Strong eventual consistency of the collaborative editing framework WOOT

Commutative Replicated Data Types (CRDTs) are a promising new class of data structures for large-scale shared mutable content in applications that only require eventual consistency. The WithOut Operational Transforms (WOOT) framework is the first CRDT for collaborative text editing introduced by Oster et al. (In: Conference on Computer Supported Cooperative Work (CSCW). ACM, New York, pp 259–268, 2006a). Its eventual consistency property was verified only for a bounded model to date. While the consistency of many other previously published CRDTs had been shown immediately with their publication, the property for WOOT remained open for 14 years. We use a novel approach identifying a previously unknown sort-key based protocol that simulates the WOOT framework to show its consistency. We formalize the proof using the Isabelle/HOL proof assistant to machine-check its correctness.

Strong Time-Consistency of a Core: An Application to the Pollution Control Problem in Eastern Siberia

In this paper, we study the (strong) time-consistency property of the core for a linear-quadratic differential game of pollution control with nonzero absorption coefficient and real values of the model parameters. The values of parameters are evaluated based on the data for the largest aluminum enterprises of Eastern Siberia region of the Russian Federation for the year 2016. The obtained results are accompanied with illustrations.

Issues in clustering algorithm consistency in fixed dimensional spaces. Some solutions for k-means

Kleinberg introduced an axiomatic system for clustering functions. Out of three axioms, he proposed, two (scale invariance and consistency) are concerned with data transformations that should produce the same clustering under the same clustering function. The so-called consistency axiom provides the broadest range of transformations of the data set. Kleinberg claims that one of the most popular clustering algorithms, k-means does not have the property of consistency. We challenge this claim by pointing at invalid assumptions of his proof (infinite dimensionality) and show that in one dimension in Euclidean space the k-means algorithm has the consistency property. We also prove that in higher dimensional space, k-means is, in fact, inconsistent. This result is of practical importance when choosing testbeds for implementation of clustering algorithms while it tells under which circumstances clustering after consistency transformation shall return the same clusters. Two types of remedy are proposed: gravitational consistency property and dataset consistency property which both hold for k-means and hence are suitable when developing the mentioned testbeds.

Time Consistency of the Mean-Risk Problem

When dealing with dynamic optimization problems, time consistency is a desirable property as it allows one to solve the problem efficiently through a backward recursion. The mean-risk problem is known to be time inconsistent when considered in its scalarized form. However, when left in its original bi-objective form, it turns out to satisfy a more general time consistency property that seems better suited to a vector optimization problem. In “Time Consistency of the Mean-Risk Problem,” Kováĉova and Rudloff introduce a set-valued version of the famous Bellman principle and show that the bi-objective mean-risk problem does satisfy it. Then, the upper image, a set that contains the efficient frontier on its boundary, recurses backward in time. Kováĉova and Rudloff present conditions under which this recursion can be exploited directly to compute a solution in the spirit of dynamic programming. This opens the door for a new branch in mathematics: dynamic multivariate programming.

Strong and Efficient Consistency with Consistency-aware Durability

We introduce consistency-aware durability or C ad , a new approach to durability in distributed storage that enables strong consistency while delivering high performance. We demonstrate the efficacy of this approach by designing cross-client monotonic reads , a novel and strong consistency property that provides monotonic reads across failures and sessions in leader-based systems; such a property can be particularly beneficial in geo-distributed and edge-computing scenarios. We build O rca , a modified version of ZooKeeper that implements C ad and cross-client monotonic reads. We experimentally show that O rca provides strong consistency while closely matching the performance of weakly consistent ZooKeeper. Compared to strongly consistent ZooKeeper, O rca provides significantly higher throughput (1.8--3.3×) and notably reduces latency, sometimes by an order of magnitude in geo-distributed settings. We also implement C ad in Redis and show that the performance benefits are similar to that of C ad ’s implementation in ZooKeeper.

New far-field extrapolation method for the computation of electric fields

The extrapolation of the electric field is studied theoretically both in frequency domain and time domain. Combining Gauss’s law with the approximation method in engineering, two new formulas for the scattering field calculation are derived from different logical ideas based on Stratton–Chu formula. The consistency property of the derived formulas is investigated, and the third formula for the scattering field calculation is further obtained. Finally, the time-domain extrapolation is discussed based on the formulas, followed by a simple numerical example. The results obtained are characterized by a simple form and intuitive physical meaning, and are helpful to calculate certain engineering problems.

Maximizing the Minimal Satisfaction—Characterizations of Two Proportional Values

A class of solutions are introduced by lexicographically minimizing the complaint of coalitions for cooperative games with transferable utility. Among them, the nucleolus is an important representative. From the perspective of measuring the satisfaction of coalitions with respect to a payoff vector, we define a family of optimal satisfaction values in this paper. The proportional division value and the proportional allocation of non-separable contribution value are then obtained by lexicographically maximizing two types of satisfaction criteria, respectively, which are defined by the lower bound and the upper bound of the core from the viewpoint of optimism and pessimism respectively. Correspondingly, we characterize these two proportional values by introducing the equal minimal satisfaction property and the associated consistency property. Furthermore, we analyze the duality of these axioms and propose more approaches to characterize these two values on basis of the dual axioms.

IDP-Core: Novel Cooperative Solution for Differential Games

IDP-core is a new cooperative solution for dynamic and differential games. A novel approach of constructing solutions for dynamic and differential games was employed in which the time consistency property was used as the main axiom property for the cooperative solution. Another new and important approach used for constructing IDP-core is the IDP dominance, which allows to select undominated imputation distribution procedures and construct the cooperative solution or imputation set. This approach shows the potential of using the time consistency property as the main axiom for solutions in various fields such as Social Choice and Mechanism Design. The overall procedure for defining the cooperative solution is also new since IDP-core was constructed using imputation distribution procedures but not by using imputations directly.

A principled methodology for comparing relatedness measures for clustering publications

There are many different relatedness measures, based for instance on citation relations or textual similarity, that can be used to cluster scientific publications. We propose a principled methodology for evaluating the accuracy of clustering solutions obtained using these relatedness measures. We formally show that the proposed methodology has an important consistency property. The empirical analyses that we present are based on publications in the fields of cell biology, condensed matter physics, and economics. Using the BM25 text-based relatedness measure as the evaluation criterion, we find that bibliographic coupling relations yield more accurate clustering solutions than direct citation relations and cocitation relations. The so-called extended direct citation approach performs similarly to or slightly better than bibliographic coupling in terms of the accuracy of the resulting clustering solutions. The other way around, using a citation-based relatedness measure as evaluation criterion, BM25 turns out to yield more accurate clustering solutions than other text-based relatedness measures.