Generalized Metropolis dynamics with a generalized master equation: An approach for time-independent and time-dependent Monte Carlo simulations of generalized spin systems

The extension of Boltzmann-Gibbs thermostatistics, proposed by Tsallis, introduces an additional parameter q to the inverse temperature beta. Here, we show that a previously introduced generalized Metropolis dynamics to evolve spin models is not local and does not obey the detailed energy balance. In this dynamics, locality is only retrieved for q = 1, which corresponds to the standard Metropolis algorithm. Nonlocality implies very time-consuming computer calculations, since the energy of the whole system must be reevaluated when a single spin is flipped. To circumvent this costly calculation, we propose a generalized master equation, which gives rise to a local generalized Metropolis dynamics that obeys the detailed energy balance. To compare the different critical values obtained with other generalized dynamics, we perform Monte Carlo simulations in equilibrium for the Ising model. By using short-time nonequilibrium numerical simulations, we also calculate for this model the critical temperature and the static and dynamical critical exponents as functions of q. Even for q not equal 1, we show that suitable time-evolving power laws can be found for each initial condition. Our numerical experiments corroborate the literature results when we use nonlocal dynamics, showing that short-time parameter determination works also in this case. However, the dynamics governed by the new master equation leads to different results for critical temperatures and also the critical exponents affecting universality classes. We further propose a simple algorithm to optimize modeling the time evolution with a power law, considering in a log-log plot two successive refinements.

EXISTENCE OF SOLUTIONS FOR A FRACTIONAL NEUTRAL INTEGRO-DIFFERENTIAL EQUATION WITH UNBOUNDED DELAY

In this article, we study the existence of mild solutions for fractional neutral integro-differential equations with infinite delay.

Calibration of a Species-Specific Spectral Vegetation Index for Leaf Area Index (LAI) Monitoring: Example with MODIS Reflectance Time-Series on Eucalyptus Plantations

The leaf area index (LAI) is a key characteristic of forest ecosystems. Estimations of LAI from satellite images generally rely on spectral vegetation indices (SVIs) or radiative transfer model (RTM) inversions. We have developed a new and precise method suitable for practical application, consisting of building a species-specific SVI that is best-suited to both sensor and vegetation characteristics. Such an SVI requires calibration on a large number of representative vegetation conditions. We developed a two-step approach: (1) estimation of LAI on a subset of satellite data through RTM inversion; and (2) the calibration of a vegetation index on these estimated LAI. We applied this methodology to Eucalyptus plantations which have highly variable LAI in time and space. Previous results showed that an RTM inversion of Moderate Resolution Imaging Spectroradiometer (MODIS) near-infrared and red reflectance allowed good retrieval performance (R-2 = 0.80, RMSE = 0.41), but was computationally difficult. Here, the RTM results were used to calibrate a dedicated vegetation index (called "EucVI") which gave similar LAI retrieval results but in a simpler way. The R-2 of the regression between measured and EucVI-simulated LAI values on a validation dataset was 0.68, and the RMSE was 0.49. The additional use of stand age and day of year in the SVI equation slightly increased the performance of the index (R-2 = 0.77 and RMSE = 0.41). This simple index opens the way to an easily applicable retrieval of Eucalyptus LAI from MODIS data, which could be used in an operational way.

Application of the log-conformation tensor to three-dimensional time-dependent free surface flows

The numerical simulation of flows of highly elastic fluids has been the subject of intense research over the past decades with important industrial applications. Therefore, many efforts have been made to improve the convergence capabilities of the numerical methods employed to simulate viscoelastic fluid flows. An important contribution for the solution of the High-Weissenberg Number Problem has been presented by Fattal and Kupferman [J. Non-Newton. Fluid. Mech. 123 (2004) 281-285] who developed the matrix-logarithm of the conformation tensor technique, henceforth called log-conformation tensor. Its advantage is a better approximation of the large growth of the stress tensor that occur in some regions of the flow and it is doubly beneficial in that it ensures physically correct stress fields, allowing converged computations at high Weissenberg number flows. In this work we investigate the application of the log-conformation tensor to three-dimensional unsteady free surface flows. The log-conformation tensor formulation was applied to solve the Upper-Convected Maxwell (UCM) constitutive equation while the momentum equation was solved using a finite difference Marker-and-Cell type method. The resulting developed code is validated by comparing the log-conformation results with the analytic solution for fully developed pipe flows. To illustrate the stability of the log-conformation tensor approach in solving three-dimensional free surface flows, results from the simulation of the extrudate swell and jet buckling phenomena of UCM fluids at high Weissenberg numbers are presented. (C) 2012 Elsevier B.V. All rights reserved.

Relating network rigidity, time scale hierarchies, and expression noise in gene networks

Fluctuation-dissipation theorems can be used to predict characteristics of noise from characteristics of the macroscopic response of a system. In the case of gene networks, feedback control determines the "network rigidity," defined as resistance to slow external changes. We propose an effective Fokker-Planck equation that relates gene expression noise to topology and to time scales of the gene network. We distinguish between two situations referred to as normal and inverted time hierarchies. The noise can be buffered by network feedback in the first situation, whereas it can be topology independent in the latter.

New Equation for Prediction of Reverse Remodeling after Cardiac Resynchronization Therapy

Objectives: To integrate data from two-dimensional echocardiography (2D ECHO), three-dimensional echocardiography (3D ECHO), and tissue Doppler imaging (TDI) for prediction of left ventricular (LV) reverse remodeling (LVRR) after cardiac resynchronization therapy (CRT). It was also compared the evaluation of cardiac dyssynchrony by TDI and 3D ECHO. Methods: Twenty-four consecutive patients with heart failure, sinus rhythm, QRS = 120 msec, functional class III or IV and LV ejection fraction (LVEF) = 0.35 underwent CRT. 2D ECHO, 3D ECHO with systolic dyssynchrony index (SDI) analysis, and TDI were performed before, 3 and 6 months after CRT. Cardiac dyssynchrony analyses by TDI and SDI were compared with the Pearson's correlation test. Before CRT, a univariate analysis of baseline characteristics was performed for the construction of a logistic regression model to identify the best predictors of LVRR. Results: After 3 months of CRT, there was a moderate correlation between TDI and SDI (r = 0.52). At other time points, there was no strong correlation. Nine of twenty-four (38%) patients presented with LVRR 6 months after CRT. After logistic regression analysis, SDI (SDI > 11%) was the only independent factor in the prediction of LVRR 6 months of CRT (sensitivity = 0.89 and specificity = 0.73). After construction of receiver operator characteristic (ROC) curves, an equation was established to predict LVRR: LVRR =-0.4LVDD (mm) + 0.5LVEF (%) + 1.1SDI (%), with responders presenting values >0 (sensitivity = 0.67 and specificity = 0.87). Conclusions: In this study, there was no strong correlation between TDI and SDI. An equation is proposed for the prediction of LVRR after CRT. Although larger trials are needed to validate these findings, this equation may be useful to candidates for CRT. (Echocardiography 2012;29:678-687)

STRUCTURE OF THE ELECTROMAGNETIC FIELD ALLOWING EXACT SOLUTION OF THE SCHRODINGER EQUATION IN SUPERPOSITION WITH AN AHARONOV-BOHM FIELD

A charged particle is considered in a complex external electromagnetic field. The field is a superposition of an Aharonov-Bohm field and some additional field. Here we describe all additional fields known up to the present time that allow exact solution of the Schrodinger equation in a complex field.

Optimal mean-variance control for discrete-time linear systems with Markovian jumps and multiplicative noises

In this paper, we consider the stochastic optimal control problem of discrete-time linear systems subject to Markov jumps and multiplicative noises under two criteria. The first one is an unconstrained mean-variance trade-off performance criterion along the time, and the second one is a minimum variance criterion along the time with constraints on the expected output. We present explicit conditions for the existence of an optimal control strategy for the problems, generalizing previous results in the literature. We conclude the paper by presenting a numerical example of a multi-period portfolio selection problem with regime switching in which it is desired to minimize the sum of the variances of the portfolio along the time under the restriction of keeping the expected value of the portfolio greater than some minimum values specified by the investor. (C) 2011 Elsevier Ltd. All rights reserved.

The impact of healing time before loading on orthodontic mini-implant stability: a histomophometric study in minipigs

Objective: To evaluate healing time before loading, areas compression and tension and location of insertion on mini-implant stability. Design: Six minipigs were used. Each animal received 3 mini-implants in each quadrant: 1 mini-implant was used as an unloaded control (G1, n = 24); the other 2 were loaded with 150 g-force at three time intervals (G2: immediate loading, G3: after 15 days and G4: after 30 days), with 16 mini-implant in each experimental group. After 120 days, tissue blocks of the areas of interest were harvested. Clinical analysis (exact Fisher test) determined the survival rate. Histological analysis (Kontron KS 300TM, Zeiss) quantified the fractional bone-toimplant contact (%BIC) and bone area (%BA) at each healing time point, areas of interest, and insertion site (ANOVA and t tests for dependent and independent samples). Results: The mini-implant survival rates were G1: 71%, G2: 50%, G3: 75% and G4: 63%, with no statistical differences between them. The groups presented similar %BIC and %BA. There were no differences between the compression and tension sides or maxillary and mandibular insertion sites. Conclusions: These results suggest that low-intensity immediate or early orthodontic loading does not affect mini-implant stability, because similar histomorphometric results were observed for all the groups, with partial osseointegration of the mini-implants present.

A uniqueness theorem for the determination of sources in the Germain–Lagrange plate equation

We prove a uniqueness result related to the Germain–Lagrange dynamic plate differential equation. We consider the equation {∂2u∂t2+△2u=g⊗f,in ]0,+∞)×R2,u(0)=0,∂u∂t(0)=0, where uu stands for the transverse displacement, ff is a distribution compactly supported in space, and g∈Lloc1([0,+∞)) is a function of time such that g(0)≠0g(0)≠0 and there is a T0>0T0>0 such that g∈C1[0,T0[g∈C1[0,T0[. We prove that the knowledge of uu over an arbitrary open set of the plate for any interval of time ]0,T[]0,T[, 0