Improved Bounds for Functions Related to Busy Beavers

Consider Turing machines that use a tape infinite in both directions, with the tape alphabet {0,1} . Rado's busy beaver function, ones(n), is the maximum number of 1's such a machine, with n states, started on a blank (all-zero) tape, may leave on its tape when it halts. The function ones(n) is non-computable; in fact, it grows faster than any computable function. Other functions with a similar nature can be defined also. All involve machines of n states, started on a blank tape. The function time(n) is the maximum number of moves such a machine may make before halting. The function num(n) is the largest number of 1's such a machine may leave on its tape in the form of a single run; and the function space(n) is the maximum number of tape squares such a machine may scan before it halts. This paper establishes new bounds on these functions in terms of each other. Specifically, we bound time(n) by num(n+o(n)), improving on the previously known bound num(3n+6) . This result is obtained using a kind of ``self-interpreting' Turing machine. We also improve on the trivial relation space(n) ≤ time(n) , using a technique of counting crossing sequences. Received July 18, 2000, and in revised form October 10, 2001. Online publication February 20, 2002.     

Ideales Internet-Frühwarnsystem

Wie müsste ein ideales und globales Internet-Frühwarnsystem aussehen? Der Beitrag stellt ein Modell für ein Frühwarnsystem vor und führt aus, welche Komponenten dafür ben?tigt werden und warum eine Frühwarnung nur durch kollaborative Ans?tze und eine Vielzahl von Systemen funktionieren kann. Anschlie?end werden einige aktuelle Forschungsvorarbeiten im Bereich Internet-Frühwarnung skizziert.     

Visualizing "green oil" in live algal cells

We report here that BODIPY 505/515, a green lipophilic fluorescent dye, serves as an excellent vital stain for the oil-containing lipid bodies of live algal cells. BODIPY 505/515 vital staining can be used in combination with fluorescent activated cell sorting to detect and isolate algal cells possessing high lipid content.     

A new software for initiating and optimising insulin treatment of out-patients

Two computer programs were developed, program I to optimise insulin treatment using six injections per day, and program II to convert these insulin profiles into less frequent injections of mixtures of regular and NPH insulin. The first software in an HP 41 CV pocket computer uses iterative adjustments during the day and on subsequent days to determine the optimal timing and dosage of insulin. Six self-monitored glucose values at 3 h intervals, insulin doses, and the effects of insulin on plasma glucose are memorised for calculations. The calculated insulin doses were applied by Optipen as five s.c. injections of regular insulin and one bedside injection of NPH insulin. After 5 days the optimised individual insulin profiles with six daily injections were processed by program II. It applies the pharmacokinetics of regular and NPH insulin to make suggestions for a more conventional insulin therapy with one, two, three or four daily injections of regular insulin, NPH insulin, or varying mixtures of both insulins. The procedure was well tolerated in eight insulin-dependent diabetes mellitus out-patients. Insulin therapy with two or three injections, fitted by the second program and selected according to the quality score, produced plasma glucose profiles as satisfactory as those obtained with six injections. The system allows the fine tuning of insulin therapy to out-patients with their individual diets and physical activities.     

Factor XI activation by meizothrombin: stimulation by phospholipid vesicles containing both phosphatidylserine and phosphatidylethanolamine

The activation of factor XI by meizothrombin was investigated using recombinant meizothrombin (R155A meizothrombin) that is resistant to autocatalytic removal of fragment 1. Meizothrombin was capable of activating factor XI at an activation rate similar to that of thrombin. Dextran sulphate and heparin, known cofactors of thrombin-mediated factor XI activation, did not stimulate the activation of factor XI by meizothrombin. However, the activation of factor XI by meizothrombin was markedly enhanced by vesicles containing phosphatidylcholine (PC), phosphatidylserine (PS) and phosphatidylethanolamine (PE), whereas PC/PS or PC/PE vesicles only had a minor effect on the activation. Thrombin-mediated factor XI activation was not influenced by phospholipids. The effect of PC/PS/PE and PC/PS vesicles was studied in a factor XI dependent clot lysis assay. In this assay, factor XI inhibits clot lysis by a feedback loop in the intrinsic pathway via thrombin-mediated factor XI activation. Removal of endogenous phospholipids in plasma by centrifugation resulted in an increased clot lysis, which could be restored to the pre-centrifugation level by the addition of PC/PS/PE vesicles, but not by PC/PS vesicles. When clot lysis was initiated by factor IXa in the presence of a factor XIa blocking antibody, there was no difference in inhibitory effect of PC/PS/PE or PC/PS vesicles. These data suggested that the differences in clot lysis inhibition observed between PC/PS/PE and PC/PS vesicles were caused by factor XI activation by meizothrombin. Meizothrombin-mediated factor XI activation may therefore play an important role in the antifibrinolytic feedback loop in the intrinsic pathway.     

The use of scanning electron microscope autoradiography to localize the blueberry shoestring virus in its aphid vector

Scanning electron microscopy autoradiography (SEM-AR) in conjunction with light microscope autoradiography (LM-AR) was used to follow the movement of ¹²⁵I-labeled blueberry shoestring virus (BBSSV) through its aphid vector Illinoia pepperi with varying acquisition access periods (AAP). At 6 hr AAP, the virus had reached the stomach; at 12 hr AAP, it had reached the anterior of the intestines, and after 48 hr, AAP was present throughout the aphid. SEM-AR using backscatter electron detection proved very useful because the sample bulk resulted in a shortened exposure time compared to LM sections, correlation of the autoradiograms could be made with fine structure, preparing large numbers of samples was easy, and examining whole longitudinal sections of aphids at low magnification with a clearly visible marker was possible. Limitations were mostly attributed to sample preparation and, in some cases, were easily remedied.     

Indications for contrast medium administration in MR-angiography of cerebral blood vessels

Time-of-flight MR-angiography of large volumes is limited by the occurrence of saturation effects, which lead to low signal in both veins and arteries. Alternatively to a number of other MRA-techniques, intravenous application of paramagnetic contrast media in combination with 3D-pulse sequences with or without flow refocussing allows the depiction of slow vessels in large volumes without technical extra expenses. The main intracranial indication is anatomical 3D-imaging of normal and dysplastic cerebral veins with high spatial resolution, and the additional depiction of the venous drainage in AVMs, when unenhanced MRA shows only the arteriel supply and the nidus. In large cerebral aneurysms, bridging veins and venous sinuses, partial thromboses can easily be differentiated from slow flow. Contrast-enhancing tumors can be depicted together with normal or displaced vessels. Improvements of arterial signal due to contrast media with currently used routine MRA techniques are clinically not significant. Signal loss due to spin dephasing in vessels with complex flow is not influences by contrast media. Results of contrast-enhanced MRA are determined by the timing of injection. Since arteries and veins are both imaged with high signal intensity, improvements of postprocessing procedures for secondary vessel segmentation are necessary.