Least squares volatility change point estimation for partially observed diffusion processes

A one dimensional diffusion process $X=\{X_t, 0\leq t \leq T\}$, with drift $b(x)$ and diffusion coefficient $\sigma(\theta, x)=\sqrt{\theta} \sigma(x)$ known up to $\theta>0$, is supposed to switch volatility regime at some point $t^*\in (0,T)$. On the basis of discrete time observations from $X$, the problem is the one of estimating the instant of change in the volatility structure $t^*$ as well as the two values of $\theta$, say $\theta_1$ and $\theta_2$, before and after the change point. It is assumed that the sampling occurs at regularly spaced times intervals of length $\Delta_n$ with $n\Delta_n=T$. To work out our statistical problem we use a least squares approach. Consistency, rates of convergence and distributional results of the estimators are presented under an high frequency scheme. We also study the case of a diffusion process with unknown drift and unknown volatility but constant

Near-IR imaging of T Cha: evidence for scattered-light disk structures at solar system scales

T Chamaeleontis is a young star surrounded by a transitional disk, and a plausible candidate for ongoing planet formation. Recently, a substellar companion candidate was reported within the disk gap of this star. However, its existence remains controversial, with the counter-hypothesis that light from a high inclination disk may also be consistent with the observed data. The aim of this work is to investigate the origin of the observed closure phase signal to determine if it is best explained by a compact companion. We observed T Cha in the L and K s filters with sparse aperture masking, with 7 datasets covering a period of 3 years. A consistent closure phase signal is recovered in all L and K s datasets. Data were fit with a companion model and an inclined circumstellar disk model based on known disk parameters: both were shown to provide an adequate fit. However, the absence of expected relative motion for an orbiting body over the 3-year time baseline spanned by the observations rules out the companion model. Applying image reconstruction techniques to each dataset reveals a stationary structure consistent with forward scattering from the near edge of an inclined disk.Comment: 6 pages, 3 figures, accepted for publication in MNRAS Letter

On Rényi information for ergodic diffusion processes

In this paper we derive explicit formulas of the R\'enyi information, Shannon entropy and Song measure for the invariant density of one dimensional ergodic diffusion processes. In particular, the diffusion models considered include the hyperbolic, the generalized inverse Gaussian, the Pearson, the exponential familiy and a new class of skew-t diffusion

High resolution observations of the outer disk around T Cha: the view from ALMA

T Cha is a young star surrounded by a transitional disk with signatures of planet formation. We have obtained high-resolution and high-sensitivity ALMA observations of T Cha in the ${\rm CO}(3$--$2)$, ${\rm ^{13}CO}(3$--$2)$, and ${\rm CS}(7$--$6)$ emission lines to reveal the spatial distribution of the gaseous disk around the star. In order to study the dust within the disk we have also obtained continuum images at 850$\mu$m from the line-free channels. We have spatially resolved the outer disk around T Cha. Using the CO(3-2) emission we derive a radius of $\sim$230 AU. We also report the detection of the $^{13}$CO(3-2) and the CS(7-8) molecular emissions, which show smaller radii than the CO(3-2) detection. The continuum observations at 850$\mu$m allow the spatial resolution of the dusty disk, which shows two emission bumps separated by $\sim$40AU, consistent with the presence of a dust gap in the inner regions of the disk, and an outer radius of $\sim$80AU. Therefore, T Cha is surrounded by a compact dusty disk and a larger and more diffuse gaseous disk, as previously observed in other young stars. The continuum intensity profiles are different at both sides of the disk suggesting possible dust asymmetries. We derive an inclination of i(deg)=67$\pm$5, and a position angle of PA (deg)= 113$\pm$6, for both the gas and dust disks. The comparison of the ALMA data with radiative transfer models shows that the gas and dust components can only be simultaneously reproduced when we include a tapered edge prescription for the surface density profile. The best model suggests that most of the disk mass is placed within a radius of $R<$ 50AU. Finally, we derive a dynamical mass for the central object of $M_{*}$=1.5$\pm$0.2M$_{\odot}$, comparable to the one estimated with evolutionary models for an age of $\sim$10Myr.Comment: 5 pages, 5 figures, accepted for publication in A&A Letter

VLA observations of candidate high-mass protostellar objects at 7 mm

We present radio continuum observations at 7 mm made using the Very Large Array towards three massive star forming regions thought to be in very early stages of evolution selected from the sample of Sridharan et al. (2002). Emission was detected towards all three sources (IRAS 18470-0044, IRAS 19217+1651 and IRAS 23151+5912). We find that in all cases the 7 mm emission corresponds to thermal emission from ionized gas. The regions of ionized gas associated with IRAS 19217+1651 and IRAS 23151+5912 are hypercompact with diameters of 0.009 and 0.0006 pc, and emission measures of 7.0 x 10^8 and 2.3 x 10^9 pc cm^(-6), respectively.Comment: 17 pages, 5 figures, accepted by The Astronomical Journa

On Singularity Formation of a Nonlinear Nonlocal System

We investigate the singularity formation of a nonlinear nonlocal system. This nonlocal system is a simplified one-dimensional system of the 3D model that was recently proposed by Hou and Lei in [13] for axisymmetric 3D incompressible Navier-Stokes equations with swirl. The main difference between the 3D model of Hou and Lei and the reformulated 3D Navier-Stokes equations is that the convection term is neglected in the 3D model. In the nonlocal system we consider in this paper, we replace the Riesz operator in the 3D model by the Hilbert transform. One of the main results of this paper is that we prove rigorously the finite time singularity formation of the nonlocal system for a large class of smooth initial data with finite energy. We also prove the global regularity for a class of smooth initial data. Numerical results will be presented to demonstrate the asymptotically self-similar blow-up of the solution. The blowup rate of the self-similar singularity of the nonlocal system is similar to that of the 3D model.Comment: 28 pages, 9 figure

XEN glaucoma treatment system in the management of refractory glaucomas: a short review on trial data and potential role in clinical practice

The recent development of new devices that are significantly less invasive, collectively termed minimally invasive glaucoma surgery, offers new perspective of intraocular pressure reduction with less risk, short operating times, and rapid recovery. The aim of this work is to provide a panoramic review of the currently published clinical data to assess the potential role of XEN gel stent (Allergan PLC, Irvine, CA, USA) in the management of glaucoma, which is the only filtering minimally invasive glaucoma surgery device that allows the subconjunctival filtration. The ab interno placement of the XEN gel stent offers an alternative for lowering intraocular pressure in refractory glaucoma as a final step, and in patients intolerant to medical therapy as an early surgical approach with minimum conjunctival tissue disruption, restricted flow to avoid hypotony, and long-term safety

Indigo (Cat5 & Sep5) System mechanical thrombectomy for acute mesenteric ischemia: an innovative approach for treatment of a severe but not so infrequent disease

Acute Mesenteric ischemia (AMI) is a severe and commonly underreported disease that has an annual incidence of 0.09-0.2% per patient year. However some studies have shown an increased incidence of AMI after performing an exhaustive analysis of 402 autopsies and surgeries (1970-1982 Malmo, Sweden). All mesenteric ischemia (MI) has and incidence of 12.9 cases of MI/10000 inhabitants/year, 67% thromboembolic SMA occlusion, 16% mesenteric venous thrombosis (MVT), 15% non-occlusive mesenteric ischemia (NOMI) and 2% have indeterminate cause. We present a patient with SMA treated satisfactorily with a new thromboaspiration system