lionessR: single-sample network reconstruction in R

SummaryWe recently developed LIONESS (Linear Interpolation to Obtain Network Estimates for Single Samples), a method that can be used together with network reconstruction algorithms to extract networks for individual samples in a population. LIONESS was originally made available as a function within the PANDA (Passing Attributes between Networks for Data Assimilation) regulatory network reconstruction framework. In this application note, we describe lionessR, an R implementation of LIONESS that can be applied to any network reconstruction method in R that outputs a complete, weighted adjacency matrix. As an example, we use lionessR to model single-sample co-expression networks on a bone cancer dataset, and show how lionessR can be used to identify differential co-expression between two groups of patients.Availability and implementationThe lionessR open source R package, which includes a vignette of the application, is freely available athttps://github.com/mararie/[email protected]

The Use of Weighted Adjacency Matrix for Searching Optimal Transportation Routes

This article provides a new approach to searching solutions of the ship transport optimalization problems. It brings a new variant of one algorithm of searching for the Minimum Spanning Tree. The new element in the algorithm is that it uses the Weighted Adjacency Matrix. This Weighted Adjacency Matrix is suitable for searching for the Minimum Spanning Tree (MST) of the graph. It shows how it could be used in cases where weighted edges of the graph are given. This creates a new procedure of searching for the MST of the graph and completes previously known algorithms of searching for the MST. In the field of transportation it could be succesfully used for solutions of optimizing transportation routes where smallest costs are wanted. Proposed Weighted Adjacency Matrix could be used in similar issues in the field of the graph theory, where graphs with weighted edges are given. The procedure is shown on the attached example.

An Algorithm for Identifying the Isomorphism of Planar Multiple Joint and Gear Train Kinematic Chains

Isomorphism identification of kinematic chains is one of the most important and challenging mathematical problems in the field of mechanism structure synthesis. In this paper, a new algorithm to identify the isomorphism of planar multiple joint and gear train kinematic chains has been presented. Firstly, the topological model (TM) and the corresponding weighted adjacency matrix (WAM) are introduced to describe the two types of kinematic chains, respectively. Then, the equivalent circuit model (ECM) of TM is established and solved by using circuit analysis method. The solved node voltage sequence (NVS) is used to determine the correspondence of vertices in two isomorphism identification kinematic chains, so an algorithm to identify two specific types of isomorphic kinematic chains has been obtained. Lastly, some typical examples are carried out to prove that it is an accurate, efficient, and easy mathematical algorithm to be realized by computer.

An Algorithm for Determining the Position and Orientation of 3-D Objects from Images Using Spectral Graph Theory

This paper describes an algorithm for computing the position and orientation of 3-D objects by comparing graphs. The graphs are based on feature points of the image. Comparison is performed by a spectral decomposition with obtaining eigenvectors of weighted adjacency matrix of the graph.

Content-Based Keyframe Clustering Using Near Duplicate Keyframe Identification

In this paper, the authors propose an effective content-based clustering method for keyframes of news video stories using the Near Duplicate Keyframe (NDK) identification concept. Initially, the authors investigate the near-duplicate relationship, as a content-based visual similarity across keyframes, through the Near-Duplicate Keyframe (NDK) identification algorithm presented. The authors assign a near-duplicate score to each pair of keyframes within the story. Using an efficient keypoint matching technique followed by matching pattern analysis, this NDK identification algorithm can handle extreme zooming and significant object motion. In the second step, the weighted adjacency matrix is determined for each story based on assigned near duplicate score. The authors then use the spectral clustering scheme to remove outlier keyframes and partition remainders. Two sets of experiments are carried out to evaluate the NDK identification method and assess the proposed keyframe clustering method performance.

Social Network of Faculties According to Student Preferences in Transition to Higher Education

In social network analysis, the studies on weighted adjacency matrix of nodes are increasing day by day. In thispaper, a method is proposed by including node properties to neighbourhood matrix, in order to see the structures of weightedadjacency matrix that defines the relationship between the nodes. In accordance with this proposal, the relationship betweenthe faculties of Turkish universities is studied according to student preferences. Weighted adjacency matrix between facultiesis composed based on the frequency of faculty preference of students. By using the properties of faculties, this matrix ismultiplied by the adjacency matrix, calculated by Squared Euclidian Distance. The weighted adjacency matrix of the facultiesis compared with the re-calculated weighted adjacency matrix. It is observed that the relations between faculties are turnedout to be more meaningful in new weighted neighbourhood matrix which is multiplied by Squared Euclidean Distance.

A DETERMINANT FORMULA FOR THE JONES POLYNOMIAL OF PRETZEL KNOTS

This paper presents an algorithm to construct a weighted adjacency matrix of a plane bipartite graph obtained from a pretzel knot diagram. The determinant of this matrix after evaluation is shown to be the Jones polynomial of the pretzel knot by way of perfect matchings (or dimers) of this graph. The weights are Tutte's activity letters that arise because the Jones polynomial is a specialization of the signed version of the Tutte polynomial. The relationship is formalized between the familiar spanning tree setting for the Tait graph and the perfect matchings of the plane bipartite graph above. Evaluations of these activity words are related to the chain complex for the Champanerkar–Kofman spanning tree model of reduced Khovanov homology.

Spectral Feature Matching Based on Isometric Projection of Matrix

This paper presents a spectral method to matching a pair of feature sets based on isometric projection of matrix. In the proposed method, a graph is constructed to model the structure relationships between features. Then the correspondence is found by minimizing the inner product between two isometric projections of the weighted adjacency matrix of graph. Finally, transformation between the two feature sets is estimated according to correct correspondences. The performance of the proposed approach is better than the state-of-the-art method in terms of correct ratio under position perturbation and computation time. Experiments on a number of simulated data, synthetic and real-world images show the validity of the proposed algorithm.