Gradient Bounds for Solutions of Stochastic Differential Equations Driven by Fractional Brownian Motions

We study some functional inequalities satisfied by the distribution of the solution of a stochastic differential equation driven by fractional Brownian motions. Such functional inequalities are obtained through new integration by parts formulas on the path space of a fractional Brownian motion.Comment: The paper is dedicated to Pr. David Nualart 60th's birthda

Closed form summation of C-finite sequences

We consider sums of the form $$\sum_{j=0}^{n-1}F_1(a_1n+b_1j+c_1)F_2(a_2n+b_2j+c_2)... F_k(a_kn+b_kj+c_k),$$ in which each $\{F_i(n)\}$ is a sequence that satisfies a linear recurrence of degree $D(i)<\infty$, with constant coefficients. We assume further that the $a_i$'s and the $a_i+b_i$'s are all nonnegative integers. We prove that such a sum always has a closed form, in the sense that it evaluates to a linear combination of a finite set of monomials in the values of the sequences $\{F_i(n)\}$ with coefficients that are polynomials in $n$. We explicitly describe two different sets of monomials that will form such a linear combination, and give an algorithm for finding these closed forms, thereby completely automating the solution of this class of summation problems. We exhibit tools for determining when these explicit evaluations are unique of their type, and prove that in a number of interesting cases they are indeed unique. We also discuss some special features of the case of ``indefinite summation," in which $a_1=a_2=... = a_k = 0$

The Banks of the Cohomology River

We give sharp bounds on the vanishing of the cohomology of a tensor product of vector bundles on the n-dimensional projective space in terms of the vanishing of the cohomology of the factors. For this purpose we introduce regularity indices generalizing the Castelnuovo-Mumford regularity. As an application we give a sufficient condition for a vector bundle to have an unobstructed deformation theory that depends only on the cohomology table of the bundle. We construct complete families of bundles with such cohomology tables.Comment: 16 page

A transient Markov chain with finitely many cutpoints

We give an example of a transient reversible Markov chain that almost surely has only a finite number of cutpoints. We explain how this is relevant to a conjecture of Diaconis and Freedman and a question of Kaimanovich. We also answer Kaimanovich's question when the Markov chain is a nearest-neighbor random walk on a tree.Comment: Published in at http://dx.doi.org/10.1214/193940307000000365 the IMS Collections (http://www.imstat.org/publications/imscollections.htm) by the Institute of Mathematical Statistics (http://www.imstat.org

Single institution implementation of permanent 131Cs interstitial brachytherapy for previously irradiated patients with resectable recurrent head and neck carcinoma

Purpose: Permanent interstitial brachytherapy is an appealing treatment modality for patients with locoregional recurrent, resectable head and neck carcinoma (HNC), having previously received radiation. Cesium-131 (131Cs) is a permanent implant brachytherapy isotope, with a low average photon energy of 30 keV and a short half-life of 9.7 days. Exposure to medical staff and family members is low; patient isolation and patient room shielding are not required. This work presents a single institution’s implementation process of utilizing an intraoperative, permanent 131Cs implant for patients with completely resected recurrent HNC. Materials & Methods: Fifteen patients receiving 131Cs permanent seed brachytherapy were included in this analysis. The process of pre-planning, selecting the dose prescription, seed ordering, intraoperative procedures, post-implant planning, and radiation safety protocols are described. Results: Tumor volumes were contoured on the available preoperative PET/CT scans and a pre-implant treatment plan was created using uniform source strength and uniform 1 cm seed spacing. Implants were performed intraoperatively, following tumor resection. In five of the fifteen cases, intraoperative findings necessitated a change from the planned number of seeds and recalculation of the pre-implant plan. The average prescription dose was 56.1 ±6.6 Gy (range, 40-60 Gy). The average seed strength used was 2.2 ±0.2 U (3.5 ±0.3 mCi). Patients returned to a recovery room on a standard surgical floor and remained inpatients, without radiation safety restrictions, based on standard surgical recovery protocols. A post-implant treatment plan was generated based on immediate post-operative CT imaging to verify the seed distribution and confirm delivery of the prescription dose. Patients were provided educational information regarding radiation safety recommendations. Conclusions: Cesium-131 interstitial brachytherapy is feasible and does not pose major radiation safety concerns; it should be considered as a treatment option for previously irradiated patients with recurrent, resectable HNC

New Active Asteroid 313P/Gibbs

We present initial observations of the newly-discovered active asteroid 313P/Gibbs (formerly P/2014 S4), taken to characterize its nucleus and comet-like activity. The central object has a radius $\sim$0.5 km (geometric albedo 0.05 assumed). We find no evidence for secondary nuclei and set (with qualifications) an upper limit to the radii of such objects near 25 m, assuming the same albedo. Both aperture photometry and a morphological analysis of the ejected dust show that mass-loss is continuous at rates $\sim$0.2 to 0.4 kg s$^{-1}$, inconsistent with an impact origin. Large dust particles, with radii $\sim$50 to 100 $\mu$m, dominate the optical appearance. At 2.4 AU from the Sun, the surface equilibrium temperatures are too low for thermal or desiccation stresses to be responsible for the ejection of dust. No gas is spectroscopically detected (limiting the gas mass loss rate to $<$1.8 kg s$^{-1}$). However, the protracted emission of dust seen in our data and the detection of another episode of dust release near perihelion, in archival observations from 2003, are highly suggestive of an origin by the sublimation of ice. Coincidentally, the orbit of 313P/Gibbs is similar to those of several active asteroids independently suspected to be ice sublimators, including P/2012 T1, 238P/Read and 133P/Elst-Pizarro, suggesting that ice is abundant in the outer asteroid belt.Comment: 24 pages, 7 figures, accepted The Astronomical Journa