TY - THES A1 - Hübner, Andrea T1 - Ein multityper Verzweigungsprozess als Modell zur Untersuchung der Ausbreitung von Covid-19 T1 - Modeling the spread of Covid-19 using a multitype branching process N2 - Im Zuge der Covid-19 Pandemie werden zwei Werte täglich diskutiert: Die zuletzt gemeldete Zahl der neu Infizierten und die sogenannte Reproduktionsrate. Sie gibt wieder, wie viele weitere Menschen ein an Corona erkranktes Individuum im Durchschnitt ansteckt. Für die Schätzung dieses Wertes gibt es viele Möglichkeiten - auch das Robert Koch-Institut gibt in seinem täglichen Situationsbericht stets zwei R-Werte an: Einen 4-Tage-R-Wert und einen weniger schwankenden 7-Tage-R-Wert. Diese Arbeit soll eine weitere Möglichkeit vorstellen, einige Aspekte der Pandemie zu modellieren und die Reproduktionsrate zu schätzen. In der ersten Hälfte der Arbeit werden die mathematischen Grundlagen vorgestellt, die man für die Modellierung benötigt. Hierbei wird davon ausgegangen, dass der Leser bereits ein Basisverständnis von stochastischen Prozessen hat. Im Abschnitt Grundlagen werden Verzweigungsprozesse mit einigen Beispielen eingeführt und die Ergebnisse aus diesem Themengebiet, die für diese Arbeit wichtig sind, präsentiert. Dabei gehen wir zuerst auf einfache Verzweigungsprozesse ein und erweitern diese dann auf Verzweigungsprozesse mit mehreren Typen. Um die Notation zu erleichtern, beschränken wir uns auf zwei Typen. Das Prinzip lässt sich aber auf eine beliebige Anzahl von Typen erweitern. Vor allem soll die Wichtigkeit des Parameters λ herausgestellt werden. Dieser Wert kann als durchschnittliche Zahl von Nachfahren eines Individuums interpretiert werden und bestimmt die Dynamik des Prozesses über einen längeren Zeitraum. In der Anwendung auf die Pandemie hat der Parameter λ die gleiche Rolle wie die Reproduktionsrate R. In der zweiten Hälfte dieser Arbeit stellen wir eine Anwendung der Theorie über Multitype Verzweigungsprozesse vor. Professor Yanev und seine Mitarbeiter modellieren in ihrer Veröffentlichung Branching stochastic processes as models of Covid-19 epidemic development die Ausbreitung des Corona Virus' über einen Verzweigungsprozess mit zwei Typen. Wir werden dieses Modell diskutieren und Schätzer daraus ableiten: Ziel ist es, die Reproduktionsrate zu ermitteln. Außerdem analysieren wir die Möglichkeiten, die Dunkelziffer (die Zahl nicht gemeldeter Krankheitsfälle) zu schätzen. Wir wenden die Schätzer auf die Zahlen von Deutschland an und werten diese schließlich aus. N2 - During the Covid-19 pandemic, the discussion about the situation has been dominated by two numbers: the number of daily new infected individuals and the reproduction rate. The latter is the average number of people, one infected individual will infect with the disease. Because the number of registered infected individuals is generally not equal to the actual number of people who carry the Corona virus, many facts about the pandemic have to be estimated and can not be known for certain. Since the reproduction rate is an important parameter to signify the course of the Pandemic, many ways to estimate it have been developed. The Institute of Robert Koch in Germany uses two reproduction rates R in their daily reports: The 4-days-R-value and the less fluctuating 7-days-Rvalue. This master thesis will develop another model to estimate the R-value and other interesting aspects of the pandemic. The first part of this thesis is dedicated to the mathematical foundations needed to understand the model. The reader is expected to already have basic understanding of stochastic processes. In the section Grundlagen we will discuss branching processes and present the results of their theory that are important for our work. We start by introducing simple branching processes and expand the results to multitype branching processes. In service of a simpler notation we will only consider twotype branching processes, but the results can be used for any number of types. The importance of the parameter λ shall be stressed. It can be seen as the average number of descendants of one individual and dictates the dynamic of the process over a long period of time. Applied to the modeling of the pandemic, λ plays the same role as the reproduction rate R. In the second part of this thesis will present an application of the previously developed theory about multitype branching processes. Prof. Yanev and his colleagues modeled in their publication Branching stochastic processes as models of Covid-19 epidemic development the spreading of the Corona virus by using a branching process with two types. We will discuss this model and deduce estimators from it. We want to estimate the reproduction rate and find a way to determine the number of not registered infected individuals. The estimators will be applied to the data from Germany and we will discuss the results. KW - Covid-19 KW - Corona KW - Reproduktionsrate KW - Verzweigungsprozess KW - Modellierung KW - Covid-19 KW - corona virus KW - reproduction rate KW - branching process KW - modeling Y1 - 2021 U6 - http://nbn-resolving.de/urn/resolver.pl?urn:nbn:de:kobv:517-opus4-509225 ER - TY - JOUR A1 - Heckenbach, Esther Lina A1 - Brune, Sascha A1 - Glerum, Anne C. A1 - Bott, Judith T1 - Is there a speed limit for the thermal steady-state assumption in continental rifts? JF - Geochemistry, geophysics, geosystems : G 3 ; an electronic journal of the earth sciences N2 - The lithosphere is often assumed to reside in a thermal steady-state when quantitatively describing the temperature distribution in continental interiors and sedimentary basins, but also at active plate boundaries. Here, we investigate the applicability limit of this assumption at slowly deforming continental rifts. To this aim, we assess the tectonic thermal imprint in numerical experiments that cover a range of realistic rift configurations. For each model scenario, the deviation from thermal equilibrium is evaluated. This is done by comparing the transient temperature field of every model to a corresponding steady-state model with an identical structural configuration. We find that the validity of the thermal steady-state assumption strongly depends on rift type, divergence velocity, sampling location, and depth within the rift. Maximum differences between transient and steady-state models occur in narrow rifts, at the rift sides, and if the extension rate exceeds 0.5-2 mm/a. Wide rifts, however, reside close to thermal steady-state even for high extension velocities. The transient imprint of rifting appears to be overall negligible for shallow isotherms with a temperature less than 100 degrees C. Contrarily, a steady-state treatment of deep crustal isotherms leads to an underestimation of crustal temperatures, especially for narrow rift settings. Thus, not only relatively fast rifts like the Gulf of Corinth, Red Sea, and Main Ethiopian Rift, but even slow rifts like the Kenya Rift, Rhine Graben, and Rio Grande Rift must be expected to feature a pronounced transient component in the temperature field and to therefore violate the thermal steady-state assumption for deeper crustal isotherms. KW - basin analysis KW - geodynamics KW - numerical modeling KW - rifting KW - thermal KW - modeling Y1 - 2021 U6 - https://doi.org/10.1029/2020GC009577 SN - 1525-2027 VL - 22 IS - 3 PB - Wiley CY - Hoboken, NJ ER - TY - JOUR A1 - Ayzel, Georgy T1 - Deep neural networks in hydrology BT - the new generation of universal and efficient models BT - новое поколение универсальных и эффективных моделей JF - Vestnik of Saint Petersburg University. Earth Sciences N2 - For around a decade, deep learning - the sub-field of machine learning that refers to artificial neural networks comprised of many computational layers - modifies the landscape of statistical model development in many research areas, such as image classification, machine translation, and speech recognition. Geoscientific disciplines in general and the field of hydrology in particular, also do not stand aside from this movement. Recently, the proliferation of modern deep learning-based techniques and methods has been actively gaining popularity for solving a wide range of hydrological problems: modeling and forecasting of river runoff, hydrological model parameters regionalization, assessment of available water resources. identification of the main drivers of the recent change in water balance components. This growing popularity of deep neural networks is primarily due to their high universality and efficiency. The presented qualities, together with the rapidly growing amount of accumulated environmental information, as well as increasing availability of computing facilities and resources, allow us to speak about deep neural networks as a new generation of mathematical models designed to, if not to replace existing solutions, but significantly enrich the field of geophysical processes modeling. This paper provides a brief overview of the current state of the field of development and application of deep neural networks in hydrology. Also in the following study, the qualitative long-term forecast regarding the development of deep learning technology for managing the corresponding hydrological modeling challenges is provided based on the use of "Gartner Hype Curve", which in the general details describes a life cycle of modern technologies. N2 - В течение последнего десятилетия глубокое обучение - область машинного обучения, относящаяся к искусственным нейронным сетям, состоящим из множества вычислительных слоев, - изменяет ландшафт развития статистических моделей во многих областях исследований, таких как классификация изображений, машинный перевод, распознавание речи. Географические науки, а также входящая в их состав область исследования гидрологии суши, не стоят в стороне от этого движения. В последнее время применение современных технологий и методов глубокого обучения активно набирает популярность для решения широкого спектра гидрологических задач: моделирования и прогнозирования речного стока, районирования модельных параметров, оценки располагаемых водных ресурсов, идентификации факторов, влияющих на современные изменения водного режима. Такой рост популярности глубоких нейронных сетей продиктован прежде всего их высокой универсальностью и эффективностью. Представленные качества в совокупности с быстрорастущим количеством накопленной информации о состоянии окружающей среды, а также ростом доступности вычислительных средств и ресурсов, позволяют говорить о глубоких нейронных сетях как о новом поколении математических моделей, призванных если не заменить существующие решения, то значительно обогатить область моделирования геофизических процессов. В данной работе представлен краткий обзор текущего состояния области разработки и применения глубоких нейронных сетей в гидрологии. Также в работе предложен качественный долгосрочный прогноз развития технологии глубокого обучения для решения задач гидрологического моделирования на основе использования «кривой ажиотажа Гартнера», в общих чертах описывающей жизненный цикл современных технологий. T2 - Глубокие нейронные сети в гидрологии KW - deep neural networks KW - deep learning KW - machine learning KW - hydrology KW - modeling KW - глубокие нейронные сети KW - глубокое обучение KW - машинное обучение KW - гидрология KW - моделирование Y1 - 2021 U6 - https://doi.org/10.21638/spbu07.2021.101 SN - 2541-9668 SN - 2587-585X VL - 66 IS - 1 SP - 5 EP - 18 PB - Univ. Press CY - St. Petersburg ER -