The PCP theorem gives a novel characterization of the class NP in terms of probabilistically checkable proofs (PCPs). The central role in this characterization belongs to a Verifier. Here, the probabilities are taken over the random choices of the verifier, and the notation V π means that the verifier V has random access to the string π, i.e., V may request to see the ith bit of the string π, f...

To support large-scale integration of wind power into electric energy systems, state-of-the-art wind speed forecasting methods should be able to provide accurate and adequate information to enable efficient, reliable, and cost-effective scheduling of wind power. Here, we incorporate space-time wind forecasts into electric power system scheduling. First, we propose a modified regime-switching, s...

As a consequence of an AM protocol for NISO, we get the following: Theorem 1. If Graph Isomorphism is NP-complete, then PH = Σp2. Proof. Suppose that Graph Isomorphism is NP-complete. Then the problem NISO is coNPcomplete. Hence, every coNP problem is polytime reducible to NISO, which, as we know, is in AM. We use this to get the following inclusions: Σp2 = ∃ ◦ ∀ ◦ P (definition of Σ p 2) ⊆ ∃ ◦...

Why is randomness useful? Imagine you have a stack of bank notes, with very few counterfeit ones. You want to choose a genuine bank note to pay at a store. However, suppose that you don’t know how to distinguish between a “good” bank note and a “bad” one. What can you do? Well, if you pick a bank note at random, you will be lucky with high probability (here the probability of picking a good ban...

1Faculty of Medicine, School of Medicine, National Yang-Ming University, Taipei 112, Taiwan, 2Department of Neurosurgery, Taichung Veterans General Hospital, Taichung 407, Taiwan, 3Institute of Biomedical Sciences, National Chung Hsing University, Taichung 402, Taiwan, 4Division of Gastroenterology, Department of Medicine, Taipei Veterans General Hospital, Taipei 112, Taiwan, 5Department and In...

An accoiMt of the past 50 years of research carried out on Amphipoda by the Central Marine Fisheries Research Institute and most relevant works carried out on the topic from the Indian seas are presented. The paper highlights the qualitative and quantitative composition, distribution in space and time and the taxonomy of planktonic :imphipods of neritic and oceanic waters of Indian region as we...