Reduction of mm-Regular Noncrossing Partitions

In this paper, we present a reduction algorithm which transforms $m$-regular partitions of $[n]=\{1, 2, ..., n\}$ to $(m-1)$-regular partitions of $[n-1]$. We show that this algorithm preserves the noncrossing property. This yields a simple explanation of an identity due to Simion-Ullman and Klazar in connection with enumeration problems on noncrossing partitions and RNA secondary structures. For ordinary noncrossing partitions, the reduction algorithm leads to a representation of noncrossing partitions in terms of independent arcs and loops, as well as an identity of Simion and Ullman which expresses the Narayana numbers in terms of the Catalan numbers

Separation probabilities for products of permutations

We study the mixing properties of permutations obtained as a product of two uniformly random permutations of fixed cycle types. For instance, we give an exact formula for the probability that elements $1,2,...,k$ are in distinct cycles of the random permutation of $\{1,2,...,n\}$ obtained as product of two uniformly random $n$-cycles

Rotating system for four-dimensional transverse rms-emittance measurements

Knowledge of the transverse four-dimensional beam rms-parameters is essential for applications that involve lattice elements that couple the two transverse degrees of freedom (planes). Of special interest is the removal of inter-plane correlations to reduce the projected emittances. A dedicated ROtating System for Emittance measurements (ROSE) has been proposed, developed, and successfully commissioned to fully determine the four-dimensional beam matrix. This device has been used at the High Charge injector (HLI) at GSI using a beam line which is composed of a skew quadrupole triplet, a normal quadrupole doublet, and ROSE. Mathematical algorithms, measurements, and results for ion beams of 83Kr13+ at 1.4 MeV/u are reported in this paper.Comment: 11 pages, 10 figure

Feasibility study of a hand guided robotic drill for cochleostomy

The concept of a hand guided robotic drill has been inspired by an automated, arm supported robotic drill recently applied in clinical practice to produce cochleostomies without penetrating the endosteum ready for inserting cochlear electrodes. The smart tactile sensing scheme within the drill enables precise control of the state of interaction between tissues and tools in real-time. This paper reports development studies of the hand guided robotic drill where the same consistent outcomes, augmentation of surgeon control and skill, and similar reduction of induced disturbances on the hearing organ are achieved. The device operates with differing presentation of tissues resulting from variation in anatomy and demonstrates the ability to control or avoid penetration of tissue layers as required and to respond to intended rather than involuntary motion of the surgeon operator. The advantage of hand guided over an arm supported system is that it offers flexibility in adjusting the drilling trajectory. This can be important to initiate cutting on a hard convex tissue surface without slipping and then to proceed on the desired trajectory after cutting has commenced. The results for trials on phantoms show that drill unit compliance is an important factor in the design

Action Recognition Based on Joint Trajectory Maps Using Convolutional Neural Networks

Recently, Convolutional Neural Networks (ConvNets) have shown promising performances in many computer vision tasks, especially image-based recognition. How to effectively use ConvNets for video-based recognition is still an open problem. In this paper, we propose a compact, effective yet simple method to encode spatio-temporal information carried in $3D$ skeleton sequences into multiple $2D$ images, referred to as Joint Trajectory Maps (JTM), and ConvNets are adopted to exploit the discriminative features for real-time human action recognition. The proposed method has been evaluated on three public benchmarks, i.e., MSRC-12 Kinect gesture dataset (MSRC-12), G3D dataset and UTD multimodal human action dataset (UTD-MHAD) and achieved the state-of-the-art results