Results on the niteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups. Calculations of the cohomology classes of some nite crossed modules are given, using crossed complex methods.

Crossed cerebellar diaschisis (CCD) describes a depression of oxidative metabolism glucose and blood flow in the cerebellum secondary to a supratentorial lesion in the contralateral cerebral hemisphere. PET/MR has the potential to become a powerful tool for demonstrating and imaging intracranial lesions .We herein report 3 cases of CCD imaging using a tri-modality PET/CT–MR setup for investigat...

The well-known notion of crossed module of groups is raised in this paper to the categorical level supported by the theory of categorical groups. We construct the cokernel of a categorical crossed module and we establish the universal property of this categorical group. We also prove a suitable 2-dimensional version of the kernelcokernel lemma for a diagram of categorical crossed modules. We th...

This paper presents the idea that the life cycle of an ontology is highly impacted as a result of the process of reusing it for building another ontology. One of the more important results of the experiment presented is how the different activities to be carried out during the development of a specific ontology may involve performing other types of activities on other ontologies already built o...

For n ≥ 4, we describe Artin’s braid group on n strings as a crossed module over itself. In particular, we interpret the braid relations as crossed module structure relations. Subject classification: Primary: 20F36 57M05 57M20 57M25; Secondary: 18D50 18G55 20C08 55P48

Background and Purpose—Ever since the seminal description of ataxic hemiparesis contralateral to a pontine lesion by Miller-Fisher, the question of why contralesional crossing pontocerebellar fibers do not more frequently produce ipsilesional hemiataxia was raised. The few cases of “quadrataxic hemiparesis” or bilateral leg ataxia remain exceptions. Summary of Case—We report an even more unusua...

OBJECTIVE To report two cases of right crossed non-fused renal ectopia diagnosed in male patients about 30 years of age who arrived to emergency centres with symptoms of renal colic. METHODS We report two cases of male patients who arrived to an emergency centre complaining of colic lumbar pain. Crossed renal ectopia was finally revealed by means of intravenous urogram after several analytica...

Crossed complexes are shown to have an algebra sufficiently rich to model the geometric inductive definition of simplices, and so to give a purely algebraic proof of the Homotopy Addition Lemma (HAL) for the boundary of a simplex. This leads to the fundamental crossed complex of a simplicial set. The main result is a normalisation theorem for this fundamental crossed complex, analogous to the u...

Things should be as simple as possiblèand no simpler', so they say. This paper is about simplifying a construct in Ruby, to reduce the complexity of the algebra without sacriicing expressive power. Ruby, for which Mary Sheeran is largely responsible, is a language of relations and a collection of rules { equalities { for algebraic transformation of expressions in that language. The presentation...

Keratoconus is a non-inflammatory corneal dystrophy in which the cornea deforms due to thinning and protrusion. The biomechanical strength of the cornea depends on the lamellar organization of the collagen fibers that comprise the corneal stroma, regulated by an interconnecting network of proteoglycans. Although the pathogenesis of keratoconus remains unclear, it appears that a primary event le...