General pure multipartite entangled states and the Segre variety

In this paper, we construct a measure of entanglement by generalizing the quadric polynomial of the Segre variety for general multipartite states. We give explicit expressions for general pure three-partite and four-partite states. Moreover, we will discuss and compare this measure of entanglement with the generalized concurrence.Comment: 5 page

Noncommutative geometrical structures of entangled quantum states

We study the noncommutative geometrical structures of quantum entangled states. We show that the space of a pure entangled state is a noncommutative space. In particular we show that by rewritten the conifold or the Segre variety we can get a $q$-deformed relation in noncommutative geometry. We generalized our construction into a multi-qubit state. We also in detail discuss the noncommutative geometrical structure of a three-qubit state.Comment: 7 page

Topological quantum gate entangler for a multi-qubit state

We establish a relation between topological and quantum entanglement for a multi-qubit state by considering the unitary representations of the Artin braid group. We construct topological operators that can entangle multi-qubit state. In particular we construct operators that create quantum entanglement for multi-qubit states based on the Segre ideal of complex multi-projective space. We also in detail discuss and construct these operators for two-qubit and three-qubit states.Comment: 6 page

Compact star clusters of the LMC HII region N11C

Based on imaging and spectroscopy obtained at the ESO NTT telescope and using an efficient image analysis algorithm, we study the core of the LMC OB association LH13, particularly the two compact stellar clusters Sk-6641 and HNT in the HII, region N11C. We resolve Sk-6641 into 15 components and for the first time the HNT cluster into 70 stars, and derive photometry for the members. Moreover, from medium resolution spectroscopy we determine the spectral types for sixteen stars in N11C. We compare the color-magnitude diagrams of the clusters with that of the field stars and discuss the cluster ages. With an age of ~100 Myr, the HNT cluster appears significantly older than the very young (< 5 Myr) Sk-6641 starburst. We suggest that most of the `field' O-stars in the core of N11C have actually been ejected from Sk-6641 through dynamical interactions in the compact cluster. The properties of the Sk-6641 and HNT clusters suggest that we are viewing different star formation regions lying at different distances along the same line of sight.Comment: 12 pages, 8 figure

Jabba: hybrid error correction for long sequencing reads using maximal exact matches

Third generation sequencing platforms produce longer reads with higher error rates than second generation sequencing technologies. While the improved read length can provide useful information for downstream analysis, underlying algorithms are challenged by the high error rate. Error correction methods in which accurate short reads are used to correct noisy long reads appear to be attractive to generate high-quality long reads. Methods that align short reads to long reads do not optimally use the information contained in the second generation data, and suffer from large runtimes. Recently, a new hybrid error correcting method has been proposed, where the second generation data is first assembled into a de Bruijn graph, on which the long reads are then aligned. In this context we present Jabba, a hybrid method to correct long third generation reads by mapping them on a corrected de Bruijn graph that was constructed from second generation data. Unique to our method is that this mapping is constructed with a seed and extend methodology, using maximal exact matches as seeds. In addition to benchmark results, certain theoretical results concerning the possibilities and limitations of the use of maximal exact matches in the context of third generation reads are presented

Generalized Chaplygin gas as geometrical dark energy

The generalized Chaplygin gas provides an interesting candidate for the present accelerated expansion of the universe. We explore a geometrical explanation for the generalized Chaplygin gas within the context of brane world theories where matter fields are confined to the brane by means of the action of a confining potential. We obtain the modified Friedmann equations, deceleration parameter and age of the universe in this scenario and show that they are consistent with the present observational data.Comment: 11 pages, 3 figures, to appear in PR

Localization of gravity in brane world with arbitrary extra dimensions

We study the induced 4-dimensional linearized Einstein field equations in an m-dimensional bulk space by means of a confining potential. It is shown that in this approach the mass of graviton is quantized. The cosmological constant problem is also addressed within the context of this approach. We show that the difference between the values of the cosmological constant in particle physics and cosmology stems from our measurements in two different scales, small and large.Comment: 8 pages. arXiv admin note: substantial text overlap with arXiv:gr-qc/0408004, arXiv:gr-qc/0607067, arXiv:0704.1035, arXiv:0707.3558, arXiv:0710.266

Jabba: hybrid error correction for long sequencing reads

Background: Third generation sequencing platforms produce longer reads with higher error rates than second generation technologies. While the improved read length can provide useful information for downstream analysis, underlying algorithms are challenged by the high error rate. Error correction methods in which accurate short reads are used to correct noisy long reads appear to be attractive to generate high-quality long reads. Methods that align short reads to long reads do not optimally use the information contained in the second generation data, and suffer from large runtimes. Recently, a new hybrid error correcting method has been proposed, where the second generation data is first assembled into a de Bruijn graph, on which the long reads are then aligned. Results: In this context we present Jabba, a hybrid method to correct long third generation reads by mapping them on a corrected de Bruijn graph that was constructed from second generation data. Unique to our method is the use of a pseudo alignment approach with a seed-and-extend methodology, using maximal exact matches (MEMs) as seeds. In addition to benchmark results, certain theoretical results concerning the possibilities and limitations of the use of MEMs in the context of third generation reads are presented. Conclusion: Jabba produces highly reliable corrected reads: almost all corrected reads align to the reference, and these alignments have a very high identity. Many of the aligned reads are error-free. Additionally, Jabba corrects reads using a very low amount of CPU time. From this we conclude that pseudo alignment with MEMs is a fast and reliable method to map long highly erroneous sequences on a de Bruijn graph

Entanglement measure for general pure multipartite quantum states

We propose an explicit formula for an entanglement measure of pure multipartite quantum states, then study a general pure tripartite state in detail, and at end we give some simple but illustrative examples on four-qubits and m-qubits states.Comment: 5 page