Roman Chertovskih

Rui Gonçalves, Vitor Miguel Ribeiro, Roman Chertovskih et al.

This study presents the implementation of a short-term forecasting system for price movements in exchange markets, using market depth data and a systematic procedure to enable a fully automated trading system. The case study focuses on the UK to Win Horse Racing market during the pre-live stage on the world's leading betting exchange, Betfair. Innovative convolutional attention mechanisms are introduced and applied to multiple recurrent neural networks and bi-dimensional convolutional recurrent neural network layers. Additionally, a novel padding method for convolutional layers is proposed, specifically designed for multivariate time series processing. These innovations are thoroughly detailed, along with their execution process. The proposed architectures follow a standard supervised learning approach, involving model training and subsequent testing on new data, which requires extensive pre-processing and data analysis. The study also presents a complete end-to-end framework for automated feature engineering and market interactions using the developed models in production. The key finding of this research is that all proposed innovations positively impact the performance metrics of the classification task under examination, thereby advancing the current state-of-the-art in convolutional attention mechanisms and padding methods applied to multivariate time series problems.

Roman Chertovskih, Vladislav Zheligovsky

We present a new mechanism for generation of large-scale magnetic field by thermal convection which does not involve the alpha-effect. We consider weakly nonlinear perturbations of space-periodic steady convective magnetic dynamos in a rotating layer that were identified in our previous work. The perturbations have a spatial scale in the horizontal direction that is much larger than the period of the perturbed convective magnetohydrodynamic state. Following the formalism of the multiscale stability theory, we have derived the system of amplitude equations governing the evolution of the leading terms in the expansion of the perturbations in power series in the scale ratio. This asymptotic analysis is more involved than in the cases considered earlier, because the kernel of the operator of linearisation has zero-mean neutral modes whose origin lies in the spatial invariance of the perturbed regime, the operator reduced on the generalised kernel has two Jordan normal form blocks of size two, and simplifying symmetries of the perturbed state are now missing. Numerical results for the amplitude equations show that a large-scale perturbation, periodic in slow horizontal variable, either converges to a short-scale neutral stability mode with amplitudes tending to constant values, or it blows up at a finite slow time.

Ugo Boscain, Roman Chertovskih, Jean-Paul Gauthier et al.

We present a new image inpainting algorithm, the Averaging and Hypoelliptic Evolution (AHE) algorithm, inspired by the one presented in [SIAM J. Imaging Sci., vol. 7, no. 2, pp. 669--695, 2014] and based upon a semi-discrete variation of the Citti-Petitot-Sarti model of the primary visual cortex V1. The AHE algorithm is based on a suitable combination of sub-Riemannian hypoelliptic diffusion and ad-hoc local averaging techniques. In particular, we focus on reconstructing highly corrupted images (i.e. where more than the 80% of the image is missing), for which we obtain reconstructions comparable with the state-of-the-art.