Abstract. Random Forest (RF) is a powerful ensemble method for classification and regression tasks. It consists of decision trees set. Although, a single tree is well interpretable for human, the ensemble of trees is a black-box model. The popular technique to look inside the RF model is to visualize a RF proximity matrix obtained on data samples with Multidimensional Scaling (MDS) method. Here...

In this article, we analyze the circulant structure of generalized circulant matrices to reduce the search space for finding lightweight MDS matrices. We first show that the implementation of circulant matrices can be serialized and can achieve similar area requirement and clock cycle performance as a serial-based implementation. By proving many new properties and equivalence classes for circul...

In this paper a new construction of MDS array codes is introduced. In order to obtain a code with this property, the parity-check matrix is constructed just using a superregular matrix by blocks composed by powers of the companion matrix of a primitive polynomial. Also a decoding algorithm for these codes is introduced.

In this article, we provide new methods to look for lightweight MDS matrices, and in particular involutory ones. By proving many new properties and equivalence classes for various MDS matrices constructions such as circulant, Hadamard, Cauchy and Hadamard-Cauchy, we exhibit new search algorithms that greatly reduce the search space and make lightweight MDS matrices of rather high dimension poss...

Myelodysplastic syndrome (MDS) comprises a heterogeneous group of often fatal hematopoietic stem cell disorders for which neither curative nor standard treatment exists. The complex karyotypes and multistep nature of MDS have severely restricted the identification of causative genetic mutations and thus limited insight into new and more effective therapies. Here we describe a zebrafish mutant c...

In this article, we analyze the circulant structure of generalized circulant matrices to reduce the search space for finding lightweight MDS matrices. We first show that the implementation of circulant matrices can be serialized and can achieve similar area requirement and clock cycle performance as a serial-based implementation. By proving many new properties and equivalence classes for circul...

This talk is concerned with the P1 finite element approximation of the eigenvalue problem of second-order elliptic operators subject to the Dirichlet boundary condition. The focus is on the preservation of basic properties of the principal eigenvalue and eigenfunctions of continuous problems. We shall show that when the stiffness matrix is an irreducible M-matrix, the algebraic eigenvalue probl...

The method of one parameter, point symmetric, approximate Lie group invariants is applied to the problem of determining solutions of systems of pure one-dimensional, diffusion equations. The equations are taken to be non-linear in the dependent variables but otherwise homogeneous. Moreover, the matrix of diffusion coefficients is taken to differ from a constant matrix by a linear perturbation w...

Multidimensional scaling (MDS) is a statistical tool for constructing a low-dimension configuration to represent the relationships among objects. In order to extend the conventional MDS analysis to consider the situation of uncertainty under group decision making, in this paper the interval-valued data is considered to represent the dissimilarity matrix in MDS and the rough sets concept is used...

Ahstrrrct-A class of convolutional codes called cross parity check (CPC) codes, useful for the protection of data stored on magnetic tape, is described and analyzed. CPC codes are first explained geometrically; their construction is described in terms of constraining data written onto a tape in such a way that, when lines of varying slope are drawn across the tape, the bits falling on those lin...