基于不同网络层次的集群企业知识共享演化分析

基于不同网络层次嵌入视角,考虑集群内网络和超集群网络嵌入的不同情况,综合运用Hotelling博弈和演化博弈,建立集群企业与集群外部企业间知识共享决策与演化的动态模型,探讨在无政府补贴和有政府补贴条件下高技术与低技术集群企业间的博弈决策。研究发现,高技术集群企业会挤占低技术集群企业与集群外企业的知识共享,知识共享成本是影响集群内外企业知识共享的关键因素,政府可以引导集群内企业更多地与集群外企业进行知识共享。最后运用数值仿真对研究结论进行验证。     

Dissolution point and isolation robustness: Robustness criteria for general cluster analysis methods

Two robustness criteria are presented that are applicable to general clustering methods. Robustness and stability in cluster analysis are not only data dependent, but even cluster dependent. Robustness is in the present paper defined as a property of not only the clustering method, but also of every individual cluster in a data set. The main principles are: (a) dissimilarity measurement of an original cluster with the most similar cluster in the induced clustering obtained by adding data points, (b) the dissolution point, which is an adaptation of the breakdown point concept to single clusters, (c) isolation robustness: given a clustering method, is it possible to join, by addition of g points, arbitrarily well separated clusters?Results are derived for k-means, k-medoids (k estimated by average silhouette width), trimmed k-means, mixture models (with and without noise component, with and without estimation of the number of clusters by BIC), single and complete linkage.     

凸概率密度分布簇下的多损失鲁棒优化等价模型及在直营连锁企业中的应用

首先,证明了凸概率密度分布簇的单周期期望均值下单损失鲁棒优化等价模型定理,以及凸概率密度分布簇的单周期期望均值下多损失鲁棒优化等价模型。然后,提出了直营连锁企业的产品在凸概率密度分布簇下的期望均值的单周期生产分配供应问题,建立了直营连锁企业的单周期生产分配供应期望均值鲁棒模型,在获得近似周期概率分布簇情形下给出了单周期生产分配供应鲁棒模型,这种近似鲁棒模型等价于一个线性规划问题。最后,通过已知一个产品的4个周期构成的混合分布簇进行了数值实验,数值结果表明了期望均值准则下的生产分配供应鲁棒模型的生产分配供应策略更加稳健。     

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.     

A trace formula and high-energy spectral asymptotics for the perturbed Landau Hamiltonian

A two-dimensional Schrödinger operator with a constant magnetic field perturbed by a smooth compactly supported potential is considered. The spectrum of this operator consists of eigenvalues which accumulate to the Landau levels. We call the set of eigenvalues near the nth Landau level an nth eigenvalue cluster, and study the distribution of eigenvalues in the nth cluster as n→∞. A complete asymptotic expansion for the eigenvalue moments in the nth cluster is obtained and some coefficients of this expansion are computed. A trace formula involving the eigenvalue moments is obtained.     

On the Galois coverings of a cluster-tilted algebra

We study the module category of a certain Galois covering of a cluster-tilted algebra which we call the cluster repetitive algebra. Our main result compares the module categories of the cluster repetitive algebra of a tilted algebra C and the repetitive algebra of C, in the sense of Hughes and Waschbüsch.     

基于系统动力学的产业集群对企业绩效的影响机制分析

以系统动力学为基础,研究了产业集群对企业绩效的影响机制。分别建立了外部资源环境、发展规模及科研创新能力对企业绩效的影响系统因果图,在此基础上开展了产业集群对企业绩效影响的全过程动力分析。以上海市医药制造产业集群为例开展了实证研究,使用Vensim模拟软件进行了模拟仿真,详尽探讨了影响机制中正负反馈回路。结果表明,产业集群的外部资源环境、产业集群的发展规模和产业集群的科研创新能力对集群内企业的发展有着正向影响,政府和集群内企业可以通过加大对集群科研实力的投资力度、改善产业集群外部环境、扩大产业集群发展规模三个方面来提高产业集群内的企业绩效,促进产业集群内企业的可持续性发展。     

A mathematical programming approach to clusterwise regression model and its extensions

The clusterwise regression model is used to perform cluster analysis within a regression framework. While the traditional regression model assumes the regression coefficient (β) to be identical for all subjects in the sample, the clusterwise regression model allows β to vary with subjects of different clusters. Since the cluster membership is unknown, the estimation of the clusterwise regression is a tough combinatorial optimization problem. In this research, we propose a “Generalized Clusterwise Regression Model” which is formulated as a mathematical programming (MP) problem. A nonlinear programming procedure (with linear constraints) is proposed to solve the combinatorial problem and to estimate the cluster membership and β simultaneously. Moreover, by integrating the cluster analysis with the discriminant analysis, a clusterwise discriminant model is developed to incorporate parameter heterogeneity into the traditional discriminant analysis. The cluster membership and discriminant parameters are estimated simultaneously by another nonlinear programming model.     

A reduction of lattice tiling by translates of a cubical cluster

A cluster is the union of a finite number of cubes from the standard partition ofn-dimensional Euclidean space into unit cubes. If there is lattice tiling by translates of a cluster, then must there be a lattice tiling by translates of the cluster in which the translation vectors have only integer coordinates? In this article we prove that if the interior of the cluster is connected and the dimension is at most three, then the answer is affirmative.     

Explicit calculation of the partition function of a one-dimensional δ-function bose gas

We present a method to calculate explicitly the partition function of a one-dimensional δ-function bose gas. The cluster integrals are obtained for up to the four particles and are shown to be the same as those by the thermal Bethe ansatz method (TBA).     

基于相对风险分担的集群供应链协同创新收益分配机制研究

协同创新是集群供应链企业研发新技术和进行产品升级的重要手段。但是协同创新存在风险, 集群供应链中配套企业与核心企业由于在风险承受能力方面的差异, 使他们在面对相同创新风险时所承担的实际风险却不相同。针对该问题, 本文构建了配套企业与核心企业的协同创新模型, 设计了基于相对风险分担的收益分配机制, 并与现有分配方式进行比较。研究发现:基于相对风险分担的分配机制能够增强企业双方参与协同创新的意愿, 并且使企业所获收益与所承担的风险更加匹配, 达到激励配套企业积极投入的目的。     

Sequential clustering with radius and split criteria

Sequential clustering aims at determining homogeneous and/or well-separated clusters within a given set of entities, one at a time, until no more such clusters can be found. We consider a bi-criterion sequential clustering problem in which the radius of a cluster (or maximum dissimilarity between an entity chosen as center and any other entity of the cluster) is chosen as a homogeneity criterion and the split of a cluster (or minimum dissimilarity between an entity in the cluster and one outside of it) is chosen as a separation criterion. An O(N ³) algorithm is proposed for determining radii and splits of all efficient clusters, which leads to an O(N ⁴) algorithm for bi-criterion sequential clustering with radius and split as criteria. This algorithm is illustrated on the well known Ruspini data set.     

Cluster tilting objects in generalized higher cluster categories

We prove the existence of an m-cluster tilting object in a generalized m-cluster category which is (m+1)-Calabi-Yau and Hom-finite, arising from an (m+2)-Calabi-Yau dg algebra. This is a generalization of the result for the m=1 case in Amiot’s Ph.D. thesis. Our results apply in particular to higher cluster categories associated to Ginzburg dg categories coming from suitable graded quivers with superpotential, and higher cluster categories associated to suitable finite-dimensional algebras of finite global dimension.     

A derivative-free approximate gradient sampling algorithm for finite minimax problems

In this paper we present a derivative-free optimization algorithm for finite minimax problems. The algorithm calculates an approximate gradient for each of the active functions of the finite max function and uses these to generate an approximate subdifferential. The negative projection of 0 onto this set is used as a descent direction in an Armijo-like line search. We also present a robust version of the algorithm, which uses the ‘almost active’ functions of the finite max function in the calculation of the approximate subdifferential. Convergence results are presented for both algorithms, showing that either f(x ^k )→?∞ or every cluster point is a Clarke stationary point. Theoretical and numerical results are presented for three specific approximate gradients: the simplex gradient, the centered simplex gradient and the Gupal estimate of the gradient of the Steklov averaged function. A performance comparison is made between the regular and robust algorithms, the three approximate gradients, and a regular and robust stopping condition.     

Friezes and a construction of the Euclidean cluster variables

Let Q be a Euclidean quiver. Using friezes in the sense of Assem-Reutenauer-Smith, we provide an algorithm for computing the (canonical) cluster character associated with any object in the cluster category of Q. In particular, this algorithm allows us to compute all the cluster variables in the cluster algebra associated with Q. It also allows us to compute the sum of the Euler characteristics of the quiver Grassmannians of any module M over the path algebra of Q.     

Cluster Structure on Generalized Weyl Algebras

We introduce a class of non-commutative algebras that carry non-commutative cluster structure which are generated by identical copies of generalized Weyl algebras. Equivalent conditions for the finiteness of the set of the cluster variables of these cluster structures are provided. Mutations along with some combinatorial data, called cluster strands, arising from the cluster structure are used to construct representations of generalized Weyl algebras.     

Tilting theory and cluster combinatorics

We introduce a new category C, which we call the cluster category, obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditary algebra H over a field. We show that, in the simply laced Dynkin case, C can be regarded as a natural model for the combinatorics of the corresponding Fomin-Zelevinsky cluster algebra. In this model, the tilting objects correspond to the clusters of Fomin-Zelevinsky. Using approximation theory, we investigate the tilting theory of C, showing that it is more regular than that of the module category itself, and demonstrating an interesting link with the classification of self-injective algebras of finite representation type. This investigation also enables us to conjecture a generalisation of APR-tilting.     

销售量预测的REM-GM(1,1)模型及群预测方法研究

库存管理是商业企业经营管理的重要组成部分,其管理应以销售出库量为主要依据,而客户需求的不确定性一直是困扰管理者的首要难题.提出在灰色GM(1,1)模型的基础上,结合残差时刻的灰灾变预测,建立了REM-GM(1,1)模型,并采用群预测的方法,对商业企业中的销售出库量进行了预测.经实证结果检验,表明该模型对商业企业的销售出库量的预测不论是单步预测还是多步远期预测,其预测精度与传统GM模型相比均有较大提高,且误差的波动较为稳定,其预测的结果是令人满意的.     

Denominators in cluster algebras of affine type

The Fomin–Zelevinsky Laurent phenomenon states that every cluster variable in a cluster algebra can be expressed as a Laurent polynomial in the variables lying in an arbitrary initial cluster. We give representation-theoretic formulas for the denominators of cluster variables in cluster algebras of affine type. The formulas are in terms of the dimensions of spaces of homomorphisms in the corresponding cluster category, and hold for any choice of initial cluster.     

Supercompact spaces

We prove the following theorem: Let Y be a Hausdorff space which is the continuous image of a supercompact Hausdorff space, and let K be a countably infinite subset of Y. Then (a) at least one cluster point of K is the limit of a nontrivial convergent sequence in Y (not necessarily in K), and (b) at most countably many cluster points of K are not the limit of some nontrivial sequence in Y. This theorem implies that spaces like β$\text{N}$ and β$\text{N}$?$\text{N}$ are not supercompact. Moreover we will give an example of a separable first countable compact Hausdorff space which is not supercompact.