior tongue. In most responsive genioglossal motor units, the excitatory receptive fieldwas located in the ipsi-or bilateral filiform area of the anterior tongue. In a few cats, however, the excitatory receptive field was in the ipsilateral Dosterior part of the tongue dorsum.4. Some styloglossal and hyoglossal motor units responded with spike discharges to tactile stimulation of the ventral surface of the tongue, but none of the genioglossal motor units responded to it.5. Some genioglossal and ventral hyoglossal motor units exhibited nonrespiratory spontaneous discharges, but no styloglossal and dorsal hyo-glossal motor units showed them. However, the majority of styloglossal motor units responded with spike discharges to jaw opening.6. Inhibition of spike discharges was demonstrated with styloglossal and genioglossal motor units. The inhibitory receptive field of styloglossal motor unit was located on the ipsilateral posterior part of the tongue dorsum. In most genioglossal motor units, the inhibitory receptive field was on the ipsi-, contra- or bilateral posterior part of the tongue dorsum.