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Complement Submodular Information Measures for Balanced and Robust Data Selection A Proof of a Conjecture on Positive and Negative Square Energies of Unicyclic Graphs Laplacian Spectrum of the Weakly Zero-Divisor Graph of a Finite Commutative Ring An identity for second Eulerian numbers via lattice-point counting $t$-tone edge coloring of graphs Constructing Maximal Bumpless Pipedreams for Double Grothendieck Polynomials Mubayi's Polynomial-Ideal Conjecture and Cover-Ideal Turán Methods Implicit Binarization via Complex Phase Dynamics in Combinatorial Optimization The limits of Schur multipliers in Pólya conversion problems for the $q$-permanent function Universality theorems for generalized splines Framing Triangulations for Arbitrary Integer Flow Polytopes On the Common Generalization of Gentle Algebras and Framed Directed Acyclic Graphs The complexity of frugal digraph homomorphisms Chaotic and periodic behavior of jeu de taquin on infinite Young tableaux Enumerating Pattern Avoiding Parking Functions Incidence toric ideals and three-point functions Unique Winning Opening Move in Three-Row Chomp Strong majority colorings of graphs A Balancing Theorem for Spanning Trees of Rectangular Grid Graphs Spectral radius and edge-disjoint connected factors of graphs New invariants for rank metric codes, with applications to the classification of rank two semifields of order 256 Flexible DP-4-coloring of planar graphs without 4-cycles and intersecting triangles Balanced intersection size distributions in projective planes List Reconstruction Problem with List Size Two Is Dimensionality a Barrier for Retrieval Models? The INIEP: Irreducible and Positive Realizations The number of Pfaffian orientations on punctured polygonally cellulated surfaces Explicit Construction of Polytopes whose Ehrhart Polynomials Realize any Given Sign Pattern Finite-state enumeration of adjacency-constrained 132-avoiding permutations AMDS and quantum AMDS Constacyclic codes of length $4p^ς$ over $\mathbb{F}_{{p}^{m}}$
Proceedings of TDA: Applications of Topological Data Anal...
R. W. R. Darling, John A. Emanuello, Emilie Purvine, Ahmad Ridle · 2022-04-04 · via math.CO updates on arXiv.org

Topological Data Analysis (TDA) is a rigorous framework that borrows techniques from geometric and algebraic topology, category theory, and combinatorics in order to study the "shape" of such complex high-dimensional data. Research in this area has grown significantly over the last several years bringing a deeply rooted theory to bear on practical applications in areas such as genomics, natural language processing, medicine, cybersecurity, energy, and climate change. Within some of these areas, TDA has also been used to augment AI and ML techniques. We believe there is further utility to be gained in this space that can be facilitated by a workshop bringing together experts (both theorists and practitioners) and non-experts. Currently there is an active community of pure mathematicians with research interests in developing and exploring the theoretical and computational aspects of TDA. Applied mathematicians and other practitioners are also present in community but do not represent a majority. This speaks to the primary aim of this workshop which is to grow a wider community of interest in TDA. By fostering meaningful exchanges between these groups, from across the government, academia, and industry, we hope to create new synergies that can only come through building a mutual comprehensive awareness of the problem and solution spaces.