Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.

We present an approximation algorithm for Multidimensional Scaling (MDS) for use with large datasets and interactive applications. MDS describes a class of dimensionality reduction techniques that takes a dissimilarity matrix as input. It is often used as a tool for understanding relative measurements when absolute measurements are not available. MDS is also used for visualizing high-dimensiona...

There remains a useful relation between diffusion and mobility for a Langevin particle in a periodic medium subject to nonconservative forces. The usual fluctuationdissipation relation easily gets modified and the mobility matrix is no longer proportional to the diffusion matrix, with a correction term depending explicitly on the (nonequilibrium) forces. We discuss this correction by considerin...

Group classification of systems of two coupled nonlinear reaction-diffusion equation with a diagonal diffusion matrix is carried out. Symmetries of diffusion systems with singular diffusion matrix and additional first order derivative terms are described.

Linear diffusion layer is an important part of lightweight block ciphers and hash functions. This paper presents an efficient class of lightweight 4x4 MDS matrices such that the implementation cost of them and their corresponding inverses are equal. The main target of the paper is hardware oriented cryptographic primitives and the implementation cost is measured in terms of the required number ...

— We investigate on the localization of nodes in a sensor network based on multidimensional scaling (MDS). The distances of node pairs are given and MDS attempts to locate the position of nodes given the distance matrix. However, conventional MDS addresses the mapping problem using eigenvector decomposition which is complicated in computation, mitigating the efficiency of this approach for real...

The Maximum Distance Separable (MDS) mapping, used in cryptography deploys complex Galois field multiplications, which consume lots of area in hardware, making it a costly primitive for lightweight cryptography. Recently in lightweight hash function: PHOTON, a matrix denoted as ‘Serial’, which required less area for multiplication, has been multiplied 4 times to achieve a lightweight MDS mappin...

An alternative perspective on dimensionality reduction is offered by Multidimensional scaling (MDS). MDS is another classical approach that maps the original high dimensional space to a lower dimensional space, but does so in an attempt to preserve pairwise distances. That is MDS addresses the problem of constructing a configuration of t points in Euclidean space by using information about the ...

For a linear [n, k, d] code, it is well known that d ≤ n−k+1 (see [12]), and when d = n−k+1, it is called the MDS code (maximum distance separable). For every n ≤ q + 1 there is an MDS [n, k, d] code for any given k and d satisfying d = n − k + 1. It is just the geometric codes on a rational curve (see [15]). There is a long-standing conjecture about the MDS linear codes that is called the main...