The r-parity tensor of a graph is a generalization of the adjacency matrix, where the tensor’s entries denote the parity of the number of edges in subgraphs induced by r distinct vertices. For r = 2, it is the adjacency matrix with 1’s for edges and −1’s for nonedges. It is well-known that the 2-norm of the adjacency matrix of a random graph is O( √ n). Here we show that the 2-norm of the r-par...

The symmetric interior penalty discontinuous Galerkin finite element method is presented for the numerical discretization of the second-order wave equation. The resulting stiffness matrix is symmetric positive definite and the mass matrix is essentially diagonal; hence, the method is inherently parallel and leads to fully explicit time integration when coupled with an explicit timestepping sche...

It is known that random quantum channels exhibit significant violations of multiplicativity of maximum output p-norms for any p > 1. In this work, we show that a weaker variant of multiplicativity nevertheless holds for these channels. For any constant p > 1, given a random quantum channel N (i.e. a channel whose Stinespring representation corresponds to a random subspace S), we show that with ...

H,-norm of the approximation error for both methods satisfies 16, 91 In this paper we propose an efficient computational a p rn proach to minimize the H,-norm of a transfer-function OT+I 5 /IG(s) G,(s)/Im 1 2 x ai (2) matrix depending affinely on a set of free parame.=?+I ters. The minimization problem, formulated as a semiinfinite convex programming problem, is solved via a where > . . . > 0, ...

We will be concerned with the solution to the initial value problem $$ = gy, , YJxo) = L 7 \ where y is a point in the (real) Euclidean M-space RM and ;(y,) is a 4-. mapping of s onto itself satisfying the Lipschitz condition (2) for any pair of points y,z f s. L is a constant and iv/ for vC+s ~.. 'denotes a norm. Although the particular norm used is irrelevant for most purposes, a number of de...

This article proposes a constrained 1 minimization method for estimating a sparse inverse covariance matrix based on a sample of n iid p-variate random variables. The resulting estimator is shown to have a number of desirable properties. In particular, the rate of convergence between the estimator and the true s-sparse precision matrix under the spectral norm is s √ log p/n when the population ...

There is given an axiomatization of the hybrid probabilistic-possibilistic mixture, based on a pair of t-conorm S and t-norm T satisfying (CD) condition, and the corresponding S-measure.

Moderation in virtual communities should not be a private privilege. This paper proposes a method for participants in a social network to decide their own rules for accepting (or not) contents. With the norm argument map, participants are able to argue about norms and voice their opinions about other people?s arguments. This structure, equipped with a method to fuse all the data introduced by p...

This paper studies ordered weighted `1 (OWL) norm regularization for sparse estimation problems with strongly correlated variables. We prove sufficient conditions for clustering based on the correlation/colinearity of variables using the OWL norm, of which the so-called OSCAR [4] is a particular case. Our results extend previous ones for OSCAR in several ways: for the squared error loss, our co...

If $f : S' \to S$ is a finite locally free morphism of schemes, we construct symmetric monoidal "norm" functor $f_\otimes \mathcal{H}_{\bullet}(S')\to \mathcal{H}_{\bullet}(S)$, where $\mathcal{H}_\bullet(S)$ the pointed unstable motivic homotopy category over $S$. $f$ étale, show that it stabilizes to \mathcal{S}\mathcal{H}(S') \mathcal{S}\mathcal{H}(S)$, $\mathcal{S}\mathcal{H}(S)$ $\mathbb{P...