Arithmeticity for periods of automorphic forms

A cuspidal automorphic representation \pi of a group G is said to to be distinguished with respect to a subgroup H if the integral of f along H is nonzero for a cusp form f in the space of \pi. Such period integrals are related to (non)vanishing of interesting L-values and also to Langlands functoriality. This article discusses a general principle, labelled arithmeticity, which roughly states that "\pi is H-distinguished if and only if any Galois conjugate of \pi is H-distinguished." We study this principle via several examples; starting with GL(2) and leading up to more complicated situations where the ambient group is a higher GL(n) or a classical group.Comment: 32 pages. The final version is to appear in the proceedings of the International Colloquium on Automorphic Representations and L-functions, held in TIFR, Mumbai, January 201

Teleportation and Dense Coding with Genuine Multipartite Entanglement

We present an explicit protocol ${\cal E}_0$ for faithfully teleporting an arbitrary two-qubit state via a genunie four-qubit entangled state. By construction, our four-partite state is not reducible to a pair of Bell states. Its properties are compared and contrasted with those of the four-party GHZ and W states. We also give a dense coding scheme ${\cal D}_0$ involving our state as a shared resource of entanglement. Both ${\cal D}_0$ and ${\cal E}_0$ indicate that our four-qubit state is a likely candidate for the genunine four-partite analogue to a Bell state.Comment: 9 pages, 0 figur

Excitonic Instabilities and Insulating States in Bilayer Graphene

The competing ground states of bilayer graphene are studied by applying renormalization group techniques to a bilayer honeycomb lattice with nearest neighbor hopping. In the absence of interactions, the Fermi surface of this model at half-filling consists of two nodal points with momenta $\mathbf{K}$, $\mathbf{K}'$, where the conduction band and valence band touch each other, yielding a semi-metal. Since near these two points the energy dispersion is quadratic with perfect particle-hole symmetry, excitonic instabilities are inevitable if inter-band interactions are present. Using a perturbative renormalization group analysis up to the one-loop level, we find different competing ordered ground states, including ferromagnetism, superconductivity, spin and charge density wave states with ordering vector $\mathbf{Q}=\mathbf{K}-\mathbf{K}'$, and excitonic insulator states. In addition, two states with valley symmetry breaking are found in the excitonic insulating and ferromagnetic phases. This analysis strongly suggests that the ground state of bilayer graphene should be gapped, and with the exception of superconductivity, all other possible ground states are insulating.Comment: 17 pages, 6 figures, 2 Tables, Added reference

Structural and electronic properties of Al nanowires: an ab initio pseudopotential study

The stability and electronic structure of a single monatomic Al wire has been studied using the ab initio pseudopotential method. The Al wire undergoes two structural rearrangements under compression, i.e., zigzag configurations at angles of $140^o$ and $60^o$. The evolution of electronic structures of the Al chain as a function of structural phase transition has been investigated. The relationship between electronic structure and geometric stability is also discussed. The 2p bands in the Al nanowire are shown to play a critical role in its stability. The effects of density functionals (GGA and LDA) on cohesive energy and bond length of Al nanostructures (dimmer, chains, and monolayers) are also examined. The link between low dimensional 0D structure (dimmer) to high dimensional 3D bulk Al is estimated. An example of optimized tip-suspended finite atomic chain is presented to bridge the gap between hypothetical infinite chains and experimental finite chains.Comment: 11 pages, 5 figure

Discovering the Future Canadians Want: Insights from the We Canada Cross-Country Tour

In 1972, the first United Nations Conference on Human Environment (UNCED) was held in Stockholm, Sweden. At the conference, government officials from industrialized and developing nations met alongside civil society organizations to create the United Nations Environment Programme (UNEP). “This conference put environmental issues on the international agenda for the first time, and marked a turning point in the development of international environmental politics. It has also been recognized as the beginning of modern political and public awareness of global environmental issues” (Baylis & Smith, 2005, pp. 454-455). Twenty years later, the United Nations Conference on Environment and Development (UNCED), also known as the Rio Earth Summit, was held in Rio de Janeiro. One hundred and seventy two government officials participated, of which 108 were heads of state (United Nations, 1992, United Nations Conference on Environment and Development, para. 1). This conference was one of the largest gatherings of heads of state, civil society organizations, and individuals in human history to date. Stakeholders met with the purpose of charting a course for a more sustainable future. From the conference emerged agreements, most notably Agenda 21, which created a framework for developing global, national, and regional plans for sustainability. The Rio Earth Summit has since stood as an example of what is possible when governments and citizens work together. The outcomes of this conference still affect human lives today, mainly through the United Nations Framework Convention on Climate Change meetings, which led to the Kyoto Protocol, the only legally binding agreement to cut down carbon dioxide (CO₂) emissions. The United Nations Conference on Sustainable Development, also known as Earth Summit 2012 or Rio+20, is regarded as one of the most crucial events in United Nations history and has been referred to by the Secretary General of the United Nations (2011), Ban Ki-moon, as “the most important global meeting on sustainable development in our time" (The Future We Want, p 2)

FAIR quantitative imaging in oncology:How Semantic Web and Ontologies will support reproducible science

The automated extraction of quantitative imaging biomarkers from patient's scans, could augment physician decision making in radiation oncology. Unfortunately, lack of reproducibility and robust methodology current limits this promising field to be applied in the clinic. In this paper, we state how the combination of quantitative medical imaging with Semantic Web and Ontologies techniques could speed up the role of quantitative imaging