The nonlocal nature of quantum entanglement has remained a subject of great interest since the earliest days of quantum mechanics as it causes many of the paradoxes and lies at the heart of the profound difference between quantum mechanics and classical physics. Quantum entanglement is observed primarily for simple quantum objects (photons or/and atoms) in environments specially designed to min...

This Festschrift in honour of J. A. de Azcárraga gives an introduction to the concept of duality, i.e., to the relativity of the notion of a quantum, in the context of the quantum mechanics of a finite number of degrees of freedom. Although the concept of duality arises in string and M–theory, Vafa has argued that it should also have a counterpart in quantum mechanics, before moving on to secon...

When I look at the scale of the apparatus I know what it reads. Those absurdly delicate, hopelessly inaccessible, global correlations obviously vanish when they connect up with me. Whether this is because consciousness is beyond the range of phenomena that quantum mechanics is capable of dealing with, or because it has infinitely many degrees of freedom or special super selection rules of its o...

This paper did a survey in the area of degrees of freedom (DoF) in wireless network. We give the definitions of degrees of freedom in different areas first. Then we introduce some methods used to determine the degrees of freedom in different scenario. In section IV, we discuss the applications of the degrees of freedom. We state some interesting open questions in the end of this survey.

We explore the available degrees of freedom for various multiuser MIMO communication scenarios such as the multiple access, broadcast, interference, relay, X and Z channels. For the two user MIMO interference channel, we find a general inner bound and a genie-aided outer bound that give us the exact number of degrees of freedom in many cases. We also study a share-and-transmit scheme for transm...

When using smoothing splines to estimate a function, the user faces the problem of choosing the smoothing parameter. Several techniques are available for selecting this parameter according to certain optimality criteria. Here, we take a different point of view and we propose a technique for choosing between two alternatives, for example allowing for two different levels of degrees of freedom. T...

We derive the degrees of freedom of the lasso fit, placing no assumptions on the predictor matrix X. Like the well-known result of Zou et al. (2007), which gives the degrees of freedom of the lasso fit when X has full column rank, we express our result in terms of the active set of a lasso solution. We extend this result to cover the degrees of freedom of the generalized lasso fit for an arbitr...