Deep Belief Network for Lung Nodule Segmentation and Cancer Detection

Cancer disease is a deadliest disease cause more dangerous one.By identifying the disease through Artificial intelligence to getting the mage features directly from patients.This paper presents the lung knob division and disease characterization by proposing an enhancement calculation.Most of the machine learning techniques failed to observe the feature dimensions leads inaccuracy in feature selection and classification.This cause inaccuracy in sensitivity and specificity rate to reduce the identification accuracy.To resolve this problem,to propose a Chicken Sine Cosine Algorithm based Deep Belief Network to identify the disease factor.The general technique of the created approach includes four stages,such as pre-processing,segmentation,highlight extraction,and the order.From the outset,the Computerized Tomography(CT)image of the lung is taken care of to the division.When the division is done,the highlights are extricated through morphological factors for feature observation.By getting the features are analysed and the characterization is done dependent on the Deep Belief Network(DBN)which is prepared by utilizing the proposed Chicken-Sine Cosine Algorithm(CSCA)which distinguish the lung tumour,giving two classes in particular,knob or non-knob.The proposed system produce high performance as well compared to the other system.The presentation assessment of lung knob division and malignant growth grouping dependent on CSCA is figured utilizing three measurements to be specificity,precision,affectability,and the explicitness.

THE SURVIVAL PROBABILITY IN FINITE TIME PERIOD IN FULLY DISCRETE RISK MODEL

The probabilities of the following events are first discussed in this paper: the insurance company survives to any fixed time k and the surplus at time k equals x≥1 . The formulas for calculating such probabilities are deduced through analytical and probabilistic arguments respectively. Finally, other probability laws relating to risk are determined based on the probabilities mentioned above.

MOMENT ESTIMATION FOR MULTIVARIATE EXTREME VALUE DISTRIBUTION

Moment estimation for multivariate extreme value distribution is describedin this paper. Asymptotic covariance matrix of the estimators is given. The relativeefficiencies of moment estimators as compared with the maximum likelihood and thestepwise estimators are computed. We show that when there is strong dependencebetween the variates, the generalized variance of moment estimators is much lower thanthe stepwise estimators. It becomes more obvious when the dimension increases.

The Explicit Solution to Equation AX ＋ X B = C in Matrices

Abstract： At first one of g-inverses of A （×） In＋Im（×） BT is given out, then the explicit solution to matrix equation AX ＋ XB = C is gained by using the method of matrix decomposition, finally, a numerical example is obtained.

ASYMPTOTIC EFFICIENT ESTIMATION IN SEMIPARAMETRIC NONLINEAR REGRESSION MODELS

Abstract In this paper, the estimation method based on the “generalized profile likelihood” for the conditionally parametric models in the paper given by Severini and Wong (1992) is extended to fixed design semiparametric nonlinear regression models.For these semiparametric nonlinear regression models,the resulting estimator of parametric component of the model is shown to be asymptotically efficient and the strong convergence rate of nonparametric component is investigated.Many results (for example Chen (1988),Gao & Zhao (1993), Rice (1986) et al.) are extended to fixed design semiparametric nonlinear regression models.

NOTE ON CALCULATING WIENER NUMBERS OF MOLECULAR GRAPHS WITH SYMMETRY

The authors provided a simple method for calculating Wiener numbers of molecular graphs with symmetry in 1997.This paper intends to further improve on it and simplifies the calculation of the Wiener numbers of the molecular graphs.

WAVELET ESTIMATION IN NONPARAMETRIC MODEL UNDER MARTINGALE DIFFERENCE ERRORS

This paper is concerned with the heteroscedastic regression model Y i=g(x i)+σ iei(1?i?n) under correlated errors e i, where it is assumed that σ i Emphasis>/2 =f(u i), the design points (x i, ui) are known and nonrandom, and g and f are unknown functions. Assuming that unobserved disturbances e i are martingale differences. The strong uniform convergence rates and r-th moment uniform convergence rates of wavelet estimator of g are investigated. Also, the strong uniform convergence rates are discussed for wavelet estimator of f. MR Subject Classification 62G05 Keywords regression function - martingale difference error - wavelet estimator - uniform convergence rate Partially supported by the National Natural Science Foundation of China (10171079).

P_3-FACTORIZATION OF COMPLETE MULTIPARTITE GRAPHS

In this note it is shown that a necessary and sufficient condition for the existence of a P 3 factorization of complete multipartite graph λK n m is (1) m≥3, (2) mn≡0 (mod 3) and (3) λ(m-1)n≡0 (mod 4).

THE MULTIFIT ALGORITHM FOR SET PARTITIONING CONTAINING KERNELS

Abstract This paper investigates the set partitioning containing kernels. This problem can also be considered as the identical machine scheduling problem with nonsimultaneous machine release times. That the algorithm MULTIFIT has a worst case bound of 6/5 is proved. Through combining MULTIFIT and LPT, an algorithm MULTILPT with a worst case bound of 7/6 has been obtained.

ON THE EXISTENCE OF PERIODIC SOLUTIONS FOR THE THIRD-ORDER NONLINEAR ORDINARY DIFFERENTIAL EQUATIONS

Abstract In this paper,the existence of periodic solution for the third order nonlinear ordinary differential equation of the form x…+f()+g()+h(x)=p(t) is considered,where f,g,h and p are the continuous functions,and p(t+T)=p(t). By using the Leray Schauder degree method,some sufficient conditions to guarantee the existence of T periodic solution for the equation are obtained.Some previous results are extended and improved.

SOME PROPERTIES OF THE SPECTRUM OF GRAPHS

Let G be a graph and denote by Q(G)=D(G)+A(G),L(G)=D(G)-A(G) the sum and the difference between the diagonal matrix of vertex degrees and the adjacency matrix of G, respectively.In this paper,some properties of the matrix Q(G) are studied.At the same time,a necessary and sufficient condition for the equality of the spectrum of Q(G) and L(G) is given.

ON A TWO-POINT BOUNDARY VALUE PROBLEM OF DUFFING TYPE EQUATION WITH DIRICHLET CONDITIONS

Abstract An existence and uniqueness result concerned with the Dirichlet boundary value problem u″+cu′+g(t,u)=e(t),u(0)=u(π)=0 is offered.

A CLASS OF FUNCTIONAL EQUATION AND FRACTAL INTERPOLATION FUNCTIONS

Abstract A new class of functional equation in C 0(I) is investigated. It is proved that some class of FIF satisfies the functional equation. Another functional equation is constructed. Their solutions can approximate FIF arbitrarily. And a new approximate estimate between FIF and interpolated function is given.

THE FIRST BOUNDARY VALUE PROBLEM FOR STRONGLY DEGENERATE QUASILINEAR PARABOLIC EQUATIONS IN ANISOTROPIC SOBOLEV SPACES

This article concerns the existence of weak solutions of the first boundary value problem for a kind of strongly degenerate quasilinear parabolic equation in the anisotropic Sobolev Space. With the theory of anisotropic Sobolev spaces an existence result is proved.

COEFFICIENT MULTIPLIERS ON MIXED NORM SPACES

This paper describes the characteristics of the coefficient multipliers of mixed norm spaces A p,q,α with 0<p≤1, 0<q,α<∞ into some analytic function spaces. In corollaries, the characteristics of the coefficient multipliers of G p (0<p<1) and A p (0<p≤1) into some analytic function spaces are given. MR Subject Classification 30D - 30H05 - 46E Keywords analytic function space - Hadamard product - multiplier - operator

DOMAIN DECOMPOSITION METHOD FOR PARABOLIC EQUATION ON GENERAL DOMAIN

The nonoverlapping domain decomposition method for parabolic partialdifferential equation on general domain is considered. A kind of domain decompositionthat uses the finite element procedure is given. The problem over the domains can beimplemented on parallel computer. Convergence analysis is also presented.

A SOLUTION TO A PROBLEM OF GARGANO, LEWINTER AND MALERBA

A labeled graph is an ordered pair (G, L) consisting of a graph G and its labeling L: V(G) → {1, 2, ..., n}, where n=|V(G)|. An increasing nonconsecutive path in a labeled graph (G, L) is a path (u 1, u 2, ..., u k), k≥1, in G such that L(u i)+1<L(u i+1) for all i=1, 2, ..., k?1. The total number of increasing nonconsecutive paths in (G, L) is denoted by d(G, L). The following open problem was proposed by Gargano, Lewinter and Malerba: obtaining a labeling L that produces the largest d(P n, L), where P n is a path of order n. Such a labeling is called optimal. The author have solved this problem. For each n ≥ 5 and for n=3, there are exactly four optimal labelings. Either of P 2, P 4 has exactly two optimal labelings. MR Subject Classification 05C38 Keywords labeled graph - increasing nonconsecutive paths

Improvement of the minimal residual method for solving nonsymmetric linear systems

In this paper, the minimal residual （MRES） method for solving nonsymmetric equation systems was improved, the recurrence relation was deduced between the approximate solutions of the linear equation system Ax = b, and a more effective method was presented, which can reduce the operational count and the storage.

INFLUENCE ANALYSIS ON LINEAR MODELS WITH RANDOM EFFECTS

In this paper,a unified diagnostic method for linear models with random effects based upon the joint likelihood given by Robinson (in 1991) is presented.The case deletion model is equivalent to mean shift outlier model,as well as case weights model.From this point of view,several new diagnostic measures,such as Cook distance, WK diagnostics are derived.Some previous results are improved.Numerical examples illustrate the method is available.

ENUMERATION OF ROOTED PLANAR HALIN MAPS

Abstract A Halin map is a kind of planar maps oriented by a tree. In this paper the rooted halin maps with the vertex partition as parameters are enumerated such that a famous result on rooted trees due to Harary, Prins, and Tutte is deduced as a special case. Further, by using Lagrangian inversion to obtain a number of summation free formulae directly, the various kinds of rooted Halin maps with up to three parameters have been counted.