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.

Hyperbaric Oxygen Therapy Induces Kidney Protection in an Ischemia/Reperfusion Model in Rats

Ischemia/reperfusion (I/R) injury remains a major cause of graft dysfunction, which impacts short- and long-term follow-up. Hyperbaric oxygen therapy (HBO), through plasma oxygen transport, has been currently used as an alternative treatment for ischemic tissues. The aim of this study was to analyze the effects of HBO on kidney I/R injury model in rats, in reducing the harmful effect of I/R. The renal I/R model was obtained by occluding bilateral renal pedicles with nontraumatic vascular clamps for 45 minutes, followed by 48 hours of reperfusion. HBO therapy was delivered an hypebaric chamber (2.5 atmospheres absolute). Animals underwent two sessions of 60 minutes each at 6 hours and 20 hours after initiation of reperfusion. Male Wistar rats (n = 38) were randomized into four groups: sham, sham operated rats; Sham+HBO, sham operated rats exposed to HBO; I/R, animals submitted to I/R; and I/R+HBO, I/R rats exposed to HBO. Blood, urine, and kidney tissue were collected for biochemical, histologic, and immunohistochemical analyses. The histopathological evaluation of the ischemic injury used a grading scale of 0 to 4. HBO attenuated renal dysfunction after ischemia characterized by a significant decrease in blood urea nitrogen (BUN), serum creatinine, and proteinuria in the I/R+HBO group compared with I/R alone. In parallel, tubular function was improved resulting in significantly lower fractional excretions of sodium and potassium. Kidney sections from the I/R plus HBO group showed significantly lower acute kidney injury scores compared with the I/R group. HBO treatment significantly diminished proliferative activity in I/R (P < .05). There was no significant difference in macrophage infiltration or hemoxygenase-1 expression. In conclusion, HBO attenuated renal dysfunction in a kidney I/R injury model with a decrease in BUN, serum creatinine, proteinuria, and fractional excretion of sodium and potassium, associated with reduced histological damage.