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Register a new userHarry Kesten (1931-2019), a personal and scientific tribute
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The mathematical achievements of Harry Kesten since the mid-1950s have revolutionized probability theory as a subject in its own right and in its associations with aspects of algebra, analysis, geometry, and statistical physics. Through his personality and scientific ability, he has framed the modern subject to a degree exceeded by no other. The impact of his work and personality is summarised in this memoir.
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I am an industrial mathematician. When asked to identify my profession or academic field of study, this is the most concise answer I can provide. However, this seemingly straightforward statement is commonly greeted by a blank stare or an uncomfortable silence, regardless of whether I am speaking to a fellow mathematician or a non-mathematician. I usually follow up with the clarification: I am an applied mathematician who derives much of my inspiration from the study of industrial problems that I encounter through collaborations with companies. This dispels some confusion, but unfortunately still leaves a great deal open to interpretation owing to the vagueness of the words mathematics, industry and company, each of which covers an extremely broad range of scientific or socio-economic activity. To those academics who actually work in the field of industrial mathematics (and whose perspective referred to in the title is the focus of this article) this ambiguity is familiar and untroubling. However, for anyone less acquainted with the work of industrial mathematicians, some clarification is desirable especially for anyone who might be considering entering the field. This essay therefore aims to shed light upon the nature of research being done at the interface between mathematics and industry, paying particular attention to the following questions: What is industrial mathematics? Where is industrial mathematics? How does one do industrial mathematics? Why (or more precisely, what value is there in doing) industrial mathematics? I will attempt to answer these questions by means of several case studies drawn from my own experience in tackling mathematical problems from industry.
The Coupon Collectors Problem is one of the few mathematical problems that make news headlines regularly. The reasons for this are on one hand the immense popularity of soccer albums (called Paninimania) and on the other hand that no solution is known that is able to take into account all effects such as replacement (limited purchasing of missing stickers) or swapping. In previous papers we have proven that the classical assumptions are not fulfilled in practice. Therefore we define new assumptions that match reality. Based on these assumptions we are able to derive formulae for the mean number of stickers needed (and the associated standard deviation) that are able to take into account all effects that occur in practical collecting. Thus collectors can estimate the average cost of completion of an album and its standard deviation just based on elementary calculations. From a practical point of view we consider the Coupon Collectors problem as solved. ----- Das Sammelbilderproblem ist eines der wenigen mathematischen Probleme, die regelma{ss}ig in den Schlagzeilen der Nachrichten vorkommen. Dies liegt einerseits an der gro{ss}en Popularitat von Fu{ss}ball-Sammelbildern (Paninimania genannt) und andererseits daran, dass es bisher keine Losung gibt, die alle relevanten Effekte wie Nachkaufen oder Tauschen berucksichtigt. Wir haben bereits nachgewiesen, dass die klassischen Annahmen nicht der Realitat entsprechen. Deshalb stellen wir neue Annahmen auf, die die Praxis besser abbilden. Darauf aufbauend konnen wir Formeln fur die mittlere Anzahl benotigter Bilder (sowie deren Standardabweichung) ableiten, die alle in der Praxis relevanten Effekte berucksichtigen. Damit konnen Sammler die mittleren Kosten eines Albums sowie deren Standardabweichung nur mit Hilfe von elementaren Rechnungen bestimmen. Fur praktische Zwecke ist das Sammelbilderproblem damit gelost.
In probability theory, the independence is a very fundamental concept, but with a little mystery. People can always easily manipulate it logistically but not geometrically, especially when it comes to the independence relationships among more that two variables, which may also involve conditional independence. Here I am particularly interested in visualizing Markov chains which have the well known memoryless property. I am not talking about drawing the transition graph, instead, I will draw all events of the Markov process in a single plot. Here, to simplify the question, this work will only consider dichotomous variables, but all the methods actually can be generalized to arbitrary set of discrete variables.
This is a small contribution to the (September 15, 2019) Liber Amicorum Richard Dick Allen Askey. At the end a positivity conjecture related to the First and Second Borwein Conjectures is offered.
The Energy Recovery Linac (ERL) paradigm offers the promise to generate intense electron beams of superior quality with extremely small six-dimensional phase space for many applications in the physical sciences, materials science, chemistry, health, information technology and security. Helmholtz-Zentrum Berlin started in 2010 an intensive R&D programme to address the challenges related to the ERL as driver for future light sources by setting up the bERLinPro (Berlin ERL Project) ERL with 50 MeV beam energy and high average current. The project is close to reach its major milestone in 2020, acceleration and recovery of a high brightness electron beam. The goal of bERLinProCamp 2019 was to discuss scientific opportunities for bERLinPro 2020+. bERLinProCamp 2019 was held on Tue, 17.09.2019 at Helmholtz-Zentrum Berlin, Berlin, Germany. This paper summarizes the main themes and output of the workshop.
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