We apply the Hurst exponent idea for investigation of DJIA index time-series data. The behavior of the local Hurst exponent prior to drastic changes in financial series signal is analyzed. The optimal length of the time-window over which this exponent can be calculated in order to make some meaningful predictions is discussed. Our prediction hypothesis is verified with examples of '29 and '87 c...

An energy-minimal simulation is proposed to study the patterns and mechanical properties of elastically crumpled wires in two dimensions. Our aim is to describe the behavior at the intermediate occupancy of the cavity so that its radius of gyration is varied up to one twentieth of the wire length. We tuned the bending rigidity and stretching modulus to measure the energy allocation, size-mass e...

In this paper, direct estimate of Sobolev exponent of reenable distributions and its application to the asymptotic estimate of Sobolev exponent of M band Daubechies' scaling functions are considered.

This paper presents a new nonlinear dyadic subdivision scheme eliminating the Gibbs oscillations close to discontinuities. Its convergence, stability and order of approximation are analyzed. It is proved that this scheme converges towards limit functions Hölder continuous with exponent larger than 1.299. Numerical estimates provide a Hölder exponent of 2.438. This subdivision scheme is the firs...

Boneh-Boyen signatures are widely used in many advanced cryptosystems. It has a structure of “inversion in the exponent”, and its unforgeability against q chosen-messages attack is proven under the non-static q-Strong Diffie-Hellman assumption. It has been an open problem whether the exponent-inversion signature, and its various applications, can be proved based on a weaker static assumption. W...

This note introduces a new general conjecture correlating the dimensionality dT of an infinite lattice with N nodes to the asymptotic value of its Wiener Index W(N). In the limit of large N the general asymptotic behavior W(N)≈Ns is proposed, where the exponent s and dT are related by the conjectured formula s=2+1/dT allowing a new definition of dimensionality dW=(s-2)-1. Being related to the t...

The exponent of a string is the quotient of its length over its smallest period. The exponent and the period of a string can be computed in time proportional to the string length. We design an algorithm to compute the maximal exponent of all factors of an overlap-free string. Our algorithm runs in lineartime on a fixed-size alphabet, while a naive solution of the question would run in cubic tim...