A Super-Fast Distributed Algorithm for Bipartite Metric Facility Location

The \textit{facility location} problem consists of a set of \textit{facilities} $\mathcal{F}$, a set of \textit{clients} $\mathcal{C}$, an \textit{opening cost} $f_i$ associated with each facility $x_i$, and a \textit{connection cost} $D(x_i,y_j)$ between each facility $x_i$ and client $y_j$. The goal is to find a subset of facilities to \textit{open}, and to connect each client to an open facility, so as to minimize the total facility opening costs plus connection costs. This paper presents the first expected-sub-logarithmic-round distributed O(1)-approximation algorithm in the $\mathcal{CONGEST}$ model for the \textit{metric} facility location problem on the complete bipartite network with parts $\mathcal{F}$ and $\mathcal{C}$. Our algorithm has an expected running time of $O((\log \log n)^3)$ rounds, where $n = |\mathcal{F}| + |\mathcal{C}|$. This result can be viewed as a continuation of our recent work (ICALP 2012) in which we presented the first sub-logarithmic-round distributed O(1)-approximation algorithm for metric facility location on a \textit{clique} network. The bipartite setting presents several new challenges not present in the problem on a clique network. We present two new techniques to overcome these challenges. (i) In order to deal with the problem of not being able to choose appropriate probabilities (due to lack of adequate knowledge), we design an algorithm that performs a random walk over a probability space and analyze the progress our algorithm makes as the random walk proceeds. (ii) In order to deal with a problem of quickly disseminating a collection of messages, possibly containing many duplicates, over the bipartite network, we design a probabilistic hashing scheme that delivers all of the messages in expected-$O(\log \log n)$ rounds.Comment: 22 pages. This is the full version of a paper that appeared in DISC 201

Lessons from the Congested Clique Applied to MapReduce

The main results of this paper are (I) a simulation algorithm which, under quite general constraints, transforms algorithms running on the Congested Clique into algorithms running in the MapReduce model, and (II) a distributed $O(\Delta)$-coloring algorithm running on the Congested Clique which has an expected running time of (i) $O(1)$ rounds, if $\Delta \geq \Theta(\log^4 n)$; and (ii) $O(\log \log n)$ rounds otherwise. Applying the simulation theorem to the Congested-Clique $O(\Delta)$-coloring algorithm yields an $O(1)$-round $O(\Delta)$-coloring algorithm in the MapReduce model. Our simulation algorithm illustrates a natural correspondence between per-node bandwidth in the Congested Clique model and memory per machine in the MapReduce model. In the Congested Clique (and more generally, any network in the $\mathcal{CONGEST}$ model), the major impediment to constructing fast algorithms is the $O(\log n)$ restriction on message sizes. Similarly, in the MapReduce model, the combined restrictions on memory per machine and total system memory have a dominant effect on algorithm design. In showing a fairly general simulation algorithm, we highlight the similarities and differences between these models.Comment: 15 page

Bi-allelic variants in RNF170 are associated with hereditary spastic paraplegia.

Alterations of Ca2+ homeostasis have been implicated in a wide range of neurodegenerative diseases. Ca2+ efflux from the endoplasmic reticulum into the cytoplasm is controlled by binding of inositol 1,4,5-trisphosphate to its receptor. Activated inositol 1,4,5-trisphosphate receptors are then rapidly degraded by the endoplasmic reticulum-associated degradation pathway. Mutations in genes encoding the neuronal isoform of the inositol 1,4,5-trisphosphate receptor (ITPR1) and genes involved in inositol 1,4,5-trisphosphate receptor degradation (ERLIN1, ERLIN2) are known to cause hereditary spastic paraplegia (HSP) and cerebellar ataxia. We provide evidence that mutations in the ubiquitin E3 ligase gene RNF170, which targets inositol 1,4,5-trisphosphate receptors for degradation, are the likely cause of autosomal recessive HSP in four unrelated families and functionally evaluate the consequences of mutations in patient fibroblasts, mutant SH-SY5Y cells and by gene knockdown in zebrafish. Our findings highlight inositol 1,4,5-trisphosphate signaling as a candidate key pathway for hereditary spastic paraplegias and cerebellar ataxias and thus prioritize this pathway for therapeutic interventions

Drawing-up of coagulation standards in sheep – precondition for extracorporeal oxygenation of premature lambs

Peer Reviewe

Material properties of human vertebral trabecular bone under compression can be predicted based on quantitative computed tomography

Gehweiler D, Schultz M, Schulze M, Riesenbeck O, Wähnert D, Raschke MJ. Material properties of human vertebral trabecular bone under compression can be predicted based on quantitative computed tomography. BMC Musculoskeletal Disorders. 2021;22(1): 709.**Background** The prediction of the stability of bones is becoming increasingly important. Especially osteoporotic vertebral body fractures are a growing problem and an increasing burden on the health system. Therefore, the aim of this study was to provide the best possible description of the relationship between the material properties of human vertebral trabecular bone measured under the most physiological conditions possible and the bone mineral density (BMD) determined by clinical quantitative computed tomography (QCT). **Methods** Forty eight cylindric cancellous bone samples with a diameter of 7.2 mm obtained from 13 human fresh-frozen lumbar vertebrae from 5 donors (3 men, 2 women) have been used for this study. After the specimens were temporarily reinserted into the vertebral body, the QCT was performed. For mechanical testing, the samples were embedded in a load-free manner using polymethylmetacrylate (PMMA). The surrounding test chamber was filled with phosphate buffered saline (PBS) and heated to 37 °C during the test. After 10 preconditioning load cycles, destructive testing was performed under axial compression. After determining the fracture site, BMD has been evaluated in this region only. Regression analyses have been performed. **Results** Fracture site had an average length of 2.4 (±1.4) mm and a position of 43.9 (±10.9) percent of the measurement length from the cranial end. No fracture reached the embedding. The average BMD at the fracture site was 80.2 (±28.7 | min. 14.5 | max. 137.8) mgCaHA/ml. In summary the results of the regression analyses showed for all three parameters a very good quality of fit by a power regression. **Conclusion** The results of this study show that QCT-based bone density measurements have a good predictive power for the material properties of the vertebral cancellous bone measured under near to physiological conditions. The mechanical bone properties of vertebral cancellous bone could be modelled with high accuracy in the investigated bone density range