We developed a non-parametric method of Information Decomposition (ID) of a content of any symbolical sequence. The method is based on the calculation of Shannon mutual information between analyzed and artificial symbolical sequences, and allows the revealing of latent periodicity in any symbolical sequence. We show the stability of the ID method in the… (More)
Exact solutions of the Nizhnik-Novikov-Veselov equation by Li [New kink-shaped solutions and periodic wave solutions for the (2+1)-dimensional Sine-Gordon equation, Appl. Math. Comput. 215 (2009). 3777-3781 ] are analyzed. We have observed that fourteen solutions by Li from thirty do not satisfy the equation. The other sixteen exact solutions by Li can be… (More)
We demonstrate that the G /G-expansion method which is often used in finding exact solutions of nonlinear differential equation is equivalent to the well – known tanh-method and application of these methods gives the same exact solutions of nonlinear differential equations.
Exact solutions of the (2+1) – dimensional Kadomtsev – Petviashvili by Zhang [Zhang H., Applied Mathematics and Computation 216 (2010) 2771 – 2777] are considered. To look for " new types of exact solutions travelling wave solutions " of equation Zhang has used the G'/G – expansion method. We demonstrate that there is the general solution for the reduction… (More)
We identified latent periodicity in catalytic domains of approximately 85% of annotated serine-threonine and tyrosine protein kinases. Similar results were obtained for other 22 protein families and domains. We also designed the method of noise decomposition, which is aimed to distinguish between different periodicity types of the same period length. The… (More)
Here, we have applied information decomposition, cyclic profile alignment, and noise decomposition techniques to search for latent repeats within protein families of various functions. We have identified 94 protein families with a family-specific periodicity. In each case, the periodic element was found in greater than 70% of family members. Latent… (More)