Related papers: Cluster structures and subfans in scattering diagr…
We extend the derived Algebraic bordism of Lowrey and Sch\"urg to a bivariant theory in the sense of Fulton and MacPherson, and establish some of its basic properties. As a special case, we obtain a completely new theory of cobordism rings…
Motivated by applications in social network community analysis, we introduce a new clustering paradigm termed motif clustering. Unlike classical clustering, motif clustering aims to minimize the number of clustering errors associated with…
Associated to a convex integral polygon $N$ is a cluster integrable system $\mathcal X_N$ constructed from the dimer model. We compute the group $G_N$ of symmetries of $\mathcal X_N$, called the (2-2) cluster modular group, showing that it…
A cluster variety of Fock and Goncharov is a scheme constructed by gluing split algebraic tori, called seed tori, via birational gluing maps called mutations. In quantum theory, the ring of functions on seed tori are deformed to…
Clustering in image analysis is a central technique that allows to classify elements of an image. We describe a simple clustering technique that uses the method of similarity matrices. We expand upon recent results in spectral analysis for…
Spectral clustering is widely used in practice due to its flexibility, computational efficiency, and well-understood theoretical performance guarantees. Recently, spectral clustering has been studied to find balanced clusters under…
Using a measure of clustering derived from the nearest neighbour distribution and the void probability function we are able to distinguish between regular and clustered structures. With an example we show that regularity is a property of a…
The understanding of clustering aspects at the ground state of nuclei and in fast rotating ones within the framework of covariant density functional theory has been reviewed and reanalyzed. The appearance of many exotic nuclear shapes in…
Mixture model-based frameworks are very popular for statistical inference in clustering. While convenient for producing probabilistic estimates of cluster assignments and uncertainty, they are prone to misspecification, which can lead to…
In this paper, we investigate community detection in networks in the presence of node covariates. In many instances, covariates and networks individually only give a partial view of the cluster structure. One needs to jointly infer the full…
We study the homogeneous coordinate rings of partial flag varieties and Grassmannians in their Pl\"ucker embeddings and exhibit an embedding of the former into the latter. Both rings are cluster algebras and the embedding respects the…
Biological and social systems consist of myriad interacting units. The interactions can be represented in the form of a graph or network. Measurements of these graphs can reveal the underlying structure of these interactions, which provides…
This is an introduction to some aspects of Fomin-Zelevinsky's cluster algebras and their links with the representation theory of quivers and with Calabi-Yau triangulated categories. It is based on lectures given by the author at summer…
We establish the analog for real spherical varieties of the Scattering Theorem of Sakellaridis and Venkatesh (\cite{SV}, Theorem 7.3.1) for p-adic spherical varieties. We use properties of the Harish-Chandra homomorphism of Knop for…
We analyze the structure diagram for binary clusters of Lennard-Jones particles by means of a global optimization approach for a large range of cluster sizes, compositions and interaction energies and present a publicly accessible database…
Based on the construction of polytope functions and several results about them in [LP], we take a deep look on their mutation behaviors to find a link between a face of a polytope and a sub-cluster algebra of the corresponding cluster…
We continue the study of quivers with potentials and their representations initiated in the first paper of the series. Here we develop some applications of this theory to cluster algebras. As shown in the "Cluster algebras IV" paper, the…
We investigate the topological properties of dynamical states evolving on periodic oriented graphs. This evolution, that encodes the scattering processes occurring at the nodes of the graph, is described by a single-step global operator, in…
Relationship between agents can be conveniently represented by graphs. When these relationships have different modalities, they are better modelled by multilayer graphs where each layer is associated with one modality. Such graphs arise…
We show the existence of quasi-cluster $\mathcal{A}$-structures and cluster Poisson structures on moduli stacks of sheaves with singular support in the alternating strand diagram of grid plabic graphs by studying the microlocal parallel…