Random Systems Research Articles

Possible Combinations of Electronic Data Capture and Randomization Systems

Clinical trials (CT) are in a wider sense experiments to prove and establish clinical benefit of treatments. Nowadays electronic data capture systems (EDCS) are used more often bringing a better data management and higher data quality into clinical practice. Also electronic systems for the randomization are used to assign the patients to the treatments. If the mentioned randomization system (RS) and EDCS are used, possibly identical data are collected in both, especially by stratified randomization. This separated data storage may lead to data inconsistency and in general data samples have to be aligned. The article discusses solutions to combine RS and EDCS. In detail one approach is realized and introduced. Different possible settings of combination of EDCS and RS are determined and the pros and cons for each solution are worked out. For the combination of two independent applications the necessary interfaces for the communication are defined. Thereby, existing standards are considered. An example realization is implemented with the help of open-source applications and state-of-the-art software development procedures. Three possibilities of separate usage or combination of EDCS and RS are presented and assessed: i) the complete independent usage of both systems; ii) realization of one system with both functions; and iii) two separate systems, which communicate via defined interfaces. In addition a realization of our preferred approach, the combination of both systems, is introduced using the open source tools RANDI2 and OpenClinica. The advantage of a flexible independent development of EDCS and RS is shown based on the fact that these tool are very different featured. In our opinion the combination of both systems via defined interfaces fulfills the requirements of randomization and electronic data capture and is feasible in practice. In addition, the use of such a setting can reduce the training costs and the error-prone duplicated data entry.

Single-domain particle hysteresis for a Random Anisotropy Ising System with exchange and magnetostatic interactions

In this paper we present an analysis on the hysteretic behaviour of magnetic nanoparticles described by a Random Anisotropy Ising Model. We have carried out an extensive study on the size, kinetics and inter-atomic interactions strength influences on the width and shape of the hysteresis loops of spherical particles composed by atoms situated in a cubic crystalline structure and interacting by the way of magnetostatic and exchange interactions.

Finite temperature behavior of strongly disordered quantum magnets coupled to adissipative bath**Dedicated to Professor Thomas Nattermann on the occasion of his 60th anniversary.

We study the effect of dissipation on the infinite randomness fixed point and theGriffiths–McCoy singularities of random transverse Ising systems in chains, ladders and intwo dimensions. A strong disorder renormalization group scheme is presentedthat allows the computation of the finite temperature behavior of the magneticsusceptibility and the spin specific heat. In the case of ohmic dissipation thesusceptibility displays a crossover from Griffiths–McCoy behavior (with a continuouslyvarying dynamical exponent) to classical Curie behavior at some temperatureT*. The specific heat displays Griffiths–McCoy singularities over the whole temperaturerange. For super-ohmic dissipation we find an infinite randomness fixed point within thesame universality class as the transverse Ising system without dissipation. In this case thephase diagram and the parameter dependence of the dynamical exponent in theGriffiths–McCoy phase can be determined analytically.

Dynamical behaviors of inter-out-of-equilibrium state intervals in Korean futures exchange markets

A recently discovered feature of financial markets, the two-phase phenomenon, is utilized to categorize a financial time series into two phases, namely equilibrium and out-of-equilibrium states. For out-of-equilibrium states, we analyze the time intervals at which the state is revisited. The power-law distribution of inter-out-of-equilibrium state intervals is shown and we present an analogy with discrete-time heat bath dynamics, similar to random Ising systems. In the mean-field approximation, this model reduces to a one-dimensional multiplicative process. By varying global and local model parameters, the relevance between volatilities in financial markets and the interaction strengths between agents in the Ising model are investigated and discussed.

Absorbing state phase transitions with quenched disorder.

Quenched disorder--in the sense of the Harris criterion--is generally a relevant perturbation at an absorbing state phase transition point. Here using a strong disorder renormalization group framework and effective numerical methods we study the properties of random fixed points for systems in the directed percolation universality class. For strong enough disorder the critical behavior is found to be controlled by a strong disorder fixed point, which is isomorph with the fixed point of random quantum Ising systems. In this fixed point dynamical correlations are logarithmically slow and the static critical exponents are conjecturedly exact for one-dimensional systems. The renormalization group scenario is confronted with numerical results on the random contact process in one and two dimensions and satisfactory agreement is found. For weaker disorder the numerical results indicate static critical exponents which vary with the strength of disorder, whereas the dynamical correlations are compatible with two possible scenarios. Either they follow a power-law decay with a varying dynamical exponent, like in random quantum systems, or the dynamical correlations are logarithmically slow even for a weak disorder. For models in the parity conserving universality class there is no strong disorder fixed point according to our renormalization group analysis.

Full reduction of large finite random Ising systems by real space renormalization group.

We describe how to evaluate approximately various physical interesting quantities in random Ising systems by direct renormalization of a finite system. The renormalization procedure is used to reduce the number of degrees of freedom to a number that is small enough, enabling direct summing over the surviving spins. This procedure can be used to obtain averages of functions of the surviving spins. We show how to evaluate averages that involve spins that do not survive the renormalization procedure. We show, for the random field Ising model, how to obtain Gamma(r)=<sigma(0)sigma(r)>-<sigma(0)><sigma(r)>, the "connected" correlation function, and S(r)=<sigma(0)sigma(r)>, the "disconnected" correlation function. Consequently, we show how to obtain the average susceptibility and the average energy. For an Ising system with random bonds and random fields, we show how to obtain the average specific heat. We conclude by presenting our numerical results for the average susceptibility and the function Gamma(r) along one of the principal axes. (In this work, the full three-dimensional (3D) correlation is calculated and not just parameters such nu or eta). The results for the average susceptibility are used to extract the critical temperature and critical exponents of the 3D random field Ising system.

Effect of long-range interactions on the pure and random quantum Ising transitions

It is well known that the long-range nature of interactions modifies the critical behaviour of classical and quantum systems. In the present article, we discuss some intriguing phenomena related to the phase transition in the pure and random quantum Ising systems in the presence of long-range interactions. We also propose a new model of a quantum Ising system with a ferromagnetic interaction defined on a long-range bond-diluted lattice. Using the results for the one-dimensional long-range bond percolation, we present a phenomenological phase diagram of the one-dimensional dilute model and comment on the higher-dimensional generalisations.

Volatility clustering and scaling for financial time series due to attractor bubbling.

A microscopic model of financial markets is considered, consisting of many interacting agents (spins) with global coupling and discrete-time heat bath dynamics, similar to random Ising systems. The interactions between agents change randomly in time. In the thermodynamic limit, the obtained time series of price returns show chaotic bursts resulting from the emergence of attractor bubbling or on-off intermittency, resembling the empirical financial time series with volatility clustering. For a proper choice of the model parameters, the probability distributions of returns exhibit power-law tails with scaling exponents close to the empirical ones.

Harris criterion on hierarchical lattices: rigorous inequalities and counterexamples in Ising systems.

Random bond Ising systems on a general hierarchical lattice are considered. The inequality between the specific heat exponent of the pure system, alpha(p), and the crossover exponent straight phi, alpha(p)</= phi, gives rise to the possibility of a negative alpha(p) along with a positive phi, leading to random criticality in disagreement with the Harris criterion. An explicit example where this really happens for an Ising system is presented and discussed. In addition to that, it is shown that in the presence of full long-range correlations the crossover exponent is larger than in the uncorrelated case.

Random field Ising systems on a general hierarchical lattice: rigorous inequalities.

Random Ising systems on a general hierarchical lattice with both random fields and random bonds are considered. Rigorous inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These inequalities lead to upper bounds on the crossover exponents [phi(i)].

Random bond Ising systems on a general hierarchical lattice: Exact inequalities

Random bond Ising systems on a general hierarchical lattice are considered. Interesting inequalities between eigenvalues of the Jacobian renormalization matrix at the pure fixed point are obtained. These lead to upper bounds on the crossover exponents straight phi(i).

Dynamical behavior of the random-bond transverse Ising model with four-spin interactions

We study the time evolution of the one-dimensional random-bond transverse Ising model with four-spin interactions. We calculate the time-dependent correlation function as well as the longitudinal relaxation function of the infinite chain. We analyze how the presence of disorder affect the dynamical behavior of the system in comparison with the pure model. We find that the main effect of disorder is to produce a crossover from a central mode to a collective-mode type of dynamics, as the concentration of weaker bonds is enhanced. Such crossover is also present in the case of an increase in bond dilution. The role of time evolution of one-dimensional quantum spin systems has been a long-standing theoretical and experimental problem. 1 Among them, the transverse Ising model with multispin interactions, regarded as one of the simplest with a nontrivial dynamics, has attracted considerable interest in recent years. 2,3 On the other hand, the presence of bond randomness has been shown to affect the behavior of magnetic materials in a drastic way providing a very rich area of investigation. In some materials it is present in the form of dilution caused by missing magnetic bonds or sites. In other class of systems it manifests itself through fluctuations in the magnitude of the exchange couplings due to structural disorder, as in glassy materials. Most of the research in disordered systems have been concentrated on obtaining phase diagrams and thermodynamic functions. 3 Much less effort has been made to obtain the dynamical behavior of these systems. Recently, the time evolution of the usual two-body random transverse Ising system was carried out by means of the method of recurrence relations. 4 The crossover from a central

Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems

We show that the numerical method based on the off-equilibrium fluctuation-dissipation relation does work and is very useful and powerful in the study of disordered systems which show a very slow dynamics. We have verified that it gives the right information in the known cases (diluted ferromagnets and random field Ising model far from the critical point) and we used it to obtain more convincing results on the frozen phase of four-dimensional spin glasses. Moreover we used it to study the Griffiths phase of the diluted and the random field Ising models.

Generalized off-equilibrium fluctuation-dissipation relations in random Ising systems

We show that the numerical method based on the off-equilibrium fluctuation-dissipation relation does work and is very useful and powerful in the study of disordered systems which show a very slow dynamics. We have verified that it gives the right information in the known cases (diluted ferromagnets and random field Ising model far from the critical point) and we used it to obtain more convincing results on the frozen phase of finite-dimensional spin glasses. Moreover we used it to study the Griffiths phase of the diluted and the random field Ising models.

Two-dimensional frustrated Ising model with four phases

In this paper we consider a 2d random Ising system on a square lattice with nearest neighbour interactions. The disorder is short range correlated and asymmetry between the vertical and the horizontal direction is admitted. More precisely, the vertical bonds are supposed to be non random while the horizontal bonds alternate: one row of all non random horizontal bonds is followed by one row where they are independent dichotomic random variables. We solve the model using an approximate approach that replace the quenched average with an annealed average under the constraint that the number of frustrated plaquettes is keep fixed and equals that of the true system. The surprising fact is that for some choices of the parameters of the model there are three second order phase transitions separating four different phases: antiferromagnetic, glassy-like, ferromagnetic and paramagnetic.

Exact solution of a two-dimensional random Ising model

The model considered is a $d=2$ layered random Ising system on a square lattice with a nearest-neighbor interaction. It is assumed that all the vertical couplings are equal and take the positive value $J,$ while the horizontal couplings are quenched random variables that are equal in the same row but can take the two possible values $J$ and $J\ensuremath{-}K$ in different rows. The exact solution is obtained in the limit case $K\ensuremath{\rightarrow}\ensuremath{\infty}$ for any distribution of the horizontal couplings. The model that corresponds to this limit can be seen as an ordinary Ising system where the spins of some rows, chosen at random, are frozen in an antiferromagnetic order. No phase transition is found if the horizontal couplings are independent random variables, while for correlated disorder one finds a low temperature phase with some glassy properties.

The dynamics of a Genetic Algorithm for simple random Ising systems

A formalism is presented for analysing Genetic Algorithms. It is used to study a simple Genetic Algorithm consisting of selection, mutation and crossover which is searching for the ground states of simple random Ising-spin systems: a random-field ideal paramagnet and a spin-glass chain. The formalism can also be applied to other population based search techniques and to biological models of micro-evolution. To make the problem tractable, it is assumed that the population dynamics can be described by a few macroscopic order parameters and that the remaining microscopic degrees of freedom can be averaged out. The macroscopic quantities that are used are the cumulants of the distribution of fitnesses (or energies) in the population. A statistical mechanics model is presented which describes the population configuration in terms of the cumulants, this is used to derive equations of motion for the cumulants. Predictions of the theory are compared with experiments and are shown to predict the average time to convergence and the average fitness of the final population accurately. A simplified version of the equations is produced by keeping only leading nonlinear terms, and truncating the cumulant expansion. This is shown to give a novel description of the role of genetic operators in search, e.g. it is argued that an important role of crossover is to reduce the skewness of the population.

Domain growth by aging in nonequilibrium two-dimensional random Ising systems.

The ac susceptibility in the two-dimensional Ising spin glass ${\mathrm{Rb}}_{2}$${\mathrm{Cu}}_{0.67}$${\mathrm{Co}}_{0.33}$${\mathrm{F}}_{4}$ and the two-dimensional random-exchange Ising ferromagnet ${\mathrm{Rb}}_{2}$${\mathrm{Cu}}_{0.89}$${\mathrm{Co}}_{0.11}$${\mathrm{F}}_{4}$ is observed to relax towards equilibrium on a time scale of hours following fast quenching to 3.9 K. Scaling of the in-phase and out-of-phase susceptibilities yields that the ordered domains grow according to (lnt${)}^{1/\mathrm{\ensuremath{\psi}}}$, with t expressed in units of a microscopic time, and \ensuremath{\psi}=1.07\ifmmode\pm\else\textpm\fi{}0.10 and 0.20\ifmmode\pm\else\textpm\fi{}0.05, respectively. Both values are in agreement with recent theoretical results and numerical simulations.

Universal amplitude combinations of the three-dimensional random Ising system.

The critical thermodynamics of the random quenched dilute Ising system is studied using a field-theoretical approach. A method of calculation of the universal critical amplitude combinations directly in three space dimensions is given. It is applied to both the disordered (T&gt;${\mathit{T}}_{\mathit{c}}$) and the ordered (T${\mathit{T}}_{\mathit{c}}$) phases. The detailed derivation of the relevant perturbative series expansions is presented up to the third order in powers of the renormalized coupling constants. Because of the shortness of the series, only indicative values for the amplitude combinations are proposed. Those estimates seem to be reliable except for the specific-heat amplitude ratio for which, however, the result suggests a positive sign.

Memory effects in the dynamic response of a random two-spin Ising system

Memory effects in the dynamic response of a random two-spin Ising system