A new ADMM algorithm for the Euclidean median and its application to robust patch regression

The Euclidean Median (EM) of a set of points $\Omega$ in an Euclidean space is the point x minimizing the (weighted) sum of the Euclidean distances of x to the points in $\Omega$. While there exits no closed-form expression for the EM, it can nevertheless be computed using iterative methods such as the Wieszfeld algorithm. The EM has classically been used as a robust estimator of centrality for multivariate data. It was recently demonstrated that the EM can be used to perform robust patch-based denoising of images by generalizing the popular Non-Local Means algorithm. In this paper, we propose a novel algorithm for computing the EM (and its box-constrained counterpart) using variable splitting and the method of augmented Lagrangian. The attractive feature of this approach is that the subproblems involved in the ADMM-based optimization of the augmented Lagrangian can be resolved using simple closed-form projections. The proposed ADMM solver is used for robust patch-based image denoising and is shown to exhibit faster convergence compared to an existing solver.Comment: 5 pages, 3 figures, 1 table. To appear in Proc. IEEE International Conference on Acoustics, Speech, and Signal Processing, April 19-24, 201

Tubulation pattern of membrane vesicles coated with bio filaments

Narrow membrane tubes are commonly pulled out from the surface of phospholipid vesicles using forces applied either through laser or magnetic tweezers or through the action of processive motor proteins. Recent examples have emerged where such tubes spontaneously grow from vesicles coated with bioactive cytoskeletal filaments (e.g. FtsZ, microtubule) in the presence GTP. We show how a soft vesicle deforms due to the interplay between its topology, local curvature and the forces due to the active filaments. We present results from Dynamically Triangulated Monte Carlo simulations of a spherical continuum membrane coated with a nematic field and show how the intrinsic curvature of the filaments and their ordering interactions drive membrane tubulation. We predict interesting patterns of nematic defects, on curved 2D membrane surfaces, which promote tube formation. Implication of our model for more dynamic cases where vesicles coated with an active mixture of microtubule and myosin show shape oscillation, are also discussed. All these cases point to a common theme that defect locations on 2D membrane surfaces are hot spots of membrane deformation activity.Comment: 8 pages, 7 figure

Affordances and Feedback in Nuance-Oriented Interfaces

Virtual Environments (VEs) and perceptive user interfaces must deal with complex users and their modes of interaction. One way to approach this problem is to recognize users’ nuances (subtle conscious or unconscious actions). In exploring nuance-oriented interfaces, we attempted to let users work as they preferred without being biased by feedback or affordances in the system. The hope was that we would discover the users’ innate models of interaction. The results of two user studies were that users are guided not by any innate model but by affordances and feedback in the interface. So, without this guidance, even the most obvious and useful components of an interface will be ignored

A First Step Towards Nuance-Oriented Interfaces for Virtual Environments

Designing usable interfaces for virtual environments (VEs) is not a trivial task. Much of the difficulty stems from the complexity and volume of the input data. Many VEs, in the creation of their interfaces, ignore much of the input data as a result of this. Using machine learning (ML), we introduce the notion of a nuance that can be used to increase the precision and power of a VE interface. An experiment verifying the existence of nuances using a neural network (NN) is discussed and a listing of guidelines to follow is given. We also review reasons why traditional ML techniques are difficult to apply to this problem

A computer program to predict rotor rotational noise of a stationary rotor from blade loading coefficient

The programing language used is FORTRAN IV. A description of all main and subprograms is provided so that any user possessing a FORTRAN compiler and random access capability can adapt the program to his facility. Rotor blade surface-pressure spectra can be used by the program to calculate: (1) blade station loading spectra, (2) chordwise and/or spanwise integrated blade-loading spectra, and (3) far-field rotational noise spectra. Any of five standard inline functions describing the chordwise distribution of the blade loading can be chosen in order to study parametrically the acoustic predictions. The program output consists of both printed and graphic descriptions of the blade-loading coefficient spectra and far-field acoustic spectrum. The results may also be written on binary file for future processing. Examples of the application of the program along with a description of the rotational noise prediction theory on which the program is based are also provided

Membrane mediated aggregation of curvature inducing nematogens and membrane tubulation

The shapes of cell membranes are largely regulated by membrane associated, curvature active, proteins. We use a numerical model of the membrane with elongated membrane inclusions, recently developed by us, which posses spontaneous directional curvatures that could be different along and perpendicular to its long axis. We show that, due to membrane mediated interactions these curvature inducing membrane nematogens can oligomerize spontaneously, even at low concentrations, and change the local shape of the membrane. We demonstrate that for a large group of such inclusions, where the two spontaneous curvatures have equal sign, the tubular conformation and sometime the sheet conformation of the membrane are the common equilibrium shapes. We elucidate the factors necessary for the formation of these {\it protein lattices}. Furthermore, the elastic properties of the tubes, like their compressional stiffness and persistence length are calculated. Finally, we discuss the possible role of nematic disclination in capping and branching of the tubular membranes.Comment: 15pages, 8 figure