Abstract The possibility of generating some quantum correlations the entangled or separable initial two-qubit system interacting with a deformed cavity mode in presence dipole-dipole interaction is discussed. These are coherence, non-separability and steering degrees which quantifiers by using $$ l_1 l <mml:mn...

This paper proposes distributed algorithms for multi-agent networks to achieve a solution in finite time to a linear equation Ax = b where A has full row rank, and with the minimum l1-norm in the underdetermined case (where A has more columns than rows). The underlying network is assumed to be undirected and fixed, and an analytical proof is provided for the proposed algorithm to drive all agen...

We can recover approximately a sparse signal with limited noise, i.e, a vector of length d with at least d − m zeros or near-zeros, using little more than m log(d) nonadaptive linear measurements rather than the d measurements needed to recover an arbitrary signal of length d. Several research communities are interested in techniques for measuring and recovering such signals and a variety of ap...

Abstract Sparse convex clustering is to group observations and conduct variable selection simultaneously in the framework of clustering. Although a weighted $$L_1$$ L 1 norm usually employed for regularization term sparse clustering, its use increases dependence on data...

A regularized minimization model with $l_1$-norm penalty (RP) is introduced for training the autoencoders that belong to a class of two-layer neural networks. We show RP can act as an exact which shares same global minimizers, local and d(irectional)-stationary points original under mild conditions. construct bounded box region contains at least one minimizer RP, propose linearly constrained (L...

We consider the problem of linear classification under general loss functions in limited-data setting. Overfitting is a common here. The standard approaches to prevent overfitting are dimensionality reduction and regularization. But loses information, while regularization requires user choose norm, or prior, distance metric. propose an algorithm called RoLin that needs no choice applies large c...

Sufficient conditions characterizing the asymptotic stability and the hybrid L1/`1-gain of linear positive impulsive systems under minimum and range dwell-time constraints are obtained. These conditions are stated as infinite-dimensional linear programming problems that can be solved using sum of squares programming, a relaxation that is known to be asymptotically exact in the present case. The...

Abstract. Let L and M be two finite lattices. The ideal J(L,M) is a monomial ideal in a specific polynomial ring and whose minimal monomial generators correspond to lattice homomorphisms ϕ: L→M. This ideal is called the ideal of lattice homomorphism. In this paper, we study J(L,M) in the case that L is the product of two lattices L_1 and L_2 and M is the chain [2]. We first characterize the set...