A Brief Survey of Recent Edge-Preserving Smoothers

We introduce recent and very recent smoothing methods and discuss them in the common framework of `energy functions'. Focus is on the preservation of boundaries, spikes and canyons in presence of noise

An Adaptive Gradient Algorithm for Maximum Likelihood Estimation in Imaging

Markov random fields serve as natural models for patterns or textures with random fluctuations at small scale. Given a general form of such fields each class of pattern corresponds to a collection of model parameters which critically determines the abilitity of algorithms to segment or classify. Statistical inference on parameters is based on (dependent) data given by a portion of patterns inside some observation window. Unfortunately, the corresponding maximum likelihood estimators are computationally intractable by classical methods. Until recently, they even were regarded as intractable at all. In recent years stochastic gradient algorithms for their computation were proposed and studied. An attractive class of such algorithms are those derived from adaptive algorithms, wellknown in engeneering for a long time. We derive convergence theorems following closely the lines proposed by M. Metivier and P. Priouret (1987). This allows a transparent (albeit somewhat technical) treatment. The results are weaker than those obtained by L. Younes (1988). Keywords: adaptive algorithm, stochastic approximation, stochastic gradient descent, MCMC methods, maximum likelihood, Gibbs fields, imagin

Migration of semiflexible polymers in microcapillary flow

The non-equilibrium structural and dynamical properties of a semiflexible polymer confined in a cylindrical microchannel and exposed to a Poiseuille flow is studied by mesoscale hydrodynamic simulations. For a polymer with a length half of its persistence length, large variations in orientation and conformations are found as a function of radial distance and flow strength. In particular, the polymer exhibits U-shaped conformations near the channel center. Hydrodynamic interactions lead to strong cross-streamline migration. Outward migration is governed by the polymer orientation and the corresponding anisotropy in its diffusivity. Strong tumbling motion is observed, with a tumbling time which exhibits the same dependence on Peclet number as a polymer in shear flow.Comment: 6 pages, 7 figures, accepted by EP

Moment Sets of Bell-Shaped Distributions: Extreme Points, Extremal Decomposition and Chebysheff Inequalities

The paper deals with sets of distributions which are given by moment conditions for the distributions and convex constraints on derivatives of their c.d.fs. A general albeit simple method for the study of their extremal structure, extremal decomposition and topological or measure theoretical properties is developed. Its power is demonstrated by the application to bell-shaped distributions. Extreme points of their moment sets are characterized completely (thus filling a gap in the previous theory) and inequalities of Tchebysheff type are derived by means of general integral representation theorems. Some key words: Moment sets, Tschebysheff inequalities, extremal bell-shaped distribution

Flow-Induced Helical Coiling of Semiflexible Polymers in Structured Microchannels

The conformations of semiflexible (bio)polymers are studied in flow through geometrically structured microchannels. Using mesoscale hydrodynamics simulations, we show that the polymer undergoes a rod-to-helix transition as it moves from the narrow high-velocity region into the wide low-velocity region of the channel. The transient helix formation is the result of a non-equilibrium and non-stationary buckling transition of the semiflexible polymer, which is subjected to a compressive force originating from the fluid-velocity variation in the channel. The helix properties depend on the diameter ratio of the channel, the polymer bending rigidity, and the flow strength.Comment: Accepted in Phys. Rev. Let

Physics of Microswimmers - Single Particle Motion and Collective Behavior

Locomotion and transport of microorganisms in fluids is an essential aspect of life. Search for food, orientation toward light, spreading of off-spring, and the formation of colonies are only possible due to locomotion. Swimming at the microscale occurs at low Reynolds numbers, where fluid friction and viscosity dominates over inertia. Here, evolution achieved propulsion mechanisms, which overcome and even exploit drag. Prominent propulsion mechanisms are rotating helical flagella, exploited by many bacteria, and snake-like or whip-like motion of eukaryotic flagella, utilized by sperm and algae. For artificial microswimmers, alternative concepts to convert chemical energy or heat into directed motion can be employed, which are potentially more efficient. The dynamics of microswimmers comprises many facets, which are all required to achieve locomotion. In this article, we review the physics of locomotion of biological and synthetic microswimmers, and the collective behavior of their assemblies. Starting from individual microswimmers, we describe the various propulsion mechanism of biological and synthetic systems and address the hydrodynamic aspects of swimming. This comprises synchronization and the concerted beating of flagella and cilia. In addition, the swimming behavior next to surfaces is examined. Finally, collective and cooperate phenomena of various types of isotropic and anisotropic swimmers with and without hydrodynamic interactions are discussed.Comment: 54 pages, 59 figures, review article, Reports of Progress in Physics (to appear

Cooperative Motion of Active Brownian Spheres in Three-Dimensional Dense Suspensions

The structural and dynamical properties of suspensions of self-propelled Brownian particles of spherical shape are investigated in three spatial dimensions. Our simulations reveal a phase separation into a dilute and a dense phase, above a certain density and strength of self-propulsion. The packing fraction of the dense phase approaches random close packing at high activity, yet the system remains fluid. Although no alignment mechanism exists in this model, we find long-lived cooperative motion of the particles in the dense regime. This behavior is probably due to an interface-induced sorting process. Spatial displacement correlation functions are nearly scale-free for systems with densities close to or above the glass transition density of passive systems.Comment: 6 pages, 7 figure

The performance of credit rating systems in the assessment of collateral used in Eurosystem monetary policy operations

The aims of this paper are twofold: first, we attempt to express the threshold of a single “A” rating as issued by major international rating agencies in terms of annualised probabilities of default. We use data from Standard & Poor’s and Moody’s publicly available rating histories to construct confidence intervals for the level of probability of default to be associated with the single “A” rating. The focus on the single “A” rating level is not accidental, as this is the credit quality level at which the Eurosystem considers financial assets to be eligible collateral for its monetary policy operations. The second aim is to review various existing validation models for the probability of default which enable the analyst to check the ability of credit assessment systems to forecast future default events. Within this context the paper proposes a simple mechanism for the comparison of the performance of major rating agencies and that of other credit assessment systems, such as the internal ratings-based systems of commercial banks under the Basel II regime. This is done to provide a simple validation yardstick to help in the monitoring of the performance of the different credit assessment systems participating in the assessment of eligible collateral underlying Eurosystem monetary policy operations. Contrary to the widely used confidence interval approach, our proposal, based on an interpretation of p-values as frequencies, guarantees a convergence to an ex ante fixed probability of default (PD) value. Given the general characteristics of the problem considered, we consider this simple mechanism to also be applicable in other contexts.