Remove-Win: a Design Framework for Conflict-free Replicated Data Collections

Internet-scale distributed systems often replicate data within and across data centers to provide low latency and high availability despite node and network failures. Replicas are required to accept updates without coordination with each other, and the updates are then propagated asynchronously. This brings the issue of conflict resolution among concurrent updates, which is often challenging and error-prone. The Conflict-free Replicated Data Type (CRDT) framework provides a principled approach to address this challenge. This work focuses on a special type of CRDT, namely the Conflict-free Replicated Data Collection (CRDC), e.g. list and queue. The CRDC can have complex and compound data items, which are organized in structures of rich semantics. Complex CRDCs can greatly ease the development of upper-layer applications, but also makes the conflict resolution notoriously difficult. This explains why existing CRDC designs are tricky, and hard to be generalized to other data types. A design framework is in great need to guide the systematic design of new CRDCs. To address the challenges above, we propose the Remove-Win Design Framework. The remove-win strategy for conflict resolution is simple but powerful. The remove operation just wipes out the data item, no matter how complex the value is. The user of the CRDC only needs to specify conflict resolution for non-remove operations. This resolution is destructed to three basic cases and are left as open terms in the CRDC design skeleton. Stubs containing user-specified conflict resolution logics are plugged into the skeleton to obtain concrete CRDC designs. We demonstrate the effectiveness of our design framework via a case study of designing a conflict-free replicated priority queue. Performance measurements also show the efficiency of the design derived from our design framework.Comment: revised after submissio

Entropy fluctuation formulas of fermionic Gaussian states

We study the statistical behaviour of quantum entanglement in bipartite systems over fermionic Gaussian states as measured by von Neumann entropy. The formulas of average von Neumann entropy with and without particle number constrains have been recently obtained, whereas the main results of this work are the exact yet explicit formulas of variances for both cases. For the latter case of no particle number constrain, the results resolve a recent conjecture on the corresponding variance. Different than existing methods in computing variances over other generic state models, the key ingredient in proving the results of this work relies on a new simplification framework. The framework consists of a set of new tools in simplifying finite summations of what we refer to as dummy summation and re-summation techniques. As a byproduct, the proposed framework leads to various new transformation formulas of hypergeometric functions.Comment: 64 pages, 3 figure

Gamma-ray bursts: postburst evolution of fireballs

The postburst evolution of fireballs that produce $\gamma$-ray bursts is studied, assuming the expansion of fireballs to be adiabatic and relativistic. Numerical results as well as an approximate analytic solution for the evolution are presented. Due to adoption of a new relation among $t$, $R$ and $\gamma$ (see the text), our results differ markedly from the previous studies. Synchrotron radiation from the shocked interstellar medium is attentively calculated, using a convenient set of equations. The observed X-ray flux of GRB afterglows can be reproduced easily. Although the optical afterglows seem much more complicated, our results can still present a rather satisfactory approach to observations. It is also found that the expansion will no longer be highly relativistic about 4 days after the main GRB. We thus suggest that the marginally relativistic phase of the expansion should be investigated so as to check the afterglows observed a week or more later.Comment: 17 pages, 4 figures, MNRAS in pres

Impact of template backbone heterogeneity on RNA polymerase II transcription.

Variations in the sugar component (ribose or deoxyribose) and the nature of the phosphodiester linkage (3'-5' or 2'-5' orientation) have been a challenge for genetic information transfer from the very beginning of evolution. RNA polymerase II (pol II) governs the transcription of DNA into precursor mRNA in all eukaryotic cells. How pol II recognizes DNA template backbone (phosphodiester linkage and sugar) and whether it tolerates the backbone heterogeneity remain elusive. Such knowledge is not only important for elucidating the chemical basis of transcriptional fidelity but also provides new insights into molecular evolution. In this study, we systematically and quantitatively investigated pol II transcriptional behaviors through different template backbone variants. We revealed that pol II can well tolerate and bypass sugar heterogeneity sites at the template but stalls at phosphodiester linkage heterogeneity sites. The distinct impacts of these two backbone components on pol II transcription reveal the molecular basis of template recognition during pol II transcription and provide the evolutionary insight from the RNA world to the contemporary 'imperfect' DNA world. In addition, our results also reveal the transcriptional consequences from ribose-containing genomic DNA