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Determination of the nature of the dynamical state of a system as a function of its parameters is an important problem in the study of dynamical systems. This problem becomes harder in experimental systems where the obtained data is…
Motivated by the proliferation of mobile devices, we consider a basic form of the ubiquitous problem of time-delay estimation (TDE), but with communication constraints between two non co-located sensors. In this setting, when joint…
Persistent Homology (PH) is a fundamental tool in computational topology, designed to uncover the intrinsic geometric and topological features of data across multiple scales. Originating within the broader framework of Topological Data…
In this work, we develop a pipeline that associates Persistence Diagrams to digital data via the most appropriate filtration for the type of data considered. Using a grid search approach, this pipeline determines optimal representation…
In this paper, we present a new approach for analyzing gene expression data that builds on topological characteristics of time series. Our goal is to identify cell cycle regulated genes in micro array dataset. We construct a point cloud out…
In semiconductor manufacturing, wafer map defect pattern provides critical information for facility maintenance and yield management, so the classification of defect patterns is one of the most important tasks in the manufacturing process.…
We extend the notion of the distance to a measure from Euclidean space to probability measures on general metric spaces as a way to do topological data analysis in a way that is robust to noise and outliers. We then give an efficient way to…
Deep topological data analysis (TDA) offers a principled framework for capturing structural invariants such as connectivity and cycles that persist across scales, making it a natural fit for anomaly segmentation (AS). Unlike thresholdbased…
Topological Data Analysis (TDA) allows us to extract powerful topological and higher-order information on the global shape of a data set or point cloud. Tools like Persistent Homology or the Euler Transform give a single complex description…
On account of a greater need for understanding the complexity of time series like physiological time series, financial time series, and many more that enter into picture for their inculpation with real-world problems, several complexity…
Persistent homology (PH) is one of the main methods used in Topological Data Analysis. An active area of research in the field is the study of appropriate notions of PH representatives, which allow to interpret the meaning of the…
Topological Data Analysis (TDA) involves techniques of analyzing the underlying structure and connectivity of data. However, traditional methods like persistent homology can be computationally demanding, motivating the development of neural…
This paper explores the enhancement of solution diversity in evolutionary algorithms (EAs) for the maximum matching problem, concentrating on complete bipartite graphs and paths. We adopt binary string encoding for matchings and use Hamming…
In this work we use the persistent homology method, a technique in topological data analysis (TDA), to extract essential topological features from the data space and combine them with deep learning features for classification tasks. In TDA,…
Topological phases are unique states of matter which support non-local excitations which behave as particles with fractional statistics. A universal characterization of gapped topological phases is provided by the topological entanglement…
Topological Data Analysis (TDA) has emerged as a powerful tool for extracting meaningful features from complex data structures, driving significant advancements in fields such as neuroscience, biology, machine learning, and financial…
A primary hypothesis that drives scientific and engineering studies is that data has structure. The dominant paradigms for describing such structure are statistics (e.g., moments, correlation functions) and signal processing (e.g.,…
For a given permutation $\tau$, let $P_N^{\tau}$ be the uniform probability distribution on the set of $N$-element permutations $\sigma$ that avoid the pattern $\tau$. For $\tau=\mu_k:=123\cdots k$, we consider $P_N^{\mu_k}(\sigma_I=J)$…
Topological Data Analysis (TDA) is an approach to handle with big data by studying its shape. A main tool of TDA is the persistence diagram, and one can use it to compare data sets. One approach to learn on the similarity between two…
Grid topology and line parameters are essential for grid operation and planning, which may be missing or inaccurate in distribution grids. Existing data-driven approaches for recovering such information usually suffer from ignoring 1) input…