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Purpose This study compared the clinical efficacy and safety of laparoscopic versus open resection for hilar cholangiocarcinoma (HCCA) and analyzed potential prognostic factors.Methods The study included patients who underwent HCCA resection at our center from March 2012 to February 2022. Perioperative complications and postoperative prognosis were compared between the laparoscopic surgery (LS) and open surgery (OS) groups.Results After screening 313 HCCA patients, 68 patients were eligible for the study in the LS group (n = 40) and OS group (n = 28). Kaplan-Meier survival curve analysis revealed that overall survival > 2 years and 3-year disease-free survival (DFS) were more common in the LS than OS group, but the rate of 2-year DFS was lower in the LS group than OS group. Cox multivariate regression analysis revealed age (< 65 years), radical resection, and postoperative adjuvant therapy were associated with reduced risk of death (hazard ratio [HR] = 0.380, 95% confidence interval [CI] = 0.150–0.940, P = 0.036; HR = 0.080, 95% CI = 0.010–0.710, P = 0.024 and HR = 0.380, 95% CI = 0.150–0.960, P = 0.040), whereas preoperative biliary drainage was an independent factor associated with increased risk of death (HR = 2.810, 95% CI = 1.130–6.950, P = 0.026). Perineuronal invasion was identified as an independent risk factor affecting DFS (HR = 5.180, 95% CI = 1.170–22.960, P = 0.030).Conclusions Compared with OS, laparoscopic HCCA resection does not significantly differ in terms of clinical efficacy. Age (< 65 years), radical resection, and postoperative adjuvant therapy reduce the risk of death, and preoperative biliary drainage increases the risk of death.

We say that a map $f$ from a Banach space $X$ to another Banach space $Y$ is a phase-isometry if the equality \[ \{\|f(x)+f(y)\|, \|f(x)-f(y)\|\}=\{\|x+y\|, \|x-y\|\} \]holds for all $x,\,y\in X$. A Banach space $X$ is said to have the Wigner property if for any Banach space $Y$ and every surjective phase-isometry $f : X\rightarrow Y$, there exists a phase function $\varepsilon : X \rightarrow \{-1,\,1\}$ such that $\varepsilon \cdot f$ is a linear isometry. We present some basic properties of phase-isometries between two real Banach spaces. These enable us to show that all finite-dimensional polyhedral Banach spaces and CL-spaces possess the Wigner property.

We say that a map $f$ from a Banach space $X$ to another Banach space $Y$ is a phase-isometry if the equality \[ \{\|f(x)+f(y)\|, \|f(x)-f(y)\|\}=\{\|x+y\|, \|x-y\|\} \]holds for all $x,\,y\in X$. A Banach space $X$ is said to have the Wigner property if for any Banach space $Y$ and every surjective phase-isometry $f : X\rightarrow Y$, there exists a phase function $\varepsilon : X \rightarrow \{-1,\,1\}$ such that $\varepsilon \cdot f$ is a linear isometry. We present some basic properties of phase-isometries between two real Banach spaces. These enable us to show that all finite-dimensional polyhedral Banach spaces and CL-spaces possess the Wigner property.

Let $$\Gamma ,\Delta $$ be nonempty index sets, and let H, K be inner product spaces. We prove that for $$p\ge 1$$ any surjective phase-isometry between $$\ell ^p(\Gamma ,H)$$ and $$\ell ^p(\Delta , K)$$ is a plus–minus linear isometry. This can be considered as an extension of Wigner’s theorem for real $$\ell ^p(\Gamma , H)$$ -type spaces.

In this paper, we show that if X is a two-dimensional real normed space such that its unit sphere contains a line segment with the distance between its endpoints being greater than 1, then X has the Mazur–Ulam property. That is, every isometry from the unit sphere of X onto the unit sphere of any normed space Y can be extended to a linear isometry from X onto Y.

Background. To date, microRNA-21 (miR-21) has been reported to be associated with the prognosis of hepatocellular carcinoma (HCC) in various studies, yet the results were inconsistent. The purpose of this two-part study, consisting of a retrospective cohort study and a meta-analysis, sets out to determine the prognostic role of miR-21 expression among HCC patients who underwent surgical resection. Methods. In this study, we first detected miR-21 expression in HCC patients by quantitative real-time PCR (qRT-PCR). Patients were divided into a high miR-21 expression group and a low miR-21 expression group according to the median level of miR-21 expression in tumor tissues. The survival outcomes of the two groups were analyzed by the Kaplan-Meier method with the log-rank test. Multivariate analysis of the prognostic factors was performed with the Cox regression model. Subsequently, eligible studies were obtained by searching on PubMed, Cochrane Library, and Web of Science, and a meta-analysis was performed to assess the prognostic role of miR-21 expression among HCC. Results. The qRT-PCR analysis results of our cohort study showed miR-21 expression was significantly upregulated in HCC tissues when compared with adjacent nontumor tissues. Multivariate analysis suggested that miR-21 expression was an independent prognostic factor for overall survival (OS) (hazard ratio, HR = 2.361 ) and disease-free survival (DFS) ( HR = 2.024 ) in HCC patients who underwent surgical resection. A total of 10 studies with 969 patients were enrolled in the meta-analysis, consisting of 9 studies from the database search and our cohort study. We observed that elevated miR-21 expression can predict poor OS ( HR = 2.24 , 95 % CI = 1.73 ‐ 2.91 , P < 0.001 ) and DFS/recurrence-free survival (RFS) ( HR = 2.44 , 95 % CI = 1.62 ‐ 3.67 , P < 0.001 ) in surgically resected HCC patients. Conclusions. Our study demonstrated that miR-21 high expression among surgically resected HCC patients is a prognostic factor that indicated adverse survival.

Recently, many countries have spent great efforts on wind power generation. Although there have been many methods in the field of wind power forecasting, the persistence statistics model based on historical data is still being challenged due to the randomness and uncontrollability in wind power. Hence, a more accurate and effective wind power forecasting method is still required. In this paper, a new forecasting method is proposed by combining stacked auto-encoders (SAE) and the back propagation (BP) algorithm. First, an SAE with three hidden layers is designed to extract the characteristics from the reference data sequence, and the subsequent loss function is used in the pre-training process to obtain the optimal initial connection weights of the deep network. Second, after adding one output layer to the stacked auto encoders, the BP algorithm is used to fine tune the weights of the whole network. To achieve the best network architecture, the particle swarm optimization is adopted to decide the number of neurons of the hidden layer and the learning rate of each auto encoder. Experimental results show that, for short-term wind power forecasting, the proposed method achieves more stable and effective performance than the existing BP neural network and support vector machines. The improvement in accuracy is 12% on average under different time steps.

In this paper, we introduce the notion of strictly convex n-normed space as a generalization strictly convex normed space and give few characterizations for such space. We also prove that every map...

We show that any mapping between two real $p$-normed spaces, which preserves the unit distance and the midpoint of segments with distance $2^{p}$, is an isometry. Making use of it, we provide an alternative proof of some known results on the Aleksandrov question in normed spaces and also generalise these known results to $p$-normed spaces.

Background: Accurate clinical staging of patients with cholangiocarcinoma (CCA) has a significant impact on treatment decisions. In this study, we aimed to compare the diagnostic value of magnetic resonance imaging (MRI) and 18-fludeoxyglucose positron emission tomography/computed tomography (18F-FDG PET/CT) for staging of CCA. Methods: We performed comprehensive systematic search in Web of Science (including MEDLINE) and Excerpta Medica Database for relevant diagnostic studies in accordance with the preferred reporting items for systematic reviews and meta-analysis statement. Based on data extracted from patient-based analysis, we calculated the pooled sensitivity and specificity with the 95% confidence intervals (CIs). In addition, the publication bias was assessed by Deek funnel plot of the asymmetry test. The potential heterogeneity was explored by threshold effect analysis and subgroup analyses. Results: Thirty-two studies with 1626 patients were included in present analysis. In T stage, the pooled sensitivity and specificity of MRI were 0.90 (95% CI 0.86–0.93), 0.84 (95% CI 0.73–0.91) respectively. The pooled sensitivity and specificity of 18F-FDG PET/CT were 0.91 (95% CI 0.83–0.95) and 0.85 (0.64–0.95) respectively. In N stage, the pooled sensitivity and specificity of MRI were 0.64 (95% CI 0.52–0.74) and 0.69 (95% CI 0.51–0.87) respectively. The pooled sensitivity and specificity of PET/CT were 0.52 (95% CI 0.37–0.66) and 0.92 (95% CI 0.79–0.97) respectively. In M stage, the pooled sensitivity and specificity of 18F-FDG PET/CT were 0.56 (95% CI, 0.42–0.69) and 0.95 (95% CI, 0.91–0.97) respectively. The Deek test revealed no significant publication bias. No threshold effect was identified. The subgroup analyses showed that pathological type (extrahepatic cholangiocarcinoma vs hilar cholangiocarcinoma/intrahepatic cholangiocarcinoma), country (Asia vs non-Asia) and type of MRI (1.5T vs. 3.0T) were potential causes for the heterogeneity of MRI studies and country (Asia vs non-Asia) was a potential source for 18F-FDG PET/CT studies. Conclusion: The analysis suggested that both modalities provide reasonable diagnostic accuracy in T stage without significant differences between them. We recommend that both modalities be considered based on local availability and practice for the diagnosis of primary CCA tumors. In N stage, the diagnosis of lymph node metastasis (N) of CCA is still limited by MRI and 18F-FDG PET/CT, due to unsatisfactory diagnostic accuracy of both. Nevertheless, 18F-FDG PET/CT can be used to confirm lymph node metastasis while a negative result may not rule out metastasis. Furthermore, 18F-FDG PET/CT have a low sensitivity and a high specificity for detection of distant metastasis.

We say that a mapping $f: X \rightarrow Y$ between two real normed spaces is a phase-isometry if it satisfies the functional equation \begin{eqnarray*} \{\|f(x)+f(y)\|, \|f(x)-f(y)\|\}=\{\|x+y\|, \|x-y\|\} \quad (x,y\in X).\end{eqnarray*} A generalized Mazur-Ulam question is whether every surjective phase-isometry is a multiplication of a linear isometry and a map with range $\{-1, 1\}$. This assertion is also an extension of a fundamental statement in the mathematical description of quantum mechanics, Wigner's theorem to real normed spaces. In this paper, we show that for every space $Y$ the problem is solved in positive way if $X$ is a smooth normed space, an $\mathcal{L}^{\infty}(\Gamma)$-type space or an $\ell^1(\Gamma)$-space with $\Gamma$ being an index set., Comment: 16pages

We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (specially, separable $C$-rich subspaces of $C(K)$), and even the two-dimensional space with hexagonal norm. We obtain that the space $C(K,E)$ of the vector-valued continuous functions is a GL-space whenever $E$ is, and show that the GL-space is stable under $c_0$-, $l_1$- and $l_\infty$-sums. As an application, we prove that the Mazur-Ulam property holds for a larger class of Banach spaces, called local-GL-spaces, including all lush spaces and GL-spaces. Furthermore, we generalize the stability properties of GL-spaces to local-GL-spaces. From this, we can obtain many examples of Banach spaces having the Mazur-Ulam property.

The main theme of this paper is to consider a notion of ‘approximately unital operator systems’ including both C*-algebras and unital operator systems. The goals are to prove a version of the Choi-Effros theorem for these systems, to introduce a functorial process for forming an approximately unital operator systems from a given matrix ordered vector space with a proper approximate order unit, to study second duals of these objects and to prove that a C*-algebra can be characterized as an approximately unital operator system that is also an approximately unital matrix ordered *-algebra.

We study the numerical radius of Lipschitz operators on Banach spaces via the Lipschitz numerical index, which is an analogue of the numerical index in Banach space theory. We give a characterization of the numerical radius and obtain a necessary and sufficient condition for Banach spaces to have Lipschitz numerical index 1. As an application, we show that real lush spaces and $C$-rich subspaces have Lipschitz numerical index 1. Moreover, using the G$\hat{a}$teaux differentiability of Lipschitz operators, we characterize the Lipschitz numerical index of separable Banach spaces with the RNP. Finally, we prove that the Lipschitz numerical index has the stability properties for the $c_0$-, $l_1$-, and $l_\infty$-sums of spaces and vector-valued function spaces. From this, we show that the $C(K)$ spaces, $L_1(\mu)$-spaces and $L_\infty(\nu)$ spaces have Lipschitz numerical index 1., Comment: 23 pages