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PubMed2007

A finite size pencil beam algorithm for IMRT dose optimization: density corrections.

For beamlet-based IMRT optimization, fast and less accurate dose computation algorithms are frequently used, while more accurate algorithms are needed to recompute the final dose for verification. In order to speed up the optimization process and ensure close proximity between dose in optimization and verification, proper consideration of dose gradients and tissue inhomogeneity effects should be ensured at every stage of the optimization. Due to their speed, pencil beam algorithms are often used for precalculation of beamlet dose distributions in IMRT treatment planning systems. However, accounting for tissue heterogeneities with these models requires the use of approximate rescaling methods. Recently, a finite size pencil beam (fsPB) algorithm, based on a simple and small set of data, was proposed which was specifically designed for the purpose of dose pre-computation in beamlet-based IMRT. The present work describes the incorporation of 3D density corrections, based on Monte Carlo simulations in heterogeneous phantoms, into this method improving the algorithm accuracy in inhomogeneous geometries while keeping its original speed and simplicity of commissioning. The algorithm affords the full accuracy of 3D density corrections at every stage of the optimization, hence providing the means for density related fluence modulation like penumbra shaping at field edges.

Algorithms↗

PubMed2002

A multi-shell algorithm to reconstruct EIT images of brain function.

Electrical impedance tomography (EIT) may be used to image brain function, but an important consideration is the effect of the highly resistive skull and other extracerebral layers on the flow of injected current. We describe a new reconstruction algorithm, based on a forward solution which models the head as four concentric, spherical shells, with conductivities of the brain, cerebrospinal fluid, skull and scalp. The model predicted that the mean current travelling in the brain in the diametric plane for current injection from polar electrodes was 5.6 times less than if the head was modelled as a homogeneous sphere; this suggests that an algorithm based on this should be more accurate than one based on a homogeneous sphere model. In images reconstructed from computer-simulated data or data from a realistic saline-filled tank containing a real skull, a Perspex rod was localized to within 17% or 20% of the tank diameter of its true position, respectively. Contrary to expectation, the tank images were less accurate than those obtained with a reconstruction algorithm based on a homogeneous sphere. It is not yet clear if the theoretical advantages of this algorithm will yield practical advantages for head EIT imaging; it may be necessary to proceed to more complex algorithms based on numerical models which incorporate realistic head geometry. If so, this analytical forward model and algorithm may be used to validate numerical solutions.

Algorithms↗

PubMed2006

Algorithms and architectures for low power spike detection and alignment.

We introduce algorithms and architectures for automatic spike detection and alignment that are designed for low power. Some of the algorithms are based on principal component analysis (PCA). Others employ a novel integral transform analysis and achieve 99% of the precision of a PCA detector, while requiring only 0.05% of the computational complexity. The algorithms execute autonomously, but require off-line training and setting of computational parameters. We employ pre-recorded neuronal signals to evaluate the accuracy of the proposed algorithms and architectures: the recorded data are processed by a standard PCA spike detection and alignment software algorithm, as well as by the several hardware algorithms, and the outcomes are compared.

Action Potentials↗

PubMed2000

Algorithms for identifying Boolean networks and related biological networks based on matrix multiplication and fingerprint function.

Due to the recent progress of the DNA microarray technology, a large number of gene expression profile data are being produced. How to analyze gene expression data is an important topic in computational molecular biology. Several studies have been done using the Boolean network as a model of a genetic network. This paper proposes efficient algorithms for identifying Boolean networks of bounded indegree and related biological networks, where identification of a Boolean network can be formalized as a problem of identifying many Boolean functions simultaneously. For the identification of a Boolean network, an O(mnD+1) time naive algorithm and a simple O (mnD) time algorithm are known, where n denotes the number of nodes, m denotes the number of examples, and D denotes the maximum in degree. This paper presents an improved O(momega-2nD + mnD+omega-3) time Monte-Carlo type randomized algorithm, where omega is the exponent of matrix multiplication (currently, omega < 2.376). The algorithm is obtained by combining fast matrix multiplication with the randomized fingerprint function for string matching. Although the algorithm and its analysis are simple, the result is nontrivial and the technique can be applied to several related problems.

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PubMed2002

Efficient algorithms for quantitative trait loci mapping problems.

Rapid advances in molecular genetics push the need for efficient data analysis. Advanced algorithms are necessary for extracting all possible information from large experimental data sets. We present a general linear algebra framework for quantitative trait loci (QTL) mapping, using both linear regression and maximum likelihood estimation. The formulation simplifies future comparisons between and theoretical analyses of the methods. We show how the common structure of QTL analysis models can be used to improve the kernel algorithms, drastically reducing the computational effort while retaining the original analysis results. We have evaluated our new algorithms on data sets originating from two large F(2) populations of domestic animals. Using an updating approach, we show that 1-3 orders of magnitude reduction in computational demand can be achieved for matrix factorizations. For interval-mapping/composite-interval-mapping settings using a maximum likelihood model, we also show how to use the original EM algorithm instead of the ECM approximation, significantly improving the convergence and further reducing the computational time. The algorithmic improvements makes it feasible to perform analyses which have previously been deemed impractical or even impossible. For example, using the new algorithms, it is reasonable to perform permutation testing using exhaustive search on populations of 200 individuals using an epistatic two-QTL model.

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PubMed1995

Fast algorithms for inferring evolutionary trees.

We present algorithms for the perfect phylogeny problem restricted to binary characters. The first algorithm is faster than a previous algorithm by Gusfield when the input matrix for the problem is sparse. Next, we present two online algorithms. For the first of these, the set of species is fixed and the characters are given as input one at a time, while, for the second, the set of characters is fixed and the species are given as input one at a time. These two online algorithms are then combined into an algorithm that can process any sequence of additions and deletions of species and characters.

Algorithms↗

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.

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PubMed2005

An approximation algorithm for haplotype inference by maximum parsimony.

This paper studies haplotype inference by maximum parsimony using population data. We define the optimal haplotype inference (OHI) problem as given a set of genotypes and a set of related haplotypes, find a minimum subset of haplotypes that can resolve all the genotypes. We prove that OHI is NP-hard and can be formulated as an integer quadratic programming (IQP) problem. To solve the IQP problem, we propose an iterative semidefinite programming-based approximation algorithm, (called SDPHapInfer). We show that this algorithm finds a solution within a factor of O(log n) of the optimal solution, where n is the number of genotypes. This algorithm has been implemented and tested on a variety of simulated and biological data. In comparison with three other methods, (1) HAPAR, which was implemented based on the branching and bound algorithm, (2) HAPLOTYPER, which was implemented based on the expectation-maximization algorithm, and (3) PHASE, which combined the Gibbs sampling algorithm with an approximate coalescent prior, the experimental results indicate that SDPHapInfer and HAPLOTYPER have similar error rates. In addition, the results generated by PHASE have lower error rates on some data but higher error rates on others. The error rates of HAPAR are higher than the others on biological data. In terms of efficiency, SDPHapInfer, HAPLOTYPER, and PHASE output a solution in a stable and consistent way, and they run much faster than HAPAR when the number of genotypes becomes large.

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PubMed1994

An algorithm based on graph theory for the assembly of contigs in physical mapping of DNA.

An algorithm is described for mapping DNA contigs based on an interval graph (IG) representation. In general terms, the input to the algorithm is a set of binary overlapping relations among finite intervals spread along a real line, from which the algorithm generates sets of ordered overlapping fragments spanning that line. The implications of a more general case of the IG, called a probe interval graph (PIG), in which only a subset of cosmids are used as probes, are also discussed. In the specific case of cosmids hybridizing to regions of a YAC, the algorithm takes cross-hybridization information using the cosmids as probes, and orders them along the YAC; if gaps exist due to insufficient coverage of cosmid contigs along the length of the YAC, repetitive use of the algorithm generates sets of ordered overlapping fragments. Both the IG and the PIG can expose problems caused by false overlaps, such as hybridizations due to repetitive elements. The algorithm, has been coded in C; CPU time is essentially linear with respect to the number of cosmids analyzed. Results are presented for the application of a PIG to cosmid contig assembly along a human chromosome 13-specific YAC. An alignment of 67 cosmids spanning a YAC took 0.28 seconds of CPU time on a Convex 220 computer.

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PubMed1995

Comprehensive study on iterative algorithms of multiple sequence alignment.

Multiple sequence alignment is an important problem in the biosciences. To date, most multiple alignment systems have employed a tree-based algorithm, which combines the results of two-way dynamic programming in a tree-like order of sequence similarity. The alignment quality is not, however, high enough when the sequence similarity is low. Once an error occurs in the alignment process, that error can never be corrected. Recently, an effective new class of algorithms has been developed. These algorithms iteratively apply dynamic programming to partially aligned sequences to improve their alignment quality. The iteration corrects any errors that may have occurred in the alignment process. Such an iterative strategy requires heuristic search methods to solve practical alignment problems. Incorporating such methods yields various iterative algorithms. This paper reports our comprehensive comparison of iterative algorithms. We proved that performance improves remarkably when using a tree-based iterative method, which iteratively refines an alignment whenever two subalignments are merged in a tree-based way. We propose a tree-dependent, restricted partitioning technique to efficiently reduce the execution time of iterative algorithms.

Algorithms↗

PubMed1998

SALSA: improved protein database searching by a new algorithm for assembly of sequence fragments into gapped alignments.

MOTIVATION: Optimal sequence alignment based on the Smith-Waterman algorithm is usually too computationally demanding to be practical for searching large sequence databases. Heuristic programs like FASTA and BLAST have been developed which run much faster, but at the expense of sensitivity. RESULTS: In an effort to approximate the sensitivity of an optimal alignment algorithm, a new algorithm has been devised for the computation of a gapped alignment of two sequences. After scanning for high-scoring words and extensions of these to form fragments of similarity, the algorithm uses dynamic programming to build an accurate alignment based on the fragments initially identified. The algorithm has been implemented in a program called SALSA and the performance has been evaluated on a set of test sequences. The sensitivity was found to be close to the Smith-Waterman algorithm, while the speed was similar to FASTA (ktup = 2). AVAILABILITY: Searches can be performed from the SALSA homepage at http://dna.uio.no/salsa/ using a wide range of databases. Source code and precompiled executables are also available. CONTACT: torbjorn.rognes@labmed.uio.no

Algorithms↗

PubMed1999

Docking of hydrophobic ligands with interaction-based matching algorithms.

MOTIVATION: Matching of chemical interacting groups is a common concept for docking and fragment placement algorithms in computer-aided drug design. These algorithms have been proven to be reliable and fast if at least a certain number of hydrogen bonds or salt bridges occur. However, the algorithms typically run into problems if hydrophobic fragments or ligands should be placed. In order to dock hydrophobic fragments without significant loss of computational efficiency, we have extended the interaction model and placement algorithms in our docking tool FlexX. The concept of multi-level interactions is introduced into the algorithms for automatic selection and placement of base fragments. RESULTS: With the multi-level interaction model and the corresponding algorithmic extensions, we were able to improve the overall performance of FlexX significantly. We tested the approach with a set of 200 protein-ligand complexes taken from the Brookhaven Protein Data Bank (PDB). The number of test cases which can be docked within 1.5 A RMSD from the crystal structure can be increased from 58 to 64%. The performance gain is paid for by an increase in computation time from 73 to 91 s on average per protein-ligand complex. AVAILABILITY: The FlexX molecular docking software is available for UNIX platforms IRIX, Solaris and Linux. See http://cartan.gmd.de/FlexX for additional information.

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PubMed2001

A simple algorithm to infer gene duplication and speciation events on a gene tree.

MOTIVATION: When analyzing protein sequences using sequence similarity searches, orthologous sequences (that diverged by speciation) are more reliable predictors of a new protein's function than paralogous sequences (that diverged by gene duplication), because duplication enables functional diversification. The utility of phylogenetic information in high-throughput genome annotation ('phylogenomics') is widely recognized, but existing approaches are either manual or indirect (e.g. not based on phylogenetic trees). Our goal is to automate phylogenomics using explicit phylogenetic inference. A necessary component is an algorithm to infer speciation and duplication events in a given gene tree. RESULTS: We give an algorithm to infer speciation and duplication events on a gene tree by comparison to a trusted species tree. This algorithm has a worst-case running time of O(n(2)) which is inferior to two previous algorithms that are approximately O(n) for a gene tree of sequences. However, our algorithm is extremely simple, and its asymptotic worst case behavior is only realized on pathological data sets. We show empirically, using 1750 gene trees constructed from the Pfam protein family database, that it appears to be a practical (and often superior) algorithm for analyzing real gene trees. AVAILABILITY: http://www.genetics.wustl.edu/eddy/forester.

Algorithms↗

PubMed1988

A finite state machine algorithm for finding restriction sites and other pattern matching applications.

Existing algorithms for finding restriction endonuclease recognition sites use brute-force algorithms which run in time 0(NM) where N is the number of nucleotides in the sequence under analysis and M is the total number of nucleotides in all the different sites being searched for. This paper presents a deterministic finite state machine algorithm which runs in time 0(N). Memory use can be as high as 0(M4) but a slight modification to the basic algorithm can impose a theoretical upper bound of 0(M) at the cost of some added complexity in the execution of the state machine. The algorithm can operate with a single pass through the sequence under analysis, with no need to back up or (for non-circular sequences) store more than a single input character at a time. This type of algorithm can be adapted to many pattern-matching tasks and is simple enough to implement in hardware that it could, for example, be built into a disk controller as part of a specialized database machine.

Algorithms↗

PubMed1991

Improved algorithms for searching restriction maps.

We present algorithms for searching a DNA restriction enzyme map for a region that best matches a shorter 'probe' map. Our algorithms utilize a new model of map alignments, and extensive experiments prove our model superior to earlier approaches for certain applications. Let M be the number of map sites and P be the number of probe sites. Our first algorithm, which optimizes only over a restricted class of alignments, requires O(MP log P) worst-case time and O(M + P) space. Our second algorithm, which optimizes over all alignments, runs in O(MP3) time and O(M + P2) space, under reasonable assumptions about the distribution of restriction enzyme cleavage sites. Combining the algorithms gives a map-searching method that optimizes over all alignments in O(MP log P) time in practice. The algorithms' effectiveness is illustrated by searches involving a genomic restriction map of Escherichia coli.

Algorithms↗

PubMed2003

New algorithms for multi-class cancer diagnosis using tumor gene expression signatures.

MOTIVATION: The increasing use of DNA microarray-based tumor gene expression profiles for cancer diagnosis requires mathematical methods with high accuracy for solving clustering, feature selection and classification problems of gene expression data. RESULTS: New algorithms are developed for solving clustering, feature selection and classification problems of gene expression data. The clustering algorithm is based on optimization techniques and allows the calculation of clusters step-by-step. This approach allows us to find as many clusters as a data set contains with respect to some tolerance. Feature selection is crucial for a gene expression database. Our feature selection algorithm is based on calculating overlaps of different genes. The database used, contains over 16 000 genes and this number is considerably reduced by feature selection. We propose a classification algorithm where each tissue sample is considered as the center of a cluster which is a ball. The results of numerical experiments confirm that the classification algorithm in combination with the feature selection algorithm perform slightly better than the published results for multi-class classifiers based on support vector machines for this data set. AVAILABILITY: Available on request from the authors.

Algorithms↗

PubMed2004

Algorithms for sequence analysis via mutagenesis.

MOTIVATION: Despite many successes of conventional DNA sequencing methods, some DNAs remain difficult or impossible to sequence. Unsequenceable regions occur in the genomes of many biologically important organisms, including the human genome. Such regions range in length from tens to millions of bases, and may contain valuable information such as the sequences of important genes. The authors have recently developed a technique that renders a wide range of problematic DNAs amenable to sequencing. The technique is known as sequence analysis via mutagenesis (SAM). This paper presents a number of algorithms for analysing and interpreting data generated by this technique. RESULTS: The essential idea of SAM is to infer the target sequence using the sequences of mutants derived from the target. We describe three algorithms used in this process. The first algorithm predicts the number of mutants that will be required to infer the target sequence with a desired level of accuracy. The second algorithm infers the target sequence itself, using the mutant sequences. The third algorithm assigns quality values to each inferred base. The algorithms are illustrated using mutant sequences generated in the laboratory.

Algorithms↗

PubMed2004

A nearest-neighboring-end algorithm for genetic mapping.

MOTIVATION: High-throughput methods are beginning to make possible the genotyping of thousands of loci in thousands of individuals, which could be useful for tightly associating phenotypes to candidate loci. Current mapping algorithms cannot handle so many data without building hierarchies of framework maps. RESULTS: A version of Kruskal's minimum spanning tree algorithm can solve any genetic mapping problem that can be stated as marker deletion from a set of linkage groups. These include backcross, recombinant inbred, haploid and double-cross recombinational populations, in addition to conventional deletion and radiation hybrid populations. The algorithm progressively joins linkage groups at increasing recombination fractions between terminal markers, and attempts to recognize and correct erroneous joins at peaks in recombination fraction. The algorithm is O (mn3) for m individuals and n markers, but the mean run time scales close to mn2. It is amenable to parallel processing and has recovered true map order in simulations of large backcross, recombinant inbred and deletion populations with up to 37,005 markers. Simulations were used to investigate map accuracy in response to population size, allelic dominance, segregation distortion, missing data and random typing errors. It produced accurate maps when marker distribution was sufficiently uniform, although segregation distortion could induce translocated marker orders. The algorithm was also used to map 1003 loci in the F7 ITMI population of bread wheat, Triticum aestivum L. emend Thell., where it shortened an existing standard map by 16%, but it failed to associate blocks of markers properly across gaps within linkage groups. This was because it depends upon the rankings of recombination fractions at individual markers, and is susceptible to sampling error, typing error and joint selection involving the terminal markers of nearly finished linkage groups. Therefore, the current form of the algorithm is useful mainly to improve local marker ordering in linkage groups obtained in other ways. AVAILABILITY: The source code and supplemental data are http://www.iubio.bio.indiana.edu/soft/molbio/qtl/flipper/ CONTACT: ccrane@purdue.edu.

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