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Hard Instances of Hard Problems

2000
This paper investigates the instance complexities of problems that are hard or weakly hard for exponential time under polynomial time, many-one reductions. It is shown that almost every instance of almost every problem in exponential time has essentially maximal instance complexity.
Jack H. Lutz   +2 more
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Thermodynamic hardness and the maximum hardness principle

The Journal of Chemical Physics, 2017
An alternative definition of hardness (called the thermodynamic hardness) within the grand canonical ensemble formalism is proposed in terms of the partial derivative of the electronic chemical potential with respect to the thermodynamic chemical potential of the reservoir, keeping the temperature and the external potential constant.
Marco Franco-Pérez   +3 more
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On the Hardness of Reoptimization

2008
We consider the following reoptimization scenario: Given an instance of an optimization problem together with an optimal solution, we want to find a high-quality solution for a locally modified instance. The naturally arising question is whether the knowledge of an optimal solution to the unaltered instance can help in solving the locally modified ...
Hans-Joachim Böckenhauer   +3 more
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The Hard Problem is Mainly Hard Work

Cognitive Neuroscience, 2020
Doerig et al. point out that there is now a great deal of evidence bearing directly on our understanding of consciousness. However, they argue that the multiplicity of theories suggest that we have a 'lack of stringent criteria specifying how empirical data constrains ToCs.'
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Hard Times, Hard Feelings, Hard Money

1992
Abstract The Panic of 1819 was a traumatic awakening to the capitalist reality of boom and-bust. Not until the postwar boom had the market spread far enough to inflict general prostration in bust. Suddenly everyone committed to the money economy was in peril, as bank notes depreciated in their pockets.
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The Hardness of Hard Treatment

1998
Abstract In February, 1996, Rosemary West was convicted of ten murders of young women, including a daughter and stepdaughter. The British public were shocked by the gruesome details as they gradually unfolded. West (whose co-defendant husband committed suicide in custody) was sentenced to life imprisonment on each count.
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