In a model drift wave system that is interesting both in fluids and plasmas, we find that an embedded moving saddle point plays an important role at the onset of turbulence. Here the saddle point is actually a saddle steady wave, in its moving frame the wave system can be transformed into a set of coupled oscillators whose motion is affected by the saddle steady wave as if it is a potential. It...

We present a probabilistic registration algorithm that robustly solves the problem of rigid-body alignment between two shapes with high accuracy, by aptly modeling measurement noise in each shape, whether isotropic or anisotropic. For point-cloud shapes, the probabilistic framework additionally enables modeling locally-linear surface regions in the vicinity of each point to further improve regi...

Motivated in part by a problem in Metropolis-coupled, Markov chain Monte Carlo, we seek to minimise, in a suitable sense, the time it takes a (regular) diffusion with instantaneous reflection at 0 and 1 to travel from the origin to 1 and then return. The control mechanism is that we are allowed to chose the diffusion’s drift at each point in [0,1]. We consider the static and dynamic versions of...

The complex interactions of localized vortices with waves is investigated using a model of point vortices in the presence of a transverse or longitudinal wave. This simple model shows a rich dynamical behavior including oscillations of a dipole, splitting and merging of two like-circulation vortices, and chaos. The analytical and numerical results of this model have been found to predict under ...

We develop a kinetic theory for point vortices in two-dimensional hydrodynamics. Using standard projection operator techniques, we derive a Fokker-Planck equation describing the relaxation of a "test" vortex in a bath of "field" vortices at statistical equilibrium. The relaxation is due to the combined effect of a diffusion and a drift. The drift is shown to be responsible for the organization ...

We present a theory of zonal flow drift wave dynamics. Zonal flows are generated by modulational instability of a drift wave spectrum, and are damped by collisions. Drift waves undergo random shearing-induced refraction, resulting in increased mean square radial wavenumber. Drift waves and zonal flows together form a simple dynamical system, which has a single stable fixed point. In this state,...

In this paper we address the problem of learning Gaussian Mixture Models (GMMs) incrementally. Unlike previous approaches which universally assume that new data comes in blocks representable by GMMs which are then merged with the current model estimate, our method works for the case when novel data points arrive oneby-one, while requiring little additional memory. We keep only two GMMs in the m...

The area under the ROC curve (AUC), a wellknown measure of ranking performance, is also often used as a measure of classification performance, aggregating over decision thresholds as well as class and cost skews. However, David Hand has recently argued that AUC is fundamentally incoherent as a measure of aggregated classifier performance and proposed an alternative measure (Hand, 2009). Specifi...

For a locally normal state of a boson system we construct, based on the Skorokhod integral and Malliavin derivative respectively their compound versions, weights showing similar properties as the reduced and the compound Campbell measures of classical point process theory. As application we provide several characterisations of coherent states and states with property (γh), generalising a respec...

Identification of a real time of a change in a process, when an out-of-control signal is present is significant. This may reduce costs of defective products as well as the time of exploring and fixing the cause of defects. Another popular topic in the Statistical Process Control (SPC) is profile monitoring, where knowing the distribution of one or more quality characteristics may not be appropr...