Starting from inhomogeneous time scaling and linear decorrelation between successive price returns, Baldovin and Stella recently devised a model describing the time evolution of a financial index. We first make it fully explicit by using Student distributions instead of power law-truncated Levy...

Bidirectional valuation models are based on numerical methods to obtain kernels of parabolic equations. Here we address the problem of robustness of kernel calculations vis a vis floating point errors from a theoretical standpoint. We are interested in kernels of one-dimensional diffusion...

The application of renormalization group (RG) theory to the asymptotic analysis of differential equations is considered. It is found that there is a class of small structural perturbations whose effects cannot be systematically treated using the Gell-Mann–Low RG approach applied in this...

A reduction procedure, suggested for classical systems some years ago, is extended to systems with quantum-phase transitions with the aim to generate exactly solvable models capturing fluctuation effects beyond the mean field approximation. For the reduced isotropic m-vector quantum models, an...

Although much progress has been made in recent years in describing the dynamics of genetic systems, both in population genetics and evolutionary computation, there is still a conspicuous lack of tools with which to derive systematic, approximate solutions to their dynamics. In this article, we...

We review recent results obtained for the dynamics of incipient chaos. These results suggest a common picture underlying the three universal routes to chaos displayed by the prototypical logistic and circle maps. Namely, the period doubling, intermittency, and quasiperiodicity routes. In these...

The one-loop renormalization-group equations for Bose systems with quenched long-range correlated impurities are derived and analyzed with the help of three small expansion parameters. The classical-to-quantum crossover in a wide class of systems with long-range impurity correlations is...

We examine the pitchfork and tangent bifurcations in unimodal maps to illustrate a connection between renormalization group (RG) fixed points and entropy extremal properties. We observe that the exact RG solution for the tangent bifurcation is also applicable to the period-doubling cascade and...

We employ a real-space renormalization-group (RSRG) approach to study a mixed-spin (spin-12 and spin-1) antiferromagnetic Ising model on the square lattice. The model incorporates next-nearest-neighbor interactions which are relevant to describe ferrimagnetism. We present an RSRG calculation of...

The travelling salesman problem, in which the best route between cities to be visited is chosen from a large number of possible routes, is reconsidered using the time reversal of physical dynamics, e.g. an inverse of the diffusion process. Information mediators assigned to every city diffuse as...