Error Distribution for One-Dimensional Stochastic Differential Equation Driven By Fractional Brownian Motion

We can define the error distribution as the limiting distribution of the error between the solution $Y$ of a given stochastic differential equation (SDE) and its numerical approximation $\hat{Y}^{(m)}$, weighted by the convergence rate between the two. A goal when studying the error distribution is to provide a way of determination for error distributions for any SDE and numerical scheme that converge to the exact solution. By dividing the error into a main term and a remainder term in a particular way, the author shows that the remainder term can be negligible compared to the main term under certain suitable conditions. Under these conditions, deriving the error distribution reduces to deriving the limiting distribution of the main term. Even if the dimension is one, there are unsolved problems about the asymptotic behavior of the error when the SDE has a drift term and $0<H\leq 1/3$, but our result in the one-dimensional case can be adapted to any Hurst exponent. The main idea of the proof is to define a stochastic process $Y^{m, \rho}$ with the parameter $\rho$ interpolating between $Y$ and $\hat{Y}^{(m)}$ and to estimate the asymptotic expansion for it. Using this estimate, we determine the error distribution of the ($k$)-Milstein scheme and of the Crank-Nicholson scheme in unsolved cases.Comment: 55 page

New physics searches at the ILC positron and electron beam dumps

We study capability of the ILC beam dump experiment to search for new physics, comparing the performance of the electron and positron beam dumps. The dark photon, axion-like particles, and light scalar bosons are considered as new physics scenarios, where all the important production mechanisms are included: electron-positron pair-annihilation, Primakoff process, and bremsstrahlung productions. We find that the ILC beam dump experiment has higher sensitivity than past beam dump experiments, with the positron beam dump having slightly better performance for new physics particles which are produced by the electron-positron pair-annihilation.Comment: 26 pages, 7 figure

Half-Integer Shapiro Steps in a Short Ballistic InAs Nanowire Josephson Junction

We report on half-integer Shapiro steps observed in an InAs nanowire Josephson junction. We observed the Shapiro steps of the short ballistic InAs nanowire Josephson junction and found anomalous half-integer steps in addition to the conventional integer steps. The half-integer steps disappear as the temperature increases or transmission of the junction decreases. These experimental results agree closely with numerical calculation of the Shapiro response for the skewed current phase relation in a short ballistic Josephson junction

Equal-Spin Andreev Reflection in Junctions of Spin-Resolved Quantum Hall Bulk State and Spin-Singlet Superconductor

The recent development of superconducting spintronics has revealed the spin-triplet superconducting proximity effect from a spin-singlet superconductor into a spin-polarized normal metal. In addition recently superconducting junctions using semiconductors are in demand for highly controlled experiments to engineer topological superconductivity. Here we report experimental observation of Andreev reflection in junctions of spin-resolved quantum Hall (QH) states in an InAs quantum well and the spin-singlet superconductor NbTi. The measured conductance indicates a sub-gap feature and two peaks on the outer side of the sub-gap feature in the QH plateau-transition regime increases. The observed structures can be explained by considering transport with Andreev reflection from two channels, one originating from equal-spin Andreev reflection intermediated by spin-flip processes and second arising from normal Andreev reflection. This result indicates the possibility to induce the superconducting proximity gap in the the QH bulk state, and the possibility for the development of superconducting spintronics in semiconductor devices

Dominant non-local superconducting proximity effect due to electron-electron interaction in a ballistic double nanowire

Cooper pair splitting (CPS) can induce non-local correlation between two normal conductors coupling to a superconductor. CPS into a double one-dimensional electron gas is an appropriate platform for extracting large amount of entangled electron pairs and one of the key ingredients for engineering Majorana Fermions with no magnetic field. Here we study CPS using a Josephson junction of a gate-tunable ballistic InAs double nanowire. The measured switching current into the two nanowires significantly larger than sum of that into the respective nanowires, indicating the inter-wire superconductivity dominant compared to the intra-wire superconductivity. From dependence on the number of propagating channels in the nanowires, the observed CPS is assigned to one-dimensional electron-electron interaction. Our results will pave the way for utilizing one-dimensional electron-electron interaction to reveal physics of high-efficient CPS and engineer Majorana Fermions in double nanowire systems via CPS

Volumetric measurement of paranasal sinuses and its clinical significance in pituitary neuroendocrine tumors operated using an endoscopic endonasal approach

ObjectiveEndoscopic endonasal surgery (EES) for deep intracranial lesions has gained popularity following recent developments in endoscopic technology. The operability of invasive pituitary neuroendocrine tumors (PitNETs) depends on the anatomy of the nasal cavity and paranasal sinus. This study aimed to establish a simple volume reconstruction algorithm of the nasal cavity and paranasal sinus. Additionally, this is the first study to demonstrate the relationship between the segmentation method and the clinical significance in patients with PitNET.MethodsPre-and postoperative tumor volumes were analyzed in 106 patients with primary (new-onset) PitNETs (80 nonfunctioning and 26 functioning) who underwent EES. The efficiency and accuracy of the semiautomatic segmentation with manual adjustments (SSMA) method was compared with other established segmentation methods for volumetric analysis in the nasal cavity and paranasal sinuses. Correlations between the measured nasal cavity and paranasal sinus volumes and the extent of tumor removal were evaluated.ResultsThe SSMA method yielded accurate and time-saving results following the volumetric analyses of nasal cavity and paranasal sinuses with complex structures. Alternatively, the manual and semiautomatic segmentation methods proved time-consuming and inaccurate, respectively. The sphenoid sinus volume measured by SSMA was significantly correlated with the extent of tumor removal in patients with nonfunctioning Knosp grade 3 and 4 PitNET (r = 0.318; p = 0.015).ConclusionThe volume of sphenoid sinus potentially could predict the extent of resection due to better visualization of the tumor for PitNETs with CS invasion

Surface Oxide Film and its Influence on the Oxygen Reduction on Pd-Co and Pt-Co PEFC Cathodes

PtCo and PdCo alloy electrodes were investigated in a 0.5 M sulfuric acid solution by electrochemistry, ellipsometry, laser Raman scattering spectroscopy, XPS, and GD-OES. The corrosion resistibility of Pt-Co and Pd-Co alloys decreased with increase of Co addition. The increase of Co addition, however, enhanced the catalytic efficiency on the ORR. The alloy surfaces may be covered by CoOOH and Pt or Pd oxide 2-3nm thick. At the potential of 1.2V vs. Ag/ AgCl/ sat. KCl, the thickness of oxide film increased with the Co addition. The presence of the oxide film on the alloy electrodes increases the overvoltage for the ORR. The effect of the oxide thickness on the ORR was discussed