A variant of Peres-Mermin proof for testing noncontextual realist models

For any state in four-dimensional system, the quantum violation of an inequality based on the Peres-Mermin proof for testing noncontextual realist models has experimentally been corroborated. In the Peres-Mermin proof, an array of nine holistic observables for two two-qubit system was used. We, in this letter, present a new symmetric set of observables for the same system which also provides a contradiction of quantum mechanics with noncontextual realist models in a state-independent way. The whole argument can also be cast in the form of a new inequality that can be empirically tested.Comment: 3 pages, To be published in Euro. Phys. Let

Finite-precision measurement does not nullify the Kochen-Specker theorem

It is proven that any hidden variable theory of the type proposed by Meyer [Phys. Rev. Lett. {\bf 83}, 3751 (1999)], Kent [{\em ibid.} {\bf 83}, 3755 (1999)], and Clifton and Kent [Proc. R. Soc. London, Ser. A {\bf 456}, 2101 (2000)] leads to experimentally testable predictions that are in contradiction with those of quantum mechanics. Therefore, it is argued that the existence of dense Kochen-Specker-colorable sets must not be interpreted as a nullification of the physical impact of the Kochen-Specker theorem once the finite precision of real measurements is taken into account.Comment: REVTeX4, 5 page

The Clumping Transition in Niche Competition: a Robust Critical Phenomenon

We show analytically and numerically that the appearance of lumps and gaps in the distribution of n competing species along a niche axis is a robust phenomenon whenever the finiteness of the niche space is taken into account. In this case depending if the niche width of the species $\sigma$ is above or below a threshold $\sigma_c$, which for large n coincides with 2/n, there are two different regimes. For $\sigma > sigma_c$ the lumpy pattern emerges directly from the dominant eigenvector of the competition matrix because its corresponding eigenvalue becomes negative. For $\sigma </- sigma_c$ the lumpy pattern disappears. Furthermore, this clumping transition exhibits critical slowing down as $\sigma$ is approached from above. We also find that the number of lumps of species vs. $\sigma$ displays a stair-step structure. The positions of these steps are distributed according to a power-law. It is thus straightforward to predict the number of groups that can be packed along a niche axis and it coincides with field measurements for a wide range of the model parameters.Comment: 16 pages, 7 figures; http://iopscience.iop.org/1742-5468/2010/05/P0500

Kochen-Specker Theorem for Finite Precision Spin One Measurements

Unsharp spin 1 observables arise from the fact that a residual uncertainty about the actual orientation of the measurement device remains. If the uncertainty is below a certain level, and if the distribution of measurement errors is covariant under rotations, a Kochen-Specker theorem for the unsharp spin observables follows: There are finite sets of directions such that not all the unsharp spin observables in these directions can consistently be assigned approximate truth-values in a non-contextual way.Comment: 4 page

On Invariant Notions of Segre Varieties in Binary Projective Spaces

Invariant notions of a class of Segre varieties \Segrem(2) of PG(2^m - 1, 2) that are direct products of $m$ copies of PG(1, 2), $m$ being any positive integer, are established and studied. We first demonstrate that there exists a hyperbolic quadric that contains \Segrem(2) and is invariant under its projective stabiliser group \Stab{m}{2}. By embedding PG(2^m - 1, 2) into \PG(2^m - 1, 4), a basis of the latter space is constructed that is invariant under \Stab{m}{2} as well. Such a basis can be split into two subsets whose spans are either real or complex-conjugate subspaces according as $m$ is even or odd. In the latter case, these spans can, in addition, be viewed as indicator sets of a \Stab{m}{2}-invariant geometric spread of lines of PG(2^m - 1, 2). This spread is also related with a \Stab{m}{2}-invariant non-singular Hermitian variety. The case $m=3$ is examined in detail to illustrate the theory. Here, the lines of the invariant spread are found to fall into four distinct orbits under \Stab{3}{2}, while the points of PG(7, 2) form five orbits.Comment: 18 pages, 1 figure; v2 - version accepted in Designs, Codes and Cryptograph

Body odor quality predicts behavioral attractiveness in humans

Growing effort is being made to understand how different attractive physical traits co-vary within individuals, partly because this might indicate an underlying index of genetic quality. In humans, attention has focused on potential markers of quality such as facial attractiveness, axillary odor quality, the second-to-fourth digit (2D:4D) ratio and body mass index (BMI). Here we extend this approach to include visually-assessed kinesic cues (nonverbal behavior linked to movement) which are statistically independent of structural physical traits. The utility of such kinesic cues in mate assessment is controversial, particularly during everyday conversational contexts, as they could be unreliable and susceptible to deception. However, we show here that the attractiveness of nonverbal behavior, in 20 male participants, is predicted by perceived quality of their axillary body odor. This finding indicates covariation between two desirable traits in different sensory modalities. Depending on two different rating contexts (either a simple attractiveness rating or a rating for long-term partners by 10 female raters not using hormonal contraception), we also found significant relationships between perceived attractiveness of nonverbal behavior and BMI, and between axillary odor ratings and 2D:4D ratio. Axillary odor pleasantness was the single attribute that consistently predicted attractiveness of nonverbal behavior. Our results demonstrate that nonverbal kinesic cues could reliably reveal mate quality, at least in males, and could corroborate and contribute to mate assessment based on other physical traits

Projective Ring Line Encompassing Two-Qubits

The projective line over the (non-commutative) ring of two-by-two matrices with coefficients in GF(2) is found to fully accommodate the algebra of 15 operators - generalized Pauli matrices - characterizing two-qubit systems. The relevant sub-configuration consists of 15 points each of which is either simultaneously distant or simultaneously neighbor to (any) two given distant points of the line. The operators can be identified with the points in such a one-to-one manner that their commutation relations are exactly reproduced by the underlying geometry of the points, with the ring geometrical notions of neighbor/distant answering, respectively, to the operational ones of commuting/non-commuting. This remarkable configuration can be viewed in two principally different ways accounting, respectively, for the basic 9+6 and 10+5 factorizations of the algebra of the observables. First, as a disjoint union of the projective line over GF(2) x GF(2) (the "Mermin" part) and two lines over GF(4) passing through the two selected points, the latter omitted. Second, as the generalized quadrangle of order two, with its ovoids and/or spreads standing for (maximum) sets of five mutually non-commuting operators and/or groups of five maximally commuting subsets of three operators each. These findings open up rather unexpected vistas for an algebraic geometrical modelling of finite-dimensional quantum systems and give their numerous applications a wholly new perspective.Comment: 8 pages, three tables; Version 2 - a few typos and one discrepancy corrected; Version 3: substantial extension of the paper - two-qubits are generalized quadrangles of order two; Version 4: self-dual picture completed; Version 5: intriguing triality found -- three kinds of geometric hyperplanes within GQ and three distinguished subsets of Pauli operator

Soil conservation and sustainable development goals(SDGs) achievement in Europe and central Asia: Which role for the European soil partnership?

Voluntary soil protection measures are not sufficient to achieve sustainable soil management at a global scale. Additionally, binding soil protection legislation at national and international levels has also proved to be insufficient for the effective protection of this almost non-renewable natural resource. The European Soil Partnership (ESP) and its sub-regional partnerships (Eurasian Sub-Regional Soil Partnership, Alpine Soil Partnership) were established in the context of FAO's Global Soil Partnership (GSP) with the mission to facilitate and contribute to the exchange of knowledge and technologies related to soils, to develop dialogue and to raise awareness for the need to establish a binding global agreement for sustainable soil management. The ESP has taken a role of an umbrella network covering countries in Europe and Central Asia. It aims to improve the dialogue in the whole region and has encouraged establishing goals that would promote sustainable soil management, taking into account various national and local approaches and priorities, as well as cultural specificities. The ESP first regional implementation plan for the 2017–2020 period was adopted and implemented along the five GSP pillars of action. Building on the experience of the last four years, this study demonstrates that establishing sub-regional and national partnerships is an additional step in a concrete sustainable soil management implementation process. It also suggests that a complementary approach between legal instruments and voluntary initiatives linked to the development of efficient communication and strong commitment is the key to success

Existential Contextuality and the Models of Meyer, Kent and Clifton

It is shown that the models recently proposed by Meyer, Kent and Clifton (MKC) exhibit a novel kind of contextuality, which we term existential contextuality. In this phenomenon it is not simply the pre-existing value but the actual existence of an observable which is context dependent. This result confirms the point made elsewhere, that the MKC models do not, as the authors claim, ``nullify'' the Kochen-Specker theorem. It may also be of some independent interest.Comment: Revtex, 7 pages, 1 figure. Replaced with published versio