Fat fractal percolation and k-fractal percolation

We consider two variations on the Mandelbrot fractal percolation model. In the k-fractal percolation model, the d-dimensional unit cube is divided in N^d equal subcubes, k of which are retained while the others are discarded. The procedure is then iterated inside the retained cubes at all smaller scales. We show that the (properly rescaled) percolation critical value of this model converges to the critical value of ordinary site percolation on a particular d-dimensional lattice as N tends to infinity. This is analogous to the result of Falconer and Grimmett that the critical value for Mandelbrot fractal percolation converges to the critical value of site percolation on the same d-dimensional lattice. In the fat fractal percolation model, subcubes are retained with probability p_n at step n of the construction, where (p_n) is a non-decreasing sequence with \prod p_n > 0. The Lebesgue measure of the limit set is positive a.s. given non-extinction. We prove that either the set of connected components larger than one point has Lebesgue measure zero a.s. or its complement in the limit set has Lebesgue measure zero a.s.Comment: 27 pages, 3 figure

Characteristics of Long-Stay Patients in a PICU and Healthcare Resource Utilization after Discharge

OBJECTIVES: To examine the characteristics of long-stay patients (LSPs) admitted to a PICU and to investigate discharge characteristics of medical complexity among discharged LSP. DESIGN: We performed a retrospective cohort study where clinical data were collected on all children admitted to our PICU between July 1, 2017, and January 1, 2020. SETTING: A single-center study based at Erasmus MC Sophia Children's Hospital, a level III interdisciplinary PICU in The Netherlands, providing all pediatric and surgical subspecialties. PATIENTS:LSP was defined as those admitted for at least 28 consecutive days. INTERVENTIONS: None. MEASUREMENTS: Length of PICU stay, diagnosis at admission, length of mechanical ventilation, need for extracorporeal membrane oxygenation, mortality, discharge location after PICU and hospital admission, medical technical support, medication use, and involvement of allied healthcare professionals after hospital discharge. MAIN RESULTS: LSP represented a small proportion of total PICU patients (108 patients; 3.2%) but consumed 33% of the total admission days, 47% of all days on extracorporeal membrane oxygenation, and 38% of all days on mechanical ventilation. After discharge, most LSP could be classified as children with medical complexity (CMC) (76%); all patients received discharge medications (median 5.5; range 2-19), most patients suffered from a chronic disease (89%), leaving the hospital with one or more technological devices (82%) and required allied healthcare professional involvement after discharge (93%). CONCLUSIONS: LSP consumes a considerable amount of resources in the PICU and its impact extends beyond the point of PICU discharge since the majority are CMC. This indicates complex care needs at home, high family needs, and a high burden on the healthcare system across hospital borders.</p

Intracerebral adenosine during sleep deprivation : A meta-analysis and new experimental data

Funding Information: The systematic review was funded by The Netherlands Organisation for Health Research and Development (ZonMW; 114024101); R2N, Federal State of Lower Saxony; and the DFG (FOR2591, BL 953/11-1). The microdialysis experiment was funded by Netherlands Organization for Scientific Research (NWO; 051-04-010, to Eus van Some-ren). The HPLC adenosine measurements were funded by the University of Helsinki sleep team and a travel grant from the European Sleep Research Society. Publisher Copyright: © 2018 Ubiquity Press. All rights reserved.The neuroregulator adenosine is involved in sleep-wake control. Basal forebrain (BF) adenosine levels increase during sleep deprivation. Only a few studies have addressed the effect of sleep deprivation on extracellular adenosine concentrations in other brain regions. In this paper, we describe a microdialysis experiment as well as a meta-analysis of published data. The 64 h microdialysis experiment determined the extracellular adenosine and adenosine monophosphate (AMP) concentrations in the medial prefrontal cortex of rats before, during and after 12 h of sleep deprivation by forced locomotion. The meta-analysis comprised published sleep deprivation animal experiments measuring adenosine by means of microdialysis. In the animal experiment, the overall median adenosine concentration was 0.36 nM and ranged from 0.004 nM to 27 nM. No significant differences were observed between the five conditions: 12 h of washout, baseline light phase, baseline dark phase, 12 h of sleep deprivation and 12 h of subsequent recovery. The overall median AMP concentration was 0.10 nM and ranged from 0.001 nM to 7.56 nM. Median AMP concentration increased during sleep deprivation (T = 47; p = 0.047) but normalised during subsequent recovery. The meta-analysis indicates that BF dialysate adenosine concentrations increase with 74.7% (95% CI: 54.1-95.3%) over baseline during sleep deprivation. Cortex dialysate adenosine concentrations during sleep deprivation were so far only reported by 2 publications. The increase in adenosine during sleep deprivation might be specific to the BF. At this stage, the evidence for adenosine levels in other brain regions is based on single experiments and insufficient for generalised conclusions. Further experiments are currently still warranted.Peer reviewe

Endocrine and metabolic responses in children with meningoccocal sepsis: striking differences between survivors and nonsurvivors

To get insight in the endocrine and metabolic responses in children with meningococcal sepsis 26 children were studied the first 48 h after admission. On admission there was a significant difference in cortisol/ACTH levels between nonsurvivors (n = 8) and survivors (n = 18). Nonsurvivors showed an inadequate cortisol stress response in combination to very high ACTH levels, whereas survivors showed a normal stress response with significantly higher cortisol levels (0.62 vs. 0.89 micromol/L) in combination with moderately increased ACTH levels (1234 vs. 231 ng/L). Furthermore, there was a significant difference between nonsurvivors and survivors regarding pediatric risk of mortality score (31 vs. 17), TSH (0.97 vs. 0.29 mE/L), T3 (0.53 vs. 0.38 nmol/L), reverse T3 (rT3) (0.75 vs. 1.44 nmol/L), C-reactive protein (34 vs. 78 mg/L), nonesterified fatty acids (0.32 vs. 0.95 mmol/L), and lactate (7.3 vs. 3.2 mmol/L). In those who survived, the most importan

Identification of quiescent, stem-like cells in the distal female reproductive tract

In fertile women, the endometrium undergoes regular cycles of tissue build-up and regression. It is likely that uterine stem cells are involved in this remarkable turn over. The main goal of our current investigations was to identify slow-cycling (quiescent) endometrial stem cells by means of a pulse-chase approach to selectively earmark, prospectively isolate, and characterize label-retaining cells (LRCs). To this aim, transgenic mice expressing histone2B-GFP (H2B-GFP) in a Tet-inducible fashion were administered doxycycline (pulse) which was thereafter withdrawn from the drinking water (chase). Over time, dividing cells progressively loose GFP signal whereas infrequently dividing cells retain H2B-GFP expression. We evaluated H2B-GFP retaining cells at different chase time points and identified long-term (LT; >12 weeks) LRCs. The LT-LRCs are negative for estrogen receptor-α and express low levels of progesterone receptors. LRCs sorted by FACS are able to form spheroids capable of self-renewal and differentiation. Upon serum stimulation spheroid cells are in

Dimension (in)equalities and H\"older continuous curves in fractal percolation

We relate various concepts of fractal dimension of the limiting set C in fractal percolation to the dimensions of the set consisting of connected components larger than one point and its complement in C (the "dust"). In two dimensions, we also show that the set consisting of connected components larger than one point is a.s. the union of non-trivial H\"older continuous curves, all with the same exponent. Finally, we give a short proof of the fact that in two dimensions, any curve in the limiting set must have Hausdorff dimension strictly larger than 1.Comment: 22 pages, 3 figures, accepted for publication in Journal of Theoretical Probabilit

Trivial, Critical and Near-critical Scaling Limits of Two-dimensional Percolation

It is natural to expect that there are only three possible types of scaling limits for the collection of all percolation interfaces in the plane: (1) a trivial one, consisting of no curves at all, (2) a critical one, in which all points of the plane are surrounded by arbitrarily large loops and every deterministic point is almost surely surrounded by a countably infinite family of nested loops with radii going to zero, and (3) an intermediate one, in which every deterministic point of the plane is almost surely surrounded by a largest loop and by a countably infinite family of nested loops with radii going to zero. We show how one can prove this using elementary arguments, with the help of known scaling relations for percolation. The trivial limit corresponds to subcritical and supercritical percolation, as well as to the case when the density p approaches the critical probability, p_c, sufficiently slowly as the lattice spacing is sent to zero. The second type corresponds to critical percolation and to a faster approach of p to p_c. The third, or near-critical, type of limit corresponds to an intermediate speed of approach of p to p_c. The fact that in the near-critical case a deterministic point is a.s. surrounded by a largest loop demonstrates the persistence of a macroscopic correlation length in the scaling limit and the absence of scale invariance.Comment: 15 pages, 3 figure

Dysregulated innate and adaptive immune responses discriminate disease severity in COVID-19

The clinical spectrum of COVID-19 varies and the differences in host response characterizing this variation have not been fully elucidated. COVID-19 disease severity correlates with an excessive pro-inflammatory immune response and profound lymphopenia. Inflammatory responses according to disease severity were explored by plasma cytokine measurements and proteomics analysis in 147 COVID-19 patients. Furthermore, peripheral blood mononuclear cell cytokine production assays and whole blood flow cytometry were performed. Results confirm a hyperinflammatory innate immune state, while highlighting hepatocyte growth factor and stem cell factor as potential biomarkers for disease severity. Clustering analysis reveals no specific inflammatory endotypes in COVID-19 patients. Functional assays reveal abrogated adaptive cytokine production (interferon-gamma, interleukin-17 and interleukin-22) and prominent T cell exhaustion in critically ill patients, whereas innate immune responses were intact or hyperresponsive. Collectively, this extensive analysis provides a comprehensive insight into the pathobiology of severe to critical COVID-19 and highlight potential biomarkers of disease severity

Resolving sepsis-induced immunoparalysis via trained immunity by targeting interleukin-4 to myeloid cells.

Immunoparalysis is a compensatory and persistent anti-inflammatory response to trauma, sepsis or another serious insult, which increases the risk of opportunistic infections, morbidity and mortality. Here, we show that in cultured primary human monocytes, interleukin-4 (IL4) inhibits acute inflammation, while simultaneously inducing a long-lasting innate immune memory named trained immunity. To take advantage of this paradoxical IL4 feature in vivo, we developed a fusion protein of apolipoprotein A1 (apoA1) and IL4, which integrates into a lipid nanoparticle. In mice and non-human primates, an intravenously injected apoA1-IL4-embedding nanoparticle targets myeloid-cell-rich haematopoietic organs, in particular, the spleen and bone marrow. We subsequently demonstrate that IL4 nanotherapy resolved immunoparalysis in mice with lipopolysaccharide-induced hyperinflammation, as well as in ex vivo human sepsis models and in experimental endotoxemia. Our findings support the translational development of nanoparticle formulations of apoA1-IL4 for the treatment of patients with sepsis at risk of immunoparalysis-induced complications.We thank M. Jaeger (Radboudumc) for kindly providing flourescein isothiocyanate-labelled Candida albicans. D. Williams (East Tennessee State University) provided the β-glucan we used in our initial experiments. H. Lemmers (Radboudumc) kindly prepared the purified lipopolysaccharide used for stimulation of primary human monocytes and macrophages. Part of the figures were prepared using (among other software) Biorender.com. B.N. is supported by a National Health and Medical Research Council (Australia) Investigator Grant (APP1173314). This work was supported by National Institutes of Health grants R01 HL144072, R01 CA220234 and P01 HL131478, as well as a Vici grant from the Dutch Research Council NWO and an ERC Advanced Grant (all to W.J.M.M.). M.G.N. was supported by a Spinoza grant from Dutch Research Council NWO and an ERC Advanced Grant (#833247).S