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This paper mainly discusses the existence and finite-time stability of solutions for impulsive fractional stochastic differential equations (IFSDEs). By applying the Picard-Lindelöf iteration method of successive approximation scheme, we establish the existence results of solutions. Subsequently, the uniqueness of solution is derived by the method of contradiction. In addition, we investigate the finite-time stability by means of the generalized Grönwall-Bellman inequality. As an application, examples are provided to expound our theoretical conclusions.

In this article, we consider the relatively exact controllability of fractional stochastic delay system (FSDS) driven by Lévy noise. Firstly, we derive the solution of linear FSDS via delayed matrix functions of Mittag-Leffler (M-L). Subsequently, by virtue of the controllability Grammian matrix, we explore the relatively exact controllability of linear FSDS. In addition, with the aid of Jensen’s inequality, Hölder’s inequality and Itô’s isometry, the existence and uniqueness of the considered nonlinear FSDS are investigated by employing Banach contraction principle.Thereafter, the relatively exact controllability of nonlinear FSDS is discussed. Finally, the theoretical results are supported through an example.

This article studies a new kind of Ψ -Hilfer fractional system driven by m -dimensional Brownian motion. By utilizing the generalized Laplace transform and its inverse, the contraction mapping principle, and the properties of a semigroup, we establish the uniqueness of the solution. In addition, finite-time stability is investigated by means of the properties of norm and inequalities scaling technique. As verification, an example is given to show the deduced conclusions.

Purpose: Tumor metastasis continues to be the major obstacle to cancer therapy and the leading cause of cancer-related death. Methods used to detect metastasis, especially occult metastases, have received a great deal attention. In this study, a novel selective peptide was assessed for its specific binding to metastasis.Methods: The FliTrx bacterial peptide display system, an alternative to phage peptide display, was used to identify a 5-amino acid peptide termed TMTP1 (NVVRQ), which binds to the highly metastatic prostate cancer cell line PC-3M-1E8. The synthetic TMTP1 was tested in vitro for its binding specificity and affinity to highly metastatic cancer cells. The tumor targeting assays were done in vivo by i.v. injection of FITC-conjugated TMTP1 into tumor-bearing mice.Results: TMTP1 specifically bound to a series of highly metastatic tumor cells, including prostate cancer PC-3M-1E8, breast cancer MDA-MB-435S, lung cancer PG-BE1, and gastric cancer MKN-45sci, in vitro and in vivo but not to the poorly metastatic or nonmetastatic cell line, including prostate cancer PC-3M-2B4, breast cancer MCF-7, lung cancer PG-LH7, or murine fibroblast cell NIH/3T3. FITC-TMTP1 strongly and specifically targeted the metastasis foci in tumor-bearing mice 24 h after i.v. peptide injection. Moreover, the occult metastases were specifically detected by FITC-TMTP1.Conclusion: Our results suggest that TMTP1 is a potential strategy for the development of new diagnostic tracers or alternative anticancer agents for tumor metastasis.

Supplementary Data from TMTP1, a Novel Tumor-Homing Peptide Specifically Targeting Metastasis

We explore a new kind of Caputo-type fractional fuzzy stochastic differential equations (FFSDEs) with delay. We establish the existence result of FFSDEs with delay by monotone iterative technique combined with the method of upper and lower solutions, and then the uniqueness is proved. Subsequently, we study the Ulam–Hyers (U–H) stability. Finally, three examples with numerical simulations are provided to illustrate the theoretical results.

In this paper, a class of stochastic fractional differential equations (SFDEs) with impulses is considered. By virtue of the Monch’s fixed point theorem and Banach contraction principle, we explore the existence and uniqueness of solutions to the addressed system. Furthermore, with the aid of the Jensen’s inequality, Holder inequality, Burkholder-Davis-Gundy inequality, Gronwall-Bellman inequality and some novel assumptions, the averaging principle of our considered system is obtained. At the end of this paper, an example is provided to illustrate the theoretical results.

VEGFR-3 plays an indispensable role in lymphangiogenesis. Previous findings suggest that blocking the VEGFR-3 signaling pathway can inhibit lymph node metastasis effectively, thus reduce the incidence of distant metastasis. The development of new VEGFR-3 targeting drugs for early detection and effective treatments is, therefore, urgently requied. Here, in vitro biopanning of a phage-displayed peptide library was used to identify specific peptides binding to the extracellular domain of VEGFR-3. We obtained a novel VEGFR-3 targeting peptide TMVP1 (LARGR), our combined immunofluorescence and radiopharmaceutical studies revealed that FITC-TMVP1 and 99mTc-labeled TMVP1 specifically accumulated in VEGFR-3 positive lymphatic vessels of tumors after i.v administration in tumor xenograft models in vivo. The accumulation of the TMVP1 in lymphatic vessels was specific, because this accumulation can be significantly reduced by blocking experiments. To enhance the therapeutic efficacy of anticancer drugs, we fused TMVP1 to a proapoptotic peptide D(KLAKLAK)2, the fusion peptide strongly inhibited tumor lymphangiogenesis in vitro and in vivo, and specifically suppressed lung metastasis in a 4T1 breast cancer xenograft model. Our results suggest that TMVP1 is a promising therapeutic strategy for the development of new diagnostic tracers or alternative anticancer agents for tumor lymphangiogenesis and lymphatic metastasis.

This paper focuses on a kind of mixed fractional-order nonlinear delay difference equations with parameters. Under some new criteria and by applying the Brouwer theorem and the contraction mapping principle, the new existence and uniqueness results of the solutions have been established. In addition, we deduce that the solution of the addressed equation is Hyers–Ulam stable. Some results in the literature can be generalized and improved. As an application, three typical examples are delineated to demonstrate the effectiveness of our theoretical results.

Solutions to fractional differential equations is an emerging part of current research, since such equations appear in different applied fields. A study of existence, uniqueness, and stability of solutions to a coupled system of fractional differential equations with non-separated boundary conditions is the main target of this paper. The existence and uniqueness results are obtained by employing the Leray–Schauder fixed point theorem and the Banach contraction principle. Additionally, we examine different types of stabilities in the sense of Ulam–Hyers such as Ulam–Hyers stability, generalized Ulam–Hyers stability, Ulam–Hyers–Rassias stability, and generalized Ulam–Hyers–Rassias stability. To prove the effectiveness of our main results, we study a few interesting examples.

In this paper, we mainly consider the existence and Hyers-Ulam stability of solutions for a class of fractional differential equations involving time-varying delays and non-instantaneous impulses. By the Krasnoselskii’s fixed point theorem, we present the new constructive existence results for the addressed equation. In addition, we deduce that the equations have Hyers-Ulam stable solutions by utilizing generalized Grönwall’s inequality. Some results in this literature are new and improve some early conclusions.

In this article, we consider conformable fractional stochastic differential equations (CFSDEs) driven by fBm with infinite delay via measures of noncompactness (MNC). As far as we know, there are few papers considering this issue. First, by virtue of a Mönch fixed point theorem and MNC, we explore the existence of solutions for CFSDEs. Subsequently, with the aid of Jensen inequality, Hölder inequality, stochastic analysis techniques, and semigroup theory, the controllability for this considered CFSDEs is investigated by employing a Mönch fixed point theorem. Thereafter, the controllability of CFSDEs with nonlocal conditions is discussed. Finally, the theoretical result is supported through an example.

ObjectiveThe aim of the present study was to determine overall survival (OS) and risk factors associated with early recurrence in patients with FIGO I–II stage endometrial carcinoma (EC).MethodsClinical features were retrospectively extracted from the database of China Endometrial Cancer Consortium from January 2000 to December 2019. A total of 2,974 patients with Federation International of Gynecology and Obstetrics (FIGO) I–II stage endometrial cancer were included. Kaplan-Meier survival analysis was used to assess OS and disease-specific survival. Cox proportional hazard model and Fine-Gray model were used to determine the factors related to OS. Binary logistic regression model was used to determine independent predictors of early relapse patients.ResultsOf these 2,974 ECs, 189 patients were confirmed to have relapse. The 5-year OS was significantly different between the recurrence and non-recurrence patients (p < 0.001). Three quarters of the relapse patients were reported in 36 months. The 5-year OS for early recurrence patients was shorter than late recurrence [relapse beyond 36 months, p < 0.001]. The grade 3 [odds ratio (OR) = 1.55, 95%CI 1.17–2.05, p = 0.002], lymphatic vascular infiltration (LVSI; OR = 3.36; 95%CI 1.50–7.54, p = 0.003), and myometrial infiltration (OR = 2.07, 95%CI 1.17—3.65, p = 0.012) were independent risk factors of early relapse. The protective factor of that is progesterone receptor (PR)-positive (OR = 0.50, 95%CI 0.27–0.92, p = 0.02). Bilateral ovariectomy could reduce recurrence risk rate (OR = 0.26, 95%CI 0.14–0.51, p < 0.001).ConclusionThe OS of early relapse EC is worse. Grade 3, LVSI, and myometrial infiltration are independent risk factors for early relapse EC. In addition, the protective factor is PR-positive for those people and bilateral salpingo-oophorectomy could reduce the risk of recurrence.

The prognostic impact and treatment responses among cervical cancer patients with different histological types remains inconclusive. To determine the prognostic effects of different histologic types, we identified 39,088 patients with a diagnosis of cervical cancer between 2004 and 2016 from the Surveillance, Epidemiology, and End Results program.Variables related to the prognosis of cervical cancer were evaluated using log-rank method and univariate/multivariate Cox models before and after propensity score matching.Of the 36,310 patients, Squamous cell carcinoma (SCC) was the most common histological type (n = 27,043, 74.5%), followed by adenocarcinoma (AC, n = 7755, 21.4%) and adenosquamous carcinoma (ASC, n = 1512, 4.1%). Compared to SCC patients, patients with AC (HR = 1.14, 95%CI = 1.09-1.20, P 0.01) and ASC (HR = 1.28, 95%CI = 1.18-1.40, P 0.01) showed significantly poorer prognosis. Subgroup analyses indicated that the differences in prognosis between AC and SCC were only observed in stage II and III patients (P 0.01). In patients with concurrent chemoradiotherapy, survival rates of patients with AC were significantly worse compared with similar patients with SCC (HR = 1.14, 95%CI = 1.03-1.27; P 0.01).The prognostic impact of histologic types among patients with cervical cancer depends on tumor stages and therapeutic approaches. Tailored treatment and follow-up planning need to be developed across patients with different histological types and stages.

Guiying Jiang,1,* Xueqian Wang,1,* Ying Zhou,1 Chenming Zou,2,3 Ling Wang,1 Wei Wang,1 Danya Zhang,1 Hanjie Xu,1 Jie Li,1 Fei Li,1 Danfeng Luo,1 Xiangyi Ma,1 Ding Ma,1 Songwei Tan,2 Rui Wei,1 Ling Xi1 1Department of Obstetrics & Gynecology, Tongji Hospital, Tongji Medical College, Huazhong University of Science & Technology, Wuhan, Hubei Province, People’s Republic of China; 2Tongji School of Pharmacy, Tongji Medical College, Huazhong University of Science & Technology, Wuhan, Hubei Province, People’s Republic of China; 3School of Pharmacy, Shanghai Jiao Tong University, Shanghai, People’s Republic of China*These authors contributed equally to this workCorrespondence: Ling Xi; Rui WeiDepartment of Obstetrics & Gynecology, Tongji Hospital, Tongji Medical College, Huazhong University of Science & Technology, Wuhan, Hubei, People’s Republic of ChinaTel/Fax +86 27 83662688Email lxi@tjh.tjmu.edu.cn; weirui2018@tjh.tjmu.edu.cnBackground and Purpose: Cisplatin–paclitaxel (TP) combination chemotherapy as the first-line therapy for numerous cancers is hindered by its inadequate accumulation in tumors and severe side effects resulting from non-specific distribution. The aim of this study is to explore whether TMTP1-modified, cisplatin and paclitaxel prodrugs co-loaded nanodrug could improve cervical cancer chemotherapy and relieve its side effects through active and passive tumor targeting accumulation and controlled drug release.Methods: TDNP, with capacities of active targeting for tumors and controlled drug release, was prepared to co-deliver cisplatin and paclitaxel prodrugs. The characteristics were investigated, including the diameter, surface zeta potential, stability and tumor microenvironment (TME) dependent drug release profiles. Cellular uptake, cytotoxicity, drug accumulation in tumors, antitumor effects and safety analysis were evaluated in vitro and in vivo.Results: The oxidized cisplatin and the paclitaxel linked to the polymer achieved a high loading effciency of over 80% and TME-dependent sustained drug release. Moreover, TMTP1 modification enhanced cellular uptake of TDNP and further improved the cytotoxicity of TDNP in vitro. In vivo, TDNP showed an extended blood circulation and increased accumulation in SiHa xenograft models with the aid of TMTP1. More importantly, TDNP controlled tumor growth without life-threatening side effects.Conclusion: Our study provided a novel TP co-delivery platform for targeted chemotherapy of cervical cancer, which was promising to improve the therapeutic effcacy of TP and may also have application in other tumors.Keywords: TME-responsive, targeted co-delivery, combined chemotherapy, cervical cancer

Metastasis is one of the most threatening aspects of cervical cancer. We developed a method to intraoperatively map the primary tumor, metastasis and metastatic sentinel lymph nodes (SLNs), providing real-time intraoperative guidance in cervical cancer. Methods: TMTP1, a tumor metastasis targeting peptide, was employed to modify the indocyanine green (ICG)-loaded poly (ethylene glycol)- poly (lactic-co-glycolic acid) (PEG-PLGA) micelles. The cervical cancer subcutaneous tumor model and lung metastasis model were established to determine the active targeting of ICG-loaded TMTP1-PEG-PLGA micelles (ITM) for the primary tumor and occult metastasis of cervical cancer. Human cervical cancer HeLa cells engineered by firefly luciferase were injected into the right hocks of BALB/c nude mice to develop the SLN metastasis model. The ITM and control ICG-loaded PEG-PLGA micelles (IM) were injected into the right hind footpads in the SLN metastasis model, and the migration and retention of micelles were recorded under near-infrared fluorescence. K14-HPV16 transgenic mice were also used to detect the image capability of ITM to target cancerous lesions. Results: ITM could actively target imaging of the primary tumor and cervical cancer metastasis. ITM quickly diffused from the injection site to SLNs along lymphatic capillaries and remained in the SLNs for 12 h. Moreover, ITM specifically accumulated in the tumor metastatic SLNs (T-SLNs), which could be successfully distinguished from normal SLNs (N-SLNs). Conclusion: ITM could achieve active targeting of the primary tumor, metastasis and T-SLNs, providing precise and real-time intraoperative guidance for cervical cancer.

As we reported in our previous studies, TMTP1, a tumor-homing peptide, selectively targets highly metastatic tumors and their metastatic foci. Aminopeptidase P2 (XPNPEP2) is a receptor for TMTP1 tumor-homing peptide. However, the biological and clinical significance of Aminopeptidase P2 in human cancers remains unknown. In this study, the high-density multiple organ tumor tissue array was employed for the analysis of XPNPEP2 expression profiles in human specimens. The results showed that XPNPEP2 was moderately expressed in the normal prostate tissues, but significantly decreased in the prostate cancer. Hence we used TCGA, IHC, and ELISA to further analyze the expression of XPNPEP2 in tissues and serum of prostate cancer patients. In general, XPNPEP2 expression was lower in prostate cancer tissue than in normal prostate tissue, but was higher in prostate cancer tissues with local invasion and LN metastasis than in tissues with localized Pca. Western blot clarified XPNPEP2 had a secreted form in the serum. Then the serums of 128 Pca patients, 70 healthy males and 40 prostate hyperplasia patients were obtained for detecting serum XPNPEP2 levels.The results indicated that the concentration of XPNPEP2 in serums of Pca patients with LN metastasis (142.7 ± 14.40 ng/mL) were significantly higher than levels in Pca patients without LN metastasis (61.63 ± 5.50 ng/mL) (p

In this paper, we mainly consider the existence of solutions for a kind of ?-Hilfer fractional differential inclusions involving non-instantaneous impulses. Utilizing another nonlinear alternative of Leray-Schauder type, we present a new constructive result for the addressed system with the help of generalized Gronwall inequality and Lagrange mean-value theorem, and some achievements in the literature can be generalized and improved. As an application, a typical example is delineated to demonstrate the effectiveness of our theoretical results.

This paper is devoted to presenting an averaging principle for stochastic pantograph equations. Under suitable non-Lipschitz conditions, the solutions to stochastic pantograph equations can be approximated by solutions to averaged stochastic systems in the mean-square sense and probability. At last, an example is given to demonstrate the feasibility of obtained results. Moreover, our results have generalized significantly some previous ones.

In this paper, we study a class of Caputo-type fractional stochastic differential equations (FSDEs) with time delays. Under some new criteria, we get the existence and uniqueness of solutions to FSDEs by Carath e ´ odory approximation. Furthermore, with the help of H o ¨ lder’s inequality, Jensen’s inequality, It o ^ isometry, and Gronwall’s inequality, the Ulam–Hyers stability of the considered system is investigated by using Lipschitz condition and non-Lipschitz condition, respectively. As an application, we give two representative examples to show the validity of our theories.

In this article, we make analysis of the implicit fractional differential equations involving integral boundary conditions associated with Stieltjes integral and its corresponding coupled system. We use some sufficient conditions to achieve the existence and uniqueness results for the given problems by applying the Banach contraction principle, Schaefer’s fixed point theorem, and Leray–Schauder result of the cone type. Moreover, we present different kinds of stability such as Hyers–Ulam stability, generalized Hyers–Ulam stability, Hyers–Ulam–Rassias stability, and generalized Hyers–Ulam–Rassias stability by using the classical technique of functional analysis. At the end, the results are verified with the help of examples.

In this paper, we investigate a class of stochastic Hilfer-type fractional differential equations (SHFDEs) involving non-Lipschitz coefficients. With the aid of the Laplace transform and its inverse, we derive an implicit solution to the SHFDEs. Subsequently, we present the averaging principle result using Jensen’s inequality, the Cauchy–Schwarz inequality, Doob’s martingale inequality, and the Gronwall–Bellman inequality. Finally, we solve an example problem numerically to prove the correctness of the theoretical solution.

// Rui Wei 1 , Mengqin Lv 1, * , Fei Li 1 , Teng Cheng 1 , Zhengzhong Zhang 1 , Guiying Jiang 1 , Ying Zhou 1 , Ruiqiu Gao 1 , Xiao Wei 1 , Jicheng Lou 1 , Xizi Wu 1 , Danfeng Luo 1 , Xiangyi Ma 1 , Jin Jiang 2 , Ding Ma 1 and Ling Xi 1 1 Cancer Biology Research Center, Key Laboratory of The Ministry of Education, Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, People’s Republic of China 2 Department of Molecular Biology, UT Southwestern Medical Center at Dallas, TX, Dallas, USA * Co-first author Correspondence to: Ling Xi, email: lxi@tjh.tjmu.edu.cn Keywords: ovarian cancer, hedgehog signaling, cancer associated fibroblasts, VEGF-C, lymphangiogenesis Received: October 07, 2016 Accepted: May 01, 2017 Published: June 27, 2017 ABSTRACT Cancer-associated fibroblasts (CAFs) play a pivotal role in the development and progression of many human cancers. Recent studies have shown that Hedgehog (Hh) signalling modulates the stromal microenvironment and prepares a suitable niche for tumour metastasis. However, the detailed molecular mechanisms underlying CAF-mediated lymphangiogenesis have not been fully elucidated. Therefore, our goal is to illustrate whether Hh ligands can activate Hh signalling in CAFs in a paracrine fashion and elucidate the effect of CAFs on lymphangiogenesis. We determined here that Sonic Hedgehog (SHH) secreted by ovarian cancer (OC) cells activated Hh signalling in CAFs and promoted the proliferation of CAFs. Moreover, we co-injected SHH-overexpressing OC cells and CAFs in a xenograft model and found that the CAFs accelerated tumourigenesis and lymphangiogenesis in OC. Mechanistically, we found that SHH secreted by the OC cells induced VEGF-C expression in CAFs. Inhibition of Hh signalling in CAFs decreased VEGF-C expression and diminished the positive role of CAFs in supporting tumourigenesis and lymphangiogenesis in a murine xenograft model. Our results demonstrate that CAFs constitute a supportive niche for cancer lymphangiogenesis via the Hh/VEGF-C signalling axis and provide evidence for the clinical application of Hh inhibitors in the treatment of OC.

// Qian Sun 1 , Haiyue Zhao 1 , Cong Zhang 1 , Ting Hu 1 , Jianli Wu 1 , Xingguang Lin 1 , Danfeng Luo 1 , Changyu Wang 1 , Li Meng 1 , Ling Xi 1 , Kezhen Li 1 , Junbo Hu 1 , Ding Ma 1 and Tao Zhu 1 1 Cancer Biology Research Center, Key Laboratory of the Ministry of Education, Tongji Hospital, Tongji Medical College, Huazhong University of Science and Technology, Wuhan, People’s Republic of China Correspondence to: Tao Zhu, email: zhutao@tjh.tjmu.edu.cn Keywords: ovarian cancer, WGCNA, gene co-expression network, grade, stage Received: October 13, 2016 Accepted: April 15, 2017 Published: May 11, 2017 ABSTRACT Serous ovarian cancer (SOC) is the most lethal gynecological cancer. Clinical studies have revealed an association between tumor stage and grade and clinical prognosis. Identification of meaningful clusters of co-expressed genes or representative biomarkers related to stage or grade may help to reveal mechanisms of tumorigenesis and cancer development, and aid in predicting SOC patient prognosis. We therefore performed a weighted gene co-expression network analysis (WGCNA) and calculated module-trait correlations based on three public microarray datasets (GSE26193, GSE9891, and TCGA), which included 788 samples and 10402 genes. We detected four modules related to one or more clinical features significantly shared across all modeling datasets, and identified one stage-associated module and one grade-associated module. Our analysis showed that MMP2, COL3A1, COL1A2, FBN1, COL5A1, COL5A2, and AEBP1 are top hub genes related to stage, while CDK1, BUB1, BUB1B, BIRC5, AURKB, CENPA, and CDC20 are top hub genes related to grade. Gene and pathway enrichment analyses of the regulatory networks involving hub genes suggest that extracellular matrix interactions and mitotic signaling pathways are crucial determinants of tumor stage and grade. The relationships between gene expression modules and tumor stage or grade were validated in five independent datasets. These results could potentially be developed into a more objective scoring system to improve prediction of SOC outcomes.

In this paper, we present some alternative results concerning the uniqueness and Ulam–Hyers stability of solutions for a kind of $$\psi $$ -Hilfer fractional differential equations with time-varying delays. Under some updated criteria along with the generalized Gronwall inequality, the new constructive results have been established in the literature. The derived analysis has the ability to generalize and improve some other results from the literature. As an application, two typical examples are delineated to demonstrate the effectiveness of our theoretical results.

In this paper, we mainly study the finite-time stability for a kind of uncertain fractional-order delay differential equations with noninstantaneous impulses. By using the Lyapunov functions along with the generalized Grönwall inequality, we present the new stability results for the considered equations. Finally, two examples are given to demonstrate the effectiveness of our theoretical results.