Mixingale Estimation Function for SPDEs with Random Sampling

We study the mixingale estimation function estimator of the drift parameter in the stochastic partial differential equation when the process is observed at the arrival times of a Poisson process. We use a two stage estimation procedure. We first estimate the intensity of the Poisson process. Then we substitute this estimate in the estimation function to estimate the drift parameter. We obtain the strong consistency and the asymptotic normality of the mixingale estimation function estimator.

"HAVE A GREAT, POSITIVE, BEAUTIFUL DAY!": GOOD MORNING MEMES AND THE CROSS-CULTURAL ARTICULATION OF VALUES

This paper adopts the lens of social media rituals to study a new incarnation of ritualized greetings: good morning memes. These are a popular yet under-studied form of ritualized greeting posted every morning by social media users across the global. Such memes feature text with a wish for the incoming day paired with elements such as flowers, food or animals. In this paper, I focus on the ways in which these memes construct values, broadly defined as guiding beliefs about the desirable. My analysis is based on a sample of 414 good morning memes posted to Instagram in English and Italian. I conducted a content analysis examining the posts for content (protagonist and background), the main values conveyed (e.g. achievement and self-efficacy, happiness and positivity), and their stance (serious or ironic). A preliminary analysis revealed strong consistency in the dataset. Overall, good morning memes embed the general mandate for “politeness” that infuses the communicative genre of greetings, transposing it in the meme format through impersonal messages and a saccharine aesthetic. Furthermore, the memes voice a shared core of values, namely: “Happiness and positivity” and “performative kindness.” However, the English and Italian subsets also diverge in significant ways. The English language version of the meme upholds the value of “achievement and self-efficacy,” possibly because of the influence of American values on globalized social media content. Conversely, the Italian-language version of the meme uses humor to pushback against the idea that the morning is a time to be energetic and productive.

On the Strong Law of Large Numbers for Nonnegative Random Variables. With an Application in Survey Sampling

Strong laws of large numbers with arbitrary norming sequences for nonnegative not necessarily independent random variables are obtained. From these results we establish, among other things, stability results for weighted sums of nonnegative random variables. A survey sampling application is provided on strong consistency of the Horvitz--Thompson estimator and the ratio estimator.

Higher-Order Spectral Clustering for Geometric Graphs

The present paper is devoted to clustering geometric graphs. While the standard spectral clustering is often not effective for geometric graphs, we present an effective generalization, which we call higher-order spectral clustering. It resembles in concept the classical spectral clustering method but uses for partitioning the eigenvector associated with a higher-order eigenvalue. We establish the weak consistency of this algorithm for a wide class of geometric graphs which we call Soft Geometric Block Model. A small adjustment of the algorithm provides strong consistency. We also show that our method is effective in numerical experiments even for graphs of modest size.

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.

Balanced Leader Distribution Algorithm in Kubernetes Clusters

Container-based virtualization is becoming a de facto way to build and deploy applications because of its simplicity and convenience. Kubernetes is a well-known open-source project that provides an orchestration platform for containerized applications. An application in Kubernetes can contain multiple replicas to achieve high scalability and availability. Stateless applications have no requirement for persistent storage; however, stateful applications require persistent storage for each replica. Therefore, stateful applications usually require a strong consistency of data among replicas. To achieve this, the application often relies on a leader, which is responsible for maintaining consistency and coordinating tasks among replicas. This leads to a problem that the leader often has heavy loads due to its inherent design. In a Kubernetes cluster, having the leaders of multiple applications concentrated in a specific node may become a bottleneck within the system. In this paper, we propose a leader election algorithm that overcomes the bottleneck problem by evenly distributing the leaders throughout nodes in the cluster. We also conduct experiments to prove the correctness and effectiveness of our leader election algorithm compared with a default algorithm in Kubernetes.