Symmetries and fixed point stability of stochastic differential equations modeling self-organized criticality

A stochastic nonlinear partial differential equation is constructed for two different models exhibiting self-organized criticality: the Bak-Tang-Wiesenfeld (BTW) sandpile model [Phys. Rev. Lett. 59, 381 (1987); Phys. Rev. A 38, 364 (1988)] and the Zhang model [Phys. Rev. Lett. 63, 470 (1989)]. The dynamic renormalization group (DRG) enables one to compute the critical exponents. However, the nontrivial stable fixed point of the DRG transformation is unreachable for the original parameters of the models. We introduce an alternative regularization of the step function involved in the threshold condition, which breaks the symmetry of the BTW model. Although the symmetry properties of the two models are different, it is shown that they both belong to the same universality class. In this case the DRG procedure leads to a symmetric behavior for both models, restoring the broken symmetry, and makes accessible the nontrivial fixed point. This technique could also be applied to other problems with threshold dynamics.

Phenomenological approach to nonlinear Langevin equations

In this paper we address the problem of consistently constructing Langevin equations to describe fluctuations in nonlinear systems. Detailed balance severely restricts the choice of the random force, but we prove that this property, together with the macroscopic knowledge of the system, is not enough to determine all the properties of the random force. If the cause of the fluctuations is weakly coupled to the fluctuating variable, then the statistical properties of the random force can be completely specified. For variables odd under time reversal, microscopic reversibility and weak coupling impose symmetry relations on the variable-dependent Onsager coefficients. We then analyze the fluctuations in two cases: Brownian motion in position space and an asymmetric diode, for which the analysis based in the master equation approach is known. We find that, to the order of validity of the Langevin equation proposed here, the phenomenological theory is in agreement with the results predicted by more microscopic models

Test of the fluctuation theorem for stochastic entropy production in a nonequilibrium steady state

We derive a simple closed analytical expression for the total entropy production along a single stochastic trajectory of a Brownian particle diffusing on a periodic potential under an external constant force. By numerical simulations we compute the probability distribution functions of the entropy and satisfactorily test many of the predictions based on Seiferts integral fluctuation theorem. The results presented for this simple model clearly illustrate the practical features and implications derived from such a result of nonequilibrium statistical mechanics.

Generalized Langevin equations: Anomalous diffusion and probability distributions

We study the motion of a particle governed by a generalized Langevin equation. We show that, when no fluctuation-dissipation relation holds, the long-time behavior of the particle may be from stationary to superdiffusive, along with subdiffusive and diffusive. When the random force is Gaussian, we derive the exact equations for the joint and marginal probability density functions for the position and velocity of the particle and find their solutions.

Paroxetine increases steady-state concentrations of (R)-methadone in CYP2D6 extensive but not poor metabolizers

Steady-state blood concentrations of (R)- methadone (i.e., the active form), (S)-methadone, and (R,S)-methadone were measured before and after introduction of paroxetine 20 mg/day during a mean period of 12 days in 10 addict patients in methadone maintenance treatment. Eight patients were genotyped as CYP2D6 homozygous extensive metabolizers (EMs) and two patients as poor metabolizers (PMs). Paroxetine significantly increased concentrations of both enantiomers of methadone in the whole group (mean increase for (R)-methadone +/- SD, 26 +/- 32%; range, -14% to +83%, p = 0.032; for (S)-methadone, 49 +/- 51%; range, -29% to +137%, p = 0.028; for (R,S)-methadone, 35 +/- 41%; range, -20% to +112%, p = 0.032) and in the group of eight EMs (mean increase, 32%, p = 0.036; 53%, p = 0.028; and 42%, p = 0.036, for (R)-methadone, (S)-methadone, and (R,S)-methadone, respectively). On the other hand, in the two PMs, (S)-methadone but not (R)-methadone concentrations were increased by paroxetine (mean increases of 36% and 3%, respectively). Paroxetine is a strong CYP2D6 inhibitor, and these results confirm previous studies showing an involvement of CYP2D6 in methadone metabolism with a stereoselectivity toward the (R)-enantiomer. Because paroxetine is a mild inhibitor of CYP1A2, CYP2C9, CYP2C19, and CYP3A4, increase of (S)-methadone concentrations in both EMs and PMs could be mediated by inhibition of any of these isozymes.

On a class of exact solutions to the Fokker-Planck equations

In this paper we study under which circumstances there exists a general change of gross variables that transforms any FokkerPlanck equation into another of the OrnsteinUhlenbeck class that, therefore, has an exact solution. We find that any FokkerPlanck equation will be exactly solvable by means of a change of gross variables if and only if the curvature tensor and the torsion tensor associated with the diffusion is zero and the transformed drift is linear. We apply our criteria to the Kubo and Gompertz models.

Three-dimensional aspects of fluid flows in channels. II. Effects of meniscus and thin film regimes on viscous fingers

We perform a three-dimensional study of steady state viscous fingers that develop in linear channels. By means of a three-dimensional lattice-Boltzmann scheme that mimics the full macroscopic equations of motion of the fluid momentum and order parameter, we study the effect of the thickness of the channel in two cases. First, for total displacement of the fluids in the channel thickness direction, we find that the steady state finger is effectively two-dimensional and that previous two-dimensional results can be recovered by taking into account the effect of a curved meniscus across the channel thickness as a contribution to surface stresses. Second, when a thin film develops in the channel thickness direction, the finger narrows with increasing channel aspect ratio in agreement with experimental results. The effect of the thin film renders the problem three-dimensional and results deviate from the two-dimensional prediction.

Constitution of the State of Iowa Adopted in Convention, November 1, 1844 : 28th Congress, 2d sess. Ho. of Reps. Doc no. 5.

Constitution of the State of Iowa 1844.

Effect of age and gender on citalopram and desmethylcitalopram steady-state plasma concentrations in adults and elderly depressed patients.

The effect of aging on steady-state plasma concentrations of citalopram (CIT) and desmethylcitalopram (DCIT) was investigated in 128 depressive patients treated with 10-80 mg/day CIT. They were separated into three groups, with age up to 64 years (mean age+/-S.D.: 47+/-12 years; n=48), between 65 and 79 years (72+/-1 years; n=57), and from 80 years or older (84+/-1 years; n=23). Body mass index (BMI), renal and hepatic functions were similar in the three groups. A large interindividual variability of plasma levels of CIT (16-fold) and DCIT (12-fold) was measured for a given dose. The mean plasma levels of CIT corrected for a 20 mg daily dose were 55% higher in the very elderly (>=80 years) patients (65+/-30 ng/ml; p<0.001) and 38% higher in the elderly (65-79 years) patients (58+/-24 ng/ml; p<0.001) when compared to the adult patients (42+/-17 ng/ml). DCIT mean plasma level was 38% higher (p<0.05) in the group of very elderly patients (22+/-10 ng/ml) when compared to the adult patients (16+/-9 ng/ml). As a consequence, the mean plasma concentration of CIT+DCIT was 48% higher in the very elderly patients (86+/-36 ng/ml; p<0.001) and 33% higher in the elderly patients (77+/-28 ng/ml; p<0.001) when compared to the adult patients (58+/-21 ng/ml). Age correlated significantly with CIT (r=0.43, p<0.001), DCIT (r=0.28, p<0.01), and CIT+DCIT plasma levels (r=0.44, p<0.001), and thus accounts for 18% of the variability of CIT plasma levels, with no influence of gender. The recommended dose reduction of CIT in elderly patients seems therefore justified.

Flow targeted 3D steady-state free-precession coronary MR angiography: comparison of three different imaging approaches.

PURPOSE: To compare 3 different flow targeted magnetization preparation strategies for coronary MR angiography (cMRA), which allow selective visualization of the vessel lumen. MATERIAL AND METHODS: The right coronary artery of 10 healthy subjects was investigated on a 1.5 Tesla MR system (Gyroscan ACS-NT, Philips Healthcare, Best, NL). A navigator-gated and ECG-triggered 3D radial steady-state free-precession (SSFP) cMRA sequence with 3 different magnetization preparation schemes was performed referred to as projection SSFP (selective labeling of the aorta, subtraction of 2 data sets), LoReIn SSFP (double-inversion preparation, selective labeling of the aorta, 1 data set), and inflow SSFP (inversion preparation, selective labeling of the coronary artery, 1 data set). Signal-to-noise ratio (SNR) of the coronary artery and aorta, contrast-to-noise ratio (CNR) between the coronary artery and epicardial fat, vessel length and vessel sharpness were analyzed. RESULTS: All cMRA sequences were successfully obtained in all subjects. Both projection SSFP and LoReIn SSFP allowed for selective visualization of the coronary arteries with excellent background suppression. Scan time was doubled in projection SSFP because of the need for subtraction of 2 data sets. In inflow SSFP, background suppression was limited to the tissue included in the inversion volume. Projection SSFP (SNR(coro): 25.6 +/- 12.1; SNR(ao): 26.1 +/- 16.8; CNR(coro-fat): 22.0 +/- 11.7) and inflow SSFP (SNR(coro): 27.9 +/- 5.4; SNR(ao): 37.4 +/- 9.2; CNR(coro-fat): 24.9 +/- 4.8) yielded significantly increased SNR and CNR compared with LoReIn SSFP (SNR(coro): 12.3 +/- 5.4; SNR(ao): 11.8 +/- 5.8; CNR(coro-fat): 9.8 +/- 5.5; P &lt; 0.05 for both). Longest visible vessel length was found with projection SSFP (79.5 mm +/- 18.9; P &lt; 0.05 vs. LoReIn) whereas vessel sharpness was best in inflow SSFP (68.2% +/- 4.5%; P &lt; 0.05 vs. LoReIn). Consistently good image quality was achieved using inflow SSFP likely because of the simple planning procedure and short scanning time. CONCLUSION: Three flow targeted cMRA approaches are presented, which provide selective visualization of the coronary vessel lumen and in addition blood flow information without the need of contrast agent administration. Inflow SSFP yielded highest SNR, CNR and vessel sharpness and may prove useful as a fast and efficient approach for assessing proximal and mid vessel coronary blood flow, whereas requiring less planning skills than projection SSFP or LoReIn SSFP.

Free-breathing renal MR angiography with steady-state free-precession (SSFP) and slab-selective spin inversion: initial results.

BACKGROUND: The aim of our study was the investigation of a novel navigator-gated three-dimensional (3D) steady-state free-precession (SSFP) sequence for free-breathing renal magnetic resonance angiography (MRA) without contrast medium, and to examine the advantage of an additional inversion prepulse for improved contrast. METHODS: Eight healthy volunteers (mean age 29 years) and eight patients (mean age 53 years) were investigated on a 1.5 Tesla MR system (ACS-NT, Philips, Best, The Netherlands). Renal MRA was performed using three navigator-gated free-breathing cardiac-triggered 3D SSFP sequences [repetition time (TR) = 4.4 ms, echo time (TE) = 2.2 ms, flip angle 85 degrees, spatial resolution 1.25 x 1.25 x 4.0 mm(3), scanning time approximately 1 minute 30 seconds]. The same sequence was performed without magnetization preparation, with a non-slab selective and a slab-selective inversion prepulse. Signal-to-noise ratio (SNR), contrast-to-noise (CNR) vessel length, and subjective image quality were compared. RESULTS: Three-dimensional SSFP imaging combined with a slab-selective inversion prepulse enabled selective and high contrast visualization of the renal arteries, including the more distal branches. Standard SSFP imaging without magnetization preparation demonstrated overlay by veins and renal parenchyma. A non-slab-selective prepulse abolished vessel visualization. CNR in SSFP with slab-selective inversion was 43.6 versus 10.6 (SSFP without magnetization preparation) and 0.4 (SSFP with non-slab-selective inversion), P < 0.008. CONCLUSION: Navigator-gated free-breathing cardiac-triggered 3D SSFP imaging combined with a slab-selective inversion prepulse is a novel, fast renal MRA technique without the need for contrast media.

Free-breathing 3D steady-state free precession coronary MR angiography with radial k-space sampling: comparison with cartesian k-space sampling and cartesian gradient-echo coronary MR angiography--pilot study.

The authors compared radial steady-state free precession (SSFP) coronary magnetic resonance (MR) angiography, cartesian k-space sampling SSFP coronary MR angiography, and gradient-echo coronary MR angiography in 16 healthy adults and four pilot study patients. Standard gradient-echo MR imaging with a T2 preparatory pulse and cartesian k-space sampling was the reference technique. Image quality was compared by using subjective motion artifact level and objective contrast-to-noise ratio and vessel sharpness. Radial SSFP, compared with cartesian SSFP and gradient-echo MR angiography, resulted in reduced motion artifacts and superior vessel sharpness. Cartesian SSFP resulted in increased motion artifacts (P <.05). Contrast-to-noise ratio with radial SSFP was lower than that with cartesian SSFP and similar to that with the reference technique. Radial SSFP coronary MR angiography appears preferable because of improved definition of vessel borders.

Stochastic delay equations with non-negativity constraints driven by fractional Brownian motion

In this note we prove an existence and uniqueness result for the solution of multidimensional stochastic delay differential equations with normal reflection. The equations are driven by a fractional Brownian motion with Hurst parameter H > 1/2. The stochastic integral with respect to the fractional Brownian motion is a pathwise Riemann¿Stieltjes integral.