Cerebellar ataxias (CAs) represent a group of autosomal dominant and recessive neurodegenerative disorders affecting cerebellum with or without spinal cord. Overall, CAs have preponderance for tandem nucleotide repeat expansions as an etiological factor (10 TREs explain nearly 30–40% of ataxia cohort globally). The experience of 10 years of common genetic ataxia subtypes for ≈5600 patients’ referrals (Pan‐India) received at a single center is shared herein. Frequencies (in %, n) of SCA types and FRDA in the sample cohort are observed as follows: SCA12 (8.6%, 490); SCA2 (8.5%, 482); SCA1 (4.8%, 272); SCA3 (2%, 113); SCA7 (0.5%, 28); SCA6 (0.1%, 05); SCA17 (0.1%, 05), and FRDA (2.2%, 127). A significant amount of variability in TRE lengths at each locus is observed, we noted presence of biallelic expansion, co‐occurrence of SCA‐subtypes, and the presence of premutable normal alleles. The frequency of mutated GAA‐FRDA allele in healthy controls is 1/158 (0.63%), thus an expected FRDA prevalence of 1:100 000 persons. The data of this study are relevant not only for clinical decision making but also for guidance in direction of genetic investigations, transancestral comparison of genotypes, and lastly provide insight for policy decision for the consideration of SCAs under rare disease category.

Wavelet frames have gained considerable popularity during the past decade, primarily due to their substantiated applications in diverse and widespread fields of engineering and science. In this article, we obtain the characterization of nonhomogeneous wavelet frames and nonhomogeneous dual wavelet frames in a Sobolev spaces on a local field of positive characteristic by means of a pair of equations.

In this paper, we introduce a new type of inner product called a-inner product or Bracket inner product on local fields. We define a-orthogonality and prove some results and Bessel inequality in this concern. Finally, we conclude by introducing the notion of a-frame.