The problem of collecting different body fluids from drivers in the surveys

Objectives: It is not easy to obtain a blood sample from drivers at the roadside for use in epidemiological studies. Therefore, use of saliva samples has become popular. On the other hand, in studies in injured drivers, obtaining a saliva sample can be problematic, e.g. because of injuries. When drug concentrations in blood and saliva need to be compared e.g. in risk calculations, results from different matrices need to be comparable. Because of the different recoveries with saliva collection devices, saliva:blood ratios should be determined for each collection device. Methods: Drug concentrations in blood and saliva samples from different studies (Rosita-2, roadside surveys) were analysed by GC-MS and UPLC-MS/MS and the results were compared for different drugs. Results: While for some drugs like diazepam, relatively good correlation can be observed (r2 = 0.98, n=23, Saliva blood ratio 0.033), for most other drugs there is a very wide scatter when comparing saliva and blood concentrations. These findings confirm those of other published studies. One of the possible explanations is the trapping of basic drugs in saliva because of the pH effects. Conclusion: The correlation between drug concentrations in saliva and whole blood is poor for most drugs. It might be advisable to use whole blood also in a roadside surveys

A classification of spin 1/2 matrix product states with two dimensional auxiliary matrices

e classify the matrix product states having only spin-flip and parity symmetries, which can be constructed from two dimensional auxiliary matrices. We show that there are three distinct classes of such states and in each case, we determine the parent Hamiltonian and the points of possible quantum phase transitions. For two of the models, the interactions are three-body and for one the interaction is two-bodyComment: 17 pages, 3 figure

A comparison of the entanglement measures negativity and concurrence

In this paper we investigate two different entanglement measures in the case of mixed states of two qubits. We prove that the negativity of a state can never exceed its concurrence and is always larger then $\sqrt{(1-C)^2+C^2}-(1-C)$ where $C$ is the concurrence of the state. Furthermore we derive an explicit expression for the states for which the upper or lower bound is satisfied. Finally we show that similar results hold if the relative entropy of entanglement and the entanglement of formation are compared

Using level-2 fuzzy sets to combine uncertainty and imprecision in fuzzy regions

In many applications, spatial data need to be considered but are prone to uncertainty or imprecision. A fuzzy region - a fuzzy set over a two dimensional domain - allows the representation of such imperfect spatial data. In the original model, points of the fuzzy region where treated independently, making it impossible to model regions where groups of points should be considered as one basic element or subregion. A first extension overcame this, but required points within a group to have the same membership grade. In this contribution, we will extend this further, allowing a fuzzy region to contain subregions in which not all points have the same membership grades. The concept can be used as an underlying model in spatial applications, e.g. websites showing maps and requiring representation of imprecise features or websites with routing functions needing to handle concepts as walking distance or closeby

On the geometry of entangled states

The basic question that is addressed in this paper is finding the closest separable state for a given entangled state, measured with the Hilbert Schmidt distance. While this problem is in general very hard, we show that the following strongly related problem can be solved: find the Hilbert Schmidt distance of an entangled state to the set of all partially transposed states. We prove that this latter distance can be expressed as a function of the negative eigenvalues of the partial transpose of the entangled state, and show how it is related to the distance of a state to the set of positive partially transposed states (PPT-states). We illustrate this by calculating the closest biseparable state to the W-state, and give a simple and very general proof for the fact that the set of W-type states is not of measure zero. Next we show that all surfaces with states whose partial transposes have constant minimal negative eigenvalue are similar to the boundary of PPT states. We illustrate this with some examples on bipartite qubit states, where contours of constant negativity are plotted on two-dimensional intersections of the complete state space.Comment: submitted to Journal of Modern Optic

Variational Numerical Renormalization Group: Bridging the gap between NRG and Density Matrix Renormalization Group

The numerical renormalization group (NRG) is rephrased as a variational method with the cost function given by the sum of all the energies of the effective low-energy Hamiltonian. This allows to systematically improve the spectrum obtained by NRG through sweeping. The ensuing algorithm has a lot of similarities to the density matrix renormalization group (DMRG) when targeting many states, and this synergy of NRG and DMRG combines the best of both worlds and extends their applicability. We illustrate this approach with simulations of a quantum spin chain and a single impurity Anderson model (SIAM) where the accuracy of the effective eigenstates is greatly enhanced as compared to the NRG, especially in the transition to the continuum limit.Comment: As accepted to PRL. Main text: 4 pages, 4 (PDF) figures; Supplementary material: 4 pages, 6 PDF figures; revtex4-