The Kimura 3-parameter model on a tree of n leaves is one of the most used in phylogenetics. The affine algebraic variety W associated to it is a toric variety. We study its geometry and we prove that it is isomorphic to a geometric quotient of the affine space by a finite group acting on it. As a consequence, we are able to study the singularities of W and prove that the biologically meaningfu...

Kimura’s disease is a very rare chronic inflammatory pathology of unknown etiology. It actually an allergic or autoimmune reaction process involving blood vessels, lymphocytes and eosinophils. We report first case Kimura with cervical localization in 37-year-old male Patient who saw the appearance swelling right parotid region evolving for 2 years. The patient benefited from total parotidectomy...

In the early 1970s, protein electrophoresis was the primary tool geneticists used to discover and measure allelic variation in natural populations. It was a relatively simple and inexpensive technique and, most importantly, it permitted the detection of multiple alleles regardless of polymorphism levels. This was a critical point because before the age of protein electrophoresis, segregating al...

R. Hirota and K. Kimura discovered integrable discretizations of the Euler and the Lagrange tops, given by birational maps. Their method is a specialization to the integrable context of a general discretization scheme introduced by W. Kahan and applicable to any vector field with a quadratic dependence on phase variables. According to a proposal by T. Ratiu, discretizations of the Hirota-Kimura...

OBJECTIVE To investigate the expressions of interleukin (IL)-21 and phosphorylated extracellular signal regulated kinase 1/2 (pERK1/2) in Kimura disease (KD) and to correlate the findings with clinical and prognostic variables. METHODS Immunohistochemical analysis of IL-21 and pERK1/2 was performed in 18 cases of KD and five gender- and age-matched control samples. Clinical data were extracte...