Combinatorial rigidity for some infinitely renormalizable unicritical polynomials

We prove combinatorial rigidity of infinitely renormalizable unicritical polynomials, P_c :z mapsto z^d+c, with complex c, under the a priori bounds and a certain combinatorial condition . This implies the local connectivity of the connectedness loci (the Mandelbrot set when d = 2) at the corresponding parameters

Arithmetic geometric model for the renormalisation of irrationally indifferent attractors

In this paper we build a geometric model for the renormalisation of irrationally indifferent fixed points. The geometric model incorporates the fine arithmetic properties of the rotation number at the fixed point. Using this model for the renormalisation, we build a topological model for the dynamics of a holomorphic map near an irrationally indifferent fixed point. We also explain the topology of the maximal invariant set for the model, and also explain the dynamics of the map on the maximal invariant set

Statistical properties of quadratic polynomials with a neutral fixed point

We describe the statistical properties of the dynamics of the quadratic polynomials P_a(z):=e^{2\pi a i} z+z^2 on the complex plane, with a of high return times. In particular, we show that these maps are uniquely ergodic on their measure theoretic attractors, and the unique invariant probability is a physical measure describing the statistical behavior of typical orbits in the Julia set. This confirms a conjecture of Perez-Marco on the unique ergodicity of hedgehog dynamics, in this class of maps

Analytic maps of parabolic and elliptic type with trivial centralisers

We prove that for a dense set of irrational numbers α, the analytic centraliser of the map e^{2πiα} z+ z2 near 0 is trivial. We also prove that some analytic circle diffeomorphisms in the Arnold family, with irrational rotation numbers, have trivial centralisers. These provide the first examples of such maps with trivial centralisers

Investigating the relationship between low serum cholesterol and suicide in attempters with depression

Background & Objective: It has been postulated that depressed individuals with low total cholesterol levels may be more likely to die prematurely from suicide. This study aimed to examine the association between low serum cholesterol and suicide in depressed attempters. Materials & Methods: In this cross-sectional study, 180 suicide attempters, who met the inclusion criteria and were willing to participate in the study, were recruited in 2017. The data was collected using a demographic questionnaire and the Beck Depression Inventory-Second Edition (BDI-II). The blood cholesterol level was measured via an auto-analyzer. Results: The mean age was 26.39±10.75 years. The average cholesterol level in the moderate, severe, and serious depression groups was 151.30±35.23, 145.89±36.32, and 145.15±33.33, respectively. The mean age was higher in the group with a higher depression level, though the difference was not significant (P=0.06). The percentage of suicide attempts in single individuals was significantly higher (P=0.02). The mean cholesterol level in the group with the highest level of depression was the lowest, but the difference was insignificant (r=-.01, P=0.85). Only in females, the level of blood cholesterol showed a nearly significant difference between groups with different severities of depression (P=0.05). Cholesterol had a significant correlation with suicide frequency (P=0.008, r=0.28). Conclusion: Our results revealed no significant association between low serum cholesterol and suicide in attempters with depression; but low total serum cholesterol may be associated with depression and suicide in depressed subjects. Yet, more studies are required for verification of this causality. © 2020, Journal of Advances in Medical and Biomedical Research. All rights reserved

Validation of the Framingham hypertension risk score in a middle eastern population: Tehran lipid and glucose study (TLGS)

Background The Framingham hypertension risk score is a well-known and simple model for predicting hypertension in adults. In the current study, we aimed to assess the predictive ability of this model in a Middle Eastern population.MethodsWe studied 5423 participants, aged 20-69years, without hypertension, who participated in two consecutive examination cycles of the Tehran Lipid and Glucose Study (TLGS). We assessed discrimination based on Harrell's concordance statistic (c-index) and calibration (graphical comparison of predicted vs. observed). We evaluated the original, recalibrated (for intercept and slope), and revised (for beta coefficients) models.ResultsOver the 3-year follow-up period, 319 participants developed hypertension. The Framingham hypertension risk score performed well in discriminating between individuals who developed hypertension and those who did not (c-index=0.81, 95% CI: 0.79-0.83). Initially, there was a systematic underestimation of the original risk score (events predicted), which was readily corrected by a simple model revision.ConclusionsThe revised Framingham hypertension risk score can be used as a screening tool in public health and clinical practice to facilitate the targeting of preventive interventions in high-risk Middle Eastern people.Development and application of statistical models for medical scientific researc

Transport time scales in soil erosion modelling

Unlike sediment transport in rivers, erosion of agricultural soil must overcome its cohesive strength to move soil particles into suspension. Soil particle size variability also leads to fall velocities covering many orders of magnitude, and hence to different suspended travel distances in overland flow. Consequently, there is a large range of inherent time scales involved in transport of eroded soil. For conditions where there is a constant rainfall rate and detachment is the dominant erosion mechanism, we use the Hairsine-Rose (HR) model to analyze these timescales, to determine their magnitude (bounds) and to provide simple approximations for them. We show that each particle size produces both fast and slow timescales. The fast timescale controls the rapid adjustment away from experimental initial conditions – this happens so quickly that it cannot be measured in practice. The slow time scales control the subsequent transition to steady state and are so large that true steady state is rarely achieved in laboratory experiments. Both the fastest and slowest time scales are governed by the largest particle size class. Physically, these correspond to the rate of vertical movement between suspension and the soil bed, and the time to achieve steady state, respectively. For typical distributions of size classes, we also find that there is often a single dominant time scale that governs the growth in the total mass of sediment in the non-cohesive deposited layer. This finding allows a considerable simplification of the HR model leading to analytical expressions for the evolution of suspended and deposited layer concentrations

Catchment drainage network scaling laws found experimentally in overland flow morphologies

The scaling relation between the drainage area and stream length (Hack's law), along with exceedance probabilities of drainage area, discharge, and upstream flow network length, is well known for channelized fluvial regions. We report here on a laboratory experiment on an eroding unconsolidated sediment for which no channeling occurred. Laser scanning was used to capture the morphological evolution of the sediment. High-intensity, spatially nonuniform rainfall ensured that the morphology changed substantially over the 16-hr experiment. Based on the surface scans and precipitation distribution, overland flow was estimated with the D8 algorithm, which outputs a flow network that was analyzed statistically. The above-mentioned scaling and exceedance probability relationships for this overland flow network are the same as those found for large-scale catchments and for laboratory experiments with observable channels. In addition, the scaling laws were temporally invariant, even though the network dynamically changed over the course of experiment