Computer simulation of field ion images of nanoporous structure in the irradiated materials

Computer simulation and interpretation of field ion microscopy images of ion irradiated platinum are discussed. Field ion microscopy technique provides direct precise atomic scale investigation of crystal lattice defects of atomically pure surface of material; at the same time it allows to analyze the structural defects in volume by controlled and sequential removal of surface atoms by electric field. Defects identification includes the following steps: at the first stage the type of crystalline structure and spatial orientation of crystallographic directions were determined. Thus, we obtain the data about exact position of all atoms of the given volume, i.e. the model image of an ideal crystal. At the second stage, the ion image was processed used the program to obtain the data about real arrangement of atoms of the investigated sample. At the third stage the program compares these two data sets, with a split-hair accuracy revealing a site of all defects in a material. Results of the quantitative analysis show that shape of nanopores are spherical or cylindrical, diameter on nanopores was varied from 1 to 5 run, their depth was fond to be from 1 to 9 nm. It was observed that nearly 40% of nanopores are concentrated in the subsurface layer 10 nm thick, the concentration of nanopores decreased linearly with the distance from the irradiated surface

Morphometric study of hippocampal neurons in chronic immobilization stress

Hippocampus ensures the implementation of the memory mechanisms, behavioral reactions, including avoidance of stress, aversive effects etc. The study was performed on the material of 20 male Wistar rats weighing 220-250 g, 10 of which were intact control group and 10 were experimental group, in which chronic immobilization stress was simulated. We determined the relative number of neurons in multiple fields of view on the total area of the pyramidal and polymorphic layers of CA1 and CA3 regions (further recalculated per 10,000 μm), larger and smaller diameters of neuron’s bodies, their perimeters and areas with diameters of nuclei and nucleoli, nuclear-cytoplasmic rati

Maximum Performance at Minimum Cost in Network Synchronization

We consider two optimization problems on synchronization of oscillator networks: maximization of synchronizability and minimization of synchronization cost. We first develop an extension of the well-known master stability framework to the case of non-diagonalizable Laplacian matrices. We then show that the solution sets of the two optimization problems coincide and are simultaneously characterized by a simple condition on the Laplacian eigenvalues. Among the optimal networks, we identify a subclass of hierarchical networks, characterized by the absence of feedback loops and the normalization of inputs. We show that most optimal networks are directed and non-diagonalizable, necessitating the extension of the framework. We also show how oriented spanning trees can be used to explicitly and systematically construct optimal networks under network topological constraints. Our results may provide insights into the evolutionary origin of structures in complex networks for which synchronization plays a significant role.Comment: 29 pages, 9 figures, accepted for publication in Physica D, minor correction

General Stability Analysis of Synchronized Dynamics in Coupled Systems

We consider the stability of synchronized states (including equilibrium point, periodic orbit or chaotic attractor) in arbitrarily coupled dynamical systems (maps or ordinary differential equations). We develop a general approach, based on the master stability function and Gershgorin disc theory, to yield constraints on the coupling strengths to ensure the stability of synchronized dynamics. Systems with specific coupling schemes are used as examples to illustrate our general method.Comment: 8 pages, 1 figur

Modeling of Spiking-Bursting Neural Behavior Using Two-Dimensional Map

A simple model that replicates the dynamics of spiking and spiking-bursting activity of real biological neurons is proposed. The model is a two-dimensional map which contains one fast and one slow variable. The mechanisms behind generation of spikes, bursts of spikes, and restructuring of the map behavior are explained using phase portrait analysis. The dynamics of two coupled maps which model the behavior of two electrically coupled neurons is discussed. Synchronization regimes for spiking and bursting activity of these maps are studied as a function of coupling strength. It is demonstrated that the results of this model are in agreement with the synchronization of chaotic spiking-bursting behavior experimentally found in real biological neurons.Comment: 9 pages, 12 figure

Synchronous bursts on scale-free neuronal networks with attractive and repulsive coupling

This paper investigates the dependence of synchronization transitions of bursting oscillations on the information transmission delay over scale-free neuronal networks with attractive and repulsive coupling. It is shown that for both types of coupling, the delay always plays a subtle role in either promoting or impairing synchronization. In particular, depending on the inherent oscillation period of individual neurons, regions of irregular and regular propagating excitatory fronts appear intermittently as the delay increases. These delay-induced synchronization transitions are manifested as well-expressed minima in the measure for spatiotemporal synchrony. For attractive coupling, the minima appear at every integer multiple of the average oscillation period, while for the repulsive coupling, they appear at every odd multiple of the half of the average oscillation period. The obtained results are robust to the variations of the dynamics of individual neurons, the system size, and the neuronal firing type. Hence, they can be used to characterize attractively or repulsively coupled scale-free neuronal networks with delays.Comment: 15 pages, 9 figures; accepted for publication in PLoS ONE [related work available at http://arxiv.org/abs/0907.4961 and http://www.matjazperc.com/