scholarly journals A Framework for Collective Behavior in Plant Inspired Growth-Driven Systems, Based on Kinematics of Allotropism

2019 ◽  
Author(s):  
Renaud Bastien ◽  
Amir Porat ◽  
Yasmine Meroz
Keyword(s):  
Phase Space ◽  
Collective Behavior ◽  
Initial Conditions ◽  
Plant Root ◽  
Growth Dynamics ◽  
Theoretical Framework ◽  
Form Complex ◽  
Main Driver ◽  
Adaptive Structure ◽  
Nearby Point

A variety of biological systems are not motile, but sessile in nature, relying on growth as the main driver of their movement. Groups of such growing organisms can form complex structures, such as the functional architecture of growing axons, or the adaptive structure of plant root systems. These processes are not yet understood, however the decentralized growth dynamics bear similarities to the collective behavior observed in groups of motile organisms, such as flocks of birds or schools of fish. Equivalent growth mechanisms make these systems amenable to a theoretical framework inspired by tropic responses of plants, where growth is considered implicitly as the driver of the observed bending towards a stimulus. We introduce two new concepts related to plant tropisms: point tropism, the response of a plant to a nearby point signal source, and allotropism, the growth-driven response of plant organs to neighboring plants. We first analytically and numerically investigate the 2D dynamics of single organs responding to point signals fixed in space. Building on this we study pairs of organs interacting via allotropism, i.e.each organ senses signals emitted at the tip of their neighbor and responds accordingly. In the case of local sensing we find a rich phase space. We describe the different phases, as well as the sharp transitions between them. We also find that the form of the phase space depends on initial conditions. This work sets the stage towards a theoretical framework for the investigation and understanding of systems of interacting growth-driven individuals.

scholarly journals A mechanochemical model recapitulates distinct vertebrate gastrulation modes

2021 ◽  
Author(s):  
Mattia Serra ◽  
Guillermo Serrano Najera ◽  
Manli Chuai ◽  
Vamsi Spandan ◽  
Cornelis J Weijer ◽  
...  
Keyword(s):  
Phase Space ◽  
Initial Conditions ◽  
Theoretical Framework ◽  
Self Organization ◽  
Critical Event ◽  
Wild Type ◽  
Cellular Processes ◽  
Uniform State ◽  
Mechanochemical Model ◽  
Predictive Theory

Gastrulation is a critical event in vertebrate morphogenesis driven by cellular processes, and characterized by coordinated multi-cellular movements that form the robust morphological structures. How these structures emerge in a developing organism and vary across vertebrates remains unclear. Inspired by experiments on the chick, we derive a theoretical framework that couples actomyosin activity to tissue flow, and provides a basis for the dynamics of gastrulation morphologies. Our model predicts the onset and development of observed experimental patterns of wild-type and perturbations of chick gastrulation as a spontaneous instability of a uniform state. Varying the initial conditions and a parameter in our model, allows us to recapitulate the phase space of gastrulation morphologies seen across vertebrates, consistent with experimental observations in the accompanying paper. All together, this suggests that early embryonic self-organization follows from a minimal predictive theory of active mechano-sensitive flows.

Proteomic Analyses of Soybean Root Tips During Germination

2014 ◽  
Vol 21 (12) ◽  
pp. 1308-1319
Author(s):  
Setsuko Komatsu ◽  
Myeong W. Oh ◽  
Hee Y. Jang ◽  
Soo J. Kwon ◽  
Hye R. Kim ◽  
...  
Keyword(s):  
Protein Synthesis ◽  
Proteomic Analysis ◽  
Plant Root ◽  
Root Tip ◽  
Root Tips ◽  
Form Complex ◽  
Molecular Weights ◽  
Soybean Seedlings ◽  
2D Gel ◽  
Proteomic Techniques

Plant root systems form complex networks with the surrounding soil environment and are controlled by both internal and external factors. To better understand the function of root tips of soybean during germination, three proteomic techniques were used to analyze the protein profiles of root tip cells. Proteins were extracted from the root tips of 4-dayold soybean seedlings and analyzed using two-dimensional (2D) gel electrophoresis-based proteomics, SDS-gel based proteomics, and gel-free proteomics techniques. A total of 121, 862, and 341 proteins were identified in root tips using the 2D gel-based, SDS gel-based, and gel-free proteomic techniques, respectively. The proteins identified by 2D gel-based proteomic analysis were predominantly localized in the cytoplasm, whereas nuclear-localized proteins were most commonly identified by the SDS gel-based and gel-free proteomics techniques. Of the 862 proteins identified in the SDS gelbased proteomic analysis, 190 were protein synthesis-related proteins. Furthermore, 24 proteins identified using the 2Dgel based proteomic technique shifted between acidic and basic isoelectric points, and 2 proteins, heat shock protein 70.2 and AAA-type ATPase, displayed two different molecular weights at the same isoelectric point. Taken together, these results suggest that a number of proteins related to protein synthesis and modification are activated in the root tips of soybean seedlings during germination.

scholarly journals Market of Stocks During Crisis Looks Like a Flock of Birds

2020 ◽  
Author(s):  
Bahar Afsharizand ◽  
Pooya H. Chaghoei ◽  
A A. Kordbacheh ◽  
A Trufanov ◽  
G.Reza Jafari
Keyword(s):  
Phase Space ◽  
Collective Behavior ◽  
Unique Point ◽  
Property A ◽  
Vicsek Model ◽  
Cooperative Effects ◽  
Cooperative Movement ◽  
Vector Velocity ◽  
Work Cooperative ◽  
The One

According to its inner property, a crisis in the financial market can be considered as a collective behavior phenomenon. Through the prism of collective behavior, the crisis does not happen if the companies are independent of each other. In this work, cooperative movement processes in a stock market are investigated in a manner similar to that Vicsek first described collective behavior for self-propelled entities. To this end, a phase space is defined as the one in which the return of volume of transactions versus return of price is represented with each share in each day corresponding to a unique point in the space. The findings of the observation show that during times of crisis, the phase space is limited with the vector velocity of shares in the same direction. In contrast, on a regular day, the phase space is entirely accessible, with vector velocity aligned randomly. Moreover, in line with the Vicsek model, an order parameter is introduced, which evaluates the cooperative effects for the shares so that the higher the value of this parameter, the stronger the collective behavior of the shares.

scholarly journals On the apparent power law in CDM halo pseudo-phase space density profiles

2017 ◽  
Vol 470 (1) ◽  
pp. 500-511 ◽  
Author(s):  
Ethan O. Nadler ◽  
S. Peng Oh ◽  
Suoqing Ji
Keyword(s):  
Phase Space ◽  
Power Law ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Phase Space Density ◽  
Fluid Approximation ◽  
Density Profiles ◽  
Space Density ◽  
Scale Free ◽  
Hydrodynamic Calculations

Abstract We investigate the apparent power-law scaling of the pseudo-phase space density (PPSD) in cold dark matter (CDM) haloes. We study fluid collapse, using the close analogy between the gas entropy and the PPSD in the fluid approximation. Our hydrodynamic calculations allow for a precise evaluation of logarithmic derivatives. For scale-free initial conditions, entropy is a power law in Lagrangian (mass) coordinates, but not in Eulerian (radial) coordinates. The deviation from a radial power law arises from incomplete hydrostatic equilibrium (HSE), linked to bulk inflow and mass accretion, and the convergence to the asymptotic central power-law slope is very slow. For more realistic collapse, entropy is not a power law with either radius or mass due to deviations from HSE and scale-dependent initial conditions. Instead, it is a slowly rolling power law that appears approximately linear on a log–log plot. Our fluid calculations recover PPSD power-law slopes and residual amplitudes similar to N-body simulations, indicating that deviations from a power law are not numerical artefacts. In addition, we find that realistic collapse is not self-similar; scalelengths such as the shock radius and the turnaround radius are not power-law functions of time. We therefore argue that the apparent power-law PPSD cannot be used to make detailed dynamical inferences or extrapolate halo profiles inwards, and that it does not indicate any hidden integrals of motion. We also suggest that the apparent agreement between the PPSD and the asymptotic Bertschinger slope is purely coincidental.

Chaos in blood flow control in genetic and renovascular hypertensive rats

1991 ◽  
Vol 261 (3) ◽  
pp. F400-F408 ◽  
Author(s):  
K. P. Yip ◽  
N. H. Holstein-Rathlou ◽  
D. J. Marsh
Keyword(s):  
Time Series ◽  
Blood Flow ◽  
Phase Space ◽  
Renal Artery ◽  
Initial Conditions ◽  
Pressure Fluctuations ◽  
Deterministic Chaos ◽  
Tubuloglomerular Feedback ◽  
Hypertensive Rats ◽  
Statistical Measures

Hydrostatic pressure and flow in renal proximal tubules oscillate at 30–40 mHz in normotensive rats anesthetized with halothane. The oscillations originate in tubuloglomerular feedback, a mechanism that provides local blood flow regulation. Instead of oscillations, spontaneously hypertensive rats (SHR) have aperiodic tubular pressure fluctuations; the pattern is suggestive of deterministic chaos. Normal rats made hypertensive by clipping one renal artery had similar aperiodic tubular pressure fluctuations in the unclipped kidney, and the fraction of rats with irregular fluctuations increased with time after the application of the renal artery clip. Statistical measures of deterministic chaos were applied to tubular pressure data. The correlation dimension, a measure of the dimension of the phase space attractor generating the time series, indicated the presence of a low-dimension strange attractor, and the largest Lyapunov exponent, a measure of the rate of divergence in phase space, was positive, indicating sensitivity to initial conditions. These time series therefore satisfy two criteria of deterministic chaos. The measures were the same in SHR as in rats with renovascular hypertension. Since two different models of hypertension displayed similar dynamics, we suggest that chaotic behavior is a common feature of renal vascular control in the natural history of the disease.

scholarly journals Cosmic flows and the expansion of the local Universe from non-linear phase–space reconstructions

2016 ◽  
Vol 456 (4) ◽  
pp. 4247-4255 ◽  
Author(s):  
Steffen Heß ◽  
Francisco-Shu Kitaura
Keyword(s):  
Phase Space ◽  
Cold Dark Matter ◽  
Initial Conditions ◽  
Hubble Constant ◽  
Linear Phase ◽  
Local Universe ◽  
Non Linear ◽  
Galaxy Sample ◽  
Fisher Relation ◽  
The Impact

Abstract In this work, we investigate the impact of cosmic flows and density perturbations on Hubble constant H0 measurements using non-linear phase–space reconstructions of the Local Universe (LU). In particular, we rely on a set of 25 precise constrained N-body simulations based on Bayesian initial conditions reconstructions of the LU using the Two-Micron Redshift Survey galaxy sample within distances of about 90  h−1 Mpc. These have been randomly extended up to volumes enclosing distances of 360  h−1 Mpc with augmented Lagrangian perturbation theory (750 simulations in total), accounting in this way for gravitational mode coupling from larger scales, correcting for periodic boundary effects, and estimating systematics of missing attractors (σlarge = 134  s−1 km). We report on Local Group (LG) speed reconstructions, which for the first time are compatible with those derived from cosmic microwave background-dipole measurements: |vLG| = 685 ± 137  s−1 km. The direction (l, b) = (260$_{.}^{\circ}$5 ± 13$_{.}^{\circ}$3, 39$_{.}^{\circ}$1 ± 10$_{.}^{\circ}$4) is found to be compatible with the observations after considering the variance of large scales. Considering this effect of large scales, our local bulk flow estimations assuming a Λ cold dark matter model are compatible with the most recent estimates based on velocity data derived from the Tully–Fisher relation. We focus on low-redshift supernova measurements out to 0.01 < z < 0.025, which have been found to disagree with probes at larger distances. Our analysis indicates that there are two effects related to cosmic variance contributing to this tension. The first one is caused by the anisotropic distribution of supernovae, which aligns with the velocity dipole and hence induces a systematic boost in H0. The second one is due to the inhomogeneous matter fluctuations in the LU. In particular, a divergent region surrounding the Virgo Supercluster is responsible for an additional positive bias in H0. Taking these effects into account yields a correction of ΔH0 = -1.76 ± 0.21  s− 1 km Mpc− 1, thereby reducing the tension between local probes and more distant probes. Effectively H0 is lower by about 2 per cent.

COEXISTENCE OF LOW- AND HIGH-DIMENSIONAL SPATIOTEMPORAL CHAOS IN A CHAIN OF DISSIPATIVELY COUPLED CHUA’S CIRCUITS

1994 ◽  
Vol 04 (03) ◽  
pp. 639-674 ◽  
Author(s):  
A.L. ZHELEZNYAK ◽  
L.O. CHUA
Keyword(s):  
Phase Space ◽  
Initial Conditions ◽  
Coupling Parameter ◽  
Reaction Diffusion ◽  
Cellular Neural Network ◽  
Spatiotemporal Chaos ◽  
Matrix Phase ◽  
High Dimensional ◽  
The Matrix ◽  
A Chain

Spatiotemporal dynamics of a one-dimensional cellular neural network (CNN) made of Chua’s circuits which mimics a reaction-diffusion medium is considered. An approach is presented to analyse the properties of this reaction-diffusion CNN through the characteristics of the attractors of an associated infinite-dimensional dynamical system with a matrix phase space. Using this approach, the spatiotemporal correlation dimension of the CNN’s spatiotemporal patterns is computed over various ranges of the diffusion coupling parameter, length of the chain, and initial conditions. It is shown that in a finite-dimensional projection of the matrix phase space of the CNN, both low- and high-dimensional attractors corresponding to different initial conditions coexist.

scholarly journals A ‘metric’ semi-Lagrangian Vlasov–Poisson solver

2017 ◽  
Vol 83 (3) ◽  
Author(s):  
Stéphane Colombi ◽  
Christophe Alard
Keyword(s):  
Phase Space ◽  
Initial Conditions ◽  
Second Order ◽  
Space Distribution ◽  
Third Order ◽  
One Dimensional ◽  
Phase Space Distribution ◽  
Poisson Solver ◽  
Dimensional Phase Space ◽  
Speed Up

We propose a new semi-Lagrangian Vlasov–Poisson solver. It employs metric elements to follow locally the flow and its deformation, allowing one to find quickly and accurately the initial phase-space position $\boldsymbol{Q}(\boldsymbol{P})$ of any test particle $\boldsymbol{P}$, by expanding at second order the geometry of the motion in the vicinity of the closest element. It is thus possible to reconstruct accurately the phase-space distribution function at any time $t$ and position $\boldsymbol{P}$ by proper interpolation of initial conditions, following Liouville theorem. When distortion of the elements of metric becomes too large, it is necessary to create new initial conditions along with isotropic elements and repeat the procedure again until next resampling. To speed up the process, interpolation of the phase-space distribution is performed at second order during the transport phase, while third-order splines are used at the moments of remapping. We also show how to compute accurately the region of influence of each element of metric with the proper percolation scheme. The algorithm is tested here in the framework of one-dimensional gravitational dynamics but is implemented in such a way that it can be extended easily to four- or six-dimensional phase space. It can also be trivially generalised to plasmas.

scholarly journals Orbit Classification and Sensitivity Analysis in Dynamical Systems Using Surrogate Models

2021 ◽  
Vol 2 (1) ◽  
pp. 5
Author(s):  
Katharina Rath ◽  
Christopher G. Albert ◽  
Bernd Bischl ◽  
Udo von Toussaint
Keyword(s):  
Sensitivity Analysis ◽  
Phase Space ◽  
Dynamical Systems ◽  
Hamiltonian Systems ◽  
Initial Conditions ◽  
Plasma Boundary ◽  
Surrogate Models ◽  
Alpha Particles ◽  
Hamiltonian Flow ◽  
Chaotic Orbits

Dynamics of many classical physics systems are described in terms of Hamilton’s equations. Commonly, initial conditions are only imperfectly known. The associated volume in phase space is preserved over time due to the symplecticity of the Hamiltonian flow. Here we study the propagation of uncertain initial conditions through dynamical systems using symplectic surrogate models of Hamiltonian flow maps. This allows fast sensitivity analysis with respect to the distribution of initial conditions and an estimation of local Lyapunov exponents (LLE) that give insight into local predictability of a dynamical system. In Hamiltonian systems, LLEs permit a distinction between regular and chaotic orbits. Combined with Bayesian methods we provide a statistical analysis of local stability and sensitivity in phase space for Hamiltonian systems. The intended application is the early classification of regular and chaotic orbits of fusion alpha particles in stellarator reactors. The degree of stochastization during a given time period is used as an estimate for the probability that orbits of a specific region in phase space are lost at the plasma boundary. Thus, the approach offers a promising way to accelerate the computation of fusion alpha particle losses.

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