The boundary between the middle Eocene Brussel sand and the Lede sand formations in the Zaventem-Nederokkerzeel area (northeast of Brussels, Belgium)

In the Zaventem airport railway cutting, to the north-east of Brussels, the upper part of the Brussel Sand Formation consists of two major units, both attributable to calcareous nannofossil zone NP14a. The lower predomi­nantly sandy unit ZB1 (including subunits A, B and C, belonging to NP14al) is built up of sparsely glauconitic, relatively coarse tidal current deposits with nodule levels cemented by carbonate and silica, of which one shows slump­ing structures and is interpreted as a seismite. The uppermost unit ZB2 (also labelled D, belonging to NP14a2), com­posed of alternating thin fine sandstone bands and silty marls, represents the fill of a large channel. In the Berg-Nederokkerzeel sandpit the carbonate-rich Brussel Sand Formation is finer grained and more homogeneous. Here, the basal sand (unit A) is attributable to NP14a3 and consequently, younger than the section exposed at Zaventem. It is incised at its the top by a rather narrow erosive gully, filled in with well-sorted fine sand rich in washed-in molluscs (unit B), some of which seem to point to a brackish influence. The extreme top is made up of half a meter of sand with abundant Callianassa burrows and echinid fragments (unit C). From the nannofossil data it appears that, east of Brus­sels, at least two generations of tidal channel systems seem to have occurred within the Brussel Sand Formation, followed by a partial emersion at the end of the filling of the uppermost channel (Nederokkerzeel B). This was suc­ceeded by a relative sea-level rise, as shown by unit C and the remains of a completely eroded fully marine deposit, reworked in the base of the overlying Lede Sand Formation. The lowest relative sea level, with at least partial emer­gence of the Brussels area, occurred during middle to late Biochron NP14b. In both outcrops the Lede Sand Formation displays its characteristic pale grey relatively fine-grained homogeneous nature with a stone layer near its base. It can be concluded that, at the beginning of the "Lede transgression", an erosion of older deposits, containing already lifhified stone layers, occurred. This was, apparently, at least locally, caused by storms, which could redistribute, imbricate and turn over the stones, explaining their bio-perforation on both sides. Afterwards the stones have been above water for a relatively long time, enough to allow the dissolution of the perforating organisms and consequently an important oxidation of their surfaces. These stones have subsequently been colonised by a new marine fauna. Part of the shark teeth and calcareous nannofossil assemblages found in the coarse base of the Lede Sand is definitely older than the taxa normally found in the Lede Sand Formation. These fossils are the remains of a sediment package, believed to represent the formerly "Laekenian" stage

Local Hidden Variable Theories for Quantum States

While all bipartite pure entangled states violate some Bell inequality, the relationship between entanglement and non-locality for mixed quantum states is not well understood. We introduce a simple and efficient algorithmic approach for the problem of constructing local hidden variable theories for quantum states. The method is based on constructing a so-called symmetric quasi-extension of the quantum state that gives rise to a local hidden variable model with a certain number of settings for the observers Alice and Bob.Comment: 8 pages Revtex; v2 contains substantial changes, a strengthened main theorem and more reference

Budget Feasible Mechanisms for Experimental Design

In the classical experimental design setting, an experimenter E has access to a population of $n$ potential experiment subjects $i\in \{1,...,n\}$, each associated with a vector of features $x_i\in R^d$. Conducting an experiment with subject $i$ reveals an unknown value $y_i\in R$ to E. E typically assumes some hypothetical relationship between $x_i$'s and $y_i$'s, e.g., $y_i \approx \beta x_i$, and estimates $\beta$ from experiments, e.g., through linear regression. As a proxy for various practical constraints, E may select only a subset of subjects on which to conduct the experiment. We initiate the study of budgeted mechanisms for experimental design. In this setting, E has a budget $B$. Each subject $i$ declares an associated cost $c_i >0$ to be part of the experiment, and must be paid at least her cost. In particular, the Experimental Design Problem (EDP) is to find a set $S$ of subjects for the experiment that maximizes V(S) = \log\det(I_d+\sum_{i\in S}x_i\T{x_i}) under the constraint $\sum_{i\in S}c_i\leq B$; our objective function corresponds to the information gain in parameter $\beta$ that is learned through linear regression methods, and is related to the so-called $D$-optimality criterion. Further, the subjects are strategic and may lie about their costs. We present a deterministic, polynomial time, budget feasible mechanism scheme, that is approximately truthful and yields a constant factor approximation to EDP. In particular, for any small $\delta > 0$ and $\epsilon > 0$, we can construct a (12.98, $\epsilon$)-approximate mechanism that is $\delta$-truthful and runs in polynomial time in both $n$ and $\log\log\frac{B}{\epsilon\delta}$. We also establish that no truthful, budget-feasible algorithms is possible within a factor 2 approximation, and show how to generalize our approach to a wide class of learning problems, beyond linear regression

Semidefinite Representation of the kk-Ellipse

The $k$-ellipse is the plane algebraic curve consisting of all points whose sum of distances from $k$ given points is a fixed number. The polynomial equation defining the $k$-ellipse has degree $2^k$ if $k$ is odd and degree $2^k{-}\binom{k}{k/2}$ if $k$ is even. We express this polynomial equation as the determinant of a symmetric matrix of linear polynomials. Our representation extends to weighted $k$-ellipses and $k$-ellipsoids in arbitrary dimensions, and it leads to new geometric applications of semidefinite programming.Comment: 16 pages, 5 figure

Generalized phonon-assisted Zener tunneling in indirect semiconductors with non-uniform electric fields : a rigorous approach

A general framework to calculate the Zener current in an indirect semiconductor with an externally applied potential is provided. Assuming a parabolic valence and conduction band dispersion, the semiconductor is in equilibrium in the presence of the external field as long as the electronphonon interaction is absent. The linear response to the electron-phonon interaction results in a non-equilibrium system. The Zener tunneling current is calculated from the number of electrons making the transition from valence to conduction band per unit time. A convenient expression based on the single particle spectral functions is provided, enabling the numerical calculation of the Zener current under any three-dimensional potential profile. For a one dimensional potential profile an analytical expression is obtained for the current in a bulk semiconductor, a semiconductor under uniform field and a semiconductor under a non-uniform field using the WKB (Wentzel-Kramers-Brillouin) approximation. The obtained results agree with the Kane result in the low field limit. A numerical example for abrupt p - n diodes with different doping concentrations is given, from which it can be seen that the uniform field model is a better approximation than the WKB model but a direct numerical treatment is required for low bias conditions.Comment: 29 pages, 7 figure