Abstract:
Decreased mitochondrial function plays a pivotal role in the pathogenesis of type 2 diabetes mellitus (T2DM). Recently, it was reported that mitochondrial DNA (mtDNA) haplogroups confer genetic susceptibility to T2DM in Koreans and Japanese. Particularly, mtDNA haplogroup N9a is associated with a decreased risk of T2DM, whereas haplogroups D5 and F are associated with an increased risk. To examine functional consequences of these haplogroups without being confounded by the heterogeneous nuclear genomic backgrounds of different subjects, we constructed transmitochondrial cytoplasmic hybrid (cybrid) cells harboring each of the three haplogroups (N9a, D5, and F) in a background of a shared nuclear genome. We compared the functional consequences of the three haplogroups using cell-based assays and gene expression microarrays. Cell-based assays did not detect differences in mitochondrial functions among the haplogroups in terms of ATP generation, reactive oxygen species production, mitochondrial membrane potential, and cellular dehydrogenase activity. However, differential expression and clustering analyses of microarray data revealed that the three haplogroups exhibit a distinctive nuclear gene expression pattern that correlates with their susceptibility to T2DM. Pathway analysis of microarray data identified several differentially regulated metabolic pathways. Notably, compared to the T2DM-resistant haplogroup N9a, the T2DM-susceptible haplogroup F showed down-regulation of oxidative phosphorylation and up-regulation of glycolysis. These results suggest that variations in mtDNA can affect the expression of nuclear genes regulating mitochondrial functions or cellular energetics. Given that impaired mitochondrial function caused by T2DM-associated mtDNA haplogroups is compensated by the nuclear genome, we speculate that defective nuclear compensation, under certain circumstances, might lead to the development of T2DM.

Abstract:
Next-generation sequencing (NGS) has enabled the high-throughput discovery of germline and somatic mutations. However, NGS-based variant detection is still prone to errors, resulting in inaccurate variant calls. Here, we categorized the variants detected by NGS according to total read depth (TD) and SNP quality (SNPQ), and performed Sanger sequencing with 348 selected non-synonymous single nucleotide variants (SNVs) for validation. Using the SAMtools and GATK algorithms, the validation rate was positively correlated with SNPQ but showed no correlation with TD. In addition, common variants called by both programs had a higher validation rate than caller-specific variants. We further examined several parameters to improve the validation rate, and found that strand bias (SB) was a key parameter. SB in NGS data showed a strong difference between the variants passing validation and those that failed validation, showing a validation rate of more than 92% (filtering cutoff value: alternate allele forward [AF]≥20 and AF<80 in SAMtools, SB<–10 in GATK). Moreover, the validation rate increased significantly (up to 97–99%) when the variant was filtered together with the suggested values of mapping quality (MQ), SNPQ and SB. This detailed and systematic study provides comprehensive recommendations for improving validation rates, saving time and lowering cost in NGS analyses.

Abstract:
For a negative integer $k$ let $J_k$ be the space of modified Jacobi forms of weight $k$ and index 0 on $\mathrm{SL}_2(\mathbb{Z})$. For each positive integer $m$ we consider certain subspace $J_k^{m}$ of $J_k$ which satisfies $J_k=\cup_{m=1}^\infty J_k^m$. By observing a relation between coefficients of the Fourier development of a modified Jacobi form we show that $J_k^m$ is finite-dimensional.

Abstract:
By modifying a slash operator of index zero we define \textit{modified Jacobi forms} of \textit{index zero}. Such forms play a role of generating nearly holomorphic modular forms of integral weight. Furthermore, by observing a relation between the coefficients of Fourier development of a modified Jacobi form we construct a family of finite-dimensional subspaces.

Abstract:
By a change of variables we obtain new $y$-coordinates of elliptic curves. Utilizing these $y$-coordinates as modular functions, together with the elliptic modular function, we generate the modular function fields of level $N\geq3$. Furthermore, by means of the singular values of the $y$-coordinates we construct the ray class fields modulo $N$ over imaginary quadratic fields as well as normal bases of these ray class fields.

Abstract:
We will generalize Osburn's work about a congruence for traces defined in terms of Hauptmodul associated to certain genus zero groups of higher levels.

Abstract:
Let $K$ be an imaginary biquadratic field, $K_1$, $K_2$ be its imaginary quadratic subfields and $K_3$ be its real quadratic subfield. For integers $N>0$, $\mu\geq 0$ and an odd prime $p$ with $\gcd(N,p)=1$, let $K_{(Np^\mu)}$ and $(K_i)_{(Np^\mu)}$ for $i=1,2,3$ be the ray class fields of $K$ and $K_i$, respectively, modulo $Np^\mu$. We first present certain class fields $\widetilde{K_{N,p,\mu}^{1,2}}$ of $K$, in the sense of Hilbert, which are generated by ray class invariants of $(K_i)_{(Np^{\mu+1})}$ for $i=1,2$ over $K_{(Np^\mu)}$ and show that $K_{(Np^{\mu+1})}=\widetilde{K_{N,p,\mu}^{1,2}}$ for almost all $\mu$. And we shall further construct a primitive generator of the composite field $K_{(Np^\mu)}(K_3)_{(Np^{\mu+1})}$ over $K_{(Np^\mu)}$ by means of norms of the above ray class invariants, which is a real algebraic integer. Using this value we also generate a primitive generator of $(K_3)_{(p)}$ over the Hilbert class field of the real quadratic field $K_3$, and further find its normal basis.

Abstract:
We first generate ray class fields over imaginary quadratic fields in terms of Siegel-Ramachandra invariants, which would be an extension of Schertz's result. And, by making use of quotients of Siegel-Ramachandra invariants we also construct ray class invariants over imaginary quadratic fields whose minimal polynomials have relatively small coefficients, from which we are able to solve certain quadratic Diophantine equations.

Abstract:
Let $n$ be a positive integer. We discuss pairs of distinct odd primes $p$ and $q$ not dividing $n$ for which the Diophantine equations $pq=x^2+ny^2$ have integer solutions in $x$ and $y$. As its examples we classify all such pairs of $p$ and $q$ when $n=5$ and $14$.

Abstract:
We extend Norton-Borcherds-Koike's replication formulae to super-replicable ones by working with the congruence groups $\Gamma_1(N)$ and find the product identities which characterize super-replicable functions. These will provide a clue for constructing certain new infinite dimensional Lie superalgebras whose denominator identities coincide with the above product identities. Therefore it could be one way to find a connection between modular functions and infinite dimensional Lie algebras.