Positive solutions of a nonlinear three-point boundary value problem
In this paper, by using Krasnoselskii's fixed point theorem in a cone, we study the existence of single and multiple positive solutions to the three-point boundary value problem (BVP)y''(t)+a(t)f(y(t))=0,0

title: Solvability of multi-point boundary value problem at resonance (III)
abstract: In this paper, we consider the following second order ordinary differential equation(1.1)x^'^'=f(t,x(t),x^'(t))+e(t),t@?(0,1),subject to one of the following boundary value conditions: (1.2)x(0)=@?"i"="1^m^-^2@a"ix(@x"i),x(1)=@?"j"="1^n^-^2@b"jx(@h"j),(1.3)x(0)=@?"i"="1^m^-^2@a"ix(@x"i),x^'(1)=@?"j"="1^n^-^2@b"jx^'(@h"j),(1.4)x^'(0)=@?"i"="1^m^-^2@a"ix^'(@x"i),x(1)=@?"j"="1^n^-^2@b"jx(@h"j),where @a"i(1=

title: Positive solutions of a nonlinear four-point boundary value problems
abstract: In this paper, by using the Krasnoselskii's theorem in a cone, we study the existence of at least one or two positive solutions to the four-point boundary value problemy^''(t)+a(t)f(y(t))=0,00. As an application, we also give some examples to demonstrate our results.

title: Note on third-order boundary value problem for differential equations with deviating arguments
abstract: A third-order boundary value problem for differential equations with deviating arguments is considered in this note. An existence result is obtained by the help of the well-known Leray-Schauder Alternative. Also, a uniqueness result is given.

title: Solvability of multi-point boundary value problem at resonance--Part IV

title: Existence and uniqueness of solutionsto first-order multipoint boundary value problems
abstract: In this paper, we give existence and uniqueness results for solutions of multipoint boundary value problems of the form 
x'=f(t,x(t))+e(t),t∈(0,1),∑j=1mAjx(ηj)=0, 
where ƒ : [0,1] × Rn → Rn is a Caratheodory function, Ajs (j = 1, 2,, m) are constant square matrices of order n, 0 < η1 η2 << ηm−1, < ηm ⪯ 1, and e(t) ∈ L1([0,1], Rn). The existence of solutions is proven by the coincidence degree theory. As an application, we also give one example to demonstrate our results.

title: Building text classifiers using positive and unlabeled examples
abstract: We study the problem of building text classifiers using positive and unlabeled examples. The key feature of this problem is that there is no negative example for learning. Recently, a few techniques for solving this problem were proposed in the literature. These techniques are based on the same idea, which builds a classifier in two steps. Each existing technique uses a different method for each step. We first introduce some new methods for the two steps, and perform a comprehensive evaluation of all possible combinations of methods of the two steps. We then propose a more principled approach to solving the problem based on a biased formulation of SVM, and show experimentally that it is more accurate than the existing techniques.

title: What's behind topic formation and development: a perspective of community core groups
abstract: Over the past several years, there has been a great interest in topic detection and tracking (TDT). Recently, analyzing general research trend from the huge amount of history documents also arouses considerable attention. However, existing work on TDT mainly focuses on overall trend analysis, and is unable to address questions such as "what determines the evolution of a topic?" and "when and how does a new topic get formed?".
 In this paper, we propose a core group model to explain the dynamics and further segment topic development. According to the division phase and interphase in the life cycle of a core group, a topic is separated into four states, i.e. birth state, extending state, saturation state and shrinkage state. Experimental results on a real dataset show that the division of a core group brings on the generation of a new topic, and the progress of an entire topic is closely correlated to the growth of a core group during its interphase.

title: A Neural Network Approach To Shape From Shading
abstract: In this paper, we propose a method of recovering shape from shading that solves directly for the surface height using neural networks. The main motivation of this paper is to provide an answer to the open problem proposed by Zhou and Chellappa [11]. We first formulate the shape from shading problem by combining a triangular element surface model with a linearized reflectance map. Then, we use a linear feed-forward network architecture with six layers to compute the surface height with a singular value decomposition. The weights in the model initialized using eigenvectors and eigen-values of the stiffness matrix of objective functional. Experimental results show that our solution is very effective.

title: Concurrent Discretization of Multiple Attributes
abstract: Better decision trees can be learnt by merging continuous values into intervals. Merging of values, however, could introduce inconsistencies to the data, or information loss. When it is desired to maintain a certain consistency, interval mergings in one attribute could disable those in another attribute. This interaction raises the issue of determining the order of mergings. We consider a globally greedy heuristic that selects the “best” merging from all continuous attributes at each step. We present an implementation of the heuristic in which the best merging is determined in a time independent of the number of possible mergings. Experiments show that intervals produced by the heuristic lead to improved decision trees.

title: Extracting Web Data Using Instance-Based Learning
abstract: This paper studies structured data extraction from Web pages, e.g., online product description pages. Existing approaches to data extraction include wrapper induction and automatic methods. In this paper, we propose an instance-based learning method, which performs extraction by comparing each new instance (or page) to be extracted with labeled instances (or pages). The key advantage of our method is that it does not need an initial set of labeled pages to learn extraction rules as in wrapper induction. Instead, the algorithm is able to start extraction from a single labeled instance (or page). Only when a new page cannot be extracted does the page need labeling. This avoids unnecessary page labeling, which solves a major problem with inductive learning (or wrapper induction), i.e., the set of labeled pages may not be representative of all other pages. The instance-based approach is very natural because structured data on the Web usually follow some fixed templates and pages of the same template usually can be extracted using a single page instance of the template. The key issue is the similarity or distance measure. Traditional measures based on the Euclidean distance or text similarity are not easily applicable in this context because items to be extracted from different pages can be entirely different. This paper proposes a novel similarity measure for the purpose, which is suitable for templated Web pages. Experimental results with product data extraction from 1200 pages in 24 diverse Web sites show that the approach is surprisingly effective. It outperforms the state-of-the-art existing systems significantly.