arXiv research

It will be discussed the statistics of the extreme values in time series characterized by finite-term correlations with non-exponential decay. Precisely, it will be considered the results of numerical analyses concerning the return intervals of extreme values of the fluctuations of resistance and defect-fraction displa…

Quadratic-time algorithm computes stretch factors and foliations for pseudo-Anosov mapping classes.

Modeling financial returns as conditionally independent random variables explains power-law tails.

A large consensus now seems to take for granted that the distributions of empirical returns of financial time series are regularly varying, with a tail exponent close to 3. We revisit this results and use standard tests as well as develop a battery of new non-parametric and parametric tests (in particular with stretche…

The distribution of recurrence times or return intervals between extreme events is important to characterize and understand the behavior of physical systems and phenomena in many disciplines. It is well known that many physical processes in nature and society display long range correlations. Hence, in the last few year…

Starting from the generalized exponential function $\exp_κ(x)=(\sqrt{1+κ^{2}x^{2}}+κx)^{1/κ}$, with $\exp_{0}(x)=\exp(x)$, proposed in Ref. [G. Kaniadakis, Physica A \textbf{296}, 405 (2001)], the survival function $P_{>}(x)=\exp_κ(-βx^α)$, where $x\in\mathbf{R}^{+}$, $α,β>0$, and $κ\in[0,1)$, is considered in order to…

New theory explains signal propagation in normalization-free transformers.

We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can assume also an algebraic …

Study on price fluctuations in NFT market, showing heavy-tailed distributions and long-range memory.

New model explains volatility after extreme stock market events.

The study examines cryptocurrency market activity, revealing multifractal inter-transaction times and challenging traditional statistical models.

New stretch maps minimize distortion in geometric group theory.

We prove stability and exponential convergence of the Perfectly Matched Layer (PML) method for acoustic scattering on manifolds with axial analytic quasicylindrical ends. These manifolds model long-range geometric perturbations (e.g. bending or stretching) of tubular waveguides filled with homogeneous or inhomogeneous …

The paper explores properties of Finsler manifolds with specific curvature conditions.

Every weak Perron number is realized as a stretch factor of a homeomorphism on a surface.

Lower bound on stretch factor for periodic maps.

In the present work we demonstrate the application of different physical methods to high-frequency or tick-by-tick financial time series data. In particular, we calculate the Hurst exponent and inverse statistics for the price time series taken from a range of futures indices. Additionally, we show that in a limit orde…

In 1974, Thurston proved that, up to isotopy, every automorphism of closed orientable surface is either periodic, reducible, or pseudo-Anosov. The latter case has lead to a rich theory with applications ranging from dynamical systems to low dimensional topology. Associated with every pseudo-Anosov map is a real number …

Study stretch laminations in hyperbolic 3-manifolds via circle-valued maps.

The Teichmüller space $\mathcal{T}(Σ)$ of a surface $Σ$ is equipped with Thurston's asymmetric metric. Stretch lines are oriented geodesics for this metric on $\mathcal{T}(Σ)$. We give the asymptotic behavior of the lengths of the measured geodesic laminations as one follows a stretch line in the positive direction.

We use daily data on bilateral interbank exposures and monthly bank balance sheets to study network characteristics of the Russian interbank market over Aug 1998 - Oct 2004. Specifically, we examine the distributions of (un)directed (un)weighted degree, nodal attributes (bank assets, capital and capital-to-assets ratio…

Study finds how periodic surfaces can bend without stretching.

Minimal stretch factor for non-orientable surfaces is small.

The paper studies maximal stretch and Lipschitz maps on negatively curved manifolds.

We explicitly construct pseudo-Anosov maps on the closed surface of genus $g$ with orientable foliations whose stretch factor $λ$ is a Salem number with algebraic degree $2g$. Using this result, we show that there is a pseudo-Anosov map whose stretch factor has algebraic degree $d$, for each positive even integer $d$ s…

Minimal stretch factors for certain pseudo-Anosov maps are bounded.

Study how large-scale flows align small-scale vortices in 3D Euler equations.

Study on solvable Lie groups with specific Weyl connections.

In this paper, we study the Galois conjugates of stretch factors of pseudo-Anosov elements of the mapping class group of a surface. We show that - except in low-complexity cases - these conjugates are dense in the complex plane. For this, we use Penner's construction of pseudo-Anosov mapping classes. As a consequence, …

We investigate the probability distribution of the return intervals $τ$ between successive 1-min volatilities of two Chinese indices exceeding a certain threshold $q$. The Kolmogorov-Smirnov (KS) tests show that the two indices exhibit multiscaling behavior in the distribution of $τ$, which follows a stretched exponent…

Study connects group invariants through outer automorphisms and polynomial relations.

The paper examines properties of spherical Finsler metrics, proving their semi-C-reducibility and conditions for vanishing mean stretch curvature.

We determine the smallest stretch factor among pseudo-Anosov maps with an orientable invariant foliation on the closed nonorientable surfaces of genus 4, 5, 6, 7, 8, 10, 12, 14, 16, 18 and 20. We also determine the smallest stretch factor of an orientation-reversing pseudo-Anosov map with orientable invariant foliation…

Study reveals uniform difference in stretch factors between genus two handlebody group and outer automorphism group.

The motivation for this paper is to justify a remark of Thurston that the algebraic degree of stretch factors of pseudo-Anosov maps on a surface $S$ can be as high as the dimension of the Teichmüller space of $S$. In addition to proving this, we completely determine the set of possible algebraic degrees of pseudo-Anoso…

New geometric invariant limits the number of semi-arithmetic groups.

We quantitatively relate the Patterson-Sullivant currents and generic stretching factors for free group automorphisms to the asymmetric Lipschitz metric on Outer space and to Guirardel's intersection number.

We consider the problem of distortion minimal morphing of $n$-dimensional compact connected oriented smooth manifolds without boundary embedded in $\R^{n+1}$. Distortion involves bending and stretching. In this paper, minimal distortion (with respect to stretching) is defined as the infinitesimal relative change in vol…

Analyzes financial return distributions over various time scales.

Upper bound found for 2-systole in stretched S² x S² metrics.

The paper compares inserting and stretching points for grid refinement near critical points.

Unique geodesics selected by energy minimization in Teichmüller space.

Scaling properties in financial fluctuations are reviewed from the standpoint of statistical physics. We firstly show theoretically that the balance of demand and supply enhances fluctuations due to the underlying phase transition mechanism. By analyzing tick data of yen-dollar exchange rates we confirm two fractal pro…

The study examines the stretch factors of outer automorphisms and their latent symmetry.

The study improves bounds on the number of closed geodesics and logarithmic improvements in the Weyl law.

New periodic solutions found in 2n-body problem, braids of pseudo-Anosov type with stretch factors as metallic ratios.

A cylindrical stretch line is a stretch line, in the sense of Thurston, whose horocyclic lamination is a weighted multicurve. In this paper, we show that two correctly parameterized cylindrical lines are parallel if and only if these lines converge towards the same point in Thurston's boundary of Teichmüller space.

We study the tick dynamical behavior of the bond futures in Korean Futures Exchange(KOFEX) market. Since the survival probability in the continuous-time random walk theory is applied to the bond futures transaction, the form of the decay function in our bond futures model is discussed from two kinds of Korean Treasury …