I prove that if markets are efficient, meaning current prices fully reflect all information available in past prices, then P = NP , meaning every computational problem whose solution can be verified in polynomial time can also be solved in polynomial time. I also prove the converse by showing how we can “program” the market to solve NP -complete problems. Since P probably does not equal NP , ma...

Safety standards (e.g., ISO 26262) define safety life-cycles to be adopted for the development of safety-critical systems. Professionals (i.e., safety engineers, safety managers, and, more broadly safety cultureaware personnel) who are responsible of the development of such systems can be, in turn, considered as safety-critical systems. Coursemodules aimed at forming such professionals are crit...

Sample size calculations require specification of the treatment effect, but what if this is not known? Two-stage tests use the first stage to estimate the treatment effect and modify the sample size accordingly. The purpose of this paper is to unify the theory of two-stage testing based on treatment effect. The conditional error function approach of Proschan and Hunsberger (1995) is shown to be...

In standard arithmetic, if we, e.g., accidentally add a wrong number y to the preliminary result x, we can undo this operation by subtracting y from the result x+ y. In this paper, we prove the following two results: • First, a similar possibility to invert (undo) addition holds for fuzzy numbers (although in case of fuzzy numbers, we cannot simply undo addition by subtracting y from the sum). ...

This study evaluates how people represent “even if” conditionals when they have to integrate them with previous “if then” conditionals and also make an inference. The terms in the premises were ordered to facilitate their integration (Figure 1: If A then B; Even if B C). In half the cases, the “even if” conditional was expressed with a negation instead of an affirmation (If A then B; Even if no...