Spatial patterns of competing random walkers

We review recent results obtained from simple individual-based models of biological competition in which birth and death rates of an organism depend on the presence of other competing organisms close to it. In addition the individuals perform random walks of different types (Gaussian diffusion and L\'{e}vy flights). We focus on how competition and random motions affect each other, from which spatial instabilities and extinctions arise. Under suitable conditions, competitive interactions lead to clustering of individuals and periodic pattern formation. Random motion has a homogenizing effect and then delays this clustering instability. When individuals from species differing in their random walk characteristics are allowed to compete together, the ones with a tendency to form narrower clusters get a competitive advantage over the others. Mean-field deterministic equations are analyzed and compared with the outcome of the individual-based simulations.Comment: 38 pages, including 6 figure

Segue: Overviewing Evolution Patterns of Egocentric Networks by Interactive Construction of Spatial Layouts

Getting the overall picture of how a large number of ego-networks evolve is a common yet challenging task. Existing techniques often require analysts to inspect the evolution patterns of ego-networks one after another. In this study, we explore an approach that allows analysts to interactively create spatial layouts in which each dot is a dynamic ego-network. These spatial layouts provide overviews of the evolution patterns of ego-networks, thereby revealing different global patterns such as trends, clusters and outliers in evolution patterns. To let analysts interactively construct interpretable spatial layouts, we propose a data transformation pipeline, with which analysts can adjust the spatial layouts and convert dynamic egonetworks into event sequences to aid interpretations of the spatial positions. Based on this transformation pipeline, we developed Segue, a visual analysis system that supports thorough exploration of the evolution patterns of ego-networks. Through two usage scenarios, we demonstrate how analysts can gain insights into the overall evolution patterns of a large collection of ego-networks by interactively creating different spatial layouts.Comment: Published at IEEE Conference on Visual Analytics Science and Technology (IEEE VAST 2018

Synthesizing Dynamic Patterns by Spatial-Temporal Generative ConvNet

Video sequences contain rich dynamic patterns, such as dynamic texture patterns that exhibit stationarity in the temporal domain, and action patterns that are non-stationary in either spatial or temporal domain. We show that a spatial-temporal generative ConvNet can be used to model and synthesize dynamic patterns. The model defines a probability distribution on the video sequence, and the log probability is defined by a spatial-temporal ConvNet that consists of multiple layers of spatial-temporal filters to capture spatial-temporal patterns of different scales. The model can be learned from the training video sequences by an "analysis by synthesis" learning algorithm that iterates the following two steps. Step 1 synthesizes video sequences from the currently learned model. Step 2 then updates the model parameters based on the difference between the synthesized video sequences and the observed training sequences. We show that the learning algorithm can synthesize realistic dynamic patterns

Grid Cell Hexagonal Patterns Formed by Fast Self-Organized Learning within Entorhinal Cortex

Grid cells in the dorsal segment of the medial entorhinal cortex (dMEC) show remarkable hexagonal activity patterns, at multiple spatial scales, during spatial navigation. How these hexagonal patterns arise has excited intense interest. It has previously been shown how a selforganizing map can convert firing patterns across entorhinal grid cells into hippocampal place cells that are capable of representing much larger spatial scales. Can grid cell firing fields also arise during navigation through learning within a self-organizing map? A neural model is proposed that converts path integration signals into hexagonal grid cell patterns of multiple scales. This GRID model creates only grid cell patterns with the observed hexagonal structure, predicts how these hexagonal patterns can be learned from experience, and can process biologically plausible neural input and output signals during navigation. These results support a unified computational framework for explaining how entorhinal-hippocampal interactions support spatial navigation.CELEST, a National Science Foundation Science of Learning Center (SBE-0354378); SyNAPSE program of Defense Advanced Research Projects Agency (HR00ll-09-3-0001, HR0011-09-C-0011

Spatial Current Patterns, Dephasing and Current Imaging in Graphene Nanoribbons

Using the non-equilibrium Keldysh Green's function formalism, we investigate the local, non-equilibrium charge transport in graphene nanoribbons (GNRs). In particular, we demonstrate that the spatial current patterns associated with discrete transmission resonances sensitively depend on the GNRs' geometry, size, and aspect ratio, the location and number of leads, and the presence of dephasing. We identify a relation between the spatial form of the current patterns, and the number of degenerate energy states participating in the charge transport. Furthermore, we demonstrate a principle of superposition for the conductance and spatial current patterns in multiple-lead configurations. We demonstrate that scanning tunneling microscopy (STM) can be employed to image spatial current paths in GNR with atomic resolution, providing important insight into the form of local charge transport. Finally, we investigate the effects of dephasing on the spatial current patterns, and show that with decreasing dephasing time, the current patterns evolve smoothly from those of a ballistic quantum network to those of classical resistor network.Comment: 25 pages, 12 figure

Spatial patterns in intermunicipal Danish commuting

Intermunicipal variations in in-commuting are mainly explained by variations in number of workplaces, urbanization degree and wealth, whereas variations in out- commuting are mainly determined by variations in workforce size, number of workplaces, living patterns and unemployment. This is quite satisfactory according to existing theory. However, of these explanatory factors only the number of workplaces influences the net in-commuting. But by using spatial lag structures it is shown that unemployment in neighbourhood municipalities influences net in-commuting. Finally, evidence of impact of local spatial industrial patterns on the commuting behaviour is provided, and the nature and reasons for these spatial patterns are discussed.

Nonlinear diffusion effects on biological population spatial patterns

Motivated by the observation that anomalous diffusion is a realistic feature in the dynamics of biological populations, we investigate its implications in a paradigmatic model for the evolution of a single species density $u(x,t)$. The standard model includes growth and competition in a logistic expression, and spreading is modeled through normal diffusion. Moreover, the competition term is nonlocal, which has been shown to give rise to spatial patterns. We generalize the diffusion term through the nonlinear form $\partial_t u(x,t) = D \partial_{xx} u(x,t)^\nu$ (with $D, \nu>0$), encompassing the cases where the state-dependent diffusion coefficient either increases ($\nu>1$) or decreases ($\nu<1$) with the density, yielding subdiffusion or superdiffusion, respectively. By means of numerical simulations and analytical considerations, we display how that nonlinearity alters the phase diagram. The type of diffusion imposes critical values of the model parameters for the onset of patterns and strongly influences their shape, inducing fragmentation in the subdiffusive case. The detection of the main persistent mode allows analytical prediction of the critical thresholds

Spatial Patterns in Chemically and Biologically Reacting Flows

We present here a number of processes, inspired by concepts in Nonlinear Dynamics such as chaotic advection and excitability, that can be useful to understand generic behaviors in chemical or biological systems in fluid flows. Emphasis is put on the description of observed plankton patchiness in the sea. The linearly decaying tracer, and excitable kinetics in a chaotic flow are mainly the models described. Finally, some warnings are given about the difficulties in modeling discrete individuals (such as planktonic organisms) in terms of continuous concentration fields.Comment: 41 pages, 10 figures; To appear in the Proceedings of the 2001 ISSAOS School on 'Chaos in Geophysical Flows