Quantum algorithms for problems in number theory, algebraic geometry, and group theory

Quantum computers can execute algorithms that sometimes dramatically outperform classical computation. Undoubtedly the best-known example of this is Shor's discovery of an efficient quantum algorithm for factoring integers, whereas the same problem appears to be intractable on classical computers. Understanding what other computational problems can be solved significantly faster using quantum algorithms is one of the major challenges in the theory of quantum computation, and such algorithms motivate the formidable task of building a large-scale quantum computer. This article will review the current state of quantum algorithms, focusing on algorithms for problems with an algebraic flavor that achieve an apparent superpolynomial speedup over classical computation.Comment: 20 pages, lecture notes for 2010 Summer School on Diversities in Quantum Computation/Information at Kinki Universit

Fetal calf serum increased the zona pellucida penetrability of rat oocytes matured in vitro.

We examined the effect of fetal calf serum (FCS) on meiotic division, subsequent fertilization, and first cleavage to the 2-cell stage of rat oocytes during in vitro maturation. FCS had no effect on the nuclear progression from dictiate to metaphase of the second maturation in vitro and, FCS had no effect on the first cleavage to the 2-cell stage of fertilized oocytes. However, FCS efficiently increased penetration rate of oocytes and shortened the time required for dissolution of the zona pellucida by alpha-chymotrypsin. These results showed that FCS did not affect cytoplasmic maturation necessary for oocytes to develop to the 2-cell stages. We found that FCS only affects the zona pellucida and does not affect the nucleus or cytoplasm of rat oocytes. FCS may prevent hardening of the zona pellucida. </p

Lipomatous Pseudohypertrophy of the Pancreas Taking the Form of Huge Massive Lesion of the Pancreatic Head

A 70-year-old woman presented with hypogastric pain. Computed tomography and magnetic resonance imaging revealed a retroperitoneal tumor 18.0 cm in diameter with fatty tissue density, ventrally compressing the pancreatic head. We suspected a well-differentiated liposarcoma compressing the pancreas. At laparotomy, the tumor mass was the size of an infant's head; its center was located in the area corresponding to the pancreatic uncus. It was continuous with the pancreatic parenchyma through a poorly demarcated border, and we resected as much of the tumor mass as possible while conserving the pancreatic capsule. Histopathological examination indicated lipomatous pseudohypertrophy of the pancreas with proliferation of mature fatty tissue as the main constituent. At the periphery, islands of acinar tissue were retained among the fatty infiltration, which also contained branches of the pancreatic duct and islets of Langerhans. Previous reports have stated that this disorder only causes fatty replacements throughout the pancreas or in the pancreatic body and tail; however, in this patient, imaging and macroscopic examination revealed no fatty replacements in the pancreatic body and tail. We report this case, which we consider extremely rare, along with a brief review of the literature

Suzaku Observations of AWM 7 Cluster of Galaxies: Temperature, Abundance and Bulk Motions

We carried out 3 observations of the cluster of galaxies AWM 7, for the central region and 20'-east and 20'-west offset regions, with Suzaku. Temperature and abundance profiles are measured out to 27'~ 570 /h_70 kpc, which corresponded to ~0.35 r_180. The temperature of the intra-cluster medium (ICM) slightly decreases from 3.8 keV at the center to 3.4 keV in ~0.35 r_180 region, indicating a flatter profile than those in other nearby clusters. Abundance ratio of Si to Fe is almost constant in our observation, while Mg to Fe ratio increases with radius from the cluster center. O to Fe ratio in the west region shows increase with radius, while that in the east region is almost flat, though the errors are relatively large. These features suggest that the enrichment process is significantly different between products of type II supernovae (O and Mg) and those by type Ia supernovae (Si and Fe). We also examined positional shift of the central energy of He-like Fe-Ka line, in search of possible rotation of the ICM. The 90% upper limit for the line-of-sight velocity difference was derived to be v ~ 2000 km/s, suggesting that the ellipticity of AWM 7 is rather caused by a recent directional infall of the gas along the large-scale filament.Comment: 11 pages, 7 figures, accepted for publication in PAS