A Game-theoretic Approach for Provably-Uniform Random Number Generation in Decentralized Networks

Many protocols in distributed computing rely on a source of randomness, usually called a random beacon, both for their applicability and security. This is especially true for proof-of-stake blockchain protocols in which the next miner or set of miners have to be chosen randomly and each party's likelihood to be selected is in proportion to their stake in the cryptocurrency. Current random beacons used in proof-of-stake protocols, such as Ouroboros and Algorand, have two fundamental limitations: Either (i)~they rely on pseudorandomness, e.g.~assuming that the output of a hash function is uniform, which is a widely-used but unproven assumption, or (ii)~they generate their randomness using a distributed protocol in which several participants are required to submit random numbers which are then used in the generation of a final random result. However, in this case, there is no guarantee that the numbers provided by the parties are uniformly random and there is no incentive for the parties to honestly generate uniform randomness. Most random beacons have both limitations. In this thesis, we provide a protocol for distributed generation of randomness. Our protocol does not rely on pseudorandomness at all. Similar to some of the previous approaches, it uses random inputs by different participants to generate a final random result. However, the crucial difference is that we provide a game-theoretic guarantee showing that it is in everyone's best interest to submit uniform random numbers. Hence, our approach is the first to incentivize honest behavior instead of just assuming it. Moreover, the approach is trustless and generates unbiased random numbers. It is also tamper-proof and no party can change the output or affect its distribution. Finally, it is designed with modularity in mind and can be easily plugged into existing distributed protocols such as proof-of-stake blockchains.Comment: 36 pages excluding reference. Game-theoretic Randomness for Proof-of-Stake in MARBLE (2023

The standard cohomology of regular Courant algebroids

For any regular Courant algebroid $E$ over a smooth manifold $M$ with characteristic distribution $F$ and ample Lie algebroid $A_E$, we prove that there exists a canonical homological vector field on the graded manifold $A_E[1] \oplus (TM/F)^\ast[2]$ such that the associated dg manifold $\mathcal{M}_E$, which we call the minimal model of the Courant algebroid $E$, encodes all cohomological data of $E$. Thereby, the standard cohomology $H^\bullet_{\operatorname{st}}(E)$ of $E$ can be identified with the cohomology $H^\bullet(\mathcal{M}_E)$ of the function space on $\mathcal{M}_E$. To compute it, we find a natural transgression map [d_T] \colon H^{\bullet}_{\operatorname{CE}}\big(A_E; S^{\diamond}(TM/F[-2])\big) \to H^{\bullet+3}_{\CE}\big(A_E; S^{\diamond-1}(TM/F[-2])\big) from which we construct a spectral sequence which converges to $H^\bullet_{\operatorname{st}}(E)$. Moreover, we give applications to generalized exact Courant algebroids and those arising from regular Lie algebroids .Comment: 41 pages; the main body is rewritten; typos remove

Geographic structure of Chinese dialects: a computational dialectometric approach

Dialect classification is a long-standing issue in Chinese dialectology. Although various theories of Chinese dialect regions have been proposed, most have been limited by similar methodological issues, especially due to their reliance on the subjective analysis of dialect maps both individually and in the aggregate, as well as their focus on phonology over syntax and vocabulary. Consequently, we know relatively little about the geolinguistic underpinnings of Chinese dialect variation. Following a review of previous research in this area, this article presents a theory of Chinese dialect regions based on the first large-scale quantitative analysis of the data from the Linguistic Atlas of Chinese Dialects, which was collected between 2000 and 2008, providing the most up-to-date picture of the full Chinese dialect landscape. We identify and map a hierarchy of 10 major Chinese dialect regions, challenging traditional accounts. In addition, we propose a new theory of Chinese dialect formation to account for our findings

Scheme for sharing classical information via tripartite entangled states

We investigate schemes for quantum secret sharing and quantum dense coding via tripartite entangled states. We present a scheme for sharing classical information via entanglement swapping using two tripartite entangled GHZ states. In order to throw light upon the security affairs of the quantum dense coding protocol, we also suggest a secure quantum dense coding scheme via W state in analogy with the theory of sharing information among involved users.Comment: 4 pages, no figure. A complete rewrritten vession, accepted for publication in Chinese Physic

Effect of Samarium doping on the nucleation of fcc-Aluminum in undercooled liquids

The effect of Sm doping on the fcc-Al nucleation was investigated in Al-Sm liquids with low Sm concentrations (xSm) with molecular dynamics simulations. The nucleation in the moderately undercooled liquid is achieved by the recently developed persistent-embryo method. Systematically computing the nucleation rate with different xSm (xSm=0%, 1%, 2%, 3%, 5%) at 700 K, we found Sm dopant reduces the nucleation rate by up to 25 orders of magnitudes with only 5% doping concentration. This effect is mostly associated with the increase in the free energy barrier with a minor contribution from suppression of the attachment to the nucleus caused by Sm doping.Comment: 4 figure