We introduce a constrained empirical loss minimization framework for estimating highdimensional sparse precision matrices and propose a new loss function, called the D-trace loss, for that purpose. A novel sparse precision matrix estimator is defined as the minimizer of the lasso penalized D-trace loss under a positive-definiteness constraint. Under a new irrepresentability condition, the lasso...

We show here that the problem of maximizing a family of quantitative functions, encompassing both the modularity (Q-measure) and modularity density (D-measure), for community detection can be uniformly understood as a combinatoric optimization involving the trace of a matrix called modularity Laplacian. Instead of using traditional spectral relaxation, we apply additional nonnegative constraint...

We develop the embedded gradient vector field method, introduced in [8] and [9], for case of special unitary group $\mathcal{SU}(N)$ regarded as a constraint submanifold $\mathcal{U}(N)$. The optimization problem associated to trace fidelity cost function defined on that appears context quantum control landscapes is completely solved using method. prove $N\geq 5$, landscape not $\mathcal{SU}(N)...

We give a security proof of the ‘Round Robin Differential Phase Shift’ Quantum Key Distribution scheme, and we give a tight bound on the required amount of privacy amplification. Our proof consists of the following steps. We construct an EPR variant of the scheme. We identify Eve’s optimal way of coupling an ancilla to an EPR qudit pair under the constraint that the bit error rate between Alice...

A model for a historical database is described which is based upon time-stamped tuples as the unit of storage. The model includes both physical and logical time-stamps. The technical characteristics of write-once laser discs prevent the use of double logical time-stamps. The model distinguishes version from correction-updates. It is shown that if set-valued attributes are involved the use of nu...

Noisy data recovery is an important problem in machine learning field, which has widely applications for collaborative prediction, recommendation systems, etc. One popular model is to use trace norm model for noisy data recovery. However, it is ignored that the reconstructed data could be shrank (i.e., singular values could be greatly suppressed). In this paper, we present novel noisy data reco...

A bstract In this paper, we study a class of symmetry reduced models $$ \mathcal{N} N = 1 super- gravity using self-dual variables. It is based on particular Ansatz for the gravitino field as proposed by D’Eath et al. We show that essential part constraint algebra in classical theory closes. particular, (grad...

In our paper, we deal with the Germanic–Romance language contact, focusing on Cimbrian, a Germanic minority spoken in Northern Italy. Specifically, focus violation of well-known that-trace filter, as it appears to be an interesting case superficial convergence that ascribe status T, which is either too rich (model language) or weak (replica represent viable landing site for subject extraction.

The ZETA system is a Z-based tool environment for developing formal specifications. It contains a component for executing the Z language based on the implementation technique of concurrent constraint resolution. In this paper, we present a case-study for the environment, by providing an executable encoding of temporal interval logics in the Z language. As an application of this setting, test-ca...