Papers by Umar Islambekov
We establish locality estimates, known as Lieb-Robinson bounds, for the Toda lattice. In contrast... more We establish locality estimates, known as Lieb-Robinson bounds, for the Toda lattice. In contrast to harmonic models, the Lieb-Robinson velocity for these systems do depend on the initial condition. Our results also apply to the entire Toda as well as the Kac-van Moerbeke hierarchy. Under suitable assumptions, our methods also yield a finite velocity for certain perturbations of these systems.
Role of Local Geometry in Robustness of Power Grid Networks
2018 IEEE Global Conference on Signal and Information Processing (GlobalSIP)
We introduce a novel approach to study robustness of a power grid network employing the tools of ... more We introduce a novel approach to study robustness of a power grid network employing the tools of topological data analysis (TDA). This approach not only enables one to incorporate intrinsic network properties such as electrical conductance but more importantly also offers a systematic and comprehensive framework to study the role of topology in its functionality and robustness. This is achieved by viewing the network as a weighted graph, equipping it with a nested simplicial complex structure and extracting topological summaries in the form of the Betti numbers and persistent diagrams. These summaries are then used to characterize network vulnerability under critical conditions such as targeted attacks.
2019 IEEE International Conference on Data Mining (ICDM)
With emergence of blockchain technologies and the associated cryptocurrencies, such as Bitcoin, u... more With emergence of blockchain technologies and the associated cryptocurrencies, such as Bitcoin, understanding network dynamics behind Blockchain graphs has become a rapidly evolving research direction. Unlike other financial networks, such as stock and currency trading, blockchain based cryptocurrencies have the entire transaction graph accessible to the public (i.e., all transactions can be downloaded and analyzed). A natural question is then to ask whether the dynamics of the transaction graph impacts the price of the underlying cryptocurrency. We show that standard graph features such as degree distribution of the transaction graph may not be sufficient to capture network dynamics and its potential impact on fluctuations of Bitcoin price. In contrast, the new graph associated topological features computed using the tools of persistent homology, are found to exhibit a high utility for predicting Bitcoin price dynamics. Using the proposed persistent homology-based techniques, we offer a new elegant, easily extendable and computationally light approach for graph representation learning on Blockchain.
Proceedings of the 2020 SIAM International Conference on Data Mining
The Blockchain technology and, in particular blockchainbased cryptocurrencies, offer us informati... more The Blockchain technology and, in particular blockchainbased cryptocurrencies, offer us information that has never been seen before in the financial world. In contrast to fiat currencies, all transactions of crypto-currencies and cryptotokens are permanently recorded on distributed ledgers and are publicly available. This allows us to construct a transaction graph and to assess not only its organization but to glean relationships between transaction graph properties and crypto price dynamics. The goal of this paper is to facilitate our understanding on horizons and limitations of what can be learned on crypto-tokens from local topology and geometry of the Ethereum transaction network whose even global network properties remain scarcely explored. By introducing novel tools based on Topological Data Analysis and Functional Data Depth into Blockchain Data Analytics, we show that Ethereum network (one of the most popular blockchains for creating new crypto-tokens) can provide critical insights on price changes of crypto-tokens that are otherwise largely inaccessible with conventional data sources and traditional analytic methods.
Environmetrics
We introduce a novel geometry-oriented methodology, based on the emerging tools of topological da... more We introduce a novel geometry-oriented methodology, based on the emerging tools of topological data analysis, into the change-point detection framework. The key rationale is that change points are likely to be associated with changes in geometry behind the data-generating process. While the applications of topological data analysis to change-point detection are potentially very broad, in this paper, we primarily focus on integrating topological concepts with the existing nonparametric methods for change-point detection. In particular, the proposed new geometry-oriented approach aims to enhance detection accuracy of distributional regime shift locations. Our simulation studies suggest that integration of topological data analysis with some existing algorithms for change-point detection leads to consistently more accurate detection results. We illustrate our new methodology in application to the two closely related environmental time series data sets-ice phenology of the Lake Baikal and the North Atlantic Oscillation indices, in a research query for a possible association between their estimated regime shift locations.
Environmetrics
This paper presents a new clustering algorithm for space-time data based on the concepts of topol... more This paper presents a new clustering algorithm for space-time data based on the concepts of topological data analysis and in particular, persistent homology. Employing persistent homology-a flexible mathematical tool from algebraic topology used to extract topological information from data-in unsupervised learning is an uncommon and a novel approach. A notable aspect of this methodology consists in analyzing data at multiple resolutions which allows to distinguish true features from noise based on the extent of their persistence. We evaluate the performance of our algorithm on synthetic data and compare it to other well-known clustering algorithms such as K-means, hierarchical clustering and DBSCAN. We illustrate its application in the context of a case study of water quality in the Chesapeake Bay.
Uploads
Papers by Umar Islambekov