We already know that different interaction structures can give rise to a common functionality, understood as a common macroscopic observable. Building upon this fact, here we propose network transformations that keep the collective behavior of a large system of Kuramoto oscillators invariant. We derive a method based on information theory principles, that allows us to adjust the weights of the structural interactions to map random homogeneous in-degree networks into random heterogeneous networks and vice versa, keeping synchronization values invariant.
The results of the proposed transformations reveal an interesting principle; heterogeneous networks can be mapped to homogeneous ones with local information, but the reverse process needs to exploit higher-order information. The formalism provides analytical insight to tackle real complex scenarios when dealing with uncertainty in the measurements of the underlying connectivity structure. We present a comprehensive computational study of the collective behavior emerging from the competition between self-propulsion, excluded volume interactions and velocity-alignment in a two-dimensional model of active particles.
We consider an extension of the active brownian particles model where the self-propulsion direction of the particles aligns with the one of their neighbors. However, above the flocking threshold, the system presents a richer pattern formation scenario than analogous models without alignment interactions active brownian particles or excluded volume effects Vicsek-like models. Depending on the parameter regime, the structure of the system is characterized by either a broad distribution of finite-sized polar clusters or the presence of an amorphous, highly fluctuating, large-scale traveling structure which can take a lane-like or band-like form and usually a hybrid structure which is halfway in between both.
We establish a phase diagram that summarizes collective behavior of polar active brownian particles and propose a generic mechanism to describe the complexity of the large-scale structures observed in systems of repulsive self-propelled particles.
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Several approaches to cognition and intelligence research rely on statistics-based model testing, namely, factor analysis. In the present work, we exploit the emerging dynamical system perspective putting the focus on the role of the network topology underlying the relationships between cognitive processes.
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We go through a couple of models of distinct cognitive phenomena and yet find the conditions for them to be mathematically equivalent. We find a nontrivial attractor of the system that corresponds to the exact definition of a well-known network centrality and hence stresses the interplay between the dynamics and the underlying network connectivity, showing that both of the two are relevant. Correlation matrices evince there must be a meaningful structure underlying real data. Nevertheless, the true architecture regarding the connectivity between cognitive processes is still a burning issue of research.
Regardless of the network considered, it is always possible to recover a positive manifold of correlations. Furthermore, we show that different network topologies lead to different plausible statistical models concerning the correlation structure, ranging from one to multiple factor models and richer correlation structures.
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What happens when a new social convention replaces an old one? While the possible forces favoring norm change—such as institutions or committed activists—have been identified for a long time, little is known about how a population adopts a new convention, due to the difficulties of finding representative data. Here, we address this issue by looking at changes that occurred to 2, orthographic and lexical norms in English and Spanish through the analysis of a large corpora of books published between the years and We detect three markedly distinct patterns in the data, depending on whether the behavioral change results from the action of a formal institution, an informal authority, or a spontaneous process of unregulated evolution.
We propose a simple evolutionary model able to capture all of the observed behaviors, and we show that it reproduces quantitatively the empirical data. This work identifies general mechanisms of norm change, and we anticipate that it will be of interest to researchers investigating the cultural evolution of language and, more broadly, human collective behavior. The topology of many real complex networks has been conjectured to be embedded in hidden metric spaces, where distances between nodes encode their likelihood of being connected.
Here we present empirical evidence that this geometric interpretation also applies to the weighted organization of real complex networks. We introduce a very general and versatile model and use it to quantify the level of coupling between their topology, their weights and an underlying metric space. Our model accurately reproduces both their topology and their weights, and our results suggest that the formation of connections and the assignment of their magnitude are ruled by different processes.
Identifying and quantifying dissimilarities among graphs is a fundamental and challenging problem of practical importance in many fields of science.
Current methods of network comparison are limited to extract only partial information or are computationally very demanding. Here we propose an efficient and precise measure for network comparison, which is based on quantifying differences among distance probability distributions extracted from the networks. An example of degree guided solution-substitution operation and final equation group construction for undirected networks.
Target node 1, the node whose local connecting topology is to be inferred, has only two neighbors, nodes 2 and 3. The occurring probabilities of the corresponding x 2 , x 3 configurations are listed as percentages in the left column of each panel. Solution examples of compressive sensing and K -means clustering results. Presented are the reconstruction results for a single node, the target node, for different networks and dynamical processes. Each panel is for a specific network structure and a specific type of dynamical process, where the actual and null links associated with the target node are indicated.
The compressive sensing solutions green squares are compared, elementwise, with the true values of the original connection vectors dark purple triangles , where the x axis is the index of nodes with different degree values for different network topologies and dynamics types. The target nodes and the correctly detected existent connections via the K means are marked as light blue and light purple bars, respectively.
The false negative and the false positive estimations are marked as red and gray bars, respectively. In d — f , the element values of the original connection vector are set to unity since no true weight values are given. For cases a , b , c , and f , there are no false negative detections, i. For cases a , c , and e , there are no false positive detections, i.
Structural estimation success rates and parameter estimation errors versus the normalized data amount.
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The absolute values of the errors in estimating the link weights and the nodal biases for the existent links purple squares and nonexistent links white squares are also shown. Most data points have quite small error bars, indicating the performance stability of our method. Distributions of the conditional probability estimation errors for various complex network dynamics.
A schematic illustration of reconstruction of network structure and parameter estimation for directed complex networks. Among these four nodes, there are bidirectional links between the blue and the red nodes and between the red and the green nodes. Links between other pairs of nodes are directional, if they exist. Executing compressive sensing and K -means clustering for each of the four nodes identifies its true incoming links, marked by the links with the same color of the node and pointing inward. The calculation is repeated for every node in the system.
Comparison between the conditional probabilities of the original system and that generated via the reconstructed SDBM. Comparison between the conditional probabilities of the original system and the approximator using the self-generated state configuration time series.
E 97 , — Published 28 March Abstract Revealing the structure and dynamics of complex networked systems from observed data is a problem of current interest. Research Areas. Classical statistical mechanics Network evolution Network structure. Statistical Physics Networks. Issue Vol. Authorization Required. Log In.
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Figure 1 A schematic illustration of structural reconstruction using SDBM for undirected complex networks. Figure 2 A schematic illustration of the K -means algorithm for two-dimensional data clustering.
Figure 4 An example of degree guided solution-substitution operation and final equation group construction for undirected networks. Figure 5 Solution examples of compressive sensing and K -means clustering results.
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