Related papers: Mysterious points in keys but not trees
Clusters of galaxies are large gravitationally bound systems which consist of several observable components: hundreds of galaxies, hot gas between the galaxies and sometimes relativistic particles. These components are emitting in different…
Recently it has been conjectured that string theory does not allow for dS vacua or dS extrema. To scrutinize such a conjecture, it is important to study concrete string theory compactifications and spell out their assumptions and potential…
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…
Clifford codes can be understood as a generalization of stabilizer codes. To show the existence of a true Clifford code which is better than any stabilizer code is a well known open problem in the theory of Clifford codes. One of the main…
For any quiver mutation sequence, we define a pair of matrices that describe a fixed point equation of a cluster transformation determined from the mutation sequence. We give an explicit relationship between this pair of matrices and the…
The regularized theories are non-local at the scale of the cutoff, leading so to the usual difficulties of non-local theories. In this work the conservation laws and causality are investigated for classical field theories with multi-cluster…
Given one of an infinite class of supersymmetric quiver gauge theories, string theorists can associate a corresponding toric variety (which is a Calabi-Yau 3-fold) as well as an associated combinatorial model known as a brane tiling. In…
In the context of continuous first-order logic, special attention is often given to theories that are somehow continuous in an 'essential' way. A common feature of such theories is that they do not interpret any infinite discrete…
We define the notion of a weighted unfolding of quivers with real weights, and use this to provide a categorification of mutations of quivers of finite types $H_4$, $H_3$ and $I_2(2n+1)$. In particular, the (un)folding induces a semiring…
Subspace clustering is an important unsupervised clustering approach. It is based on the assumption that the high-dimensional data points are approximately distributed around several low-dimensional linear subspaces. The majority of the…
Let $H$ be a finite dimensional hereditary algebra over an algebraically closed field, and let $\mathcal{C}_{H}$ be the corresponding cluster category. We give a description of the (standard) fundamental domain of $\mathcal{C}_{H} $ in the…
Given a marked surface (S,M) we can add arcs to the surface to create a triangulation, T, of that surface. For each triangulation, T, we can associate a cluster algebra. In this paper we will consider the torus of genus n with two interior…
We give explicit and elementary constructions of the categorical extensions of a torus by the circle and discuss an application to loop group extensions. Examples include maximal tori of simple and simply connected compact Lie groups and…
A new class of rings, the class of left localizable rings, is introduced. A ring $R$ is left localizable if each nonzero element of $R$ is invertible in some left localization $S^{-1}R$ of the ring $R$. Explicit criteria are given for a…
We introduce a new class of self-sustained states, which may exist as single solitons or form multisoliton clusters, in driven passive cylindrical microresonators. Remarkably, such states are stabilized by the radiation they emit, which…
This paper studies a discrete dynamical system belonging to the class of the networks introduced by A.P.~Buslaev. The systems contains a finite set of contours. In any contour, there are cells and a group of particles. This group is called…
Inference of species networks from genomic data under the Network Multispecies Coalescent Model is currently severely limited by heavy computational demands. It also remains unclear how complicated networks can be for consistent inference…
In this paper, we propose a methodology to improvise the technique of deep transfer clustering (DTC) when applied to the less variant data distribution. Clustering can be considered as the most important unsupervised learning problem. A…
We study the cluster algebras arising from cluster tubes with rank bigger than $1$. Cluster tubes are $2-$Calabi-Yau triangulated categories which contain no cluster tilting objects, but maximal rigid objects. Fix a certain maximal rigid…
Clusters of galaxies are often embedded in larger-scale superclusters with dimensions of tens or perhaps even hundreds of Mpc. Observational and theoretical evidence suggest an important connection between cluster properties and their…