Academic literature on the topic 'Permutation Embedding Sequence'

A color image watermarking scheme using the chaotic properties of 2D tent map and Chebyshev map is proposed. Given control parameters and initial values, one can iterate the 2D tent map to get one chaotic sequence and obtain one permutation by sorting the chaotic sequence in ascending order. The permutation is then utilized to shuffle the blue channel components of color image as a preprocessing stage to enhance the security, imperceptibility and robustness of watermarking. Meanwhile, one can iterate the Chebyshev map to generate another chaotic sequence to determine the embedding bit positions and strengthen the security as well. Experiment results show that the watermarking scheme is secure with large key space, imperceptible and robust against cropping, noise attacks.

AbstractThe irregular domain and lack of ordering make it challenging to design deep neural networks for point cloud processing. This paper presents a novel framework named Point Cloud Transformer (PCT) for point cloud learning. PCT is based on Transformer, which achieves huge success in natural language processing and displays great potential in image processing. It is inherently permutation invariant for processing a sequence of points, making it well-suited for point cloud learning. To better capture local context within the point cloud, we enhance input embedding with the support of farthest point sampling and nearest neighbor search. Extensive experiments demonstrate that the PCT achieves the state-of-the-art performance on shape classification, part segmentation, semantic segmentation, and normal estimation tasks.

In this paper we are concerned with the following conjecture.Conjecture. For any positive integers n and k satisfying k < n, and any sequence a1, a2, … ak of not necessarily distinct elements of Zn, there exists a permutation π ∈ Sk such that the elements aπ(i)+i are all distinct modulo n.We prove this conjecture when 2k [les ] n+1. We then apply this result to tree embeddings. Specifically, we show that, if T is a tree with n edges and radius r, then T decomposes Kt for some t [les ] 32(2r+4)n2+1.

AbstractMotivated by a question of A. Skalski and P. M. Sołtan (2016) about inner faithfulness of S. Curran’s map of extending a quantum increasing sequence to a quantum permutation, we revisit the results and techniques of T. Banica and J. Bichon (2009) and study some group-theoretic properties of the quantum permutation group on points. This enables us not only to answer the aforementioned question in the positive for the case where n = 4, k = z, but also to classify the automorphisms of , describe all the embeddings O−1(2) ⊂ and show that all the copies of O−1(2) ⊂ are conjugate. We then use these results to show that the converse to the criterion we applied to answer the aforementioned question is not valid.

We introduce an operational model of concurrent systems, called automata with concurrency relations. These are labeled transition systems [Formula: see text] in which the event set is endowed with a collection of symmetric binary relations which describe when two events at a particular state of [Formula: see text] commute. This model generalizes the recent concept of Stark’s trace automata. A permutation equivalence for computation sequences of [Formula: see text] arises canonically, and we obtain a natural domain [Formula: see text] comprising the induced equivalence classes. We give a complete order-theoretic characterization of all such partial orders [Formula: see text] which turn out to be particular finitary domains. The arising domains [Formula: see text] are particularly pleasant Scott-domains, if [Formula: see text] is assumed to be concurrent, i.e. if the concurrency relations of [Formula: see text] depend (in a natural way) locally on each other, but not necessarily globally. We show that both event domains and dI-domains arise, up to isomorphism, as domains [Formula: see text] with well-behaved such concurrent automata [Formula: see text]. We introduce a subautomaton relationship for concurrent automata and show that, given two concurrency domains (D, ≤), (D′, ≤), there exists a nice stable embedding-projection pair from D to D′ iff D, D′ can be generated by concurrent automata [Formula: see text] such that [Formula: see text] is a subautomaton of [Formula: see text]. Finally, we introduce the concept of locally finite concurrent automata as a limit of finite concurrent automata and show that there exists a universal homogeneous locally finite concurrent automaton, which is unique up to isomorphism.

A new approach to image-space hardware-based rendering of Constructive Solid Geometry (CSG) models is presented. The work is motivated by the evolving functionality and performance of computer graphics hardware. This work is also motivated by a specific industrial application --- interactive verification of five axis grinding machine tool programs. The goal is to minimise the amount of time required to render each frame in an animation or interactive application involving boolean combinations of three dimensional shapes. The Sequenced Convex Subtraction (SCS) algorithm utilises sequenced subtraction of convex objects for the purpose of interactive CSG rendering. Concave shapes must be decomposed into convex shapes for the purpose of rendering. The length of Permutation Embedding Sequences (PESs) used as subtraction sequences are shown to have a quadratic lower bound. In many situations shorter sequences can be used, in the best case linear. Approaches to s ubtraction sequence encoding are presented including the use of object-space overlap information. The implementation of the algorithm is experimentally shown to perform better on modern commodity graphics hardware than previously reported methods. This work also examines performance aspects of the SCS algorithm itself. Overall performance depends on hardware characteristics, the number and spatial arrangement of primitives, and the structure and boolean operators of the CSG tree.