We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the q-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in ]0, 1[. Numerous properties of the modified Bernstein Polynomials are extended to their q-analogues: simultaneous approximation, p...

Abstract. Integrability, algebraic structures and orthogonal basis of the Calogero model are studied by the quantum Lax and Dunkl operator formulations. The commutator algebra among operators including conserved operators and creation-annihilation operators has the structure of the W-algebra. Through an algebraic construction of the simultaneous eigenfunctions of all the commuting conserved ope...

The ordered weighted `1 (OWL) norm is a newly developed generalization of the Octogonal Shrinkage and Clustering Algorithm for Regression (OSCAR) norm. This norm has desirable statistical properties and can be used to perform simultaneous clustering and regression. In this paper, we show how to compute the projection of an n-dimensional vector onto the OWL norm ball in O(n log(n)) operations. I...

In this paper we review a multilinear generalization of the singular value decomposition and the best rank-(R1, R2, . . . , RN) approximation of higher-order tensors. We show that they are important tools for dimensionality reduction in higher-order signal processing. We discuss applications in independent component analysis, simultaneous matrix diagonalization and subspace variants of algorith...

We introduce here a generalization of the modified Bernstein polynomials for Jacobi weights using the q-Bernstein basis proposed by G.M. Phillips to generalize classical Bernstein Polynomials. The function is evaluated at points which are in geometric progression in ]0, 1[. Numerous properties of the modified Bernstein Polynomials are extended to their q-analogues: simultaneous approximation, p...

In this paper we prove that testing the cyclic level planarity of a cyclic level graph is a polynomial-time solvable problem. This is achieved by introducing and studying a generalization of this problem, which we call cyclic T -level planarity. Moreover, we show a complexity dichotomy for testing the simultaneous level planarity of a set of level graphs, with respect to both the number of leve...

We address a generalization of the classical 1and 2-processor UET scheduling problem on dedicated machines. In our chromatic model of scheduling machines have non-simultaneous availability times and tasks have arbitrary release times and due dates. Also, the versatility of our approach makes it possible to generalize all known classical criteria of optimality. Under these constraints we show th...

the concept of algebraic hyperstructures introduced by marty as a generalization of ordinary algebraic structures. in an ordinary algebraic structure, the composition of two elements is an element, while in an algebraic hyperstructure, the composition of two elements is a set. the concept of ?-semihyperrings is a generalization of semirings, a generalization of semihyper rings and a generalizat...

Multi-Task Learning is a learning paradigm that uses correlated tasks to improve performance generalization. A common way learn multiple through the hard parameter sharing approach, in which single architecture used share same subset of parameters, creating an inductive bias between them during training process. Due its simplicity, potential generalization, and reduce computational cost, it has...