The phenomenon of quantum steering and probabilistic meaning of the correlations are discussed for the state of the single qudit. The method of qubit portrait of the qudit states is used to extend the known steering detection inequality to the system without subsystems. The example of the X-state with j = 3/2 is studied in detail.

Despite numerical procedures often supply a necessary accuracy, closed-form expressions allow to escape any accumulation of errors. In this paper we discuss the possibility of obtaining explicit results for a variance gamma process. The exact distribution of the maximum of the variance gamma process over a finite interval of time is derived. The prices of path-dependent options including digital barrier, fixed-strike lookback and lookback options are established. The obtained formulas are based on values of hypergeometric functions.

Choline-containing preparations are used in the medical practice for treatment and prevention of the neurologic disorders of different genesis. We have used mathematical simulation to study the influence of the content of choline in the food ration of rats on the dynamics of the expression of nicotinic acetylcholine receptors of brain, as well as changes in the indices associated with the metabolism of choline in the organism – mass of the body of animals and amount of consumed food and water. The model was verified on the experimental data. The results of our work might be useful for developing a neuroprotection strategy based on the use of choline-containing preparations and minimizing the consequences of cerebral disorders after brain injury.

Modern principles for the construction are considered, and the optimal structure for converting the parameters of multicomponent two-terminal networks is proposed. Pulse and frequency methods of measuring these parameters are compared and a universal algorithm for calculating them from measurement data is described.

We explore the dependence structure in the sampled sequence of complex networks. We consider randomized algorithms to sample the nodes and study extremal properties in any associated stationary sequence of characteristics of interest like node degrees, number of followers or income of the nodes in Online Social Networks etc, which satisfy two mixing conditions. Several useful extremes of the sampled sequence like $k$th largest value, clusters of exceedances over a threshold, first hitting time of a large value etc are investigated. We abstract the dependence and the statistics of extremes into a single parameter that appears in Extreme Value Theory, called extremal index (EI). In this work, we derive this parameter analytically and also estimate it empirically. We propose the use of EI as a parameter to compare different sampling procedures. As a specific example, degree correlations between neighboring nodes are studied in detail with three prominent random walks as sampling techniques.