The Multiplicative Inverse Eigenvalue Problem over an Algebraically Closed Field

Let $M$ be a square matrix and let $p(t)$ be a monic polynomial of degree $n$. Let $Z$ be a set of $n\times n$ matrices. The multiplicative inverse eigenvalue problem asks for the construction of a matrix in $Z$ such that the product matrix $MZ$ has characteristic polynomial $p(t)$. In this paper we provide new necessary and sufficient conditions when $Z$ is an affine variety over an algebraically closed field.Comment: 9 Page

Diagnostic prediction of complex diseases using phase-only correlation based on virtual sample template

Motivation: Complex diseases induce perturbations to interaction and regulation networks in living systems, resulting in dynamic equilibrium states that differ for different diseases and also normal states. Thus identifying gene expression patterns corresponding to different equilibrium states is of great benefit to the diagnosis and treatment of complex diseases. However, it remains a major challenge to deal with the high dimensionality and small size of available complex disease gene expression datasets currently used for discovering gene expression patterns. Results: Here we present a phase-only correlation (POC) based classification method for recognizing the type of complex diseases. First, a virtual sample template is constructed for each subclass by averaging all samples of each subclass in a training dataset. Then the label of a test sample is determined by measuring the similarity between the test sample and each template. This novel method can detect the similarity of overall patterns emerged from the differentially expressed genes or proteins while ignoring small mismatches. Conclusions: The experimental results obtained on seven publicly available complex disease datasets including microarray and protein array data demonstrate that the proposed POC-based disease classification method is effective and robust for diagnosing complex diseases with regard to the number of initially selected features, and its recognition accuracy is better than or comparable to other state-of-the-art machine learning methods. In addition, the proposed method does not require parameter tuning and data scaling, which can effectively reduce the occurrence of over-fitting and bias

A WENO Algorithm of the Temperature and Ionization Profiles around a Point Source

We develop a numerical solver for radiative transfer problems based on the weighted essentially nonoscillatory (WENO) scheme modified with anti-diffusive flux corrections, in order to solve the temperature and ionization profiles around a point source of photons in the reionization epoch. Algorithms for such simulation must be able to handle the following two features: 1. the sharp profiles of ionization and temperature at the ionizing front (I-front) and the heating front (T-front), and 2. the fraction of neutral hydrogen within the ionized sphere is extremely small due to the stiffness of the rate equations of atom processes. The WENO scheme can properly handle these two features, as it has been shown to have high order of accuracy and good convergence in capturing discontinuities and complicated structures in fluid as well as to be significantly superior over piecewise smooth solutions containing discontinuities. With this algorithm, we show the time-dependence of the preheated shell around a UV photon source. In the first stage the I-front and T-front are coincident, and propagate with almost the speed of light. In later stage, when the frequency spectrum of UV photons is hardened, the speeds of propagation of the ionizing and heating fronts are both significantly less than the speed of light, and the heating front is always beyond the ionizing front. In the spherical shell between the I- and T-fronts, the IGM is heated, while atoms keep almost neutral. The time scale of the preheated shell evolution is dependent on the intensity of the photon source. We also find that the details of the pre-heated shell and the distribution of neutral hydrogen remained in the ionized sphere are actually sensitive to the parameters used. The WENO algorithm can provide stable and robust solutions to study these details.Comment: 24 pages, 7 figures, accepted in New Astronom

Predicting the continuance usage of information systems: A comparison of three alternative models

This study examines the explanatory power of three prospective models in predicting users¡¦ continuous adoption of information system. The three models include: Expectation-Confirmation Theory Model (ECTM, Model 1), the integration of ECTM with Technology Acceptance Model (ECT-TAM, Model 2), and a hybrid model integrating ECT, TAM and emotions (Model 3). Three hundred and fifty web portal site users were obtained from a survey. Data analysis using LISREL shows that all three models meet the various goodness-of-fit criteria. In terms of variance explained for intention to continue IS usage, all three models perform equally well. As for the explanatory power of satisfaction, Model 3 has the highest R2 (71%), followed by Model 2 (69%), and Model 1 (68%). This result confirms the erstwhile discussion of continuance intention behavior in which adding emotion factors to the cognitive process model will enhance the predictive power of the satisfaction.

RESEARCH ON THE RELATIONSHIP AMONG MARKET ORIENTATION, CUSTOMER RELATIONSHIP MANAGEMENT, CUSTOMER KNOWLEDGE MANAGEMENT AND BUSINESS PERFORMANCE

In the age of knowledge-based economy, business must effectively to improve its performance rely on implement customer relationship management and customer knowledge management. Market orientation is a kind of marketing logic which is focus on customers, it can help to construct the relationship and communicate knowledge with customers, in order to improve customer satisfaction, customer loyalty and gain and accumulate value for the business. This paper is intended to construct an integrated model. In this model it discusses the relationship between market orientation, customer relationship management and customer knowledge management, and their contribution to business performance. Key words: market orientation, customer knowledge management, customer relationship management; business performanc