http://publications.mfo.de/handle/mfo/61 Tue, 07 Apr 2026 06:22:38 GMT 2026-04-07T06:22:38Z http://publications.mfo.de/handle/mfo/4123 Eine visuelle Analyse der Sterblichkeit männlicher Spanier Marron, J. S. Die statistische Visualisierung benutzt graphische Methoden um Erkenntnisse aus Daten zu gewinnen. Wir zeigen wie mit dem Verfahren der Hauptkomponentenanalyse die Sterblichkeit in Spanien im Laufe der letzten hundert Jahre analysiert werden kann. Diese Datenzerlegung zeigt sowohl erwartete geschichtliche Ereignisse auf, als auch einige, teilweise überraschende Entwicklungen der Sterblichkeit im Laufe der Zeit. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/4123 2016-01-01T00:00:00Z Marron, J. S. Die statistische Visualisierung benutzt graphische Methoden um Erkenntnisse aus Daten zu gewinnen. Wir zeigen wie mit dem Verfahren der Hauptkomponentenanalyse die Sterblichkeit in Spanien im Laufe der letzten hundert Jahre analysiert werden kann. Diese Datenzerlegung zeigt sowohl erwartete geschichtliche Ereignisse auf, als auch einige, teilweise überraschende Entwicklungen der Sterblichkeit im Laufe der Zeit. http://publications.mfo.de/handle/mfo/4122 Wie man einen Sieger wählt: die Mathematik der Sozialwahl Powers, Victoria Ann Angenommen, eine Gruppe von Einzelpersonen möchte unter verschiedenen Optionen wählen, zum Beispiel einen von mehreren Kandidaten für ein politisches Amt oder den besten Teilnehmer einer Eiskunstlaufmeisterschaft. Man könnte fragen: Was ist die beste Methode, einen Sieger in dem Sinne zu wählen, dass er die individuellen Präferenzen der Gruppenmitglieder am besten widerspiegelt? Wir werden anhand einiger Beispiele sehen, dass viele Wahlverfahren, die weltweit in Gebrauch sind, zu Paradoxa und nachgerade schlechten Ergebnissen führen können, und wir werden uns ein mathematisches Modell von Gruppenentscheidungen ansehen. Wir diskutieren das Unmöglichkeitstheorem von Arrow, das Folgendes besagt: Hat man mehr als zwei Wahlmöglichkeiten, dann gibt es in einem ganz exakten Sinn keine gute Methode für die Wahl eines Siegers. Fri, 01 Jan 2016 00:00:00 GMT http://publications.mfo.de/handle/mfo/4122 2016-01-01T00:00:00Z Powers, Victoria Ann Angenommen, eine Gruppe von Einzelpersonen möchte unter verschiedenen Optionen wählen, zum Beispiel einen von mehreren Kandidaten für ein politisches Amt oder den besten Teilnehmer einer Eiskunstlaufmeisterschaft. Man könnte fragen: Was ist die beste Methode, einen Sieger in dem Sinne zu wählen, dass er die individuellen Präferenzen der Gruppenmitglieder am besten widerspiegelt? Wir werden anhand einiger Beispiele sehen, dass viele Wahlverfahren, die weltweit in Gebrauch sind, zu Paradoxa und nachgerade schlechten Ergebnissen führen können, und wir werden uns ein mathematisches Modell von Gruppenentscheidungen ansehen. Wir diskutieren das Unmöglichkeitstheorem von Arrow, das Folgendes besagt: Hat man mehr als zwei Wahlmöglichkeiten, dann gibt es in einem ganz exakten Sinn keine gute Methode für die Wahl eines Siegers. http://publications.mfo.de/handle/mfo/4121 Billard und ebene Flächen Davis, Diana Billard, die Zick-Zack-Bewegungen eines Balls auf einem Tisch, ist ein reichhaltiges Feld gegenwärtiger mathematischer Forschung. In diesem Artikel diskutieren wir Fragen und Antworten zum Thema Billard, und zu dem damit verwandten Thema ebener Flächen. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/4121 2015-01-01T00:00:00Z Davis, Diana Billard, die Zick-Zack-Bewegungen eines Balls auf einem Tisch, ist ein reichhaltiges Feld gegenwärtiger mathematischer Forschung. In diesem Artikel diskutieren wir Fragen und Antworten zum Thema Billard, und zu dem damit verwandten Thema ebener Flächen. http://publications.mfo.de/handle/mfo/444 From computer algorithms to quantum field theory: an introduction to operads Krähmer, Ulrich An operad is an abstract mathematical tool encoding operations on specific mathematical structures. It finds applications in many areas of mathematics and related fields. This snapshot explains the concept of an operad and of an algebra over an operad, with a view towards a conjecture formulated by the mathematician Pierre Deligne. Deligne’s (by now proven) conjecture also gives deep inights into mathematical physics. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/444 2015-01-01T00:00:00Z Krähmer, Ulrich An operad is an abstract mathematical tool encoding operations on specific mathematical structures. It finds applications in many areas of mathematics and related fields. This snapshot explains the concept of an operad and of an algebra over an operad, with a view towards a conjecture formulated by the mathematician Pierre Deligne. Deligne’s (by now proven) conjecture also gives deep inights into mathematical physics. http://publications.mfo.de/handle/mfo/443 Domino tilings of the Aztec diamond Rué, Juanjo Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can cover exactly two squares of the squared paper. How many different ways are there to cover the entire paper cutout with dominoes? One specific paper cutout can be mathematically described as the so-called Aztec Diamond, and a way to cover it with dominoes is a domino tiling. In this snapshot we revisit some of the seminal combinatorial ideas used to enumerate the number of domino tilings of the Aztec Diamond. The existing connection with the study of the so-called alternating-sign matrices is also explored. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/443 2015-01-01T00:00:00Z Rué, Juanjo Imagine you have a cutout from a piece of squared paper and a pile of dominoes, each of which can cover exactly two squares of the squared paper. How many different ways are there to cover the entire paper cutout with dominoes? One specific paper cutout can be mathematically described as the so-called Aztec Diamond, and a way to cover it with dominoes is a domino tiling. In this snapshot we revisit some of the seminal combinatorial ideas used to enumerate the number of domino tilings of the Aztec Diamond. The existing connection with the study of the so-called alternating-sign matrices is also explored. http://publications.mfo.de/handle/mfo/442 The mystery of sleeping sickness – why does it keep waking up? Funk, Sebastian Sleeping sickness is a neglected tropical disease that affects rural populations in Africa. Deadly when untreated, it is being targeted for elimination through case finding and treatment. Yet, fundamental questions about its transmission cycle remain unanswered. One of them is whether transmission is limited to humans, or whether other species play a role in maintaining circulation of the disease. In this snapshot, we introduce a mathematical model for the spread of Trypanosoma brucei, the parasite responsible for causing sleeping sickness, and present some results based on data collected in Cameroon. Understanding how important animals are in harbouring Trypanosoma brucei that can infect humans is important for assessing whether the disease could be reintroduced in human populations even after all infected people have been successfully treated. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/442 2015-01-01T00:00:00Z Funk, Sebastian Sleeping sickness is a neglected tropical disease that affects rural populations in Africa. Deadly when untreated, it is being targeted for elimination through case finding and treatment. Yet, fundamental questions about its transmission cycle remain unanswered. One of them is whether transmission is limited to humans, or whether other species play a role in maintaining circulation of the disease. In this snapshot, we introduce a mathematical model for the spread of Trypanosoma brucei, the parasite responsible for causing sleeping sickness, and present some results based on data collected in Cameroon. Understanding how important animals are in harbouring Trypanosoma brucei that can infect humans is important for assessing whether the disease could be reintroduced in human populations even after all infected people have been successfully treated. http://publications.mfo.de/handle/mfo/441 Quantum diffusion Knowles, Antti If you place a drop of ink into a glass of water, the ink will slowly dissipate into the surrounding water until it is perfectly mixed. If you record your experiment with a camera and play the film backwards, you will see something that is never observed in the real world. Such diffusive and irreversible behaviour is ubiquitous in nature. Nevertheless, the fundamental equations that describe the motion of individual particles – Newton’s and Schrödinger’s equations – are reversible in time: a film depicting the motion of just a few particles looks as realistic when played forwards as when played backwards. In this snapshot, we discuss how one may try to understand the origin of diffusion starting from the fundamental laws of quantum mechanics. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/441 2015-01-01T00:00:00Z Knowles, Antti If you place a drop of ink into a glass of water, the ink will slowly dissipate into the surrounding water until it is perfectly mixed. If you record your experiment with a camera and play the film backwards, you will see something that is never observed in the real world. Such diffusive and irreversible behaviour is ubiquitous in nature. Nevertheless, the fundamental equations that describe the motion of individual particles – Newton’s and Schrödinger’s equations – are reversible in time: a film depicting the motion of just a few particles looks as realistic when played forwards as when played backwards. In this snapshot, we discuss how one may try to understand the origin of diffusion starting from the fundamental laws of quantum mechanics. http://publications.mfo.de/handle/mfo/440 Modelling the spread of brain tumours Swan, Amanda; Murtha, Albert The study of mathematical biology attempts to use mathematical models to draw useful conclusions about biological systems. Here, we consider the modelling of brain tumour spread with the ultimate goal of improving treatment outcomes. Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/440 2015-01-01T00:00:00Z Swan, Amanda Murtha, Albert The study of mathematical biology attempts to use mathematical models to draw useful conclusions about biological systems. Here, we consider the modelling of brain tumour spread with the ultimate goal of improving treatment outcomes. http://publications.mfo.de/handle/mfo/439 Visual analysis of Spanish male mortality Marron, J. S. Statistical visualization uses graphical methods to gain insights from data. Here we show how a technique called principal component analysis is used to analyze mortality in Spain over about the last hundred years. This data decomposition both reflects expected historical events and reveals some perhaps less expected trends in mortality over the years.; [Also available in German] Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/439 2015-01-01T00:00:00Z Marron, J. S. Statistical visualization uses graphical methods to gain insights from data. Here we show how a technique called principal component analysis is used to analyze mortality in Spain over about the last hundred years. This data decomposition both reflects expected historical events and reveals some perhaps less expected trends in mortality over the years. [Also available in German] http://publications.mfo.de/handle/mfo/438 Curriculum development in university mathematics: where mathematicians and education collide Sangwin, Christopher J. This snapshot looks at educational aspects of the design of curricula in mathematics. In particular, we examine choices textbook authors have made when introducing the concept of the completness of the real numbers. Can significant choices really be made? Do these choices have an effect on how people learn, and, if so, can we understand what they are? Thu, 01 Jan 2015 00:00:00 GMT http://publications.mfo.de/handle/mfo/438 2015-01-01T00:00:00Z Sangwin, Christopher J. This snapshot looks at educational aspects of the design of curricula in mathematics. In particular, we examine choices textbook authors have made when introducing the concept of the completness of the real numbers. Can significant choices really be made? Do these choices have an effect on how people learn, and, if so, can we understand what they are?