On an explicit finite difference method for fractional diffusion equations

A numerical method to solve the fractional diffusion equation, which could also be easily extended to many other fractional dynamics equations, is considered. These fractional equations have been proposed in order to describe anomalous transport characterized by non-Markovian kinetics and the breakdown of Fick's law. In this paper we combine the forward time centered space (FTCS) method, well known for the numerical integration of ordinary diffusion equations, with the Grunwald-Letnikov definition of the fractional derivative operator to obtain an explicit fractional FTCS scheme for solving the fractional diffusion equation. The resulting method is amenable to a stability analysis a la von Neumann. We show that the analytical stability bounds are in excellent agreement with numerical tests. Comparison between exact analytical solutions and numerical predictions are made.Comment: 22 pages, 6 figure

Solitaire Clobber

Clobber is a new two-player board game. In this paper, we introduce the one-player variant Solitaire Clobber where the goal is to remove as many stones as possible from the board by alternating white and black moves. We show that a checkerboard configuration on a single row (or single column) can be reduced to about n/4 stones. For boards with at least two rows and two columns, we show that a checkerboard configuration can be reduced to a single stone if and only if the number of stones is not a multiple of three, and otherwise it can be reduced to two stones. We also show that in general it is NP-complete to decide whether an arbitrary Clobber configuration can be reduced to a single stone.Comment: 14 pages. v2 fixes small typ

Effect of Intraduodenal Bile and Taurodeoxycholate on Exocrine Pancreatic Secretion and on Plasma Levels of Vasoactive Intestinal Polypeptide and Somatostatin in Man

Intraduodenal (i.d.) application of bile or Na-taurodeoxycholate (TDC) dose dependently enhances basal exocrine pancreatic secretion. The hydrokinetic effect is mediated at least in part by secretin. This study should show, whether vasoactive intestinal polypeptide (VIP), a partial agonist of secretin, may also be involved in the mediation of the hydrokinetic effect. Furthermore, plasma concentrations of somatostatin-like immunoreactivity (SLI) were measured in order to check whether this counterregulating hormone is also released by bile and TDC. Twenty investigations were carried out on 10 fasting healthy volunteers provided with a double-lumen Dreiling tube. Bile and TDC were intraduodenally applied in doses of 2-6 g and 200-600 mg, respectively, at 65-min intervals. Plasma samples were withdrawn at defined intervals for radioimmunological determination of VIP and SLI. Duodenal juice was collected in 10-min fractions and analyzed for volume, pH, bicarbonate, lipase, trypsin, and amylase. I.d. application of bile or TDC dose dependently stimulated hydrokinetic and ecbolic pancreatic secretion. Bile exerted a slightly stronger effect than TDC. Pancreatic response was simultaneously accompanied by a significant increase of plasma VIP and SLI concentrations. The effect of bile on integrated plasma VIP and SLI concentrations seems to be dose dependent; the effect of TDC on integrated SLI, too. For the increase of integrated plasma VIP concentrations after TDC no dose-response relation could be established. We conclude that VIP may be a further mediator of bile-induced volume and bicarbonate secretion. The release of plasma SLI indicates that inhibitory mechanisms concomitantly are triggered by i.d. bile and TDC, as already shown during digestion for the intestinal phase of pancreatic secretion

Immunoreactive human chorionic gonadotropin and its free ß-subunit in serum and ascites of patients with malignant tumors

Human chorionic gonadotropin (hCG) is a clinically relevant marker of trophoblastic and nontrophoblastic malignancies. In the present studies, in addition to determining serum hCG, we investigated the presence and properties of hCG immunoreactivity in ascites of patients with nontrophoblastic malignant tumors and, for comparison, in ascites caused by cirrhotic liver disease. Total hCG immunoreactivity [hCG (+hCG-ß)] was found to be elevated above the reference value (>5 IU/liter) in the serum of 2 of 20 patients with cirrhosis and 11 of 20 patients with malignant tumors. For comparison, in ascites, hCG (+hCG-ß) concentrations were frequently higher than in the corresponding serum samples and exceeded 10 IU/liter in 0 of 20 cirrhotic samples and in 16 of 20 malignant samples. In order to elucidate the nature of the hCG immunoreactive material, all samples were then assessed by immunoradiometric assays specific for the intact hCG molecule (holo-hCG) and the free hCG-ß subunit, respectively. In the holo-hCG assay, elevated values were detected in 0 of 20 (0 of 20) cirrhotic ascites (serum) samples and 0 of 20 (1 of 20) malignant ascites (serum) samples. In the free hCG-ß assay, on the other hand, no positive results were obtained in the ascites or serum of 20 patients with liver cirrhosis; however, 8 of 20 serum samples and 16 of 20 ascites samples derived from tumor patients were positive. In accord with the immunological data, gel chromatographical studies of malignant ascites revealed the abundance of free hCG-ß subunit rather than that of holo-hCG. In contrast to malignancy-related ascites, in ascites of patients receiving hCG injections for treatment of infertility, holo-hCG was more abundant than free hCG-ß immunoreactivity. Incubation experiments of purified holo-hCG in ascites for 24 h at -20, 20, or 37°C showed no substantial dissociation of the hCG molecule and release of free hCG-ß immunoreactivity, thus arguing against production of free hCG-ß by degradation of holo-hCG and in favor of its tumor-related secretion. In conclusion, hCG-ß immunoreactivity is frequently elevated in malignancy-related ascites and appears to be related to the presence of free ß subunit of hCG rather than that of the intact hCG molecule. Interestingly, hCG-ß determination in ascites proved to be clearly superior to serum measurement in discriminating between tumor and cirrhosis. Thus, hCG-ß might be a useful marker of malignancy-related ascites and should be prospectively assessed for possible clinical use in comparison with other well-established parameters, such as cytology and protein determination. For this purpose, according to our results, only assays that exhibit a high sensitivity for free hCG-ß subunit appear to be suitable

Combined Effects of Knowledge About Others' Opinions and Anticipation of Group Discussion on Confirmatory Information Search

There is conclusive evidence that information search processes are typically biased in favor of the information seeker’s own opinion (confirmation bias). Less is known about how knowledge about others’ opinions affects this confirmatory information search. In the present study, the authors manipulated feedback about others’ opinions and anticipation of group interaction. As predicted, the effect of knowledge about others’ opinions on confirmatory information search depended on whether participants anticipated interacting with these others. Specifically, minority members anticipating a group discussion exhibited a particularly strong confirmation bias, whereas minority members who did not anticipate a discussion predominantly sought information opposing their opinion. For participants not anticipating group interaction, confidence about the correctness of one’s decision mediated the impact of knowledge about others’ opinions on confirmatory information search. Results are discussed with regard to the debiasing effect of preference heterogeneity on confirmatory information search in groups

Spectrally resolved single-shot wavefront sensing of broadband high-harmonic sources

Wavefront sensors are an important tool to characterize coherent beams of extreme ultraviolet radiation. However, conventional Hartmann-type sensors do not allow for independent wavefront characterization of different spectral components that may be present in a beam, which limits their applicability for intrinsically broadband high-harmonic generation (HHG) sources. Here we introduce a wavefront sensor that measures the wavefronts of all the harmonics in a HHG beam in a single camera exposure. By replacing the mask apertures with transmission gratings at different orientations, we simultaneously detect harmonic wavefronts and spectra, and obtain sensitivity to spatiotemporal structure such as pulse front tilt as well. We demonstrate the capabilities of the sensor through a parallel measurement of the wavefronts of 9 harmonics in a wavelength range between 25 and 49 nm, with up to lambda/32 precision.Comment: 12 pages, 6 figure