The Planar Tree Packing Theorem

Packing graphs is a combinatorial problem where several given graphs are being mapped into a common host graph such that every edge is used at most once. In the planar tree packing problem we are given two trees T1 and T2 on n vertices and have to find a planar graph on n vertices that is the edge-disjoint union of T1 and T2. A clear exception that must be made is the star which cannot be packed together with any other tree. But according to a conjecture of Garc\'ia et al. from 1997 this is the only exception, and all other pairs of trees admit a planar packing. Previous results addressed various special cases, such as a tree and a spider tree, a tree and a caterpillar, two trees of diameter four, two isomorphic trees, and trees of maximum degree three. Here we settle the conjecture in the affirmative and prove its general form, thus making it the planar tree packing theorem. The proof is constructive and provides a polynomial time algorithm to obtain a packing for two given nonstar trees.Comment: Full version of our SoCG 2016 pape

Hysteresis and bi-stability by an interplay of calcium oscillations and action potential firing

Many cell types exhibit oscillatory activity, such as repetitive action potential firing due to the Hodgkin-Huxley dynamics of ion channels in the cell membrane or reveal intracellular inositol triphosphate (IP$_3$) mediated calcium oscillations (CaOs) by calcium-induced calcium release channels (IP$_3$-receptor) in the membrane of the endoplasmic reticulum (ER). The dynamics of the excitable membrane and that of the IP$_3$-mediated CaOs have been the subject of many studies. However, the interaction between the excitable cell membrane and IP$_3$-mediated CaOs, which are coupled by cytosolic calcium which affects the dynamics of both, has not been studied. This study for the first time applied stability analysis to investigate the dynamic behavior of a model, which includes both an excitable membrane and an intracellular IP$_3$-mediated calcium oscillator. Taking the IP$_3$ concentration as a control parameter, the model exhibits a novel rich spectrum of stable and unstable states with hysteresis. The four stable states of the model correspond in detail to previously reported growth-state dependent states of the membrane potential of normal rat kidney fibroblasts in cell culture. The hysteresis is most pronounced for experimentally observed parameter values of the model, suggesting a functional importance of hysteresis. This study shows that the four growth-dependent cell states may not reflect the behavior of cells that have differentiated into different cell types with different properties, but simply reflect four different states of a single cell type, that is characterized by a single model.Comment: 29 pages, 6 figure

Lipid metabolism during pregnancy:Consequences for mother and child

Purpose of review:Accommodating fetal growth and development, women undergo multiple physiological changes during pregnancy. In recent years, several studies contributed to the accumulating evidence about the impact of gestational hyperlipidemia on cardiovascular risk for mother and child. This review aims to provide a comprehensive overview of the current research on lipid profile alterations during pregnancy and its associated (cardiovascular) outcomes for mother and child from a clinical perspective.Recent findings:In a normal pregnancy, total and LDL-cholesterol levels increase by approximately 30-50%, HDL-cholesterol by 20-40%, and triglycerides by 50-100%. In some women, for example, with familial hypercholesterolemia (FH), a more atherogenic lipid profile is observed. Dyslipidemia during pregnancy is found to be associated with adverse (cardiovascular) outcomes for the mother (e.g. preeclampsia, gestational diabetes, metabolic syndrome, unfavorable lipid profile) and for the child (e.g. preterm birth, large for gestational age, preatherosclerotic lesions, unfavorable lipid profile).Summary:The lipid profile of women during pregnancy provides a unique window of opportunity into the potential future cardiovascular risk for mother and child. Better knowledge about adverse outcomes and specific risk groups could lead to better risk assessment and earlier cardiovascular prevention. Future research should investigate implementation of gestational screening possibilities.</p

Using local and historical data to enhance understanding of spatial and temporal rainfall patterns

Farmers face uncertainty in their businesses from many factors, but rainfall is a key determinant of both the nature of the production system and variation in financial returns. Currently, various weather forecasting services are available from the Australian Bureau of Meteorology (BoM) based on about 7000 stations covering all of Australia. Seasonal Climate Forecasts are seen as another tool that can help to improve farm productivity. It is well known that many farmers keep their own rainfall records, and likely that the farmers have a high degree of confidence in their own records. Australian Bureau of Statistics figures indicate that there were possibly 7000 grain related ‘agricultural businesses’ in NSW alone in 2009/10 indicating that there is the potential to increase data density by up to an order of magnitude. This project is part of a broader study to improve rainfall predictions for grain farmers using data collected locally to the users (crowd sourcing). The data is collected directly on farm, and from other sources which may be available. The focus is on the historical data, its collection and analysis, in terms of discerning patterns in time and space which may help provide a local framework, within which coarser scale forecasts can be interpreted and understood. Data will be stored on secure database systems at the University of Sydney. Results indicate that farm data does provide more local detail, temporally and spatially. Deficit and surplus analysis demonstrates the predictive capacity of the local temporal data, despite limited data precluding the definition of ideal criteria and parameters for predictive ‘similar year’ selection. The spatial data demonstrates quantifiable site specific differences from institutional data. Testing across more climate types may allow these differences to be defined within and across regions. Tests for an indicator time period show that farm rainfall in the early part of the growing season (April and May) may indeed be indicative of seasonal condtions, while more data is needed to confirm this. The use of southern oscillation life cycle information to select appropriate years considerably improved the relationships revealed, with a doubling of relationship strength across all climatic types, although the strength of the relationships differed across the climatic types, and the strongest relationships were split between the months of April and May. More extensive analysis, with more data across more BoM districts (and therefore climate classes) will be required to confirm this conclusion, but it appears that farm rainfall records and SOI information can provide an indicator time period to help farmers interpret, refine and utilise seasonal forecasts

When the Right (Drug) Should Be Left:Prenatal Drug Exposure and Heterotaxy Syndrome

Background: Recent studies reported an association between prenatal propylthiouracil exposure and birth defects, including abnormal arrangement across the left-right body axis, suggesting an association with heterotaxy syndrome. Methods: This case-control and case-finding study used data from 1981 to 2013 from the EUROCAT birth defect registry in the Northern Netherlands. First, we explored prenatal exposures in heterotaxy syndrome (cases) and Down syndrome (controls). Second, we describe the specific birth defects in offspring of mothers using propylthiouracil (PTU) prenatally. RESULTS: A total of 66 cases with heterotaxy syndrome (incidence 12.1 per 100,000 pregnancies) and 783 controls with Down syndrome (143.3 per 100,000 pregnancies) were studied. No differences in intoxication use during pregnancy were found between cases and controls, including smoking (28.0% vs. 22.7%; p = 0.40), alcohol (14.0% vs. 26.9%; p = 0.052), and recreational drugs (0 vs. 0.3%; p = 1.00). We found an association between heterotaxy syndrome and prenatal drug exposure to follitropin-alfa (5.6% vs. 1.1%; p = 0.04), and drugs used in nicotine dependence (3.7% vs. 0.2%; p = 0.02). Five mothers used PTU during pregnancy and gave birth to a child with trisomy 18, renal abnormalities, or hypospadias and cardiac defects. Conclusion: This study identified follitropin-alfa and drugs used in nicotine dependence as possible teratogens of heterotaxy syndrome. Our data suggest the possibility that there is an increased risk of birth defects (including renal, urological, and cardiac abnormalities) in children born among mothers taking PTU prenatally, but not for heterotaxy syndrome. (C) 2016 Wiley Periodicals, Inc.</p

Topological Phase Diagram of a Two-Subband Electron System

We present a phase diagram for a two-dimensional electron system with two populated subbands. Using a gated GaAs/AlGaAs single quantum well, we have mapped out the phases of various quantum Hall states in the density-magnetic filed plane. The experimental phase diagram shows a very different topology from the conventional Landau fan diagram. We find regions of negative differential Hall resistance which are interpreted as preliminary evidence of the long sought reentrant quantum Hall transitions. We discuss the origins of the anomalous topology and the negative differential Hall resistance in terms of the Landau level and subband mixing.Comment: 4 pages, 4 figure