Kinematic Analysis and Trajectory Planning of the Orthoglide 5-axis

The subject of this paper is about the kinematic analysis and the trajectory planning of the Orthoglide 5-axis. The Orthoglide 5-axis a five degrees of freedom parallel kinematic machine developed at IRCCyN and is made up of a hybrid architecture, namely, a three degrees of freedom translational parallel manip-ulator mounted in series with a two degrees of freedom parallel spherical wrist. The simpler the kinematic modeling of the Or-thoglide 5-axis, the higher the maximum frequency of its control loop. Indeed, the control loop of a parallel kinematic machine should be computed with a high frequency, i.e., higher than 1.5 MHz, in order the manipulator to be able to reach high speed motions with a good accuracy. Accordingly, the direct and inverse kinematic models of the Orthoglide 5-axis, its inverse kine-matic Jacobian matrix and the first derivative of the latter with respect to time are expressed in this paper. It appears that the kinematic model of the manipulator under study can be written in a quadratic form due to the hybrid architecture of the Orthoglide 5-axis. As illustrative examples, the profiles of the actuated joint angles (lengths), velocities and accelerations that are used in the control loop of the robot are traced for two test trajectories.Comment: Appears in International Design Engineering Technical Conferences \& Computers and Information in Engineering Conference, Aug 2015, Boston, United States. 201

Brane Gases on K3 and Calabi-Yau Manifolds

We initiate the study of Brane Gas Cosmology (BGC) on manifolds with non-trivial holonomy. Such compactifications are required within the context of superstring theory in order to make connections with realistic particle physics. We study the dynamics of brane gases constructed from various string theories on background spaces having a K3 submanifold. The K3 compactifications provide a stepping stone for generalising the model to the case of a full Calabi-Yau three-fold. Duality symmetries are discussed within a cosmological context. Using a duality, we arrive at an N=2 theory in four-dimensions compactified on a Calabi-Yau manifold with SU(3) holonomy. We argue that the Brane Gas model compactified on such spaces maintains the successes of the trivial toroidal compactification while greatly enhancing its connection to particle physics. The initial state of the universe is taken to be a small, hot and dense gas of p-branes near thermal equilibrium. The universe has no initial singularity and the dynamics of string winding modes allow three spatial dimensions to grow large, providing a possible solution to the dimensionality problem of string theory.Comment: 26 pages; Significant revisions: review material truncated; presentation improve

Modelling the conditional distribution of daily stock index returns: an alternative Bayesian semiparametric model

This paper introduces a new family of Bayesian semi-parametric models for the conditional distribution of daily stock index returns. The proposed models capture key stylized facts of such returns, namely heavy tails, asymmetry, volatility clustering, and the ‘leverage effect’. A Bayesian nonparametric prior is used to generate random density functions that are unimodal and asymmetric.Volatility is modelled parametrically. The new model is applied to the daily re- turns of the S&P 500, FTSE 100, and EUROSTOXX 50 indices and is compared to GARCH, Stochastic Volatility, and other Bayesian semi-parametric models

News and price returns from threshold behaviour and vice-versa: exact solution of a simple agent-based market model

Starting from an exact relationship between news, threshold and price return distributions in the stationary state, I discuss the ability of the Ghoulmie-Cont-Nadal model of traders to produce fat-tailed price returns. Under normal conditions, this model is not able to transform Gaussian news into fat-tailed price returns. When the variance of the news so small that only the players with zero threshold can possibly react to news, this model produces Levy-distributed price returns with a -1 exponent. In the special case of super-linear price impact functions, fat-tailed returns are obtained from well-behaved news.Comment: 4 pages, 3 figures. This is quite possibly the final version. To appear in J. Phys

Taxonomy Induction using Hypernym Subsequences

We propose a novel, semi-supervised approach towards domain taxonomy induction from an input vocabulary of seed terms. Unlike all previous approaches, which typically extract direct hypernym edges for terms, our approach utilizes a novel probabilistic framework to extract hypernym subsequences. Taxonomy induction from extracted subsequences is cast as an instance of the minimumcost flow problem on a carefully designed directed graph. Through experiments, we demonstrate that our approach outperforms stateof- the-art taxonomy induction approaches across four languages. Importantly, we also show that our approach is robust to the presence of noise in the input vocabulary. To the best of our knowledge, no previous approaches have been empirically proven to manifest noise-robustness in the input vocabulary

Fresnel and Fourier digital holography architectures: a comparison.

In this manuscript we examine the characteristics of holograms that are captured using both Fresnel and lens-less Fourier digital holographic systems. We begin by introducing some of the fundamental equations describing the intensity distribution captured by the camera. Naturally this captured intensity will vary depending on whether the system used is a Fourier or a Fresnel due to the different reference field in each case, however as we shall see with appropriate numerical processing it is possible to obtain similar performance from both systems. We discuss a reconstruction algorithm for changing the focus depth in Fourier holograms and examine how it effects the twin image and dc terms. A theoretical comparison with Fresnel holograms is made. Experimental results are provided to support our analysis. We finish with a brief conclusion

Review of Twin Reduction and Twin Removal Techniques in Holography

In this paper we review the major contributions over the past sixty years to the subject of twin reduction and twin removal in holography. We show that this collective work may be broken down into a number of categories including the well known techniques of off-axis holography and phase retrieval

Twin suppression in digital holography by means of speckle reduction

A method for numerically removing the twin image in on-axis digital holography, based on multiple digital holograms, is discussed. The digital holograms under examination are captured experimentally using an in-line modified Mach-Zehnder interferometric setup and subsequently reconstructed numerically. The technique is suitable for both transmission and reflection geometry. Each individual hologram is recorded with a statistically independent diffuse illumination field. This is achieved by shifting a glass diffuser in the x-y plane of the object path. By recording the holograms in this manner the twin image, from a numerical reconstruction, appears as speckle. By reducing this speckle pattern the twin image can be effectively removed in the reconstruction plane. A theoretical model is developed and experimental results are presented that validate this model

Factorization of Numbers with the temporal Talbot effect: Optical implementation by a sequence of shaped ultrashort pulses

We report on the successful operation of an analogue computer designed to factor numbers. Our device relies solely on the interference of classical light and brings together the field of ultrashort laser pulses with number theory. Indeed, the frequency component of the electric field corresponding to a sequence of appropriately shaped femtosecond pulses is determined by a Gauss sum which allows us to find the factors of a number

Self-Motions of General 3-RPR Planar Parallel Robots

This paper studies the kinematic geometry of general 3-RPR planar parallel robots with actuated base joints. These robots, while largely overlooked, have simple direct kinematics and large singularity-free workspace. Furthermore, their kinematic geometry is the same as that of a newly developed parallel robot with SCARA-type motions. Starting from the direct and inverse kinematic model, the expressions for the singularity loci of 3-RPR planar parallel robots are determined. Then, the global behaviour at all singularities is geometrically described by studying the degeneracy of the direct kinematic model. Special cases of self-motions are then examined and the degree of freedom gained in such special configurations is kinematically interpreted. Finally, a practical example is discussed and experimental validations performed on an actual robot prototype are presented