We study minimal degenerations between preprojective modules over wild quivers. Asymptotic properties of such degenerations are studied, with respect to codimension and numbers of indecomposable direct summands. We provide families of minimal disjoint degenerations of arbitrary codimension for almost all wild quivers and show that no such examples exist in the remaining cases.

In this paper we study degenerations of nilpotent Lie algebras. If λ, μ are two points in the variety of nilpotent Lie algebras, then λ is said to degenerate to μ , λ→deg μ , if μ lies in the Zariski closure of the orbit of λ . It is known that all degenerations of nilpotent Lie algebras of dimension n < 7 can be realized via a one-parameter subgroup. We construct degenerations between characte...

3 Type 1: The CAG/Polyglutamine Repeat Diseases 9 3.1 Spinal and Bulbar Muscular Atrophy 9 3.2 Huntington’s Disease 12 3.3 Dentatorubral Pallidoluysian Atrophy 15 3.4 Spinocerebellar Ataxia Type 1 16 3.5 Spinocerebellar Ataxia Type 2 18 3.6 Spinocerebellar Ataxia Type 3/Machado–Joseph Disease 19 3.7 Spinocerebellar Ataxia Type 6 21 3.8 Spinocerebellar Ataxia Type 7 22 3.9 Spinocerebellar Ataxia...

Spinocerebellar ataxia type 3, spinocerebellar ataxia type 6 and Friedreich's ataxia are common hereditary ataxias. Different patterns of atrophy of the cerebellar cortex are well known. Data on cerebellar nuclei are sparse. Whereas cerebellar nuclei have long been thought to be preserved in spinocerebellar ataxia type 6, histology shows marked atrophy of the nuclei in Friedreich's ataxia and s...

We study degenerations of Kummer surfaces associated to certain divisors in Nieto’s quintic threefold and show how they arise from boundary components of a suitable toroidal compactification of the corresponding Siegel modular threefold. The aim of this paper is to study the degenerations of an interesting class of Kummer surfaces in P in terms of degenerations of the corresponding abelian surf...

Retinal degenerations, regardless of the initiating event or gene defect, often result in a loss of photoreceptors. This formal deafferentation of the neural retina eliminates the intrinsic glutamatergic drive of the sensory retina and, perhaps more importantly, removes coordinated Ca++-coupled signaling to the neural retina. As in other central nervous system degenerations, deafferentation act...

Computing all critical points of a monomial on very affine variety is fundamental task in algebraic statistics, particle physics and other fields. The number known as the maximum likelihood (ML) degree. When smooth, it coincides with Euler characteristic. We introduce degeneration techniques that are inspired by soft limits CEGM theory, we answer several questions raised literature. These perta...

Degenerations are defi ned as the gradual deterioration of a tissue or an organ that was previously normal with frequent loss of functional activity. Corneal degenerations are characterized by the deposition of material, thinning of tissue, and vascularization. Contrary to corneal dystrophies, they are not hereditary and could be unilateral. Moreover, because of the continuous exposure to envir...

OBJECTIVE To assess the frequency and clinical features of different types of hereditary spinocerebellar ataxia in Hong Kong. DESIGN Cross-sectional study using a questionnaire and clinical examination, with the majority of the information retrospectively collected. SETTING Three regional hospitals, Hong Kong. PARTICIPANTS All patients with spinocerebellar ataxia that was confirmed by mol...