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

Complex maps without invariant densities

We consider complex polynomials $f(z) = z^\ell+c_1$ for $\ell \in 2\N$ and $c_1 \in \R$, and find some combinatorial types and values of $\ell$ such that there is no invariant probability measure equivalent to conformal measure on the Julia set. This holds for particular Fibonacci-like and Feigenbaum combinatorial types when $\ell$ sufficiently large and also for a class of `long-branched' maps of any critical order.Comment: Typos corrected, minor changes, principally to Section

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

Abstract basins of attraction

Abstract basins appear naturally in different areas of several complex variables. In this survey we want to describe three different topics in which they play an important role, leading to interesting open problems

Critical curves in conformally invariant statistical systems

We consider critical curves -- conformally invariant curves that appear at critical points of two-dimensional statistical mechanical systems. We show how to describe these curves in terms of the Coulomb gas formalism of conformal field theory (CFT). We also provide links between this description and the stochastic (Schramm-) Loewner evolution (SLE). The connection appears in the long-time limit of stochastic evolution of various SLE observables related to CFT primary fields. We show how the multifractal spectrum of harmonic measure and other fractal characteristics of critical curves can be obtained.Comment: Published versio

Two-Dimensional Critical Percolation: The Full Scaling Limit

We use SLE(6) paths to construct a process of continuum nonsimple loops in the plane and prove that this process coincides with the full continuum scaling limit of 2D critical site percolation on the triangular lattice -- that is, the scaling limit of the set of all interfaces between different clusters. Some properties of the loop process, including conformal invariance, are also proved.Comment: 45 pages, 12 figures. This is a revised version of math.PR/0504036 without the appendice

Spectral bounds for the Neumann-Poincaré operator on planar domains with corners

The boundary double layer potential, or the Neumann-Poincaré operator, is studied on the Sobolev space of order 1/2 along the boundary, coinciding with the space of charges giving rise to double layer potentials with finite energy in the whole space. Poincaré’s program of studying the spectrum of the boundary double layer potential is developed in complete generality on closed Lipschitz hypersurfaces in euclidean space. Furthermore, the Neumann-Poincaré operator is realized as a singular integral transform bearing similarities to the Beurling-Ahlfors transform in 2 dimensions. As an application, in the case of planar curves with corners, bounds for the spectrum of the Neumann-Poincaré operator are derived from recent results in quasi-conformal mapping theory