Precision medicine aims to overcome the traditional one-model-fits-the-whole-population approach that is unable detect heterogeneous disease patterns and make accurate personalized predictions. Heterogeneity particularly relevant for patients with complications of type 2 diabetes, including diabetic kidney (DKD). We focus on a DKD longitudinal dataset, aiming find specific subgroups characteris...

The purpose of this paper is to give an explicit formula for the number of non-isomorphic cluster-tilted algebras of type An, by counting the mutation class of any quiver with underlying graph An. It will also follow that if T and T ′ are cluster-tilting objects in a cluster category C, then EndC(T ) is isomorphic to EndC(T ) if and only if T = τ T . 1. Cluster-tilted algebras The cluster categ...

A novel study is presented that explores the effect that learning internally organized categories has on the ability to subsequently discriminate category members. The results demonstrate the classic categorical perception effect whereby discrimination of stimuli that belong to different categories is improved following training, while the ability to discriminate stimuli belonging to the same c...

We introduce the continuous Frobenius category. This category is constructed using representations of the circle over a discrete valuation ring. We show that it is Krull-Schmidt with one indecomposable object for each pair of not necessarily distinct points on the circle. By putting restrictions on these points we obtain various subquotient categories with good properties. The main purpose of o...

Given a certain triangulation of punctured surface with boundary, we construct new triangulated without punctures which covers it. This is naturally equipped an action group order two, and its quotient by this recovers the original surface. We show that acts on quivers potentials associated to surfaces, their Ginzburg dg algebras are skew each other, up Morita equivalence. then use these result...

We present a categorification of four mutation finite cluster algebras by the cluster category of the category of coherent sheaves over a weighted projective line of tubular weight type. Each of these cluster algebras which we call tubular is associated to an elliptic root system. We show that via a cluster character the cluster variables are in bijection with the positive real Schur roots asso...

Text categorization is an interesting problem in artificial intelligence that gets more and more attention from researchers and industry. One central problem of text categorization is the selection of a good feature set. We propose a novel method for term selection for each category based on segmenting the documents belonging to a category into cohesive sub-parts that define the subtopics of th...

in this survey, we give an overview over some aspects of the set of tilting objects in an $m-$cluster category, with focus on those properties which are valid for all $m geq 1$. we focus on the following three combinatorial aspects: modeling the set of tilting objects using arcs in certain polygons, the generalized assicahedra of fomin and reading, and colored quiver mutation.

We introduce a new category C, which we call the cluster category, obtained as a quotient of the bounded derived category D of the module category of a finite-dimensional hereditary algebra H over a field. We show that, in the simply-laced Dynkin case, C can be regarded as a natural model for the combinatorics of the corresponding Fomin–Zelevinsky cluster algebra. In this model, the tilting obj...