Local Interaction Structure Research Articles

Local and regional processes drive distance decay in structure in a spatial multilayer plant-pollinator network.

Understanding spatial variation in species distribution and community structure is at the core of community ecology. Nevertheless, the effect of distance on metacommunity structure remains little studied. We examine how plant-pollinator community structure changes across geographical distances at a regional scale and disentangle its underlying local and regional processes. We use a multilayer network to represent linked plant-pollinator communities as a metacommunity in the Canary Islands. We used modularity (i.e. the extent to which the community is partitioned into groups of densely interacting species) to quantify distance decay in structure across space. In multilayer modularity, the same species can belong to different modules in different communities, and modules can span communities. This enabled quantifying how similarity in module composition varied with distance between islands. We developed three null models, each controlling for a separate component of the multilayer network, to disentangle the role of species turnover, interaction rewiring and local factors in driving distance decay in structure. We found a pattern of distance decay in structure, indicating that islands tended to share fewer modules with increasing distance. Species turnover (but not interaction rewiring) was the primary regional process triggering distance decay in structure. Local interaction structure also played an essential role in determining the structure similarity of communities at a regional scale. Therefore, local factors that determine species interactions occurring at a local scale drive distance decay in structure at a regional scale. Our work highlights the interplay between local and regional processes underlying community structure. The methodology, and specifically the null models, we developed provides a general framework for linking communities in space and testing different hypotheses regarding the factors generating spatial structure.

Portfolio Correlations in the Bank-Firm Credit Market of Japan

The recent global financial crisis has shown portfolio correlations between agents as one of the major channels of risk contagion and amplification. In this work, we analyse the structure and dynamics of the cross-correlation matrix of banks’ loan portfolios in the yearly bank-firm credit network of Japan during the period from 1980 to 2012. Using the methods of Random Matrix Theory (RMT), Principal Component Analysis and complex networks, we aim to detect non-random patterns in the empirical cross-correlations as well as to identify different states of such correlations over time. Our findings suggest that although a majority of portfolio correlations between banks in lending relations to firms are contributed by noise, the top largest eigenvalues always deviate from the random bulk explained by RMT, indicating the presence of non-random patterns governing the correlation dynamics. In particular, we show that this dynamics is mainly driven by a global common factor and a couple of “groups” factors. Furthermore, different states in the credit market can be identified based on the evolution of eigenvalues and associated eigenvectors. For example, during the asset price bubble period in Japan from 1986 to 1991, we find that banks’ loan portfolios tend to be more correlated, showing a significant increase in the level of systemic risk in the credit market. In addition, building Planar Maximally Filtered Graphs from the correlations of different eigenmodes, notably, we observe that the local interaction structure between banks changes in different periods. Typically, when the dominance of a group of banks in one period gradually vanishes, the credit market starts to build-up a different structure in the next period in which another group of banks will become the main actors in the backbone of the cross-correlations.

How motifs condition critical thresholds for tipping cascades in complex networks: Linking micro- to macro-scales.

In this study, we investigate how specific micro-interaction structures (motifs) affect the occurrence of tipping cascades on networks of stylized tipping elements. We compare the properties of cascades in Erdős-Rényi networks and an exemplary moisture recycling network of the Amazon rainforest. Within these networks, decisive small-scale motifs are the feed forward loop, the secondary feed forward loop, the zero loop, and the neighboring loop. Of all motifs, the feed forward loop motif stands out in tipping cascades since it decreases the critical coupling strength necessary to initiate a cascade more than the other motifs. We find that for this motif, the reduction of critical coupling strength is 11% less than the critical coupling of a pair of tipping elements. For highly connected networks, our analysis reveals that coupled feed forward loops coincide with a strong 90% decrease in the critical coupling strength. For the highly clustered moisture recycling network in the Amazon, we observe regions of a very high motif occurrence for each of the four investigated motifs, suggesting that these regions are more vulnerable. The occurrence of motifs is found to be one order of magnitude higher than in a random Erdős-Rényi network. This emphasizes the importance of local interaction structures for the emergence of global cascades and the stability of the network as a whole.

Fairness Concerns on Networks

We develop a model of social preferences for network games and study its predictions in a local public goods game with multiple equilibria. The key feature of our model is that players’ social preferences are heterogeneous. This gives room for disagreement between players about the “right” payoff ordering. When preferences are compatible, however, players succeed in coordinating on a refined set of equilibria. How easily the requirements for preference compatibility are met crucially depends on a property of the network structure: neighborhood nestedness. This means that equilibrium selection succeeds in small, tightly connected structures but also in very centralized networks. It fails, in contrast, in loosely connected local interaction structures. We experimentally validate our predictions and confirm the mechanisms on which our theory builds.

Portfolio Correlations in the Bank-Firm Credit Market of Japan

The recent global financial crisis has shown portfolio correlations between agents as one of the key channels of risk contagion and amplification. In this work, we analyse the structure and dynamics of the cross-correlation matrix of banks' loan portfolios in the yearly bank-firm credit network of Japan during the period from 1980 to 2012. Employing the methods of Random Matrix Theory (RMT), Principal Component Analysis (PCA) and complex networks, we aim to detect non-random patterns in the empirical cross-correlations as well as to identify different states of such correlations over time. Our findings suggest that although a majority of correlations between banks in lending relations to firms are contributed by noise, the top largest eigenvalues always deviate from the random bulk explained by RMT, indicating the presence of patterns governing such correlations. In particular, the correlation dynamics are mainly driven by a global common factor and a couple of groups factors. Furthermore, different states in the market can be identified based on the analysis of the evolution of eigenvalues and associated eigenvectors. For example, during the asset price bubble period in Japan from 1986 to 1991, we find that banks' loan portfolios tend to be more correlated, showing a significant increase in the level of systemic risk in the credit market. In addition, building dynamically Planar Maximally Filtered Graphs (PMFG) from the correlations of different eigenmodes, notably, we observe that the local interaction structure between banks changes in different periods. In particular, typically when the dominance of a group of banks in one period gradually disappears, the credit market starts to build-up a different structure in the next period in which another group of banks will dominate in the backbone of the cross-correlations.

Adaptation, coordination, and local interactions via distributed approachability

This paper investigates the relation between cooperation, competition, and local interactions in large distributed multi-agent systems. The main contribution is the game-theoretic problem formulation and solution approach based on the new framework of distributed approachability, and the study of the convergence properties of the resulting game model. Approachability theory is the theory of two-player repeated games with vector payoffs, and distributed approachability is here presented for the first time as an extension to the case where we have a team of agents cooperating against a team of adversaries under local information and interaction structure. The game model turns into a nonlinear differential inclusion, which after a proper design of the control and disturbance policies, presents a consensus term and an exogenous adversarial input. Local interactions enter into the model through a graph topology and the corresponding graph-Laplacian matrix. Given the above model, we turn the original questions on cooperation, competition, and local interactions, into convergence properties of the differential inclusion. In particular, we prove convergence and exponential convergence conditions around zero under general Markovian strategies. We illustrate our results in the case of decentralized organizations with multiple decision-makers.

Contextual Interactions in Grating Plaid Configurations Are Explained by Natural Image Statistics and Neural Modeling.

Processing natural scenes requires the visual system to integrate local features into global object descriptions. To achieve coherent representations, the human brain uses statistical dependencies to guide weighting of local feature conjunctions. Pairwise interactions among feature detectors in early visual areas may form the early substrate of these local feature bindings. To investigate local interaction structures in visual cortex, we combined psychophysical experiments with computational modeling and natural scene analysis. We first measured contrast thresholds for 2 × 2 grating patch arrangements (plaids), which differed in spatial frequency composition (low, high, or mixed), number of grating patch co-alignments (0, 1, or 2), and inter-patch distances (1° and 2° of visual angle). Contrast thresholds for the different configurations were compared to the prediction of probability summation (PS) among detector families tuned to the four retinal positions. For 1° distance the thresholds for all configurations were larger than predicted by PS, indicating inhibitory interactions. For 2° distance, thresholds were significantly lower compared to PS when the plaids were homogeneous in spatial frequency and orientation, but not when spatial frequencies were mixed or there was at least one misalignment. Next, we constructed a neural population model with horizontal laminar structure, which reproduced the detection thresholds after adaptation of connection weights. Consistent with prior work, contextual interactions were medium-range inhibition and long-range, orientation-specific excitation. However, inclusion of orientation-specific, inhibitory interactions between populations with different spatial frequency preferences were crucial for explaining detection thresholds. Finally, for all plaid configurations we computed their likelihood of occurrence in natural images. The likelihoods turned out to be inversely related to the detection thresholds obtained at larger inter-patch distances. However, likelihoods were almost independent of inter-patch distance, implying that natural image statistics could not explain the crowding-like results at short distances. This failure of natural image statistics to resolve the patch distance modulation of plaid visibility remains a challenge to the approach.

Modeling criminality: the impact of emotions, norms and interaction structures

Criminal behavior has been explained in the literature by rational or normative arguments. We propose a game theory framework of criminal behavior integrating both concepts. Specifically the modeling includes three factors, namely the gain from criminality, the adherence to a legal norm and social pressure from criminal peers. We show that criminality cannot be lower with increasing gain from criminality, lower adherence to the legal norm or higher social pressure from criminal peers. Finally, we observe by agent-based simulations that small local interaction structures lead to spatial segregation in criminality in the case where a polymorphic equilibrium is expected.

Multivariate Spartan spatial random field models

This paper introduces a family of stationary multivariate spatial random fields with D scalar components that extend the scalar model of Gibbs random fields with local interactions (i.e., Spartan spatial random fields). We derive permissibility conditions for Spartan multivariate spatial random fields with a specific structure of local interactions. We also present explicit expressions for the respective matrix covariance functions obtained at the limit of infinite spectral cutoff in one, two and three spatial dimensions. Finally, we illustrate the proposed covariance models by means of simulated bivariate time series and two-dimensional random fields.

Structure of local interactions in complex financial dynamics.

With the network methods and random matrix theory, we investigate the interaction structure of communities in financial markets. In particular, based on the random matrix decomposition, we clarify that the local interactions between the business sectors (subsectors) are mainly contained in the sector mode. In the sector mode, the average correlation inside the sectors is positive, while that between the sectors is negative. Further, we explore the time evolution of the interaction structure of the business sectors, and observe that the local interaction structure changes dramatically during a financial bubble or crisis.

Long-run equilibria, dominated strategies, and local interactions

We revisit a result by Kim and Wong (2010) showing that under global interactions any strict Nash equilibrium of a coordination game can be supported as long run equilibrium by properly adding dominated strategies. We show that in the circular city model of local interactions and in the torus model of local interactions the selection of 12-dominant strategies remains when adding strictly dominated strategies if interaction is sufficiently local. Conversely, if the local interaction structure is “central” in the circular city model any equilibrium strategy of the original game can be supported as long run equilibrium by adding properly suited dominated strategies.

Electronic structure calculations and physicochemical experiments quantify the competitive liquid ion association and probe stabilisation effects for nitrobenzospiropyran in phosphonium-based ionic liquids

Liquid ion association in ionic liquids (ILs) has been examined using a comprehensive series of electronic structure calculations that measure the relative extents of ion association and probe stabilisation for the photochromic dye nitrobenzospiropyran (BSP) in a range of ILs featuring both long-tailed phosphonium cations and short-tailed imidazolium cations, paired with both chloride and NTf(2) anions. New physicochemical experiments measured the photochromic properties of BSP in the phosphonium-based room temperature ILs. Taken together, the computed complexation energies and measured spectroscopic properties support recent Walden plots of unusual conductivity-viscosity behaviour obtained for the same ILs and reveal some new features in the atom-scale structure and energetics of local, ion-ion and ion-molecule interactions. Calculations show inter-ion interactions strengthened by between 0.4 and 0.7 eV as stronger constituent ions are used, which contributes to the longer range rigidity of the Cl-based IL structure as reflected in the doubled |zwitterion → closed| probe relaxation time measured for Cl(-)vs. NTf(2)(-) in phosphonium-based ILs. Calculations further reveal a similar, approximately 0.6-0.7 eV maximum "residual" IL headgroup-mediated probe stabilisation potentially available for the anion-probe-cation complexes via the stabilising interaction that remains following the "quenching" interaction between the IL anion and cation. This potential stabilisation, however, is offset by both longer-range charge networks, beyond the scope of the current purely quantum mechanical simulations, and also energetic penalties for disruption of the highly-interdigitated alkyl tail networks in the phosphonium-based ILs which may be estimated from known diffusion data. Overall the electronic calculations of local, individual ion-ion and ion-molecule interactions serve to clarify some of the measured physicochemical properties and provide new data for the development of classical force field-based approaches to measure also the longer range effects that, together with the electronic effects, provide the condensed phase IL structure and properties. More generally, the combined simulation and experimental results serve as a further example of how both the polar hydrophilic headgroup and non-polar hydrophobic tail of the constituent ions serve as distinct targets for IL rational design.

Local Interaction on Random Graphs

We analyze dynamic local interaction in population games where the local interaction structure (modeled as a graph) can change over time: A stochastic process generates a random sequence of graphs. This contrasts with models where the initial interaction structure (represented by a deterministic graph or the realization of a random graph) cannot change over time.

Structural characterization and modeling of ncRNA–protein interactions

Recent studies have suggested that noncoding RNA (ncRNA) molecules could play an important role in the regulatory architecture of eukaryotic cells. This new RNA-based regulation might indicate the existence of a hidden layer in the central dogma. In spite of its importance, the large-scale structure as well as the local interaction pattern of the ncRNA regulatory network has not been investigated. In this work, we collected regulatory interactions between ncRNA molecules and their regulated protein targets. We then constructed the ncRNA–protein interaction network corresponding to six model organisms, including Homo sapiens. The large-scale network analysis of ncRNA–protein interactions revealed a high degree of similarity for the degree distribution to that of the transcription regulatory network. Moreover, characterization of the local interaction structure of these networks based on motifs abundance also reveals significant similarities between ncRNA–protein and TFs–gene regulatory networks. Based on the identified motif abundance, we propose an evolutionary model that rebuilds the degree distribution and predicts the observed degree exponent. Taken together, our findings offer insights into the noncoding RNA-mediated regulation and provide knowledge about its structure and evolutionary mechanisms.

Effects of strategy-migration direction and noise in the evolutionary spatial prisoner’s dilemma

Spatial games are crucial for understanding patterns of cooperation in nature (and to some extent society). They are known to be more sensitive to local symmetries than, e.g., spin models. This paper concerns the evolution of the prisoner's dilemma game on regular lattices with three different types of neighborhoods--the von Neumann, Moore, and kagomé types. We investigate two kinds of dynamics for the players to update their strategies (that can be unconditional cooperator or defector). Depending on the payoff difference, an individual can adopt the strategy of a random neighbor [a voter-model-like dynamics (VMLD)] or impose its strategy on a random neighbor, i.e., invasion-process-like dynamics (IPLD). In particular, we focus on the effects of noise, in combination with the strategy dynamics, on the evolution of cooperation. We find that VMLD, compared to IPLD, better supports the spreading and sustaining of cooperation. We see that noise has nontrivial effects on the evolution of cooperation: maximum cooperation density can be realized either at a medium noise level, in the limit of zero noise or in both these regions. The temptation to defect and the local interaction structure determine the outcome. Especially, in the low noise limit, the local interaction plays a crucial role in determining the fate of cooperators. We elucidate these both by numerical simulations and mean-field cluster approximation methods.

Unraveling the functional interaction structure of a biomolecular network through alternate perturbation of initial conditions

Various approaches attempting to infer the functional interaction structure of a hidden biomolecular network from experimental time-series measurements have been developed; however, due to both experimental limitations and methodological complexities, a large majority of these approaches have been unsuccessful. In particular, with respect to the elucidation of such networks, there are (i) a dimensionality problem: too many network nodes with too few available sampling points, (ii) a computational complexity problem: exponential complexity if a priori information is unavailable for regulatory nodes, and (iii) an experimental measurement problem: no guidelines for an appropriate experimental design for distinguishing direct and indirect influences among network nodes. Here, we sought to develop a new methodology capable of identifying the correct functional interaction structure with only a few sampling points through relatively simple computations. We also attempted to provide guidelines for an experimental design capable of supporting this methodology by taking proper measurements of the direct influences among the network nodes. In the present study, we considered an experiment where measurements were taken at two sampling time points with alternate perturbation (up-regulation or down-regulation) of initial conditions while keeping the same initial conditions for unperturbed network nodes, and propose a new method of identifying the functional interaction structure from such measurements. The proposed method is able to avoid the dimensionality problem caused by the practically limited number of sampling time points, and does not suffer from the computational complexity problem, as it only uses a simple algebra based on the Mean Value Theorem (see Supplementary mathematical descriptions) without any other complicated computation. In addition, we provide a detailed guideline for an experimental design that can take proper measurements of the direct influences among the network nodes through perturbation of initial conditions. The proposed method is particularly useful for cases investigating the local interaction structure around a specific network node of interest. An example, based on simulated data, is provided to illustrate the proposed method.

The annotation of RNA motifs

The recent deluge of new RNA structures, including complete atomic-resolution views of both subunits of the ribosome, has on the one hand literally overwhelmed our individual abilities to comprehend the diversity of RNA structure, and on the other hand presented us with new opportunities for comprehensive use of RNA sequences for comparative genetic, evolutionary and phylogenetic studies. Two concepts are key to understanding RNA structure: hierarchical organization of global structure and isostericity of local interactions. Global structure changes extremely slowly, as it relies on conserved long-range tertiary interactions. Tertiary RNA–RNA and quaternary RNA–protein interactions are mediated by RNA motifs, defined as recurrent and ordered arrays of non-Watson–Crick base-pairs. A single RNA motif comprises a family of sequences, all of which can fold into the same three-dimensional structure and can mediate the same interaction(s). The chemistry and geometry of base pairing constrain the evolution of motifs in such a way that random mutations that occur within motifs are accepted or rejected insofar as they can mediate a similar ordered array of interactions. The steps involved in the analysis and annotation of RNA motifs in 3D structures are: (a) decomposition of each motif into non-Watson–Crick base-pairs; (b) geometric classification of each basepair; (c) identification of isosteric substitutions for each basepair by comparison to isostericity matrices; (d) alignment of homologous sequences using the isostericity matrices to identify corresponding positions in the crystal structure; (e) acceptance or rejection of the null hypothesis that the motif is conserved.

Conventions and Local Interaction Structures: Experimental Evidence

We present a series of experimental coordination games with a payoff-dominant and a risk-dominant Nash equilibrium. We examine how much local interaction structures affect players' strategy choices. Our three major observations are the following: First, local interaction with open neighborhoods along a circle leads to less coordination on the payoff-dominant equilibrium than interaction in closed neighborhoods. Second, when players are allocated around a circle, the neighborhood size has, in the long run, no effect on the players' strategy choices. Third, with the same neighborhood size, players allocated on a lattice tend less than players allocated around a circle to coordinate on the payoff-dominant equilibrium. This is true even though the players are given exactly the same instructions. Journal of Economic Literature Classification Numbers: C72, C92.

Cooperation, Mimesis, and Local Interaction

In a population with a local interaction structure, where individuals interact with their neighbors and learning is by way of imitating a successful neighbor, cooperation is shown to be a stable strategy that cannot easily be eliminated from the population.

Stochastic learning and the evolution of conventions

This paper shows that aspiration driven, stochastic learning processes can enable the members of a population to reach more efficient conventions, which are modeled as equilibria of a coordination game. As opposed to adaptation processes based on either myopic optimization or imitating behaviour, which generally select the risk dominant equilibrium, the present paper provides conditions under which the efficient equilibrium is selected, even if it is risk dominated by another equilibrium. Further, the impact of players' aspiration levels on the existence and local stability of a convention is analyzed. In general, higher aspirations induce more efficient outcomes. In addition, in the case of a local interaction structure there exist an inverse relation between the size of the individual neighbourhoods and the aspiration level required in order to sustain efficient outcomes.