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We show that realistic aftershock sequences with space-time characteristics compatible with observations are generated by a model consisting of brittle fault segments separated by creeping zones. The dynamics of the brittle regions is governed by static/kinetic friction, 3D elastic stress transfer and small creep deformation. The creeping parts are characterized by high ongoing creep velocities. These regions store stress during earthquake failures and then release it in the interseismic periods. The resulting postseismic deformation leads to aftershock sequences following the modified Omori law. The ratio of creep coefficients in the brittle and creeping sections determines the duration of the postseismic transients and the exponent p of the modified Omori law
Analysis of protrusion dynamics in amoeboid cell motility by means of regularized contour flows
(2021)
Amoeboid cell motility is essential for a wide range of biological processes including wound healing, embryonic morphogenesis, and cancer metastasis. It relies on complex dynamical patterns of cell shape changes that pose long-standing challenges to mathematical modeling and raise a need for automated and reproducible approaches to extract quantitative morphological features from image sequences. Here, we introduce a theoretical framework and a computational method for obtaining smooth representations of the spatiotemporal contour dynamics from stacks of segmented microscopy images. Based on a Gaussian process regression we propose a one-parameter family of regularized contour flows that allows us to continuously track reference points (virtual markers) between successive cell contours. We use this approach to define a coordinate system on the moving cell boundary and to represent different local geometric quantities in this frame of reference. In particular, we introduce the local marker dispersion as a measure to identify localized membrane expansions and provide a fully automated way to extract the properties of such expansions, including their area and growth time. The methods are available as an open-source software package called AmoePy, a Python-based toolbox for analyzing amoeboid cell motility (based on time-lapse microscopy data), including a graphical user interface and detailed documentation. Due to the mathematical rigor of our framework, we envision it to be of use for the development of novel cell motility models. We mainly use experimental data of the social amoeba Dictyostelium discoideum to illustrate and validate our approach. <br /> Author summary Amoeboid motion is a crawling-like cell migration that plays an important key role in multiple biological processes such as wound healing and cancer metastasis. This type of cell motility results from expanding and simultaneously contracting parts of the cell membrane. From fluorescence images, we obtain a sequence of points, representing the cell membrane, for each time step. By using regression analysis on these sequences, we derive smooth representations, so-called contours, of the membrane. Since the number of measurements is discrete and often limited, the question is raised of how to link consecutive contours with each other. In this work, we present a novel mathematical framework in which these links are described by regularized flows allowing a certain degree of concentration or stretching of neighboring reference points on the same contour. This stretching rate, the so-called local dispersion, is used to identify expansions and contractions of the cell membrane providing a fully automated way of extracting properties of these cell shape changes. We applied our methods to time-lapse microscopy data of the social amoeba Dictyostelium discoideum.
In this study we re-evaluate the estimation of the self-similarity exponent of fixational eye movements using Bayesian theory. Our analysis is based on a subsampling decomposition, which permits an analysis of the signal up to some scale factor. We demonstrate that our approach can be applied to simulated data from mathematical models of fixational eye movements to distinguish the models' properties reliably.
Change points in time series are perceived as isolated singularities where two regular trends of a given signal do not match. The detection of such transitions is of fundamental interest for the understanding of the system's internal dynamics or external forcings. In practice observational noise makes it difficult to detect such change points in time series. In this work we elaborate on a Bayesian algorithm to estimate the location of the singularities and to quantify their credibility. We validate the performance and sensitivity of our inference method by estimating change points of synthetic data sets. As an application we use our algorithm to analyze the annual flow volume of the Nile River at Aswan from 1871 to 1970, where we confirm a well-established significant transition point within the time series.
The parameters of the nutations are now known with a good accuracy, and the theory accounts for most of their values. Dissipative friction at the core-mantle boundary (CMB) and at the inner core boundary is an important ingredient of the theory. Up to now, viscous coupling at a smooth interface and electromagnetic coupling have been considered. In some cases they appear hardly strong enough to account for the observations. We advocate here that the CMB has a small- scale roughness and estimate the dissipation resulting from the interaction of the fluid core motion with this topography. We conclude that it might be significant
Amoebae explore their environment in a random way, unless external cues like, e. g., nutrients, bias their motion. Even in the absence of cues, however, experimental cell tracks show some degree of persistence. In this paper, we analyzed individual cell tracks in the framework of a linear mixed effects model, where each track is modeled by a fractional Brownian motion, i.e., a Gaussian process exhibiting a long-term correlation structure superposed on a linear trend. The degree of persistence was quantified by the Hurst exponent of fractional Brownian motion. Our analysis of experimental cell tracks of the amoeba Dictyostelium discoideum showed a persistent movement for the majority of tracks. Employing a sliding window approach, we estimated the variations of the Hurst exponent over time, which allowed us to identify points in time, where the correlation structure was distorted ("outliers"). Coarse graining of track data via down-sampling allowed us to identify the dependence of persistence on the spatial scale. While one would expect the (mode of the) Hurst exponent to be constant on different temporal scales due to the self-similarity property of fractional Brownian motion, we observed a trend towards stronger persistence for the down-sampled cell tracks indicating stronger persistence on larger time scales.
The motility of adherent eukaryotic cells is driven by the dynamics of the actin cytoskeleton. Despite the common force-generating actin machinery, different cell types often show diverse modes of locomotion that differ in their shape dynamics, speed, and persistence of motion. Recently, experiments in Dictyostelium discoideum have revealed that different motility modes can be induced in this model organism, depending on genetic modifications, developmental conditions, and synthetic changes of intracellular signaling. Here, we report experimental evidence that in a mutated D. discoideum cell line with increased Ras activity, switches between two distinct migratory modes, the amoeboid and fan-shaped type of locomotion, can even spontaneously occur within the same cell. We observed and characterized repeated and reversible switchings between the two modes of locomotion, suggesting that they are distinct behavioral traits that coexist within the same cell. We adapted an established phenomenological motility model that combines a reaction-diffusion system for the intracellular dynamics with a dynamic phase field to account for our experimental findings.
We investigate the influence of spatial heterogeneities on various aspects of brittle failure and seismicity in a model of a large strike-slip fault. The model dynamics is governed by realistic boundary conditions consisting of constant velocity motion of regions around the fault, static/kinetic friction laws, creep with depth-dependent coefficients, and 3-D elastic stress transfer. The dynamic rupture is approximated on a continuous time scale using a finite stress propagation velocity ("quasidynamic model''). The model produces a "brittle- ductile'' transition at a depth of about 12.5 km, realistic hypocenter distributions, and other features of seismicity compatible with observations. Previous work suggested that the range of size scales in the distribution of strength-stress heterogeneities acts as a tuning parameter of the dynamics. Here we test this hypothesis by performing a systematic parameter-space study with different forms of heterogeneities. In particular, we analyze spatial heterogeneities that can be tuned by a single parameter in two distributions: ( 1) high stress drop barriers in near- vertical directions and ( 2) spatial heterogeneities with fractal properties and variable fractal dimension. The results indicate that the first form of heterogeneities provides an effective means of tuning the behavior while the second does not. In relatively homogeneous cases, the fault self-organizes to large-scale patches and big events are associated with inward failure of individual patches and sequential failures of different patches. The frequency-size event statistics in such cases are compatible with the characteristic earthquake distribution and large events are quasi-periodic in time. In strongly heterogeneous or near-critical cases, the rupture histories are highly discontinuous and consist of complex migration patterns of slip on the fault. In such cases, the frequency-size and temporal statistics follow approximately power-law relations
The magnetosphere-ionosphere-thermosphere (MIT) dynamic system significantly depends on the highly variable solar wind conditions, in particular, on changes of the strength and orientation of the interplanetary magnetic field (IMF). The solar wind and IMF interactions with the magnetosphere drive the MIT system via the magnetospheric field-aligned currents (FACs). The global modeling helps us to understand the physical background of this complex system. With the present study, we test the recently developed high-resolution empirical model of field-aligned currents MFACE (a high-resolution Model of Field-Aligned Currents through Empirical orthogonal functions analysis). These FAC distributions were used as input of the time-dependent, fully self-consistent global Upper Atmosphere Model (UAM) for different seasons and various solar wind and IMF conditions. The modeling results for neutral mass density and thermospheric wind are directly compared with the CHAMP satellite measurements. In addition, we perform comparisons with the global empirical models: the thermospheric wind model (HWM07) and the atmosphere density model (Naval Research Laboratory Mass Spectrometer and Incoherent Scatter Extended 2000). The theoretical model shows a good agreement with the satellite observations and an improved behavior compared with the empirical models at high latitudes. Using the MFACE model as input parameter of the UAM model, we obtain a realistic distribution of the upper atmosphere parameters for the Northern and Southern Hemispheres during stable IMF orientation as well as during dynamic situations. This variant of the UAM can therefore be used for modeling the MIT system and space weather predictions.
This paper is devoted to the digital processing of multicomponent seismograms using wavelet analysis. The goal of this processing is to identify Rayleigh surface elastic waves and determine their properties. A new method for calculating the ellipticity parameters of a wave in the form of a time-frequency spectrum is proposed, which offers wide possibilities for filtering seismic signals in order to suppress or extract the Rayleigh components. A model of dispersion and dissipation of elliptic waves written in terms of wavelet spectra of complex (two-component) signals is also proposed. The model is used to formulate a nonlinear minimization problem that allows for a high-accuracy calculation of the group and phase velocities and the attenuation factor for a propagating elliptic Rayleigh wave. All methods considered in the paper are illustrated with the use of test signals. (c) 2005 Pleiades Publishing, Inc