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Primary care systems are generally considered to be the backbone of universal health care. However, as the population ages and the number of primary care physicians declines, this foundation is starting to crumble. There result increasing access distances, waiting times, and workloads up to the point where the system's functioning can no longer be guaranteed. To counteract these developments, representatives from the government, insurances, and associations discuss an array of novel supply concepts and policy changes. This thesis aims to advance this discussion by providing suitable decision support tools, algorithms, and theoretic results. Special attention is thereby put on rural primary care systems, as these are particularly vulnerable due to their geographic-demographic facts. The resulting contributions can be categorized into three main groups and we summarize them hereinafter.The first part of this thesis addresses the fundamental question of how the quality of primary care systems can be quantified. Due to the inherent complexity and micro-level detail of primary care systems, this turns out to be a highly non-trivial problem and the predominant method of choice is therefore still an assessment of the physician-to-population ratio. To facilitate a more refined analysis, this thesis introduces the hybrid agent-based simulation model SiM-Care. SiM-Care models and tracks the micro-interactions of patients and primary care physicians on an individual level. The model thereby enables decision makers to access several performance indicators such as patient waiting times and physician utilization that can serve as a sound basis for the assessment and comparison of primary care systems. Furthermore, it becomes possible to evaluate changes in the infrastructure, patient behavior, and service design which is impossible with purely ratio-based assessments.The second part of this thesis examines mobile medical units (MMUs) for the supply of primary care services in rural environments. MMUs are customized vehicles ...

Wichtige Methoden des quantitativen Risikomanagements, insbesondere aus den Bereichen der Extremwerttheorie und der multivariaten Statistik, wurden von Emil J. Gumbel entwickelt und in verschiedenen Anwendungsgebieten popularisiert. Zeugnis dafür sind die Gumbel-Verteilung und die Gumbel-Copula. Anlässlich seines 125. Geburtstags, er wurde am 18. Juli 1891 in München geboren, geben wir einen Einblick in seinen mathematischen Nachlass und beleuchten seine Biographie als Wissenschaftler, Publizist, Zeitzeuge und Pazifist. Neben seinen mathematischen Arbeiten veröffentlichte er mehrere politische Bücher und unzählige Zeitungsartikel über politische Morde, das Justizsystem und nationalistische Geheimbünde in der Weimarer Republik, was ihn 1932 seine Stelle an der Universität Heidelberg kostete und 1933 auf die erste Ausbürgerungsliste des Deutschen Reichs brachte. Er emigrierte 1932 nach Frankreich und musste, um den deutschen Besatzungstruppen zu entkommen, 1940 weiter in die USA fliehen. Am 10. September 1966 verstarb er in New York.

The paper determines the vertices and surface volumes of all rounding polytopes for commonly used rounding methods: the quota method of greatest remainders, and the divisor methods. These methods are used to round continuous non-negative weights summing to one to non-negative integers summing to a predetermined accuracy, e.g. to 100 when rounding to percentages. Our results are of interest when average properties of rounding methods are investigated, and an example from political science is included.

Short-term probabilistic forecasts of the trajectory of the COVID-19 pandemic in the United States have served as a visible and important communication channel between the scientific modeling community and both the general public and decision-makers. Forecasting models provide specific, quantitative, and evaluable predictions that inform short-term decisions such as healthcare staffing needs, school closures, and allocation of medical supplies. Starting in April 2020, the US COVID-19 Forecast Hub (https://covid19forecasthub.org/) collected, disseminated, and synthesized tens of millions of specific predictions from more than 90 different academic, industry, and independent research groups. A multimodel ensemble forecast that combined predictions from dozens of groups every week provided the most consistently accurate probabilistic forecasts of incident deaths due to COVID-19 at the state and national level from April 2020 through October 2021. The performance of 27 individual models that submitted complete forecasts of COVID-19 deaths consistently throughout this year showed high variability in forecast skill across time, geospatial units, and forecast horizons. Two-thirds of the models evaluated showed better accuracy than a naïve baseline model. Forecast accuracy degraded as models made predictions further into the future, with probabilistic error at a 20-wk horizon three to five times larger than when predicting at a 1-wk horizon. This project underscores the role that collaboration and active coordination between governmental public-health agencies, academic modeling teams, and industry partners can play in developing modern modeling capabilities to support local, state, and federal response to outbreaks.

General pedagogical objectives such as the promotion of civic engagement and individual empowerment apply to teaching mathematics. Heinrich Winter has combined the social expectation of the formation of fully-fledged citizens with mathematical contents, as there is a reciprocal relation between universal educational and subject-oriented objectives. One aim of the present thesis is to concretise this ideal of mathematical literacy by means of exemplary issues and to offer adequate learning environments. Given the significance of the mathematical and contextual dichotomy, mathematical modelling becomes crucial for an enlightenment via mathematics. In particular, normative modelling is of interest, being defined as a procedure where mathematics is used to shape reality – in distinction to descriptive modelling where existing phenomena are described with the help of mathematics. But you can only pay taxes in reality, if a tax rate has been mathematically predetermined. This use of mathematics is ambiguous and normally biased as well as a subject of negotiation. These characteristics are rather rare in the context of learning mathematics, but even more instructive for a public discussion and judgement. German curriculums focus on – or are even limited to – descriptive modelling. This thesis exposes the educational value inhering in teaching normative modelling, even from a content-related perspective. The result is a catalogue of concrete learning targets which decisively add to the existing competencies in mathematical modelling and that rounds off the vision of mathematics. Apportionment methods for proportional representation are a paradigmatic example for normative modelling. On the one hand, normative decisions in the modelling process reflect classical problems of the mathematics of apportionment, on the other hand the German debate about the current increase in parliament's size is an authentic occasion to analyse the reciprocity between mathematics and context. An associated analysis starts with a comparison ...

This paper examines the effects of financial development on income inequality and poverty. The results of both cross-country and panel data regressions suggest that inequality and poverty are reduced not only through enhanced loan markets, but also through more developed stock markets. We show that ethnic diversity and the distribution of land are significant and robust determinants of both income inequality and poverty. Finally, we find evidence that government spending leads to a reduction in income inequality in high income countries. In low income countries, however, we find no significant effect.

Since 1980, the aggregate income of oil-exporting countries relative to that of oil-poor countries has been remarkably constant despite structural gaps in productivity growth rates. This stylized fact is analyzed in a two-country model where resource- poor (Home) and resource-rich (Foreign) economies display productivity differences but stable income shares due to terms-of-trade dynamics. We show that Home's income share is positively related to the national tax on domestic resource use, a prediction con rmed by dynamic panel estimations for sixteen oil-poor economies. National governments have incentives to deviate from both efficient and laissez-faire allocations. In Home, increasing the oil tax improves welfare through a rent-transfer mechanism. In Foreign, subsidies (taxes) on domestic oil use improve welfare if R&D productivity is lower (higher) than in Home.

We examine how the final say in a sequence of proposals for local public project provision, financing, and redistribution can be channeled towards socially desirable outcomes, thereby breaking the dictatorial power of the last agenda-setter. Individuals are heterogeneous with some citizens benefiting from the public project (winners) and the rest losing (losers) relative to per-capita costs. Our main insight is that a simple ban on subsidies for the proposal-makers can achieve the purpose whenever the first proposal-maker is a winner and the second proposal-maker is a loser. Such a ban induces project winners to make efficient public project proposals that are however coupled with socially undesirable subsidy schemes. The best possible amendment for project losers is then to match the project proposal and to eliminate all subsidies. We further show that two-round proposal-making constitutes the minimal form of political competition yielding first-best outcomes and that restrictions on tax schemes are socially desirable.

The absence of the deselection threat in incumbents' last term in office can be negative or positive for society. Some politicians may reduce their efforts, while others may pursue beneficial long-term policies that may be unpopular in the short term. We propose a novel pension system that solves the effort problem while preserving willingness to implement long-term policies. The idea is to give politicians the option to choose between a flexible pension scheme and a fixed pension scheme. In a flexible pension scheme, the pension increases with short term performance as measured by the vote share of the officeholder's party in the next election. This system increases social welfare by letting officeholders self-select into those activities that most benefit society. We analyze the properties and consequences of such a system and assess its robustness. Finally, we extend the pension system with choice to non-last-term situations and derive a general welfare result.

This article opens up a discussion on the power that teachers have in mathematics curriculum at the Further Education and Training level. It is related to the general question: who holds the power in school mathematics education in South Africa? To what extent is the teacher given an opportunity to exercise their power in mathematics assessment? If the teacher is given power, what does that power allow teachers to do, and under what conditions does this happen? The case of mathematics is presented here to illustrate the above complex questions of teacher power in new forms of assessment in the curriculum.

Apportionment methods round vote proportions to integer numbers of seats in a parliament. The seat excess is the difference between the integer seat allocation and the fractional ideal share of seats. In order to quantify biased treatment of larger versus smaller parties, previous studies derived the conditional expectation of the seat excess, when the vote proportions are conditioned to be ordered. We complement these studies by computing the conditional seat excess variance for popular apportionment methods.

Apportionment methods are used to round the vote proportions of parties in a proportional representation system to integer numbers of seats in the parliament. Seat biases quantify by how much on average a particular apportionment method favors larger (or smaller) parties. In this paper, we prove a previous conjecture on asymptotic seat biases of stationary divisor methods and the quota method of greatest remainders, as the size of the parliament tends to infinity.

In a proportional representation system, apportionment methods are used to round the vote proportion of a party to an integer number of seats in parliament. Assuming uniformly distributed vote proportions, we derive the seat allocation distributions for stationary divisor methods. An important characteristic of apportionment methods are seat biases, that is, expected differences between actual seat numbers and ideal shares of seats, when the parties are ordered from largest to smallest. We obtain seat bias formulas for the stationary divisor methods and for the quota method of greatest remainders.

In this paper, we introduce a joint bond and stock market model based on the state price density approach as a mean to discount future payments - whether these are stochastic dividend payments or secure repayments of government zerobonds. Based upon a recipe of Rogers (1997), we define a state price density model, the so-called Hyperbolic Gaussian model which allows for closed form zerobond prices and stock prices in an arbitrage-free way. It is particularly useful for insurance applications where large time horizons are considered. We estimate the joint factor model using the extended Kalman filter. The model we propose here is computationally much simpler than other models which have been considered in the ...

In this thesis we consider modular forms of orthogonal type. We consider lattices which can be represented as an orthogonal sum of two integral hyperbolic planes anda negative definite even lattice. The modular groups are subgroups of finite index ofthe group of all lattice automorphisms intersected with the real spinor kernel. The associated modular forms are defined on a homogeneous domain of type IV in Cartan's classification. Due to some low-dimensional exceptional isogenies this setting covers degree two modular forms of Siegel, Hermitian and quaternionic type which have been studied intensively by Igusa, Freitag, Krieg and others. In 2010 Gritsenko found three towers of orthogonal type modular forms with simple divisors. We resume Gritsenko's construction and develop a framework to construct modular forms for several seriesof lattices. In contrast to earlier approaches our methods are very direct and reflect the configuration of the underlying definite lattice. This allows us to construct all generators of the associated graded rings of modular forms. Moreover we provide very natural coordinates in this case. We perform this process completely for one of the forementioned series. We indicate how our methods can be adapted to other series.