A Graph-Based Semi-Supervised k Nearest-Neighbor Method for Nonlinear Manifold Distributed Data Classification

$k$ Nearest Neighbors ($k$NN) is one of the most widely used supervised learning algorithms to classify Gaussian distributed data, but it does not achieve good results when it is applied to nonlinear manifold distributed data, especially when a very limited amount of labeled samples are available. In this paper, we propose a new graph-based $k$NN algorithm which can effectively handle both Gaussian distributed data and nonlinear manifold distributed data. To achieve this goal, we first propose a constrained Tired Random Walk (TRW) by constructing an $R$-level nearest-neighbor strengthened tree over the graph, and then compute a TRW matrix for similarity measurement purposes. After this, the nearest neighbors are identified according to the TRW matrix and the class label of a query point is determined by the sum of all the TRW weights of its nearest neighbors. To deal with online situations, we also propose a new algorithm to handle sequential samples based a local neighborhood reconstruction. Comparison experiments are conducted on both synthetic data sets and real-world data sets to demonstrate the validity of the proposed new $k$NN algorithm and its improvements to other version of $k$NN algorithms. Given the widespread appearance of manifold structures in real-world problems and the popularity of the traditional $k$NN algorithm, the proposed manifold version $k$NN shows promising potential for classifying manifold-distributed data.Comment: 32 pages, 12 figures, 7 table

JGraphT -- A Java library for graph data structures and algorithms

Mathematical software and graph-theoretical algorithmic packages to efficiently model, analyze and query graphs are crucial in an era where large-scale spatial, societal and economic network data are abundantly available. One such package is JGraphT, a programming library which contains very efficient and generic graph data-structures along with a large collection of state-of-the-art algorithms. The library is written in Java with stability, interoperability and performance in mind. A distinctive feature of this library is the ability to model vertices and edges as arbitrary objects, thereby permitting natural representations of many common networks including transportation, social and biological networks. Besides classic graph algorithms such as shortest-paths and spanning-tree algorithms, the library contains numerous advanced algorithms: graph and subgraph isomorphism; matching and flow problems; approximation algorithms for NP-hard problems such as independent set and TSP; and several more exotic algorithms such as Berge graph detection. Due to its versatility and generic design, JGraphT is currently used in large-scale commercial, non-commercial and academic research projects. In this work we describe in detail the design and underlying structure of the library, and discuss its most important features and algorithms. A computational study is conducted to evaluate the performance of JGraphT versus a number of similar libraries. Experiments on a large number of graphs over a variety of popular algorithms show that JGraphT is highly competitive with other established libraries such as NetworkX or the BGL.Comment: Major Revisio

Learning parametric dictionaries for graph signals

In sparse signal representation, the choice of a dictionary often involves a tradeoff between two desirable properties -- the ability to adapt to specific signal data and a fast implementation of the dictionary. To sparsely represent signals residing on weighted graphs, an additional design challenge is to incorporate the intrinsic geometric structure of the irregular data domain into the atoms of the dictionary. In this work, we propose a parametric dictionary learning algorithm to design data-adapted, structured dictionaries that sparsely represent graph signals. In particular, we model graph signals as combinations of overlapping local patterns. We impose the constraint that each dictionary is a concatenation of subdictionaries, with each subdictionary being a polynomial of the graph Laplacian matrix, representing a single pattern translated to different areas of the graph. The learning algorithm adapts the patterns to a training set of graph signals. Experimental results on both synthetic and real datasets demonstrate that the dictionaries learned by the proposed algorithm are competitive with and often better than unstructured dictionaries learned by state-of-the-art numerical learning algorithms in terms of sparse approximation of graph signals. In contrast to the unstructured dictionaries, however, the dictionaries learned by the proposed algorithm feature localized atoms and can be implemented in a computationally efficient manner in signal processing tasks such as compression, denoising, and classification

Combined 3D thinning and greedy algorithm to approximate realistic particles with corrected mechanical properties

The shape of irregular particles has significant influence on micro- and macro-scopic behavior of granular systems. This paper presents a combined 3D thinning and greedy set-covering algorithm to approximate realistic particles with a clump of overlapping spheres for discrete element method (DEM) simulations. First, the particle medial surface (or surface skeleton), from which all candidate (maximal inscribed) spheres can be generated, is computed by the topological 3D thinning. Then, the clump generation procedure is converted into a greedy set-covering (SCP) problem. To correct the mass distribution due to highly overlapped spheres inside the clump, linear programming (LP) is used to adjust the density of each component sphere, such that the aggregate properties mass, center of mass and inertia tensor are identical or close enough to the prototypical particle. In order to find the optimal approximation accuracy (volume coverage: ratio of clump's volume to the original particle's volume), particle flow of 3 different shapes in a rotating drum are conducted. It was observed that the dynamic angle of repose starts to converge for all particle shapes at 85% volume coverage (spheres per clump < 30), which implies the possible optimal resolution to capture the mechanical behavior of the system.Comment: 34 pages, 13 figure

Automatic Computation of Feynman Diagrams

Quantum corrections significantly influence the quantities observed in modern particle physics. The corresponding theoretical computations are usually quite lengthy which makes their automation mandatory. This review reports on the current status of automatic calculation of Feynman diagrams in particle physics. The most important theoretical techniques are introduced and their usefulness is demonstrated with the help of simple examples. A survey over frequently used programs and packages is provided, discussing their abilities and fields of applications. Subsequently, some powerful packages which have already been applied to important physical problems are described in more detail. The review closes with the discussion of a few typical applications for the automated computation of Feynman diagrams, addressing current physical questions like properties of the $Z$ and Higgs boson, four-loop corrections to renormalization group functions and two-loop electroweak corrections.Comment: Latex, 62 pages. Typos corrected, references updated and some comments added. Vertical offset changed. The complete paper is also available via anonymous ftp at ftp://ttpux2.physik.uni-karlsruhe.de/ttp98/ttp98-41/ or via www at http://www-ttp.physik.uni-karlsruhe.de/Preprints

Pseudoknots in a Homopolymer

After a discussion of the definition and number of pseudoknots, we reconsider the self-attracting homopolymer paying particular attention to the scaling of the number of pseudoknots at different temperature regimes in two and three dimensions. Although the total number of pseudoknots is extensive at all temperatures, we find that the number of pseudoknots forming between the two halves of the chain diverges logarithmically at (in both dimensions) and below (in 2d only) the theta-temparature. We later introduce a simple model that is sensitive to pseudoknot formation during collapse. The resulting phase diagram involves swollen, branched and collapsed homopolymer phases with transitions between each pair.Comment: submitted to PR

An efficient genetic algorithm for large-scale transmit power control of dense and robust wireless networks in harsh industrial environments

The industrial wireless local area network (IWLAN) is increasingly dense, due to not only the penetration of wireless applications to shop floors and warehouses, but also the rising need of redundancy for robust wireless coverage. Instead of simply powering on all access points (APs), there is an unavoidable need to dynamically control the transmit power of APs on a large scale, in order to minimize interference and adapt the coverage to the latest shadowing effects of dominant obstacles in an industrial indoor environment. To fulfill this need, this paper formulates a transmit power control (TPC) model that enables both powering on/off APs and transmit power calibration of each AP that is powered on. This TPC model uses an empirical one-slope path loss model considering three-dimensional obstacle shadowing effects, to enable accurate yet simple coverage prediction. An efficient genetic algorithm (GA), named GATPC, is designed to solve this TPC model even on a large scale. To this end, it leverages repair mechanism-based population initialization, crossover and mutation, parallelism as well as dedicated speedup measures. The GATPC was experimentally validated in a small-scale IWLAN that is deployed a real industrial indoor environment. It was further numerically demonstrated and benchmarked on both small- and large-scales, regarding the effectiveness and the scalability of TPC. Moreover, sensitivity analysis was performed to reveal the produced interference and the qualification rate of GATPC in function of varying target coverage percentage as well as number and placement direction of dominant obstacles. (C) 2018 Elsevier B.V. All rights reserved