Global first-passage times of fractal lattices

The global first passage time density of a network is the probability that a random walker released at a random site arrives at an absorbing trap at time T. We find simple expressions for the mean global first passage time for five fractals: the d-dimensional Sierpinski gasket, T fractal, hierarchical percolation model, Mandelbrot-Given curve, and a deterministic tree. We also find an exact expression for the second moment and show that the variance of the first passage time, Var(T), scales with the number of nodes within the fractal N such that Var(T)similar to N(4/d), where d is the spectral dimension

SPECT- and PET-Based Approaches for Noninvasive Diagnosis of Acute Renal Allograft Rejection

Molecular imaging techniques such as single photon emission computed tomography (SPECT) or positron emission tomography are promising tools for noninvasive diagnosis of acute allograft rejection (AR). Given the importance of renal transplantation and the limitation of available donors, detailed analysis of factors that affect transplant survival is important. Episodes of acute allograft rejection are a negative prognostic factor for long-term graft survival. Invasive core needle biopsies are still the “goldstandard” in rejection diagnostics. Nevertheless, they are cumbersome to the patient and carry the risk of significant graft injury. Notably, they cannot be performed on patients taking anticoagulant drugs. Therefore, a noninvasive tool assessing the whole organ for specific and fast detection of acute allograft rejection is desirable. We herein review SPECT- and PET-based approaches for noninvasive molecular imaging-based diagnostics of acute transplant rejection

Existence of a Meromorphic Extension of Spectral Zeta Functions on Fractals

We investigate the existence of the meromorphic extension of the spectral zeta function of the Laplacian on self-similar fractals using the classical results of Kigami and Lapidus (based on the renewal theory) and new results of Hambly and Kajino based on the heat kernel estimates and other probabilistic techniques. We also formulate conjectures which hold true in the examples that have been analyzed in the existing literature

Hydroxyfasudil-Mediated Inhibition of ROCK1 and ROCK2 Improves Kidney Function in Rat Renal Acute Ischemia-Reperfusion Injury

Renal ischemia-reperfusion (IR) injury (IRI) is a common and important trigger of acute renal injury (AKI). It is inevitably linked to transplantation. Involving both, the innate and the adaptive immune response, IRI causes subsequent sterile inflammation. Attraction to and transmigration of immune cells into the interstitium is associated with increased vascular permeability and loss of endothelial and tubular epithelial cell integrity. Considering the important role of cytoskeletal reorganization, mainly regulated by RhoGTPases, in the development of IRI we hypothesized that a preventive, selective inhibition of the Rho effector Rho-associated coiled coil containing protein kinase (ROCK) by hydroxyfasudil may improve renal IRI outcome. Using an IRI-based animal model of AKI in male Sprague Dawley rats, animals treated with hydroxyfasudil showed reduced proteinuria and polyuria as well as increased urine osmolarity when compared with sham-treated animals. In addition, renal perfusion (as assessed by 18F-fluoride Positron Emission Tomography (PET)), creatinine- and urea-clearances improved significantly. Moreover, endothelial leakage and renal inflammation was significantly reduced as determined by histology, 18F-fluordesoxyglucose-microautoradiography, Evans Blue, and real-time PCR analysis. We conclude from our study that ROCK-inhibition by hydroxyfasudil significantly improves kidney function in a rat model of acute renal IRI and is therefore a potential new therapeutic option in humans

Point sets on the sphere S2\mathbb{S}^2 with small spherical cap discrepancy

In this paper we study the geometric discrepancy of explicit constructions of uniformly distributed points on the two-dimensional unit sphere. We show that the spherical cap discrepancy of random point sets, of spherical digital nets and of spherical Fibonacci lattices converges with order $N^{-1/2}$. Such point sets are therefore useful for numerical integration and other computational simulations. The proof uses an area-preserving Lambert map. A detailed analysis of the level curves and sets of the pre-images of spherical caps under this map is given