Archiv des Autors: dieter

Probability Problem Number 3 of Frederick Mostellers Book

In 1916 Frederick Mosteller published a collection of problems with solutions in his famous book „Fifty Challenging Problems in Probability„.

Problem Number 3 is called „The Flippand Juror“ and is described with the following lines:

A three-man jury has two members each of whom independently has a probability p of making the correct decision and a third member who flips a coin for each decision (majority rules). A one-man jury has a probability p of making the correct decision. Which jury has the better probability of making the right decision?

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Nassim Nicholas Taleb’s Archer Example for Nonexistence of the Expected Value with a little Python

Example from Nassim Taleb for \(E(g(x)) \neq g(E(x))\)

The Problem:

An archer stands one meter away from a wall and shoots uniformly randomly to his right with his angle between zero and \( \pi / 2 \) . Mark a spot right in front of the archer on the wall. What is the average distance between the arrows mark and that spot?

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Publikationen / Publications

Publications in refereed journals

2002

Fliedner TM, Friesecke I, Graessle DH, Weiss M: Hemopoietic cell renewal as the limiting factor in low-level radiation exposure: Diagnostic implications and therapeutic options. Mil Med. 2002 Feb;167(2 Suppl ):46-8

Fliedner TM, Graessle DH, Paulsen C, Reimers K: Structure and function of bone marrow hemopoiesis: mechanisms of response to ionizing radiation exposure. Cancer Biother Radiopharm. 2002 Aug;17(4):405-26

Feinendegen LE, Graessle DH: Energy deposition in tissue during chronic irradiation and the biological consequences. Br J Radiol. 2002, Supplement_26:6-14

Graessle DH: Mathematical modelling of the blood platelet renewal system as an approach to analysing the effects of chronic irradiation on haematopoiesis. Br J Radiol. 2002, Supplement_26:202-208

Fliedner TM, Graessle DH, Paulsen C, Reimers K, Weiss M: The hematopoietic system: determinants of response to chronic ionizing radiation exposure. Br J Radiol. 2002, Supplement_ 26:247-257

Fliedner TM, Graessle DH, Paulsen C, Reimers K: Strategy and tactics for stimulation of haemopoiesis in patients developing the acute radiation syndrome. In: Follow-up of delayed
health consequences of acute accidental radiation exposure – Lessons to be learned from their
medical management. International Atomic Energy Agency, 2002, IAEA-TECDOC-1300

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Simulation of Radiation Effects Using Biomathematical Models of the Megakaryocytic Cell Renewal System

 PhD-Thesis, University of Ulm, 2000

Dieter Hans Graessle

 

Abstract / Summary

The thesis presents the development and application of biomathematical models of the megakaryocyte-platelet renewal system as a tool for the analysis of radiation effects on hematopoiesis and thrombocytopoiesis. The basic structure of the used biomathematical models follows the currently accepted biological concepts of hematopoiesis and thrombocytopoiesis in mammalians and humans. It contains compartments for pluripotent stem cells, noncommitted progenitor cells, committed progenitor cells, endoreduplicating precursor cells, megakaryocytes in different ploidy groups, average megakaryocyte volume within ploidy groups and thrombocytes. Regulation functions are included to represent the compensatory feedback mechanisms of the megakaryocyte-platelet system. The compartments, the regulator structure and the cell-kinetic parameters of the model are derived from biological experiments. Seen from the mathematical perspective, the model consists of a set of concatenated nonlinear first-order ordinary differential equations. For analyzing the effects of acute irradiation to the hematopoietic system, the basic model was extended to simulate acute irradiation effects. This model was included into an estimation method based on optimization algorithms, which is capable to calculate survival fractions of stem cells, based on thrombocyte counts after radiation exposure. To analyze chronic radiation effects to hematopoiesis, the model was extended by components describing an radiation induced excess cell loss in radiosensitive compartments. A method for the estimation of excess cell loss rates from thrombocyte counts based on the model and optimization algorithms was developed. Computational mathematical analysis with stochastic simulations of the model showed the existence of a turbulence region of the excess cell loss rate, in which the hematopoietic system is at high risk to fail.

Read the full text of the PhD-Thesis.

Bergauf und bergrunter – halte drunter: Geschossbahn beim Bergschuss

Modellierung und Simulation der Geschossbahn unter Berücksichtigung des Luftwiderstandes

Außenballistik, Luftreibung, Geschossbahn, Trajektorie, Python

Dieter Graessle
email: dieter@dieter-graessle.de
web: https://www.dieter-graessle.de

Einleitung

Bergauf und bergrunter – halte drunter!

Jeder Jäger hat diesen Merksatz im Rahmen seiner Schießausbildung gelernt und in vielen Internetforen wird darüber diskutiert: Woran liegt das, wieviel macht das aus, ist das nur Jägerlatein?

Diese kleine Studie soll dieser Frage nachgehen, und zwar unter Anwendung der physikalischen Grundlagen: Kräfte und deren Wirkung auf die Bewegung eines Geschosses.

Die Berechnung von ballistischen Bahnkurven erfolgt im einfachsten Fall ohne Berücksichtigung des Luftwiderstandes. Dadurch ergeben sich sehr einfache und analytisch lösbare Bahngleichungen. Für Geschossbahnen kann der Luftwiderstand, der mit dem Quadrat der Geschwindigkeit steigt, in der Regel kaum vernachlässigt werden. Die entstehenden Gleichungen sind Differenzialgleichungen bzw. Differenzialgleichungssysteme, die mit entsprechenden numerischen Iterationsverfahren gelöst ( = simuliert ) werden können. Das verwendete physikalische Prinzip zum Aufbau der Gleichungsstruktur ist das der Superposition der zueinander orthogonalen Bewegungskomponenten in waag- und senkrechter Richtung. Im Gegensatz zum reibungsfreien Modell ist hier, bedingt durch die quadratisch von der Gesamtgeschwindigkeit abhängige Luftreibung, eine vollständige Entkoppelung der Bewegungskomponenten nicht mehr möglich.

Die Programmcodes sind für die Betrachtung der Resultate nicht wichtig. Sie sind für Interessierte jedoch mit dargestellt.

Der gesamte Artikel findet sich unter folgendem Link: https://www.dieter-graessle.de/wp-content/uploads/geschossbahn/2020_04_14_Geschossbahn.html