Related papers: Greedy algorithms and Zipf laws
We propose hypotheses describing the empirical finding of an association between the exponents of urban GDP scaling and Zipf's law for cities. These hypotheses represent various combinations of directional or reciprocal causal links between…
In this paper, we consider a novel two-dimensional randomized Kaczmarz method and its improved version with simple random sampling, which chooses two active rows with probability proportional to the square of their cross-product-like…
In this experimental study we consider Steiner tree approximations that guarantee a constant approximation of ratio smaller than $2$. The considered greedy algorithms and approaches based on linear programming involve the incorporation of…
We propose coalescent mechanism of economic grow because of redistribution of external resources. It leads to Zipf distribution of firms over their sizes, turning to stretched exponent because of size-dependent effects, and predicts…
We study here numerically the behavior of an ideal gas like model of markets having only one non-consumable commodity. We investigate the behavior of the steady-state distributions of money, commodity and total wealth, as the dynamics of…
The agent-based Yard-Sale model of wealth inequality is generalized to incorporate exponential economic growth and its distribution. The distribution of economic growth is nonuniform and is determined by the wealth of each agent and a…
We study offline reinforcement learning problems with a long-run average reward objective. The state-action pairs generated by any fixed behavioral policy thus follow a Markov chain, and the {\em empirical} state-action-next-state…
The problem of minimization of a quadratic functional depending on great number of binary variables is examined. 3 variants of minimization procedure are studied with the aid of computer simulation for spin-glass matrices. It is shown that…
A new angle of view is proposed to find the simple rules dominating complex systems and regular patterns behind random phenomena such as cities. Hierarchy of cities reflects the ubiquitous structure frequently observed in the natural world…
Is the large influence that mutual funds assert on the U.S. financial system spread across many funds, or is it is concentrated in only a few? We argue that the dominant economic factor that determines this is market efficiency, which…
Following the work of Okuyama, Takayasu and Takayasu [Okuyama, Takayasu and Takayasu 1999] we analyze huge databases of Japanese companies' financial figures and confirm that the Zipf's law, a power law distribution with the exponent -1,…
We study a deliberately simple, fully non-linguistic model of text: a sequence of independent draws from a finite alphabet of letters plus a single space symbol. A word is defined as a maximal block of non-space symbols. Within this…
We study a model of a population making a binary decision based on information spreading within the population, which is fully connected or covering a square grid. We assume that a fraction of the population wants to make the choice of the…
It is shown that the distribution of low variability periods in the activity of human heart rate typically follows a multi-scaling Zipf's law. The presence or failure of a power law, as well as the values of the scaling exponents, are…
Organizational growth processes have consistently been shown to exhibit a fatter-than-Gaussian growth-rate distribution in a variety of settings. Long periods of relatively small changes are interrupted by sudden changes in all size scales.…
Explaining empirically observed wealth and income distributions, featuring power-law tails alongside gamma or log-normal bulk shapes, challenges models that focus on either pairwise competition or individual investment mechanisms. This…
Tokenization is a fundamental step in natural language processing (NLP) and other sequence modeling domains, where the choice of vocabulary size significantly impacts model performance. Despite its importance, selecting an optimal…
In this article, the relationship between two well-accepted empirical propositions regarding the distribution of population in cities, namely, Gibrat's law and Zipf's law, are rigorously examined using the Chinese census data. Our findings…
Two fundamental issues surrounding research on Zipf's law regarding city sizes are whether and why this law holds. This paper does not deal with the latter issue with respect to why, and instead investigates whether Zipf's law holds in a…
A plethora of natural and socio-economic phenomena share a striking statistical regularity, that is the magnitude of elements decreases with a power law as a function of their position in a ranking of magnitude. Such regularity is known as…