A Placebo-Controlled Trial to Evaluate Two Locally Delivered Antibiotic Gels (Piperacillin Plus Tazobactam vs. Doxycycline) in Stage III-IV Periodontitis Patients.

Background and objectives: this study aims to evaluate the clinical and microbiological effects of a single subgingival administration of a locally delivered antibiotic gel containing piperacillin plus tazobactam and compare it with a slow-release doxycycline (14%) gel and a placebo gel, following subgingival instrumentation (SI) in patients with severe periodontitis. Materials and methods: sixty-four patients diagnosed with stage III-IV periodontitis were enrolled, were randomly assigned into three groups, and were treated additionally with a single subgingival administration of piperacillin plus tazobactam gel (group A); doxycycline gel (group B); and placebo gel (group C). The primary outcome variable was the change in mean probing pocket depth (PPD) 6 months after the intervention. Secondary outcome variables were changes in mean full-mouth bleeding score (FMBS); full-mouth plaque score (FMPS); overall bleeding index (BOP); pocket closure; and clinical attachment level (CAL), along with changes in the numbers of five keystone bacteria: Aggregatibacter actinomycetemcomitans (A.a.), Porphyromonas gingivalis (P.g.), Prevotella intermedia (P.i.), Tannerella forsythia (T.f.), and Treponema denticola (T.d.). Intergroup and intragroup differences were evaluated at 3 and 6 months. Results: at baseline, the three groups were comparable. An improvement in clinical parameters such as PPD, CAL, and BOP between groups was observed at 3 and 6 months, but without statistical significance (p > 0.05). At 6 months, the intragroup analysis showed a significant reduction in clinical parameters. Even though the piperacillin plus tazobactam group showed slightly higher PPD reduction, this was not statistically significant when compared to both control groups. Conclusions: The groups had similar results, and subgingival instrumentation can be executed without adjunctive antimicrobials, reducing the costs for the patient and the working time/load of the professional.

Statistical symmetries of the Lundgren-Monin-Novikov hierarchy.

It was shown by Oberlack and Rosteck [Discr. Cont. Dyn. Sys. S, 3, 451 2010] that the infinite set of multipoint correlation (MPC) equations of turbulence admits a considerable extended set of Lie point symmetries compared to the Galilean group, which is implied by the original set of equations of fluid mechanics. Specifically, a new scaling group and an infinite set of translational groups of all multipoint correlation tensors have been discovered. These new statistical groups have important consequences for our understanding of turbulent scaling laws as they are essential ingredients of, e.g., the logarithmic law of the wall and other scaling laws, which in turn are exact solutions of the MPC equations. In this paper we first show that the infinite set of translational groups of all multipoint correlation tensors corresponds to an infinite dimensional set of translations under which the Lundgren-Monin-Novikov (LMN) hierarchy of equations for the probability density functions (PDF) are left invariant. Second, we derive a symmetry for the LMN hierarchy which is analogous to the scaling group of the MPC equations. Most importantly, we show that this symmetry is a measure of the intermittency of the velocity signal and the transformed functions represent PDFs of an intermittent (i.e., turbulent or nonturbulent) flow. Interesting enough, the positivity of the PDF puts a constraint on the group parameters of both shape and intermittency symmetry, leading to two conclusions. First, the latter symmetries may no longer be Lie group as under certain conditions group properties are violated, but still they are symmetries of the LMN equations. Second, as the latter two symmetries in its MPC versions are ingredients of many scaling laws such as the log law, the above constraints implicitly put weak conditions on the scaling parameter such as von Karman constant κ as they are functions of the group parameters. Finally, let us note that these kind of statistical symmetries are of much more general type, i.e., not limited to MPC or PDF equations emerging from Navier-Stokes, but instead they are admitted by other nonlinear partial differential equations like, for example, the Burgers equation when in conservative form and if the nonlinearity is quadratic.

Extended Kramers-Moyal analysis applied to optical trapping.

The Kramers-Moyal analysis is a well-established approach to analyze stochastic time series from complex systems. If the sampling interval of a measured time series is too low, systematic errors occur in the analysis results. These errors are labeled as finite time effects in the literature. In the present article, we present some new insights about these effects and discuss the limitations of a previously published method to estimate Kramers-Moyal coefficients at the presence of finite time effects. To increase the reliability of this method and to avoid misinterpretations, we extend it by the computation of error estimates for estimated parameters using a Monte Carlo error propagation technique. Finally, the extended method is applied to a data set of an optical trapping experiment yielding estimations of the forces acting on a Brownian particle trapped by optical tweezers. We find an increased Markov-Einstein time scale of the order of the relaxation time of the process, which can be traced back to memory effects caused by the interaction of the particle and the fluid. Above the Markov-Einstein time scale, the process can be very well described by the classical overdamped Markov model for Brownian motion.

Structure formation by dynamic self-assembly.

This review summarizes the work conducted in the last decade on the fabrication of mesostructured patterns, which have lateral dimensions within the nano- and microscales, over a wafer-scaled size by means of dynamic self-assembly using Langmuir-Blodgett (LB) transfer or dip-coating. First, strategies to form mesostructures from a homogeneous Langmuir monolayer with controlled shape, size, and patterns alignment will be presented, followed by a detailed theoretical explanation of the pattern formation. In addition, the patterning of nanocrystals and other chemicals with LB transfer or other dynamic processes, such as dip-coating, will be summarized.

Estimation of Kramers-Moyal coefficients at low sampling rates.

An optimization procedure for the estimation of Kramers-Moyal coefficients from stationary, one-dimensional, Markovian time series data is presented. The method takes advantage of a recently reported approach that allows one to calculate exact finite sampling interval effects by solving the adjoint Fokker-Planck equation. Therefore, it is well suited for the analysis of sparsely sampled time series. The optimization can be performed either by making a parametric ansatz for drift and diffusion functions or parameter free. We demonstrate the power of the method in several numerical examples with synthetic time series.

Langevin dynamics deciphers the motility pattern of swimming parasites.

The parasite African trypanosome swims in the bloodstream of mammals and causes the highly dangerous human sleeping sickness. Cell motility is essential for the parasite's survival within the mammalian host. We present an analysis of the random-walk pattern of a swimming trypanosome. From experimental time-autocorrelation functions for the direction of motion we identify two relaxation times that differ by an order of magnitude. They originate from the rapid deformations of the cell body and a slower rotational diffusion of the average swimming direction. Velocity fluctuations are athermal and increase for faster cells whose trajectories are also straighter. We demonstrate that such a complex dynamics is captured by two decoupled Langevin equations that decipher the complex trajectory pattern by referring it to the microscopic details of cell behavior.

Dynamics of a thin liquid film with surface rigidity and spontaneous curvature.

The effect of rigid surfaces on the dynamics of thin liquid films that are amenable to the lubrication approximation is considered. It is shown that the Helfrich energy of the layer gives rise to additional terms in the time-evolution equations of the liquid film. The dynamics is found to depend on the absolute value of the spontaneous curvature, irrespective of its sign. Due to the additional terms, the effective surface-tension can be negative and an instability at intermediate wavelengths is observed. Furthermore, the dependence of the shape of a droplet on the bending rigidity as well as on the spontaneous curvature is discussed.

Controlled nanochannel lattice formation utilizing prepatterned substrates.

Solid substrates can be endued with self-organized regular stripe patterns of nanoscopic length scale by Langmuir-Blodgett transfer of organic monolayers. Here we consider the effect of periodically prepatterned substrates on this process of pattern formation. It leads to a time periodic forcing of the oscillatory behavior at the meniscus. Utilizing higher-order synchronization with this forcing, complex periodic patterns of predefined wavelength can be created. The dependence of the synchronization on the amplitude and the wavelength of the wetting contrast is investigated in one and two spatial dimensions, and the resulting patterns are discussed. Furthermore, the effect of prepatterned substrates on the pattern selection process is investigated.

Pattern formation in monolayer transfer systems with substrate-mediated condensation.

The formation of regular stripe patterns during transfer of surfactant monolayers onto solid substrates is investigated. Two coupled differential equations describing the surfactant density and the height profile of the water subphase are derived within the lubrication approximation. If the transfer is carried out in the vicinity of a first order phase transition of the surfactant, the interaction with the substrate plays a key role. This effect is included in the surfactant free-energy functional via a height-dependent external field. Using transfer velocity as a control parameter, a bifurcation from a homogeneous transfer to regular stripe patterns arranged parallel to the contact line is investigated in one and two dimensions. Moreover, in the two-dimensional case, a secondary bifurcation to perpendicular stripes is observed in a certain control parameter range.

Continuous-time multidimensional Markovian description of Lévy walks.

The paper presents a multidimensional model for nonlinear Markovian random walks that generalizes the one we developed previously [I. Lubashevsky, R. Friedrich, and A. Heuer, Phys. Rev. E 79, 011110 (2009)] in order to describe the Lévy-type stochastic processes in terms of continuous trajectories of walker motion. This approach may open a way to treat Lévy flights or Lévy random walks in inhomogeneous media or systems with boundaries in the future. The proposed model assumes the velocity of a wandering particle to be affected by a linear friction and a nonlinear Langevin force whose intensity is proportional to the magnitude of the velocity for its large values. Based on the singular perturbation technique, the corresponding Fokker-Planck equation is analyzed and the relationship between the system parameters and the Lévy exponent is found. Following actually the previous paper we demonstrate also that anomalously long displacements of the wandering particle are caused by extremely large fluctuations in the particle velocity whose duration is determined by the system parameters rather than the duration of the observation interval. In this way we overcome the problem of ascribing to Lévy random-walk non-Markov properties.

Dynamical origins for non-Gaussian vorticity distributions in turbulent flows.

We present results on the connection between the vorticity equation and the shape and evolution of the single-point vorticity probability density function. The statistical framework for these observations is based on the classical hierarchy of evolution equations for the probability density functions by Lundgren, Novikov, and Monin combined with conditional averaging of the unclosed terms. The numerical evaluation of these conditional averages provides insights into the intimate relation of dynamical effects such as vortex stretching and vorticity diffusion and non-Gaussian vorticity statistics.

Realization of Lévy walks as Markovian stochastic processes.

Based on multivariate Langevin processes we present a realization of Lévy flights as a continuous process. For the simple case of a particle moving under the influence of friction and a velocity-dependent stochastic force we explicitly derive the generalized Langevin equation and the corresponding generalized Fokker-Planck equation describing Lévy flights. Our procedure is similar to the treatment of the Kramers-Fokker-Planck equation in the Smoluchowski limit. The proposed approach may open a way to treat Lévy flights in inhomogeneous media or systems with boundaries in the future.

Markov properties in presence of measurement noise.

Recently, several powerful tools for the reconstruction of stochastic differential equations from measured data sets have been proposed [e.g., Siegert, Phys. Lett. A 243, 275 (1998); Hurn, J. Time Series Anal. 24, 45 (2003)]. Efficient application of the methods, however, generally requires Markov properties to be fulfilled. This constraint typically seems to be violated on small scales, which frequently is attributed to physical effects. On the other hand, measurement noise such as uncorrelated measurement and discretization errors has large impacts on the statistics of measurements on small scales. We demonstrate that the presence of measurement noise, likewise, spoils Markov properties of an underlying Markov process. This fact is promising for the further development of techniques for the reconstruction of stochastic processes from measured data, since limitations at small scales might stem from artificial noise sources rather than from intrinsic properties of the dynamics of the underlying process. Measurement noise, however, can be controlled much better than the intrinsic dynamics of the underlying process.

Reconstruction of complex dynamical systems affected by strong measurement noise.

This Letter reports on a new approach to properly analyze time series of dynamical systems which are spoilt by the simultaneous presence of dynamical noise and measurement noise. It is shown that even strong external measurement noise as well as dynamical noise which is an intrinsic part of the dynamical process can be quantified correctly, solely on the basis of measured time series and proper data analysis. Finally, real world data sets are presented pointing out the relevance of the new approach.

Motion of defects in rotating fluids.

We study defect motion in a rotating convection cell. We present numerical results of a generalized Swift-Hohenberg equation, which provides a model description of the vertically averaged three-dimensional (3-D) hydrodynamic equations. Our model includes non-Boussinesq effects. It also accounts for the effects of the Coriolis force induced by a rotation of the fluid layer around its vertical symmetry axis. We show that even a slow rotation well below the Kuppers-Lortz instability causes defect motion perpendicular to the convective rolls. We derive an analytic estimation of that motion.