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An analysis of the stylized facts in financial time series is carried out. We find that, instead of the heavy tails in asset return distributions, the slow decay behaviour in autocorrelation functions of absolute returns is actually…
We report about universality of rank-integration distributions of open spaces in city space syntax similar to the famous rank-size distributions of cities (Zipf's law). We also demonstrate that the degree of choice an open space represents…
We reanalyze high resolution data from the New York Stock Exchange and find a monotonic (but not power law) variation of the mean value per trade, the mean number of trades per minute and the mean trading activity with company…
We observe the statistical properties of blogs that are expected to reflect social human interaction. Firstly, we introduce a basic normalization preprocess that enables us to evaluate the genuine word frequency in blogs that are…
We model financial transactions as random walks on activity-driven temporal networks. By enforcing fund conservation, our framework analytically derives heavy-tailed distributions for the stationary balances and transaction sizes.…
Financial markets provide an ideal frame for studying decision making in crowded environments. Both the amount and accuracy of the data allows to apply tools and concepts coming from physics that studies collective and emergent phenomena or…
We propose a general interpretation for long-range correlation effects in the activity and volatility of financial markets. This interpretation is based on the fact that the choice between `active' and `inactive' strategies is subordinated…
The remarkable success of large language pretraining and the discovery of scaling laws signify a paradigm shift in machine learning. Notably, the primary objective has evolved from minimizing generalization error to reducing approximation…
Based on empirical financial time-series, we show that the "silence-breaking" probability follows a super-universal power law: the probability of observing a large movement is inversely proportional to the length of the on-going…
Complexity develops via the incorporation of innovative properties. Chess is one of the most complex strategy games, where expert contenders exercise decision making by imitating old games or introducing innovations. In this work, we study…
Dynamical systems theory provides a framework for analyzing iterative processes and evolution over time. Within such systems, repetitive transformations can lead to stable configurations, known as attractors, including fixed points and…
Using data from gene expression databases on various organisms and tissues, including yeast, nematodes, human normal and cancer tissues, and embryonic stem cells, we found that the abundances of expressed genes exhibit a power-law…
In this paper we consider wildly ramified power series, \emph{i.e.}, power series defined over a field of positive characteristic, fixing the origin, where it is tangent to the identity. In this setting we introduce a new invariant under…
Financial volatility obeys two fascinating empirical regularities that apply to various assets, on various markets, and on various time scales: it is fat-tailed (more precisely power-law distributed) and it tends to be clustered in time.…
Words in natural language follow a Zipfian distribution whereby some words are frequent but most are rare. Learning representations for words in the "long tail" of this distribution requires enormous amounts of data. Representations of rare…
A time series that represents daily values of the WIG index (the main index of Warsaw Stock Exchange) over last 5 years is examined. Non-Gaussian features of distributions of fluctuations, namely returns, over a time scale are considered.…
We prove a law of large numbers and a functional central limit theorem for multivariate Hawkes processes observed over a time interval $[0,T]$ in the limit $T \rightarrow \infty$. We further exhibit the asymptotic behaviour of the…
In this article, we evaluate computational models of natural language with respect to the universal statistical behaviors of natural language. Statistical mechanical analyses have revealed that natural language text is characterized by…
A so called Zipf analysis portofolio management technique is introduced in order to comprehend the risk and returns. Two portofoios are built each from a well known financial index. The portofolio management is based on two approaches: one…
The empirical studies of city-size distribution show that Zipf's law and the hierarchical scaling law are linked in many ways. The rank-size scaling and hierarchical scaling seem to be two different sides of the same coin, but their…