arXiv subjects

János Török

Publications and source records attributed to János Török.

At least 19 recordsLinked to original sources

arXiv2026

Convergence criteria for self-consistent measures in bipartite networks

Many quantities that characterize network elements are defined in an explicit form and calculated directly from the network structure; examples of include several centrality measures like degree, closeness, or betweenness. However, there are also implicitly defined quantitative measures, which are usually calculated iteratively, in a self-consistent manner, like PageRank or countries' fitness / products' complexity relations. The iteration algorithms involve calculations over the entire network; therefore, their convergence properties depend on the structure of the network. Here, we focus on investigating self-consistently defined quantities in bipartite networks of two sets of nodes where the quantities in one set are determined by the quantities in the other set and vice versa. We derive an explicit convergence criterion for iterations of these quantities and describe two different approaches to improve the convergence properties. In the first one, we identify "problematic nodes" that can be removed or merged while in the second one, we introduce a regularization scheme and show how to estimate the regularization parameter.

physics.soc-ph↗

arXiv2026

Chaos in reason: How chain-of-thought LLMs can look for an answer

Large Language Models (LLMs) have achieved remarkable performance across a wide range of tasks, yet their internal dynamics remain poorly understood. In this work, we apply the tools of nonlinear dynamics and chaos theory to LLMs. By analyzing both text and hidden state trajectories, we demonstrate that LLMs exhibit hallmark signatures of chaos, including strong sensitivity to initial conditions, manifested as intermittent, jump-like divergence of nearby trajectories combined with bounded evolution, with consistent results across different distance metrics. An exact Jacobian analysis of the Transformer's sub-blocks shows that self-attention and the feed-forward network expand and propagate perturbations, while normalization and residual connections counteract this expansion and promote stability. Recurrence plots show structural similarities between LLMs and canonical chaotic systems such as the Lorenz attractor, while dimension analysis reveals fractal structures in the hidden state space, particularly pronounced in the last layers. We propose that the nonlinear coupling induced by attention mechanisms plays a key role in driving this chaotic behavior.

nlin.CD↗

arXiv2024

Homophilic organization of egocentric communities in ICT services

Members of a society can be characterized by a large number of features, such as gender, age, ethnicity, religion, social status, and shared activities. One of the main tie-forming factors between individuals in human societies is homophily, the tendency of being attracted to similar others. Homophily has been mainly studied with focus on one of the features and little is known about the roles of similarities of different origins in the formation of communities. To close this gap, we analyze three datasets from Information and Communications Technology (ICT) services, namely, two online social networks and a network deduced from mobile phone calls, in all of which metadata about individual features are available. We identify communities within egocentric networks and surprisingly find that the larger the community is, the more overlap is found between features of its members and the ego. We interpret this finding in terms of the effort needed to manage the communities; the larger diversity requires more effort such that to maintain a large diverse group may exceed the capacity of the members. As the ego reaches out to her alters on an ICT service, we observe that the first alter in each community tends to have a higher feature overlap with the ego than the rest. Moreover the feature overlap of the ego with all her alters displays a non-monotonic behaviors as a function of the ego's degree. We propose a simple mechanism of how people add links in their egocentric networks of alters that reproduces all the empirical observations and shows the reason behind non-monotonic tendency of the egocentric feature overlap as a function of the ego's degree.

cs.SI↗

arXiv2021

Evolution of shear zones in granular packings under pressure

Stress transmission in realistic granular media often occurs under external load and in the presence of boundary slip. We investigate shear localization in a split-bottom Couette cell with smooth walls subject to a confining pressure experimentally and by means of numerical simulations. We demonstrate how the characteristics of the shear zone, such as its center position and width, evolve as the confining pressure and wall slip modify the local effective friction coefficient of the material. For increasing applied pressure, the shear zone evolves toward the center of the cylinder and grows wider and the angular velocity reduces compared to the driving rate of the bottom disk. Moreover, the presence of slip promotes the transition from open shear zones at the top surface to closed shear zones inside the bulk. We also systematically vary the ratio of the effective friction near the bottom plate and in the bulk in simulations and observe the resulting impact on the surface flow profile. Besides the boundary conditions and external load, material properties such as grain size are also known to influence the effective friction coefficient. However, our numerical results reveal that the center position and width of the shear zone are insignificantly affected by the choice of the grain size as far as it remains small compared to the radius of the rotating bottom disk.

cond-mat.soft↗

arXiv2021

Deep learning based parameter search for an agent based social network model

Interactions between humans give rise to complex social networks that are characterized by heterogeneous degree distribution, weight-topology relation, overlapping community structure, and dynamics of links. Understanding such networks is a primary goal of science due to serving as the scaffold for many emergent social phenomena from disease spreading to political movements. An appropriate tool for studying them is agent-based modeling, in which nodes, representing persons, make decisions about creating and deleting links, thus yielding various macroscopic behavioral patterns. Here we focus on studying a generalization of the weighted social network model, being one of the most fundamental agent-based models for describing the formation of social ties and social networks. This Generalized Weighted Social Network (GWSN) model incorporates triadic closure, homophilic interactions, and various link termination mechanisms, which have been studied separately in the previous works. Accordingly, the GWSN model has an increased number of input parameters and the model behavior gets excessively complex, making it challenging to clarify the model behavior. We have executed massive simulations with a supercomputer and using the results as the training data for deep neural networks to conduct regression analysis for predicting the properties of the generated networks from the input parameters. The obtained regression model was also used for global sensitivity analysis to identify which parameters are influential or insignificant. We believe that this methodology is applicable for a large class of complex network models, thus opening the way for more realistic quantitative agent-based modeling.

physics.soc-ph↗

arXiv2021

Gravity Governs Shear Localization in Confined Dense Granular Flows

Prediction of flow profiles of slowly sheared granular materials is a major geophysical and industrial challenge. Understanding the role of gravity is particularly important for future planetary exploration in varying gravitational environments. Using the principle of minimization of energy dissipation, and combining experiments and variational analysis, we disentangle the contributions of the gravitational acceleration and confining pressure on shear strain localization induced by moving fault boundaries at the bottom of a granular layer. The flow profile is independent of the gravity for geometries with a free top surface. However, under a confining pressure or if the sheared layer withstands the weight of the upper layers, increasing gravity promotes the transition from closed shear zones buried in the bulk to open ones that intersect the top surface. We show that the center position and width of the shear zone and the axial angular velocity at the top surface follow universal scaling laws when properly scaled by the gravity, applied pressure, and layer thickness. Our finding that the flow profiles lie on a universal master curve opens the possibility to predict the quasistatic shear flow of granular materials in extraterrestrial environments.

cond-mat.soft↗

arXiv2021

Flow in an hourglass: particle friction and stiffness matter

Granular flow out of a silo is studied experimentally and numerically. The time evolution of the discharge rate as well as the normal force (apparent weight) at the bottom of the container is monitored. We show, that particle stiffness has a strong effect on the qualitative features of silo discharge. For deformable grains with a Young's modulus of about $Y_m\approx 40$ kPa in a silo with basal pressure of the order of 4 kPa lowering the friction coefficient leads to a gradual change in the discharge curve: the flow rate becomes filling height dependent, it decreases during the discharge process. For hard grains with a Young's modulus of about $Y_m\approx 500$ MPa the flow rate is much less sensitive to the value of the friction coefficient. Using DEM data combined with a coarse-graining methodology allows us to compute all the relevant macroscopic fields, namely, linear momentum, density and stress tensors. The observed difference in the discharge in the low friction limit is connected to a strong difference in the pressure field: while for hard grains Janssen-screening is effective, leading to high vertical stress near the silo wall and small pressure above the orifice region, for deformable grains the pressure above the orifice is larger and gradually decreases during the discharge process. We have analyzed the momentum balance in the region of the orifice (near the location of the outlet) for the case of soft particles with low friction coefficient, and proposed a phenomenological formulation that predicts the linear decrease of the flow rate with decreasing filling height.

cond-mat.soft↗

arXiv2021

Interacting jammed granular systems

More than 30 years ago Edwards and co-authors proposed a model to describe the statistics of granular packings by an ensemble of equiprobable jammed states. Experimental tests of this model remained scarce so far. We introduce a simple system to analyze statistical properties of jammed granular ensembles to test Edwards theory. Identical spheres packed in a nearly two-dimensional geometrical confinement were studied in experiments and numerical simulations. When tapped, the system evolves towards a ground state, but due to incompatible domain structures it gets trapped. Analytical calculations reproduce relatively well our simulation results, which allows us to test Edwards theory on a coupled system of two subsystems with different properties. We find that the joint system can only be described by the Edwards theory if considered as a single system due to the constraints in the stresses. The results show counterintuitive effects as in the coupled system the change in the order parameter is opposite to what is expected from the change in the compactivity.

cond-mat.stat-mech↗

arXiv2020

Plato's cube and the natural geometry of fragmentation

Plato envisioned Earth's building blocks as cubes, a shape rarely found in nature. The solar system is littered, however, with distorted polyhedra -- shards of rock and ice produced by ubiquitous fragmentation. We apply the theory of convex mosaics to show that the average geometry of natural 2D fragments, from mud cracks to Earth's tectonic plates, has two attractors: "Platonic" quadrangles and "Voronoi" hexagons. In 3D the Platonic attractor is dominant: remarkably, the average shape of natural rock fragments is cuboid. When viewed through the lens of convex mosaics, natural fragments are indeed geometric shadows of Plato's forms. Simulations show that generic binary breakup drives all mosaics toward the Platonic attractor, explaining the ubiquity of cuboid averages. Deviations from binary fracture produce more exotic patterns that are genetically linked to the formative stress field. We compute the universal pattern generator establishing this link, for 2D and 3D fragmentation.

cond-mat.soft↗

arXiv2019

Sampling networks by nodal attributes

In a social network individuals or nodes connect to other nodes by choosing one of the channels of communication at a time to re-establish the existing social links. Since available data sets are usually restricted to a limited number of channels or layers, these autonomous decision making processes by the nodes constitute the sampling of a multiplex network leading to just one (though very important) example of sampling bias caused by the behavior of the nodes. We develop a general setting to get insight and understand the class of network sampling models, where the probability of sampling a link in the original network depends on the attributes $h$ of its adjacent nodes. Assuming that the nodal attributes are independently drawn from an arbitrary distribution $ρ(h)$ and that the sampling probability $r(h_i , h_j)$ for a link $ij$ of nodal attributes $h_i$ and $h_j$ is also arbitrary, we derive exact analytic expressions of the sampled network for such network characteristics as the degree distribution, degree correlation, and clustering spectrum. The properties of the sampled network turn out to be sums of quantities for the original network topology weighted by the factors stemming from the sampling. Based on our analysis, we find that the sampled network may have sampling-induced network properties that are absent in the original network, which implies the potential risk of a naive generalization of the results of the sample to the entire original network. We also consider the case, when neighboring nodes have correlated attributes to show how to generalize our formalism for such sampling bias and we get good agreement between the analytic results and the numerical simulations.

physics.soc-ph↗

arXiv2019

Structural transition in social networks: The role of homophily

We introduce a model for the formation of social networks, which takes into account the homophily or the tendency of individuals to associate and bond with similar others, and the mechanisms of global and local attachment as well as tie reinforcement due to social interactions between people. We generalize the weighted social network model such that the nodes or individuals have $F$ features and each feature can have $q$ different values. Here the tendency for the tie formation between two individuals due to the overlap in their features represents homophily. We find a phase transition as a function of $F$ or $q$, resulting in a phase diagram. For fixed $q$ and as a function of $F$ the system shows two phases separated at $F_c$. For $F{<}F_c$ large, homogeneous, and well separated communities can be identified within which the features match almost perfectly (segregated phase). When $F$ becomes larger than $F_c$, the nodes start to belong to several communities and within a community the features match only partially (overlapping phase). Several quantities reflect this transition, including the average degree, clustering coefficient, feature overlap, and the number of communities per node. We also make an attempt to interpret these results in terms of observations on social behavior of humans.

physics.soc-ph↗

arXiv2017

Cascading collapse of online social networks

Online social networks have increasing influence on our society, they may play decisive roles in politics and can be crucial for the fate of companies. Such services compete with each other and some may even break down rapidly. Using social network datasets we show the main factors leading to such a dramatic collapse. At early stage mostly the loosely bound users disappear, later collective effects play the main role leading to cascading failures. We present a theory based on a generalised threshold model to explain the findings and show how the collapse time can be estimated in advance using the dynamics of the churning users. Our results shed light to possible mechanisms of instabilities in other competing social processes.

physics.soc-ph↗

arXiv2017

Stylized facts in social networks: Community-based static modeling

The past analyses of datasets of social networks have enabled us to make empirical findings of a number of aspects of human society, which are commonly featured as stylized facts of social networks, such as broad distributions of network quantities, existence of communities, assortative mixing, and intensity-topology correlations. Since the understanding of the structure of these complex social networks is far from complete, for deeper insight into human society more comprehensive datasets and modeling of the stylized facts are needed. Although the existing dynamical and static models can generate some stylized facts, here we take an alternative approach by devising a community-based static model with heterogeneous community sizes and larger communities having smaller link density and weight. With these few assumptions we are able to generate realistic social networks that show most stylized facts for a wide range of parameters, as demonstrated numerically and analytically. Since our community-based static model is simple to implement and easily scalable, it can be used as a reference system, benchmark, or testbed for further applications.

physics.soc-ph↗

arXiv2016

What does Big Data tell? Sampling the social network by communication channels

Big Data has become the primary source of understanding the structure and dynamics of the society at large scale. The network of social interactions can be considered as a multiplex, where each layer corresponds to one communication channel and the aggregate of all of them constitutes the entire social network. However, usually one has information only about one of the channels or even a part of it, which should be considered as a subset or sample of the whole. Here we introduce a model based on a natural bilateral communication channel selection mechanism, which for one channel leads to consistent changes in the network properties. For example, while it is expected that the degree distribution of the whole social network has a maximum at a value larger than one, we get a monotonously decreasing distribution as observed in empirical studies of single channel data. We also find that assortativity may occur or get strengthened due to the sampling method. We analyze the far-reaching consequences of our findings.

physics.soc-ph↗

arXiv2016

Understanding and coping with extremism in an online collaborative environment

The Internet has provided us with great opportunities for large scale collaborative public good projects. Wikipedia is a predominant example of such projects where conflicts emerge and get resolved through bottom-up mechanisms leading to the emergence of the largest encyclopedia in human history. Disaccord arises whenever editors with different opinions try to produce an article reflecting a consensual view. The debates are mainly heated by editors with extremist views. Using a model of common value production, we show that the consensus can only be reached if extremist groups can actively take part in the discussion and if their views are also represented in the common outcome, at least temporarily. We show that banning problematic editors mostly hinders the consensus as it delays discussion and thus the whole consensus building process. To validate the model, relevant quantities are measured both in simulations and Wikipedia which show satisfactory agreement. We also consider the role of direct communication between editors both in the model and in Wikipedia data (by analysing the Wikipedia {\it talk} pages). While the model suggests that in certain conditions there is an optimal rate of "talking" vs "editing", it correctly predicts that in the current settings of Wikipedia, more activity in talk pages is associated with more controversy.

physics.soc-ph↗

arXiv2015

Modeling the role of relationship fading and breakup in social network formation

In social networks of human individuals, social relationships do not necessarily last forever as they can either fade gradually with time, resulting in link aging, or terminate abruptly, causing link deletion, as even old friendships may cease. In this paper, we study a social network formation model where we introduce several ways by which a link termination takes place. If we adopt the link aging, we get a more modular structure with more homogeneously distributed link weights within communities than when link deletion is used. By investigating distributions and relations of various network characteristics, we find that the empirical findings are better reproduced with the link deletion model. This indicates that link deletion plays a more prominent role in organizing social networks than link aging.

physics.soc-ph↗

arXiv2014

Multilayer weighted social network model

Recent empirical studies using large-scale data sets have validated the Granovetter hypothesis on the structure of the society in that there are strongly wired communities connected by weak ties. However, as interaction between individuals takes place in diverse contexts, these communities turn out to be overlapping. This implies that the society has a multilayered structure, where the layers represent the different contexts. To model this structure we begin with a single-layer weighted social network (WSN) model showing the Granovetterian structure. We find that when merging such WSN models, a sufficient amount of interlayer correlation is needed to maintain the relationship between topology and link weights, while these correlations destroy the enhancement in the community overlap due to multiple layers. To resolve this, we devise a geographic multilayer WSN model, where the indirect interlayer correlations due to the geographic constraints of individuals enhance the overlaps between the communities and, at the same time, the Granovetterian structure is preserved.

physics.soc-ph↗

arXiv2014

Modeling Social Dynamics in a Collaborative Environment

Wikipedia is a prime example of today's value production in a collaborative environment. Using this example, we model the emergence, persistence and resolution of severe conflicts during collaboration by coupling opinion formation with article editing in a bounded confidence dynamics. The complex social behavior involved in editing articles is implemented as a minimal model with two basic elements; (i) individuals interact directly to share information and convince each other, and (ii) they edit a common medium to establish their own opinions. Opinions of the editors and that represented by the article are characterised by a scalar variable. When the pool of editors is fixed, three regimes can be distinguished: (a) a stable mainstream article opinion is continuously contested by editors with extremist views and there is slow convergence towards consensus, (b) the article oscillates between editors with extremist views, reaching consensus relatively fast at one of the extremes, and (c) the extremist editors are converted very fast to the mainstream opinion and the article has an erratic evolution. When editors are renewed with a certain rate, a dynamical transition occurs between different kinds of edit wars, which qualitatively reflect the dynamics of conflicts as observed in real Wikipedia data.

physics.soc-ph↗