Global Sequence Alignment by Dynamic Programming
... • N-M involves an iterative matrix method of calculation • All possible pairs (nucleotides or amino acids) are represented in a twodimensional array. • All possible alignments are represented by pathways through this array. ...
... • N-M involves an iterative matrix method of calculation • All possible pairs (nucleotides or amino acids) are represented in a twodimensional array. • All possible alignments are represented by pathways through this array. ...
Optimization of (s, S) Inventory Systems with Random Lead Times
... A review of the literature on service level constraints reveals that the two most relevant works are Schneider and Ringuest (1990) and Tijms and Groenevelt (1984). Schneider and Ringuest consider a periodic review system operating under a -service level measure, where (1 ? ) is the fraction of ...
... A review of the literature on service level constraints reveals that the two most relevant works are Schneider and Ringuest (1990) and Tijms and Groenevelt (1984). Schneider and Ringuest consider a periodic review system operating under a -service level measure, where (1 ? ) is the fraction of ...
copenhagen 1996
... Solve the linear relaxation of the problem. If the solution is integer, then we are done. Otherwise create two new subproblems by branching on a fractional variable. A subproblem is not active when any of the following occurs: you have already used the subproblem to branch on all variables in th ...
... Solve the linear relaxation of the problem. If the solution is integer, then we are done. Otherwise create two new subproblems by branching on a fractional variable. A subproblem is not active when any of the following occurs: you have already used the subproblem to branch on all variables in th ...
Slides - Biomedical Informatics
... Not only are there many possible gapped alignments, but introducing too many gaps makes nonsense alignments possible: s--e-----qu---en--ce sometimesquipsentice Need to distinguish between alignments that occur due to homology, and those that could be expected to be seen just by chance. Define a scor ...
... Not only are there many possible gapped alignments, but introducing too many gaps makes nonsense alignments possible: s--e-----qu---en--ce sometimesquipsentice Need to distinguish between alignments that occur due to homology, and those that could be expected to be seen just by chance. Define a scor ...
A min max problem
... Covering the node N e by its optimal solution X e and continuing, determine/7(4), F(5) etc. If F(2) = F( 1)' XN a ,is alternative optimal solution of the problem (P). If /7(2 ) > F(1), then XNd is 2nd best basic feasible solution of the problem (P). Let F(1 )
... Covering the node N e by its optimal solution X e and continuing, determine/7(4), F(5) etc. If F(2) = F( 1)' XN a ,is alternative optimal solution of the problem (P). If /7(2 ) > F(1), then XNd is 2nd best basic feasible solution of the problem (P). Let F(1 )
TU-simplex-ellipsoid_rev
... If not, there is a linear inequality ax <=b for which c is violated. Find a minimum ellipsoid which contains the intersection of the previous ellipsoid and ax <= b. Continue the process with the new (smaller) ellipsoid. ...
... If not, there is a linear inequality ax <=b for which c is violated. Find a minimum ellipsoid which contains the intersection of the previous ellipsoid and ax <= b. Continue the process with the new (smaller) ellipsoid. ...
A Neoclassical Optimal Growth Model
... Using a Phase Diagram to Characterize the Two Dimensional Differential Equation System We now characterize the path followed by c (t ) and k (t ) diagrammatically in a “phase diagram.” The first step in constructing the phase diagram is to plot the “nullclines” associated with the steady state condi ...
... Using a Phase Diagram to Characterize the Two Dimensional Differential Equation System We now characterize the path followed by c (t ) and k (t ) diagrammatically in a “phase diagram.” The first step in constructing the phase diagram is to plot the “nullclines” associated with the steady state condi ...
495-210
... and the environment involved (whether a near-tooptimal solution is sufficient or an optimal result is a must, or if the response time is critical or not). The system may find a near-to-optimal or “good” solution or several possible solutions or that there exists no combination of variable’s values f ...
... and the environment involved (whether a near-tooptimal solution is sufficient or an optimal result is a must, or if the response time is critical or not). The system may find a near-to-optimal or “good” solution or several possible solutions or that there exists no combination of variable’s values f ...
UFMG/ICEx/DCC Projeto e Análise de Algoritmos Pós
... Copy a character from x to z by setting z[j] ← x[i] and then incrementing both i and j. This operation examines x[i]. Replace a character from x by another character c, by setting z[j] ← c, and then incrementing both i and j. This operation examines x[i]. Delete a character from x by incrementing i ...
... Copy a character from x to z by setting z[j] ← x[i] and then incrementing both i and j. This operation examines x[i]. Replace a character from x by another character c, by setting z[j] ← c, and then incrementing both i and j. This operation examines x[i]. Delete a character from x by incrementing i ...
Document
... this element, if this element is greater, add 1 to the corresponding p[], that is, • a[] 2 3 1 5 4 ...
... this element, if this element is greater, add 1 to the corresponding p[], that is, • a[] 2 3 1 5 4 ...
Lesson 7 Solutions - Full
... 1. Count the number of beads in Rows 1 – 10. SOLUTION: There are j beads in row j. Summing for j = 1, 2, 3, …, 10, we find that the total number of beads is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55. 2. Can you derive a formula for the number of beads in Rows 1 – n, where n is any positive integer ...
... 1. Count the number of beads in Rows 1 – 10. SOLUTION: There are j beads in row j. Summing for j = 1, 2, 3, …, 10, we find that the total number of beads is 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 = 55. 2. Can you derive a formula for the number of beads in Rows 1 – n, where n is any positive integer ...
Optimal Stopping and Free-Boundary Problems Series
... reductions and to find the solving optimal N. Shiryaev, the disciple the function V solution of the initial stopping of A. N. Kolmogorov, solves. problems. problems. one of the greatest Some In some previous In probabilists of all time, is methods of papers, Mikhalevich, Chapter III it is an eminent ...
... reductions and to find the solving optimal N. Shiryaev, the disciple the function V solution of the initial stopping of A. N. Kolmogorov, solves. problems. problems. one of the greatest Some In some previous In probabilists of all time, is methods of papers, Mikhalevich, Chapter III it is an eminent ...
The Robustness-Performance Tradeoff in Markov Decision Processes
... In this section we address the RP tradeoff for infinite horizon MDPs with a discounted reward criterion. For a fixed λ, the problem is equivalent to a zero-sum game, with the decision maker trying to maximize the weighted sum and Nature trying to minimize it by selecting an adversarial reward realiz ...
... In this section we address the RP tradeoff for infinite horizon MDPs with a discounted reward criterion. For a fixed λ, the problem is equivalent to a zero-sum game, with the decision maker trying to maximize the weighted sum and Nature trying to minimize it by selecting an adversarial reward realiz ...
Iterative Solution of Linear Systems
... • Suppose we have some fast way of finding A-1 for some matrix A • Now A changes in a special way: A* = A + uvT for some n1 vectors u and v • Goal: find a fast way of computing (A*)-1 – Eventually, a fast way of solving (A*) x = b ...
... • Suppose we have some fast way of finding A-1 for some matrix A • Now A changes in a special way: A* = A + uvT for some n1 vectors u and v • Goal: find a fast way of computing (A*)-1 – Eventually, a fast way of solving (A*) x = b ...
18.06 Linear Algebra, Problem set 3 solutions
... so that Cx = 0 if and only if Ax = 0 and Bx = 0. (...and as a nitpick, it wouldn’t be quite sloppy instead write “if and only if Ax = Bx = 0”—those are zero vectors of potentially different length, hardly equal). � Problem 4. (§3.2, #37) Kirchoff’s Law says that current in = current out at every node. ...
... so that Cx = 0 if and only if Ax = 0 and Bx = 0. (...and as a nitpick, it wouldn’t be quite sloppy instead write “if and only if Ax = Bx = 0”—those are zero vectors of potentially different length, hardly equal). � Problem 4. (§3.2, #37) Kirchoff’s Law says that current in = current out at every node. ...
LINEAR PROGRAMMING MODELS
... Given a CPF solution, it is much quicker to gather information about its adjacent CPF solutions than its non-adjacent CPF solutions. After the current CPF solution is identified, the simplex method examines each of the edges of the feasible region. that emanate from this CPF solution. The most p ...
... Given a CPF solution, it is much quicker to gather information about its adjacent CPF solutions than its non-adjacent CPF solutions. After the current CPF solution is identified, the simplex method examines each of the edges of the feasible region. that emanate from this CPF solution. The most p ...
A Constructive Heuristic for the Travelling Tournament Problem
... 6, 8, 9, 11–14]). Agnostopoulos et al. [1] present the current best results for the problems presented on the TTP website (http://mat.gsia.cmu.edu/TOURN/). Instead of tackling the entire tournament as one problem, we propose a two-stage approach in which we solve the problem for individual teams fir ...
... 6, 8, 9, 11–14]). Agnostopoulos et al. [1] present the current best results for the problems presented on the TTP website (http://mat.gsia.cmu.edu/TOURN/). Instead of tackling the entire tournament as one problem, we propose a two-stage approach in which we solve the problem for individual teams fir ...
Notes for Lecture 11
... We want to show that if the longest simple path problem is in P, then the Hamilton circuit problem is in P. Design a polynomial time algorithm to solve HC by using an algorithm for LSP. Step 0: Set the length of each edge in G to be 1 Step 1: for each edge (u, v)E do find the longest simple path P ...
... We want to show that if the longest simple path problem is in P, then the Hamilton circuit problem is in P. Design a polynomial time algorithm to solve HC by using an algorithm for LSP. Step 0: Set the length of each edge in G to be 1 Step 1: for each edge (u, v)E do find the longest simple path P ...
lecture1212
... We want to show that if the longest simple path problem is in P, then the Hamilton circuit problem is in P. Design a polynomial time algorithm to solve HC by using an algorithm for LSP. Step 0: Set the length of each edge in G to be 1 Step 1: for each edge (u, v)E do find the longest simple path P ...
... We want to show that if the longest simple path problem is in P, then the Hamilton circuit problem is in P. Design a polynomial time algorithm to solve HC by using an algorithm for LSP. Step 0: Set the length of each edge in G to be 1 Step 1: for each edge (u, v)E do find the longest simple path P ...
ST4004Lecture12 Multi-objective decision making
... a wrt to every objective and strictly better than a wrt at least one objective. • That is a is Pareto optimal if for all b s.t. ui(b)>ui(a) then there exists j s.t. uj(a)>uj(b). • Pareto optimal = not dominated. ...
... a wrt to every objective and strictly better than a wrt at least one objective. • That is a is Pareto optimal if for all b s.t. ui(b)>ui(a) then there exists j s.t. uj(a)>uj(b). • Pareto optimal = not dominated. ...
Deployment of Sensing Devices on Critical Infrastructure
... Recursion is a repetitive process in which an algorithm calls itself. Usually recursion is organized in such a way that a subroutine calls itself or a function calls itself ...
... Recursion is a repetitive process in which an algorithm calls itself. Usually recursion is organized in such a way that a subroutine calls itself or a function calls itself ...
Elements of Optimal Control Theory Pontryagin’s Maximum Principle
... velocity). The lander is equipped with a braking system, which applies a force u, in order to slow down the descent. The braking force cannot exceed a given (maximum) value U . Let x(t) be the distance from the landing site. Then Newton’s Law gives mẍ = −mg − k ẋ + u. The objective is to find the ...
... velocity). The lander is equipped with a braking system, which applies a force u, in order to slow down the descent. The braking force cannot exceed a given (maximum) value U . Let x(t) be the distance from the landing site. Then Newton’s Law gives mẍ = −mg − k ẋ + u. The objective is to find the ...
The Efficient Outcome Set of a Bi-criteria Linear Programming and
... Iteration 1. (with n=2) The equation of the line through y 1 and y 2 can be written in the form: 0.2y1 + 0.5y2 = 2.7. Hence G1,2 = {y ∈ Y |h`1,2 , yi ≥ α1,2 }, where `1,2 = (0.2, 0.5) and α1,2 = 2.7. Solve the linear programming max{h`1,2 , yi|y ∈ G1,2 i} we obtain ŷ = (5, 4) 6∈ {y 1 , y 2 }. Then ...
... Iteration 1. (with n=2) The equation of the line through y 1 and y 2 can be written in the form: 0.2y1 + 0.5y2 = 2.7. Hence G1,2 = {y ∈ Y |h`1,2 , yi ≥ α1,2 }, where `1,2 = (0.2, 0.5) and α1,2 = 2.7. Solve the linear programming max{h`1,2 , yi|y ∈ G1,2 i} we obtain ŷ = (5, 4) 6∈ {y 1 , y 2 }. Then ...
pdf
... coincide. The case (i) can indeed occur, but there is nothing to prove. The cases (ii) and (iii) were already proved in the weak duality theorem. So we must only prove the last (and most interesting) case. Assume that Problem (D) is feasible and bounded (so it has an optimal solution). Let y ∗ be an ...
... coincide. The case (i) can indeed occur, but there is nothing to prove. The cases (ii) and (iii) were already proved in the weak duality theorem. So we must only prove the last (and most interesting) case. Assume that Problem (D) is feasible and bounded (so it has an optimal solution). Let y ∗ be an ...
Dynamic programming
In mathematics, computer science, economics, and bioinformatics, dynamic programming is a method for solving a complex problem by breaking it down into a collection of simpler subproblems. It is applicable to problems exhibiting the properties of overlapping subproblems and optimal substructure (described below). When applicable, the method takes far less time than other methods that don't take advantage of the subproblem overlap (like depth-first search).In order to solve a given problem using a dynamic programming approach, we need to solve different parts of the problem (subproblems), then combine the solutions of the subproblems to reach an overall solution. Often when using a more naive method, many of the subproblems are generated and solved many times. The dynamic programming approach seeks to solve each subproblem only once, thus reducing the number of computations: once the solution to a given subproblem has been computed, it is stored or ""memoized"": the next time the same solution is needed, it is simply looked up. This approach is especially useful when the number of repeating subproblems grows exponentially as a function of the size of the input.Dynamic programming algorithms are used for optimization (for example, finding the shortest path between two points, or the fastest way to multiply many matrices). A dynamic programming algorithm will examine the previously solved subproblems and will combine their solutions to give the best solution for the given problem. The alternatives are many, such as using a greedy algorithm, which picks the locally optimal choice at each branch in the road. The locally optimal choice may be a poor choice for the overall solution. While a greedy algorithm does not guarantee an optimal solution, it is often faster to calculate. Fortunately, some greedy algorithms (such as minimum spanning trees) are proven to lead to the optimal solution.For example, let's say that you have to get from point A to point B as fast as possible, in a given city, during rush hour. A dynamic programming algorithm will look at finding the shortest paths to points close to A, and use those solutions to eventually find the shortest path to B. On the other hand, a greedy algorithm will start you driving immediately and will pick the road that looks the fastest at every intersection. As you can imagine, this strategy might not lead to the fastest arrival time, since you might take some ""easy"" streets and then find yourself hopelessly stuck in a traffic jam.Sometimes, applying memoization to a naive basic recursive solution already results in a dynamic programming solution with asymptotically optimal time complexity; however, the optimal solution to some problems requires more sophisticated dynamic programming algorithms. Some of these may be recursive as well but parametrized differently from the naive solution. Others can be more complicated and cannot be implemented as a recursive function with memoization. Examples of these are the two solutions to the Egg Dropping puzzle below.