Modeling Reputation Management System on Online C2C Market

This paper discusses the effectiveness of sharing information concerning the reputations of buyers and sellers making online transactions in a consumer-to-consumer (C2C) market. We developed a computer simulation model that describes online transactions with a reputation management system that shares information concerning the reputations of consumers. The model takes an agent-based approach in which agents' actions are based on the iterated prisoner's dilemma. No model exists to analyze C2C markets even though there are many case studies concerning the effectiveness of sharing reputation information among participants in a market. The simulation results revealed that a positive reputation system can be more effective than a negative reputation system for an online transaction, even though the negative one can work for a traditional transaction. The result should be an important consideration when designing practical reputation management systems for online transactions.     

An option-theoretic model of a reputation network

This paper constructs a new theory of social networks based on reputation. The model assumes that reputation is an asset and that individuals connect by buying options on the reputation of others. In networking, individuals construct portfolios of call options to leverage the reputations of others and put options to hedge the connections with others. A network then consists of portfolios of reputation options. The option model confers advantages not present in existing models. First, the payoff to connecting is the payoff on a portfolio of reputation options. Second, the network forms as individuals take option positions; the network evolves as individuals adjust those positions. Third, networking strategies become option strategies. The model allows for insights into network structure, the price of connecting and the value of connecting.     

Nonlinear Elasticity in a Deforming Ambient Space

In this paper, we formulate a nonlinear elasticity theory in which the ambient space is evolving. For a continuum moving in an evolving ambient space, we model time dependency of the metric by a time-dependent embedding of the ambient space in a larger manifold with a fixed background metric. We derive both the tangential and the normal governing equations. We then reduce the standard energy balance written in the larger ambient space to that in the evolving ambient space. We consider quasi-static deformations of the ambient space and show that a quasi-static deformation of the ambient space results in stresses, in general. We linearize the nonlinear theory about a reference motion and show that variation of the spatial metric corresponds to an effective field of body forces.     

Reputation-based winner determination problem for combinatorial transportation procurement auctions

This paper proposes a reputation-based winner determination problem for transportation procurement auctions where the allocation of long-term contracts to carriers is decided with respect to both bid ask-prices and carriers reputation. The objective is to manage the trade-off between transport costs and the quality of service during operations. Carriers reputation is translated into unexpected hidden cost that represents the possible additional cost that the shipper may incur when dealing with a set of winning carriers. This cost depends essentially on the carriers reputation as evaluated by the shipper running the auction. To evaluate carriers reputations, the shipper uses a number of service attributes with different weights depending on shipping contracts.     

Metric nonlinear connections

For a system of second order differential equations we determine a nonlinear connection that is compatible with a given generalized Lagrange metric. Using this nonlinear connection, we can find the whole family of metric nonlinear connections that can be associated with a system of SODE and a generalized Lagrange metric. For the particular case when the system of SODE and the metric structure are Lagrangian, we prove that the canonical nonlinear connection of the Lagrange space is the only nonlinear connection which is metric and compatible with the symplectic structure of the Lagrange space. For this particular case, the metric tensor determines the symmetric part of the canonical nonlinear connection, while the symplectic structure determines the skew-symmetric part of the nonlinear connection.     

Hilbert投影距离与Banach空间的范数

In this paper, we establish some relations between the Hilbert＇s projective metric and the norm on a Banach space and show that the metric and the norm induce equivalent convergences at certain set. As applications, we utilize the main results to discuss the eigenvalue problems for a class of positive homogeneous operators of degree a and the positive solutions for a class of nonlinear algebraic system.     

Nonlinear limit for a system of diffusing particles which alternate between two states

We study a system of particles and the nonlinear McKean-Vlasov diffusion that is its limit for weak interactions. Each particle switches between two states, both with their own diffusion dynamics. There is interaction, in particular, in the rates of the switches. We show existence and uniqueness for the system of particles by stopping-time techniques. For the nonlinear martingale problem, we use a time-change that allows us to return to a strong pathwise representation, and then we use a contraction argument for an appropriate metric. Finally, we show propagation of chaos.     

Applications of Hilbert’s projective metric to a class of positive nonlinear operators

The purpose of this paper is to study the eigenvalue problems for a class of positive nonlinear operators. Using projective metric techniques and the contraction mapping principle, we establish existence, uniqueness and continuity results for positive eigensolutions of a particular type of positive nonlinear operator. In addition, we prove the existence of a unique fixed point of the operator with explicit norm-estimates. Applications to nonlinear systems of equations and to matrix equations are considered.     

具凸结构的概率度量空间中的重合点定理

本文在具凸结构的概率度量空间中，对非线性混合压缩映象得出了几个重合点和公共不动点定理。     

Density based fuzzy c-means clustering of non-convex patterns

We propose a new technique to perform unsupervised data classification (clustering) based on density induced metric and non-smooth optimization. Our goal is to automatically recognize multidimensional clusters of non-convex shape. We present a modification of the fuzzy c-means algorithm, which uses the data induced metric, defined with the help of Delaunay triangulation. We detail computation of the distances in such a metric using graph algorithms. To find optimal positions of cluster prototypes we employ the discrete gradient method of non-smooth optimization. The new clustering method is capable to identify non-convex overlapped d-dimensional clusters.     

Unsupervised quadratic surface support vector machine with application to credit risk assessment

Unsupervised classification is a highly important task of machine learning methods. Although achieving great success in supervised classification, support vector machine (SVM) is much less utilized to classify unlabeled data points, which also induces many drawbacks including sensitive to nonlinear kernels and random initializations, high computational cost, unsuitable for imbalanced datasets. In this paper, to utilize the advantages of SVM and overcome the drawbacks of SVM-based clustering methods, we propose a completely new two-stage unsupervised classification method with no initialization: a new unsupervised kernel-free quadratic surface SVM (QSSVM) model is proposed to avoid selecting kernels and related kernel parameters, then a golden-section algorithm is designed to generate the appropriate classifier for balanced and imbalanced data. By studying certain properties of proposed model, a convergent decomposition algorithm is developed to implement this non-covex QSSVM model effectively and efficiently (in terms of computational cost). Numerical tests on artificial and public benchmark data indicate that the proposed unsupervised QSSVM method outperforms well-known clustering methods (including SVM-based and other state-of-the-art methods), particularly in terms of classification accuracy. Moreover, we extend and apply the proposed method to credit risk assessment by incorporating the T-test based feature weights. The promising numerical results on benchmark personal credit data and real-world corporate credit data strongly demonstrate the effectiveness, efficiency and interpretability of proposed method, as well as indicate its significant potential in certain real-world applications.     

New cone fixed point theorems for nonlinear multivalued maps with their applications

In this paper, we first establish some new types of fixed point theorems for nonlinear multivalued maps in cone metric spaces. From those results, we obtain new fixed point theorems for nonlinear multivalued maps in metric spaces and the generalizations of Mizoguchi–Takahashi’s fixed point theorem and Berinde–Berinde’s fixed point theorem. Some applications to the study of metric fixed point theory are given.     

传统节会的声誉溢出效应:基于Kreps-Milgrom-Roberts-Wilson声誉模型

中国经济繁荣带来传统节会复苏,但是传统节会市场的鱼龙混杂导致传统节会声誉参差不齐,该现象引起了政府部门的重视和学术界的关注.现有文献侧重于对节会概念、意义、文化层面的讨论,缺乏对节会声誉问题的研究,因此本文参考Kreps-Milgrom-Roberts-Wilson声誉模型,在四个基本假设基础上建立了传统节会的声誉模型,分析了传统节会的声誉溢出效应及均衡条件.研究发现:第一,参与者认为传统节会承办方的声誉越好,承办方选择不欺骗参与者的概率就越大,承办方建立声誉的积极性也就越高;第二,一旦承办方出现欺骗参与者的行为,参与者就会认为其是弱承办方,在下一期承办方会失去参与者的信任,从而失去长期获利的机会;第三,无论是强承办方还是弱承办方,不去欺骗参与者才是最优选择,此时承办方和参与者可以实现合作共赢,这是一种更有效率的文化旅游发展模式.因此,文章提出了建立传统节会声誉评价制度与信息公开制度、加强对传统节会的监管以及完善相关法律法规的政策建议.     

Coincidence and fixed point theorems for nonlinear hybrid generalized contractions

In this paper we first prove some coincidence and fixed point theorems for nonlinear hybrid generalized contractions on metric spaces. Secondly, using the concept of an asymptotically regular sequence, we give some fixed point theorems for Kannan type multi-valued mappings on metric spaces. Our main results improve and extend several known results proved by other authors.     

Nonlinear nonparametric mixed-effects models for unsupervised classification

In this work we propose a novel EM method for the estimation of nonlinear nonparametric mixed-effects models, aimed at unsupervised classification. We perform simulation studies in order to evaluate the algorithm performance and we apply this new procedure to a real dataset.     

Perturbations of Moore–Penrose Metric Generalized Inverses of Linear Operators in Banach Spaces

In this paper,the perturbations of the Moore–Penrose metric generalized inverses of linear operators in Banach spaces are described.The Moore–Penrose metric generalized inverse is homogeneous and nonlinear in general,and the proofs of our results are different from linear generalized inverses.By using the quasi-additivity of Moore–Penrose metric generalized inverse and the theorem of generalized orthogonal decomposition,we show some error estimates of perturbations for the singlevalued Moore–Penrose metric generalized inverses of bounded linear operators.Furthermore,by means of the continuity of the metric projection operator and the quasi-additivity of Moore–Penrose metric generalized inverse,an expression for Moore–Penrose metric generalized inverse is given.     

Coupled fixed points in partially ordered metric spaces and application

In this paper, we prove some coupled fixed point theorems for mappings having a mixed monotone property in partially ordered metric spaces. The main results of this paper are generalizations of the main results of Bhaskar and Lakshmikantham [T. Gnana Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal. TMA 65 (2006) 1379-1393]. As an application, we discuss the existence and uniqueness for a solution of a nonlinear integral equation.     

Global structure of positive solution sets of nonlinear operator equations

In this paper we investigate the existence of unbounded maximal subcontinua of positive solution sets of some nonlinear operator equations that bifurcates from infinity. The main feature of the paper is that the nonlinearity may not be of asymptotically linear type and may not be positone. The methods used to show our main results are different from that of Rabinowitz’ well-known global bifurcation theorems and that of some other related papers. We first obtain a sequence of unbounded subcontinua located in a pipe that bifurcates from nontrivial solutions by using a topological degree argument. Then using a result on subcontinua of superior limit in metric spaces we obtain the main results concerning unbounded maximal subcontinua of positive solution sets of the nonlinear operator equation. The main results can be applied to the semipositone problems to obtain the existence of positive solutions.     

Rayleigh dissipation from the general recurrence of metrics in path spaces

Given a pair (metric g, symmetric 2-covariant tensor field H though as a Rayleigh dissipation) on a path space (manifold M, semispray S), the family of nonlinear connections N such that H equals the dynamical derivative of g with respect to (S,N) is determined by using the Obata tensors. In this way, we generalize the case of metric nonlinear connections as well as that of recurrent metrics. As applications, we treat firstly the case of Finslerian (α,β)-metrics finding all nonlinear connections for which the associated Finsler-Sasaki metric is exactly the dynamical derivative of the Riemannian-Sasaki metric. Secondly, we apply our results for the case of Beil metrics used in Relativity and field theories.