Narrow Results

We investigate whether the fractal markets hypothesis and its focus on liquidity and investment horizons give reasonable predictions about the dynamics of the financial markets during turbulences such as the Global Financial Crisis of late 2000s. Compared to the mainstream efficient markets hypothesis, the fractal markets hypothesis considers the financial markets as complex systems consisting of many heterogenous agents, which are distinguishable mainly with respect to their investment horizon. In the paper, several novel measures of trading activity at different investment horizons are introduced through the scaling of variance of the underlying processes. On the three most liquid US indices — DJI, NASDAQ and S&P500 — we show that the predictions of the fractal markets hypothesis actually fit the observed behavior adequately.

Experimental data on transverse momentum spectra of strange particles $(K_S^0,K^{-},K^{\ast 0},\varphi ,\mathrm{\Lambda },{\mathrm{\Lambda }}^{\ast },{\mathrm{\Sigma }}^{\ast },{\mathrm{\Xi }}^{-},\mathrm{\Omega })$ produced in $pp$ collisions at $\sqrt{s}=200\mathrm{\text{GeV}}$ obtained by the STAR and PHENIX collaborations at RHIC are analyzed in the framework of $z$-scaling approach. The concept of the $z$-scaling is based on fundamental principles of self-similarity, locality, and fractality of hadron interactions at high energies. General properties of the data $z$-presentation are studied. Self-similarity of fractal structure of protons and fragmentation processes with strange particles is discussed. A microscopic scenario of constituent interactions developed within the $z$-scaling scheme is used to study the dependence of momentum fractions and recoil mass on the collision energy, transverse momentum and mass of produced inclusive particle, and to estimate the constituent energy loss. We consider that obtained results can be useful in study of strangeness origin, in searching for new physics with strange probes, and can serve for better understanding of fractality of hadron interactions at small scales.

Fractal self-similarity of hadron interactions demonstrated by the $z$-scaling of inclusive spectra is studied. The scaling regularity reflects fractal structure of the colliding hadrons (or nuclei) and takes into account general features of fragmentation processes expressed by fractal dimensions. The self-similarity variable $z$ is a function of the momentum fractions $x_1$ and $x_2$ of the colliding objects carried by the interacting hadron constituents and depends on the momentum fractions $y_a$ and $y_b$ of the scattered and recoil constituents carried by the inclusive particle and its recoil counterpart, respectively. Based on entropy principle, new properties of the $z$-scaling concept are found. They are conservation of fractal cumulativity in hadron interactions and quantization of fractal dimensions characterizing hadron structure and fragmentation processes at a constituent level.

The two-dimensional intermittency and its self-affine nature are investigated for p–p collisions at $\sqrt{s}=13$TeV in the two-dimensional anisotropic $(\eta -\varphi )$ space. The UrQMD model has been employed to generate and accumulate the p–p collisions data. Our investigation is made in the framework of scaled factorial moment (SFM) method. The concept of Hurst exponent $H$ is incorporated to bring a qualitative comparison between the UrQMD generated minimum bias (MB) events and the events at a particular impact parameter $b=0.4$ fm. The variation of the fractal strength with the variation of $H$ as well as with the variation of the order of the moment $q$ has been analyzed. Also, the nonlinearity in the variation of SFM with that of $H$ has been accompanied in this paper. It is observed that the fractal strength and the intermittent type of fluctuations are found to be much stronger in the region with $H<1$ compared to the region with $H>1$ and the self-affine nature in the fluctuations increases as $H$ deviates from unity.

Since the existence of market memory could implicate the rejection of the efficient market hypothesis, the aim of this paper is to find any evidence that selected emergent capital markets (eight European and BRIC markets, namely Hungary, Romania, Estonia, Czech Republic, Brazil, Russia, India and China) evince long-range dependence or the random walk hypothesis. In this paper, the Hurst exponent as calculated by R/S fractal analysis and Detrended Fluctuation Analysis is our measure of long-range dependence in the series. The results reinforce our previous findings and suggest that if stock returns present long-range dependence, the random walk hypothesis is not valid anymore and neither is the market efficiency hypothesis.

Using the covering theory in fractal geometry, we obtain the fractality of self-similar substitution networks introduced by Li et al. [Scale-free effect of substitution networks, Physica A 492 (2018) 1449–1455].

In the context of current Narratology, a novel can be regarded as an information generator system. This information can be symbolically and numerically codified and, subsequently, studied by nonlinear characteristic geometrical methods. Using this approach, geometric structures underlying the narrative discourse become evident. In this work, using a particular novel as our experimental data source, a formal expression for a discrete dynamical system is deduced, which generates a representative orbit of the narrative discourse evolution. The fractal dimension of this orbit is calculated from the correlation dimension and its deterministic character is unambiguously proved by solving the associated embedding problem. Finally, we describe the general features that a novel must satisfy in order to apply the proposed procedure.