In this paper, we present a method for time series analysis based on empirical intrinsic geometry (EIG). EIG enables one to reveal the low-dimensional parametric manifold as well as to infer the underlying dynamics of high-dimensional time series. By incorporating concepts of information geometry, this method extends existing geometric analysis tools to support stochastic settings and parametri...

This paper reviews methods for mapping from the acoustical properties of a speech signal to the geometry of the vocal tract that generated the signal. Such mapping techniques are studied for their potential application in speech synthesis, coding, and recognition. Mathematically, the estimation of the vocal tract shape from its output speech is a so-called inverse problem, where the direct prob...

This paper uses a method for shape reconstruction of a 2-D homogeneous object with arbitrary geometry and known electrical properties. In this method, the object is illuminated by a Gaussian pulse, modulated with sinusoidal carrier plane wave and the time domains’ footprint signal due to object presence is used for the shape reconstruction. A nonlinear feedback loop is used to minimize the diff...

We analyze nonlinear collective effects in periodic systems with multigap transmission spectra such as light in waveguide arrays or Bose-Einstein condensates in optical lattices. We reveal that the interband interactions in nonlinear periodic structures can be efficiently managed by controlling their geometry. We predict novel types of discrete vector solitons supported by nonlinear coupling be...

Robinson-Trautman solutions with nonlinear electrodynamics are investigated for both $\mathbb{L}(F)$ and $\mathbb{L}(F,G)$ Lagrangians, the presence of electric magnetic charges as well electromagnetic radiation is assumed. Particular interest devoted to models representing regular black holes spherically symmetric situations. The results show clear uniqueness Maxwell respect compatibility clas...