1 citations · 1 across the 10 of their papers we have counts for
16 papers
The K-theory of uniform Roe algebras for coarse structures generated by finite-rank free abelian subgroups
Charles Fanning, Mehmet Emin Aktas
For a uniformly locally finite coarse space , the uniform Roe algebra is the operator norm closure of the controlled operators on . The -theory of unifo…
On the Spectral Synthesis of Lipschitz Vectorizations of Persistence Diagrams
Charles Fanning, Mehmet Emin Aktas
Persistence diagrams are fundamental descriptors in topological data analysis. Many statistical and machine learning methods require persistence diagrams to be mapped into vector s…
Square Metric Spaces
Charles Fanning, Mehmet Aktas
Product decompositions of metric spaces are built from coordinate maps, but these maps are not part of the resulting metric space. We recover this missing coordinate structure thro…
Higher-order Persistence Diagrams
Charles Fanning, Mehmet Aktas
Many topological data analysis (TDA) pipelines compute large collections of persistence diagrams, yet vectorizations and kernel methods discard the rank-induced implication relatio…
Random Walks on Virtual Persistence Diagrams
Charles Fanning, Mehmet Aktas
In the uniformly discrete case of virtual persistence diagram groups , we construct a translation-invariant heat semigroup. The kernels are supported on a countable subgrou…
Topology-guided Hypergraph Transformer Network: Unveiling Structural Insights for Improved Representation
Khaled Mohammed Saifuddin, Mehmet Emin Aktas, Esra Akbas
Hypergraphs, with their capacity to depict high-order relationships, have emerged as a significant extension of traditional graphs. Although Graph Neural Networks (GNNs) have remar…
Hypergraph Classification via Persistent Homology
Mehmet Emin Aktas, Thu Nguyen, Rakin Riza +2
Persistent homology is a mathematical tool used for studying the shape of data by extracting its topological features. It has gained popularity in network science due to its applic…
Liars are more influential: Effect of Deception in Influence Maximization on Social Networks
Mehmet Emin Aktas, Esra Akbas, Ashley Hahn
Detecting influential users, called the influence maximization problem on social networks, is an important graph mining problem with many diverse applications such as information p…
Identifying critical higher-order interactions in complex networks
Mehmet Emin Aktas, Thu Nguyen, Sidra Jawaid +2
Information diffusion on networks is an important concept in network science observed in many situations such as information spreading and rumor controlling in social networks, dis…
Hypergraph Laplacians in Diffusion Framework
Mehmet Emin Aktas, Esra Akbas
Networks are important structures used to model complex systems where interactions take place. In a basic network model, entities are represented as nodes, and interaction and rela…
Graph Classification via Heat Diffusion on Simplicial Complexes
Mehmet Emin Aktas, Esra Akbas
In this paper, we study the graph classification problem in vertex-labeled graphs. Our main goal is to classify the graphs comparing their higher-order structures thanks to heat di…
Persistence Homology of Networks: Methods and Applications
Mehmet Emin Aktas, Esra Akbas, Ahmed El Fatmaoui
Information networks are becoming increasingly popular to capture complex relationships across various disciplines, such as social networks, citation networks, and biological netwo…
Network Embedding: on Compression and Learning
Esra Akbas, Mehmet Aktas
Recently, network embedding that encodes structural information of graphs into a vector space has become popular for network analysis. Although recent methods show promising perfor…
A polynomial invariant for plane curve complements: Krammer polynomials
Mehmet Emin Aktas, Serdar Cellat, Hubeyb Gurdogan
We use the Krammer representation of the braid group in Libgober's invariant and construct a new multivariate polynomial invariant for curve complements: Krammer polynomial. We sho…
Dessins d'Enfants of Trigonal Curves
Mehmet Emin Aktas
In this paper, we focus on properties of dessins d'enfants associated to trigonal curves. Degtyarev studied dessins d'enfants to compute braid monodromies and fundamental groups of…
Computing the Braid Monodromy of Completely Reducible -gonal Curves
Mehmet Aktas, Esra Akbas
Braid monodromy is an important tool for computing invariants of curves and surfaces. In this paper, the \emph{rectangular braid diagram (RBD)} method is proposed to compute the br…