On the Profitability of Selfish Blockchain Mining Under Consideration of Ruin

Mining blocks on a blockchain equipped with a proof of work consensus protocol is well known to be resource consuming. A miner bears the operational cost, mainly electricity consumption and IT gear, of mining and is compensated by a capital gain when a block is discovered. This paper aims at quantifying the profitability of mining when the possible event of ruin is also considered. This is done by formulating a tractable stochastic model and using tools from applied probability and analysis, including the explicit solution of a certain type of advanced functional differential equation. The expected profit at a future time point is determined for the situation when the miner follows the protocol as well as when the miner withholds blocks. The obtained explicit expressions allow us to analyze the sensitivity with respect to the different model components and to identify conditions under which selfish mining is a strategic advantage.

The Ties that Bind: Kymlicka and the Problem of Political Unity in Multination States

As asserted by Will Kymlicka, the recognition and accommodation of national minorities leads to a dilemma. Indeed, if denying them these rights can contribute to their willingness to secede, allowing them to self-govern can also ultimately lead to the weakening of their ties with the state in which they are integrated. This tension well described in Kymlicka’s Multicultural Citizenship and in his later works remains nonetheless without an explicit solution. This text addresses this question by suggesting that the dialogical dynamic behind the recognition and accommodation of national minorities hides a purely political patriotism stemming from the neo-republican tradition that is complementary to the nationalist sense of attachment that members of national minorities will inevitably come to feel toward their societal culture.

A note on the axisymmetric diffusion equation

We consider the explicit solution to the axisymmetric diffusion equation. We recast the solution in the form of a Mellin inversion formula, and outline a method to compute a formula for \(u(r,t)\) as a series using the Cauchy residue theorem. As a consequence, we are able to represent the solution to the axisymmetric diffusion equation as a rapidly converging series. doi:10.1017/S1446181121000110

On a class of q -orthogonal polynomials and the q -Riemann–Hilbert problem

We give an explicit solution of a q -Riemann–Hilbert problem that arises in the theory of orthogonal polynomials, prove that it is unique and deduce several properties. In particular, we describe the asymptotic behaviour of zeros in the limit as the degree of the polynomial approaches infinity.