An influential hypothesis from the last decade proposed that regions within the right inferior frontal cortex of the human brain were dedicated to supporting response inhibition. There is growing evidence, however, to support an alternative model, which proposes that neural areas associated with specific inhibitory control tasks co-exist as common network mechanisms, supporting diverse cognitive processes. This meta-analysis of 225 studies comprising 323 experiments examined the common and distinct neural correlates of cognitive processes for response inhibition, namely interference resolution, action withholding, and action cancellation. Activation coordinates for each subcategory were extracted using multilevel kernel density analysis (MKDA). The extracted activity patterns were then mapped onto the brain functional network atlas to derive the common (i.e., process-general) and distinct (i.e., domain-oriented) neural network correlates of these processes. Independent of the task types, activation of the right hemispheric regions (inferior frontal gyrus, insula, median cingulate, and paracingulate gyri) and superior parietal gyrus was common across the cognitive processes studied. Mapping the activation patterns to a brain functional network atlas revealed that the fronto-parietal and ventral attention networks were the core neural systems that were commonly engaged in different processes of response inhibition. Subtraction analyses elucidated the distinct neural substrates of interference resolution, action withholding, and action cancellation, revealing stronger activation in the ventral attention network for interference resolution than action inhibition. On the other hand, action withholding/cancellation primarily engaged the fronto-striatal circuit. Overall, our results suggest that response inhibition is a multidimensional cognitive process involving multiple neural regions and networks for coordinating optimal performance. This finding has significant implications for the understanding and assessment of response inhibition.Electronic supplementary materialThe online version of this article (doi:10.1007/s00429-017-1443-x) contains supplementary material, which is available to authorized users.

A method is developed for systematically constructing trigonometric and rational solutions of the Yang-Baxter equation using the representation theory of quantum supergroups. New quantum R-matrices are obtained by applying the method to the vector representations of quantum osp (1/2) and gl (m/n).

A category of Brauer diagrams, analogous to Turaev's tangle category, is introduced, and a presentation of the category is given; specifically, we prove that seven relations among its four generating homomorphisms suffice to deduce all equations among the morphisms. Full tensor functors are constructed from this category to the category of tensor representations of the orthogonal group O(V ) or the symplectic group Sp(V ) over any field of characteristic zero. The first and second fundamental theorems of invariant theory for these classical groups are generalised to the category theoretic setting. The major outcome is that we obtain new presentations for the endomorphism algebras of the module V ⊗r . These are obtained by appending to the standard presentation of the Brauer algebra of degree r one additional relation. This relation stipulates the vanishing of an element of the Brauer algebra which is quasi-idempotent, and which we describe explicitly both in terms of diagrams and algebraically. In the symplectic case, if dim V = 2n, the element is precisely the central idempotent in the Brauer subalgebra of degree n + 1, which corresponds to its trivial representation. Since this is the Brauer algebra of highest degree which is semisimple, our generator is an exact analogue for the Brauer algebra of the Jones idempotent of the Temperley-Lieb algebra. In the orthogonal case the additional relation is also a quasi-idempotent in the integral Brauer algebra. Both integral and quantum analogues of these results are given, the latter of which involve the BMW algebras.

The cohomology groups of Lie superalgebras and, more generally, of ε Lie algebras, are introduced and investigated. The main emphasis is on the case where the module of coefficients is non-trivial. Two general propositions are proved, which help to calculate the cohomology groups. Several examples are included to show the peculiarities of the super case. For L = sl(1|2), the cohomology groups H 1 (L, V ) and H 2 (L, V ), with V a finite-dimensional simple graded L-module, are determined, and the result is used to show that H 2 (L, U (L)) (with U (L) the enveloping algebra of L) is trivial. This implies that the superalgebra U (L) does not admit of any non-trivial formal deformations (in the sense of Gerstenhaber). Garland's theory of universal central extensions of Lie algebras is generalized to the case of ε Lie algebras.q-alg/9701037