Truthful Approximation Mechanisms for Scheduling Selfish Related Machines

We consider the problem of scheduling jobs on related machines owned by selfish agents. We provide a 5-approximation deterministic truthful mechanism, the first deterministic truthful result for the problem. Previously, Archer and Tardos showed a 2-approximation randomized mechanism which is truthful in expectation only (a weaker notion of truthfulness). In case the number of machines is constant, we provide a deterministic Fully Polynomial-Time Approximation Scheme (FPTAS) and a suitable payment scheme that yields a truthful mechanism for the problem. This result, which is based on converting FPTAS to monotone FPTAS, improves a previous result of Auletta et al., who showed a (4 + ε)-approximation truthful mechanism.     

Switching to Directional Antennas with Constant Increase in Radius and Hop Distance

For any angle α<2π, we show that any connected communication graph that is induced by a set P of n transceivers using omni-directional antennas of radius 1, can be replaced by a strongly connected communication graph, in which each transceiver in P is equipped with a directional antenna of angle α and radius r _dir, for some constant r _dir=r _dir(α). Moreover, the new communication graph is a c-spanner of the original graph, for some constant c=c(α), with respect to number of hops.     

Equi-affine Invariant Geometry for Shape Analysis

Traditional models of bendable surfaces are based on the exact or approximate invariance to deformations that do not tear or stretch the shape, leaving intact an intrinsic geometry associated with it. These geometries are typically defined using either the shortest path length (geodesic distance), or properties of heat diffusion (diffusion distance) on the surface. Both measures are implicitly derived from the metric induced by the ambient Euclidean space. In this paper, we depart from this restrictive assumption by observing that a different choice of the metric results in a richer set of geometric invariants. We apply equi-affine geometry for analyzing arbitrary shapes with positive Gaussian curvature. The potential of the proposed framework is explored in a range of applications such as shape matching and retrieval, symmetry detection, and computation of Voroni tessellation. We show that in some shape analysis tasks, equi-affine-invariant intrinsic geometries often outperform their Euclidean-based counterparts. We further explore the potential of this metric in facial anthropometry of newborns. We show that intrinsic properties of this homogeneous group are better captured using the equi-affine metric.     

Adaptive water management in Israel: structure and policy options

Difficulties in integrating technical, economic and institutional factors present a major gap in analytical capacity to guide water policy. This article presents an integrated framework to support water policy and guide water management choices, with application to Israel. That framework rests on the theory of economic policy originally developed by Tinbergen. It sees national water challenges as consisting of external factors, constraints, policy instruments and targets. The need for a modern implementation of the theory of economic policy is motivated by emerging environmental requirements, scarce water, growing demands for domestic use, and ongoing needs to implement existing and potential peace agreements.     

Over-Parameterized Variational Optical Flow

A novel optical flow estimation process based on a spatio-temporal model with varying coefficients multiplying a set of basis functions at each pixel is introduced. Previous optical flow estimation methodologies did not use such an over parameterized representation of the flow field as the problem is ill-posed even without introducing any additional parameters: Neighborhood based methods of the Lucas–Kanade type determine the flow at each pixel by constraining the flow to be described by a few parameters in small neighborhoods. Modern variational methods represent the optic flow directly via the flow field components at each pixel. The benefit of over-parametrization becomes evident in the smoothness term, which instead of directly penalizing for changes in the optic flow, accumulates a cost of deviating from the assumed optic flow model. Our proposed method is very general and the classical variational optical flow techniques are special cases of it, when used in conjunction with constant basis functions. Experimental results with the novel flow estimation process yield significant improvements with respect to the best results published so far.     

Study of DNA Origami Dimerization and Dimer Dissociation Dynamics and of the Factors that Limit Dimerization

Organizing DNA origami building blocks into higher order structures is essential for fabrication of large structurally and functionally diverse devices and molecular machines. Unfortunately, the yields of origami building block attachment reactions are typically not sufficient to allow programed assembly of DNA devices made from more than a few origami building blocks. To investigate possible reasons for these low yields, a detailed single‐molecule fluorescence study of the dynamics of rectangular origami dimerization and origami dimer dissociation reactions is conducted. Reactions kinetics and yields are investigated at different origami and ion concentrations, for different ion types, for different lengths of bridging strands, and for the “sticky end” and “weaving welding” attachment techniques. Dimerization yields are never higher than 86%, which is typical for such systems. Analysis of the dynamic data shows that the low yield cannot be explained by thermodynamic instability or structural imperfections of the origami constructs. Atomic force microscopy and gel electrophoresis evidence reveal self‐dimerization of the origami monomers, likely via blunt‐end interactions made possible by the presence of bridging strands. It is suggested that this mechanism is the major factor that inhibits correct dimerization and means to overcome it are discussed.     

Regularizing Flows over Lie Groups

In this paper we discuss regularization of images that take their value in matrix Lie groups. We describe an image as a section in a principal bundle which is a fibre bundle where the fiber (the feature space) is a Lie group. Via the scalar product on the Lie algebra, we define a bi-invariant metric on the Lie-group manifold. Thus, the fiber becomes a Riemannian manifold with respect to this metric. The induced metric from the principal bundle to the image manifold is obtained by means of the bi-invariant metric. A functional over the space of sections, i.e., the image manifolds, is defined. The resulting equations of motion generate a flow which evolves the sections in the spatial-Lie-group manifold. We suggest two different approaches to treat this functional and the corresponding PDEs. In the first approach we derive a set of coupled PDEs for the local coordinates of the Lie-group manifold. In the second approach a coordinate-free framework is proposed where the PDE is defined directly with respect to the Lie-group elements. This is a parameterization-free method. The differences between these two methods are discussed. We exemplify this framework on the well-known orientation diffusion problem, namely, the unit-circle S ¹ which is identified with the group of rotations in two dimensions, SO(2). Regularization of the group of rotations in 3D and 4D, SO(3) and SO(4), respectively, is demonstrated as well.