Viral Infection Spreading and Mutation in Cell Culture

A new model of viral infection spreading in cell cultures is proposed taking into account virus mutation. This model represents a reaction-diffusion system of equations with time delay for the concentrations of uninfected cells, infected cells and viral load. Infection progression is characterized by the virus replication number Rv, which determines the total viral load. Analytical formulas for the speed of propagation and for the viral load are obtained and confirmed by numerical simulations. It is shown that virus mutation leads to the emergence of a new virus variant. Conditions of the coexistence of the two variants or competitive exclusion of one of them are found, and different stages of infection progression are identified.

On asymptotic behavior of solution to a nonlinear wave equation with Space-time speed of propagation and damping terms

In this paper, we consider the asymptotic behavior of solution to the nonlinear damped wave equation utt – div(a(t, x)∇u) + b(t, x)ut = −|u|p−1u t ∈ [0, ∞), x ∈ Rn u(0, x) = u0(x), ut(0, x) = u1(x) x ∈ Rn with space-time speed of propagation and damping potential. We obtained L2 decay estimates via the weighted energy method and under certain suitable assumptions on the functions a(t, x) and b(t, x). The technique follows that of Lin et al.[8] with modification to the region of consideration in Rn. These decay result extends the results in the literature.

Number of autonomous agents in a neural network

This paper considers several aspects of the relationship between size, structure, speed of propagation and the number of autonomous cognitive agents in a neural network. Whereas, memory and function generation capacities of neural networks with scale invariant structure have been investigated extensively, the number of autonomous agents has not received prior attention. We propose the emergence of the dichotomy of causal and noncausal regions that is related to speed of propagation, in which the autonomous cognitive agents are not bound in a causal relationship with other agents. Arguments are presented for why the count of autonomous agents is best estimated with respect to the dimensionality of the underlying space. The number of autonomous agents obtained for the human brain equals twenty-five, and it is significant that the number in the sub-system modules also turns out to be close to the same value. It is possible that this near equality across layers provides a special uniqueness to the human brain. We argue that the findings of this study will be useful in the design of neural-network based AI systems that are designed to emulate human cognitive capacity. <br><br><br><br>

Number of autonomous agents in a neural network

This paper considers several aspects of the relationship between size, structure, speed of propagation and the number of autonomous cognitive agents in a neural network. Whereas, memory and function generation capacities of neural networks with scale invariant structure have been investigated extensively, the number of autonomous agents has not received prior attention. We propose the emergence of the dichotomy of causal and noncausal regions that is related to speed of propagation, in which the autonomous cognitive agents are not bound in a causal relationship with other agents. Arguments are presented for why the count of autonomous agents is best estimated with respect to the dimensionality of the underlying space. The number of autonomous agents obtained for the human brain equals twenty-five, and it is significant that the number in the sub-system modules also turns out to be close to the same value. It is possible that this near equality across layers provides a special uniqueness to the human brain. We argue that the findings of this study will be useful in the design of neural-network based AI systems that are designed to emulate human cognitive capacity. <br><br><br><br>

Comparing information diffusion mechanisms by matching on cascade size

Do some types of information spread faster, broader, or further than others? To understand how information diffusions differ, scholars compare structural properties of the paths taken by content as it spreads through a network, studying so-called cascades. Commonly studied cascade properties include the reach, depth, breadth, and speed of propagation. Drawing conclusions from statistical differences in these properties can be challenging, as many properties are dependent. In this work, we demonstrate the essentiality of controlling for cascade sizes when studying structural differences between collections of cascades. We first revisit two datasets from notable recent studies of online diffusion that reported content-specific differences in cascade topology: an exhaustive corpus of Twitter cascades for verified true- or false-news content by Vosoughi et al. [S. Vosoughi, D. Roy, S. Aral. Science 359, 1146–1151 (2018)] and a comparison of Twitter cascades of videos, pictures, news, and petitions by Goel et al. [S. Goel, A. Anderson, J. Hofman, D. J. Watts. Manage. Sci. 62, 180–196 (2016)]. Using methods that control for joint cascade statistics, we find that for false- and true-news cascades, the reported structural differences can almost entirely be explained by false-news cascades being larger. For videos, images, news, and petitions, structural differences persist when controlling for size. Studying classical models of diffusion, we then give conditions under which differences in structural properties under different models do or do not reduce to differences in size. Our findings are consistent with the mechanisms underlying true- and false-news diffusion being quite similar, differing primarily in the basic infectiousness of their spreading process.

Stability Result for a Weakly Nonlinearly Damped Porous System with Distributed Delay

In this paper, we consider a one-dimensional porous system damped with a single weakly nonlinear feedback and distributed delay term. Without imposing any restrictive growth assumption near the origin on the damping term, we establish an explicit and general decay rate, using a multiplier method and some properties of convex functions in case of the same speed of propagation in the two equations of the system. The result is new and opens more research areas into porous-elastic system.

Navigation of Underwater Drones and Integration of Acoustic Sensing with Onboard Inertial Navigation System

The navigation of autonomous underwater vehicles is a major scientific and technological challenge. The principal difficulty is the opacity of the water media for usual types of radiation except for the acoustic waves. Thus, an acoustic transducer (array) composed of an acoustic sonar is the only tool for external measurements of the AUV attitude and position. Another difficulty is the inconstancy of the speed of propagation of acoustic waves, which depends on the temperature, salinity, and pressure. For this reason, only the data fusion of the acoustic measurements with data from other onboard inertial navigation system sensors can provide the necessary estimation quality and robustness. This review presents common approaches to underwater navigation and also one novel method of velocity measurement. The latter is an analog of the well-known Optical Flow method but based on a sequence of sonar array measurements.

Correlation between Anatomical Grading and Acoustic–Elastic Properties of Resonant Spruce Wood Used for Musical Instruments

This paper deals with the acoustic and elastic properties of resonant wood, classified into four classes, according to the classification of wood quality by the manufacturers of musical instruments. Traditionally, the quality grades of resonant wood are determined on the basis of the visual inspections of the macroscopic characteristics of the wood (annual ring width, regularity, proportion of early and late wood, absence of defects, etc.). Therefore, in this research, we studied whether there are correlations between the acoustic and elastic properties and the anatomical characteristics of wood used for the construction of violins. The results regarding the identification of the anatomical properties of resonant spruce, the wood color, and the acoustic/elastic properties, determined by ultrasonic measurements, were statistically analyzed to highlight the connection between the determined properties. From the statistical analysis, it can be seen that the only variables with the power to separate the quality classes are (in descending order of importance) the speed of sound propagation in the radial direction, Poisson’s ratio in the longitudinal–radial direction, and the speed of propagation of sounds in the longitudinal direction.

Obtaining the relativistic formula for the refraction of light and the practice of its application

The aim of this scientific study was to obtain a new physical formula for determining the refractive indices of light as a function of wavelength, which can be applied to the widest range of transparent substances. This study was based on the hypothesis of the dependence of the speed of propagation of photons inside matter on the density of electron clouds of atoms of matter. In the course of research on the basis of Einstein's relativistic formula, this dispersion formula was obtained. The new physical formula was used to calculate 26 refractive indices of light in 5 transparent substances in three states of aggregation. Comparison of the obtained indicators with laboratory indicators showed the high accuracy of the new dispersion formula, which amounted to T10 -7h10 -5 in the calculated wavelength ranges of more than 100 nm. The successful application of the relativistic formula to processes occurring at the atomic level allows us to look at the nature of the interaction of light and matter from a new angle.