A. V. Dmitriev

• Professor, Doctor of Sciences
• Professor at National Research University Higher School of Economics

Many real-world systems of various origins are capable of self-organization to the edge of a phase transition, characterized by avalanche-like behavior. Therefore, it is important, by observing the behavior of early warning measures for dynamical series generated by systems, to timely see the early warning signals (precursors) of such self-organiza...

Many different precursors are known, but not all of which are effective, i.e., giving enough time to take preventive measures and with a minimum number of false early warning signals. The study aims to select and study effective early warning measures from a set of measures directly related to critical slowing down as well as to the change in the s...

Critical phenomena in stock exchange are regularly occurring and difficult to predict events, often leading to disastrous consequences. The presented paper is devoted to the search and research of early warning signals of critical transitions in stock exchange based on the results of a multifractal analysis of a series of transactions in shares of...

The sandpile cellular automata, despite the simplicity of their basic rules, are adequate mathematical models of real-world systems, primarily open nonlinear systems capable to self-organize into the critical state. Such systems surround us everywhere. Starting from processes at microscopic distances in the human brain and ending with large-scale w...

Detection the precursors of critical transitions in complex systems is one of the most difficult and still unsolved problems. This problem has not received a final solution, not only for real complex systems, but also for model systems capable to self-organize into the critical state. The presented paper is devoted to early detection of time moment...

There is a number of studies, in which it is established that the observed flows of microposts generated by microblogging social networks (e.g., Twitter) are characterized by avalanche-like behavior. Time series of microposts depicting such streams are the time series with a power-law distribution, with 1/f noise and long memory. Despite this, ther...

Recently, there has been an increasing number of empirical evidence supporting the hypothesis that spread of avalanches of microposts on social networks, such as Twitter, is associated with some sociopolitical events. Typical examples of such events are political elections and protest movements. Inspired by this phenomenon, we built a phenomenologi...

A kinetic model is proposed to describe the self-organized criticality on Twitter. The model is based on a fractional three-parameter self-organization scheme with stochastic sources. It is shown that the adiabatic regime of self-organization to the critical state is determined by the coordinated action of a relatively small number of network users...

By 2018, there are more than 70 million people suffering from various forms of one of the most common neurological diseases – epilepsy. In fact, epipelsy is a central nervous system (neurological) disorder, manifesting itself in anomalous brain activity. Nowadays, most of the patients do not have the ability to foresee the onset of an attack in adv...

Mathematical modeling of a stock market functioning is one of the actual and at the same time complex task of the modern theoretical economics. From our point of view, building such mathematical models “ab initio”, by using analogy between the stock market and a certain physical system (in our work, laser), is the most promising approach. This pape...

A simple sociophysical model is proposed to describe the transition between a chaotic and a coherent state of a microblogging social network. The model is based on the equations of evolution of the order parameter, the conjugated field, and the control parameter. The self-consistent evolution of the networks is presented by equations in which the c...

Recent developments in nonlinear science have caused the formation of a new paradigm called the paradigm of complexity. The self-organized criticality theory constitutes the foundation of this paradigm. To estimate the complexity of a microblogging social network, we used one of the conceptual schemes of the paradigm, namely, the system of key sign...

The present paper is devoted to the investigation into the nonlinear dynamics of Twitter. A newmodel of Twitter as a thermodynamic non-equilibrium system is suggested. Dynamic variables of such system are represented by the variations of tweet/retweet number and instantaneous diversity between the densities of population on different levels around...

The present paper is devoted to the research into complexity of microblogging social networks regardless of their internal structure. This approach assumes using the results of nonlinear dynamical analysis of signals generated by the networks. The existence of the main indicators of social network complexity, such as scale invariance, tendency to u...

The nonlinear field dependences of the hot electron drift velocity have been calculated by means of numerical solution of the Boltzman kinetic equation in two families of nitride semiconductor solid solutions: InxGa1–xN and InxAl1–xN. The calculations have been carried out in the electric field up to 30 kV/cm at lattice temperatures of 77 and 300 K...

In this paper, we study theoretically the hot electron transport in two nitride semiconductor solid solutions, InxGa1−xN and InxAl1−xN, in the electric fields up to 30 kV/cm. We calculate the electron drift velocity field dependence at 77 and 300 K for the bulk samples with the electron concentration of 1 × 10¹⁸ and 1 × 10¹⁹ cm⁻³ and alloy composit...

The generality of synergetic principles in the processes of autowave self-organization in active media makes allows us to apply a model that describes evolving physicochemical and biophysical systems based on a modified system of FitzHugh–Nagumo equations for the development of a spatiotemporal stock market model with motive Elliott waves as its mo...

The present research is devoted to the application of stochastic bifurcation theory to the early detection of economic bubbles. A nonlinear random dynamical system with the possible appearance of stochastic P-bifurcations with a fat-tailed probability density function is deduced. The possibility of application of chaotic bifurcation theory to the e...

Building of adequate dynamical models of microblogging social networks is a topical task that is of interest from both theoretical and practical aspects. Experimental and theoretical results of studies related to choice of the adequate model are presented. The choice was made between two models: a nonlinear dynamical system and a nonlinear random d...

The present paper is devoted to the research into the topical questions of network evolution modeling considering the constant changes in the data environment as well as the data exchange rate. A two-level approach to the network community analysis based on the division into macro-and micro-levels of monitoring is suggested. Functionality of both l...

The research deals with the construction, implementation and analysis of the model of the non-equilibrium financial market using econophysical approach and the theory of nonlinear oscillations. We used the scaled variation of supply and demand prices and elasticity of these two variables as dynamic variables in the simulation of the non-equilibrium...

This scientific work is dedicated to the development, improvement and application of double layer interval weighted graphs (DLIG) for non-stationary time series forecasting. This model appears to be the universal and easy-to-use tool for modeling the non-stationary time series and forecasting. We observe the double layer version of the model becaus...

This scientific work is dedicated to applying of two-layer interval weighted graphs in nonstationary time series forecasting and evaluation of market risks. The first layer of the graph, formed with the primary system training, displays potential system fluctuations at the time of system training. Interval vertexes of the second layer of the graph...

Native and chiral modified (with non-enzymatic Asn racemization) NR1-ligand binding core of NMDA-receptor was modeled by means of molecular dynamic ligand modeling. Results demonstrated that Gly, D-Ser, D-Asn and D-Thr are ligands of the NR1-binding core of native NMDA-receptor, whereas the chiral modified NR1-binding core is characterized by the a...

The structure and ion selectivity of the potential-dependent potassium channel is investigated. It is shown that the channel constructed by joining the α-subunit with the β-subunit concave, when the axial symmetry axes coincide, is the potential-dependent potassium channel in the open state.

The ion selectivity of the bacterial potassium channel KCSA is explained upon comparing the energy characteristics of the interaction of cations (Li+, Na+, K+) with atoms of the selectivity filter of the protein pore. Quantum-chemical calculations reveal a deeper potential well for potassium ions, which accounts for preferred K+ permeation. It is s...

An explanation for the ionic selectivity of the bacterial potassium channel K(CS)A is offered, which is based on a comparison of energy interactions of lithium, sodium, and potassium cations with the atoms of the selective filter of an protein pore. Using quantum-chemical calculations, the presence of a deeper potential hole for potassium ions was...

The effect of isomerization of amino acid residues on the structure and water permeability of aquaporin has been investigated. It was established that the equilibrium configuration of the model D isomer is energetically less favorable than that of its natural L isomer. It is shown that the model D isomer of aquaporin is waterproof.

A calculation approach is proposed that is based on the separation of long-and short-range interactions. It allows adequate energy distribution of ions in axially symmetric ion channels to be obtained. The present approach has been tested on a bacterial potassium channel, for which the energy distribution of ions was calculated and its potassium se...

By the example of gramicidine channel, a comparative analysis of different approximate representations (heavy atoms, polar protons, near-by atoms) of AMBER force field has been carried out to calculate the electrostatic potential distribution of ionic channels in biological membranes. The results obtained are compared with the potential computed in...

The profiles of the electrostatic potential along the axis of a gramicidin channel were calculated using two quantum chemistry methods (EHT and CNDO/2) and three methods of force fields (AMBER, CHARMM, and OPLS). The calculations were performed without taking into account the contribution of water. A comparative analysis of the calculated profiles...

Two quantum-chemical methods (EHT and CNDO/2) and three force field methods (AMBER, CHARMM, and OPLS) are used to calculate the electrostatic potential profiles along the axis of the gramicidin channel. The calculations are performed without taking into account the contribution of water. A comparative analysis of the calculated profiles shows that...

A model study of the motion of Na+ ions in the cavity of membrane gramicidin channels was performed by the methods of quantum mechanics. An approximation of the distribution of the electrostatic potential along the channel axis, determined by charges on the atoms of the gramicidin A molecule, was obtained. The energy distribution and the wave funct...

A theoretical study of intermolecular interactions between local anesthetics of the acetanilide series and model ionic channels was performed. A dimer of gramicidine A and melittin were used as models of ionic channels. The geometry of molecules was determined by the method of molecular mechanics. Statistically significant correlation equations wer...

Testing the semiempirical methods of the NDO approximation (CNDO/2, INDO, MINDO/3, ZINDO/1, MNDO, MNDO/AM1, MNDO/PM3) for dipole moment calculations for compounds with an anilide bond [2] revealed that these methods fail to give correct values of the dipole moment of the acetanilide molecule. The deviation of the dipole moment µemp = 3.75D [3] from...

Intermolecular interactions occurring in anesthetic-biomembrane and anesthetic-cell fluid systems near membrane surfaces were studied. It was shown that polarization interactions prevail in such systems. An empirical dependence of the minimum number of local anesthetic molecules required to block nerve conduction on the molecular refraction of the...

The orientation interaction of a molecule of a local anesthetic with a biomembrane and cell-like liquid was studied, based on the model of adsorption of the anesthetic from a cell-like solution on the surface of a biomembrane for compounds of the trimecaine series. A statistically significant correlation equation was obtained, which relates the min...

A state of emotional stress in animals, whether arising in the course of a natural conflict situation or during stimulation of "emotiogenic" brain zones, is accompanied by eleva~ tion of the arterial blood pressure (BP) and by tachycardia, in the formation of which an important role is played by central modulation of baroreceptor reflexes [6-8], Pr...

Chronic experiments on cats showed that analgesics, in subanalgesic doses, not only exhibit an antinociceptive effect when accompanied by subthreshold stimulation of the mesencephalon, but also potentiate the analgesic action of central stimulation. Tranquilizers only facilitate the development of an analgesic effect during subthreshold mesencephal...

It was shown in chronic experiments on cats that analgetics in subanalgetic doses not only revealed the antinociceptive effect under subthreshold stimulation of the midbrain, but also enhanced the analgetic effect of the central stimulation. The tranquilizers promoted only the analgetic action under the subthreshold stimulation of the midbrain. Pos...

Chronic experiments on cats showed that stimulation of certain zones of the mesencephalon reduces or completely suppresses responses to pain caused by stimulation of the dental pulp. Depending on the parameters of brain stimulation the antinociceptive effect was manifested as differential changes in individual motor, autonomic, emotional, and behav...

Experiments on decerebrate cats showed that fentanyl, in a dose of 10 µg/kg or more, inhibits neurons of the bulbar respiratory center, with a resulting decrease in the mean firing rate, a change in the number of spikes in the discharge and its duration, and disturbance of the temporal distribution of spikes in the discharge. The degree of inhibiti...