Model-checking ecological state-transition graphs

Model-checking is a methodology developed in computer science to automatically assess the dynamics of discrete systems, by checking if a system modelled as a state-transition graph satisfies a dynamical property written as a temporal logic formula. The dynamics of ecosystems have been drawn as state-transition graphs for more than a century, from state-and-transition models to assembly graphs. Thus, model-checking can provide insights into both empirical data and theoretical models, as long as they sum up into state-transition graphs. While model-checking proved to be a valuable tool in systems biology, it remains largely underused in ecology. Here we promote the adoption of the model-checking toolbox in ecology through its application to an illustrative example. We assessed the dynamics of a vegetation model inspired from state-and-transition models by model-checking Computation Tree Logic formulas built from a proposed catalogue of patterns. Model-checking encompasses a wide range of concepts and available software, mentioned in discussion, thus its implementation can be fitted to the specific features of the described system. In addition to the automated analysis of ecological state-transition graphs, we believe that defining ecological concepts with temporal logics could help clarifying and comparing them.

Periodic Property and Instability of a Rotating Pendulum System

The current paper investigates the dynamical property of a pendulum attached to a rotating rigid frame with a constant angular velocity about the vertical axis passing to the pivot point of the pendulum. He’s homotopy perturbation method is used to obtain the analytic solution of the governing nonlinear differential equation of motion. The fourth-order Runge-Kutta method (RKM) and He’s frequency formulation are used to verify the high accuracy of the obtained solution. The stability condition of the motion is examined and discussed. Some plots of the time histories of the gained solutions are portrayed graphically to reveal the impact of the distinct parameters on the dynamical motion.

STUDYING OF EFFICIENT AND SEMI-EFFICIENT CURING SYSTEMS INFLUENCE ON DYNAMICAL PROPERTY AND OZONRESISTANT OF RUBBER

There was showed dependence of the storage modulus and the loss modulus on shear deformation in torsion. For the first time type of curing system influence on Payne and Mullins effect is investigated. The Cole-Cole plots exhibit the contribution of the cross-linking system effect in the dynamic properties of rubber. There was increase of ozone resistance of rubber based on efficient curing system in condition general stress to critical stress is showed.

Reconstruction of the right-hand part of a distributed differential equation using a positional controlled model

In this paper, we consider the stable reconstruction problem of the unknown input of a distributed system of second order by results of inaccurate measurements of its solution. The content of the problem considered is as follows. We consider a distributed equation of second order. The solution of the equation depends on the input varying in the time. The input, as well as the solution, is not given in advance. At discrete times the solution of the equation is measured. These measurements are not accurate in general. It is required to design an algorithm for approximate reconstruction of the input that has dynamical and stability properties. The dynamical property means that the current values of approximations of the input are produced on-line, and the stability property means that the approximations are arbitrarily accurate for a sufficient accuracy of measurements. The problem refers to the class of inverse problems. The algorithm presented in the paper is based on the constructions of a stable dynamical inversion and on the combination of the methods of ill-posed problems and positional control theory.

Inferring the dark matter velocity anisotropy to the cluster edge

ABSTRACT Dark matter (DM) dominates the properties of large cosmological structures such as galaxy clusters, and the mass profiles of the DM have been inferred for these equilibrated structures for years by using cluster X-ray surface brightnesses and temperatures. A new method has been proposed, which should allow us to infer a dynamical property of the DM, namely the velocity anisotropy. For the gas, a similar velocity anisotropy is zero due to frequent collisions; however, the collisionless nature of DM allows it to be non-trivial. Numerical simulations have for years found non-zero and radially varying DM velocity anisotropies. Here we employ the method proposed by Hansen & Piffaretti, and developed by Høst et al. to infer the DM velocity anisotropy in the bright galaxy cluster Perseus, to near five times the radii previously obtained. We find the DM velocity anisotropy to be consistent with the results of numerical simulations, however, still with large error bars. At half the virial radius, we find the DM velocity anisotropy to be non-zero at 1.7$\, \sigma$, lending support to the collisionless nature of DM.

A particle-field approach bridges phase separation and collective motion in active matter

Whereas self-propelled hard discs undergo motility-induced phase separation, self-propelled rods exhibit a variety of nonequilibrium phenomena, including clustering, collective motion, and spatio-temporal chaos. In this work, we present a theoretical framework representing active particles by continuum fields. This concept combines the simplicity of alignment-based models, enabling analytical studies, and realistic models that incorporate the shape of self-propelled objects explicitly. By varying particle shape from circular to ellipsoidal, we show how nonequilibrium stresses acting among self-propelled rods destabilize motility-induced phase separation and facilitate orientational ordering, thereby connecting the realms of scalar and vectorial active matter. Though the interaction potential is strictly apolar, both, polar and nematic order may emerge and even coexist. Accordingly, the symmetry of ordered states is a dynamical property in active matter. The presented framework may represent various systems including bacterial colonies, cytoskeletal extracts, or shaken granular media.

A co-infection model for Two-Strain Malaria and Cholera with Optimal Control

A mathematical model for two strains of Malaria and Cholera with optimal control is studied and analyzed to assess the impact of treatment controls in reducing the burden of the diseases in a population, in the presence of malaria drug resistance. The model is shown to exhibit the dynamical property of backward bifurcation when the associated reproduction number is less than unity. The global asymptotic stability of the disease-free equilibrium of the model is proven not to exist. The necessary conditions for the existence of optimal control and the optimality system for the model is established using the Pontryagin's Maximum Principle. Numerical simulations of the optimal control model reveal that malaria drug resistance can greatly influence the co-infection cases averted, even in the presence of treatment controls for co-infected individuals.

General theory of topological explanations and explanatory asymmetry

In this paper, I present a general theory of topological explanations, and illustrate its fruitfulness by showing how it accounts for explanatory asymmetry. My argument is developed in three steps. In the first step, I show what it is for some topological property A to explain some physical or dynamical property B . Based on that, I derive three key criteria of successful topological explanations: a criterion concerning the facticity of topological explanations, i.e. what makes it true of a particular system; a criterion for describing counterfactual dependencies in two explanatory modes, i.e. the vertical and the horizontal and, finally, a third perspectival one that tells us when to use the vertical and when to use the horizontal mode. In the second step, I show how this general theory of topological explanations accounts for explanatory asymmetry in both the vertical and horizontal explanatory modes. Finally, in the third step, I argue that this theory is universally applicable across biological sciences, which helps in unifying essential concepts of biological networks. This article is part of the theme issue ‘Unifying the essential concepts of biological networks: biological insights and philosophical foundations'.

Partial Differential Equation-Based Trajectory Planning for Multiple Unmanned Air Vehicles in Dynamic and Uncertain Environments

This paper proposes a physics-inspired method for unmanned aerial vehicle (UAV) trajectory planning in three dimensions using partial differential equations (PDEs) for application in dynamic hostile environments. The proposed method exploits the dynamical property of fluid flowing through a porous medium. This method evaluates risk to generate porosity values throughout the computational domain. The trajectory that encounters the highest porosity values determines the trajectory from the point of origin to the goal position. The best trajectory is found using the reaction of the fluid in porous media by the way of streamlines obtained by numerically solving the PDEs representing the fluid flow. Constraints due to UAV dynamics, obstacles, and predefined way points are applied to the problem after solving for the best trajectory to find the optimal and feasible trajectory. This method shows near-optimality and much reduced computational effort when compared to the other typical numerical optimization methods.