Local dynamics for fibered holomorphic transformations

Fibered holomorphic dynamics are skew-product transformations over an irrational rotation, whose fibers are holomorphic functions. In this paper we study such a dynamics on a neighborhood of an invariant curve. We obtain some results analogous to the results in the non fibered case

FDTD Data Extrapolation Using Multilayer Perceptron (MLP)

This work compares MLP with the matrix pencil method, a linear eigenanalysis-based extrapolator, in terms of their effectiveness in finite difference time domain (FDTD) data extrapolation. Matrix pencil method considers the signal as superposed complex exponentials while MLP considers each time step to be a nonlinear function of previous time steps

Perturbation theorems for Hele-Shaw flows and their applications

In this work, we give a perturbation theorem for strong polynomial solutions to the zero surface tension Hele-Shaw equation driven by injection or suction, so called the Polubarinova-Galin equation. This theorem enables us to explore properties of solutions with initial functions close to but are not polynomial. Applications of this theorem are given in the suction or injection case. In the former case, we show that if the initial domain is close to a disk, most of fluid will be sucked before the strong solution blows up. In the later case, we obtain precise large-time rescaling behaviors for large data to Hele-Shaw flows in terms of invariant Richardson complex moments. This rescaling behavior result generalizes a recent result regarding large-time rescaling behavior for small data in terms of moments. As a byproduct of a theorem in this paper, a short proof of existence and uniqueness of strong solutions to the Polubarinova-Galin equation is given.Comment: 25 page

Increasing emergency number utilisation is not driven by low-acuity calls: an observational study of 1.5 million emergency calls (2018 – 2021) from Berlin

Background: The Emergency Medical Service (EMS) in Germany is increasingly challenged by strongly rising demand. Speculations about a greater utilisation for minor cases have led to intensive media coverage, but empirical evidence is lacking. We investigated the development of low-acuity calls from 2018 to 2021 in the federal state of Berlin and its correlations with sociodemographic characteristics. Methods: We analysed over 1.5 million call documentations including medical dispatch codes, age, location and time using descriptive and inferential statistics and multivariate binary logistic regression. We defined a code list to classify low-acuity calls and merged the dataset with sociodemographic indicators and data on population density. Results: The number of emergency calls (phone number 112 in Germany) increased by 9.1% from 2018 to 2021; however, the proportion of low-acuity calls did not increase. The regression model shows higher odds of low-acuity for young to medium age groups (especially for age 0–9, OR 1.50 [95% CI 1.45–1.55]; age 10–19, OR 1.77 [95% CI 1.71–1.83]; age 20–29, OR 1.64 [95% CI 1.59–1.68] and age 30–39, OR 1.40 [95% CI 1.37–1.44]; p < 0.001, reference group 80–89) and for females (OR 1.12 [95% CI 1.1–1.13], p < 0.001). Odds were slightly higher for calls from a neighbourhood with lower social status (OR 1.01 per index unit increase [95% CI 1.0–1.01], p < 0.05) and at the weekend (OR 1.02 [95% CI 1.0–1.04, p < 0.05]). No significant association of the call volume with population density was detected. Conclusions: This analysis provides valuable new insights into pre-hospital emergency care. Low-acuity calls were not the primary driver of increased EMS utilisation in Berlin. Younger age is the strongest predictor for low-acuity calls in the model. The association with female gender is significant, while socially deprived neighbourhoods play a minor role. No statistically significant differences in call volume between densely and less densely populated regions were detected. The results can inform the EMS in future resource planning

Sharp inequalities for the coefficients of concave schlicht functions

Let D denote the open unit disc and let f: D → ℂ be holomorphic and injective in D. We further assume that f(D) is unbounded and ℂ \ f(D) is a convex domain. In this article, we consider the Taylor coefficients a n(f) of the normalized expansion f(z) = z + Σ n=2 ∞an(f)zn, z ∈ D, n=2 and we impose on such functions f the second normalization f(1) = ∞. We call these functions concave schlicht functions, as the image of D is a concave domain. We prove that the sharp inequalities |an(f)-n+1/2 ≤ n-1/2, n≥2, are valid. This settles a conjecture formulated in [2]. © Swiss Mathematical Society

On the coefficients of concave univalent functions

Let D denote the open unit disc and f : D → ℂ̄ be meromorphic and injective in D. We assume that f is holomorphic at zero and has the expansion f(z) = z + ∞σ anzn Especially, we consider f that map D onto a domain whose complement with respect to ℂ̄ is convex. We call these functions concave univalent functions and denote the set of these functions by Co. We prove that the sharp inequalities |an| ≥ 1, n ∈ ℕ, are valid for all concave univalent functions. Furthermore, we consider those concave univalent functions which have their pole at a point p ∈ (0, 1) and determine the precise domain of variability for the coefficients a2 and a3 for these classes of functions. © 2004 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Interface growth in the channel geometry and tripolar Loewner evolutions

A class of Laplacian growth models in the channel geometry is studied using the formalism of tripolar Loewner evolutions, in which three points, namely, the channel corners and infinity, are kept fixed. Initially, the problem of fingered growth, where growth takes place only at the tips of slit-like fingers, is revisited and a class of exact exact solutions of the corresponding Loewner equation is presented for the case of stationary driving functions. A model for interface growth is then formulated in terms of a generalized tripolar Loewner equation and several examples are presented, including interfaces with multiple tips as well as multiple growing interfaces. The model exhibits interesting dynamical features, such as tip and finger competition.Comment: 9 pages, 11 figure

Hydrodynamic object recognition using pressure sensing

Hydrodynamic sensing is instrumental to fish and some amphibians. It also represents, for underwater vehicles, an alternative way of sensing the fluid environment when visual and acoustic sensing are limited. To assess the effectiveness of hydrodynamic sensing and gain insight into its capabilities and limitations, we investigated the forward and inverse problem of detection and identification, using the hydrodynamic pressure in the neighbourhood, of a stationary obstacle described using a general shape representation. Based on conformal mapping and a general normalization procedure, our obstacle representation accounts for all specific features of progressive perceptual hydrodynamic imaging reported experimentally. Size, location and shape are encoded separately. The shape representation rests upon an asymptotic series which embodies the progressive character of hydrodynamic imaging through pressure sensing. A dynamic filtering method is used to invert noisy nonlinear pressure signals for the shape parameters. The results highlight the dependence of the sensitivity of hydrodynamic sensing not only on the relative distance to the disturbance but also its bearing

Schramm-Loewner Equations Driven by Symmetric Stable Processes

We consider shape, size and regularity of the hulls of the chordal Schramm-Loewner evolution driven by a symmetric alpha-stable process. We obtain derivative estimates, show that the complements of the hulls are Hoelder domains, prove that the hulls have Hausdorff dimension 1, and show that the trace is right-continuous with left limits almost surely.Comment: 22 pages, 4 figure