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Numerical results indicate that the proposed model seriously challenge other optimization approaches on this important class of hard, fundamental problems.
Our study indicates that the new modeling framework together with simple constraints to avoid symmetric layout solutions can be successfully used to find optimal layout solutions; therefore, seriously challenging other optimization methods on this important class of hard, fundamental problems.
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The Mets have to go back to good, hard, solid, fundamental baseball and focus on doing the little things right.
Their speculation about a hard, indivisible fundamental particle of nature was replaced slowly by a scientific theory supported by experiment and mathematical deduction.
"All these problems where you want to duplicate something biology does, such as perception, touch, planning or grasping, turn out to be hard in fundamental ways," said Gary Bradski, a vision specialist at Willow Garage, a robot development company based here in Silicon Valley.
"The answer is hard work, fundamentals.
And Congress, the states and cities need to push a lot harder for fundamental reforms in the voting machine business and the way Americans vote.
In spite of effort on part of many researchers over the years to design efficient optimization algorithms for the problem, or alternatively prove that it is NP-hard, this fundamental question was left unanswered.
And, naturally, the humble, hard-working fundamentals are good.
Despite its other benefits, the framework didn't address the fundamental hard currency needs of the North Korean leadership.
But banks are also reflecting hard on some fundamental internal questions, such as how to manage risk, compensation and growth itself.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com