Related papers: The Euler Characteristic: A General Topological De…
Topological Data Analysis has grown in popularity in recent years as a way to apply tools from algebraic topology to large data sets. One of the main tools in topological data analysis is persistent homology. This paper uses undergraduate…
Characterization of materials via electron micrographs is an important and challenging task in several materials processing industries. Classification of electron micrographs is complex due to the high intra-class dissimilarity, high…
We represent excursion sets of smooth random fields as unions of a topological basis consisting of a sequence of simply and multiply connected compact subsets of the underlying manifold. The associated coefficients, which are non-negative…
A theorem due to D. Bernstein states that Euler characteristic of a hypersurface defined by a polynomial f in (C\{0})^n is equal (upto a sign) to n! times volume of the Newton polyhedron of f. This result is related to algebaric torus…
We have initiated the study of topology of the space of coverings on grid domains. The space has the following constraint: while all the covering agents can move freely (we allow overlapping) on the domain, their union must cover the whole…
The variational properties of the scalar so--called ``Universal'' equations are reviewed and generalised. In particular, we note that contrary to earlier claims, each member of the Euler hierarchy may have an explicit field dependence. The…
We demonstrate that graphs embedded on surfaces are a powerful and practical tool to generate, characterize and simulate networks with a broad range of properties. Remarkably, the study of topologically embedded graphs is non-restrictive…
Data intensive research requires the support of appropriate datasets. However, it is often time-consuming to discover usable datasets matching a specific research topic. We formulate the dataset discovery problem on an attributed…
Named Entity Recognition seeks to extract substrings within a text that name real-world objects and to determine their type (for example, whether they refer to persons or organizations). In this survey, we first present an overview of…
Entity resolution (ER) is a key data integration problem. Despite the efforts in 70+ years in all aspects of ER, there is still a high demand for democratizing ER - humans are heavily involved in labeling data, performing feature…
Large datasets represented by multidimensional data point clouds often possess non-trivial distributions with branching trajectories and excluded regions, with the recent single-cell transcriptomic studies of developing embryo being notable…
Let $V$ be a closed subscheme of a projective space $\mathbb{P}^n$. We give an algorithm to compute the Chern-Schwartz-MacPherson class, Euler characteristic and Segre class of $ V$. The algorithm can be implemented using either symbolic or…
Topological Data Analysis (TDA) is an emergent field that aims to discover topological information hidden in a dataset. TDA tools have been commonly used to create filters and topological descriptors to improve Machine Learning (ML)…
The resolution of the P vs. NP problem, a cornerstone in computational theory, remains elusive despite extensive exploration through mathematical logic and algorithmic theory. This paper takes a novel approach by integrating information…
Each complex network (or class of networks) presents specific topological features which characterize its connectivity and highly influence the dynamics of processes executed on the network. The analysis, discrimination, and synthesis of…
Many works in the recent literature introduce semantic mapping methods that use CNNs (Convolutional Neural Networks) to recognize semantic properties in images. The types of properties (eg.: room size, place category, and objects) and their…
The shape of objects is an important source of visual information in a wide range of applications. One of the core challenges of shape quantification is to ensure that the extracted measurements remain invariant to transformations that…
This research addresses a new tool for data analysis known as Topological Data Analysis TDA It underlies an area of Mathematics known as Combinatorial Algebra or more recently Algebraic Topology which through making strong use of…
A graph theoretic approach is proposed for object shape representation in a hierarchical compositional architecture called Compositional Hierarchy of Parts (CHOP). In the proposed approach, vocabulary learning is performed using a hybrid…
This article studies a large, general class of orthogonal polytopes which we may call "generic orthotopes". These objects emerged from a desire to represent a Coxeter complex by an orthogonal polytope that is particularly nice with respect…