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A novel approach to computationally enhance the sampling of molecular crystal structures is proposed and tested. This method is based on the use of extended variables coupled to a Monte Carlo based crystal polymorph generator. Inspired by the established technique of quasi-random sampling of polymorphs using the rigid molecule constraint, this approach represents molecular clusters as extended variables within a thermal reservoir. Polymorph unit-cell variables are generated using pseudo-random sampling. Within this framework, a harmonic coupling between the extended variables and polymorph configurations is established. The extended variables remain fixed during the inner loop dedicated to polymorph sampling, enforcing a stepwise propagation of the extended variables to maintain system exploration. The final processing step results in a polymorph energy landscape, where the raw structures sampled to create the extended variable trajectory are re-optimized without the thermal coupling term. The foundational principles of this approach are described and its effectiveness using both a Metropolis Monte Carlo type algorithm and modifications that incorporate replica exchange is demonstrated. A comparison is provided with pseudo-random sampling of polymorphs for the molecule coumarin. The choice to test a design of this algorithm as relevant for enhanced sampling of crystal structures was due to the obvious relation between molecular structure variables and corresponding crystal polymorphs as representative of the inherent vapor to crystal transitions that exist in nature. Additionally, it is shown that the trajectories of extended variables can be harnessed to extract fluctuation properties that can lead to valuable insights. A novel thermodynamic variable is introduced: the free energy difference between ensembles ofZ′ = 1 andZ′ = 2 crystal polymorphs. 

Byzantine quorum systems provide higher throughput than proof-of-work and incur modest energy consumption. Further, their modern incarnations incorporate personalized and heterogeneous trust. Thus, they are emerging as an appealing candidate for global financial infrastructure. However, since their quorums are not uniform across processes anymore, the properties that they should maintain to support abstractions such as reliable broadcast and consensus are not well-understood. It has been shown that the two properties quorum intersection and availability are necessary. In this paper, we prove that they are not sufficient. We then define the notion of quorum subsumption, and show that the three conditions together are sufficient: we present reliable broadcast and consensus protocols, and prove their correctness for quorum systems that provide the three properties. 

In recent years, many different cryptocurrencies have risen in popularity. Since coins vary in fiat value and functionality, it has become important to securely exchange between them. A common exchange method is hashed timelock contracts (HTLC). However, this method did not support brokerage transactions that allow parties to leverage assets they gain during the transaction. We consider HTLC with brokering. The transaction fees for HTLC is a direct function of the size of the leader set. Thus, brokers are interested in finding the minimum leader set of a given transaction graph. We show that finding the minimum leader set on general transaction graphs with brokering is NP-hard. We then introduce flower transaction graphs, a common type of transaction graphs with brokering, and show that finding the minimum leader set of a flower graph is also NP-hard through a reduction from the knapsack problem.