Acquiring a second language phonetic contrast involves learning new sound categories from examples. Consequently, research in category learning should have important implications for research examining how a foreign sound contrast is acquired. The current project is an initial attempt to apply work in category learning to work in second language sound acquisition. Here, I advance that a cluster...

Let k be a field and Q a finite quiver without oriented cycles. Let kQ be the path algebra of Q and mod kQ the category of k-finite-dimensional right kQ-modules. The cluster category CQ was introduced in [1] (for general Q) and, independently, in [4] (for Q of type An). It is defined as the orbit category of the bounded derived category D(mod kQ) under the action of the automorphism Σ−1 ◦ S, wh...

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 show that in a triangulated category, the existence of a cluster tilting object often implies that the homomorphism groups are bounded in size. This holds for the stable module category of a selfinjective algebra, and as a corollary we recover a theorem of Erdmann and Holm. We then apply our result to Calabi-Yau triangulated categories, in particular stable categories of maximal Cohen-Macaul...

Abstract We continue the work started in parts (I) and (II) of this series. In paper, we classify which continuous quivers type A are derived equivalent. Next, define new ${\mathcal {C}(A_{{\mathbb {R}},S})}$ , call weak cluster category. It is a triangulated category, it does not have structure but has weaker notion “cluster theory.” show that original category [15] localization theories to be...

We study the ion density and temperature in the predipolarization and postdipolarization plasma sheets in the Earth's magnetotail using 9 years (2001-2009) of Cluster data. For our study we selected cases when Cluster observed dipolarization fronts (DFs) with an earthward plasma flow greater than 150km/s. We perform a statistical study of the temperature and density variations during the DF cro...

Buan, Marsh and Reiten proved that if a cluster-tilting object T in a cluster category C associated to an acyclic quiver Q satisfies certain conditions with respect to the exchange pairs in C, then the denominator in its reduced form of every cluster variable in the cluster algebra associated to Q has exponents given by the dimension vector of the corresponding module over the endomorphism alge...

BACKGROUND We hypothesized that heterogeneity exists within the Global Initiative for Chronic Obstructive Lung Disease (GOLD) 1 spirometric category and that different subgroups could be identified within this GOLD category. METHODS Pre-randomization study participants from two clinical trials were symptomatic/asymptomatic GOLD 1 chronic obstructive pulmonary disease (COPD) patients and healt...

We introduce continuous Frobenius categories. These are topological categories which are constructed using representations of the circle over a discrete valuation ring. We show that they are 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 Frobenius subcategories. The main pur...

Our mental representation of object categories is hierarchically organized, and our rapid and seemingly effortless categorization ability is crucial for our daily behavior. Here, we examine responses of a large number (>600) of neurons in monkey inferior temporal (IT) cortex with a large number (>1,000) of natural and artificial object images. During the recordings, the monkeys performed a pass...