Nonlocality without inequality for spin-s system

We analyze Hardy's non-locality argument for two spin-s systems and show that earlier solution in this regard was restricted due to imposition of some conditions which have no role in the argument of non-locality. We provide a compact form of non-locality condition for two spin-s systems and extend it to n number of spin-s particles. We also apply more general kind of non-locality argument still without inequality, to higher spin system.Comment: 6 page

21-Hy­droxy­pregna-1,4-diene-3,20-dione

The title compound, C21H28O3, is a fungal transformed metabolite of decoxycorticosterone acetate, consisting of four fused rings A, B, C and D. Ring A is nearly planar, with a maximum deviation of 0.010 (3) Å from the least-squares plane, while the trans-fused rings B and C adopt chair conformations. The five-membered ring D is in an envelope conformation. The orientation of the side chain is stabilized by an intramolecular O—H⋯O hydrogen bond. In the crystal, adjecent mol­ecules are linked by C—H⋯O hydrogen bonds into extended zigzag chains along the a axis

Nonlocality without inequality for almost all two-qubit entangled state based on Cabello's nonlocality argument

Here we deal with a nonlocality argument proposed by Cabello which is more general than Hardy's nonlocality argument but still maximally entangled states do not respond. However, for most of the other entangled states maximum probability of success of this argument is more than that of the Hardy's argument.Comment: 9 pages, 1 figur

Sparse Nerves in Practice

Topological data analysis combines machine learning with methods from algebraic topology. Persistent homology, a method to characterize topological features occurring in data at multiple scales is of particular interest. A major obstacle to the wide-spread use of persistent homology is its computational complexity. In order to be able to calculate persistent homology of large datasets, a number of approximations can be applied in order to reduce its complexity. We propose algorithms for calculation of approximate sparse nerves for classes of Dowker dissimilarities including all finite Dowker dissimilarities and Dowker dissimilarities whose homology is Cech persistent homology. All other sparsification methods and software packages that we are aware of calculate persistent homology with either an additive or a multiplicative interleaving. In dowker_homology, we allow for any non-decreasing interleaving function $\alpha$. We analyze the computational complexity of the algorithms and present some benchmarks. For Euclidean data in dimensions larger than three, the sizes of simplicial complexes we create are in general smaller than the ones created by SimBa. Especially when calculating persistent homology in higher homology dimensions, the differences can become substantial

Ethnobotany of Acacia jacquemontii Benth. - An Uncharted Tree of Thar Desert, Rajasthan, India

The present ethnobotanical study describes the traditional knowledge related to the use of Acacia jacquemontii and its derived products used by the tribes and communities reside in the Thar Desert of Rajasthan, India. Acacia jacquemontii is a versatile tree suitable for afforestation, social and agroforestry. In addition to their normal utility in wood production, soil improvement, nitrogen fixation, these provide certain other products like fodder, fruits, gums, fibers and roofs. During the survey, it was noted that tree parts such as bark, roots and gum were commonly used by the tribals to cure various diseases and disorders. Indigenous healthcare practices, provide low cost alternatives in situation where modern health care services are not available or too expensive. This preliminary study about this unexplored tree would be valuable resource for humankind

The relation between Hardy's non-locality and violation of Bell inequality

We give a analytic quantitative relation between Hardy's non-locality and Bell operator. We find that Hardy's non-locality is a sufficient condition for violation of Bell inequality, the upper bound of Hardy's non-locality allowed by information causality just correspond to Tsirelson bound of Bell inequality, and the upper bound of Hardy's non-locality allowed by the principle of no-signaling just correspond to the algebraic maximum of Bell operator. Then we study the Cabello's argument of Hardy's non-locality (a generalization of Hardy's argument) and find a similar relation between it and violation of Bell inequality. Finally, we give a simple derivation of the bound of Hardy's non-locality under the constraint of information causality with the aid of above derived relation between Hardy's non-locality and Bell operator, this bound is the main result of a recent work of Ahanj \emph{et al.} [Phys. Rev. A {\bf81}, 032103(2010)].Comment: 4 pages, no figure, minor chang