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

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

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

Classification of Complex Polynomial Vector Fields in One Complex Variable

A classification of the global structure of monic and centered one-variable complex polynomial vector fields is presented.Comment: 57 pages, 35 figures, submitted to the Journal of Difference Equations and Application

Signal Link-Path Characterization Up to 20 GHz Based on a Stripline Structure

Dielectric properties and losses are two critical issues in signal link-path characterization. To obtain the substrate dielectric properties for a planar transmission line, an analytical solution is derived and validated based on a stripline structure and measured scattering parameters with TRL de-embedding. The characterized dielectric property is used to evaluate dielectric loss and conductor loss. The total loss is thereby found from their summation. The calculated total loss is compared to the measured total loss, and the conductor loss and dielectric loss are then quantifiable. Since the conventional description using the loss tangent and dielectric constant to represent material properties is usually insufficient as the frequency reaches 20 GHz, a Debye model is proposed. The second order Debye parameters are subsequently extracted using a genetic algorithm. A full wave simulation is implemented to verify the determination of two-term Debye model parameters