arXiv subjects
Publications and source records attributed to Mainak Ghosh.
In this paper, we extend Ocneanu's theory of connections on graphs to define a 2-category whose 0-cells are tracial Bratteli diagrams, and whose 1-cells are generalizations of unitary connections. We show that this 2-category admits an embedding into the 2-category of hyperfinite von Neumann algebras, generalizing fundamental results from subfactor theory to a 2-categorical setting.
We have witnessed a boosted demand for graph analytics at Twitter in recent years, and graph analytics has become one of the key parts of Twitter's large-scale data analytics and machine learning for driving engagement, serving the most relevant content, and promoting healthier conversations. However, infrastructure for graph analytics has historically not been an area of investment at Twitter, resulting in a long timeline and huge engineering effort for each project to deal with graphs at the Twitter scale. How do we build a unified graph analytics user experience to fulfill modern data analytics on various graph scales spanning from thousands to hundreds of billions of vertices and edges? To bring fast and scalable graph analytics capability into production, we investigate the challenges we are facing in large-scale graph analytics at Twitter and propose a unified graph analytics platform for efficient, scalable, and reliable graph analytics across on-premises and cloud, to fulfill the requirements of diverse graph use cases and challenging scales. We also conduct quantitative benchmarking on Twitter's production-level graph use cases between popular graph analytics frameworks to certify our solution.
The demand for data analytics has been consistently increasing in the past years at Twitter. In order to fulfill the requirements and provide a highly scalable and available query experience, a large-scale in-house SQL system is heavily relied on. Recently, we evolved the SQL system into a hybrid-cloud SQL federation system, compliant with Twitter's Partly Cloudy strategy. The hybrid-cloud SQL federation system is capable of processing queries across Twitter's data centers and the public cloud, interacting with around 10PB of data per day. In this paper, the design of the hybrid-cloud SQL federation system is presented, which consists of query, cluster, and storage federations. We identify challenges in a modern SQL system and demonstrate how our system addresses them with some important design decisions. We also conduct qualitative examinations and summarize instructive lessons learned from the development and operation of such a SQL system.
With the advent of the Big Data era, it is usually computationally expensive to calculate the resource usages of a SQL query with traditional DBMS approaches. Can we estimate the cost of each query more efficiently without any computation in a SQL engine kernel? Can machine learning techniques help to estimate SQL query resource utilization? The answers are yes. We propose a SQL query cost predictor service, which employs machine learning techniques to train models from historical query request logs and rapidly forecasts the CPU and memory resource usages of online queries without any computation in a SQL engine. At Twitter, infrastructure engineers are maintaining a large-scale SQL federation system across on-premises and cloud data centers for serving ad-hoc queries. The proposed service can help to improve query scheduling by relieving the issue of imbalanced online analytical processing (OLAP) workloads in the SQL engine clusters. It can also assist in enabling preemptive scaling. Additionally, the proposed approach uses plain SQL statements for the model training and online prediction, indicating it is both hardware and software-agnostic. The method can be generalized to broader SQL systems and heterogeneous environments. The models can achieve 97.9\% accuracy for CPU usage prediction and 97\% accuracy for memory usage prediction.
We prove an extension of the Kato-Saito class field theory for smooth projective schemes over a finite field to schemes with singularities. As an application, we obtain Bloch's formula for the Chow groups of 0-cycles on such schemes. We identify the Chow group of 0-cycles on a normal projective scheme over an algebraically closed field to the Suslin homology of its regular locus. Our final result is a Roitman torsion theorem for smooth quasi-projective schemes over algebraically closed fields. This completes the missing $p$-torsion part in the torsion theorem of Spiess and Szamuely.
A novel low cost, near equi-atomic alloy comprising of Al, Cu, Fe and Mn is synthesized using arc-melting technique. The cast alloy possesses a dendritic microstructure where the dendrites consist of disordered FCC and ordered FCC phases. The inter-dendritic region is comprised of ordered FCC phase and spinodally decomposed BCC phases. A Cu segregation is observed in the inter-dendritic region while dendritic region is rich in Fe. The bulk hardness of the alloy is ~ 380 HV, indicating significant yield strength.