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Single-point mutations in the transmembrane (TM) region of receptor tyrosine kinases (RTKs) can lead to abnormal ligand-independent activation. We use a combination of computational modeling, NMR spectroscopy and cell experiments to analyze in detail the mechanism of how TM domains contribute to the activation of wild-type (WT) PDGFRA and its oncogenic V536E mutant. Using a computational framework, we scan all positions in PDGFRA TM helix for identification of potential functional mutations for the WT and the mutant and reveal the relationship between the receptor activity and TM dimerization via different interfaces. This strategy also allows us design a novel activating mutation in the WT (I537D) and a compensatory mutation in the V536E background eliminating its constitutive activity (S541G). We show both computationally and experimentally that single-point mutations in the TM region reshape the TM dimer ensemble and delineate the structural and dynamic determinants of spontaneous activation of PDGFRA via its TM domain. Our atomistic picture of the coupling between TM dimerization and PDGFRA activation corroborates the data obtained for other RTKs and provides a foundation for developing novel modulators of the pathological activity of PDGFRA.
A stratified liquid with two layers separated by a fast oscillating interface in the case of Raleigh--Taylor instability is considered. The averaged equations are derived, and it is shown that a mushy region of a certain density appears after averaging. The similarity between this fact and the case of unstable jump decay is discussed.
A novel method of finding and classifying irreducible invariant surfaces of non-autonomous polynomial dynamical systems in the plane is presented. The general structure of irreducible invariant surfaces and their cofactors is found. The complete set of irreducible invariant surfaces for the classical forced Duffing-van der Pol oscillator is obtained. It is proved that the forced Duffing-van der Pol oscillator possesses only one independent generalized Darboux first integral provided that a constraint on the parameters is valid. In other cases generalized Darboux first integrals do not exist. Consequently, the forced Duffing-van der Pol oscillator is not integrable with two independent generalized Darboux first integrals.
We consider the Wiener algebra A(T^d) of absolutely convergent Fourier series on the d-torus. For phase functions \phi of a certain special form we obtain lower bounds for the A -norms of e^{i\lambda\varphi} as \lambda tends to \infty.
We study the stability conditions of the multiserver queueing system in which each customer requires a random number of servers simultaneously. The input flow is supposed to be a regenerative one and service times of a given customer are independent at the occupied servers. The service time has an exponential, phase-type or hyper-exponential distribution. We define an auxiliary service process that is the number of completed services by all m servers under the assumption that there are always customers in the system. Then we construct the sequence of common regeneration points for the regenerative input flow and the auxiliary service process. It allows us to deduce the stability criterion of the model under consideration. It turns out that the stability condition does not depend on the structure of the input flow, only the rate of this process plays a role. Nevertheless the distribution of the service time is a very important factor. We give examples which show that the stability condition can not be expressed in terms of the mean of the service time.
We present a study of viscosities of methane, n-butane and their mixtures by the non-equilibrium molecular dynamics simulations and derivation of semiempirical volume-based mixing rules. The Batchinski equation $\eta = C / (V - b)$ is used to describe the viscosities of pure components, with parameters fitted to reproduce molecular dynamics results. Cubic root, Arrhenius and Batchinski mixing rules are tested for mixtures. The viscosities of pure components used in mixing equations are expressed as functions of volume of component rather than pressure. This allows to apply the mixing rules to metastable and stable liquids, dense supercritical fluids and solutions of gas in liquid. To obtain volumes of components in mixture, molecular dynamics method is used. The mixing rules predictions are compared against direct non-equilibrium molecular dynamics calculations of mixture viscosities. The best agreement with the molecular dynamics data is found when Batchinski mixing is used. The proposed viscosity model predictions are in agreement with the experimental data on viscosities of methane-butane mixtures. The model can be used for the interpretation and interpolation of the experimental data on viscosities of liquids, which is demonstrated on the example of methane + propane system.
Plasmon spectroscopy methods are highly sensitive to the small volumes of material due to subwavelength localization of light increasing light-matter interaction. Recent research has shown a high potential of plasmon quantum generator (spaser) or amplifier (sped) for sensing in the infrared optical region. Trinitrotoluene (TNT) molecules fingerprints are considered as an example. Basing on Lindblad equations, we implement full quantum mechanical theory of graphene plasmon generator to investigate how a small amount of absorbing atoms influences the spectrum of a graphene spaser. We analyze the optimal type of an active medium, the number of active molecules, and the pump level to achieve the highest sensitivity and show that optimized structure is sensitive to dozens of atoms. Our research is useful for the development of near- and mid-IR spectroscopy based on plasmon quantum amplifier.
For the three-frequency quantum resonance oscillator, the reducible case, where its frequencies are integer and at least one pair of frequencies has a nontrivial common divisor, is studied. It is shown how the description of the algebra of symmetries of such an oscillator can be reduced to the irreducible case of pairwise coprime integer frequencies. Polynomial algebraic relations are written, and irreducible representations and coherent states are constructed.
We point out that superconducting quantum computers are prospective for the simulation of the dynamics of spin models far from equilibrium, including nonadiabatic phenomena and quenches. The important advantage of these machines is that they are programmable, so that different spin models can be simulated in the same chip, as well as various initial states can be encoded into it in a controllable way. This opens an opportunity to use superconducting quantum computers in studies of fundamental problems of statistical physics such as the absence or presence of thermalization in the free evolution of a closed quantum system depending on the choice of the initial state as well as on the integrability of the model. In the present paper, we performed proof-of-principle digital simulations of two spin models, which are the central spin model and the transverse-field Ising model, using 5- and 16-qubit superconducting quantum computers of the IBM Quantum Experience. We found that these devices are able to reproduce some important consequences of the symmetry of the initial state for the system’s subsequent dynamics, such as the excitation blockade. However, lengths of algorithms are currently limited due to quantum gate errors. We also discuss some heuristic methods which can be used to extract valuable information from the imperfect experimental data.
The problem of optimal control is formulated for a class of nonlinear objects that can be represented as objects with a linear structure and parameters that depend on the state. The linear structure of the transformed nonlinear system and the quadratic functional of quality allow for the synthesis of optimal control, i.e. parameters of the regulator, move from the need to search for solutions of the Hamilton-Jacobi equation to an equation of the Riccati type with parameters that depend on the state. The main problem of implementing optimal control is related to the problem of finding a solution to such an equation at the pace of object functioning. The paper proposes an algorithmic method of parametric optimization of the regulator. This method is based on the use of the necessary conditions for the optimality of the control system under consideration. The constructed algorithms can be used both to optimize the non-stationary objects themselves, if the corresponding parameters are selected for this purpose, and to optimize the entire managed system by means of the corresponding parametric adjustment of the regulators. The example of drug treatment of patients with HIV is demonstrated the effectiveness of the developed algorithms.
A lot of files and data, in general, are transferred throughout the networks. But the data may be corrupted by intrusions or package loss so, the executable files may be marked as non-executable and violate the local network policy. Thus, it’s necessary to detect such files. In this paper, we present a novel method for detecting broken bytes of a file, so the corrupted files may be detected. Also, the positions of wrong bytes might be helpful in restoring the original file content. This work is devoted to study of modern neural network models applied to detect corrupted bytes of a file problem. Since recurrent neural networks (RNNs) seem to be well suited for such tasks, the main tasks of this work are to analyze the efficiency of popular state-of-the-art RNNs solving the problem mentioned above and to compare results of different models. We use data consisting of the most popular file types collected from the Internet and manually randomly added noise to that data to test our models. An experiment on this data demonstrates the advantages and disadvantages of the considered models.
Researchers face fundamental challenges applying the stochastic geometry framework to analysis of terahertz (THz) communications systems. The two major problems are the principally new propagation model that now includes exponential term responsible for molecular absorption and blocking of THz radiation by the human crowd around the receiver. These phenomena change the probability density function (pdf) of the interference from a single node such that it no longer has an analytical Laplace transform (LT) preventing characterization of the aggregated interference and signal-to-interference ratio (SIR) distributions. The expected use of highly directional antennas at both transmitter and receiver adds to this problem increasing the complexity of modeling efforts. In this paper, we consider Poisson deployment of interferers in ℜ 2 and provide accurate analytical approximations for pdf of interference from a randomly chosen node for blocking and non-blocking cases. We then derive LTs of pdfs of aggregated interference and SIR. Using the Talbot’s algorithm for inverse transform we provide numerical results indicating that failure to capture atmospheric absorption, blocking or antenna directivity leads to significant modeling errors. Finally, we investigate the response of SIR densities to a wide range of system parameters highlighting the specific effects of THz communications systems. The model developed in this paper can be used as a building block for performance analysis of realistic THz network deployments providing metrics such as outage and coverage probabilities.
model for deep bed filtration of a monodisperse suspension in a porous medium with multiple geometric particle capture mechanisms is considered. It is assumed that identical suspended particles can block pores of different sizes. The pores smaller than the particle size are clogged by single particles; if the pore size exceeds the diameter of the particles, it can be blocked by bridging— several particles forming various stable structures. An exact solution is obtained for constant filtration coefficients. Exact solutions for non-constant filtration functions are obtained on the concentrations front of the suspended and retained particles and at the porous medium inlet. Asymptotic solutions are constructed near these lines. For small and close to constant filtration functions, global asymptotic solutions are obtained. A basic model with two mechanisms of particle capture is studied in detail. Asymptotic solutions are compared to the results of numerical simulation. The applicability of various types of asymptotics is analyzed.
It is proved that the distributions of the analytic number theory coincide with the Bose–Einstein distribution. The transition of the boson branch of the decomposition of an integer number (with repeated terms) into the fermion branch (without repeated terms) is described in detail near a small activity. Analytic formulas for the energy of transition of the Bose gas to the Fermi gas are obtained in the three-dimensional case and the nine-dimensional case (diatomic molecule). The radius of the Bose gas “jump” in the transition to the Fermi gas is calculated. The relationship between the constructed concept and the thermodynamics is described based on the obtained experimental values of gas characteristics on critical lines.
In the article, it is considered a modification of an integral model of an unsteady turbulent jet with a pressure force. Stationary solutions of the presented model are compared with well-known analytical results of classical models. It is shown that the inclusion of the pressure forces changes the dynamic parameters of a jet by about 12%. Analytical solutions of a steady forced buoyant jet of the atmospheric convective boundary layer and a spontaneous jet of a surface layer are presented. The simplest model of an ensemble of spontaneous jets of convective surface layer is constructed. It is shown that an ensemble of spontaneous jets forms a dependence of the turbulent moments and heat eddy diffusivity on the altitude within the convective boundary layer.
The effect of an interplay between electrostatic and excluded volume interactions on the conformational behavior of a dipolar chain has been studied theoretically and by means of molecular dynamics simulations. Every monomer unit of the dipolar chain comprises a dipole formed by a charged group of the chain and an oppositely charged counterion. The counterion is assumed to freelymove around the chain but keeping the distance between oppositely charged ions (the dipole length) fixed. The novelty of the developed mean-field theory is that variations of the dipole parameters (the dipole length and the counterion size) have been accounted for in both electrostatic and excluded volume contributions to the total free energy of the dipolar chain. It has been shown that conformational transitions between swollen and collapsed states of the chain can be induced by fine-tuning the balance between electrostatic and excluded volume interactions. In particular, in lowpolar media not only globule but also extended coil conformations can be realized even under strong electrostatic attraction. The results ofMD simulations of a dipolar chain with variable dipolar length support theoretical conclusions.
The anomalous magnetic moment (AMM) for excited states of an electron in a constant magnetic field has been calculated within the framework of two-dimensional electrodynamics. The analytical results for the interaction energy of the anomalous magnetic moment with the external magnetic field are obtained in two limiting cases of nonrelativistic and relativistic energy values in a comparatively weak magnetic field. It is shown that the interaction energy of the spin with the external field does not contain infrared divergence and tends to zero as magnetic field decreases, while the electron’s AMM increases logarithmically.