A Practical Exact Algorithm for the Individual Haplotyping Problem MEC/GI

Author(s):  
Minzhu Xie ◽  
Jianxin Wang ◽  
Jianer Chen
2010 ◽  
Vol 20 (5) ◽  
pp. 851-863 ◽  
Author(s):  
MINZHU XIE ◽  
JIANXIN WANG ◽  
JIANER CHEN

Haplotypes are more useful in complex disease gene mapping than single-nucleotide polymorphisms (SNPs). However, haplotypes are difficult to obtain directly using biological experiments, which has prompted research into efficient computational methods for determining haplotypes. The individual haplotyping problem called Minimum Letter Flip (MLF) is a computational problem that, given a set of aligned DNA sequence fragment data of an individual, induces the corresponding haplotypes by flipping minimum SNPs. There has been no practical exact algorithm for solving the problem. Due to technical limits in DNA sequencing experiments, the maximum length of a fragment sequenced directly is about 1kb. In consequence, with a genome-average SNP density of 1.84 SNPs per 1 kb of DNA sequence, the maximum number k1 of SNP sites that a fragment covers is usually small. Moreover, in order to save time and money, the maximum number k2 of fragments that cover an SNP site is usually no more than 19. Building on these fragment data properties, the current paper introduces a new parameterised algorithm with running time O(nk22k2 + mlogm + mk1), where m is the number of fragments and n is the number of SNP sites. In practical biological applications, the algorithm solves the MLF problem efficiently even if m and n are large.


2021 ◽  
Vol 27 (1) ◽  
pp. 3-8
Author(s):  
M. V. Ulyanov ◽  
◽  
M. I. Fomichev ◽  
◽  
◽  
...  

The exact algorithm that implements the Branch and Boimd method with precomputed tour which is calculated by Lin-Kernighan-Helsgaun metaheuristic algorithm for solving the Traveling Salesman Problem is concerned here. Reducing the number of decision tree nodes, which are created by the Branches and Bound method, due to a "good" precomputed tour leads to the classical balancing dilemma of time costs. A tour that is close to optimal one takes time, even when the Lin-Kernighan-Helsgaun algorithm is used, however it reduces the working time of the Branch and Bound method. The problem of determining the scope of such a combined algorithm arises. In this article it is solved by using a special characteristic of the individual Traveling Salesman Problem — the number of changes tracing direction in the search decision tree generated by the Branch and Bound Method. The use of this characteristic allowed to divide individual tasks into three categories, for which, based on experimental data, recommendations of the combined algorithm usage are formulated. Based on the data obtained in a computational experiment (in range from 30 to 45), it is recommended to use a combined algorithm for category III problems starting with n = 36, and for category II problems starting with n = 42.


Algorithmica ◽  
2009 ◽  
Vol 56 (3) ◽  
pp. 283-296 ◽  
Author(s):  
Jianxin Wang ◽  
Minzhu Xie ◽  
Jianer Chen

JAMA ◽  
1966 ◽  
Vol 195 (12) ◽  
pp. 1036-1037 ◽  
Author(s):  
P. Rubin
Keyword(s):  

Author(s):  
C.N. Sun

The present study demonstrates the ultrastructure of the gingival epithelium of the pig tail monkey (Macaca nemestrina). Specimens were taken from lingual and facial gingival surfaces and fixed in Dalton's chrome osmium solution (pH 7.6) for 1 hr, dehydrated, and then embedded in Epon 812.Tonofibrils are variable in number and structure according to the different region or location of the gingival epithelial cells, the main orientation of which is parallel to the long axis of the cells. The cytoplasm of the basal epithelial cells contains a great number of tonofilaments and numerous mitochondria. The basement membrane is 300 to 400 A thick. In the cells of stratum spinosum, the tonofibrils are densely packed and increased in number (fig. 1 and 3). They seem to take on a somewhat concentric arrangement around the nucleus. The filaments may occur scattered as thin fibrils in the cytoplasm or they may be arranged in bundles of different thickness. The filaments have a diameter about 50 A. In the stratum granulosum, the cells gradually become flatted, the tonofibrils are usually thin, and the individual tonofilaments are clearly distinguishable (fig. 2). The mitochondria and endoplasmic reticulum are seldom seen in these superficial cell layers.


Author(s):  
Anthony J. Godfrey

Aldehyde-fixed chick retina was embedded in a water-containing resin of glutaraldehyde and urea, without dehydration. The loss of lipids and other soluble tissue components, which is severe in routine methods involving dehydration, was thereby minimized. Osmium tetroxide post-fixation was not used, lessening the amount of protein denaturation which occurred. Ultrathin sections were stained with 1, uranyl acetate and lead citrate, 2, silicotungstic acid, or 3, osmium vapor, prior to electron microscope examination of visual cell outer segment ultrastructure, at magnifications up to 800,000.Sections stained with uranyl acetate and lead citrate (Fig. 1) showed that the individual disc membranes consisted of a central lipid core about 78Å thick in which dark-staining 40Å masses appeared to be embedded from either side.


Author(s):  
Anthony A. Paparo ◽  
Judith A. Murphy

The purpose of this study was to localize the red neuronal pigment in Mytilus edulis and examine its role in the control of lateral ciliary activity in the gill. The visceral ganglia (Vg) in the central nervous system show an over al red pigmentation. Most red pigments examined in squash preps and cryostat sec tions were localized in the neuronal cell bodies and proximal axon regions. Unstained cryostat sections showed highly localized patches of this pigment scattered throughout the cells in the form of dense granular masses about 5-7 um in diameter, with the individual granules ranging from 0.6-1.3 um in diame ter. Tissue stained with Gomori's method for Fe showed bright blue granular masses of about the same size and structure as previously seen in unstained cryostat sections.Thick section microanalysis (Fig.l) confirmed both the localization and presence of Fe in the nerve cell. These nerve cells of the Vg share with other pigmented photosensitive cells the common cytostructural feature of localization of absorbing molecules in intracellular organelles where they are tightly ordered in fine substructures.


Author(s):  
William W. Thomson ◽  
Elizabeth S. Swanson

The oxidant air pollutants, ozone and peroxyacetyl nitrate, are produced in the atmosphere through the interaction of light with nitrogen oxides and gaseous hydrocarbons. These oxidants are phytotoxicants and are known to deleteriously affect plant growth, physiology, and biochemistry. In many instances they induce changes which lead to the death of cells, tissues, organs, and frequently the entire plant. The most obvious damage and biochemical changes are generally observed with leaves.Electron microscopic examination of leaves from bean (Phaseolus vulgaris L.) tobacco (Nicotiana tabacum L.) and cotton (Gossipyum hirsutum L.) fumigated for .5 to 2 hours with 0.3 -1 ppm of the individual oxidants revealed that changes in the ultrastructure of the cells occurred in a sequential fashion with time following the fumigation period. Although occasional cells showed severe damage immediately after fumigation, the most obvious change was an enhanced clarity of the cell membranes.


Author(s):  
D. E. Becker

An efficient, robust, and widely-applicable technique is presented for computational synthesis of high-resolution, wide-area images of a specimen from a series of overlapping partial views. This technique can also be used to combine the results of various forms of image analysis, such as segmentation, automated cell counting, deblurring, and neuron tracing, to generate representations that are equivalent to processing the large wide-area image, rather than the individual partial views. This can be a first step towards quantitation of the higher-level tissue architecture. The computational approach overcomes mechanical limitations, such as hysterisis and backlash, of microscope stages. It also automates a procedure that is currently done manually. One application is the high-resolution visualization and/or quantitation of large batches of specimens that are much wider than the field of view of the microscope.The automated montage synthesis begins by computing a concise set of landmark points for each partial view. The type of landmarks used can vary greatly depending on the images of interest. In many cases, image analysis performed on each data set can provide useful landmarks. Even when no such “natural” landmarks are available, image processing can often provide useful landmarks.


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