Comment on the Calculation of the Angular Momentum and Mass for the (Anti-) Self Dual Charged Spinning BTZBTZ Black Hole

A recent paper [M. Kamata and T. Koikawa, Phys. Lett. {\bf B353} (1995) 196.] claimed to obtain the charged version of the $(2+1)$-dimensional spinning $BTZ$ black hole solution by assuming a (anti-) self dual condition imposed on the electric and magnetic fields. We point out that the angular momentum and mass diverge at spatial infinity and as a consequence the solution is unphysicalComment: 4 pages, Latex, no figures, final version to be publised in Phys. Lett.

Scatterings of Massive String States from D-brane and Their Linear Relations at High Energies

We study scatterings of bosonic massive closed string states at arbitrary mass levels from D-brane. We discover that all the scattering amplitudes can be expressed in terms of the generalized hypergeometric function with special arguments, which terminates to a finite sum and, as a result, the whole scattering amplitudes consistently reduce to the usual beta function. For the simple case of D-particle, we explicitly calculate high-energy limits of a series of the above scattering amplitudes for arbitrary mass levels, and derive infinite linear relations among them for each fixed mass level. The ratios of these high-energy scattering amplitudes are found to be consistent with the decoupling of high-energy zero-norm states of our previous works.Comment: 19 pages, no figure. v2:some minor corrections, refs added. v3:minor changes and final in Nucl.Phys.

Homological mirror symmetry for local Calabi-Yau manifolds via SYZ

This is a write-up of the author's talk in the conference "Algebraic Geometry in East Asia 2016" held at the University of Tokyo in January 2016. We give a survey on a series of papers of the author and his collaborators Daniel Pomerleano and Kazushi Ueda where we show how Strominger-Yau-Zaslow (SYZ) transforms can be applied to understand the geometry of Kontsevich's homological mirror symmetry (HMS) conjecture for certain local Calabi-Yau manifolds.Comment: 19 pages, 10 figures; v2: minor revision, references added; to appear in a special issue of TJM for the proceedings of "Algebraic Geometry in East Asia 2016

A formula equating open and closed Gromov-Witten invariants and its applications to mirror symmetry

We prove that open Gromov-Witten invariants for semi-Fano toric manifolds of the form $X=\mathbb{P}(K_Y\oplus\mathcal{O}_Y)$, where $Y$ is a toric Fano manifold, are equal to certain 1-pointed closed Gromov-Witten invariants of $X$. As applications, we compute the mirror superpotentials for these manifolds. In particular, this gives a simple proof for the formula of the mirror superpotential for the Hirzebruch surface $\mathbb{F}_2$.Comment: v3: many minor changes, published in Pacific J. Math.; v2: 16 pages. Completely rewritten and improve

Parkin uses the UPS to ship off dysfunctional mitochondria

Parkin is a ubiquitin E3 ligase that is implicated in familial Parkinson disease (PD). Previous studies have established its role in mitophagy, a pathway whereby dysfunctional mitochondria are targeted for autophagic degradation. We recently reported that a major function of Parkin in dysfunctional mitochondria is to activate the ubiquitin-proteasome system (UPS) for proteolysis of multiple outer membrane proteins, and that such activation of the UPS is a critical step in Parkin-mediated mitophagy. Here, we discuss the possible roles of the UPS in mitophagy and the pathogenesis of PD