Different Levels Of Randomness Research Articles

Deterministic, random, or in between? Inferring the randomness level of wildlife movements

BackgroundWhen assessing connectivity, it is crucial to rely on accurate modeling frameworks that consider species movement preferences and patterns. One important aspect is the level of randomness or unpredictability in the route selection. In this respect, traditional approaches (based on least-cost path or circuit theory) consider species movements unrealistically as totally deterministic or as totally random. A recent approach (randomized shortest path) advocates for choosing intermediate levels of randomness through a single parameter. This parameter may be optimized by validating connectivity surfaces developed from different levels of randomness against observed movement data. However, connectivity models are seldom validated, and it is still unclear how to approach this task. To address this knowledge gap, this paper aims at comparing different validation methods to infer the optimal randomness level in connectivity studies. Additionally, we aimed to disentangle the practical consequences of applying traditional connectivity approaches versus using an optimized level of movement randomness when delineating corridors.MethodsThese objectives were accomplished through the study case of the Iberian lynx, an endangered species whose maintenance and recovery depend on the current connectivity among its population nuclei. We firstly determined a conductance surface based on point selection functions accounting for the behavioral state (territorial or exploratory) of individuals. Secondly, we identified the level of randomness that better fits lynxes’ movements with independent GPS locations and different validation techniques. Lastly, we delineated corridors between lynx population nuclei through a) the randomized shortest path approach and the extreme and optimal levels of randomness of each validation method, and b) the traditional connectivity approaches.ResultsAccording to all used validation methodologies, models with intermediate levels of randomness outperformed those with extreme randomness levels representing totally deterministic or random movements. We found differences in the optimal randomness level among validation methods but similar results in the delineation of corridors. Our results also revealed that models with extreme randomness levels (deterministic and random walk) of the randomized path approach provided equivalent corridor networks to those from traditional approaches. Moreover, these corridor networks calculated with traditional approaches showed notable differences in patterns from the corridor network calculated with an optimized randomness level.ConclusionsHere we presented a connectivity model with a solid biological basis that calibrates the level of movement randomness and is supported by comprehensive validation methods. It is thus a step forward in the search and evaluation of connectivity approaches that lead to improved, efficient, and successful management actions.

Role of cell regularity and relative density on elasto-plastic compression response of random honeycombs generated using Voronoi diagrams

The Voronoi tessellation technique and solid modeling methods are used in this work to create virtual random structures and link cell morphology with the mechanical behavior. Their compression responses are analyzed using the finite element method. First, the effect of loading direction is analyzed for structures with different levels of randomness characterized by a regularity parameter to assess the degree of scatter in the results. Subsequently, morphological characteristics such as arrangement of cells and randomness are analyzed separately. The effect of relative density on structures with different levels of randomness is also studied. Simulations suggest that at low relative densities the arrangement of cells has a negligible effect on the compression response of random honeycombs. On the contrary, the cellular randomness has significant influence on the elastic and plastic characteristics especially when fully random structures are compared with the regular counterparts.

Effect of random positions for coherent dipole transport

We calculate the effect of two kinds of randomness on the hopping of an excitation through a nearly regular Rydberg gas. We present calculations for how fast the excitation can hop away from its starting position for different dimensional lattices and for different levels of randomness. We also examine the asymptotic in time final position of the excitation to determine whether or not the excitation can be localized. The one dimensional system is an example of Anderson localization where the randomness is in the off-diagonal elements although the long-range nature of the interaction leads to non-exponential decay with distance. The two dimensional square lattice shows a mixture of extended and localized states for large randomness while there is no visible sign of localized states for weak randomness. The three dimensional cubic lattice has few localized states even for strong randomness.

Wave propagation in random granular chains

The influence of randomness on wave propagation in one-dimensional chains of spherical granular media is investigated. The interaction between the elastic spheres is modeled using the classical Hertzian contact law. Randomness is introduced in the discrete model using random distributions of particle mass, Young's modulus, or radius. Of particular interest in this study is the quantification of the attenuation in the amplitude of the impulse associated with various levels of randomness: two distinct regimes of decay are observed, characterized by an exponential or a power law, respectively. The responses are normalized to represent a vast array of material parameters and impact conditions. The virial theorem is applied to investigate the transfer from potential to kinetic energy components in the system for different levels of randomness. The level of attenuation in the two decay regimes is compared for the three different sources of randomness and it is found that randomness in radius leads to the maximum rate of decay in the exponential regime of wave propagation.

A hierarchy of randomness for graphs

In this paper we formulate four families of problems with which we aim at distinguishing different levels of randomness. The first one is completely non-random, being the ordinary Ramsey–Turán problem and in the subsequent three problems we formulate some randomized variations of it. As we will show, these four levels form a hierarchy. In a continuation of this paper we shall prove some further theorems and discuss some further, related problems.

Different levels of randomness in Random Ramsey theorems

Abstract Extremal graph theory, Ramsey theory and the theory of Random graphs are strongly connected to each other. Starting from these fields, we formulate some problems and results which are related to different levels of randomness. The first one is completely non-random, being the ordinary Ramsey-Turan problem and in the subsequent three problems we formulate some randomized variations of the problem. Speaking of graph properties, we shall consider them as sets of graphs and occasionally write G ∈ P instead of writing that G has property P. A graph property P is called monotone if adding an edge to a H n ∈ P, we get an H ∗ n ∈ P. We shall use three models of random graphs: the binomial, the hypergeometric and the stopping-rule model. This abstract contains the most important definitions.

Two-dimensional nonlinear sigma model on a random lattice.

The O(n) nonlinear \ensuremath{\sigma} model is simulated on two-dimensional regular and random lattices. We use two different levels of randomness in the construction of the random lattices and give a detailed explanation of the geometry of such lattices. In the simulations we calculate the mass gap for n=3, 4, and 8, analyzing the asymptotic scaling of the data and computing the ratio of lambda parameters ${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{random}}$/${\mathrm{\ensuremath{\Lambda}}}_{\mathrm{regular}}$. These ratios are in agreement with previous semianalytical calculations. We also numerically calculate the topological susceptibility by using the cooling method.