12 citations · 31 across the 18 of their papers we have counts for
18 papers
Infinite hierarchies of Poisson structures for integrable systems and spectral curves
K. L. Vaninsky
In this short survey, we describe our approach for constructing hierarchies of Poisson brackets for classical integrable systems using its' spectral curves.
The hierarchy of Poisson brackets for the open Toda lattice and its' spectral curves
K. L. Vaninsky
We establish a new representation of the infinite hierarchy of Pois- son brackets (PB) for the open Toda lattice in terms of its spectral curve. For the classical Poisson bracket (…
Analytic Poisson brackets on rational functions on the Riemann sphere and their generalization
K. L. Vaninsky
We consider a hierarchy of Poisson structures defined on rational functions on the Riemann sphere. This hierarchy is originated in the theory of the integrable Camassa-Holm equatio…
On Simulation of Various Effects in Consolidated Order Book
A. O. Glekin, A. Lykov, K. L. Vaninsky
This paper consists of two parts. The first part is devoted to empirical analysis of consolidated order book (COB) for the index RTS futures. In the second part we consider Poisson…
The AdaBoost Flow
A. Lykov, S. Muzychka, K. Vaninsky
We introduce a dynamical system which we call the AdaBoost flow. The flow is defined by a system of ODEs with control. We show that three algorithms of the AdaBoost family (i) the…
A class of nonlinear random walks related to the Ornstein-Uhlenbeck process
S. A. Muzychka, K. L. Vaninsky
Contrary to the theory of Markov processes, no general theory exists for the so called nonlinear Markov processes. We study an example of "nonlinear Markov process" related to clas…