Stefan Balint

Complex and chaotic dynamics in a discrete-time-delayed Hopfield neural network with ring architecture

This paper is devoted to the analysis of a discrete-time-delayed Hopfield-type neural network of p neurons with ring architecture. The stability domain of the null solution is found, the values of the characteristic parameter for which bifurcations occur at the origin are identified and the existence of Fold/Cusp, Neimark-Sacker and Flip bifurcations is proved. These bifurcations are analyzed by applying the center manifold theorem and the normal form theory. It is proved that resonant 1:3 and 1:4 bifurcations may also be present. It is shown that the dynamics in a neighborhood of the null solution become more and more complex as the characteristic parameter grows in magnitude and passes through the bifurcation values. A theoretical proof is given for the occurrence of Marottos chaotic behavior, if the magnitudes of the interconnection coefficients are large enough and at least one of the activation functions has two simple real roots.

Configurations of steady states for Hopfield-type neural networks

The dependence of the steady states on the external input vector I for the continuous-time and discrete-time Hopfield-type neural networks of n neurons is discussed. Conditions for the existence of one or several paths of steady states are derived. It is shown that, in some conditions, for an external input I there may exist at least 2^n exponentially stable steady states (called configuration of steady states), and their regions of attraction are estimated. This means that there exist 2^n paths of exponentially stable steady states defined on a certain set of input values. Conditions assuring the transfer of a configuration of exponentially stable steady states to another configuration of exponentially stable steady states by successive changes of the external input are obtained. These results may be important for the design and maneuvering of Hopfield-type neural networks used to analyze associative memories.

Diffusion–Convection in a Porous Medium with Impervious Inclusions at Low Flow Rates

The aim of this paper is to develop a macroscopic model for the transport of a passive solute, by diffusion and convection, in a heterogeneous medium consisting of impervious solids periodically distributed in a porous matrix. In the porous part, the flow is described by Darcys law. Attempt is made to derive the macroscopic equation governing the average concentration field in the equivalent macroscopic medium and the macroscopic transport parameters. The analysis is conducted in the case when convection and diffusion are of the same order of magnitude at the macroscopic level, that is, when the Péclet number is of order 1. The proposed macroscopic model is obtained using the homogenization method for periodic structures with a double scale asymptotic expansion, in which the small parameter ε is the ratio between the two characteristic lengths l (the period scale of the impervious bodies distribution) and L (the scale of the macroscopic sample). The macroscopic parameters, which characterize the multiporous medium, depend solely on the transport parameters in the porous matrix and on the geometry of the impervious inclusions without any phenomenological assumption. Numerical computations are performed using a finite element method for several geometries of the solid inclusions, in two- and three-dimensional cases.

Oscillation Susceptibility Analysis of the ADMIRE Aircraft along the Path of Longitudinal Flight Equilibriums in Two Different Mathematical Models

The oscillation susceptibility of the ADMIRE aircraft along the path of longitudinal flight equilibriums is analyzed numerically in the general and in a simplified flight model. More precisely, the longitudinal flight equilibriums, the stability of these equilibriums, and the existence of bifurcations along the path of these equilibriums are researched in both models. Maneuvers and appropriate piloting tasks for the touch-down moment are simulated in both models. The computed results obtained in the models are compared in order to see if the movement concerning the landing phase computed in the simplified model is similar to that computed in the general model. The similarity we find is not a proof of the structural stability of the simplified system, what as far we know never been made, but can increase the confidence that the simplified system correctly describes the real phenomenon.

The axial and radial segregation due to the thermo-convection, the decrease of the melt in the ampoule and the effect of the precrystallization-zone in the semiconductor crystals grown in a Bridgman–Stockbarger system in a low gravity environment

Abstract In this paper, we give a model based simulation of the evolution of axisymmetric flow, heat transport and Ga dispersion in the melt and we predict the axial and radial Ga distribution in a Ga-doped Ge semiconductor crystal grown in a low gravity environment using the Bridgman–Stockbarger growth method.

The Concepts of Well-Posedness and Stability in Different Function Spaces for the 1D Linearized Euler Equations

This paper considers the stability of constant solutions to the 1D Euler equation. The idea is to investigate the effect of different function spaces on the well-posedness and stability of the null solution of the 1D linearized Euler equations. It is shown that the mathematical tools and results depend on the meaning of the concepts “perturbation,” “small perturbation,” “solution of the propagation problem,” and “small solution, that is, solution close to zero,” which are specific for each function space.

Homology Modeling and Validation of the Human M1 Muscarinic Acetylcholine Receptor.

One of the major targets of available drugs on the market is the family of G-protein coupled receptors (GPCR). In practice 14 % (earlier 30 %) of the available pharmaceutical compounds develops its effect on this site of action. Although these receptors themselves are important targets, drugs developed with other therapeutic aim can also act on these receptors and cause adverse side effects. Therefore these targets are antitargets as well and the screening for the possible side effects is very important in the early phase of drug development. From the point of view of the GPCRs, the main antitargets are as follows (in paranthesis the action of the compounds and their main adverse effect is enumerated): adrenergic a1a (antagonist, orthostatic hypotension, dizziness and fainting spells), dopaminergic D2 (antagonist, extrapyramidal syndrome, tardive dyskinesia), serotonin 5-HT2C (antagonist, weight gain, obesity), serotonin 5-HT2B (agonist, valvular heart disease) and muscarinic M1 (antagonist, attention deficits, hallucinations and memory deficits). Nowadays the accurate structure-based description of the GPCR ligand interaction is more feasible due to the increased number of available crystal structures. Experimental structures of the aforementioned GPCRs are not available, therefore the initial structure has to be built up using a homology modeling (HM) approach and the structure obtained should be submitted for validation (structural and ligand recognition). In the past several years a few 3D structures of the human M1 muscarinic acetylcholine receptor (hM1acr) have been developed using various methods. Recently Haga et al. solved the crystal structure of the human M2 muscarinic acetylcholine receptor (hM2acr), which can be used as the most appropriate template for the 3D structure generation of other muscarinic receptors. The aim of our study was to build a relevant 3D structure (Model#1) of the hM1acr using the most appropriate reference structure, the crystallographic structure of hM2acr as a template. This model was compared to the model developed by McRobb et al.(a b2 adrenergic receptor based structure, Model#2) from structural and enrichment factor point of views (using the recently developed GPCR ligand library (GLL) and GPCR decoy database (GDD) set). These sets of active and decoy compounds were prepared in order to obtain chemically diverse molecules with similar physical properties (molecular weight, formal charge, number of rotatable bonds, number of hydrogen bond acceptors and donors, octanol-water partition coefficient, and topological polar surface area) which resulted in unbiased enrichment compared to random selection. The structure obtained from HM was analyzed in order to verify its 3D structure from structural points of view. On the Ramachandran surface we did not find any residue in the disallowed region (see Supporting Information, Figure S1) and outliers were not found in the angle and torsional angle space either. Between Model#1 and Model#2, structural comparison was performed regarding the overall structural similarity/ dissimilarity (backbone root-mean square deviation (RMSD) calculations) and the binding pocket forming residues (all atom RMSD calculations). The per residue RMSD values as well as the segment RMSD values were calculated (see Supporting Information, Figure S2). In these cases the two structures were aligned along the backbone forming atoms (C, CA and N) and the RMSD values were calculated only for these atoms. The overall RMSD between the two models is 2.8 , which suggests an overall similarity between these models. As it was expected, larger deviation was obtained for the extra(EC) and intracellular (IC) loops compared to the transmembrane (TM) segments. Among the more flexible and variable part of the receptors the largest difference was obtained for the IC2 and EC2 loops (see Supporting Information, Figure S3). The intracellular part of the receptor does not take part in the ligand recognition process; therefore this structural difference has no impact on the docking results. In contrast the extracellular part, especially the EC2

On the controllability of the continuous-time Hopfield-type neural networks

In this paper, the dependence of the steady states on the external input vector I for the analytical Hopfield-type neural network is discussed. It is shown that in some conditions, for any input vector I belonging to a certain set, the system has a unique steady state x = x(I) which depends analytically on I. Conditions for the local exponential stability of the steady state x(I) are given and estimates of its region of attraction are obtained employing Lyapunov functions. The estimates are compared with those reported in the literature. Conditions assuring the transfer of a steady state x(I*) into a steady state x(I**) by successive changes of the external input vector I are obtained, i.e. the steady states can be controlled.

The Dependence of the Period and Range of the Oscillations on the Elevator Deflection for the ADMIRE Simplified Model

If, during a longitudinal flight with constant forward velocity of an unmanned aerial vehicle (UAV), the automatic flight control system (AFCS) fails and the elevator deflection is not in the safe interval, then the flight becomes oscillatory. In this paper, the dependence of the period and the range of the oscillations of the pitch rate and angle of attack on the elevator deflection of the possible oscillatory flights is numerically investigated, aided by the Scala-based Akka actor system. It is numerically shown that, for a given initial data, the period of oscillations is symmetric with respect to the safe interval and, for an elevator deflection close enough to the boundary of the safe interval, the period is very large while when the value of elevator deflection is far from the boundary of the safe interval the period is small. Additionally, the boundaries of the range of the oscillations of the pitch rate and of the angle of attack decreases when the elevator deflection increases.

Existence of oscillatory solutions in the non simplified model

The purpose of this paper is a numerical investigation of the existence of oscillatory movement of an unmanned aircraft whose automatic flight control system fails at a moment when the aircraft is not in equilibrium and the value of the angle of attack is high. This investigation is made in the framework of the non simplified mathematical model.