Is Gravitational Lensing by Intercluster Filaments Always Negligible?

Intercluster filaments negligibly contribute to the weak lensing signal in general relativity (GR), $\gamma_{N}\sim 10^{-4}-10^{-3}$. In the context of relativistic modified Newtonian dynamics (MOND) introduced by Bekenstein, however, a single filament inclined by $\approx 45^\circ$ from the line of sight can cause substantial distortion of background sources pointing towards the filament's axis ($\kappa=\gamma=(1-A^{-1})/2\sim 0.01$); this is rigorous for infinitely long uniform filaments, but also qualitatively true for short filaments ($\sim 30$Mpc), and even in regions where the projected matter density of the filament is equal to zero. Since galaxies and galaxy clusters are generally embedded in filaments or are projected on such structures, this contribution complicates the interpretation of the weak lensing shear map in the context of MOND. While our analysis is of mainly theoretical interest providing order-of-magnitude estimates only, it seems safe to conclude that when modeling systems with anomalous weak lensing signals, e.g. the "bullet cluster" of Clowe et al., the "cosmic train wreck" of Abell 520 from Mahdavi et al., and the "dark clusters" of Erben et al., filamentary structures might contribute in a significant and likely complex fashion. On the other hand, our predictions of a (conceptual) difference in the weak lensing signal could, in principle, be used to falsify MOND/TeVeS and its variations.Comment: 11 pages, 6 figures, published versio

Global Structure of Moduli Space for BPS Walls

We study the global structure of the moduli space of BPS walls in the Higgs branch of supersymmetric theories with eight supercharges. We examine the structure in the neighborhood of a special Lagrangian submanifold M, and find that the dimension of the moduli space can be larger than that naively suggested by the index theorem, contrary to previous examples of BPS solitons. We investigate BPS wall solutions in an explicit example of M using Abelian gauge theory. Its Higgs branch turns out to contain several special Lagrangian submanifolds including M. We show that the total moduli space of BPS walls is the union of these submanifolds. We also find interesting dynamics between BPS walls as a byproduct of the analysis. Namely, mutual repulsion and attraction between BPS walls sometimes forbid a movement of a wall and lock it in a certain position; we also find that a pair of walls can transmute to another pair of walls with different tension after they pass through.Comment: 42 pages, 11 figures; a few comments adde

Remote control of a robotic hand using a leap sensor

This paper presents a low-cost gesture-based remote control of a ro-botic hand. The proposed control architecture is based on a commercial leap motion sensor and an Arduino board, which have been chosen due to their low-cost and user-friendly features. A specific Matlab code has been implemented to collect data from the leap motion sensor and to generate proper instructions to control a robotic hand, which has been 3D print at Sheffield Hallam Univer-sity. Experimental tests have been carried out validate the effectiveness of the proposed remote control for performing various grasping tasks

Optimization of the Kinematic Chain of the Thumb for a Hand Prosthesis Based on the Kapandji Opposition Test

Ponènica presentada a International Symposium on Computer Methods in Biomechanics and Biomedical Engineering - CMBBE 2019The thumb plays a key role in the performance of the hand for grasp-ing and manipulating objects. In artificial hands the complex thumb’s kinematic chain (TKC) is simplified and its five degrees of freedom are reduced to only one or two with the consequent loss of dexterity of the hand. The Kapandji op-position test (KOT) has been clinically used in pathological human hands for evaluating the thumb opposition and it has also been employed in some previ-ous studies as reference for the design of the TKC in artificial hands, but with-out a clearly stated methodology. Based on this approaches, in this study we present a computational method to optimize the whole TKC (base placement, link lengths and joint orientation angles) of an artificial hand based on its per-formance in the KOT. The cost function defined for the optimization (MPE) is a weighted mean position error when trying to reproduce the KOT postures and can be used also as a metric to quantify thumb opposition in the hand. As a case study, the method was applied to the improvement of the TKC of an artificial hand developed by the authors and the MPE was reduced to near one third of that of the original design, increasing significantly the number of reachable po-sitions in the KOT. The metric proposed based on the KOT can be used directly or in combination with other to improve the kinematic chain of artificial hands

On Five-dimensional Superspaces

Recent one-loop calculations of certain supergravity-mediated quantum corrections in supersymmetric brane-world models employ either the component formulation (hep-th/0305184) or the superfield formalism with only half of the bulk supersymmetry manifestly realized (hep-th/0305169 and hep-th/0411216). There are reasons to expect, however, that 5D supergraphs provide a more efficient setup to deal with these and more involved (in particular, higher-loop) calculations. As a first step toward elaborating such supergraph techniques, we develop in this letter a manifestly supersymmetric formulation for 5D globally supersymmetric theories with eight supercharges. Simple rules are given to reduce 5D superspace actions to a hybrid form which keeps manifest only the 4D, N=1 Poincare supersymmetry. (Previously, such hybrid actions were carefully worked out by rewriting the component actions in terms of simple superfields). To demonstrate the power of this formalism for model building applications, two families of off-shell supersymmetric nonlinear sigma-models in five dimensions are presented (including those with cotangent bundles of Kahler manifolds as target spaces). We elaborate, trying to make our presentation maximally clear and self-contained, on the techniques of 5D harmonic and projective superspaces used at some stages in this letter.Comment: 46 pages, 3 figures. V5: version published in JHE

A unification in the theory of linearization of second order nonlinear ordinary differential equations

In this letter, we introduce a new generalized linearizing transformation (GLT) for second order nonlinear ordinary differential equations (SNODEs). The well known invertible point (IPT) and non-point transformations (NPT) can be derived as sub-cases of the GLT. A wider class of nonlinear ODEs that cannot be linearized through NPT and IPT can be linearized by this GLT. We also illustrate how to construct GLTs and to identify the form of the linearizable equations and propose a procedure to derive the general solution from this GLT for the SNODEs. We demonstrate the theory with two examples which are of contemporary interest.Comment: 8 page