Global dynamics and stability limits for planetary systems around HD 12661, HD 38529, HD 37124 and HD 160691

In order to distinguish between regular and chaotic planetary orbits we apply a new technique called MEGNO in a wide neighbourhood of orbital parameters determined using standard two-body Keplerian fits for HD 12661, HD 38529, HD 37124 and HD 160691 planetary systems. We show that the currently announced orbital parameters place these systems in very different situations from the point of view of dynamical stability. While HD 38529 and HD 37124 are located within large stability zones in the phase space around their determined orbits, the preliminary orbits in HD 160691 are highly unstable. The orbital parameters of the HD 12661 planets are located in a border region between stable and unstable dynamical regimes, so while its currently determined orbital parameters produce stable regular orbits, a minor change within the margin of error of just one parameter may result in a chaotic dynamical system.Comment: 12 pages, 3 figures, accepted ApJ, revised version following the referee's repor

Bifurcations of optimal vector fields in the shallow lake model

The solution structure of the set of optimal solutions of the shallow lake problem, a problem of optimal pollution management, is studied as we vary the values of the system parameters: the natural resilience, the relative importance of the resource for social welfare and the future discount rate. We find parameter values at which qualitative changes occur. Using theoretical results on the bifurcations of the solution structure to infinite horizon optimization problems obtained earlier, we give a fairly complete bifurcation analysis of the shallow lake problem. In particular, we show how the increase of the discount rate affects the parameter regions where an oligotrophic steady state, corresponding to low pollution level, is globally stable or locally stable under optimal dynamics. Asymptotically, an increase of the discount rate can be offset with a proportional increase of the relative social weight of the resource.

Bifurcations of optimal vector fields in the shallow lake system

The shallow lake problem is a nonconvex production-pollution dynamic optimisation problem whose solution structure depends nonlinearly on the system parameters. We perform a bifurcation analysis to investigate the consequences of varying the relative cost of pollution and the discount rate.

Changes in Education under the Influence of Digital Technologies: main Problems and Risk of Division

Digital technologies are rapidly changing the process of education. Online courses have become a common tool of gaining knowledge outside the university. Multimedia education, penetrating traditional educational institutions (schools, colleges, and universities), changes the structure of education and brings new elements to the communications during the educational process. This article considers one level of change in the model of education. On the one hand, there are advantages associated with the democratization of education. At the time of their foundation, universities were the creators of new elites – scientific and educational meanwhile, in the twenty-first century, the process of democratization and the accessibility of university education has been linked to the digitalization. On the other hand, territorial and other restrictions have been lifted. And this is a very controversial process that poses many challenges for students, one of the most noticeable of which is the lack of real contact with the teacher and the transformation of the educational process into an ”educational conveyor belt.” At the same time, personal contact with the teacher is becoming more expensive. The authors have collected studies that examine the dynamics of this emerging stratification of education. Based on the work of the pioneers in the study of digital education, the authors develop their ideas, focusing on the formation of the modern models of education, defined as affordable electronic and elite traditional. Keywords: online courses, online education, MOO

Unsupervised query segmentation using click data and dictionaries information

We describe results of experiments with an unsupervised framework for query segmentation, transforming keyword queries into structured queries. The resulting queries be used to more accurately search product databases, and potentially improve result presentation and query suggestion. The key to developing an accurate and scalable system for task is to train a query segmentation or attribute detection system over labeled data, which be acquired automatically from query and click-through logs. The main contribution of work is a improving method to automatically acquire such training data — resulting in significantly higher segmentation performance, compared to previously reported methods