Expanding the differential diagnosis of inherited neuropathies with non-uniform conduction: Andermann syndrome

Uniform conduction slowing has been considered a characteristic of inherited demyelinating neuropathies. We present an 18-year-old girl, born from first cousins, that presented a late motor and psychological development, cerebellar ataxia, facial diplegia, abnormal eye movement, scoliosis, and corpus callosum agenesis, whose compound muscle action potentials were slowed and dispersed. A mutation was found on KCC3 gene, confirming Andermann syndrome, a disease that must be included in the differential diagnosis of inherited neuropathies with non-uniform conduction slowing.

Kurzweil integral for Riesz space-valued functions: Uniform convergence theorem

Our objective here is to prove that the uniform convergence of a sequence of Kurzweil integrable functions implies the convergence of the sequence formed by its corresponding integrals.

Weak quasi-randomness for uniform hypergraphs

We study quasi-random properties of k-uniform hypergraphs. Our central notion is uniform edge distribution with respect to large vertex sets. We will find several equivalent characterisations of this property and our work can be viewed as an extension of the well known Chung-Graham-Wilson theorem for quasi-random graphs. Moreover, let K(k) be the complete graph on k vertices and M(k) the line graph of the graph of the k-dimensional hypercube. We will show that the pair of graphs (K(k),M(k)) has the property that if the number of copies of both K(k) and M(k) in another graph G are as expected in the random graph of density d, then G is quasi-random (in the sense of the Chung-Graham-Wilson theorem) with density close to d. (C) 2011 Wiley Periodicals, Inc. Random Struct. Alg., 40, 1-38, 2012