these are notes from introductory survey lectures given at the institute for studies in theoretical physics and mathematics (ipm), teheran, in 2008 and 2010. we present the definition and the fundamental properties of fomin-zelevinsky’s cluster algebras. then, we introduce quiver representations and show how they can be used to construct cluster variables, which are the canonical generators of ...

We aim to detect all instances of a category in an image and, for each instance, mark the pixels that belong to it. We call this task Simultaneous Detection and Segmentation (SDS). Unlike classical bounding box detection, SDS requires a segmentation and not just a box. Unlike classical semantic segmentation, we require individual object instances. We build on recent work that uses convolutional...

Relational reasoning is often viewed as the pinnacle of human intelligence. Accordingly, one common viewpoint is that learning categories defined by relational regularities is more difficult than learning categories defined by featural regularities. This view is supported by developmental trends in learning. Studies comparing featural and relational category learning in adults also find a featu...

‎in this paper first we define the morphism between geometric spaces in two different types‎. ‎we construct two categories of $uu$ and $l$ from geometric spaces then investigate some properties of the two categories‎, ‎for instance $uu$ is topological‎. ‎the relation between hypergroups and geometric spaces is studied‎. ‎by constructing the category $qh$ of $h_{v}$-groups we answer the question...

Abstract We introduce a general definition for coloured cyclic operads over symmetric monoidal ground category, which has several appealing features. The forgetful functor from to both adjoints, each of is relatively simple. Explicit formulae these adjoints allow us lift the Cisinski–Moerdijk model structure on category enriched in simplicial sets sets.

Past research has shown that variation in the target objects depicting a given spatial relation disrupts the formation of a category representation for that relation. In the current research, we asked whether changing the orientation of the referent frame depicting the spatial relation would also disrupt the formation of a category representation for that relation. Experiments 1 to 3 provided e...

The main result of [Barr (1967)] is that the cohomology of an algebra with respect to the free associate algebra cotriple can be described by the resolution given by U. Shukla in [Shukla (1961)]. That looks like a composite resolution; first an algebra is resolved by means of free modules (over the ground ring) and then this resolution is given the structure of a DG-algebra and resolved by the ...

This paper presents a batch classifier that splits dataset into tree branches depending on the category type. It has been improved from earlier version and fixed mistake in paper. Two important changes have made. The first is to represent each with separate classifier. Each then classifies its own subset of data rows, using input values create centroid also itself. If contains more than one how...

Complete lattices are considered with suitable families of lattice morphisms that provide a structure (L,Φ), useful to characterize ground categories of L-sets by means of powerset operators associated to morphisms of these categories. The construction of ground categories and powerset operators presented here extends and unifies most approaches previously considered, allowing the use of noncri...