Provably Good Planar Mappings - The Faculty of Mathematics and
... Previous deformation models can be roughly divided into meshbased and meshless models. Mesh-based maps are predominantly constructed using linear finite elements, and are inherently not smooth, but can be made to look smooth by using highly dense elements. Although the methods for creating maps with ...
... Previous deformation models can be roughly divided into meshbased and meshless models. Mesh-based maps are predominantly constructed using linear finite elements, and are inherently not smooth, but can be made to look smooth by using highly dense elements. Although the methods for creating maps with ...
All Soviet Union Math Competitions
... array. A reachable array differs from the original only in that some or all of the signs of its mn entries may be different. There are at most 2 possibilities for each sign and hence at most 2mn different reachable arrays. For each reachable array calculate the sum of all its entries. Take the reach ...
... array. A reachable array differs from the original only in that some or all of the signs of its mn entries may be different. There are at most 2 possibilities for each sign and hence at most 2mn different reachable arrays. For each reachable array calculate the sum of all its entries. Take the reach ...
Risk-Averse Strategies for Security Games with
... A strategy profile hx, ti i for this game is a mixed strategy x for the defender, and the attacked target ti . The mixed strategy x = hxi i is a vector of probabilities of defender coverage over all targets (Yin et al. 2010), such that the sum total of coverage is not more than the number of availab ...
... A strategy profile hx, ti i for this game is a mixed strategy x for the defender, and the attacked target ti . The mixed strategy x = hxi i is a vector of probabilities of defender coverage over all targets (Yin et al. 2010), such that the sum total of coverage is not more than the number of availab ...
The given function f is continuous at
... Therefore, the given function f is continuous at x = π Q.21 Discuss the continuity of the following functions.(a) f (x) = sin x + cos x (b) f (x) = sin x − cos x (c) f (x) = sin x × cos x It is known that if g and h are two continuous functions, then are also continuous. It has to proved first that ...
... Therefore, the given function f is continuous at x = π Q.21 Discuss the continuity of the following functions.(a) f (x) = sin x + cos x (b) f (x) = sin x − cos x (c) f (x) = sin x × cos x It is known that if g and h are two continuous functions, then are also continuous. It has to proved first that ...
Numerical solution of saddle point problems
... structural and sparsity properties, in this paper we are mainly interested in problems that are both large and sparse. This justifies our emphasis on iterative solvers. Direct solvers, however, are still the preferred method in optimization and other areas. Furthermore, direct methods are often used ...
... structural and sparsity properties, in this paper we are mainly interested in problems that are both large and sparse. This justifies our emphasis on iterative solvers. Direct solvers, however, are still the preferred method in optimization and other areas. Furthermore, direct methods are often used ...
The Traveling Salesman Problem
... Subtour constraints The no subtour constraint can also be formulated in two ways ◮ The number of links in any subset should be less than the number of cities in the subset. ...
... Subtour constraints The no subtour constraint can also be formulated in two ways ◮ The number of links in any subset should be less than the number of cities in the subset. ...
Multi-Period Stock Allocation Via Robust Optimization
... 1. Robust optimization models lead to solutions whose expected cost is close to the minimum expected cost in cases where the optimum can be computed, especially when compared to the error possible from selecting probability distribution models incorrectly; 2. Robust optimization models do not su¤er ...
... 1. Robust optimization models lead to solutions whose expected cost is close to the minimum expected cost in cases where the optimum can be computed, especially when compared to the error possible from selecting probability distribution models incorrectly; 2. Robust optimization models do not su¤er ...
Martingale problem approach to Markov processes
... These extensions were crucial for application to Filtering theory. Kallianpur, Karandikar and Bhatt used these results to prove that Fujisaki-Kallianpur-Kunita equation and Zakai equation (these are infinite dimensional stochastic differential equations) admit unique solution and thus characterize t ...
... These extensions were crucial for application to Filtering theory. Kallianpur, Karandikar and Bhatt used these results to prove that Fujisaki-Kallianpur-Kunita equation and Zakai equation (these are infinite dimensional stochastic differential equations) admit unique solution and thus characterize t ...
High order schemes based on operator splitting and - HAL
... algorithmic complexity and computational requirements. Operator splitting techniques have been used over the past years to carry out numerical simulations in several domains, from biomedical models to combustion or air pollution modeling applications. Moreover, these methods continue to be widely us ...
... algorithmic complexity and computational requirements. Operator splitting techniques have been used over the past years to carry out numerical simulations in several domains, from biomedical models to combustion or air pollution modeling applications. Moreover, these methods continue to be widely us ...
Differential Equations
... If each linear DEqn in the system has constant coefficients then the system is also said to be a constant coefficient system of linear ODEs. We will see how to solve any constant coefficient linear system. Linear differential equations with nonconstant coefficients are not as simple to solve, howeve ...
... If each linear DEqn in the system has constant coefficients then the system is also said to be a constant coefficient system of linear ODEs. We will see how to solve any constant coefficient linear system. Linear differential equations with nonconstant coefficients are not as simple to solve, howeve ...
On the Maximum Benefit Chinese Postman Problem
... (i; j)), and bene"t de"ned as bij1 = dij + c0 ; bij2 = dij − c1 , and bijrij = 0, for rij ¿ 3, where c0 ; c1 are constants with c0 ¿ c1 ¿ 0. The net bene"t for traversing each edge for the "rst time is c0 , and the second time is −c1 . If the postman traverses each edge on the network G(V; E) exactl ...
... (i; j)), and bene"t de"ned as bij1 = dij + c0 ; bij2 = dij − c1 , and bijrij = 0, for rij ¿ 3, where c0 ; c1 are constants with c0 ¿ c1 ¿ 0. The net bene"t for traversing each edge for the "rst time is c0 , and the second time is −c1 . If the postman traverses each edge on the network G(V; E) exactl ...
Math428Week1.pdf
... The application of mathematical methods, e.g., optimization, to study or plan a process. Management science ... perhaps in the sense of da Vinci: No human investigation can be called real science if it cannot be demonstrated mathematically. None is quite right. What about statistical or comput ...
... The application of mathematical methods, e.g., optimization, to study or plan a process. Management science ... perhaps in the sense of da Vinci: No human investigation can be called real science if it cannot be demonstrated mathematically. None is quite right. What about statistical or comput ...
for Sublinear Time Maximum Inner Product Search (MIPS)
... If there are N items to recommend, solving (3) requires computing N inner products. Recommendation systems are typically deployed in on-line application over web where the number N is huge. A brute force linear scan over all items, for computing arg max, would be prohibitively expensive. Large-scale ...
... If there are N items to recommend, solving (3) requires computing N inner products. Recommendation systems are typically deployed in on-line application over web where the number N is huge. A brute force linear scan over all items, for computing arg max, would be prohibitively expensive. Large-scale ...
38. A preconditioner for the Schur complement domain
... with successive and multiple right-hand sides. This technique is based on the exploitation of previously computed conjugate directions. Figure 5.2 shows the iteration history with respect to the number of right-hand sides using different methods, and we report also the total number of iterations, the ...
... with successive and multiple right-hand sides. This technique is based on the exploitation of previously computed conjugate directions. Figure 5.2 shows the iteration history with respect to the number of right-hand sides using different methods, and we report also the total number of iterations, the ...
Multiple-criteria decision analysis
Multiple-criteria decision-making or multiple-criteria decision analysis (MCDA) is a sub-discipline of operations research that explicitly considers multiple criteria in decision-making environments. Whether in our daily lives or in professional settings, there are typically multiple conflicting criteria that need to be evaluated in making decisions. Cost or price is usually one of the main criteria. Some measure of quality is typically another criterion that is in conflict with the cost. In purchasing a car, cost, comfort, safety, and fuel economy may be some of the main criteria we consider. It is unusual that the cheapest car is the most comfortable and the safest one. In portfolio management, we are interested in getting high returns but at the same time reducing our risks. Again, the stocks that have the potential of bringing high returns typically also carry high risks of losing money. In a service industry, customer satisfaction and the cost of providing service are two conflicting criteria that would be useful to consider.In our daily lives, we usually weigh multiple criteria implicitly and we may be comfortable with the consequences of such decisions that are made based on only intuition. On the other hand, when stakes are high, it is important to properly structure the problem and explicitly evaluate multiple criteria. In making the decision of whether to build a nuclear power plant or not, and where to build it, there are not only very complex issues involving multiple criteria, but there are also multiple parties who are deeply affected from the consequences.Structuring complex problems well and considering multiple criteria explicitly leads to more informed and better decisions. There have been important advances in this field since the start of the modern multiple-criteria decision-making discipline in the early 1960s. A variety of approaches and methods, many implemented by specialized decision-making software, have been developed for their application in an array of disciplines, ranging from politics and business to the environment and energy.