Price dynamics from a simple multiplicative random process model

The existence of stylized facts suggests that there might be `universal' mechanism which drives price evolution on financial markets in general. Based on empirical estimates of 10 major indices, we propose a stylized model of endogenous price formation on an aggregate level whose key issue is that price evolution is driven by the `market's' expectations about future growth rates of investment. The model is a multiplicative random process with a stochastic, state-dependent growth rate which establishes a negative feedback component in the price dynamics which admits some far reaching formal analysis. Generated return trails exhibit statistical properties such as 'volatility clustering', multi scaling, and a non-Gaussian distribution which is in quantitative in agreement with stylized facts from empirical asset returns. Additionally non-equilibrium entropies are also considered. These results suggests that the structure of the model mimicks a mechanism which is essential in driving price dynamics of financial markets in general.     

Buckling of a compressed elastic membrane: a simple model

The buckling of a folded membrane submitted to a bi-axial compression is studied in the framework of the continuum non-linear elasticity theory. We show that the formation of the fold patterning can be quantitatively well described with a simple non-linear model. As a matter of fact, with this model, we recover the experimental phase diagram of a secondary buckling instability with a very good precision. In addition, depending on the anisotropy of the applied compressive stress, we find that the buckling coarsening dynamics can be described as a 1D spinodal decomposition (for a uni-axial stress) or as a 2D XY model (for an isotropic bi-axial stress) with an irrotational non-scalar order parameter. For an isotropic bi-axial stress, we indeed recover the famous coarsening exponent: n=1/4. This exponent has to be confirmed experimentally.     

Evolution of species from Darwin theory: A simple model

Evolution of species is a complex phenomenon. Some theoretical models take into account evolution of species, like the Bak–Sneppen model that obtain punctuated equilibrium from self-organized criticality and the Penna model for biological aging that consists in a bit-string model subjected to aging, reproduction and death. In this work we propose a simple model to study different scenarios used to simulate the evolution of species. This model is based on Darwin’s ideas of evolution. The present findings show that punctuated equilibria and stasis seem to be obtained directly from the mutation, selection of parents and the genetic crossover, and are very close to the fossil data analysis.     

Dose determination on tooth enamel fragments from two human fossils

The ESR dose values of two human tooth enamel fragments were measured in 10° steps with an automated goniometer. ESR spectra were deconvoluted using four Gaussian peaks. The central region of the spectra is interfered with by at least one additional line which yields significantly lower dose values than the central, apparently axial region. There is a clear relationship between dose and width of the deconvoluted axial peaks which is attributable to incomplete separation between the axial and interfering peaks. A simple model is presented that coherently explains all observations. We conclude that deconvolution is necessary for the estimation of the most likely dose value of enamel pieces.     

Superconductivity in a model with overlapping wide and flat bands

The density of one-electron states at the Fermi level with allowance for weak Coulomb correlations between the band electrons is calculated in a superconductivity model having overlapping wide and flat bands. The dependence of the superconducting transition temperature on the doping level is obtained. Fiz. Tverd. Tela (St. Petersburg) 39, 237–239 (February 1997)     

Pump and probe nonlinear processes: new modified sum rules from a simple oscillator model

The nonlinear oscillator model is useful to basically understand the most important properties of nonlinear optical processes. It has been shown to give the correct asymptotic behaviour and to provide the general features of harmonic generation to all orders, in particular dispersion relations and sum rules. We investigate the properties of pump and probe processes using this model, and study those cases where general theorems based on the holomorphic character of the Kubo response functions cannot be applied. We show that it is possible to derive new sum rules and new Kramers-Kr?nig relations for the two lowest moments of the real and of the imaginary part of the third order susceptibility and that new specific contributions become relevant as the intensity of the probe increases. Since the analytic properties of the susceptibility functions depend only upon the time causality of the system we are confident that these results are not model dependent and therefore have a general validity, provided one substitutes for the equilibrium values of the potential derivatives the density matrix expectation values of the corresponding operators. Received 25 January 1999 and Received in final form 26 April 1999     

DNA sequencing through graphene nanogap: a model of sequential electron transport

Transverse electron transport through DNA nucleobases in graphene nanogap with armchair edges is investigated within the sequential tunneling model using the tight-binding approximation and the master equation technique. The effects of both random positions of nucleotides when DNA repeatedly pulls through graphene nanogap during the decoding process and the Coulomb blockade are studied. We have shown that combined measurements of the tunnel current and its root-mean-square deviation in the regime of sequential electron transport allow to facilitate identification of nucleotides while the effects of Coulomb blockade disturb DNA sequencing.     

Self-interaction correction in a simple model

We discuss various ways to handle self-interaction corrections (SIC) to Density Functional Theory (DFT) calculations. To that end, we use a simple model of few particles in a finite number of states together with a simple zero-range interaction for which full Hartree-Fock can easily be computed as a benchmark. The model allows to shed some light on the balance between orthonormality of the involved states and energy variance.     

Velocity autocorrelations in a simple model

A one-dimensional Lorentz-type model is studied where a point particle is reflected with some given probability p off randomly located fixed scatterers. The diffusion constant is calculated exactly, and the velocity autocorrelation is shown to decay like $\text{t}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$, for 0<p<1. For finite times, there are oscillations superimposed on this power decay. For p → 1, these oscillations dominate the behaviour for all times.     

Period-doubling bifurcations in a simple model

Periodic solutions in a simple model, whose solution shows successive period-doubling bifurcations leading to chaotic motion, are calculated by using the harmonic balance method. The result is in good agreement with that of computer simulation.     

Multiple-electron excitation in X-ray absorption: a simple generic model

The probability of multiple-electron excitation in X-ray absorption is calculated using a simple generic model. The model permits calculations to be made for all atoms with little input data or computing effort. The high-energy limit of this probability, which gives the usual EXAFS amplitude reduction factor, is calculated in the 'sudden approximation' using Slater orbitals. Good agreement with experiment is found. The energy dependence of this probability is also calculated using a simple model form of perturbing potential and found to agree well with experiment for rare gas atoms. The effect on the X-ray absorption coefficient of including multiple-electron excitations is also determined and is found to be small, again in agreement with observation.     

From semiconductors to superconductors: a simple model for pseudogaps

We consider a two-dimensional semiconductor with a local attraction among the carriers. We study the ground state of this system as a function of the semiconductor gap. We find a direct transition from a superconducting to an insulating phase for no doping at a critical value, the single particle excitations being always gapped. For finite doping we find a smooth crossover. We calculate the critical temperature due to both the particle excitations and the Berezinkii-Kosterlitz-Thouless transition. Received 8 December 1998     

Properties of a simple bilinear stochastic model: Estimation and predictability

We analyze the properties of arguably the simplest bilinear stochastic multiplicative process, proposed as a model of financial returns and of other complex systems combining both nonlinearity and multiplicative noise. By construction, it has no linear predictability (zero two-point correlation) but a certain nonlinear predictability (non-zero three-point correlation). It can thus be considered as a paradigm for testing the existence of a possible nonlinear predictability in a given time series. We present a rather exhaustive study of the process, including its ability to produce fat-tailed distributions from Gaussian innovations, the unstable characteristics of the inversion of the key nonlinear parameters and of the two initial conditions necessary for the implementation of a prediction scheme and an analysis of the associated super-exponential sensitivity of the inversion of the innovations in the presence of a large impulse. Our study emphasizes the conditions under which a degree of predictability can be achieved and describe a number of different attempts, which overall illuminates the properties of the process. In conclusion, notwithstanding its remarkable simplicity, the bilinear stochastic process exhibits remarkably rich and complex behavior, which makes it a serious candidate for the modeling of financial time series among others.     

Paper II: The interpretation of measurement-time-dependent single-aliquot equivalent-dose estimates using predictions from a simple empirical model

Narrow spectrum (blue-green) laboratory partial bleaching of aliquots of natural sedimentary quartz has been shown to have a significant effect on equivalent dose (measured using a single aliquot procedure) calculated as a function of measurement time (D_e(t)). A simple model, based on empirical data, is presented in which the effects of partial bleaching on D_e(t) are predicted, taking into account the influences of pre- and post-burial doses. The model is applied to the case of heterogeneous populations of partially bleached single grains with various ranges of residual doses. Modelling shows that under realistic conditions, D_e histogram plots are unable to distinguish between samples having age overestimates and those with correct ages, whereas the proposed D_e–Z plot is able to make this distinction. Furthermore, modelling shows that D_e–Z plots can identify sub-populations of grains/aliquots that show most evidence of full bleaching, which can then be used to estimate a correct mean D_e value.     

Space-time in a simple model of a physical system

A model of space-time is worked out starting from the two primitive concepts of preparticle and of membership relation of set theory. We obtain as derivative concepts those of space-time and inertial reference frame, also those of energy, frequency, momentum, and wavelength of a physical system in a given reference frame. Proportionality relations between energy and frequency, and between momentum and (wavelength)^–1 are shown to be satisfied in our model. The same constant of proportionality intervenes in these two relations, and we interpret it as the Planck constant expressed in a particular system of units. Energy and momentum are conserved in the usual sense, provided we consider sufficiently large regions of the space-time diagram associated to the reference frame under consideration. Lorentz transformations and Heisenberg's inequalities are discussed within the framework of our model.     

Time in a simple model of a physical system

We build a model of time starting from the primitive concept of base-setB≡{α _i |i∈I} of all physical systems, whose elements are called pre-particles α _i . We assume thatB is a denumerably infinite set. Particles or bodies are represented by the subsets of the power setP (B) of the base-setB. A physical system is represented by a set of particles. We introduce the distinction between evolving and non-evolving particles, and assume that the former are represented by those subsets ofP (B) which are chains. Making use of the above concepts we define the state of a particle and the indicator of the state of a particle with respect to a given state of the same or another particle. Then we define in terms of indicators the concepts of instant, time-set, degenerate time-set, event, and clock. For the time related to a given clock one has a set in which the order relation is is in general not connected. Some theorems are proved.