On the Complexity of Distributed Splitting Problems

One of the fundamental open problems in the area of distributed graph algorithms is the question of whether randomization is needed for efficient symmetry breaking. While there are fast, $\text{poly}\log n$-time randomized distributed algorithms for all of the classic symmetry breaking problems, for many of them, the best deterministic algorithms are almost exponentially slower. The following basic local splitting problem, which is known as the \emph{weak splitting} problem takes a central role in this context: Each node of a graph $G=(V,E)$ has to be colored red or blue such that each node of sufficiently large degree has at least one node of each color among its neighbors. Ghaffari, Kuhn, and Maus [STOC '17] showed that this seemingly simple problem is complete w.r.t. the above fundamental open question in the following sense: If there is an efficient $\text{poly}\log n$-time determinstic distributed algorithm for weak splitting, then there is such an algorithm for all locally checkable graph problems for which an efficient randomized algorithm exists. In this paper, we investigate the distributed complexity of weak splitting and some closely related problems. E.g., we obtain efficient algorithms for special cases of weak splitting, where the graph is nearly regular. In particular, we show that if $\delta$ and $\Delta$ are the minimum and maximum degrees of $G$ and if $\delta=\Omega(\log n)$, weak splitting can be solved deterministically in time $O\big(\frac{\Delta}{\delta}\cdot\text{poly}(\log n)\big)$. Further, if $\delta = \Omega(\log\log n)$ and $\Delta\leq 2^{\varepsilon\delta}$, there is a randomized algorithm with time complexity $O\big(\frac{\Delta}{\delta}\cdot\text{poly}(\log\log n)\big)$

Brief Announcement: Local Distributed Algorithms in Highly Dynamic Networks

We define a generalization of local distributed graph problems to (synchronous round-based) dynamic networks and present a framework for developing algorithms for these problems. We require two properties from our algorithms: (1) They should satisfy non-trivial guarantees in every round. The guarantees should be stronger the more stable the graph has been during the last few rounds and they coincide with the definition of the static graph problem if no topological change appeared recently. (2) If a constant neighborhood around some part of the graph is stable during an interval, the algorithms quickly converge to a solution for this part of the graph that remains unchanged throughout the interval. We demonstrate our generic framework with two classic distributed graph, namely (degree+1)-vertex coloring and maximal independent set (MIS)

Strong Exchange Couplings Drastically Slow Down Magnetization Relaxation in an Air‐Stable Cobalt(II)‐Radical Single‐Molecule Magnet (SMM)

The energy barrier leading to magnetic bistability in molecular clusters is determined by the magnetic anisotropy of the cluster constituents. By incorporating a highly anisotropic four‐coordinate cobalt(II) building block into a strongly coupled fully air‐ and moisture‐stable three‐spin system, it proved possible to suppress under‐barrier Raman processes leading to 350‐fold increase of magnetization relaxation time and pronounced hysteresis. Relaxation times of up to 9 hours at low temperatures were found

Control of human endometrial stromal cell motility by PDGF-BB, HB-EGF and trophoblast-secreted factors

Human implantation involves extensive tissue remodeling at the fetal-maternal interface. It is becoming increasingly evident that not only trophoblast, but also decidualizing endometrial stromal cells are inherently motile and invasive, and likely contribute to the highly dynamic processes at the implantation site. The present study was undertaken to further characterize the mechanisms involved in the regulation of endometrial stromal cell motility and to identify trophoblast-derived factors that modulate migration. Among local growth factors known to be present at the time of implantation, heparin-binding epidermal growth factor-like growth factor (HB-EGF) triggered chemotaxis (directed locomotion), whereas platelet-derived growth factor (PDGF)-BB elicited both chemotaxis and chemokinesis (non-directed locomotion) of endometrial stromal cells. Supernatants of the trophoblast cell line AC-1M88 and of first trimester villous explant cultures stimulated chemotaxis but not chemokinesis. Proteome profiling for cytokines and angiogenesis factors revealed neither PDGF-BB nor HB-EGF in conditioned media from trophoblast cells or villous explants, while placental growth factor, vascular endothelial growth factor and PDGF-AA were identified as prominent secretory products. Among these, only PDGF-AA triggered endometrial stromal cell chemotaxis. Neutralization of PDGF-AA in trophoblast conditioned media, however, did not diminish chemoattractant activity, suggesting the presence of additional trophoblast-derived chemotactic factors. Pathway inhibitor studies revealed ERK1/2, PI3 kinase/Akt and p38 signaling as relevant for chemotactic motility, whereas chemokinesis depended primarily on PI3 kinase/Akt activation. Both chemotaxis and chemokinesis were stimulated upon inhibition of Rho-associated, coiled-coil containing protein kinase. The chemotactic response to trophoblast secretions was not blunted by inhibition of isolated signaling cascades, indicating activation of overlapping pathways in trophoblast-endometrial communication. In conclusion, trophoblast signals attract endometrial stromal cells, while PDGF-BB and HB-EGF, although not identified as trophoblast-derived, are local growth factors that may serve to fine-tune directed and non-directed migration at the implantation site

p53 and TAp63 promote keratinocyte proliferation and differentiation in breeding tubercles of the zebrafish

p63 is a multi-isoform member of the p53 family of transcription factors. There is compelling genetic evidence that ΔNp63 isoforms are needed for keratinocyte proliferation and stemness in the developing vertebrate epidermis. However, the role of TAp63 isoforms is not fully understood, and TAp63 knockout mice display normal epidermal development. Here, we show that zebrafish mutants specifically lacking TAp63 isoforms, or p53, display compromised development of breeding tubercles, epidermal appendages which according to our analyses display more advanced stratification and keratinization than regular epidermis, including continuous desquamation and renewal of superficial cells by derivatives of basal keratinocytes. Defects are further enhanced in TAp63/p53 double mutants, pointing to partially redundant roles of the two related factors. Molecular analyses, treatments with chemical inhibitors and epistasis studies further reveal the existence of a linear TAp63/p53->Notch->caspase 3 pathway required both for enhanced proliferation of keratinocytes at the base of the tubercles and their subsequent differentiation in upper layers. Together, these studies identify the zebrafish breeding tubercles as specific epidermal structures sharing crucial features with the cornified mammalian epidermis. In addition, they unravel essential roles of TAp63 and p53 to promote both keratinocyte proliferation and their terminal differentiation by promoting Notch signalling and caspase 3 activity, ensuring formation and proper homeostasis of this self-renewing stratified epithelium

Ueber Verbindungen von Arsen und Jod

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