Diversification Across Mining Pools: Optimal Mining Strategies under PoW

Mining is a central operation of all proof-of-work (PoW) based cryptocurrencies. The vast majority of miners today participate in "mining pools" instead of "solo mining" in order to lower risk and achieve a more steady income. However, this rise of participation in mining pools negatively affects the decentralization levels of most cryptocurrencies. In this work, we look into mining pools from the point of view of a miner: We present an analytical model and implement a computational tool that allows miners to optimally distribute their computational power over multiple pools and PoW cryptocurrencies (i.e. build a mining portfolio), taking into account their risk aversion levels. Our tool allows miners to maximize their risk-adjusted earnings by diversifying across multiple mining pools which enhances PoW decentralization. Finally, we run an experiment in Bitcoin historical data and demonstrate that a miner diversifying over multiple pools, as instructed by our model/tool, receives a higher overall Sharpe ratio (i.e. average excess reward over its standard deviation/volatility).Comment: 13 pages, 16 figures. Presented at WEIS 201

Chiral extensions of the WZNW phase space, Poisson-Lie symmetries and groupoids

The chiral WZNW symplectic form $\Omega^{\rho}_{chir}$ is inverted in the general case. Thereby a precise relationship between the arbitrary monodromy dependent 2-form appearing in $\Omega^{\rho}_{chir}$ and the exchange r-matrix that governs the Poisson brackets of the group valued chiral fields is established. The exchange r-matrices are shown to satisfy a new dynamical generalization of the classical modified Yang-Baxter (YB) equation and Poisson-Lie (PL) groupoids are constructed that encode this equation analogously as PL groups encode the classical YB equation. For an arbitrary simple Lie group G, exchange r-matrices are found that are in one-to-one correspondence with the possible PL structures on G and admit them as PL symmetries

Leptogenesis for Pedestrians

During the process of thermal leptogenesis temperature decreases by about one order of magnitude while the baryon asymmetry is generated. We present an analytical description of this process so that the dependence on the neutrino mass parameters becomes transparent. In the case of maximal CP asymmetry all decay and scattering rates in the plasma are determined by the mass M_1 of the decaying heavy Majorana neutrino, the effective light neutrino mass tilde{m}_1 and the absolute mass scale bar{m} of the light neutrinos. In the mass range suggested by neutrino oscillations, m_{sol} \simeq 8*10^{-3} eV \lesssim \tilde{m}_1 \lesssim m_{atm} \simeq 5*10^{-2} eV, leptogenesis is dominated just by decays and inverse decays. The effect of all other scattering processes lies within the theoretical uncertainty of present calculations. The final baryon asymmetry is dominantly produced at a temperature T_B which can be about one order of magnitude below the heavy neutrino mass M_1. We also derive an analytical expression for the upper bound on the light neutrino masses implied by successful leptogenesis.Comment: 55 pages, 14 figures include

An Improved Calculation of the Non-Gaussian Halo Mass Function

The abundance of collapsed objects in the universe, or halo mass function, is an important theoretical tool in studying the effects of primordially generated non-Gaussianities on the large scale structure. The non-Gaussian mass function has been calculated by several authors in different ways, typically by exploiting the smallness of certain parameters which naturally appear in the calculation, to set up a perturbative expansion. We improve upon the existing results for the mass function by combining path integral methods and saddle point techniques (which have been separately applied in previous approaches). Additionally, we carefully account for the various scale dependent combinations of small parameters which appear. Some of these combinations in fact become of order unity for large mass scales and at high redshifts, and must therefore be treated non-perturbatively. Our approach allows us to do this, and to also account for multi-scale density correlations which appear in the calculation. We thus derive an accurate expression for the mass function which is based on approximations that are valid over a larger range of mass scales and redshifts than those of other authors. By tracking the terms ignored in the analysis, we estimate theoretical errors for our result and also for the results of others. We also discuss the complications introduced by the choice of smoothing filter function, which we take to be a top-hat in real space, and which leads to the dominant errors in our expression. Finally, we present a detailed comparison between the various expressions for the mass functions, exploring the accuracy and range of validity of each.Comment: 28 pages, 13 figures; v2: text reorganized and some figured modified for clarity, results unchanged, references added. Matches version published in JCA

Seesaw geometry and leptogenesis

The representation of the seesaw orthogonal matrix in the complex plane establishes a graphical correspondence between neutrino mass models and geometrical configurations, particularly useful to study relevant aspects of leptogenesis. We first derive the CP asymmetry bound for hierarchical heavy neutrinos and then an expression for the effective leptogenesis phase, determining the conditions for maximal phase and placing a lower bound on the phase suppression for generic models. Reconsidering the lower bounds on the lightest right-handed (RH) neutrino mass M_1 and on the reheating temperature T_reh, we find that models where one of the two heavier neutrino masses is dominated by the lightest right-handed (RH) neutrinos, typically arising from connections with quark masses, undergo both phase suppression and strong wash-out such that M_1 (T_reh)\gtrsim 10^{11} (10^{10}) GeV. The window 10^9 GeV \lesssim M_1,T_reh \lesssim 10^{10}GeV is accessible only for a class of models where m_1 is dominated by the lightest RH neutrino, with no straightforward connections with quark masses. Within this class we describe a new scenario of thermal leptogenesis where the baryon asymmetry of the Universe is generated by the decays of the second lightest RH neutrino, such that the lower bound on M_1 disappears and is replaced by a lower bound on M_2. Interestingly, the final asymmetry is independent on the initial conditions. We also discuss the validity of the approximation of hierarchical heavy neutrinos in a simple analytical way.Comment: 48 pages, 11 figures; v2: typos corrected; added 1 figure, references, footnotes, more details at the end of 5.1 and in Section 7; to appear on NP

Finite Element Method Modeling of Sensible Heat Thermal Energy Storage with Innovative Concretes and Comparative Analysis with Literature Benchmarks

energie

Regular Languages Definable by Lindström Quantifiers

In our main result, we establish a formal connection between Lindström quantifiers with respect to regular languages and the double semidirect product of finite monoids with a distinguished set of generators. We use this correspondence to characterize the expressive power of Lindström quantifiers associated with a class of regular languages