High-performance Ge/Si electro-absorption optical modulator up to 85°C and its highly efficient photodetector operation

We studied a high-speed Ge/Si electro-absorption optical modulator (EAM) evanescently coupled with a Si waveguide of a lateral p–n junction for a high-bandwidth optical interconnect over a wide range of temperatures from 25 °C to 85 °C. We demonstrated 56 Gbps high-speed operation at temperatures up to 85 °C. From the photoluminescence spectra, we confirmed that the bandgap energy dependence on temperature is relatively small, which is consistent with the shift in the operation wavelengths with increasing temperature for a Ge/Si EAM. We also demonstrated that the same device operates as a high-speed and high-efficiency Ge photodetector with the Franz-Keldysh (F-K) and avalanche-multiplication effects. These results demonstrate that the Ge/Si stacked structure is promising for both high-performance optical modulators and photodetectors integrated on Si platforms

Functional central limit theorems for vicious walkers

We consider the diffusion scaling limit of the vicious walker model that is a system of nonintersecting random walks. We prove a functional central limit theorem for the model and derive two types of nonintersecting Brownian motions, in which the nonintersecting condition is imposed in a finite time interval $(0,T]$ for the first type and in an infinite time interval $(0,\infty)$ for the second type, respectively. The limit process of the first type is a temporally inhomogeneous diffusion, and that of the second type is a temporally homogeneous diffusion that is identified with a Dyson's model of Brownian motions studied in the random matrix theory. We show that these two types of processes are related to each other by a multi-dimensional generalization of Imhof's relation, whose original form relates the Brownian meander and the three-dimensional Bessel process. We also study the vicious walkers with wall restriction and prove a functional central limit theorem in the diffusion scaling limit.Comment: AMS-LaTeX, 20 pages, 2 figures, v6: minor corrections made for publicatio

Widespread enlarged perivascular spaces associated with dementia and focal brain dysfunction: case report

Abstract Background Enlarged perivascular spaces (PVS) are common magnetic resonance imaging (MRI) findings, whereas widespread enlarged PVS are extremely rare. Although most patients with widespread enlarged PVS remain asymptomatic, some develop neurological dysfunctions; however, it remains unclear whether these are the consequence of widespread enlarged PVS. Case presentation A 64-year-old female patient developed consciousness disturbance, cognitive dysfunctions, fluent aphasia, agraphia, acalculia, and left-right disorientation after suffering from bronchopneumonia. Brain MRI revealed unusually widespread enlarged PVS predominantly in the left cerebral hemisphere. Following bronchopneumonia treatment, her cognitive dysfunction, fluent aphasia, agraphia, acalculia, and left-right disorientation persisted despite improvement of her general condition. Furthermore, the hypoperfusion area on single photon emission computed tomography and slow wave sites on electroencephalography were consistent with the location of enlarged PVS, indicating that severe enlarged PVS impaired focal brain functions. Conclusions This case suggested that widespread enlarged PVS could be a potential cause of neurological deficits. We propose that impaired perivascular circulation due to enlarged PVS might lead to focal brain dysfunction