Analyzing the function of gene sets is a critical step in interpreting the results of high-throughput experiments in systems biology. A variety of enrichment analysis tools have been developed in recent years, but mos...Analyzing the function of gene sets is a critical step in interpreting the results of high-throughput experiments in systems biology. A variety of enrichment analysis tools have been developed in recent years, but most output a long list of significantly enriched terms that are often redundant, making it difficult to extract the most meaningful functions. In this paper, we present GOMA, a novel enrichment analysis method based on the new concept of enriched functional Gene Ontology (GO) modules. With this method, we systematically revealed functional GO modules, i.e., groups of functionally similar GO terms, via an optimization model and then ranked them by enrichment scores. Our new method simplifies enrichment analysis results by reducing redundancy, thereby preventing inconsistent enrichment results among functionally similar terms and providing more biologically meaningful results.展开更多
The Minimum Fragments Removal （MFR） problem is one of the haplotyping problems： given a set of fragments, remove the minimum number of fragments so that the resulting fragments can be partitioned into k classes of ...The Minimum Fragments Removal （MFR） problem is one of the haplotyping problems： given a set of fragments, remove the minimum number of fragments so that the resulting fragments can be partitioned into k classes of non-conflicting subsets. In this paper, we formulate the κ-MFR problem as an integer linear programming problem, and develop a dynamic programming approach to solve the κ-MFR problem for both the gapless and gap eases.展开更多
This paper addresses the simultaneous determination of pricing and inventory replenishment strate- gies under a fluctuating environment. Specifically, we analyze the single item, periodic review model. The demand cons...This paper addresses the simultaneous determination of pricing and inventory replenishment strate- gies under a fluctuating environment. Specifically, we analyze the single item, periodic review model. The demand consists of two parts： the deterministic component, which is influenced by the price, and the stochastic component （perturbation）. The distribution of the stochastic component is determined by the current state of an exogenous Markov chain. The price that is charged in any given period can be specified dynamically. A replenishment order may be placed at the beginning of some or all of the periods, and stockouts are fully backlogged. Ordering costs that are lower semicontinuous, and inventory/backlog （or surplus） costs that are continuous with polynomial growth. Finite-horizon and infinite-horizon problems are addressed. Existence of optimal policies is established. Furthermore, optimality of （s,S,p）-type policies is proved when the ordering cost consists of fixed and proportional cost components and the surplus cost （these costs are all state-dependent） is convex.展开更多
Given an edge weighted graph, the maximum edge-weight connected graph （MECG） is a connected subgraph with a given number of edges and the maximal weight sum. Here we study a special case, i.e. the Constrained Maximu...Given an edge weighted graph, the maximum edge-weight connected graph （MECG） is a connected subgraph with a given number of edges and the maximal weight sum. Here we study a special case, i.e. the Constrained Maximum Edge-Weight Connected Graph problem （CMECG）, which is an MECG whose candidate subgraphs must include a given set of k edges, then also called the k-CMECG. We formulate the k-CMECG into an integer linear programming model based on the network flow problem. The k-CMECG is proved to be NP-hard. For the special case 1-CMECG, we propose an exact algorithm and a heuristic algorithm respectively. We also propose a heuristic algorithm for the k-CMECG problem. Some simulations have been done to analyze the quality of these algorithms. Moreover, we show that the algorithm for 1-CMECG problem can lead to the solution of the general MECG problem.展开更多
基金supported by grants from the National Natural Science Foundation of China(No.60970091, 61171007, 11131009)
文摘Analyzing the function of gene sets is a critical step in interpreting the results of high-throughput experiments in systems biology. A variety of enrichment analysis tools have been developed in recent years, but most output a long list of significantly enriched terms that are often redundant, making it difficult to extract the most meaningful functions. In this paper, we present GOMA, a novel enrichment analysis method based on the new concept of enriched functional Gene Ontology (GO) modules. With this method, we systematically revealed functional GO modules, i.e., groups of functionally similar GO terms, via an optimization model and then ranked them by enrichment scores. Our new method simplifies enrichment analysis results by reducing redundancy, thereby preventing inconsistent enrichment results among functionally similar terms and providing more biologically meaningful results.
基金This research is partially supported by the National Natural Science Foundation of China under Grant No. 60873205, Innovation Project of Chinese Academy of Sciences, kjcsyw-sT.
基金Supported by the National Natural Science Foundation of China （No. 60503004, No. 10471141）. Thc authors gratefully acknowledge the support of K.G.Wang Education Foundation of Hong Kong.
文摘The Minimum Fragments Removal （MFR） problem is one of the haplotyping problems： given a set of fragments, remove the minimum number of fragments so that the resulting fragments can be partitioned into k classes of non-conflicting subsets. In this paper, we formulate the κ-MFR problem as an integer linear programming problem, and develop a dynamic programming approach to solve the κ-MFR problem for both the gapless and gap eases.
基金This research is supported by the National Natural Science Foundation of China under Grant Nos 10631070, 60873205, 10701080, and the Beijing Natural Science Foundation under Grant No. 1092011. It is also partially supported by the Foundation of Beijing Education Commission under Grant No. SM200910037005, the Funding Project for Academic Human Resources Development in Institutions of Higher Learning under the Jurisdiction of Beijing Municipality （PHR201006217）, and the Foundation of WYJD200902.
基金Supported by the National Natural Science Foundation of China (No. 70621061,70890082,70671100)Science Foundation of Beijing Jiaotong University (2007RC014)
文摘This paper addresses the simultaneous determination of pricing and inventory replenishment strate- gies under a fluctuating environment. Specifically, we analyze the single item, periodic review model. The demand consists of two parts： the deterministic component, which is influenced by the price, and the stochastic component （perturbation）. The distribution of the stochastic component is determined by the current state of an exogenous Markov chain. The price that is charged in any given period can be specified dynamically. A replenishment order may be placed at the beginning of some or all of the periods, and stockouts are fully backlogged. Ordering costs that are lower semicontinuous, and inventory/backlog （or surplus） costs that are continuous with polynomial growth. Finite-horizon and infinite-horizon problems are addressed. Existence of optimal policies is established. Furthermore, optimality of （s,S,p）-type policies is proved when the ordering cost consists of fixed and proportional cost components and the surplus cost （these costs are all state-dependent） is convex.
基金supported by National Natural Science Foundation of China under Grant,No.60873205Beijing Natural Science Foundation under Grant No. 1092011+1 种基金Foundation of Beijing Education Commission under Grant No.SM200910037005the Funding Project for Academic Human Resources Development in Institutions of Higher Learning Under the Jurisdiction of Beijing Municipality(PHR(IHLB))and Foundation of WYJD200902
文摘Given an edge weighted graph, the maximum edge-weight connected graph （MECG） is a connected subgraph with a given number of edges and the maximal weight sum. Here we study a special case, i.e. the Constrained Maximum Edge-Weight Connected Graph problem （CMECG）, which is an MECG whose candidate subgraphs must include a given set of k edges, then also called the k-CMECG. We formulate the k-CMECG into an integer linear programming model based on the network flow problem. The k-CMECG is proved to be NP-hard. For the special case 1-CMECG, we propose an exact algorithm and a heuristic algorithm respectively. We also propose a heuristic algorithm for the k-CMECG problem. Some simulations have been done to analyze the quality of these algorithms. Moreover, we show that the algorithm for 1-CMECG problem can lead to the solution of the general MECG problem.
