Improved Convergence Rate of Stochastic Gradient Langevin Dynamics with Variance Reduction and its Application to Optimization

The stochastic gradient Langevin Dynamics is one of the most fundamental algorithms to solve sampling problems and non-convex optimization appearing in several machine learning applications. Especially, its variance reduced versions have nowadays gained particular attention. In this paper, we study two variants of this kind, namely, the Stochastic Variance Reduced Gradient Langevin Dynamics and the Stochastic Recursive Gradient Langevin Dynamics. We prove their convergence to the objective distribution in terms of KL-divergence under the sole assumptions of smoothness and Log-Sobolev inequality which are weaker conditions than those used in prior works for these algorithms. With the batch size and the inner loop length set to $\sqrt{n}$, the gradient complexity to achieve an $\epsilon$-precision is $\tilde{O}((n+dn^{1/2}\epsilon^{-1})\gamma^2 L^2\alpha^{-2})$, which is an improvement from any previous analyses. We also show some essential applications of our result to non-convex optimization

A case report of intracranial hemorrhage after spinal anesthesia

Abstract Background Chronic subdural hematoma (CSDH) after spinal anesthesia is a rare complication. We experienced a patient who developed CSDH after postdural puncture headache (PDPH) following combined spinal and epidural anesthesia (CSE). Case presentation A 38-week-gestation parturient with a history of previous cesarean delivery underwent elective cesarean section under CSE. She had been receiving aspirin therapy for Kawasaki disease for many years. She developed a symptom of PDPH 1 day after the surgery. Fluid administration and analgesics were started. Although the headache was relatively severe and persistent, it suddenly disappeared on the third postoperative day. Aspirin administration was restarted on the third postoperative day, and the patient was discharged 1 week after the surgery. 2 weeks after being discharged, she was readmitted to our hospital for severe headache and was diagnosed as having CSDH. An epidural blood patch was performed, resulting in resolution of the hematoma. Conclusions We experienced a case of CSDH after PDPH in a patient who was receiving aspirin therapy. Aspirin therapy should be restarted after confirmation of the absence of headache. We should consider the possibility of unexpected disappearance of PDPH in the postoperative period may be due to the development of CSDH

Potential barrier lowering and electrical transport at the LaAlO3_{3}/SrTiO3_{3} heterointerface

Using a combination of vertical transport measurements across and lateral transport measurements along the LaAlO$_{3}$/SrTiO$_{3}$ heterointerface, we demonstrate that significant potential barrier lowering and band bending are the cause of interfacial metallicity. Barrier lowering and enhanced band bending extends over 2.5 nm into LaAlO$_{3}$ as well as SrTiO$_{3}$. We explain origins of high-temperature carrier saturation, lower carrier concentration, and higher mobility in the sample with the thinnest LaAlO$_{3}$ film on a SrTiO$_{3}$ substrate. Lateral transport results suggest that parasitic interface scattering centers limit the low-temperature lateral electron mobility of the metallic channel.Comment: 10 pages, 3 figures, and 1 tabl

Development Of Climate Change Information Database And Its Use In Civic Consciousness Enlightenment

GCM outputs such as CMIP3 are available via network access to PCMDI web site. Meteorological researchers are familiar with the usage of the GCM data, but the most of researchers other than meteorology such as agriculture, civil engineering, etc., and general people are not familiar with the GCM. There are some difficulties to use GCM; 1) to download the enormous quantity of data, 2) to understand the GCM methodology, parameters and grids. In order to provide a quick access way to GCM, Climate Change Information Database has been developed. The purpose of the database is to bridge the users and meteorological specialists and to facilitate the understanding the climate changes. The resolution of the data is unified, and climate change amount or factors for each meteorological element are provided from the database. All data in the database are interpolated on the same 80km mesh. Available data are the present-future projections of 27 GCMs, 16 meteorological elements (precipitation, temperature, etc.), 3 emission scenarios (A1B, A2, B1). We showed the summary of this database to residents in Toyama prefecture and measured the effect of showing and grasped the image for the climate change by using the Internet questionary survey. The persons who feel a climate change at the present tend to feel the additional changes in the future. It is important to show the monitoring results of climate change for a citizen and promote the understanding for the climate change that had already occurred. It has been shown that general images for the climate change promote to understand the need of the mitigation, and that it is important to explain about the climate change that might occur in the future even if it did not occur at the present in order to have people recognize widely the need of the adaptation

On an integrable discretization of the modified Korteweg-de Vries equation

We find time discretizations for the two ''second flows'' of the Ablowitz-Ladik hierachy. These discretizations are described by local equations of motion, as opposed to the previously known ones, due to Taha and Ablowitz. Certain superpositions of our maps allow a one-field reduction and serve therefore as valid space-time discretizations of the modified Korteweg-de Vries equation. We expect the performance of these discretizations to be much better then that of the Taha-Ablowitz scheme. The way of finding interpolating Hamiltonians for our maps is also indicated, as well as the solution of an initial value problem in terms of matrix factorizations.Comment: 23 pages, LaTe

Nearly strain-free heteroepitaxial system for fundamental studies of pulsed laser deposition: EuTiO3 on SrTiO3

High quality epitaxial thin-films of EuTiO3 have been grown on the (001) surface of SrTiO3 using pulsed laser deposition. In situ x-ray reflectivity measurements reveal that the growth is two-dimensional and enable real-time monitoring of the film thickness and roughness during growth. The film thickness, surface mosaic, surface roughness, and strain were characterized in detail using ex situ x-ray diffraction. The thicnkess and composition were confirmed with Rutherford Backscattering. The EuTiO3 films grow two-dimensionally, epitaxially, pseudomorphically, with no measurable in-plane lattice mismatch.Comment: 7 pages, 6 figure