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Results for “Programming, Linear”

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PubMed1968

The large-scale separation of peroxisomes, mitochondria, and lysosomes from the livers of rats injected with triton WR-1339. Improved isolation procedures, automated analysis, biochemical and morphological properties of fractions.

Improved, largely automated methods are described for the purification and analysis o peroxisomes, lysosomes, and mitochondria from the livers of rats injected with Triton WR-1339. With these new methods, it has become possible to obtain, in less than 6 hr and with reliable reproducibility, mitochondria practically free of contaminants, as well as the rarer cytoplasmic particles in amounts (about 100 mg of protein) and in a state of purity (95%) that make them suitable for detailed biochemical studies. The results obtained so far on these preparations have made more conclusive and precise previous estimates of the biochemical and morphological properties of the three groups of cytoplasmic particles. In addition, peroxisomes were found to contain essentially all the L-alpha-hydroxy acid oxidase of the liver, as well as a small, but significant fraction of its NADP-linked isocitrate dehydrogenase activity. Another small fraction of the latter enzyme is present in the mitochondria, the remainder being associated with the cell sap. The mitochondrial localization of the metabolically active cytoplasmic DNA could be verified. The relative content of the fractions in mitochondria, whole peroxisomes, peroxisome cores, lysosomes, and endoplasmic reticulum was estimated independently by direct measurements on electron micrographs, and by linear programming (based on the assumption that the particles are biochemically homogeneous) of the results of enzyme assays. The two types of estimates agreed very well, except for one fraction in which low cytochrome oxidase activity was associated with mitochondrial damage.

Acid Phosphatase↗

PubMed1979

Uniform depth dose distribution for biological irradiation using negative pions.

A simple, flexible technique has been developed to generate uniform depth dose profiles for the biomedical pion beam at TRIUMF using dynamic momentum control and linear programming. Either the entrance dose or the irradiation time required for a certain dose over the uniform region can be minimised. The dynamic momentum control can operate automatically under computer control even with a highly unstable beam. Cell survival profiles have been obtained for this uniform dose distribution using the gelatin technique. The RBE increases with increasing depth through the uniform dose region.

Animals↗

PubMed2001

A practical approach to inverse planning for high-precision dose escalated conformal prostate radiotherapy.

The problem of choosing the best gantry angles and beam weights for dose-escalated conformal prostate treatment planning is formulated using a mixed-integer linear programming approach, to account for tumour dose homogeneity and dose-volume constraints. The formulation allows the number of beams to be restricted and for some of the beams to be compulsory. The present planning algorithm interfaces with and utilizes the three-dimensional planning capabilities of a commercial treatment planning system. A case study is illustrated, which represents a particularly challenging planning problem due to a large planning target volume and an unusually small bladder. Treatment plans with different numbers of beams are generated to compare with each other and with the standard six-field plan. Significant improvement is shown in the reduction of hot regions within the femoral heads and rectal wall, while not unduly compromising homogeneity constraints for the tumour.

Humans↗

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↗

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↗

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↗

PubMed1986

Limits to the relationship among recombination, disequilibrium and epistasis in two-locus models.

I determine limits to the equilibrium relationship among epistasis, recombination and disequilibrium in two-locus, two-allele models using linear programming techniques. I show that when allele frequencies are one-half at each locus, the symmetric model is the fitness pattern that generates the most disequilibrium for the smallest level of epistasis. When allele frequencies deviate from one-half much larger levels of epistasis are required to generate similar levels of disequilibrium. I determine the level of epistasis required to generate observed significant levels of disequilibrium in natural populations. The overall implication is that disequilibrium will be large at equilibrium only between strongly interacting, closely linked loci.

Alleles↗

PubMed1999

Improving the efficiency of artificial selection: more selection pressure with less inbreeding.

The use of population genetic variability in present-day selection schemes can be improved to reduce inbreeding rate and inbreeding depression without impairing genetic progress. We performed an experiment with Drosophila melanogaster to test mate selection, an optimizing method that uses linear programming to maximize the selection differential applied while at the same time respecting a restriction on the increase in inbreeding expected in the next generation. Previous studies about mate selection used computer simulation on simple additive genetic models, and no experiment with a real character in a real population had been carried out. After six selection generations, the optimized lines showed an increase in cumulated phenotypic selection differential of 10.76%, and at the same time, a reduction of 19.91 and 60.47% in inbreeding coefficient mean and variance, respectively. The increased selection pressure would bring greater selection response, and in fact, the observed change in the selected trait was on average 31.03% greater in the optimized lines. These improvements in the selection scheme were not made at the expense of the long-term expectations of genetic variability in the population, as these expectations were very similar for both mate selection and conventionally selected lines in our experiment.

Animals↗

PubMed1981

Disequilibrium, selection, and recombination: limits in two-locus, two-allele models.

All possible combinations of equilibria and fitnesses in two-locus, two-allele, deterministic, discrete-generation selection models are enumerated. This knowledge is used to obtain limits (which can be calculated to arbitrary precision) to the relationships among disequilibrium, selection and recombination for fixed values of allele frequencies. In all cases, the inequality magnitude of rD less than s/10 holds, where r is recombination and D is disequilibrium, and all selection coefficients lie between 1 - s and 1 + s times that of the double heterozygote. Linear programming techniques are used to observed nonzero values of D reported in the literature. One conclusion is that the failure to observe nonzero values of D is not surprising.

Alleles↗

PubMedDate not supplied

The efficiency of Scottish acute hospitals: an application of data envelopment analysis.

Measurement of the efficiency of health services would aid the promotion of a better allocation of health care resources. Economic analysis suggests a number of ways of defining and measuring efficiency. However, this rarely informs measures used in health service management. This paper looks at the potential for the use in the United Kingdom's National Health Service of the linear programming based method of data envelopment analysis (DEA). DEA is applied to data from 75 UK acute hospitals. The results demonstrate the capacity of DEA to produce a user-friendly array of results, based on sound theoretical underpinnings. These range from the measurement of relative efficiencies to quantified suggestions as to how hospitals may improve efficiency, by examining both their own efficiency and that of comparable units. Information is provided both about individual hospitals and the sample as a whole. DEA is also able to distinguish between hospitals demonstrating differing returns to scale. Our findings suggest that, although still very much under development, DEA is usable and, given the weakness of current means of measuring efficiency in the National Health Service, that DEA has a strong claim for further consideration.

Data Interpretation, Statistical↗

PubMed1981

Amino acid requirements of growing mice: arginine, lysine, tryptophan and phenylalanine.

Linear programmed diets designed to maximize the use of proteins and to minimize the use of free (1-) amino acids, and containing five dietary levels of each amino acid under test, were fed to weanling crossbred Carworth Farms No. 1 x Swiss mice in 14-day growth trials. Arginine dietary levels were 0.1, 0.2, 0.3, 0.4 and 0.7%; lysine: 0.2, 0.3, 0.4, 0.5 and 1.0%; tryptophan: 0.03, 0.07, 0.10, 0.13 and 0.17%; and phenylalanine: 0.10, 0.25, 0.40, 0.55 and 0.89%. Growth, feed consumption and regression-adjusted growth rates indicated the following minimum requirements: arginine less than 0.1% and probably zero, lysine 0.4%, tryptophan 0.1% and phenylalanine 0.4%. The AIN '76 reference diet was included in each amino acid test and resulted in superior growth and feed utilization. It was postulated that the greater content of free amino acids in our diets may have affected the efficiency of feed utilization adversely.

Amino Acids, Essential↗