Flying Elephants (FE) is a generalization and a new interpretation of the Hyperbolic Smoothing approach. The article introduces the fundamental smoothing procedures. It presents a general overview of successful applications of the approach for solving a select set of five important problems, namely: distance geometry, covering, clustering, Fermat-Weber and hub location. For each problem it is p...

We introduce a new model, the Recurrent Entity Network (EntNet). It is equipped with a dynamic long-term memory which allows it to maintain and update a representation of the state of the world as it receives new data. For language understanding tasks, it can reason on-the-fly as it reads text, not just when it is required to answer a question or respond as is the case for a Memory Network (Suk...

Starting from the decomposition method for operators, we consider Newton-like iterative processes approximating solutions of nonlinear operators in Banach spaces. These maintain quadratic convergence Newton's method. Since operator has its highest degree application non-differentiable situations, construct Newton-type methods using symmetric divided differences, which allow us to improve access...

In this paper, we use the Riemann-Liouville fractionalintegrals to establish some new integral inequalities related toChebyshev's functional in the case of two differentiable functions.

In recent years, deep learning techniques have been developed to improve the performance of program synthesis from input-output examples. Albeit its significant progress, the programs that can be synthesized by state-of-the-art approaches are still simple in terms of their complexity. In this work, we move a significant step forward along this direction by proposing a new class of challenging t...

In recent years, deep learning techniques have been developed to improve the performance of program synthesis from input-output examples. Albeit its significant progress, the programs that can be synthesized by state-of-the-art approaches are still simple in terms of their complexity. In this work, we move a significant step forward along this direction by proposing a new class of challenging t...