On the Parikh-de-Bruijn grid

We introduce the Parikh-de-Bruijn grid, a graph whose vertices are fixed-order Parikh vectors, and whose edges are given by a simple shift operation. This graph gives structural insight into the nature of sets of Parikh vectors as well as that of the Parikh set of a given string. We show its utility by proving some results on Parikh-de-Bruijn strings, the abelian analog of de-Bruijn sequences.Comment: 18 pages, 3 figures, 1 tabl

On the k-Abelian Equivalence Relation of Finite Words

This thesis is devoted to the so-called k-abelian equivalence relation of sequences of symbols, that is, words. This equivalence relation is a generalization of the abelian equivalence of words. Two words are abelian equivalent if one is a permutation of the other. For any positive integer k, two words are called k-abelian equivalent if each word of length at most k occurs equally many times as a factor in the two words. The k-abelian equivalence defines an equivalence relation, even a congruence, of finite words. A hierarchy of equivalence classes in between the equality relation and the abelian equivalence of words is thus obtained. Most of the literature on the k-abelian equivalence deals with infinite words. In this thesis we consider several aspects of the equivalence relations, the main objective being to build a fairly comprehensive picture on the structure of the k-abelian equivalence classes themselves. The main part of the thesis deals with the structural aspects of k-abelian equivalence classes. We also consider aspects of k-abelian equivalence in infinite words. We survey known characterizations of the k-abelian equivalence of finite words from the literature and also introduce novel characterizations. For the analysis of structural properties of the equivalence relation, the main tool is the characterization by the rewriting rule called the k-switching. Using this rule it is straightforward to show that the language comprised of the lexicographically least elements of the k-abelian equivalence classes is regular. Further word-combinatorial analysis of the lexicographically least elements leads us to describe the deterministic finite automata recognizing this language. Using tools from formal language theory combined with our analysis, we give an optimal expression for the asymptotic growth rate of the number of k-abelian equivalence classes of length n over an m-letter alphabet. Explicit formulae are computed for small values of k and m, and these sequences appear in Sloane’s Online Encyclopedia of Integer Sequences. Due to the fact that the k-abelian equivalence relation is a congruence of the free monoid, we study equations over the k-abelian equivalence classes. The main result in this setting is that any system of equations of k-abelian equivalence classes is equivalent to one of its finite subsystems, i.e., the monoid defined by the k-abelian equivalence relation possesses the compactness property. Concerning infinite words, we mainly consider the (k-)abelian complexity function. We complete a classification of the asymptotic abelian complexities of pure morphic binary words. In other words, given a morphism which has an infinite binary fixed point, the limit superior asymptotic abelian complexity of the fixed point can be computed (in principle). We also give a new proof of the fact that the k-abelian complexity of a Sturmian word is n + 1 for length n 2k. In fact, we consider several aspects of the k-abelian equivalence relation in Sturmian words using a dynamical interpretation of these words. We reprove the fact that any Sturmian word contains arbitrarily large k-abelian repetitions. The methods used allow to analyze the situation in more detail, and this leads us to define the so-called k-abelian critical exponent which measures the ratio of the exponent and the length of the root of a k-abelian repetition. This notion is connected to a deep number theoretic object called the Lagrange spectrum

Commissioning and First Science Results of the Desert Fireball Network: a Global-Scale Automated Survey for Large Meteoroid Impacts

This thesis explores the first results from the Desert Fireball Network, a distributed global observatory designed to characterise fireballs caused by meteoroid impacts. To deal with the >50 terabytes of data influx per week, innovative data reduction techniques have been developed. The science topics investigated in this work include airbursts caused by large meteoroids impacting the Earth's atmosphere, the recovery of a meteorite and its orbital history, and the structure of a meteor shower

SPATIOTEMPORAL VARIABILITY IN WINTER SEVERITY: CONSEQUENCES FOR WHITE-TAILED DEER POPULATIONS AND HABITAT SUSTAINABILITY

Winter in the northern Great Lakes presents a suite of challenging conditions for animals, in terms of limited food availability and increased energetic cost of locomotion and thermoregulation. Variable winter severity is liable to cause interannual fluctuations in habitat viability and use by animals, in addition to modulating physiological responses in animals to conserve energy. For example, white-tailed deer (Odocoileus virginianus) congregate at high densities under eastern hemlock (Tsuga canadensis) or northern white-cedar (Thuja occidentalis) stands, which provide forage, thermal cover, reduced snow depth, and enhanced vigilance. However, a suite of climatic, edaphic, and management changes, in addition to novel deer densities, have compromised regeneration of eastern hemlock in recent years, while facilitating the propagation of hardwoods. For this research, I monitored 39 randomly selected eastern hemlock stands across the western Upper Peninsula. I selected a subset of 15 of these stands to survey for forest community composition and assess changes between 2006 and 2015, and found evidence of a transition to hardwoods such as maple (Acer rubrum and A. saccharum). This change in forest composition will have significant implications for migratory white-tailed deer, particularly when coupled with more extreme winter conditions predicted to occur with climate change. I monitored local deer use in all 39 stands from winter 2014-15 to 2017-2018, building on a dataset extending back to winter 2005-2006, by counting fecal pellet groups in each stand, and found evidence of reduced use following recent severe winters, as well as a spatial shift in intensity of use. I assessed diet composition by collecting fecal samples during spring pellet surveys, and found evidence of spatial variability in the diet, likely due to spatiotemporal variation in winter severity. To further understand the physiological implications of winter severity and winter diet, I assessed physiological stress response (via non-invasive fecal glucocorticoids) and found evidence of endocrine down-regulation in animals with a poor diet and in extreme conditions. My findings underscore the importance of maintaining a mesic conifer component in northern forests to provide winter habitat for regional migratory deer populations

Deep learning models for road passability detection during flood events using social media data

During natural disasters, situational awareness is needed to understand the situation and respond accordingly. A key need is assessing open roads for transporting emergency support to victims. This can be done via analysis of photos from affected areas with known location. This paper studies the problem of detecting blocked / open roads from photos during floods by applying a two-step approach based on classifiers: does the image have evidence of road? If it does, is the road passable or not? We propose a single double-ended neural network (NN) architecture which addresses both tasks at the same time. Both problems are treated as a single class classification problem by the usage of a compactness loss. The study is performed on a set of tweets, posted during flooding events, that contain (i)~metadata and (ii)~visual information. We study the usefulness of each source of data and the combination of both. Finally, we do a study of the performance gain from ensembling different networks. Through the experimental results we prove that the proposed double-ended NN makes the model almost two times faster and memory lighter while improving the results with respect to training two separate networks to solve each problem independently