We construct closed immersions from initial degenerations of $${{\,\mathrm{Gr}\,}}_{0}(d,n)$$ —the open cell in the Grassmannian $${{\,\mathrm{Gr}\,}}(d,n)$$ given by nonvanishing all Plücker coordinates—to limits thin Schubert cells associated to diagrams induced face poset corresponding tropical linear space. These are isomorphisms when (d, n) equals (2, n), (3, 6) and 7). As an application w...

We determine the set of supports for flat family linear degenerations flag varieties in terms Motzkin combinatorics.

Spinocerebellar tract neurons are inhibited by various sources of input via pathways activated by descending tracts as well as peripheral afferents. Inhibition may be used to modulate transmission of excitatory information forwarded to the cerebellum. However it may also provide information on the degree of inhibition of motoneurons and on the operation of inhibitory premotor neurons. Our aim w...

Purpose of review Here we discuss recent advances regarding the molecular genetic basis of dominantly inherited ataxias. Recent findings Important recent observations include insights into the mechanisms by which expanded polyglutamine causes cerebellar degeneration; new findings regarding how noncoding expansions may cause disease; the discovery that conventional (i.e. nonrepeat) mutations und...

In this paper, the Euler characteristic formula for projective logarithmic minimal degenerations of surfaces with Kodaira dimension zero over a 1-dimensional complex disk is proved under a reasonable assumption and as its application, the singularity of logarithmic minimal degenerations are determined in the abelian or hyperelliptic case. By globalizing this local analysis of singular fibres vi...

In this paper, we prove that degenerations of sequences of Yamabe metrics on 3-manifolds are modeled or described by solutions to the static vacuum Einstein equations. One underlying motivation to understand such degenerations is the question of existence of constant curvature metrics on 3-manifolds, in other words with the geometrization conjecture of Thurston [Th2]. An approach towards resolv...

The authors present a historical review of spinocerebellar ataxia type 3/Machado-Joseph disease (SCA3/MJD), the most common form of spinocerebellar ataxia in Brazil, and consider the high frequency of cases in families from Itajaí, a city on the coast of the state of Santa Catarina with a large population of Portuguese/Azorean descent.

[Purpose] Spinocerebellar ataxia consists of a group of autosomal dominant disorders that cause progressive degeneration, mainly in the cerebellum and its connections. Falls, which are a significant concern of this condition, reduce patients' mobility, deteriorate their health and have physical and social consequences. The aim of this study was to test the effectiveness of a modified protocol f...

Spinocerebellar ataxia type 36 is a late-onset, slowly progressive cerebellar syndrome with motor neuron degeneration that is caused by expansions of a hexanucleotide repeat (GGCCTG) in the noncoding region of NOP56 gene, with a histopathological feature of RNA foci formation in postmortem tissues. Here, we report a cellular model using the spinocerebellar ataxia type 36 patient induced pluripo...

OBJECTIVE To assess the frequency of SCA1 (spinocerebellar ataxia type 1), SCA2, SCA3/MJD (spinocerebellar ataxia type 3/Machado-Joseph disease), SCA6, SCA7, and DRPLA (dentatorubropallidoluysian atrophy) CAG trinucleotide repeat expansions [(CAG)n] among persons diagnosed with hereditary SCA from Chinese families. PATIENTS AND METHODS Spinocerebellar ataxia type 1, SCA2, SCA3/MJD, SCA6, SCA7...