arXiv subjects

Zoltán Néda

Publications and source records attributed to Zoltán Néda.

At least 19 recordsLinked to original sources

arXiv2025

Does Excellence Correspond to Universal Inequality Level?

We study the inequality of citations received for different publications of various researchers and Nobel laureates in Physics, Chemistry, Medicine and Economics using Google Scholar data from 2012 to 2024. Citation distributions are found to be highly unequal, with even greater disparity among Nobel laureates. Measures of inequality, such as the Gini and Kolkata indices, emerge as useful indicators for distinguishing Nobel laureates from others. Such high inequality corresponds to growing critical fluctuations, suggesting that excellence aligns with an imminent (self-organized dynamical) critical point. Additionally, Nobel laureates exhibit systematically lower values of the Tsallis--Pareto parameter $ b $ and Shannon entropy, indicating more structured citation distributions. We also analyze the inequality in Olympic medal tallies across countries and find similar levels of disparity. Our results suggest that inequality measures can serve as proxies for competitiveness and excellence.

physics.soc-ph↗

arXiv2024

Jackpot statistics, a physicist's approach

At a first glance lottery is a form of gambling, a game in which the chances of winning is extremely small. But upon a deeper look, considering that the Jackpot prize of lotteries is a result of the active participation of millions of players, we come to the conclusion that the interaction of the simple rules with the high number of players creates an emergent complex system. Such a system is characterized by its time-series that presents some interesting properties. Given the inherent stochastic nature of this game, it can be described within a mean-field type approach, such as the one implemented in the Local Growth and Global Reset (LGGR) model. We argue that the Jackpot time-series behaves ergodic for six lotteries with diverse formats and player pools. Specifying this consideration in the framework of the LGGR model, we model the lotteries with growth rates confirmed by the time-series. The reset rate is deduced mathematically and confirmed by data. Given these parameters we calculate the probability density of the Jackpot prizes, that fits well the empirically observed ones. We propose to use a single w parameter, as the product of the player pools found under the jurisdiction of the lottery and the chance that a single lottery ticket wins.

physics.data-an↗

arXiv2023

Tree size distribution as the stationary limit of an evolutionary master equation

The diameter distribution of a given species of deciduous trees in mature, temperate zone forests is well approximated by a Gamma distribution. Here we give new experimental evidence for this conjecture by analyzing deciduous tree size data in mature semi-natural forest and ancient, traditionally managed wood-pasture from Central Europe. These distribution functions collapse on a universal shape if the tree sizes are normalized to the mean value in the considered sample. A novel evolutionary master equation is used to model the observed distribution. The model incorporates three probabilistic processes: tree growth, mortality and diversification. By using simple, and realistic state dependent kernel functions for the growth and reset rates together with an assumed multiplicative dilution due to diversification, the stationary solution of the master equation yields the experimentally observed Gamma distribution. The model as it is formulated allows analytically compact solution and has only two fitting parameters whose values are consistent with the experimental data for the growth and reset processes. Our results suggest also that tree size statistics can be used to infer woodland naturalness.

q-bio.PE↗

arXiv2023

Gintropic Scaling of Scientometric Indexes

The most frequently used indicators for the productivity and impact of scientists are the total number of publication ($N_{pub}$), total number of citations ($N_{cit}$) and the Hirsch (h) index. Since the seminal paper of Hirsch, in 2005, it is largely debated whether the h index can be considered as an indicator independent of $N_{pub}$ and $N_{cit}$. Exploiting the Paretian form for the distribution of citations for the papers authored by a researcher, here we discuss scaling relations between h, $N_{pub}$ and $N_{cit}$. The analysis incorporates the Gini index as an inequality measure of citation distributions and a recently proposed inequality kernel, gintropy (resembling to the entropy kernel). We find a new upper bound for the h value as a function of the total number of citations, confimed on massive data collected from Google Scholar. Our analyses reveals also that the individualized Gini index calculated for the citations received by the publications of an author peaks around 0.8, a value much higher than the one characteristic for the usual socio-economic inequalities.

cs.DL↗

arXiv2022

Computational fluid dynamics approach for understanding oscillating and interacting convective flows

A 2D numerical hydrodynamics approach is considered for modelling recent experimental results on the oscillation and collective behavior of convective flows. Our simulations consider the rising dynamics of heated fluid columns in a gravitational field. Simulations are done on two entirely different length-scales, showing also the generality of the investigated phenomena. For the flow of a single heated fluid column, the effect of the inflow yield and the nozzle diameter is studied. In agreement with the experiments, for a constant nozzle diameter the oscillation frequency increases approximately linearly as a function of the the flow yield and for a constant flow yield the frequency decreases as a power law with the increasing nozzle diameter. Concerning the collective behavior of two nearby flow we find a counter-phase synchronization of the oscillations and an increasing trend in the common oscillation frequency when the distance between the flows is decreased. These results are again in agreement with the experimental findings.

physics.flu-dyn↗

arXiv2022

Flickering candle flames and their collective behavior

Oscillation and collective behavior of diffusion flames is a fascinating phenomena. Considering candle bundles with different sizes in variable oxygen concentration, the flickering dynamics of the flames are experimentally and theoretically investigated. Trends for the flickering frequency as a function of the candle number in the bundle and oxygen concentration is revealed for various topologies of the candles packing. The collective behavior of the flames as a function of their separation distance is studied by measuring an appropriate synchronization order parameter and trough the common oscillation frequency. In agreement with previous results we find a discontinuous phase transition between an in-phase synchronized state at small separation distance and a counter-phase synchronized state at larger separation distances. A previously used dynamical model is modified in order to accommodate our experimental findings.

physics.pop-ph↗

arXiv2021

Wealth distribution in villages. Transition from socialism to capitalism in view of exhaustive wealth data and a master equation approach

Socio-economic inequalities derived from an exhaustive wealth distribution is studied in a closed geographical region from Transylvania (Romania). Exhaustive wealth data is computed from the agricultural records of the Sancraiu commune for three different economic situations. The gathered data is spanning two different periods from the communist economy and the present situation after 31 years of free market economy in Romania. The local growth and reset model based on an analytically solvable master equation is used to describe the observed data. The model with realistically chosen growth and reset rates is successful in describing both the experimentally observed distributions and the inequality indexes (Lorenz curve, Gini coefficient and Pareto point) derived from this data. The observed changes in these inequality measures are discussed in the context of the relevant socio-economic conditions.

physics.soc-ph↗

arXiv2021

Oscillation and collective behavior in convective flows

Oscillation and collective behavior in convection-driven fluid columns are investigated and discussed in analogy with similar phenomenon observed for the flickering flames of candle bundles. It is shown experimentally that an ascending circular Helium gas column performs an oscillation which is similar in several aspects to the oscillation of diffusion flames. Increasing the nozzle diameter leads to a decrease in the oscillation frequency, while increasing the flow rate results in an increase in this frequency. For helium columns oscillating at nearby frequency and placed close to each other anti-phase synchronization and beating phenomena is observed. A simple toy-model based on elementary hydrodynamics describes the observed oscillations and leads to oscillation frequencies in the right order of magnitude.

physics.flu-dyn↗

arXiv2020

Gintropy: Gini index based generalization of Entropy

Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index on the other hand is an established measure for social and economical inequalities in a society. In this paper we explore the mathematical similarities and connections in these two quantities and introduce a new measure that is capable to connect these two at an interesting analogy level. This supports the idea that a generalization of the Gibbs--Boltzmann--Shannon entropy, based on a transformation of the Lorenz curve, can properly serve in quantifying different aspects of complexity in socio- and econo-physics.

physics.soc-ph↗

arXiv2020

Synchronization patterns in rings of time-delayed Kuramoto oscillators

Phase-locked states with a constant phase shift between the neighboring oscillators are studied in rings of identical Kuramoto oscillators with time-delayed nearest-neighbor coupling. The linear stability of these states is derived and it is found that the stability maps for the dimensionless equations show a high level of symmetry. The size of the attraction basins is numerically investigated. These sizes are changing periodically over several orders of magnitude as the parameters of the model are varied. Simple heuristic arguments are formulated to understand the changes in the attraction basin sizes and to predict the most probable states when the system is randomly initialized.

nlin.PS↗

arXiv2019

Pattern selection in a ring of Kuramoto oscillators

Emergence of generalized synchronization patterns in a ring of identical and locally coupled Kuramoto-type rotators are investigated by different methods. These approaches offer a useful visual picture for understanding the complexity of the dynamics in the high dimensional state-space of this system. Beside the known stable stationary points novel unstable states are revealed. We find that the prediction of the final stationary state is limited by the presence of such saddle points. This is illustrated by considering and comparing two different attempts for forecasting the final stationary state

nlin.PS↗

arXiv2017

Entropic Distance for Nonlinear Master Equation

More and more works deal with statistical systems far from equilibrium, dominated by unidirectional stochastic processes augmented by rare resets. We analyze the construction of the entropic distance measure appropriate for such dynamics. We demonstrate that a power-like nonlinearity in the state probability in the master equation naturally leads to the Tsallis (Havrda-Charvát, Aczél-Daróczy) q-entropy formula in the context of seeking for the maximal entropy state at stationarity. A few possible applications of a certain simple and linear master equation to phenomena studied in statistical physics are listed at the end.

cond-mat.stat-mech↗

arXiv2017

Cell-size distribution and scaling in a one-dimensional KJMA lattice model with continuous nucleation

The Kolmogrov-Johnson-Mehl-Avrami (KJMA) growth model is considered on a one-dimensional (1D) lattice. Cells can growth with constant speed and continuously nucleate on the empty sites. We offer an alternative, mean-field like approach for describing theoretically the dynamics and derive an analytical cell-size distribution function. Our method reproduces the same scaling laws as the KJMA theory and has the advantage that it leads to a simple closed form for the cell-size distribution function. It is shown that a Weibull distribution is appropriate for describing the final cell-size distribution. The results are discussed in comparison with Monte Carlo simulation data.

cond-mat.soft↗

arXiv2017

Science and Facebook: the same popularity law!

The distribution of scientific citations for publications selected with different rules (author, topic, institution, country, journal, etc.) collapse on a single curve if one plots the citations relative to their mean value. We find that the distribution of shares for the Facebook posts re-scale in the same manner to the very same curve with scientific citations. This finding suggests that citations are subjected to the same growth mechanism with Facebook popularity measures, being influenced by a statistically similar social environment and selection mechanism. In a simple master-equation approach the exponential growth of the number of publications and a preferential selection mechanism leads to a Tsallis-Pareto distribution offering an excellent description for the observed statistics. Based on our model and on the data derived from PubMed we predict that according to the present trend the average citations per scientific publications exponentially relaxes to about 4.

physics.soc-ph↗

arXiv2016

Dynamical Stationarity as a Result of Sustained Random Growth

In sustained growth with random dynamics stationary distributions can exist without detailed balance. This suggests thermodynamical behavior in fast growing complex systems. In order to model such phenomena we apply both a discrete and a continuous master equation. The derivation of elementary rates from known stationary distributions is a generalization of the fluctuation--dissipation theorem. Entropic distance evolution is given for such systems. We reconstruct distributions obtained for growing networks, particle production, scientific citations and income distribution.

cond-mat.stat-mech↗

arXiv2016

Equilibrium distributions in entropy driven balanced processes

For entropy driven balanced processes we obtain final states with Poisson, Bernoulli, negative binomial and Pólya distributions. We apply this both for complex networks and particle production. For random networks we follow the evolution of the degree distribution, $P_n$, in a system where a node can activate $k$ fixed connections from $K$ possible partnerships among all nodes. The total number of connections, $N$, is also fixed. For particle physics problems $P_n$ is the probability of having $n$ particles (or other quanta) distributed among $k$ states (phase space cells) while altogether a fixed number of $N$ particles reside on $K$ states.

cond-mat.stat-mech↗

arXiv2016

Time-scale effects on the gain-loss asymmetry in stock indices

The gain-loss asymmetry, observed in the inverse statistics of stock indices is present for logarithmic return levels that are over $2\%$, and it is the result of the non-Pearson type auto-correlations in the index. These non-Pearson type correlations can be viewed also as functionally dependent daily volatilities, extending for a finite time interval. A generalized time-window shuffling method is used to show the existence of such auto-correlations. Their characteristic time-scale proves to be smaller (less than $25$ trading days) than what was previously believed. It is also found that this characteristic time-scale has decreased with the appearance of program trading in the stock market transactions. Connections with the leverage effect are also established.

q-fin.ST↗

arXiv2013

Chaos on the conveyor belt

The dynamics of a spring-block train placed on a moving conveyor belt is investigated both by simple experiments and computer simulations. The first block is connected by spring to an external static point, and due to the dragging effect of the belt the blocks undergo complex stick-slip dynamics. A qualitative agreement with the experimental results can only be achieved by taking into account the spatial inhomogeneity of the friction force on the belt's surface, modeled as noise. As a function of the velocity of the conveyor belt and the noise strength, the system exhibits complex, self-organized critical, sometimes chaotic dynamics and phase transition-like behavior. Noise induced chaos and intermittency is also observed. Simulations suggest that the maximum complexity of the dynamical states is achieved for a relatively small number of blocks, around five.

nlin.CD↗