The combinatorial Mandelbrot set as the quotient of the space of geolaminations

We interpret the combinatorial Mandelbrot set in terms of \it{quadratic laminations} (equivalence relations $\sim$ on the unit circle invariant under $\sigma_2$). To each lamination we associate a particular {\em geolamination} (the collection $\mathcal{L}_\sim$ of points of the circle and edges of convex hulls of $\sim$-equivalence classes) so that the closure of the set of all of them is a compact metric space with the Hausdorff metric. Two such geolaminations are said to be {\em minor equivalent} if their {\em minors} (images of their longest chords) intersect. We show that the corresponding quotient space of this topological space is homeomorphic to the boundary of the combinatorial Mandelbrot set. To each equivalence class of these geolaminations we associate a unique lamination and its topological polynomial so that this interpretation can be viewed as a way to endow the space of all quadratic topological polynomials with a suitable topology.Comment: 28 pages; in the new version a few typos are corrected; to appear in Contemporary Mathematic

Microbiological and geochemical characterization of As-bearing tailings and underlying sediments

Over the past 100 years, extensive oxidation of As-bearing sulfide-rich tailings from the abandoned Long Lake Gold Mine (Canada) has resulted in the formation of acid mine drainage (pH 2.0-3.9) containing high concentrations of dissolved As (∼400 mg L ), SO , Fe and other metals. Dissolved As is predominantly present as As(III), with increased As(V) near the tailings surface. Pore-gas O is depleted to < 1 vol% in the upper 30-80 cm of the tailings profile. The primary sulfides, pyrite and arsenopyrite, are highly oxidized in the upper portions of the tailings. Elevated proportions of sulfide-oxidizing prokaryotes are present in this zone (mean 32.3% of total reads). The tailings are underlain by sediments rich in organic C. Enrichment in δ S-SO in pore-water samples in the organic C-rich zone is consistent with dissimilatory sulfate reduction. Synchrotron-based spectroscopy indicates an abundance of ferric arsenate phases near the impoundment surface and the presence of secondary arsenic sulfides in the organic-C beneath the tailings. The persistence of elevated As concentrations beneath the tailings indicates precipitation of secondary As sulfides is not sufficient to completely remove dissolved As. The oxidation of sulfides and release of As is expected to continue for decades. The findings will inform future remediation efforts and provide a foundation for the long-term monitoring of the effectiveness of the remediation program. [Abstract copyright: Copyright © 2024 The Authors. Published by Elsevier B.V. All rights reserved.

A human MAP kinase interactome.

Mitogen-activated protein kinase (MAPK) pathways form the backbone of signal transduction in the mammalian cell. Here we applied a systematic experimental and computational approach to map 2,269 interactions between human MAPK-related proteins and other cellular machinery and to assemble these data into functional modules. Multiple lines of evidence including conservation with yeast supported a core network of 641 interactions. Using small interfering RNA knockdowns, we observed that approximately one-third of MAPK-interacting proteins modulated MAPK-mediated signaling. We uncovered the Na-H exchanger NHE1 as a potential MAPK scaffold, found links between HSP90 chaperones and MAPK pathways and identified MUC12 as the human analog to the yeast signaling mucin Msb2. This study makes available a large resource of MAPK interactions and clone libraries, and it illustrates a methodology for probing signaling networks based on functional refinement of experimentally derived protein-interaction maps

Impact of Sleep and Circadian Disruption on Energy Balance and Diabetes: A Summary of Workshop Discussions

A workshop was held at the National Institute for Diabetes and Digestive and Kidney Diseases with a focus on the impact of sleep and circadian disruption on energy balance and diabetes. The workshop identified a number of key principles for research in this area and a number of specific opportunities. Studies in this area would be facilitated by active collaboration between investigators in sleep/circadian research and investigators in metabolism/diabetes. There is a need to translate the elegant findings from basic research into improving the metabolic health of the American public. There is also a need for investigators studying the impact of sleep/circadian disruption in humans to move beyond measurements of insulin and glucose and conduct more in-depth phenotyping. There is also a need for the assessments of sleep and circadian rhythms as well as assessments for sleep-disordered breathing to be incorporated into all ongoing cohort studies related to diabetes risk. Studies in humans need to complement the elegant short-term laboratory-based human studies of simulated short sleep and shift work etc. with studies in subjects in the general population with these disorders. It is conceivable that chronic adaptations occur, and if so, the mechanisms by which they occur needs to be identified and understood. Particular areas of opportunity that are ready for translation are studies to address whether CPAP treatment of patients with pre-diabetes and obstructive sleep apnea (OSA) prevents or delays the onset of diabetes and whether temporal restricted feeding has the same impact on obesity rates in humans as it does in mice

Big data and data repurposing – using existing data to answer new questions in vascular dementia research

Introduction: Traditional approaches to clinical research have, as yet, failed to provide effective treatments for vascular dementia (VaD). Novel approaches to collation and synthesis of data may allow for time and cost efficient hypothesis generating and testing. These approaches may have particular utility in helping us understand and treat a complex condition such as VaD. Methods: We present an overview of new uses for existing data to progress VaD research. The overview is the result of consultation with various stakeholders, focused literature review and learning from the group’s experience of successful approaches to data repurposing. In particular, we benefitted from the expert discussion and input of delegates at the 9th International Congress on Vascular Dementia (Ljubljana, 16-18th October 2015). Results: We agreed on key areas that could be of relevance to VaD research: systematic review of existing studies; individual patient level analyses of existing trials and cohorts and linking electronic health record data to other datasets. We illustrated each theme with a case-study of an existing project that has utilised this approach. Conclusions: There are many opportunities for the VaD research community to make better use of existing data. The volume of potentially available data is increasing and the opportunities for using these resources to progress the VaD research agenda are exciting. Of course, these approaches come with inherent limitations and biases, as bigger datasets are not necessarily better datasets and maintaining rigour and critical analysis will be key to optimising data use

Practical aspects in the management of hypokalemic periodic paralysis

Management considerations in hypokalemic periodic paralysis include accurate diagnosis, potassium dosage for acute attacks, choice of diuretic for prophylaxis, identification of triggers, creating a safe physical environment, peri-operative measures, and issues in pregnancy. A positive genetic test in the context of symptoms is the gold standard for diagnosis. Potassium chloride is the favored potassium salt given at 0.5–1.0 mEq/kg for acute attacks. The oral route is favored, but if necessary, a mannitol solvent can be used for intravenous administration. Avoidance of or potassium prophylaxis for common triggers, such as rest after exercise, high carbohydrate meals, and sodium, can prevent attacks. Chronically, acetazolamide, dichlorphenamide, or potassium-sparing diuretics decrease attack frequency and severity but are of little value acutely. Potassium, water, and a telephone should always be at a patient's bedside, regardless of the presence of weakness. Perioperatively, the patient's clinical status should be checked frequently. Firm data on the management of periodic paralysis during pregnancy is lacking. Patient support can be found at