37524397
Cluster-based estimation for sufficient dimension reduction
Sufficient dimension reduction (SDR) approaches such as ordinary least squares (OLS), sliced inverse regression, sliced average variance estimation and principal Hessian directions all require a linearity condition on the marginal distribution of the predictors X. This can be a significant limitation in practice. In this article we propose the use of clustering on the predictor space with the goal of breaking the nonlinearity among the predictors. We then estimate the dimension reduction subspace by combining estimates from individual clusters. OLS is used as a demonstration of the cluster-based estimation approach. Simulations have shown that the proposed method effectively mitigates the effects of nonlinearity; it thus has the potential to widen the applicative scope of existing SDR techniques.
13836655
Dimension reduction methods for microarrays with application to censored survival data
MOTIVATION
Recent research has shown that gene expression profiles can potentially be used for predicting various clinical phenotypes, such as tumor class, drug response and survival time. While there has been extensive studies on tumor classification, there has been less emphasis on other phenotypic features, in particular, patient survival time or time to cancer recurrence, which are subject to right censoring. We consider in this paper an analysis of censored survival time based on microarray gene expression profiles.


RESULTS
We propose a dimension reduction strategy, which combines principal components analysis and sliced inverse regression, to identify linear combinations of genes, that both account for the variability in the gene expression levels and preserve the phenotypic information. The extracted gene combinations are then employed as covariates in a predictive survival model formulation. We apply the proposed method to a large diffuse large-B-cell lymphoma dataset, which consists of 240 patients and 7399 genes, and build a Cox proportional hazards model based on the derived gene expression components. The proposed method is shown to provide a good predictive performance for patient survival, as demonstrated by both the significant survival difference between the predicted risk groups and the receiver operator characteristics analysis.


AVAILABILITY
R programs are available upon request from the authors.


SUPPLEMENTARY INFORMATION
http://dna.ucdavis.edu/~hli/bioinfo-surv-supp.pdf.
27925816
A fuzzy approach to the multiobjective transportation problem
The aim of this paper is to present a fuzzy compromise programming approach to multiobjective transportation problems. A characteristic feature of the approach proposed is that various objectives are synthetically considered with the marginal evaluation for individual objectives and the global evaluation for all objectives. The decision-maker’s preference is taken into account by his/her assigning the weights of objectives. With the global evaluation for all objectives, a compromise programming model is formulated. This model covers a wide spectrum of methods with Zimmermann’s fuzzy programming approach essentially equivalent to one of its special cases. Using ordinary optimization technique, we solve the fuzzy compromise programming model to obtain a non-dominated compromise solution at which the synthetic membership degree of the global evaluation for all objectives is maximum. A numerical example is given to demonstrate the efficiency of the proposed fuzzy compromise programming approach. 
 
 
Scope and purpose 
 
In many real-world situations for transportation problems, decisions are often made in the presence of multiple, conflicting, incommensurate objectives. Intensive investigations on multiobjective linear transportation problem have been made. Among them Zimmermann’s fuzzy programming appears to be an ideal approach for obtaining the optimal compromise solution to a multiobjective transportation problem. However, due to the ease of computation, the aggregate operator used in Zimmermann’s fuzzy programming is the “min” operator, which does not guarantee a non-dominated solution. In this paper, we propose a new fuzzy compromise programming approach to multiobjective transportation problems. It is shown that the approach proposed can give a compromise solution that is not only non-dominated but also optimal in a certain sense. The proposed approach is robust enough to cover a wide spectrum of methods. Zimmermann’s fuzzy programming approach is essentially equivalent to one of the proposed method’s special cases.
8071208
Incremental Model-based Learners With Formal Learning-Time Guarantees
Model-based learning algorithms have been shown to use experience efficiently when learning to solve Markov Decision Processes (MDPs) with finite state and action spaces. However, their high computational cost due to repeatedly solving an internal model inhibits their use in large-scale problems. We propose a method based on real-time dynamic programming (RTDP) to speed up two model-based algorithms, RMAX and MBIE (model-based interval estimation), resulting in computationally much faster algorithms with little loss compared to existing bounds. Specifically, our two new learning algorithms, RTDP-RMAX and RTDP-IE, have considerably smaller computational demands than RMAX and MBIE. We develop a general theoretical framework that allows us to prove that both are efficient learners in a PAC (probably approximately correct) sense. We also present an experimental evaluation of these new algorithms that helps quantify the tradeoff between computational and experience demands.
14498579
Accurate anchoring alignment of divergent sequences
MOTIVATION
Obtaining high quality alignments of divergent homologous sequences for cross-species sequence comparison remains a challenge.


RESULTS
We propose a novel pairwise sequence alignment algorithm, ACANA (ACcurate ANchoring Alignment), for aligning biological sequences at both local and global levels. Like many fast heuristic methods, ACANA uses an anchoring strategy. However, unlike others, ACANA uses a Smith-Waterman-like dynamic programming algorithm to recursively identify near-optimal regions as anchors for a global alignment. Performance evaluations using a simulated benchmark dataset and real promoter sequences suggest that ACANA is accurate and consistent, especially for divergent sequences. Specifically, we use a simulated benchmark dataset to show that ACANA has the highest sensitivity to align constrained functional sites compared to BLASTZ, CHAOS and DIALIGN for local alignment and compared to AVID, ClustalW, DIALIGN and LAGAN for global alignment. Applied to 6007 pairs of human-mouse orthologous promoter sequences, ACANA identified the largest number of conserved regions (defined as over 70% identity over 100 bp) compared to AVID, ClustalW, DIALIGN and LAGAN. In addition, the average length of conserved region identified by ACANA was the longest. Thus, we suggest that ACANA is a useful tool for identifying functional elements in cross-species sequence analysis, such as predicting transcription factor binding sites in non-coding DNA.


AVAILABILITY
ACANA software and test sequence data are publicly available at http://BioMedEmpire.org/
6768077
A parallel multiresolution volume rendering algorithm for large data visualization
We present a new parallel multiresolution volume rendering algorithm for visualizing large data sets. Using the wavelet transform, the raw data is first converted to a multiresolution wavelet tree. To eliminate the data dependency between processors at run-time, and achieve load-balanced rendering, we design a novel algorithm to partition the tree and distribute the data along a hierarchical space-filling curve with error-guided bucketization. Further optimization is achieved by storing reconstructed data at pre-selected tree nodes for each processor based on the available storage resources to reduce the overall wavelet reconstruction cost. At run time, the wavelet tree is first traversed according to the user-specified error tolerance. Data blocks of different resolutions that satisfy the error tolerance are then decompressed and rendered to compose the final image in parallel. Experimental results showed that our algorithm can reduce the run-time communication cost to a minimum and ensure a well-balanced workload among processors when visualizing gigabytes of data with arbitrary error tolerances.
9254987
Methodological frameworks for large-scale network analysis and design
This paper emphasizes the need for methodological frameworks for analysis and design of large scale networks which are independent of specific design innovations and their advocacy, with the aim of making networking a more systematic engineering discipline. Networking problems have largely confounded existing theory, and innovation based on intuition has dominated design. This paper will illustrate potential pitfalls of this practice. The general aim is to illustrate universal aspects of theoretical and methodological research that can be applied to network design and verification. The issues focused on will include the choice of models, including the relationship between flow and packet level descriptions, the need to account for uncertainty generated by modelling abstractions, and the challenges of dealing with network scale. The rigorous comparison of proposed schemes will be illustrated using various abstractions. While standard tools from robust control theory have been applied in this area, we will also illustrate how network-specific challenges can drive the development of new mathematics that expand their range of applicability, and how many enormous challenges remain.