Multiple Pairwise Interactions Research Articles

Flock-species richness influences node importance and modularity in mixed-species flock networks.

Interdependencies in social groups of animals are a combination of multiple pairwise interactions. Heterospecific groups are often characterized by important species that contribute more to group initiation, maintenance or function than other species. However, in large heterospecific groups, many pairwise interactions are not realised, while others may not be biologically significant, confounding inferences about species importance. Hence, in this study, we examine context dependent changes in species importance and assortment in mixed-species bird flocks from a tropical field site in Southern India using social network analysis. Specifically, we ask how the structural importance of a species and the clustering patterns of species relationships depends on species richness in mixed-species flocks. We constructed both raw and filtered networks; while our results are largely correlated, we believe that filtered networks can provide insights into community-level importance of species in mixed-flocks while raw networks depict flock-level patterns. We find significant differences in flocks of different richness in that different species emerge as structurally important across flocks of varying richness. We also find that assortment is higher in two-species flocks and decreases withan increase in the number of species in the flock ('flock richness' hereafter). We argue that the link between structural importance of species in mixed-species flock networks and their functional significance in the community critically depends on the social context: namely, the species richness of the mixed-species flock. We propose that examining species structural importance at different flock-richness values provides insights into biologically meaningful functional roles of species. More generally, we suggest that it is important to consider context when interpreting species centrality and importance in network structure.

Revisiting the Ostwald Ripening: A Discrete Model Based on Multiple Pairwise Interactions

A discrete multi-particle model of Ostwald ripening based on direct pairwise interactions between precipitates with incoherent interfaces is presented. Although based on the mean field concept, it is a valid alternative to the classical LSW theory. The main differences with respect to the classical approach can be summarized as follows: i) Particles interact the one another; ii) The first Fick’s law is considered to evaluate the fluxes of matter instead of the quasi stationary solution of the concentration field around particles; iii) The rate of matter exchange depends on the average surface-to-surface interparticle distance, a characteristic feature of the system which naturally incorporates the effect of volume fraction of second phase; iv) The multi-particle diffusion is described through the definition of an interaction volume containing all the particles involved in the exchange of solute. The model is in excellent agreement with the experimental data available in the literature. The shape of the quasi-stationary 3D particle size distribution of solid-solid and solid-liquid systems is well predicted from volume fractions of 0.07, 0.30, 0.52 and 0.74. Similarly, a very good prediction of the dependence of the kinetic constant of the coarsening process on the volume fraction of precipitates is obtained with reference to literature data on solid-liquid mixtures in the volume fraction range from 0.20 to about 0.75. For volume fractions below about 0.1 the model predicts broad and right-skewed stationary size distributions resembling a lognormal function. Above this value, a transition to sharper, more symmetrical but still right-skewed shapes occurs.

Coarsening kinetics of grain-boundary precipitates: a reanalysis based on the multiple pairwise interaction model of Ostwald ripening

ABSTRACTThe topological structure of the recently developed MultiParticle (MP) model of Ostwald ripening based on direct pairwise interactions has been extended to describe the coarsening of grain-boundary (GB) precipitates by introducing a 2D diffusion geometry. In agreement with previous studies in the literature, the model predicts that the mean radius grows proportionally to t1/4. The analysis carried out in this work originates from the observation that in some cases the t1/3 kinetics, typical of a process controlled by bulk diffusion, is recovered also in systems where almost all particles are located on grain boundaries. In order to investigate this discrepancy, an ideal system with small volume fraction of second phase (0.05) where all precipitates are on GBs has been considered. By calculating the ratio between the coarsening rate predicted when the system is controlled by GB diffusion and that of the same system controlled by bulk diffusion it is found that, even by imposing a diffusion coefficient at GBs 100 times that in the bulk, GB diffusion dominates only when the mean particle size is below a limiting value. Since the system is anyway undergoing coarsening, eventually the bulk diffusion mechanism will prevail. This provides a possible explanation of the experimental results. For the sake of completeness, a kinetic equation describing the true 2D Ostwald ripening of island-like cylindrical particles within the framework of the MP model is also developed. As expected, it is characterised by a t1/3 coarsening law.

A discrete model of Ostwald ripening based on multiple pairwise interactions

ABSTRACT A discrete multi-particle model of Ostwald ripening based on direct pairwise interactions is developed for particles with incoherent interfaces as an alternative to the classical LSW mean field theory. The rate of matter exchange depends on the average surface-to-surface interparticle distance, a characteristic feature of the system which naturally incorporates the effect of volume fraction of second phase. The multi-particle diffusion is described through the definition of an interaction volume containing all the particles involved in the exchange of solute. At small volume fractions this is proportional to the size of the central particle, at higher volume fractions it gradually reduces as a consequence of diffusion screening described on a geometrical basis. The topological noise present in real systems is also included. For volume fractions below about 0.1 the model predicts broad and right-skewed stationary size distributions resembling a lognormal function. Above this value, a transition to sharper, more symmetrical but still right-skewed shapes occurs. An excellent agreement with experiments is obtained for 3D particle size distributions of solid–solid and solid–liquid systems with volume fraction 0.07, 0.30, 0.52 and 0.74. The kinetic constant of the model depends on the cube root of volume fraction up to about 0.1, then increases rapidly with an upward concavity. It is in good agreement with the available literature data on solid–liquid mixtures in the volume fraction range from 0.20 to about 0.75.

Dynamic Properties of Evolutionary Multi-player Games in Finite Populations

William D. Hamilton famously stated that “human life is a many person game and not just a disjoined collection of two person games”. However, most of the theoretical results in evolutionary game theory have been developed for two player games. In spite of a multitude of examples ranging from humans to bacteria, multi-player games have received less attention than pairwise games due to their inherent complexity. Such complexities arise from the fact that group interactions cannot always be considered as a sum of multiple pairwise interactions. Mathematically, multi-player games provide a natural way to introduce non-linear, polynomial fitness functions into evolutionary game theory, whereas pairwise games lead to linear fitness functions. Similarly, studying finite populations is a natural way of introducing intrinsic stochasticity into population dynamics. While these topics have been dealt with individually, few have addressed the combination of finite populations and multi-player games so far. We are investigating the dynamical properties of evolutionary multi-player games in finite populations. Properties of the fixation probability and fixation time, which are relevant for rare mutations, are addressed in well mixed populations. For more frequent mutations, the average abundance is investigated in well mixed as well as in structured populations. While the fixation properties are generalizations of the results from two player scenarios, addressing the average abundance in multi-player games gives rise to novel outcomes not possible in pairwise games.

Ignoring Your Neighbors: Moment Correlations Dominated by Indirect or Distant Interactions in an Ordered Nanomagnet Array

We have studied the moment correlations within triangular lattice arrays of single-domain coaligned nanoscale ferromagnetic islands. Independent variation of lattice spacing along and perpendicular to the island axis tunes the magnetostatic interactions between islands through a broad range of relative strengths. For certain lattice parameters, the sign of the correlations between near-neighbor island moments is opposite to that favored by the pairwise interaction. This finding, supported by analysis of the total correlation in terms of direct and convoluted indirect contributions across multiple pairwise interactions, indicates that indirect interactions and/or those mediated by further neighbors can be tuned to be dominant, with implications for the wide range of systems composed of interacting nanomagnets.

Interaction intensity and importance along two stress gradients: adding shape to the stress-gradient hypothesis

The stress-gradient hypothesis (SGH) predicts that the community-wide prevalence of positive interactions, relative to negative interactions, is greater under more severe environmental conditions. Because the frequency of positive and negative interactions within a community is the aggregate of multiple pair-wise interactions, one approach to testing the SGH is to examine how pair-wise interactions vary along severity gradients. While the SGH suggests that the net outcome of an interaction should monotonically become more positive with increasing environmental severity, recent studies have suggested that the severity-interaction relationship (SIR) may rather be unimodal. We tested which of the proposed shapes of the SIR best fits the variation in the interaction between two species along two types of severity gradients on sub-Antarctic Marion Island. This was done by comparing the performance of the grass Agrostis magellanica in the presence and absence of the cushion plant Azorella selago, along both species' entire altitudinal ranges (transects spanning 4-8 km), and along a shorter (transect = 0.4 km) wind exposure gradient. Along the altitudinal transects the relative intensity, but not the absolute intensity or the importance, of the Azorella selago-Agrostis magellanica interaction increased with altitude, consistently forming a plateau-shaped SIR with a positive asymptote. Thus, while the performance of Agrostis magellanica was negatively affected by Azorella selago at low altitudes, the grass benefited from growing on the cushion plant under greater environmental severity. Along the wind exposure gradient the intensity of the interaction also became more positive with increasing environmental severity for most performance measures. This suggests that the switch from a net negative to a net positive interaction can occur across both short and long distances. Therefore, this study provides strong evidence for a plateau-shaped SIR, and confirms that the SIR is unimodal along the particular non-resource severity gradients of this study.

Automatic analysis of 3D low dose CT images for early diagnosis of lung cancer

Our long term research goal is to develop a fully automated, image-based diagnostic system for early diagnosis of pulmonary nodules that may lead to lung cancer. This paper focuses on monitoring the development of lung nodules detected in successive chest low dose (LD) CT scans of a patient. We propose a new methodology for 3D LDCT data registration which is non-rigid and involves two steps: (i) global target-to-prototype alignment of one scan to another using the learned prior appearance model followed by (ii) local alignment in order to correct for intricate relative deformations. After equalizing signals for two subsequent chest scans, visual appearance of these chest images is described using a Markov–Gibbs random field (MGRF) model with multiple pairwise interaction. An affine transformation that globally registers a target to a prototype is estimated by the gradient ascent-based maximization of a special Gibbs energy function. To get an accurate visual appearance model, we developed a new approach to automatic selection of most characteristic second-order cliques that describe pairwise interactions in the LDCT data. To handle local deformations, we displace each voxel of the target over evolving closed equi-spaced surfaces (iso-surfaces) to closely match the prototype. The evolution of the iso-surfaces is guided by a speed function in the directions that minimize distances between the corresponding voxel pairs on the iso-surfaces in both the data sets. Preliminary results on the 135 LDCT data sets from 27 patients show that the proposed accurate registration could lead to precise diagnosis and identification of the development of the detected pulmonary nodules.

The Structure of Multi-Neuron Firing Patterns in Primate Retina

Current understanding of many neural circuits is limited by our ability to explore the vast number of potential interactions between different cells. We present a new approach that dramatically reduces the complexity of this problem. Large-scale multi-electrode recordings were used to measure electrical activity in nearly complete, regularly spaced mosaics of several hundred ON and OFF parasol retinal ganglion cells in macaque monkey retina. Parasol cells exhibited substantial pairwise correlations, as has been observed in other species, indicating functional connectivity. However, pairwise measurements alone are insufficient to determine the prevalence of multi-neuron firing patterns, which would be predicted from widely diverging common inputs and have been hypothesized to convey distinct visual messages to the brain. The number of possible multi-neuron firing patterns is far too large to study exhaustively, but this problem may be circumvented if two simple rules of connectivity can be established: (1) multi-cell firing patterns arise from multiple pairwise interactions, and (2) interactions are limited to adjacent cells in the mosaic. Using maximum entropy methods from statistical mechanics, we show that pairwise and adjacent interactions accurately accounted for the structure and prevalence of multi-neuron firing patterns, explaining approximately 98% of the departures from statistical independence in parasol cells and approximately 99% of the departures that were reproducible in repeated measurements. This approach provides a way to define limits on the complexity of network interactions and thus may be relevant for probing the function of many neural circuits.

Analyzing Functional Connectivity Using a Network Likelihood Model of Ensemble Neural Spiking Activity

Analyzing the dependencies between spike trains is an important step in understanding how neurons work in concert to represent biological signals. Usually this is done for pairs of neurons at a time using correlation-based techniques. Chornoboy, Schramm, and Karr (1988) proposed maximum likelihood methods for the simultaneous analysis of multiple pair-wise interactions among an ensemble of neurons. One of these methods is an iterative, continuous-time estimation algorithm for a network likelihood model formulated in terms of multiplicative conditional intensity functions. We devised a discrete-time version of this algorithm that includes a new, efficient computational strategy, a principled method to compute starting values, and a principled stopping criterion. In an analysis of simulated neural spike trains from ensembles of interacting neurons, the algorithm recovered the correct connectivity matrices and interaction parameters. In the analysis of spike trains from an ensemble of rat hippocampal place cells, the algorithm identified a connectivity matrix and interaction parameters consistent with the pattern of conjoined firing predicted by the overlap of the neurons' spatial receptive fields. These results suggest that the network likelihood model can be an efficient tool for the analysis of ensemble spiking activity.

Hydrophobic Pairwise Interactions Stabilize α-Conotoxin MI in the Muscle Acetylcholine Receptor Binding Site

The present work delineates pairwise interactions underlying the nanomolar affinity of alpha-conotoxin MI (CTx MI) for the alpha-delta site of the muscle acetylcholine receptor (AChR). We mutated all non-cysteine residues in CTx MI, expressed the alpha(2)betadelta(2) pentameric form of the AChR in 293 human embryonic kidney cells, and measured binding of the mutant toxins by competition against the initial rate of (125)I-alpha-bungarotoxin binding. The CTx MI mutations P6G, A7V, G9S, and Y12T all decrease affinity for alpha(2)betadelta(2) pentamers by 10,000-fold. Side chains at these four positions localize to a restricted region of the known three-dimensional structure of CTx MI. Mutations of the AChR reveal major contributions to CTx MI affinity by Tyr-198 in the alpha subunit and by the selectivity determinants Ser-36, Tyr-113, and Ile-178 in the delta subunit. By using double mutant cycles analysis, we find that Tyr-12 of CTx MI interacts strongly with all three selectivity determinants in the delta subunit and that deltaSer-36 and deltaIle-178 are interdependent in stabilizing Tyr-12. We find additional strong interactions between Gly-9 and Pro-6 in CTx MI and selectivity determinants in the delta subunit, and between Ala-7 and Pro-6 and Tyr-198 in the alpha subunit. The overall results reveal the orientation of CTx MI when bound to the alpha-delta interface and show that primarily hydrophobic interactions stabilize the complex.