By means of comp lete symmetric polynomials this paper gives a new proof for the Vander-monde determinant formula. Another alternative proof for this formula is obtained via the collocatio n matrices. It also gives a generalized relationship between the Vandermo nde, the Pascal and the Stirling matrices. A new app roach to obtain the explicit inverse of the Vandermo nde matrix is investigated. ...

In this paper, we consider a generalization of binomial coefficients, called C– nomial coefficients, dependent upon a sequence {un}n, with indices in arithmetic progressions. We obtain a general recurrence relation and a generating matrix, and point out some new relationships between these coefficients and the generalized Pascal matrices. Further, we obtain generating functions, combinatorial r...

This paper is concerned with the generalized Euler polynomial matrix $\E^{(\alpha)}(x)$ and $\E$. Taking into account some properties of polynomials numbers, we deduce product formulae for determine inverse We establish explicit expressions $\E(x)$, which involving Pascal, Fibonacci Lucas matrices, respectively. From these get new interesting identities numbers. Also, provide factorizations in ...

Vector Pascal is a language designed to support elegant and efficient expression of algorithms using the SIMD model of computation. It imports into Pascal features derived from the functional languages APL and J, in particular the extension of all operators to work on vectors of data. The type system is extended to handle dimensional analysis. Code generation is via the ILCG system that allows ...

S1 . Parameter estimation for finetuning with structured SVM objective . . . . . . . . . . . . . . . . . . . . . 1 S2 . Details on hard negative data mining . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 S3 . Implementation details on model parameter estimation . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 S4 . Efficiency of fine-grained search (FGS) ....

background: engineering new bone tissue with cells and a synthetic extracellular matrix represents a new approach for the regeneration of mineralized tissues compared with the transplantation of bone (autografts or allografts). methods: in this study, to mimic the mineral and organic component of natural bone, hydroxapatite (ha) and gelatin (gel) composite scaffolds were prepared. the raw mater...

This article studies two regularized robust estimators of scatter matrices proposed in parallel in (Chen et al., 2011) and (Pascal et al., 2013), based on Tyler’s robust M-estimator (Tyler, 1987) and on Ledoit and Wolf’s shrinkage covariance matrix estimator (Ledoit and Wolf, 2004). These hybrid estimators have the advantage of conveying (i) robustness to outliers or impulsive samples and (ii) ...