Dimer models and cluster categories of Grassmannians

We associate a dimer algebra A to a Postnikov diagram D (in a disk) corresponding to a cluster of minors in the cluster structure of the Grassmannian Gr(k, n). We show that A is isomorphic to the endomorphism algebra of a corresponding Cohen-Macaulay module T over the algebra B used to categorify the cluster structure of Gr(k, n) by Jensen-King-Su. It follows that B can be realised as the boundary algebra of A, that is, the subalgebra eAe for an idempotent e corresponding to the boundary of the disk. The construction and proof uses an interpretation of the diagram D, with its associated plabic graph and dual quiver (with faces), as a dimer model with boundary. We also discuss the general surface case, in particular computing boundary algebras associated to the annulus

Cluster algebras in algebraic Lie theory

We survey some recent constructions of cluster algebra structures on coordinate rings of unipotent subgroups and unipotent cells of Kac-Moody groups. We also review a quantized version of these results.Comment: Invited survey; to appear in Transformation Group

The geometry of Brauer graph algebras and cluster mutations.

In this paper we establish a connection between ribbon graphs and Brauer graphs. As a result, we show that a compact oriented surface with marked points gives rise to a unique Brauer graph algebra up to derived equivalence. In the case of a disc with marked points we show that a dual construction in terms of dual graphs exists. The rotation of a diagonal in an m-angulation gives rise to a Whitehead move in the dual graph, and we explicitly construct a tilting complex on the related Brauer graph algebras reflecting this geometrical move

The application of rules in morphology, syntax and number processing: a case of selective deficit of procedural or executive mechanisms?: Deficit of procedural or executive mechanisms

International audienceDeclarative memory is a long-term store for facts, concepts and words. Procedural memory subserves the learning and control of sensorimotor and cognitive skills, including the mental grammar. In this study, we report a single-case study of a mild aphasic patient who showed procedural deficits in the presence of preserved declarative memory abilities. We administered several experiments to explore rule application in morphology, syntax and number processing. Results partly support the differentiation between declarative and procedural memory. Moreover, the patient's performance varied according to the domain in which rules were to be applied, which underlines the need for more fine-grained distinctions in cognition between procedural rules

Priming Picture Naming with a Semantic Task: An fMRI Investigation

Prior semantic processing can enhance subsequent picture naming performance, yet the neurocognitive mechanisms underlying this effect and its longevity are unknown. This functional magnetic resonance imaging study examined whether different neurological mechanisms underlie short-term (within minutes) and long-term (within days) facilitation effects from a semantic task in healthy older adults. Both short- and long-term facilitated items were named significantly faster than unfacilitated items, with short-term items significantly faster than long-term items. Region of interest results identified decreased activity for long-term facilitated items compared to unfacilitated and short-term facilitated items in the mid-portion of the middle temporal gyrus, indicating lexical-semantic priming. Additionally, in the whole brain results, increased activity for short-term facilitated items was identified in regions previously linked to episodic memory and object recognition, including the right lingual gyrus (extending to the precuneus region) and the left inferior occipital gyrus (extending to the left fusiform region). These findings suggest that distinct neurocognitive mechanisms underlie short- and long-term facilitation of picture naming by a semantic task, with long-term effects driven by lexical-semantic priming and short-term effects by episodic memory and visual object recognition mechanisms

Independent Component Analysis of the Effect of L-dopa on fMRI of Language Processing

L-dopa, which is a precursor for dopamine, acts to amplify strong signals, and dampen weak signals as suggested by previous studies. The effect of L-dopa has been demonstrated in language studies, suggesting restriction of the semantic network. In this study, we aimed to examine the effect of L-dopa on language processing with fMRI using Independent Component Analysis (ICA). Two types of language tasks (phonological and semantic categorization tasks) were tested under two drug conditions (placebo and L-dopa) in 16 healthy subjects. Probabilistic ICA (PICA), part of FSL, was implemented to generate Independent Components (IC) for each subject for the four conditions and the ICs were classified into task-relevant source groups by a correlation threshold criterion. Our key findings include: (i) The highly task-relevant brain regions including the Left Inferior Frontal Gyrus (LIFG), Left Fusiform Gyrus (LFUS), Left Parietal lobe (LPAR) and Superior Temporal Gyrus (STG) were activated with both L-dopa and placebo for both tasks, and (ii) as compared to placebo, L-dopa was associated with increased activity in posterior regions, including the superior temporal area (BA 22), and decreased activity in the thalamus (pulvinar) and inferior frontal gyrus (BA 11/47) for both tasks. These results raise the possibility that L-dopa may exert an indirect effect on posterior regions mediated by the thalamus (pulvinar)

The neural correlates of picture naming facilitated by auditory repetition

Background: Overt repetition of auditorily presented words can facilitate picture naming performance in both unimpaired speakers and individuals with word retrieval difficulties, but the underlying neurocognitive mechanisms and longevity of such effects remain unclear. This study used functional magnetic resonance imaging to examine whether different neurological mechanisms underlie short-term (within minutes) and long-term (within days) facilitation effects from an auditory repetition task in healthy older adults