A Software Package for the Modeling of Electrophysiological Activity Data

A complex of programs has been developed for computer modeling of multichannel time series recorded in various experiments on electromagnetic fields created by the human body. Sets of coordinates and directions of sensors for magnetic encephalographs of several types, electroencephalographs and magnetic cardiographs are used as models of devices. To study the human brain, magnetic resonance tomograms are used as head models; to study the heart, a body model in the form of a half-space with a flat boundary is used. The sources are placed in the model space, for them the direct problem is solved in the physical model corresponding to the device used. For a magnetic encephalograph and an electroencephalograph, an equivalent current dipole model in a spherical conductor is used, for a magnetic cardiograph, an equivalent current dipole model in a flat conductor or a magnetic dipole model is used. For each source, a time dependence is set and a multichannel time series is calculated. Then the time series from all sources are summed and the noise component is added. The program consists of three modules: an input-output module, a calculation module and a visualization module. The input-output module is responsible for loading device models, brain models, and field source parameters. The calculation module is responsible for directly calculating the field and transforming coordinates between the index system and the head system. The visualization module is responsible for the image of the brain model, the position of the field sources, a graphical representation of the amplitude-time dependence of the field sources and the calculated values of the total field. The user interface has been developed. The software package provides: interactive placement of field sources in the head or body space and editing of the amplitude-time dependence; batch loading of a large number of sources; noise modeling; simulation of low-channel planar magnetometers of various orders, specifying the shape of the device, the number of sensors and their parameters. Magnetic and electric fields produced by sources in the brain areas responsible for processing speech stimuli are considered. The resulting multichannel signal can be used to test various data analysis methods and for the experiment planning.

A Modified SIR Model for the COVID-19 Epidemic in China

The analysis of the coronavirus disease 2019 (COVID-19) is of great importance to deeply understand the dynamics of this coronavirus spread. Based on the complexity of it, a modified susceptible-infected-removed (SIR) model is applied to analyse the time dependence of active and hospitalized cases in China. The time evolution of the virus spread in different provinces was adequately modelled. Changeable parameters among them have been obtained and turned to be not naively independent with each other. The non-extensive parameter was found to be strongly connected with the freedom of systems. Taken into the prevention and treatment of disease, more measures by the government lead to higher values of it.

Mathematical Modeling of the Pandemic Peak

BACKGROUND: The article examines the history and statistics of the pandemic spread. AIM: The study aimed to develop a mathematical model reflecting the time dependence of the parameters characterizing the spread of the pandemic. MATERIALS AND METHODS: Differential equations were used to study the spread of the pandemic. RESULTS: The case, where the coefficients of morbidity and recovery are different is considered. The patterns of change in the number of people susceptible to the disease and the number of infectious patients are revealed as a function of time. Using the developed model, the peak of the pandemic is found, i.e., the time at which the number of infectious patients will be the maximum.

Estimating the Risk of Satellite Collisions in Densely Populated Orbit Shells

Low Earth Orbit is becoming crowded with satellites. Updating estimates of collision probabilities is important as new deployments are authorised but is difficult because only limited information is given. This report investigates developing analytic estimates of collision probabilities. A survey of approaches reported in the literature is carried out. A collision involving a satellite from the Iridium cluster is reviewed. A simple analytic expression for the collision probability between two satellites is derived using the smallness of several dimensionless ratios appearing in the problem. Single collision probabilities are then extended to orbital planes populated by n satellites with the aim of finding the optimal point at which to traverse such an orbit. This report demonstrates that analytic estimates relevant to the problem can be made. Further work should focus on: making these estimates rigorous by using a formal asymptotic approach, considering multiple orbital planes and introducing time dependence

Time-covariant Schrödinger equation and invariant decay probability: the $$\Lambda $$-Kantowski–Sachs universe

The system under study is the $$\Lambda $$ Λ -Kantowski–Sachs universe. Its canonical quantization is provided based on a recently developed method: the singular minisuperspace Lagrangian describing the system, is reduced to a regular (by inserting into the dynamical equations the lapse dictated by the quadratic constraint) possessing an explicit (though arbitrary) time dependence; thus a time-covariant Schrödinger equation arises. Additionally, an invariant (under transformations $$t=f({\tilde{t}})$$ t = f ( t ~ ) ) decay probability is defined and thus “observers” which correspond to different gauge choices obtain, by default, the same results. The time of decay for a Gaussian wave packet localized around the point $$a=0$$ a = 0 (where a the radial scale factor) is calculated to be of the order $$\sim 10^{-42}{-}10^{-41}~\text {s}$$ ∼ 10 - 42 - 10 - 41 s . The acquired value is near the end of the Planck era (when comparing to a FLRW universe), during which the quantum effects are most prominent. Some of the results are compared to those obtained by following the well known canonical quantization of cosmological systems, i.e. the solutions of the Wheeler–DeWitt equation.

The Association Between Parents’ Physical Function and Adult Children’s Caregiving Burden

Using data from 544 older parents-adult children Chinese American dyads, this study aims to understand the association between older parents’ physical function and their adult children’s perceived caregiving burden. Parents’ physical function was assessed by the Katz Index of Activities of Daily Living (ADL) and the Lawton Instrumental ADL (IADL), with higher scores indicating more functional limitations. Adult children’s caregiving burden was assessed in five dimensions, including time dependence, developmental, physical, social, and emotion burden. Logistic regression was used to examine the association. More ADL limitations were associated with a higher likelihood of developmental burden (OR:1.14 (1.06-1.23)) and physical burden (OR:1.14 (1.06-1.23)) burden. More IADL limitations was associated with a higher likelihood of time dependence burden (OR:1.08 (1.03-1.12)), developmental burden (OR:1.06 (1.03-1.09)), and physical burden (OR:1.08 (1.04-1.12)). Parents’ physical function was not related to children’s social and emotional burdens. Practice and research implications will be discussed.