SEARCH · PubMed Health

Results for “Programming, Linear”

Explore indexed PubMed citations for clinical trials, systematic reviews and public health research. Read source abstracts and follow each citation to its original PubMed record.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 415 records · Page 23Linked to original sources

PubMed2003

Conversion of dose-volume constraints to dose limits.

The purpose of this study is to introduce two techniques for converting dose-volume constraints to dose limits for treatment planning optimization, and to evaluate their performance. The first technique, called dose-sorting, is based on the assumption that higher dose limits should be assigned to the constraint points receiving higher doses, and vice versa. The second technique, the hybrid technique, is a hybrid of the dose-sorting technique and the mixed integer linear programming (MILP) technique. Among all constraint points in an organ at risk, the dose limits for the points far from a dose-volume constraint are determined by dose-sorting, while the dose limits for the points close to a dose-volume constraint are determined by MILP. We evaluated the performance of the two new techniques for one treatment geometry by comparing them with the MILP technique. The dose-sorting technique had a high probability of finding the global optimum when no more than three organs at risk have dose-volume constraints. It was much faster than the MILP technique. The hybrid technique always found the global optimum when the MILP percentage (the percentage of constraint points for which the dose limits are determined by the MILP technique) was large enough, but its computation time increased dramatically with the MILP percentage. In conclusion, the dose-sorting technique and the hybrid technique with a low MILP percentage are clinically feasible.

Algorithms↗

PubMed2006

Efficient schemes for robust IMRT treatment planning.

We use robust optimization techniques to formulate an IMRT treatment planning problem in which the dose matrices are uncertain, due to both dose calculation errors and interfraction positional uncertainty of tumour and organs. When the uncertainty is taken into account, the original linear programming formulation becomes a second-order cone program. We describe a novel and efficient approach for solving this problem, and present results to compare the performance of our scheme with more conventional formulations that assume perfect knowledge of the dose matrix.

Algorithms↗

PubMed2001

Inference of haplotypes from samples of diploid populations: complexity and algorithms.

The next phase of human genomics will involve large-scale screens of populations for significant DNA polymorphisms, notably single nucleotide polymorphisms (SNPs). Dense human SNP maps are currently under construction. However, the utility of those maps and screens will be limited by the fact that humans are diploid and it is presently difficult to get separate data on the two "copies." Hence, genotype (blended) SNP data will be collected, and the desired haplotype (partitioned) data must then be (partially) inferred. A particular nondeterministic inference algorithm was proposed and studied by Clark (1990) and extensively used by Clark et al. (1998). In this paper, we more closely examine that inference method and the question of whether we can obtain an efficient, deterministic variant to optimize the obtained inferences. We show that the problem is NP-hard and, in fact, Max-SNP complete; that the reduction creates problem instances conforming to a severe restriction believed to hold in real data (Clark, 1990); and that even if we first use a natural exponential-time operation, the remaining optimization problem is NP-hard. However, we also develop, implement, and test an approach based on that operation and (integer) linear programming. The approach works quickly and correctly on simulated data.

Algorithms↗

PubMed1997

A branch-and-cut approach to physical mapping of chromosomes by unique end-probes.

A fundamental problem in computational biology is the construction of physical maps of chromosomes from hybridization experiments between unique probes and clones of chromosome fragments in the presence of error. Alizadeh, Karp, Weisser and Zweig (Algorithmica 13:1/2, 52-76, 1995) first considered a maximum-likelihood model of the problem that is equivalent to finding an ordering of the probes that minimizes a weighted sum of errors and developed several effective heuristics. We show that by exploiting information about the end-probes of clones, this model can be formulated as a Weighted Betweenness Problem. This affords the significant advantage of allowing the well-developed tools of integer linear-programming and branch-and-cut algorithms to be brought to bear on physical mapping, enabling us for the first time to solve small mapping instances to optimality even in the presence of high error. We also show that by combining the optimal solution of many small overlapping Betweenness Problems, one can effectively screen errors from larger instances and solve the edited instance to optimality as a Hamming-Distance Traveling Salesman Problem. This suggests a new approach, a Betweenness-Traveling Salesman hybrid, for constructing physical maps.

Chromosome Mapping↗

PubMed1997

Algorithms for computing and integrating physical maps using unique probes.

Current physical mapping projects based on STS-probes involve additional clues such as the fact that some probes are anchored to a known map and that others come from the ends of clones. Because of the disparate combinatorial contributions of these varied data items, it is difficult to design a "tailored" algorithm that incorporates them all. Moreover, it is inevitable that new experiments will provide new kinds of data, making obsolete any such algorithm. We show how to convert the physical mapping problem into a 0/1 linear programming (LP) problem. We further show how one can incorporate additional clues as additional constraints in the LP formulation. We give a simple relaxation of the 0/1 LP problem, which solves problems of the same scale as previously reported tailored algorithms, to equal or greater optimization levels. We also present a theorem proving that when the data is 100% accurate, then the relaxed and integer solutions coincide. The LP algorithm suffices to solve problems on the order of 80-100 probes--the typical size of the 2- or 3-connected contigs of Arratia et al. (1991). We give a heuristic algorithm which attempts to order and link the set of LP-solved contigs. Unlike previous work, this algorithm only links and orders contigs when the join is 90% or more likely to be correct. It is our view that there is no value in computing an optimal solution with respect to some criteria over very noisy data as this optimal solution rarely corresponds to the true solution. The paper involves extensive empirical trials over real and simulated data.

Algorithms↗

PubMed1998

A polyhedral approach to RNA sequence structure alignment.

Ribonucleic acid (RNA) is a polymer composed of four bases denoted A, C, G, and U. It generally is a single-stranded molecule where the bases form hydrogen bonds within the same molecule leading to structure formation. In comparing different homologous RNA molecules it is important to consider both the base sequence and the structure of the molecules. Traditional alignment algorithms can only account for the sequence of bases, but not for the base pairings. Considering the structure leads to significant computational problems because of the dependencies introduced by the base pairings. In this paper we address the problem of optimally aligning a given RNA sequence of unknown structure to one of known sequence and structure. We phrase the problem as an integer linear program and then solve it using methods from polyhedral combinatorics. In our computational experiments we could solve large problem instances--23S ribosomal RNA with more than 1400 bases--a size intractable for former algorithms.

Algorithms↗

PubMed2006

Optimizing multiple spaced seeds for homology search.

Optimized spaced seeds improve sensitivity and specificity in local homology search. Several authors have shown that multiple seeds can have better sensitivity and specificity than single seeds. We describe a linear programming (LP)-based algorithm to optimize a set of seeds. Theoretically, our algorithm offers a performance guarantee: the sensitivity of a chosen seed set is at least 70% of what can be achieved, in most reasonable models of homologous sequences. In practice, our algorithm generates a solution which is at least 90% of the optimal. Our method not only achieves performance better than or comparable to that of a greedy algorithm, but also gives this area a mathematical foundation.

Algorithms↗

PubMed2004

Poverty and obesity: the role of energy density and energy costs.

Many health disparities in the United States are linked to inequalities in education and income. This review focuses on the relation between obesity and diet quality, dietary energy density, and energy costs. Evidence is provided to support the following points. First, the highest rates of obesity occur among population groups with the highest poverty rates and the least education. Second, there is an inverse relation between energy density (MJ/kg) and energy cost (US dollars/MJ), such that energy-dense foods composed of refined grains, added sugars, or fats may represent the lowest-cost option to the consumer. Third, the high energy density and palatability of sweets and fats are associated with higher energy intakes, at least in clinical and laboratory studies. Fourth, poverty and food insecurity are associated with lower food expenditures, low fruit and vegetable consumption, and lower-quality diets. A reduction in diet costs in linear programming models leads to high-fat, energy-dense diets that are similar in composition to those consumed by low-income groups. Such diets are more affordable than are prudent diets based on lean meats, fish, fresh vegetables, and fruit. The association between poverty and obesity may be mediated, in part, by the low cost of energy-dense foods and may be reinforced by the high palatability of sugar and fat. This economic framework provides an explanation for the observed links between socioeconomic variables and obesity when taste, dietary energy density, and diet costs are used as intervening variables. More and more Americans are becoming overweight and obese while consuming more added sugars and fats and spending a lower percentage of their disposable income on food.

Adult↗

PubMed2002

Multiple sequence alignment with arbitrary gap costs: computing an optimal solution using polyhedral combinatorics.

Multiple sequence alignment is one of the dominant problems in computational molecular biology. Numerous scoring functions and methods have been proposed, most of which result in NP-hard problems. In this paper we propose for the first time a general formulation for multiple alignment with arbitrary gap-costs based on an integer linear program (ILP). In addition we describe a branch-and-cut algorithm to effectively solve the ILP to optimality. We evaluate the performances of our approach in terms of running time and quality of the alignments using the BAliBase database of reference alignments. The results show that our implementation ranks amongst the best programs developed so far.

Algorithms↗

PubMed1986

A discrete model of bacterial metabolism.

This paper describes a computer model of the intermediary metabolism of bacteria during steady-state growth and during adaptations, e.g. to new carbon sources. Metabolic regulation is represented as a process of optimisation, in which the trend is towards improved metabolic performance. The model uses linear programming techniques for the optimisation. The implementation falls into four phases: (i) assembly of model parameters; (ii) calculations; (iii) storage of solutions and (iv) projection of solutions. The use of a commercial database and a commercial spreadsheet has proved to be of great assistance in the first and third phases. A metabolic map format, with the optional addition of conversion values, names of enzymes or co-factors has been used to project the results in a form convenient for inspection.

Algorithms↗

PubMed1992

Using fragment lengths from incomplete digestion by multiply cleaving enzymes to map antibody binding sites on a protein.

The problem of mapping the positions of the unique binding sites of several monoclonal antibodies on a linear protein structure is considered. Data giving the incidence of binding of individual antibodies to fragments of the protein obtained from it by the incomplete chemical or enzymatic digestion are used to formulate a series of linear programming problems. The solution to these problems shows which orderings of binding sites are possible, and gives upper and lower bounds for the relative positions of the sites.

Algorithms↗

PubMed2026

Detecting and reconstructing breakage-fusion-bridge cycles from long-read sequencing using BFBArchitect.

MOTIVATION: Focal oncogene amplification is a key driver of tumor progression. Remarkably, the increased pathology depends on the context-whether the amplification is extrachromosomal (ecDNA) or intrachromosomal. EcDNA amplifications promote heterogeneity, therapy resistance, and poor prognosis. Focal intrachromosomal amplifications often arise through breakage-fusion-bridge (BFB) cycles, which produce highly rearranged but stable chromosomes. Distinguishing BFB from ecDNA remains challenging due to overlapping genomic signatures. To address this, we present BFBArchitect, a computational method leveraging long-read Oxford Nanopore data to identify BFB sequences consistent with both copy number and structural variations. RESULTS: We provide a novel combinatorial characterization of BFB, which naturally leads to an integer linear programming (ILP) optimization. The ILP optimization generates a BFB sequence that best explains experimentally observed copy numbers and foldback structural variants. We implement this idea in a tool called BFBArchitect, which achieves near-perfect accuracy in distinguishing BFB from non-BFB structures in extensive simulations as well as on 18 validated tumor samples. Moreover, it generates sequence-level BFB reconstructions that provide mechanistic insights into BFB formation, including repair mechanisms with template switching and other structural variants, and recapture of telomere for stabilization. AVAILABILITY AND IMPLEMENTATION: BFBArchitect is available at https://github.com/AmpliconSuite/BFBArchitect.

Sequence Analysis, DNA↗

PubMed2004

A model-based optimization framework for the inference on gene regulatory networks from DNA array data.

MOTIVATION: Identification of the regulatory structures in genetic networks and the formulation of mechanistic models in the form of wiring diagrams is one of the significant objectives of expression profiling using DNA microarray technologies and it requires the development and application of identification frameworks. RESULTS: We have developed a novel optimization framework for identifying regulation in a genetic network using the S-system modeling formalism. We show that balance equations on both mRNA and protein species led to a formulation suitable for analyzing DNA-microarray data whereby protein concentrations have been eliminated and only mRNA relative concentrations are retained. Using this formulation, we examined if it is possible to infer a set of possible genetic regulatory networks consistent with observed mRNA expression patterns. Two origins of changes in mRNA expression patterns were considered. One derives from changes in the biophysical properties of the system that alter the molecular-interaction kinetics and/or message stability. The second is due to gene knock-outs. We reduced the identification problem to an optimization problem (of the so-called mixed-integer non-linear programming class) and we developed an algorithmic procedure for solving this optimization problem. Using simulated data generated by our mathematical model, we show that our method can actually find the regulatory network from which the data were generated. We also show that the number of possible alternate genetic regulatory networks depends on the size of the dataset (i.e. number of experiments), but this dependence is different for each of the two types of problems considered, and that a unique solution requires fewer datasets than previously estimated in the literature. This is the first method that also allows the identification of every possible regulatory network that could explain the data, when the number of experiments does not allow identification of unique regulatory structure.

Algorithms↗

PubMed2004

Extracting multiple structural alignments from pairwise alignments: a comparison of a rigorous and a heuristic approach.

MOTIVATION: Multiple structural alignments (MSTAs) provide position-specific information on the sequence variability allowed by protein folds. This information can be exploited to better understand the evolution of proteins and the physical chemistry of polypeptide folding. Most MSTA methods rely on a pre-computed library of pairwise alignments. This library will in general contain conflicting residue equivalences not all of which can be realized in the final MSTA. Hence to build a consistent MSTA, these methods have to select a conflict-free subset of equivalences. RESULTS: Using a dataset with 327 families from SCOP 1.63 we compare the ability of two different methods to select an optimal conflict-free subset of equivalences. One is an implementation of Reinert et al.'s integer linear programming formulation (ILP) of the maximum weight trace problem (Reinert et al., 1997, Proc. 1st Ann. Int. Conf. Comput. Mol. Biol. (RECOMB-97), ACM Press, New York). This ILP formulation is a rigorous approach but its complexity is difficult to predict. The other method is T-Coffee (Notredame et al., 2000) which uses a heuristic enhancement of the equivalence weights which allow it to use the speed and simplicity of the progressive alignment approach while still incorporating information of all alignments in each step of building the MSTA. We find that although the ILP formulation consistently selects a more optimal set of conflict-free equivalences, the differences are small and the quality of the resulting MSTAs are essentially the same for both methods. Given its speed and predictable complexity, our results show that T-Coffee is an attractive alternative for producing high-quality MSTAs.

Algorithms↗

PubMed2005

Collateral missing value imputation: a new robust missing value estimation algorithm for microarray data.

MOTIVATION: Microarray data are used in a range of application areas in biology, although often it contains considerable numbers of missing values. These missing values can significantly affect subsequent statistical analysis and machine learning algorithms so there is a strong motivation to estimate these values as accurately as possible before using these algorithms. While many imputation algorithms have been proposed, more robust techniques need to be developed so that further analysis of biological data can be accurately undertaken. In this paper, an innovative missing value imputation algorithm called collateral missing value estimation (CMVE) is presented which uses multiple covariance-based imputation matrices for the final prediction of missing values. The matrices are computed and optimized using least square regression and linear programming methods. RESULTS: The new CMVE algorithm has been compared with existing estimation techniques including Bayesian principal component analysis imputation (BPCA), least square impute (LSImpute) and K-nearest neighbour (KNN). All these methods were rigorously tested to estimate missing values in three separate non-time series (ovarian cancer based) and one time series (yeast sporulation) dataset. Each method was quantitatively analyzed using the normalized root mean square (NRMS) error measure, covering a wide range of randomly introduced missing value probabilities from 0.01 to 0.2. Experiments were also undertaken on the yeast dataset, which comprised 1.7% actual missing values, to test the hypothesis that CMVE performed better not only for randomly occurring but also for a real distribution of missing values. The results confirmed that CMVE consistently demonstrated superior and robust estimation capability of missing values compared with other methods for both series types of data, for the same order of computational complexity. A concise theoretical framework has also been formulated to validate the improved performance of the CMVE algorithm. AVAILABILITY: The CMVE software is available upon request from the authors.

Algorithms↗

PubMed2005

Residue-rotamer-reduction algorithm for the protein side-chain conformation problem.

MOTIVATION: The protein side-chain conformation problem is a central problem in proteomics with wide applications in protein structure prediction and design. Computational complexity results show that the problem is hard to solve. Yet, instances from realistic applications are large and demand fast and reliable algorithms. RESULTS: We propose a new global optimization algorithm, which for the first time integrates residue reduction and rotamer reduction techniques previously developed for the protein side-chain conformation problem. We show that the proposed approach simplifies dramatically the topology of the underlining residue graph. Computations show that our algorithm solves problems using only 1-10% of the time required by the mixed-integer linear programming approach available in the literature. In addition, on a set of hard side-chain conformation problems, our algorithm runs 2-78 times faster than SCWRL 3.0, which is widely used for solving these problems. AVAILABILITY: The implementation is available as an online server at http://eudoxus.scs.uiuc.edu/r3.html

Algorithms↗

PubMed2006

Inferring gene regulatory networks from multiple microarray datasets.

MOTIVATION: Microarray gene expression data has increasingly become the common data source that can provide insights into biological processes at a system-wide level. One of the major problems with microarrays is that a dataset consists of relatively few time points with respect to a large number of genes, which makes the problem of inferring gene regulatory network an ill-posed one. On the other hand, gene expression data generated by different groups worldwide are increasingly accumulated on many species and can be accessed from public databases or individual websites, although each experiment has only a limited number of time-points. RESULTS: This paper proposes a novel method to combine multiple time-course microarray datasets from different conditions for inferring gene regulatory networks. The proposed method is called GNR (Gene Network Reconstruction tool) which is based on linear programming and a decomposition procedure. The method theoretically ensures the derivation of the most consistent network structure with respect to all of the datasets, thereby not only significantly alleviating the problem of data scarcity but also remarkably improving the prediction reliability. We tested GNR using both simulated data and experimental data in yeast and Arabidopsis. The result demonstrates the effectiveness of GNR in terms of predicting new gene regulatory relationship in yeast and Arabidopsis. AVAILABILITY: The software is available from http://zhangorup.aporc.org/bioinfo/grninfer/, http://digbio.missouri.edu/grninfer/ and http://intelligent.eic.osaka-sandai.ac.jp or upon request from the authors.

Algorithms↗

PubMed2006

Bayesian-based selection of metabolic objective functions.

MOTIVATION: A critical component of in silico analysis of underdetermined metabolic systems is the identification of the appropriate objective function. A common assumption is that the objective of the cell is to maximize growth. This objective function has been shown to be consistent in a few limited experimental cases, but may not be universally appropriate. Here a method is presented to quantitatively determine the most probable objective function. RESULTS: The genome-scale metabolism of Escherichia coli growing on succinate was used as a case-study for analysis. Five different objective functions, including maximization of growth rate, were chosen based on biological plausibility. A combination of flux balance analysis and linear programming was used to simulate cellular metabolism, which was then compared to independent experimental data using a Bayesian objective function discrimination technique. After comparing rates of oxygen uptake and acetate production, minimization of the production rate of redox potential was determined to be the most probable objective function. Given the appropriate reaction network and experimental data, the discrimination technique can be applied to any bacterium to test a variety of different possible objective functions. SUPPLEMENTARY INFORMATION: Additional files, code and a program for carrying out model discrimination are available at http://www.engr.uconn.edu/~srivasta/modisc.html.

Algorithms↗