Cover times for sequences of reversible Markov chains on random graphs

We provide conditions that classify cover times for sequences of random walks on random graphs into two types: One type (Type 1) is the class of cover times that are of the order of the maximal hitting times scaled by the logarithm of the size of vertex sets. The other type (Type 2) is the class of cover times that are of the order of the maximal hitting times. The conditions are described by some parameters determined by the underlying graphs: the volumes, the diameters with respect to the resistance metric, the coverings or packings by balls in the resistance metric. We apply the conditions to and classify a number of examples, such as supercritical Galton-Watson trees, the incipient infinite cluster of a critical Galton-Watson tree and the Sierpinski gasket graph.Comment: 28 pages, improved proposition 3.

Embryo culturing methodology and investigation of seed dormancy mechanisms in Mountain Silverbell (Halesia Carolina L.)

Desirable wood properties once made mountain silverbell (Halesia Carolina L.) a favored species among loggers in the southern Appalachians. Showy flowers, disease resistance, and handsome form continue to make it a desirable ornamental. Delayed and erratic germination over a one to two year period, plus a poorly understood dormancy mechanism, may be responsible for limiting its commercial availability. Prolonged warm and cold stratification has been recommended as a presowing treatment, but it is not clear whether such treatments relieve dormancy by overcoming hardseededness, inhibiting chemicals, or morphological and physiological impediments within the embryo itself. During the years 1982-84, a study was undertaken to find means of hastening germination, and to provide for a clearer understanding of dormancy. Various conventional sacrification procedures were used to quickly remove hard seed coverings, but these failed to induce germination. In vitro culturing of excised surface sterilized embryos, however, proved highly successful, yielding 100 percent germination within 7 days. Later experimentation showed that morphological and physiological dormancy factors were absent at the time of fruit abscision in mid autumn. Exogenously applied extracts from fruit and seed layers also did not inhibit germination. The primary impediments appeared to center on the hardened endocarp which physically restricted water availability to the quiescent embryo for several months, and then mechanically prevented embryo expansion once hydration occurred. Overwintering on the forest floor (or artificial stratification designed to mimic overwintering) gradually overcomes physical and mechanical barriers of hardseededness, especially under moist, non-sterile conditions. Embryo excision and culture expedites this process so that seedlings suitable for out-planting can be obtained within 1 year

The structure and permiability of protective coverings secreted by certain insect species

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Asymptotics of the visibility function in the Boolean model

23 pagesThe aim of this paper is to give a precise estimate on the tail probability of the visibility function in a germ-grain model: this function is defined as the length of the longest ray starting at the origin that does not intersect an obstacle in a Boolean model. We proceed in two or more dimensions using coverage techniques. Moreover, convergence results involving a type I extreme value distribution are shown in the two particular cases of small obstacles or a large obstacle-free region

Analysis of the influence of non-pharmaceutical interventions and cultural differences on the evolution of COVID-19

Since the beginning of the COVID-19 pandemic, countries worldwide have implemented a set of Non-Pharmaceutical Interventions (NPIs) as a way to face the evolution of the pandemic. In this dissertation we propose a detailed analysis of the evolution of the pandemic that considers the degree of restriction of NPIs from March 2020 to May 2021 and the reproduction rate in five countries: India, Brazil, United Kingdom, Israel and Portugal. In addition to this, we analyse the impact that Hofstede's cultural dimensions may have between implementations of various degrees of restriction of NPIs and the reproduction rate by applying machine learning models to understand whether cultural characteristics are useful information to improve reproduction rate predictions. To achieve these objectives, we follow the CRISP-DM methodology being that we gather data from Our World in Data COVID-19, Oxford COVID-19 Government Response Tracker and Hofstede Insights website. We show an in-depth and extensive analysis over these months of the pandemic which shows differences between the five countries that have implemented the same NPIs to different degrees and where culture plays an important role in each country's response to the various NPIs implemented.Desde o início da pandemia COVID-19 que os países do mundo inteiro implementaram um conjunto de intervenções não farmacêuticas (NPIs) como forma de combater a evolução da pandemia. Nesta dissertação propomos uma análise detalhada da evolução da pandemia que considera o grau de restrição das NPIs desde Março de 2020 a Maio de 2021 e a taxa de reprodução em cinco países: India, Brasil, Reino Unido, Israel e Portugal. Além disto, analisamos o impacto que as dimensões culturais de Hofstede podem ter entre as implementações de vários graus de restrição de NPIs e a taxa de reprodução aplicando modelos de machine learning para compreender se as características culturais são informações úteis para melhorar as previsões da taxa de reprodução. Para concretizar estes objetivos, nós seguimos a metodologia do CRISP-DM sendo que, reunimos dados de Our World in Data COVID-19, Oxford COVID-19 Government Response Tracker e o website Hofstede Insights. Mostramos uma análise aprofundada e extensa ao longo destes meses da pandemia a qual mostra diferenças entre os cinco países que implementaram as mesmas NPIs em diferentes graus e em que a cultura desempenha um papel importante na resposta de cada país às várias NPIs implementadas