We present a novel vector quantization (VQ) module for the two state-of-the-art long-range simultaneous localization and mapping (SLAM) algorithms. The VQ task in SLAM is generally performed using unsupervised methods. We provide an alternative approach trough embedding a semisupervised hyperbolic graph convolutional neural network (HGCN) in the VQ step of the SLAM processes. The SLAM platforms we have utilized for this purpose are fast appearance-based mapping (FABMAP) and oriented fast and rotated short (ORB), both of which rely on extracting the features of the captured images in their loop closure detection (LCD) module. For the first time, we have considered the space formed by these SURF features, robust image descriptors, as a graph, enabling us to apply an HGCN in the VQ section which results in an improved LCD performance. The HGCN vector quantizes the SURF feature space, leading to a bag-of-word (BoW) representation construction of the images. This representation is subsequently used to determine LCD accuracy and recall. Our approaches in this study are referred to as HGCN-FABMAP and HGCN-ORB. The main advantage of using HGCN in the LCD section is that it scales linearly when the features are accumulated. The benchmarking experiments show the superiority of our methods in terms of both trajectory generation accuracy in small-scale paths and LCD accuracy and recall for large-scale problems.

The $k$-center problem is to choose a subset of size $k$ from a set of $n$ points such that the maximum distance from each point to its nearest center is minimized. Let $Q=\{Q_1,\ldots,Q_n\}$ be a set of polygons or segments in the region-based uncertainty model, in which each $Q_i$ is an uncertain point, where the exact locations of the points in $Q_i$ are unknown. The geometric objects segments and polygons can be models of a point set. We define the uncertain version of the $k$-center problem as a generalization in which the objective is to find $k$ points from $Q$ to cover the remaining regions of $Q$ with minimum or maximum radius of the cluster to cover at least one or all exact instances of each $Q_i$, respectively. We modify the region-based model to allow multiple points to be chosen from a region and call the resulting model the aggregated uncertainty model. All these problems contain the point version as a special case, so they are all NP-hard with a lower bound 1.822. We give approximation algorithms for uncertain $k$-center of a set of segments and polygons. We also have implemented some of our algorithms on a data-set to show our theoretical performance guarantees can be achieved in practice. Comment: Accepted in Fundamenta Informaticae

In this paper, we propose an algorithm for computing the geodesic center of a simple polygon when the available workspace is limited. Our algorithm is a memory-constrained algorithm which has read-only access to the input. In addition to the input, it uses Θ(log n) words of O(log n) bits for reading and writing. The algorithm runs in O( n 4 ) expected time, where n is the number of the corners of the polygon. We also show that the geodesic farthest-site Voronoi diagram of the corners of the polygon can be computed in the same time and space. As a sub-result, we present an s-workspace algorithm for finding a geodesic farthest neighbor of a given point inside a simple polygon which runs in O( n 2 / s) expected time where [Formula: see text].

In this study, the authors concentrate on the designing of a deterministic measurement matrix. Unlike most of the studies, they employ the points on finite projective spaces rather than finite fields. These spaces provide more choices for the size of the proposed matrix. A new group of binary measurement matrices is presented through generalising DeVore's construction. For this purpose, homogenous polynomials over finite projective spaces are applied. To investigate the performance of the proposed matrix they provide an example on projective lines. It can be observed that the coherence of the result matrix is lower than DeVore's construction. The simulation results show that the proposed matrix outperforms the Gaussian matrix and DeVore's matrix in terms of noiseless and noisy signal recovery.

In this letter, we construct a class of deterministic measurement matrices which are asymptotically optimal. For this purpose, we first apply the tensor product over the Reed Solomon (R-S) generator matrix to produce a new one; then employing this generator matrix, we construct a measurement matrix. If the R-S code is defined on \BBFq, then the resulting measurement matrices are of dimensions q2×q3, where q is an arbitrary prime power and its coherence would be1/q, which is desirable for compressive sampling. We also illustrate the effectiveness of our proposed matrices in compressed sensing with some simulation examples.

In this paper, an Image Encryption System by special kind of cellular automata (cellular automata with memory) and also an appropriate transition function for the cryptosystem have been proposed. Also a lossy idea is used to present a secure cryptosystem. The use of lossy method provides a secure method and it is shown that the result is resistant to cryptanalysis attacks, especially known plaintext and chosen plaintext. When the original image is compared with the decrypted image by human visual system, it is not recognizable which one is decrypted and which one is the original image.

Blogs have become one of most important parts of web but we do not have so efficient search engines for them. One reason is differences between regular web pages and blog pages and inefficiency of conventional web pages ranking algorithms for blogs ranking. There are some works in this field but users' behavioral features have not considered yet. In this paper we present a new blogs ranking algorithm called B2Rank based on these features.