Superdiffusion in a non-Markovian random walk model with a Gaussian memory profile

Most superdiffusive Non-Markovian random walk models assume that correlations are maintained at all time scales, e. g., fractional Brownian motion, Levy walks, the Elephant walk and Alzheimer walk models. In the latter two models the random walker can always "remember" the initial times near t = 0. Assuming jump size distributions with finite variance, the question naturally arises: is superdiffusion possible if the walker is unable to recall the initial times? We give a conclusive answer to this general question, by studying a non-Markovian model in which the walker's memory of the past is weighted by a Gaussian centered at time t/2, at which time the walker had one half the present age, and with a standard deviation sigma t which grows linearly as the walker ages. For large widths we find that the model behaves similarly to the Elephant model, but for small widths this Gaussian memory profile model behaves like the Alzheimer walk model. We also report that the phenomenon of amnestically induced persistence, known to occur in the Alzheimer walk model, arises in the Gaussian memory profile model. We conclude that memory of the initial times is not a necessary condition for generating (log-periodic) superdiffusion. We show that the phenomenon of amnestically induced persistence extends to the case of a Gaussian memory profile.

Efficacy of gatifloxacin alone and in combination with cefepime against penicillin-resistant Streptococcus pneumoniae in a rabbit meningitis model and in vitro

Gatifloxacin penetrated well into cerebrospinal fluid (CSF) (49 +/- 11%), measured by comparison of AUC(CSF)/AUC(serum), and showed good bactericidal activity (leading to a decrease of 0.75 +/- 0.17 log10 cfu/mL/h) in the treatment of experimental meningitis in rabbits caused by a penicillin-resistant pneumococcal strain (MIC 4 mg/L). It was significantly more effective than the standard regimen, ceftriaxone with vancomycin, which led to a decrease of 0.53 +/- 0.17 log10 cfu/mL/h. The addition of cefepime to gatifloxacin slightly improved the killing rates (giving a decrease of 0.84 +/- 0.14 log10 cfu/mL/h). In vitro, synergy was demonstrated between cefepime and gatifloxacin by the chequerboard method (fractional inhibitory concentration index = 0.5) and by viable counts over 8 h.

Synergy between trovafloxacin and ceftriaxone against penicillin-resistant pneumococci in the rabbit meningitis model and in vitro

The bactericidal activities of monotherapy with trovafloxacin (-0.37 +/- 0.15 Delta log(10) CFU/ml. h), vancomycin (-0.32 +/- 0.12 Delta log(10) CFU/ml. h), and ceftriaxone (-0.36 +/- 0.19 Delta log(10) CFU/ml. h) for the treatment of experimental meningitis in rabbits due to a clinical penicillin-resistant pneumococcal strain (MIC, 4 mg/liter) were similar. The combination of ceftriaxone with trovafloxacin considerably improved the killing rates (-0.67 +/- 0.16 Delta log(10) CFU/ml. h) and was slightly superior to ceftriaxone with vancomycin (killing rate, -0.53 +/- 0. 22 Delta log(10) CFU/ml. h), the regimen most commonly used in clinical practice. In vitro, synergy was demonstrated between ceftriaxone and trovafloxacin by the checkerboard method (fractional inhibitory concentration index, 0.5) and by time-killing assays over 8 h.

Visualization of alveolar recruitment in a porcine model of unilateral lung lavage using 3He-MRI

BACKGROUND: In the acute respiratory distress syndrome potentially recruitable lung volume is currently discussed. (3)He-magnetic resonance imaging ((3)He-MRI) offers the possibility to visualize alveolar recruitment directly. METHODS: With the approval of the state animal care committee, unilateral lung damage was induced in seven anesthetized pigs by saline lavage of the right lungs. The left lung served as an intraindividual control (healthy lung). Unilateral lung damage was confirmed by conventional proton MRI and spiral-CT scanning. The total aerated lung volume was determined both at a positive end-expiratory pressure (PEEP) of 0 and 10 mbar from three-dimensionally reconstructed (3)He images, both for healthy and damaged lungs. The fractional increase of aerated volume in damaged and healthy lungs, followed by a PEEP increase from 0 to 10 mbar, was compared. RESULTS: Aerated gas space was visualized with a high spatial resolution in the three-dimensionally reconstructed (3)He-MR images, and aeration defects in the lavaged lung matched the regional distribution of atelectasis in proton MRI. After recruitment and PEEP increase, the aerated volume increased significantly both in healthy lungs from 415 ml [270-445] (median [min-max]) to 481 ml [347-523] and in lavaged lungs from 264 ml [71-424] to 424 ml [129-520]. The fractional increase in lavaged lungs was significantly larger than that in healthy lungs (healthy: 17% [11-38] vs. lavage: 42% [14-90] (P=0.031). CONCLUSION: The (3)He-MRI signal might offer an experimental approach to discriminate atelectatic vs. poor aerated lung areas in a lung damage animal model. Our results confirm the presence of potential recruitable lung volume by either alveolar collapse or alveolar flooding, in accordance with previous reports by computed tomography.

Quantitative diffusion tensor imaging detects dopaminergic neuronal degeneration in a murine model of Parkinson's disease.

Early diagnosis of Parkinson's disease (PD) is required to improve therapeutic responses. Indeed, a clinical diagnosis of resting tremor, rigidity, movement and postural deficiencies usually reflect >50% loss of the nigrostriatal system in disease. In a step to address this, quantitative diffusion tensor magnetic resonance imaging (DTI) was used to assess nigrostriatal degeneration in the 1-methyl-4-phenyl-1,2,3,6-tetrahydropyridine (MPTP) intoxication model of dopaminergic nigral degeneration. We now demonstrate increased average diffusion (p<0.005) and decreased fractional anisotropy (p<0.03) in the substantia nigra (SN) of 5- to 7-day MPTP-treated animals when compared to saline controls. Transverse diffusivity demonstrated the most significant differences (p < or = 0.002) and correlated with the numbers of SN dopaminergic neurons (r=-0.75, p=0.012). No differences were found in the striatum, corpus callosum, cerebral cortex, or ventricles. These results demonstrate that DTI may be used as a surrogate biomarker of nigral dopaminergic neuronal degeneration.

Non-exponential return time distributions for vorticity extremes explained by fractional Poisson processes

Serial correlation of extreme midlatitude cyclones observed at the storm track exits is explained by deviations from a Poisson process. To model these deviations, we apply fractional Poisson processes (FPPs) to extreme midlatitude cyclones, which are defined by the 850 hPa relative vorticity of the ERA interim reanalysis during boreal winter (DJF) and summer (JJA) seasons. Extremes are defined by a 99% quantile threshold in the grid-point time series. In general, FPPs are based on long-term memory and lead to non-exponential return time distributions. The return times are described by a Weibull distribution to approximate the Mittag–Leffler function in the FPPs. The Weibull shape parameter yields a dispersion parameter that agrees with results found for midlatitude cyclones. The memory of the FPP, which is determined by detrended fluctuation analysis, provides an independent estimate for the shape parameter. Thus, the analysis exhibits a concise framework of the deviation from Poisson statistics (by a dispersion parameter), non-exponential return times and memory (correlation) on the basis of a single parameter. The results have potential implications for the predictability of extreme cyclones.

Interim analysis of clinical trials: Simulation studies of fractional Brownian motion

Interim clinical trial monitoring procedures were motivated by ethical and economic considerations. Classical Brownian motion (Bm) techniques for statistical monitoring of clinical trials were widely used. Conditional power argument and α-spending function based boundary crossing probabilities are popular statistical hypothesis testing procedures under the assumption of Brownian motion. However, it is not rare that the assumptions of Brownian motion are only partially met for trial data. Therefore, I used a more generalized form of stochastic process, called fractional Brownian motion (fBm), to model the test statistics. Fractional Brownian motion does not hold Markov property and future observations depend not only on the present observations but also on the past ones. In this dissertation, we simulated a wide range of fBm data, e.g., H = 0.5 (that is, classical Bm) vs. 0.5< H <1, with treatment effects vs. without treatment effects. Then the performance of conditional power and boundary-crossing based interim analyses were compared by assuming that the data follow Bm or fBm. Our simulation study suggested that the conditional power or boundaries under fBm assumptions are generally higher than those under Bm assumptions when H > 0.5 and also matches better with the empirical results. ^

Assessment of the effect on statistical power of regression model misspecification by using techniques of mathematical statistics and simulation study

Objectives. This paper seeks to assess the effect on statistical power of regression model misspecification in a variety of situations. ^ Methods and results. The effect of misspecification in regression can be approximated by evaluating the correlation between the correct specification and the misspecification of the outcome variable (Harris 2010).In this paper, three misspecified models (linear, categorical and fractional polynomial) were considered. In the first section, the mathematical method of calculating the correlation between correct and misspecified models with simple mathematical forms was derived and demonstrated. In the second section, data from the National Health and Nutrition Examination Survey (NHANES 2007-2008) were used to examine such correlations. Our study shows that comparing to linear or categorical models, the fractional polynomial models, with the higher correlations, provided a better approximation of the true relationship, which was illustrated by LOESS regression. In the third section, we present the results of simulation studies that demonstrate overall misspecification in regression can produce marked decreases in power with small sample sizes. However, the categorical model had greatest power, ranging from 0.877 to 0.936 depending on sample size and outcome variable used. The power of fractional polynomial model was close to that of linear model, which ranged from 0.69 to 0.83, and appeared to be affected by the increased degrees of freedom of this model.^ Conclusion. Correlations between alternative model specifications can be used to provide a good approximation of the effect on statistical power of misspecification when the sample size is large. When model specifications have known simple mathematical forms, such correlations can be calculated mathematically. Actual public health data from NHANES 2007-2008 were used as examples to demonstrate the situations with unknown or complex correct model specification. Simulation of power for misspecified models confirmed the results based on correlation methods but also illustrated the effect of model degrees of freedom on power.^

Water level time series and sediment grain size model

The environment of ebb-tidal deltas between barrier island systems is characterized by a complex morphology with ebb- and flood-dominated channels, shoals and swash bars connecting the ebb-tidal delta platform to the adjacent island. These morphological features reveal characteristic surface sediment grain-size distributions and are subject to a continuous adaptation to the prevailing hydrodynamic forces. The mixed-energy tidal inlet Otzumer Balje between the East Frisian barrier islands of Langeoog and Spiekeroog in the southern North Sea has been chosen here as a model study area for the identification of relevant hydrodynamic drivers of morphology and sedimentology. We compare the effect of high-energy, wave-dominated storm conditions to mid-term, tide-dominated fair-weather conditions on tidal inlet morphology and sedimentology with a process-based numerical model. A multi-fractional approach with five grain-size fractions between 150 and 450 µm allows for the simulation of corresponding surface sediment grain-size distributions. Net sediment fluxes for distinct conditions are identified: during storm conditions, bed load sediment transport is generally onshore directed on the shallower ebb-tidal delta shoals, whereas fine-grained suspended sediment bypasses the tidal inlet by wave-driven currents. During fair weather the sediment transport mainly focuses on the inlet throat and the marginal flood channels. We show how the observed sediment grain-size distribution and the morphological response at mixed-energy tidal inlets are the result of both wave-dominated less frequent storm conditions and mid-term, tide-dominant fair-weather conditions.

Brain 5α-dihydroprogesterone and allopregnanolone synthesis in a mouse model of protracted social isolation

Allopregnanolone (ALLO), is a brain endogenous neurosteroid that binds with high affinity to γ-aminobutyric acid type A (GABAA) receptors and positively modulates the action of GABA at these receptors. Unlike ALLO, 5α-dihydroprogesterone (5α-DHP) binds with high affinity to intracellular progesterone receptors that regulate DNA transcription. To investigate the physiological roles of ALLO and 5α-DHP synthesized in brain, we have adopted a mouse model involving protracted social isolation. In the frontal cortex of mice, socially isolated for 6 weeks, both neurosteroids were decreased by approximately 50%. After administration of (17β)-17-(bis-1-methyl amino carbonyl) androstane-3,5-diene-3-carboxylic acid (SKF105,111), an inhibitor of the enzyme (5α-reductase Type I and II) that converts progesterone into 5α-DHP, the ALLO and 5α-DHP content of frontal cortex of both group-housed and socially isolated mice decreased exponentially to 10%–20% of control values in about 30 min. The fractional rate constants (k h−1) of ALLO and 5α-DHP decline multiplied by the ALLO and 5α-DHP concentrations at any given steady-state estimate the rate of synthesis required to maintain that steady state. After 6 weeks of social isolation, ALLO and 5α-DHP biosynthesis rates were decreased to 30% of the values calculated in group-housed mice. Moreover, in socially isolated mice, the expression of 5α-reductase Type I mRNA and protein was approximately 50% lower than in group-housed mice whereas 3α-hydroxysteroid oxidoreductase mRNA expression was equal in the two groups. Protracted social isolation in mice may provide a model to investigate whether 5α-DHP by a genomic action, and ALLO by a nongenomic mechanism down-regulate the action of drugs acting as agonists, partial agonists, or positive allosteric modulators of the benzodiazepine recognition sites expressed by GABAA receptors.

Cardiac βARK1 inhibition prolongs survival and augments β blocker therapy in a mouse model of severe heart failure

Chronic human heart failure is characterized by abnormalities in β-adrenergic receptor (βAR) signaling, including increased levels of βAR kinase 1 (βARK1), which seems critical to the pathogenesis of the disease. To determine whether inhibition of βARK1 is sufficient to rescue a model of severe heart failure, we mated transgenic mice overexpressing a peptide inhibitor of βARK1 (βARKct) with transgenic mice overexpressing the sarcoplasmic reticulum Ca2+-binding protein, calsequestrin (CSQ). CSQ mice have a severe cardiomyopathy and markedly shortened survival (9 ± 1 weeks). In contrast, CSQ/βARKct mice exhibited a significant increase in mean survival age (15 ± 1 weeks; P < 0.0001) and showed less cardiac dilation, and cardiac function was significantly improved (CSQ vs. CSQ/βARKct, left ventricular end diastolic dimension 5.60 ± 0.17 mm vs. 4.19 ± 0.09 mm, P < 0.005; % fractional shortening, 15 ± 2 vs. 36 ± 2, P < 0.005). The enhancement of the survival rate in CSQ/βARKct mice was substantially potentiated by chronic treatment with the βAR antagonist metoprolol (CSQ/βARKct nontreated vs. CSQ/βARKct metoprolol treated, 15 ± 1 weeks vs. 25 ± 2 weeks, P < 0.0001). Thus, overexpression of the βARKct resulted in a marked prolongation in survival and improved cardiac function in a mouse model of severe cardiomyopathy that can be potentiated with β-blocker therapy. These data demonstrate a significant synergy between an established heart-failure treatment and the strategy of βARK1 inhibition.

Estimating and forecasting generalized fractional Long memory stochastic volatility models

In recent years fractionally differenced processes have received a great deal of attention due to its flexibility in financial applications with long memory. This paper considers a class of models generated by Gegenbauer polynomials, incorporating the long memory in stochastic volatility (SV) components in order to develop the General Long Memory SV (GLMSV) model. We examine the statistical properties of the new model, suggest using the spectral likelihood estimation for long memory processes, and investigate the finite sample properties via Monte Carlo experiments. We apply the model to three exchange rate return series. Overall, the results of the out-of-sample forecasts show the adequacy of the new GLMSV model.

Absence of magnetically induced fractional quantization in atomic contacts

Using the mechanically controlled break junction technique at low temperatures and under cryogenic vacuum conditions we have studied atomic contacts of several magnetic (Fe, Co, and Ni) and nonmagnetic (Pt) metals, which recently were claimed to show fractional conductance quantization. In the case of pure metals we see no quantization of the conductance nor half quantization, even when high magnetic fields are applied. On the other hand, features in the conductance similar to (fractional) quantization are observed when the contact is exposed to gas molecules. Furthermore, the absence of fractional quantization when the contact is bridged by H2 indicates the current is never fully polarized for the metals studied here. Our results are in agreement with recent model calculations.

Statistical model of OFDMA cellular networks uplink interference using lognormal distribution

In this letter, we propose an analytical approach to model uplink intercell interference (ICI) in hexagonal grid based orthogonal frequency division multiple access (OFMDA) cellular networks. The key idea is that the uplink ICI from individual cells is approximated with a lognormal distribution with statistical parameters being determined analytically. Accordingly, the aggregated uplink ICI is approximated with another lognormal distribution and its statistical parameters can be determined from those of individual cells using Fenton-Wilkson method. Analytic expressions of uplink ICI are derived with two traditional frequency reuse schemes, namely integer frequency reuse schemes with factor 1 (IFR-1) and factor 3 (IFR-3). Uplink fractional power control and lognormal shadowing are modeled. System performances in terms of signal to interference plus noise ratio (SINR) and spectrum efficiency are also derived. The proposed model has been validated by simulations. © 2013 IEEE.

On Multi-Dimensional Random Walk Models Approximating Symmetric Space-Fractional Diffusion Processes

Mathematics Subject Classification: 26A33, 47B06, 47G30, 60G50, 60G52, 60G60.