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In the model of randomly perturbed graphs we consider the union of a deterministic graph G with minimum degree αn and the binomial random graph G(n, p). This model was introduced by Bohman, Frieze, and Martin and for Hamilton cycles their result bridges the gap between Dirac’s theorem and the results by Pósa and Korshunov on the threshold in G(n, p). In this note we extend this result in G ∪G(n, p) to sparser graphs with α = o(1). More precisely, for any ε > 0 and α: N ↦→ (0, 1) we show that a.a.s. G ∪ G(n, β/n) is Hamiltonian, where β = −(6 + ε) log(α). If α > 0 is a fixed constant this gives the aforementioned result by Bohman, Frieze, and Martin and if α = O(1/n) the random part G(n, p) is sufficient for a Hamilton cycle. We also discuss embeddings of bounded degree trees and other spanning structures in this model, which lead to interesting questions on almost spanning embeddings into G(n, p).
1.Thedescriptionandanalysisofanimalbehavioroverlongperiodsoftimeisoneof the most important challenges in ecology. However, most of these studies are limited due to the time and cost required by human observers. The collection of data via video recordings allows observation periods to be extended. However, their evaluation by human observers is very time-consuming. Progress in automated evaluation, using suitable deep learning methods, seems to be a forward-looking approach to analyze even large amounts of video data in an adequate time frame.
2. In this study, we present a multistep convolutional neural network system for detecting three typical stances of African ungulates in zoo enclosures which works with high accuracy. An important aspect of our approach is the introduction of model averaging and postprocessing rules to make the system robust to outliers.
3. Our trained system achieves an in-domain classification accuracy of >0.92, which is improved to >0.96 by a postprocessing step. In addition, the whole system per- forms even well in an out-of-domain classification task with two unknown types, achieving an average accuracy of 0.93. We provide our system at https://github. com/Klimroth/Video-Action-Classifier-for-African-Ungulates-in-Zoos/tree/main/ mrcnn_based so that interested users can train their own models to classify im- ages and conduct behavioral studies of wildlife.
4. The use of a multistep convolutional neural network for fast and accurate clas- sification of wildlife behavior facilitates the evaluation of large amounts of image data in ecological studies and reduces the effort of manual analysis of images to a high degree. Our system also shows that postprocessing rules are a suitable way to make species-specific adjustments and substantially increase the accuracy of the description of single behavioral phases (number, duration). The results in the out-of-domain classification strongly suggest that our system is robust and achieves a high degree of accuracy even for new species, so that other settings (e.g., field studies) can be considered.
Studying large discrete systems is of central interest in, non-exclusively, discrete mathematics, computer sciences and statistical physics. The study of phase transitions, e.g. points in the evolution of a large random system in which the behaviour of the system changes drastically, became of interest in the classical field of random graphs, the theory of spin glasses as well as in the analysis of algorithms [78,82, 121].
It turns out that ideas from the statistical physics’ point of view on spin glass systems can be used to study inherently combinatorial problems in discrete mathematics and theoretical computer sciences(for instance, satisfiability) or to analyse phase transitions occurring in inference problems (like the group testing problem) [68, 135, 168]. A mathematical flaw of this approach is that the physical methods only render mathematical conjectures as they are not known to be rigorous.
In this thesis, we will discuss the results of six contributions. For instance, we will explore how the
theory of diluted mean-field models for spin glasses helps studying random constraint satisfaction problems through the example of the random 2−SAT problem. We will derive a formula for the number of satisfying assignments that a random 2−SAT formula typically possesses [2].
Furthermore, we will discuss how ideas from spin glass models (more precisely, from their planted versions) can be used to facilitate inference in the group testing problem. We will answer all major open questions with respect to non-adaptive group testing if the number of infected individuals scales sublinearly in the population size and draw a complete picture of phase transitions with respect to the
complexity and solubility of this inference problem [41, 46].
Subsequently, we study the group testing problem under sparsity constrains and obtain a (not fully understood) phase diagram in which only small regions stay unexplored [88].
In all those cases, we will discover that important results can be achieved if one combines the rich theory of the statistical physics’ approach towards spin glasses and inherent combinatorial properties of the underlying random graph.
Furthermore, based on partial results of Coja-Oghlan, Perkins and Skubch [42] and Coja-Oghlan et al. [49], we introduce a consistent limit theory for discrete probability measures akin to the graph limit theory [31, 32, 128] in [47]. This limit theory involves the extensive study of a special variant of the cut-distance and we obtain a continuous version of a very simple algorithm, the pinning operation, which allows to decompose the phase space of an underlying system into parts such that a probability
measure, restricted to this decomposition, is close to a product measure under the cut-distance. We will see that this pinning lemma can be used to rigorise predictions, at least in some special cases, based on the physical idea of a Bethe state decomposition when applied to the Boltzmann distribution.
Finally, we study sufficient conditions for the existence of perfect matchings, Hamilton cycles and bounded degree trees in randomly perturbed graph models if the underlying deterministic graph is sparse [93].
Only a few studies on the nocturnal behavior of African ungulates exist so far, with mostly small sample sizes. For a comprehensive understanding of nocturnal behavior, the data basis needs to be expanded. Results obtained by observing zoo animals can provide clues for the study of wild animals and furthermore contribute to a better understanding of animal welfare and better husbandry conditions in zoos. The current contribution reduces the lack of data in two ways. First, we present a stand-alone open-source software package based on deep learning techniques, named Behavioral Observations by Videos and Images using Deep-Learning Software (BOVIDS). It can be used to identify ungulates in their enclosure and to determine the three behavioral poses “Standing,” “Lying—head up,” and “Lying—head down” on 11,411 h of video material with an accuracy of 99.4%. Second, BOVIDS is used to conduct a case study on 25 common elands (Tragelaphus oryx) out of 5 EAZA zoos with a total of 822 nights, yielding the first detailed description of the nightly behavior of common elands. Our results indicate that age and sex are influencing factors on the nocturnal activity budget, the length of behavioral phases as well as the number of phases per behavioral state during the night while the keeping zoo has no significant influence. It is found that males spend more time in REM sleep posture than females while young animals spend more time in this position than adult ones. Finally, the results suggest a rhythm between the Standing and Lying phases among common elands that opens future research directions.
In order to effectively address global environmental problems, it is important that future decision-makers in society are aware of the safe operation space for humans, which is limited by the planetary boundaries. Until now, however, there has been a lack of international studies examining how the planet's boundaries are perceived. In this study, we investigated how students of environmental and sustainability studies in 35 countries (n = 4140) assess the planetary boundaries. Based on the rating, using spectral clustering, the 35 countries were assigned to five different clusters. Four indicators (Human Development Index, Legatum Prosperity Index, Natural Resources Income and Forest Area) were used to provide explanations for the clustering result. The indices allow a distinction between the clusters and provide initial explanations for the clustering. The results provide important insights for today's decision-makers, as possible measures for action in the individual countries can be derived from the findings.
We show that throughout the satisfiable phase the normalized number of satisfying assignments of a random 2-SAT formula converges in probability to an expression predicted by the cavity method from statistical physics. The proof is based on showing that the Belief Propagation algorithm renders the correct marginal probability that a variable is set to “true” under a uniformly random satisfying assignment.
Background: The ability to approximate intra-operative hemoglobin loss with reasonable precision and linearity is prerequisite for determination of a relevant surgical outcome parameter: This information enables comparison of surgical procedures between different techniques, surgeons or hospitals, and supports anticipation of transfusion needs. Different formulas have been proposed, but none of them were validated for accuracy, precision and linearity against a cohort with precisely measured hemoglobin loss and, possibly for that reason, neither has established itself as gold standard. We sought to identify the minimal dataset needed to generate reasonably precise and accurate hemoglobin loss prediction tools and to derive and validate an estimation formula.
Methods: Routinely available clinical and laboratory data from a cohort of 401 healthy individuals with controlled hemoglobin loss between 29 and 233 g were extracted from medical charts. Supervised learning algorithms were applied to identify a minimal data set and to generate and validate a formula for calculation of hemoglobin loss.
Results: Of the classical supervised learning algorithms applied, the linear and Ridge regression models performed at least as well as the more complex models. Most straightforward to analyze and check for robustness, we proceeded with linear regression. Weight, height, sex and hemoglobin concentration before and on the morning after the intervention were sufficient to generate a formula for estimation of hemoglobin loss. The resulting model yields an outstanding R2 of 53.2% with similar precision throughout the entire range of volumes or donor sizes, thereby meaningfully outperforming previously proposed medical models.
Conclusions: The resulting formula will allow objective benchmarking of surgical blood loss, enabling informed decision making as to the need for pre-operative type-and-cross only vs. reservation of packed red cell units, depending on a patient’s anemia tolerance, and thus contributing to resource management.