Variational analysis for a generalized spiked harmonic oscillator

A variational analysis is presented for the generalized spiked harmonic oscillator Hamiltonian operator H, where H = -(d/dx)^2 + Bx^2+ A/x^2 + lambda/x^alpha, and alpha and lambda are real positive parameters. The formalism makes use of a basis provided by exact solutions of Schroedinger's equation for the Gol'dman and Krivchenkov Hamiltonian (alpha = 2), and the corresponding matrix elements that were previously found. For all the discrete eigenvalues the method provides bounds which improve as the dimension of the basis set is increased. Extension to the N-dimensional case in arbitrary angular-momentum subspaces is also presented. By minimizing over the free parameter A, we are able to reduce substantially the number of basis functions needed for a given accuracy.Comment: 15 pages, 1 figur

A Recurrent Neural Network Survival Model: Predicting Web User Return Time

The size of a website's active user base directly affects its value. Thus, it is important to monitor and influence a user's likelihood to return to a site. Essential to this is predicting when a user will return. Current state of the art approaches to solve this problem come in two flavors: (1) Recurrent Neural Network (RNN) based solutions and (2) survival analysis methods. We observe that both techniques are severely limited when applied to this problem. Survival models can only incorporate aggregate representations of users instead of automatically learning a representation directly from a raw time series of user actions. RNNs can automatically learn features, but can not be directly trained with examples of non-returning users who have no target value for their return time. We develop a novel RNN survival model that removes the limitations of the state of the art methods. We demonstrate that this model can successfully be applied to return time prediction on a large e-commerce dataset with a superior ability to discriminate between returning and non-returning users than either method applied in isolation.Comment: Accepted into ECML PKDD 2018; 8 figures and 1 tabl

Part of the D - dimensional Spiked harmonic oscillator spectra

The pseudoperturbative shifted - l expansion technique PSLET [5,20] is generalized for states with arbitrary number of nodal zeros. Interdimensional degeneracies, emerging from the isomorphism between angular momentum and dimensionality of the central force Schrodinger equation, are used to construct part of the D - dimensional spiked harmonic oscillator bound - states. PSLET results are found to compare excellenly with those from direct numerical integration and generalized variational methods [1,2].Comment: Latex file, 20 pages, to appear in J. Phys. A: Math. & Ge

Study of Digital Competence of the Students and Teachers in Ukraine

Professional fulfillment of the personality at the conditions of the digital economy requires the high level of digital competency. One of the ways to develop these competencies is education. However, to provide the implementation of digital education at a high level, the digital competency of the teachers and students is a must. This paper presents explanations on the level determination of the digital competencies for teachers and students in Ukraine according to the DigComp recommendations. We tried to identify the main factors that reflect the degree of readiness teachers and students for digital education based on their self-evaluation. We also attempted to estimate the level of digital competencies based on the analysis of Case-Studies execution results. The complex analysis let us assess the connection between respondents’ self-evaluation and their real competencies. Here we provide a methodology and a model of level competencies determination by means of a survey, expert case rating and the results of the statistical analysis. On the basis of the obtained results, this paper suggests further research prospects and recommendations on the digital competency development in educational institutions in Ukraine

Divide-and-Rule: Self-Supervised Learning for Survival Analysis in Colorectal Cancer

With the long-term rapid increase in incidences of colorectal cancer (CRC), there is an urgent clinical need to improve risk stratification. The conventional pathology report is usually limited to only a few histopathological features. However, most of the tumor microenvironments used to describe patterns of aggressive tumor behavior are ignored. In this work, we aim to learn histopathological patterns within cancerous tissue regions that can be used to improve prognostic stratification for colorectal cancer. To do so, we propose a self-supervised learning method that jointly learns a representation of tissue regions as well as a metric of the clustering to obtain their underlying patterns. These histopathological patterns are then used to represent the interaction between complex tissues and predict clinical outcomes directly. We furthermore show that the proposed approach can benefit from linear predictors to avoid overfitting in patient outcomes predictions. To this end, we introduce a new well-characterized clinicopathological dataset, including a retrospective collective of 374 patients, with their survival time and treatment information. Histomorphological clusters obtained by our method are evaluated by training survival models. The experimental results demonstrate statistically significant patient stratification, and our approach outperformed the state-of-the-art deep clustering methods