Summary The effects of complex structure in the deep mantle and D″ on PKP differential traveltimes should be estimated accurately in order to reach reliable conclusions concerning the physical and chemical properties of the Earth's inner and outer core. In particular, it is important to assess how much of the data can be explained by mantle structure alone. For this purpose, we have assembled global data sets of high‐quality PKP(AB–DF), PKP(BC–DF) and PcP–P differential traveltimes measured on mostly broad‐band records. The PKP(AB–DF) data were inverted alone or jointly with PcP–P data, to retrieve P‐velocity maps of the lowermost 300 km of the mantle. Corrections for mantle structure above D″ were performed prior to inversion using recent tomographic models and the fit to the PKP(BC–DF) data set was used to constrain damping in the inversions. We compare models obtained with and without polar PKP paths and find that their inclusion or exclusion does not significantly affect the resulting D″ model except under North America, where coverage is poor without polar paths. Our preferred model, obtained using PKP(AB–DF) and PcP–P data combined, explains over 80 per cent of the variance in PKP(AB–DF), almost 60 per cent of the variance in PcP–P and 27 per cent of the variance in PKP(BC–DF)—a significant portion considering that the PKP(BC–DF) data set was not used in the inversion. Our models are characterized by prominent fast features under mid‐America and east Asia, a fast belt across the Pacific, a slow region under the southwestern Pacific and southern Africa, as well as sharp transitions from fast to slow, for instance under Alaska and the South Atlantic. The anomalous South Sandwich to Alaska data cannot fully be explained by D″ structure alone, unless very short‐wavelength lateral variations are introduced. Models that allow for a modest level of constant transverse anisotropy in the inner core, compatible with normal mode splitting data, perform somewhat better, but still fail to explain the result of 2 s in PKP(BC–DF) residuals, on these anomalous paths.

This article deals with the mining incentives in the Bitcoin protocol. The mining process is used to confirm and secure transactions. This process is organized as a speed game between individuals or firms – the miners – with different computational powers to solve a mathematical problem, bring a proof of work, spread their solution and reach consensus among the Bitcoin network nodes with it. First, we define and specify this game. Second, we analytically find its Nash equilibria in the two-player case. We analyze the parameters for which the miners would face the proper incentives to fulfill their function of transaction processors in the current situation. Finally, we study the block space market offer.

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This paper analyzes the timing decisions of pharmaceutical firms to launch a new drug in countries involved in international reference pricing. We show three important features of launch timing when all countries refer to the prices in all other countries and in all previous periods of time. First, there is no withdrawal of drugs in any country and in any period of time. Second, whenever the drug is sold in a country, it is also sold in all countries with larger willingness to pay. Third, there is no strict incentive to delay the launch of a drug in any country. We then show that the first and third results continue to hold when the countries only refer to the prices of a subset of all countries in a transitive way and in any period of time. We also show that the second result continues to hold when the reference is on the last period prices only. Last, we show that the seller's profits increase as the sets of reference countries decrease with respect to inclusion.