For a split reductive group G over a finite field, we show that the intersection (cohomology) motive of the moduli stack of iterated G-shtukas with bounded modification and level structure is defined independently of the standard conjectures on motivic t-structures on triangulated categories of motives. This is in accordance with general expectations on the independence of ℓ in the Langlands correspondence for function fields.

We introduce the symmetricity notions of symmetric h-monoidality, symmetroidality, and symmetric flatness. As shown in our paper arXiv:1410.5675, these properties lie at the heart of the homotopy theory of colored symmetric operads and their algebras. In particular, they allow one to equip categories of algebras over operads with model structures and to show that weak equivalences of operads induce Quillen equivalences of categories of algebras. We discuss these properties for elementary model categories such as simplicial sets, simplicial presheaves, and chain complexes. Moreover, we provide powerful tools to promote these properties from such basic model categories to more involved ones, such as the stable model structure on symmetric spectra.

Cortical tissue perfusion in renal transplants was quantified noninvasively from color Doppler signal data in an easily accomplishable manner. Renal transplants showed a marked decline in tissue perfusion after transplantation. Perfusion is significantly lower in transplant function loss with elevated serum creatinine.

Objective: Perfusion quantification of tissues is an important goal to evaluate the state of blood supply of an organ. We developed a method to quantify tissue perfusion via color Doppler signal quantification from sonographic videos and applied this to describe renal parenchymal perfusion in healthy kidneys. Method: Color Doppler sonographic videos of renal perfusion from both kidneys of 87 healthy children (age 2 weeks to 16 years) were recorded under defined conditions. Perfusion data (color hue, color area) were measured in a standardized region of interest automatically. Signal intensity was calculated as whole ROIs (regions of interest) mean flow velocity (cm/s) encoded by color Doppler signals during one full heart cycle. Results: Normal signal intensity values are: 1.86 cm/s in the region encompassing central 50% of the renal cortex and 0.56 cm/s in the peripheral 50% of the renal cortex. These differences are significant. Signal intensity of both kidneys did not differ. Conclusion: Signal intensity of cortical tissue in healthy kidneys was quantified noninvasively from color Doppler signal data in an easily accomplishable manner with new measurement software. Normal values for this technique have been calculated. Possible further applications might be all situations, where perfusion changes could be expected like inflammation, renal insufficiency, vascular diseases and tumors.

We establish a highly flexible condition that guarantees that all colored symmetric operads in a symmetric monoidal model category are admissible, that is, the category of algebras over any operad admits a model structure transferred from the original model category. We also give a necessary and sufficient criterion that ensures that a given weak equivalence of admissible operads admits rectification, that is, the corresponding Quillen adjunction between the categories of algebras is a Quillen equivalence. In addition, we show that Quillen equivalences of underlying symmetric monoidal model categories yield Quillen equivalences of model categories of algebras over operads. Applications of these results include enriched categories, colored operads, prefactorization algebras, and commutative symmetric ring spectra. Contents