Differences in biological features of gastric dysplasia, indefinite dysplasia, reactive hyperplasia and discriminant analysis of these lesions

AIM: To investigate the differences in biological features of gastric dysplasia (Dys), indefinite dysplasia (IDys) and reactive hyperplasia (RH) by studying the biomarker alterations in cell proliferation, cell differentiation, cell cycle control and the expression of house-keeping genes, and further to search for markers which could be used in guiding the pathological diagnosis of three lesions. METHODS: Expressions of MUC5AC, MUC6, adenomatous polyposis coli (APC), p53, Ki-67, proliferation cell nuclear antigen (PCNA) and EGFR were studied by immunohistochemistry with a standard Envision technique in formalinfixed and paraffin-embedded specimens from 43 RH, 35 IDys, 35 Dys and 36 intestinal type gastric carcinomas (IGC). In addition, Bayes discriminant analysis was used to investigate the value of markers studied in differential diagnosis of RH, IDys, Dys and IGC. RESULTS: The MUC5AC and MUC6 antigen expressions in RH, IDys, Dys and IGC decreased gradually (MUC5AC:86.04%, 77.14%, 28.57%, 6.67%; MUC6: 65.15%, 54.29%, 20.00%, 25.00%, respectively). The expressions of the two markers had no significant difference between RH and IDys, but were all significantly higher than those ofthe other two lesions (MUC5AC: x2 = 27.607, 38.027 and 17.33, 26.092; MUC6: x2= 16.54, 12.665 and 9.282, 6.737, P＜0.01). There was no significant differencebetween RH and IDys, Dys and IGC in MUC6 expression. The APC gene expression in the four lesions had a similar decreasing tendency (RH 69.76%, IDys 68.57%, Dys39.39%, IGC 22.86%), and it was significantly higher in the first two lesions than in the last two (x2 = 7.011,16.995 and 14.737, 19.817, P＜0.05). The p53 expressionin RH, IDys, Dys and IGC was 6.98%, 20%, 57.14% and 50%, respectively. There was no significant differencebetween RH and IDys or Dys and IGC, but the p53 expression in RH and IDys was significantly lower than that in Dys and IGC (x2 = 7.011, 16.995 and 14.737, 19.817, P＜0.01).The Ki-67 label index was significantly different among four lesions (RH: 0.298±8.92%, IDys: 0.358±9.25%,Dys: 0.498±9.03%, IGC: 0.620±10.8%, P＜0.001). Positive immunostaining of PCNA was though observed in all specimens, significant differences were detected among four lesions (F= 95.318, P＜0.01). In addition, we used Bayes discriminant analysis to investigate molecular pathological classification of the lesions, and obtained the best result with the combination of MUC5AC, Ki-67 and PCNA. The overall rate of correct classification was67.4% (RH), 68.6% (IDys), 70.6% (Dys) and 84.8% (IGC), respectively.CONCLUSION: Dys has neoplastic biological characteristics, while RH and IDys display hyperplastic characteristics. MUC5AC and proliferation-related biomarkers (Ki-67, PCNA) are more specific in distinguishing Dys from RH and IDys.

Nonmonotone Adaptive Trust Region Algorithms with Indefinite Dogleg Path for Unconstrained Minimization

In this paper, we combine the nonmonotone and adaptive techniques with trust region method for unconstrained minimization problems. We set a new ratio of the actual descent and predicted descent. Then, instead of the monotone sequence, the nonmonotone sequence of function values are employed. With the adaptive technique, the radius of trust region △k can be adjusted automatically to improve the efficiency of trust region methods. By means of the Bunch-Parlett factorization, we construct a method with indefinite dogleg path for solving the trust region subproblem which can handle the indefinite approximate Hessian Bk. The convergence properties of the algorithm are established. Finally, detailed numerical results are reported to show that our algorithm is efficient.

AN EQUIVALENT PROPOSITION TO THE CONJECTURE OF GOLDBACH

In this paper,a formula is given. The formula gives the number of prime number solutions of the indefinite equation p 1+p 2=2n , and based on it, an equivalent proposition to the conjecture of Goldbach is obtained.

Intraoperative frozen section diagnosis of bile duct margin for extrahepatic cholangiocarcinoma

AIM To evaluate the usefulness of frozen section diagnosis(FSD) of bile duct margins during surgery for extrahepatic cholangiocarcinoma(CCA). METHODS We retrospectively analyzed 74 consecutive patients who underwent surgery for extrahepatic CCA from 2012 to 2017, during which FSD of bile duct margins was performed. They consisted of 40 distant and 34 perihilar CCAs(45 and 55 bile duct margins, respectively). The diagnosis was classified into three categories: negative, borderline(biliary intraepithelial neoplasia-1 and 2, and indefinite for neoplasia), or positive. FSD in the epithelial layer, subepithelial layer, and total layer was compared with corresponding permanent section diagnosis(PSD) postoperatively.Then, association between FSD and local recurrence was analyzed with special reference to borderline.RESULTS Analysis of 100 duct margins revealed that concordance rate between FSD and PSD was 68.0% in the total layer, 69.0% in the epithelial layer, and 98.0% in the subepithelial layer. The extent of remaining biliary epithelium was comparable between FSD and PSD, and more than half of the margins lost > 50% of the entire epithelium, suggesting low quality of the samples. In FSD, the rate of negative margins decreased and that of borderline and positive margins increased according to the extent of the remaining epithelium. Diagnostic discordance between FSD and PSD was observed in 31 epithelial layers and two subepithelial layers. Alteration from borderline to negative was the most frequent(20 of the 31 epithelial layers). Patients with positive margin in the total and epithelial layers by FSD demonstrated a significantly worse local recurrence-free survival(RFS) compared with patients with borderline and negative margins, which revealed comparable local RFS. Patients with borderline and negative margins in the epithelial layer by PSD also revealed comparable local RFS. These results suggested that epithelial borderline might be regarded substantially as negative. When classifying the status of the epithelial layer either as negative or positive, concordance rates between FSD and PSD in the total, epithelial, and subepithelial layers were 95.0%, 93.0%, and 98.0%, respectively.CONCLUSION During intraoperative assessment of bile duct margin, borderline in the epithelial layer can be substantially regarded as negative, under which condition FSD is comparable to PSD.

A Backward Stable Hyperbolic QR Factorization Method for Solving Indefinite Least Squares Problem

We present a numerical method for solving the indefinite least squares problem. We first normalize the coefficient matrix. Then we compute the hyperbolic QR factorization of the normalized matrix. Finally we compute the solution by solving several triangular systems. We give the first order error analysis to show that the method is backward stable. The method is more efficient than the backward stable method proposed by Chandrasekaran, Gu and Sayed.

NONTRIVIAL SOLUTIONS OF HARDY-HENON TYPE ELLIPTIC SYSTEMS

In this article, the authors investigate the existence problem for Hardy Henon type strongly indefinite elliptic systems. Existence results are obtained for such systems with superlinear subcritical nonlinearities.

ON GROUND STATE SOLUTIONS FOR SUPERLINEAR DIRAC EQUATION

This article is concerned with the nonlinear Dirac equations-iδtψ=ich ∑k=1^3 αkδkψ-mc^2βψ＋Rψ（x,ψ） in R^3.Under suitable assumptions on the nonlinearity, we establish the existence of ground state solutions by the generalized Nehari manifold method developed recently by Szulkin and Weth.

A Simple Method of Solving First-order Indefinite Equa tion

The current method of solving first order indefinite equatio n is changing the equation to first order indefinite equation gr oup to solve. But according this method, if variables are very many, it will be difficult to solve the equation using the current method. In this paper, it prov ides a simple method by discussing the structure of solution based on the theory of free abelian group. In addition, this method makes it easy to get the genera lized solution of the equation using the computer.

Standing Waves for Quasilinear Schrödinger Equations with Indefinite Nonlinearity

In this article, we consider quasilinear Schrödinger equations of the form Such equations have been derived as models of several physical phenomena. The nonlinearity here corresponds to the superfluid film equation in plasma physics. Unlike all known results in the literature, the nonlinearity is allowed to be indefinite. It is very interesting from physical and mathematical viewpoint. By mountain pass theorem and some special techniques, we prove the existence of solutions for the quasilinear Schrödinger equations with indefinite nonlinearity. This indefinite problem had never been considered so far. So our main results can be regarded as complementary work in the literature.

NONTRIVIAL SOLUTIONS OF COMPETITIVE-DIFFUSIVE SYSTEMS WITH SMALL DIFFUSION

We discuss nontrivial steady-state solutions of a competitive-diffusive systems with small diffusion in which two interacting species u and v inhibit the same bounded region. By using methods of bifurcation theory and indefinite weight function, we prove the existence and uniqueness of solutions which are positive in both u and v and asymptotically stable corresponding to the case where the populations can co-exist.

PRECONDITIONING MIXED ELEMENT METHOD FOR NONSELFADJOINT AND INDEFINITE SECOND ORDER ELLIPTIC PROBLEMS

In this paper, an equivalence between mixed element method and nonconforming element method for nonselfad joint and indefinite second order elliptic problems is established without using any bubble functions. It is proved that the H1-condition number of preconditioned operator Bh-1Ah is uniformly bounded and its Bh-singular values cluster in a positive finite interval, where Ah is the equivalent nonconforming element discretization of nonselfad joint and indefinite second order elliptic operator A, Bh is usual noncon forming element discretization of selfadjoint and positive definite second order elliptic operator B. Finally a simple V-cycle multigrid implementation of Bh-1 is given.

ON SPACELIKE AUSTERE SUBMANIFOLDS IN PSEUDO-EUCLIDEAN SPACE

In this article, we construct some spacelike austere submanifolds in pseduoEuclidean spaces. We also get some indefinite special Lagrangian submanifolds by constructing twisted normal bundle of spacelike austere submanifolds in pseduo-Euclidean spaces.

ARBITRARILY SMALL NODAL SOLUTIONS FOR PARAMETRIC ROBIN(p,q)-EQUATIONS PLUS AN INDEFINITE POTENTIAL

We consider a nonlinear Robin problem driven by the(p,q)-Laplacian plus an indefinite potential term and with a parametric reaction term.Under minimal conditions on the reaction function,which concern only its behavior near zero,we show that,for all λ>0 small,the problem has a nodal solution y_(λ)∈C^(1)(Ω)and we have y_(λ)→0 in C^(1)(Ω)asλ→0^(+).

A uniqueness theorem for indefinite Sturm-Liouville operators

In this paper, we discuss the inverse problem for indefinite Sturm-Liouville operators on the finite interval [a, b]. For a fixed index n（n = 0, 1, 2,… ）, given the weight function w（x）, we will show that the spectral sets {λn（q, ha,hk）}＋∞k=1 and {λ-n（q, hb,hk）}＋∞k=1 for distinct hk are sufficient to determine the potential q（x） on the finite interval [a, b] and coefficients ha and hb of the boundary conditions.

Cyclic Group Action of Composite Order on Indefinite 4-manifolds

In this paper, we study the possibilities for several kinds of topological, locally linear cyclic group actions of non-prime order on some closed, simply connected 4-manifolds with indefinite intersection form. Especially, we discuss the existence of locally linear pseudofree C9 action on this kind of 4-manifolds.

EXISTENCE OF GROUND STATE SOLUTIONS TOHAMILTONIAN ELLIPTIC SYSTEM WITH POTENTIALS

In this paper, we investigate nonlinear Hamiltonian elliptic system {-△u＋b（x）· u＋（V（x）＋τ）u=K（x）g（v） in R^N,-△u-b（x）· v＋（V（x）＋τ）v=K（x）f（u） in R^N,u（x）→ and v（x）→0 as ｜x｜→∞2,where N ≥ 3, τ 〉 0 is a positive parameter and V, K are nonnegative continuous functions,f and g are both superlinear at 0 with a quasicritical growth at infinity. By establishing avariational setting, the existence of ground state solutions is obtained.

Dyons of Unit Topological Charges in Gauged Skyrme Model

Dyons are an important family of topological solitons carrying both electric and magnetic charges and the presence of a nontrivial temporal component of the gauge field essential for the existence of electricity often makes the analysis of the underlying nonlinear equations rather challenging since the governing action functional assumes an indefinite form.In this work,developing a constrained variational technique,We establish an existence theorem for the dyon solitons in a Skyrme model coupled with SO(3)-gauge fields,formulated by Brihaye,Kleihaus,and Tchrakian.These solutions carry unit monopole and Skyrme charges.

Clinical significance and management of Barrett's esophagus with epithelial changes indefinite for dysplasia

Barrett's esophagus(BE) is defined as the extension of salmon-colored mucosa into the tubular esophagus ≥1 cm proximal to the gastroesophageal junction with biopsy confirmation of intestinal metaplasia. Patients with BE are at increased risk of esophageal adenocarcinoma(EAC), and undergo endoscopic surveillance biopsies to detect dysplasia or early EAC. Dysplasia in BE is classified as no dysplasia, indefinite for dysplasia(IND), low grade dysplasia(LGD) or high grade dysplasia(HGD). Biopsies are diagnosed as IND when the epithelial abnor-malities are not sufficient to diagnose dysplasia or the nature of the epithelial abnormalities is uncertain due to inflammation or technical issues. Specific diagnostic criteria for IND are not well established and its clinical significance and management has not been well studied. Previous studies have focused on HGD in BE and led to changes and improvement in the management of BE with HGD and early EAC. Only recently, IND and LGD in BE have become focus of intense study. This review summarizes the definition, neoplastic risk and clinical management of BE IND.

Study on the Relation of Definite Integral and Indefinite Integral

Relation of definite integral and indefinite integral was discussed and an important result was gotten. If f(x) is bounded and has primary function, the formal definite integral x s f(t)dt is the indefinite integral of f(x), where x is a self-variable, s is a parameter,~f(x) is a function defined in(-∞, +∞), which comes from f(x) by restriction and extension. In other words, the indefinite integral is a special form of definite integral, its lower integral limit and upper integral limit are all indefinite.

Characterizations of Null Holomorphic Sectional Curvature of GCR-Lightlike Submanifolds of Indefinite Nearly Khler Manifolds

We obtain the expressions for sectional curvature, holomorphic sectional curvature and holomorphic bisectional curvature of a GCR-lightlike submanifold of an indefinite nearly Kahler manifold and obtain characterization theorems for holo- morphic sectional and holomorphic bisectional curvature. We also establish a condi- tion for a GCR-lightlike submanifold of an indefinite complex space form to be a null holomorphically fiat.