Data-based Master Equations for the Stratosphere

Three-dimensional data-based master equations are developed and subsequently used to study climate variability in the stratosphere. Master equations are used to develop understanding of observed systems where no dynamic equations are available. Master equations are used in this thesis as prognostic equations for the probability density in a discretized phase space spanned by climate variables. The evolution of the probability density may then reveal information about the relationship between these variables. The phase space is partitioned into several hundred boxes of equal grid size representing at any one time states that the system can assume. In this discretized version of the phase space, the coefficients of a master equation may be estimated from the relative frequencies of transitions observed in a time series of the variables obtained from observations or numerical model runs. Data-based master equations are numerical structures whose success depends among other things on the resolution and volume of the available time series. These dependencies are studied on the basis of data from the famous three-component Lorenz convection model extended with a stochastic forcing. Time series of the desired length and time resolution can thus be generated easily. Furthermore, the results can be compared directly. Best results are obtained through the combination of a long data record and a coarse time resolution. The choice of the variables and their number also play a crucial role in the success of a master equation. Time series of stratospheric climate indices obtained from the reanalyses ERA-40 lead also to these last results. The stratosphere serves now as an implementation area. The master equation shows that during the eastern phase of the quasi-biennial oscillation (QBO) of equatorial zonal wind the arctic stratosphere is about 2 K warmer than during the western phase. Thus the relationship between QBO and arctic stratosphere can be quantified. The influence of the 11-year solar cycle is described by the master equation. It emerges that the relationship between QBO and temperature anomaly of the arctic stratosphere shows a dependence on solar variability. The implications of stratospheric processes on the climate in the troposphere are analysed with a master equation for a time series of an index of the Arctic Oscillation (AO) at stratospheric and tropospheric pressure levels. The master equation captures the main features of this interaction between stratosphere and troposphere. It is shown that anomalies of the AO in the middle stratospere propagate deeply into the troposphere with a time scale of 4 weeks. Furthermore the master equation shows that the influence of strong tropospheric AO-anomalies remains confined to the lower stratosphere

Efficient distributed representations beyond negative sampling

This article describes an efficient method to learn distributed representations, also known as embeddings. This is accomplished minimizing an objective function similar to the one introduced in the Word2Vec algorithm and later adopted in several works. The optimization computational bottleneck is the calculation of the softmax normalization constants for which a number of operations scaling quadratically with the sample size is required. This complexity is unsuited for large datasets and negative sampling is a popular workaround, allowing one to obtain distributed representations in linear time with respect to the sample size. Negative sampling consists, however, in a change of the loss function and hence solves a different optimization problem from the one originally proposed. Our contribution is to show that the sotfmax normalization constants can be estimated in linear time, allowing us to design an efficient optimization strategy to learn distributed representations. We test our approximation on two popular applications related to word and node embeddings. The results evidence competing performance in terms of accuracy with respect to negative sampling with a remarkably lower computational time

A unified framework for spectral clustering in sparse graphs

This article considers spectral community detection in the regime of sparse networks with heterogeneous degree distributions, for which we devise an algorithm to efficiently retrieve communities. Specifically, we demonstrate that a conveniently parametrized form of regularized Laplacian matrix can be used to perform spectral clustering in sparse networks, without suffering from its degree heterogeneity. Besides, we exhibit important connections between this proposed matrix and the now popular non-backtracking matrix, the Bethe-Hessian matrix, as well as the standard Laplacian matrix. Interestingly, as opposed to competitive methods, our proposed improved parametrization inherently accounts for the hardness of the classification problem. These findings are summarized under the form of an algorithm capable of both estimating the number of communities and achieving high-quality community reconstruction

Using airborne laser altimetry to improve river flood extents delineated from SAR data

Flood extent maps derived from SAR images are a useful source of data for validating hydraulic models of river flood flow. The accuracy of such maps is reduced by a number of factors, including changes in returns from the water surface caused by different meteorological conditions and the presence of emergent vegetation. The paper describes how improved accuracy can be achieved by modifying an existing flood extent delineation algorithm to use airborne laser altimetry (LiDAR) as well as SAR data. The LiDAR data provide an additional constraint that waterline (land-water boundary) heights should vary smoothly along the flooded reach. The method was tested on a SAR image of a flood for which contemporaneous aerial photography existed, together with LiDAR data of the un-flooded reach. Waterline heights of the SAR flood extent conditioned on both SAR and LiDAR data matched the corresponding heights from the aerial photo waterline significantly more closely than those from the SAR flood extent conditioned only on SAR data

One to many: comparing single gravitational-wave events to astrophysical populations

Gravitational-wave observations have revealed sources whose unusual properties challenge our understanding of compact-binary formation. Inferring the formation processes that are best able to reproduce such events may therefore yield key astrophysical insights. A common approach is to simulate a population of mergers and count the fraction of these synthetic events that lie within a chosen region in the measured parameters of a real event. Though appealing owing to its simplicity, this approach is flawed because it neglects the full posterior information, depends on a heuristically constructed confidence region, and fails for high signal-to-noise detections. We point out that the statistically consistent solution is to compute the posterior odds between two simulated populations, which crucially is a relative measure, and show how to include the effect of observational biases by conditioning on source detectability. Applying the approach to several gravitational-wave events and astrophysical populations, we assess the degree to which we can conclude model preference not just between distinct formation pathways but also between subpopulations within a given pathway.Comment: 13 pages, 7 figures, 2 table

A serpiginous lesion of scrotum

Background Median raphe cyst is usually benign and asymptomatic male genitalia lesions. Although uncommon, infection may be a complication. Case presentation We report the case of a 4-year-old child presented to the emergency department for a serpiginous and redness lesion extended from the basis of the penis until the perineum. An infected median raphe cyst was suspected, and the patient underwent surgical treatment and antibiotic therapy with complete resolution of symptoms. Liquid culture resulted positive for Serratia Marcescens. Conclusion Infection is a rare complication, especially in childhood. To prevent relapses and clinical symptoms, the majority of authors recommend surgical excision followed by primary closure. In case of infections caused by Serratia Marcescens, chronic granulomatous disease should always be rule out