Green functions of the spectral ball and symmetrized polydisk

The Green function of the spectral ball is constant over the isospectral varieties, is never less than the pullback of its counterpart on the symmetrized polydisk, and is equal to it in the generic case where the pole is a cyclic (non-derogatory) matrix. When the pole is derogatory, the inequality is always strict, and the difference between the two functions depends on the order of nilpotence of the strictly upper triangular blocks that appear in the Jordan decomposition of the pole. In particular, the Green function of the spectral ball is not symmetric in its arguments. Additionally, some estimates are given for invariant functions in the symmetrized polydisc, e.g. (infinitesimal versions of) the Carath\'eodory distance and the Green function, that show that they are distinct in dimension greater or equal to $3$.Comment: 12 page

Unsupervised User Stance Detection on Twitter

We present a highly effective unsupervised framework for detecting the stance of prolific Twitter users with respect to controversial topics. In particular, we use dimensionality reduction to project users onto a low-dimensional space, followed by clustering, which allows us to find core users that are representative of the different stances. Our framework has three major advantages over pre-existing methods, which are based on supervised or semi-supervised classification. First, we do not require any prior labeling of users: instead, we create clusters, which are much easier to label manually afterwards, e.g., in a matter of seconds or minutes instead of hours. Second, there is no need for domain- or topic-level knowledge either to specify the relevant stances (labels) or to conduct the actual labeling. Third, our framework is robust in the face of data skewness, e.g., when some users or some stances have greater representation in the data. We experiment with different combinations of user similarity features, dataset sizes, dimensionality reduction methods, and clustering algorithms to ascertain the most effective and most computationally efficient combinations across three different datasets (in English and Turkish). We further verified our results on additional tweet sets covering six different controversial topics. Our best combination in terms of effectiveness and efficiency uses retweeted accounts as features, UMAP for dimensionality reduction, and Mean Shift for clustering, and yields a small number of high-quality user clusters, typically just 2--3, with more than 98\% purity. The resulting user clusters can be used to train downstream classifiers. Moreover, our framework is robust to variations in the hyper-parameter values and also with respect to random initialization

El Sistema Nacional de Investigadores en 2009 : un vector para la internacionalización de las élites científicas ?

In this paper the authors expect to analyze the following hypothesis from different angles: the National Researchers System (Sistema Nacional de Investigadores, SNI) has created a standardization, progressive although incomplete, of the criteria governing the national scientific elite based on the criteria that prevail amongst the so-called developed countries. We study some of the indicators following which the SNI members who belong to the most aged groups present obvious differences with regard to the less aged ones and are a symptom of this homogenization dynamics, like, for instance, the age at which the doctorate degree is obtained. We also analyze the distortions that characterize this universe, like v.g. the fact that women are under-represented. A systematic analysis of the 2009 data about the SNI researchers, together with a sample of academic trajectories taken from the CVU (Joint Curriculum Vitae, Curriculum vitae único) helps us to show at what extent obtaining a degree in a foreign country helps to achieve a rapid career progression within the system, emphasizing the slants by disciplinary area and additional factors that allow to explain how they can get a high scientific prestige capital

Impact Of Optical Demultiplexers Based On Fiber Bragg Gratings On DWDM transmission system

This study is to measure the impact of the insertion of demultiplexers based on Bragg grating filter on DWDM transmission system. An optical link has been developed using a simulator system.The impact of demultiplexers on 10 Gbit/s DWDM system is investigated for NRZ-OOK coding formats. Performances of demultiplexers with different crosstalk, filter bandwidth and insertion losses are analyzed to get the best system performance for 10 Gbit/s DWDM transmission system with high spectral efficiency. The simulations were conducted for different fiber's lengths to assess the impact of demultiplexer on the link performance in terms of Bit Error Rate (BER)