Solution of the boundary value problem for nonlinear flows and maps

Fluctuational escape via an unstable limit cycle is investigated in stochastic flows and maps. A new topological method is suggested for analysis of the corresponding boundary value problems when the action functional has multiple local minima along the escape trajectories and the search for the global minimum is otherwise impossible. The method is applied to the analysis of the escape problem in the inverted Van der Pol oscillator and in the Henon map. An application of this technique to solution of the escape problem in chaotic maps with fractal boundaries, and in maps with chaotic saddles embedded within the basin of attraction, is discussed

Electrical, Hemodynamic, and Motor Activity in BCI Post-stroke Rehabilitation: Clinical Case Study

The goal of the paper is to present an example of integrated analysis of electrical, hemodynamic, and motor activity accompanying the motor function recovery in a post-stroke patient having an extensive cortical lesion. The patient underwent a course of neurorehabilitation assisted with the hand exoskeleton controlled by brain-computer interface based on kinesthetic motor imagery. The BCI classifier was based on discriminating covariance matrices of EEG corresponding to motor imagery. The clinical data from three successive 2 weeks hospitalizations with 4 and 8 month intervals, respectively were under analysis. The rehabilitation outcome was measured by Fugl-Meyer scale and biomechanical analysis. Both measures indicate prominent improvement of the motor function of the paretic arm after each hospitalization. The analysis of brain activity resulted in three main findings. First, the sources of EEG activity in the intact brain areas, most specific to motor imagery, were similar to the patterns we observed earlier in both healthy subjects and post-stroke patients with mild subcortical lesions. Second, two sources of task-specific activity were localized in primary somatosensory areas near the lesion edge. The sources exhibit independent mu-rhythm activity with the peak frequency significantly lower than that of mu-rhythm in healthy subjects. The peculiarities of the detected source activity underlie changes in EEG covariance matrices during motor imagery, thus serving as the BCI biomarkers. Third, the fMRI data processing showed significant reduction in size of areas activated during the paretic hand movement imagery and increase for those activated during the intact hand movement imagery, shifting the activations to the same level. This might be regarded as the general index of the motor recovery. We conclude that the integrated analysis of EEG, fMRI, and motor activity allows to account for the reorganization of different levels of the motor system and to provide a comprehensive basis for adequate assessment of the BCI+ exoskeleton rehabilitation efficiency

Multifractal characterization of stochastic resonance

We use a multifractal formalism to study the effect of stochastic resonance in a noisy bistable system driven by various input signals. To characterize the response of a stochastic bistable system we introduce a new measure based on the calculation of a singularity spectrum for a return time sequence. We use wavelet transform modulus maxima method for the singularity spectrum computations. It is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic (stochastic or chaotic) input signals. We show that in the case of periodic driving force singularity spectrum can change its structure qualitatively becoming monofractal in the regime of stochastic synchronization. This fact allows us to consider the degree of multifractality as a new measure of stochastic synchronization also. Moreover, our calculations have shown that the effect of stochastic resonance can be catched by this measure even from a very short return time sequence. We use also the proposed approach to characterize the noise-enhanced dynamics of a coupled stochastic neurons model.Comment: 10 pages, 21 EPS-figures, RevTe

Calculation Substantiation of the Parameter Values Determining the Traction Properties of a Uniaxial Mobile Pushing-Type Power Vehicle

The aim of the work is to study the static parameters of a pushing unit based on a uniaxial mobile power vehicle (UMPV). The article gives the analysis of the influence of the parameters of ballasting and traction load on the reaction of the wheel, the reaction of the support heel of the plow, the weight distribution coefficient, the force on the control handles. Using the MATLAB software, a computer model is implemented that makes it possible to take into account the influence of various parameters of the pushing unit when they change on its static indicators. It is found that in a pushing unit based on the UMPV, a growth in the weight of ballast loads Gб increases the loading of the driving wheels, improving the traction properties of the unit compared to the traction unit based on the UMPV. It is shown that increase in the traction load Rx and the distance aн to agricultural equipment leads to an increase in the load on the driving wheels and control handles, the weight of ballast loads is 0.07...0.35 kN, which is less than that for a traction unit based on UMPV (0.1...0.45 kN)

Impact of acoustic coordinated reset neuromodulation on effective connectivity in a neural network of phantom sound

Chronic subjective tinnitus is an auditory phantom phenomenon characterized by abnormal neuronal synchrony in the central auditory system. As recently shown in a proof of concept clinical trial, acoustic coordinated reset (CR) neuromodulation causes a significant relief of tinnitus symptoms combined with a significant decrease of pathological oscillatory activity in a network comprising auditory and non-auditory brain areas. The objective of the present study was to analyze whether CR therapy caused an alteration of the effective connectivity in a tinnitus related network of localized EEG brain sources. To determine which connections matter, in a first step, we considered a larger network of brain sources previously associated with tinnitus. To that network we applied a data-driven approach, combining empirical mode decomposition and partial directed coherence analysis, in patients with bilateral tinnitus before and after 12weeks of CR therapy as well as in healthy controls. To increase the signal-to-noise ratio, we focused on the good responders, classified by a reliable-change-index (RCI). Prior to CR therapy and compared to the healthy controls, the good responders showed a significantly increased connectivity between the left primary cortex auditory cortex and the posterior cingulate cortex in the gamma and delta bands together with a significantly decreased effective connectivity between the right primary auditory cortex and the dorsolateral prefrontal cortex in the alpha band. Intriguingly, after 12weeks of CR therapy most of the pathological interactions were gone, so that the connectivity patterns of good responders and healthy controls became statistically indistinguishable. In addition, we used dynamic causal modeling (DCM) to examine the types of interactions which were altered by CR therapy. Our DCM results show that CR therapy specifically counteracted the imbalance of excitation and inhibition. CR significantly weakened the excitatory connection between posterior cingulate cortex and primary auditory cortex and significantly strengthened inhibitory connections between auditory cortices and the dorsolateral prefrontal cortex. The overall impact of CR therapy on the entire tinnitus-related network showed up as a qualitative transformation of its spectral response, in terms of a drastic change of the shape of its averaged transfer function. Based on our findings we hypothesize that CR therapy restores a silence based cognitive auditory comparator function of the posterior cingulate cortex

Computational modeling of chemotactic signaling and aggregation of microglia around implantation site during deep brain stimulation

It is well established that prolonged electrical stimulation of brain tissue causes massive release of ATP in the extracellular space. The released ATP and the products of its hydrolysis, such as ADP and adenosine, become the main elements mediating chemotactic sensitivity and motility of microglial cells via subsequent activation of P2Y2,12 as well as A3A and A2A adenosine receptors. The size of the sheath around the electrode formed by the microglial cells is an important criterion for the optimization of the parameters of electrical current delivered to brain tissue. Here, we study a purinergic signaling pathway underlying the chemotactic motion of microglia towards the implanted electrode during deep brain stimulation. We present a computational model describing formation of a stable aggregate around the implantation site due to the joint chemo-attractive action of ATP and ADP together with a mixed influence of extracellular adenosine. The model was built in accordance with the classical Keller-Segel approach and includes an equation for the cells’ density as well as equations describing the hydrolysis of extracellular ATP via successive reaction steps ATP →ADP →AMP →adenosine. The results of our modeling allowed us to reveal the dependence of the width of the encapsulating layer around the electrode on the amount of ATP released due to permanent electrical stimulation. The dependences of the aggregates’ size on the parameter governing the nonlinearity of interaction between extracellular adenosine and adenosine receptors are also analyzed

Escape from a chaotic attractor with fractal basin boundaries

We study fluctuational transitions in a discrete dynamical system between two co-existing chaotic attractors separated by a fractal basin boundary. It is shown that there is a generic mechanism of fluctuational transition through a fractal boundary determined by a hierarchy of homoclinic original saddles. The most probable escape path from a chaotic attractors to the fractal boundary is found using both statistical analysis of fluctuational trajectories and Hamiltonian theory of fluctuations

Impact of sample size and global confounds removals on estimates of effective connectivity

The interactions within brain networks are inherently directional and can be detected by using thespectral Dynamic Causal Modelling (DCM) for the resting-state functional magnetic resonance imaging (fMRI). The sample size and unavoidable presence of nuisance signals during fMRI measurementare the two important factors influencing stability of the group estimates of connectivity parameters. However, most of the recent studies exploring effective connectivity were conducted for rathersmall and minimally preprocessed datasets. Here, we explore an impact of these two factors by analyzing the cleaned resting-state fMRI data for the group of 330 unrelated subjects from the HumanConnectome Project database. We demonstrate that stability of the model selection procedure andinference of connectivity parameters are both dependent on the sample size. The minimal samplesize required for the stable Dynamic Causal modelling has to be about 50. Our results show thatglobal confounds removals have weak or moderate effect on DCM stability for the datasets properlycleaned from the artifacts

Impact of sample size and regression of tissue‐specific signals on effective connectivity within the core default mode network

Interactions within brain networks are inherently directional, which are inaccessible to classical functional connectivity estimates from resting-state functional magnetic resonance imaging (fMRI) but can be detected using spectral dynamic causal modeling (DCM). The sample size and unavoidable presence of nuisance signals during fMRI measurement are the two important factors influencing the stability of group estimates of connectivity parameters. However, most recent studies exploring effective connectivity (EC) have been conducted with small sample sizes and minimally pre-processed datasets. We explore the impact of these two factors by analyzing clean resting-state fMRI data from 330 unrelated subjects from the Human Connectome Project database. We demonstrate that both the stability of the model selection procedures and the inference of connectivity parameters are highly dependent on the sample size. The minimum sample size required for stable DCM is approximately 50, which may explain the variability of the DCM results reported so far. We reveal a stable pattern of EC within the core default mode network computed for large sample sizes and demonstrate that the use of subject-specific thresholded whole-brain masks for tissue-specific signals regression enhances the detection of weak connections