scholarly journals Linearization of Median Genomes Under the Double-Cut-and-Join-Indel Model

2019 ◽  
Vol 15 ◽  
pp. 117693431882053 ◽  
Author(s):  
Pavel Avdeyev ◽  
Shuai Jiang ◽  
Max A Alekseyev
Keyword(s):  
Approximate Solution ◽  
Original Problem ◽  
Approximation Error ◽  
Combinatorial Structure ◽  
Double Cut And Join ◽  
Linear Chromosomes ◽  
Circular Chromosomes ◽  
Relaxed Problem

Reconstruction of the median genome consisting of linear chromosomes from three given genomes is known to be intractable. There exist efficient methods for solving a relaxed version of this problem, where the median genome is allowed to have circular chromosomes. We propose a method for construction of an approximate solution to the original problem from a solution to the relaxed problem and prove a bound on its approximation error. Our method also provides insights into the combinatorial structure of genome transformations with respect to appearance of circular chromosomes.

Convex Estimators for Optimization of Kriging Model Problems

2012 ◽  
Vol 134 (11) ◽  
Author(s):  
Karim Hamza ◽  
Mohammed Shalaby
Keyword(s):  
Quadratic Programming ◽  
Sequential Quadratic Programming ◽  
Original Problem ◽  
Kriging Model ◽  
Global Optimum ◽  
Water Desalination ◽  
Test Functions ◽  
Convex Underestimators ◽  
Vehicle Crashworthiness ◽  
Relaxed Problem

This paper presents a framework for identification of the global optimum of Kriging models that have been tuned to approximate the response of some generic objective function and constraints. The framework is based on a branch and bound scheme for subdivision of the search space into hypercubes while constructing convex underestimators of the Kriging models. The convex underestimators, which are the key development in this paper, provide a relaxation of the original problem. The relaxed problem has two main features: (i) convex optimization algorithms such as sequential quadratic programming (SQP) are guaranteed to find the global optimum of the relaxed problem and (ii) objective value of the relaxed problem is a lower bound within a hypercube for the original (Kriging model) problem. As accuracy of the convex estimators improves with subdivision of a hypercube, termination of a branch happens when either: (i) solution of the relaxed problem within the hypercube is no better than current best solution of the original problem or (ii) best solution of the original problem and that of the relaxed problem are within tolerance limits. To assess the significance of the proposed framework, comparison studies against genetic algorithm (GA), particle swarm optimization (PSO), random multistart sequential quadratic programming (mSQP), and DIRECT are conducted. The studies include four standard nonlinear test functions and two design application problems of water desalination and vehicle crashworthiness. The studies show the proposed framework deterministically finding the optimum for all the test problems. Among the tested stochastic search techniques (GA, PSO, mSQP), mSQP had the best performance as it consistently found the optimum in less computational time than the proposed approach except on the water desalination problem. DIRECT deterministically found the optima for the nonlinear test functions, but completely failed to find it for the water desalination and vehicle crashworthiness problems.

scholarly journals Topoisomerase IV is required for partitioning of circular chromosomes but not linear chromosomes in Streptomyces

2013 ◽  
Vol 41 (22) ◽  
pp. 10403-10413 ◽  
Author(s):  
Tzu-Wen Huang ◽  
Chin-Chen Hsu ◽  
Han-Yu Yang ◽  
Carton W. Chen
Keyword(s):  
Topoisomerase Iv ◽  
Linear Chromosomes ◽  
Circular Chromosomes

The perturbation algorithm for the realization of a four-layer semi-discrete solution scheme of an abstract evolutionary problem

2018 ◽  
Vol 25 (1) ◽  
pp. 77-92
Author(s):  
Jemal Rogava ◽  
David Gulua
Keyword(s):  
Hilbert Space ◽  
Approximate Solution ◽  
Original Problem ◽  
Evolutionary Equation ◽  
Discrete Solution ◽  
Discrete Scheme ◽  
Evolutionary Problem ◽  
Solution Scheme

AbstractIn the present paper, we use the perturbation algorithm to reduce a purely implicit four-layer semi-discrete scheme for an abstract evolutionary equation to two-layer schemes. An approximate solution of the original problem is constructed using the solutions of these schemes. Estimates of the approximate solution error are proved in a Hilbert space.

scholarly journals An error estimate of a regularizing algorithm based on the generalized residual principle when solving integral equations

2015 ◽  
pp. 1-9
Author(s):  
В.П. Танана ◽  
А.И. Сидикова
Keyword(s):  
Approximate Solution ◽  
Error Estimate ◽  
Integral Equations ◽  
Original Problem ◽  
Residual Method ◽  
Regularizing Algorithm ◽  
Finite Dimensional Approximation ◽  
Finite Dimensional ◽  
Dimensional Approximation

Исследован регуляризующий алгоритм приближенного решения интегральных уравнений первого рода, включающий в себя конечномерную аппроксимацию исходной задачи, а также получена оценка погрешности этого алгоритма. Для получения этой оценки доказана эквивалентность обобщенного метода невязки и обобщенного принципа невязки. Этот результат может быть положен в основу оценивания конечномерных аппроксимаций регуляризованных решений. A regularizing algorithm for the approximate solution of integral equations of the first kind is studied. This algorithm involves a finite-dimensional approximation of the original problem. An error estimate is proposed. In order to obtain this estimate, the equivalence of the generalized residual method and the generalized residual principle is proved. This result can be used to estimate the finite-dimensional approximations of regularized solutions.

On the Approximate Solution of Nonclassically Damped Linear Systems

1993 ◽  
Vol 60 (3) ◽  
pp. 695-701 ◽  
Author(s):  
J. H. Hwang ◽  
F. Ma
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Error Bound ◽  
Large Scale ◽  
Substantial Reduction ◽  
Approximation Error ◽  
Computational Effort ◽  
Common Procedure ◽  
Damping Matrix ◽  
Modal Damping

A common procedure in the solution of a nonclassically damped linear system is to neglect the off-diagonal elements of the associated modal damping matrix. For a large-scale system, substantial reduction in computational effort is achieved by this method of decoupling the system. In the present paper, the error introduced by disregarding the off-diagonal elements is evaluated, and a quadrature formula for the approximation error is derived. A tight error bound is then obtained. In addition, an effective scheme to improve the accuracy of the approximate solution is outlined.

scholarly journals GENOME HALVING WITH DOUBLE CUT AND JOIN

2009 ◽  
Vol 07 (02) ◽  
pp. 357-371 ◽  
Author(s):  
ROBERT WARREN ◽  
DAVID SANKOFF
Keyword(s):  
General Context ◽  
Reciprocal Translocations ◽  
Double Cut And Join ◽  
Previous Algorithm ◽  
Circular Chromosomes

The genome halving problem, previously solved by El-Mabrouk for inversions and reciprocal translocations, is here solved in a more general context allowing transpositions and block interchange as well, for genomes including multiple linear and circular chromosomes. We apply this to several datasets and compare the results to the previous algorithm.

Convex Estimators for Optimization of Kriging Model Problems

2011 ◽  
Author(s):  
Karim Hamza ◽  
Mohammed Shalaby
Keyword(s):  
Original Problem ◽  
Search Space ◽  
Kriging Model ◽  
Global Optimum ◽  
Water Desalination ◽  
Tolerance Limits ◽  
Design Variables ◽  
Search Termination ◽  
Relaxed Problem ◽  
Better Than

This paper presents a framework for identification of the global optimum of Kriging models. The framework is based on a branch and bound scheme for sub-division of the search space into hypercubes while constructing convex under-estimators of the Kriging models. The convex under-estimators, which are a key development in this paper, provide a relaxation of the original problem. The relaxed problem has two key features: i) convex optimization algorithms such as sequential quadratic programming (SQP) are guaranteed to find the global optimum of the relaxed problem, and ii) objective value of the relaxed problem is a lower bound on the best attainable solution within a hypercube for the original (Kriging model) problem. The convex under-estimators improve in accuracy as the size of a hypercube gets smaller via the branching search. Termination of a hypercube branch is done when either: i) solution of the relaxed problem within the hypercube is no better than current best solution of the original problem, or ii) best solution of the original problem and that of the relaxed problem are within tolerance limits. To assess the significance of the proposed framework, comparison studies against genetic algorithm (GA) are conducted using Kriging models that approximate standard nonlinear test functions, as well as application problems of water desalination and vehicle crashworthiness. Results of the studies show the proposed framework deterministically providing a solution within tolerance limits from the global optimum, while GA is observed to not reliably discover the best solutions in problems with larger number of design variables.

scholarly journals MIMO Detection for High Order QAM by Canonical Dual Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-8 ◽  
Author(s):  
Ye Tian ◽  
Jr-Fong Dang
Keyword(s):  
Approximate Solution ◽  
Stationary Point ◽  
Original Problem ◽  
Dual Problem ◽  
Mimo Detection ◽  
Dual Approach ◽  
Feasible Domain ◽  
Piecewise Continuous ◽  
Simulation Results ◽  
Continuous Problem

We develop a canonical dual approach for solving the MIMO problem. First, a special linear transformation is introduced to reformulate the original problem into a{−1,1}constrained quadratic programming problem. Then, we derive a canonical dual problem which is piecewise continuous problem with no duality gap. Under certain conditions, the canonical problem becomes a concave maximization dual problem over a convex feasible domain. By getting the stationary point of the canonical dual problem, we can find either an optimal or approximate solution of the original problem. A gradient decent algorithm is proposed to solve the MIMO problem and simulation results are provided to demonstrate the effectiveness of the method.

scholarly journals Linear plasmids mobilize linear but not circular chromosomes in Streptomyces: support for the ‘end first’ model of conjugal transfer

Microbiology ◽  
2011 ◽  
Vol 157 (9) ◽  
pp. 2556-2568 ◽  
Author(s):  
Hsuan-Hsuan Lee ◽  
Chin-Chen Hsu ◽  
Yen-Ling Lin ◽  
Carton W. Chen
Keyword(s):  
Rolling Circle Replication ◽  
Linear Plasmids ◽  
Terminal Protein ◽  
Rolling Circle ◽  
Gram Positive Bacteria ◽  
Circular Plasmid ◽  
Transfer Capability ◽  
Terminal Proteins ◽  
Linear Chromosomes ◽  
Circular Chromosomes

Gram-positive bacteria of the genus Streptomyces possess linear chromosomes and linear plasmids capped by terminal proteins covalently bound to the 5′ ends of the DNA. The linearity of Streptomyces chromosomes raises the question of how they are transferred during conjugation, particularly when the mobilizing plasmids are also linear. The classical rolling circle replication model for transfer of circular plasmids and chromosomes from an internal origin cannot be applied to this situation. Instead it has been proposed that linear Streptomyces plasmids mobilize themselves and the linear chromosomes from their telomeres using terminal-protein-primed DNA synthesis. In support of this ‘end first’ model, we found that artificially circularized Streptomyces chromosomes could not be mobilized by linear plasmids (SLP2 and SCP1), while linear chromosomes could. In comparison, a circular plasmid (pIJ303) could mobilize both circular and linear chromosomes at the same efficiencies. Interestingly, artificially circularized SLP2 exhibited partial self-transfer capability, indicating that, being a composite replicon, it may have acquired the additional internal origin of transfer from an ancestral circular plasmid during evolution.

scholarly journals ON PROBLEM OF REGIONAL WAREHOUSE AND TRANSPORT INFRASTRUCTURE OPTIMIZATION

2017 ◽  
Vol 16 (6) ◽  
pp. 532-536 ◽  
Author(s):  
I. Yu. Miretskiy ◽  
P. V. Popov ◽  
R. B. Ivut
Keyword(s):  
Approximate Solution ◽  
Original Problem ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Transport Infrastructure ◽  
Support Network ◽  
Separable Programming ◽  
Optimal Capacity ◽  
Continuous Relaxation ◽  
Mathematical Programming Problems

The article suggests an approach of solving the problem of warehouse and transport infrastructure optimization in a region. The task is to determine the optimal capacity and location of the support network of warehouses in the region, as well as power, composition and location of motor fleets. Optimization is carried out using mathematical models of a regional warehouse network and a network of motor fleets. These models are presented as mathematical programming problems with separable functions. The process of finding the optimal solution of problems is complicated due to high dimensionality, non-linearity of functions, and the fact that a part of variables are constrained to integer, and some variables can take values only from a discrete set. Given the mentioned above complications search for an exact solution was rejected. The article suggests an approximate approach to solving problems. This approach employs effective computational schemes for solving multidimensional optimization problems. We use the continuous relaxation of the original problem to obtain its approximate solution. An approximately optimal solution of continuous relaxation is taken as an approximate solution of the original problem. The suggested solution method implies linearization of the obtained continuous relaxation and use of the separable programming scheme and the scheme of branches and bounds. We describe the use of the simplex method for solving the linearized continuous relaxation of the original problem and the specific moments of the branches and bounds method implementation. The paper shows the finiteness of the algorithm and recommends how to accelerate process of finding a solution.

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