GPU-accelerated deformation mapping in hybrid organ models for real-time simulation

In different types of information systems, such as multimedia information systems and geographic information systems, object-based information is represented via polygons corresponding to the boundaries of object regions. In many applications, the polygons have large number of vertices and edges, thus a way of representing the polygons with less number of vertices and edges is developed. This approach, called polygon approximation, or polygon simplification, is basically motivated with the difficulties faced in processing polygons with large number of vertices. Besides, large memory usage and disk requirements, and the possibility of having relatively more noise can also be considered as the reasons for polygon simplification. In this paper, a kinematics-based method for polygon approximation is proposed. The vertices of polygons are simplified according to the velocities and accelerations of the vertices with respect to the centroid of the polygon. Another property of the proposed method is that the user may set the number of vertices to be in the approximated polygon, and may hierarchically simplify the output. The approximation method is demonstrated through the experiments based on a set of polygonal objects.

Abstract. In this paper, we present Par@Graph, a software toolbox to reconstruct and analyze complex climate networks having a large number of nodes (up to at least 106) and edges (up to at least 1012). The key innovation is an efficient set of parallel software tools designed to leverage the inherited hybrid parallelism in distributed-memory clusters of multi-core machines. The performance of the toolbox is illustrated through networks derived from sea surface height (SSH) data of a global high-resolution ocean model. Less than 8 min are needed on 90 Intel Xeon E5-4650 processors to reconstruct a climate network including the preprocessing and the correlation of 3 × 105 SSH time series, resulting in a weighted graph with the same number of vertices and about 3.2 × 108 edges. In less than 14 min on 30 processors, the resulted graph's degree centrality, strength, connected components, eigenvector centrality, entropy and clustering coefficient metrics were obtained. These results indicate that a complete cycle to construct and analyze a large-scale climate network is available under 22 min Par@Graph therefore facilitates the application of climate network analysis on high-resolution observations and model results, by enabling fast network reconstruct from the calculation of statistical similarities between climate time series. It also enables network analysis at unprecedented scales on a variety of different sizes of input data sets.

Assigning mountain-valley fold lines of flat-foldable origami patterns based on graph theory and mixed-integer linear programming

Making the right management decisions in the logging industry is a complex multi-factorial task. The multivariance of solutions consists of various options for the application of technological chains of logging operations and timber transportation. Indeed, today the market offers a lot of options for systems of forestry machines, with or without forest storage with timber transportation at different seasons. Previous studies propose mathematical dependencies, an algorithm, and methods to solve all these problems. It makes it possible to search for the maximum flow of minimum cost in the dynamic structure of the technological process of performing work at the enterprise. They determine the conditions for solving the problem by the graph method. However, the proposed calculations for graphs with a large number of vertices and arcs connecting them are very laborious and require a lot of time. To solve this problem, the article presents the development of a computer application that performs basic calculations and calculates the optimal technological sequence of operations. The algorithms of the application, its description and principle of operation have been presented. The developed program enables to automate the process of finding the optimal sequence of technological operations in the logging enterprise operating procedure. Upon receipt of the results, it is possible to compare and analyze various process options for decision making.

A computer code based on the Givens–Householder matrix diagonalization method is used to calculate the spectra of graphs containing a large number of vertices. The code is most general in that it can handle graphs containing 200 or more vertices. Further, the code can be used to generate the spectra of weighted graphs. The program requires as input only the neighborhood table of the graph. The spectra of many graphs are generated for the first time in less than a few minutes of computer time. Applications to a number of chemical systems including two forms (foot and hand) of the recently synthesized C60 cluster and the effect of bond alternation on these systems are discussed. In addition, the spectra of square and honeycomb lattices and the characteristic polynomials of the foot and hand forms of the C60 cluster are obtained.

Chapter 13 - Robust and Scalable Shape Prior Modeling via Sparse Representation and Dictionary Learning

We propose the efficient and accurate hierarchical ICIA fitting method for 3D Morphable Models (3DMMs). The conventional ICIA fitting method for 3DMMs requires a long computation time because the 3D face model contains a large number of vertices and it also requires to compute the Hessian matrix using the visible vertices every iteration. For the efficient fitting, we use the hierarchical fitting that use a set of multi-resolution 3D face model and the Gaussian image pyramid. For more accurate fitting, we use a two-stage parameter update that only update the rigid and the texture parameters and then update all parameters after the initial convergence. We present several experiment results to prove that our proposed method shows better performance than previous works.

Lattice structure lightweight triangulation for additive manufacturing

The longest path problem asks for a path with the largest number of vertices in a given graph. The first polynomial time algorithm (with running time O(n4)) has been recently developed for interval graphs. Even though interval and circular-arc graphs look superficially similar, they differ substantially, as circular-arc graphs are not perfect. In this paper, we prove that for every path P of a circular-arc graph G, we can appropriately “cut” the circle, such that the obtained (not induced) interval subgraph G′ of G admits a path P′ on the same vertices as P. This non-trivial result is of independent interest, as it suggests a generic reduction of a number of path problems on circular-arc graphs to the case of interval graphs with a multiplicative linear time overhead of O(n). As an application of this reduction, we present the first polynomial algorithm for the longest path problem on circular-arc graphs, which turns out to have the same running time O(n4) with the one on interval graphs, as we manage to get rid of the linear overhead of the reduction. This algorithm computes in the same time an n-approximation of the number of different vertex sets that provide a longest path; in the case where G is an interval graph, we compute the exact number. Moreover, our algorithm can be directly extended with the same running time to the case where every vertex has an arbitrary positive weight.

Given a graph G with n vertices and stability number α(G), Turan's Theorem gives a lower bound on the number of edges in G. Furthermore, Turan has proved that the lower bound is only attained if G is the union of α(G) disjoint balanced cliques. We prove a similar result for the 2-stability number α2(G) of G, which is defined as the largest number of vertices in a 2-colorable subgraph of G. Given a graph G with n vertices and 2-stability number α2(G), we give a lower bound on the number of edges in G and characterize the graphs for which this bound is attained. These graphs are the union of isolated vertices and disjoint balanced cliques. We then derive lower bounds on the 2-stability number, and finally discuss the extension of Turan's Theorem to the q-stability number, for q>2.

The article considers the solution of the traveling salesman problem using reinforcement learning. This task is to find the optimal route that passes through the specified cities at least once and then returns to the original city. The traveling salesman problem belongs to the class of NP-hard problems, and therefore finding an exact solution for sufficiently large data sets using classical mathematical methods turns out to be impossible in a reasonable time. The aim of the work is to increase the efficiency and speed of solving the traveling salesman problem with a large number of vertices by using the reinforcement learning method. A variant of solving the traveling salesman problem using the Q-learning algorithm is considered, which allows the agent to learn the optimal behavior strategy in the process of interacting with the environment, which is a set of cities and roads between them, which are modeled as a graph. Within the framework of this study, a software package was developed to solve the traveling salesman problem using reinforcement learning. A series of experiments related to the appearance of unforeseen conditions complicating the work of a traveling salesman, such as the appearance of "problem" zones or zones, the passage through which gives a reduction in time. The results of the experiments showed the capabilities of the developed algorithm for adaptation to changes and obstacles of the environment. The resulting algorithm shows itself to be more stable and reliable compared to the algorithms obtained by classical solution methods. The solution of this problem can be used in practice in a variety of real situations, including optimization of deliveries or network routing, assistance in the work of logistics departments of various transport, postal and courier services.

Shape information plays an important role in biomedical image analysis because of the strong shape characteristics of biological structures. It is often used as a prior to constrain or refine the intermediate shape information derived from low-level image features. In this paper, we give an overview of the sparse shape composition based prior modeling method and its various applications of biomedical image analysis. Instead of learning a generative shape model, it incorporates shape priors on-the-fly through the sparse shape composition. Particularly, a shape instance derived from low level image features is refined by a sparse linear combination of a sparse set of shapes in the repository. We also design three strategies to improve run-time efficiency. 1) When the shape repository contains a large number of instances, K-SVD can be used to learn a more compact but still informative shape dictionary. 2) If the derived shape instance has a large number of vertices, which often appears in 3D problems, affinity propagation method can be used to partition the surface into small subregions. 3) When there are multiple structures, hierarchical scheme is employed to model them simultaneously. These strategies decrease the scale of the sparse optimization problem and thus speed up the algorithm. Our method is applied on different biomedical image analysis problems, including localization, tracking and segmentation of anatomical structures. In all of these applications, this method achieves promising results.

Cayley graphs of given degree and diameters 3, 4 and 5

On large regular [formula omitted]-mixed graphs

In this work we present a new local, vertex-level measure of community change. Our measure detects vertices that change community membership due to the actions (edges) of a vertex itself and not only due to global community shifts. The local nature of our measure is important for analyzing real graphs because communities may change to a large degree from one snapshot in time to the next. Using both real and synthetic graphs, we compare our measure to an alternative, global approach. Both approaches detect community switching vertices in a synthetic example with little overall community change. However, when communities do not evolve smoothly over time, the global approach flags a very large number of vertices, while our local method does not.