Convergence rates of Gaussian ODE filters.

A recently introduced class of probabilistic (uncertainty-aware) solvers for ordinary differential equations (ODEs) applies Gaussian (Kalman) filtering to initial value problems. These methods model the true solution and its first derivatives as a Gauss-Markov process , which is then iteratively conditioned on information about . This article establishes worst-case local convergence rates of order for a wide range of versions of this Gaussian ODE filter, as well as global convergence rates of order in the case of and an integrated Brownian motion prior, and analyses how inaccurate information on coming from approximate evaluations of affects these rates.

[Volvulus of the small intestine, a rare complication during laxative period before colonoscopy].

History And Clinical Findings: A 69-year-old patient was hospitalized 16 h after investigation of the colon (screening colonoscopy), suffering from abdominal pain, which had started during the laxative period the day before colonoscopy.

Investigations: Clinical and technical investigations showed signs of a peritonitis.

Treatment And Course: By laparotomy a volvulus of the small intestine was found, caused by adhesions after appendectomy years before.

Tuber physiology and properties of starch from tubers of transgenic potato plants with altered plastidic adenylate transporter activity.

We showed recently that antisense plants with decreased activity of the plastidic ATP/ADP-transporter protein exhibit drastically reduced levels of starch and a decreased amylose/amylopectin ratio, whereas sense plants with increased activity of the transporter possessed more starch than wild-type plants and an increased amylose/amylopectin ratio. In this paper we investigate the effect of altered plastidic ATP/ADP-transporter protein expression on primary metabolism and granule morphology in more detail. Tuber tissues from antisense and sense plants exhibited substantially increased respiratory activity compared with the wild type.

[Medical correspondence].

This paper gives a short overview of the most relevant elements of medical records. It seems important to emphasise, that writing a letter to the family doctor has more meaning than simple documentation. It is a matter of communication, involving psychological and ethical requirements.