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

Gray-level co-occurrence matrix bone fracture detection

Problem statement: Currently doctors in orthopedic wards inspect the bone x-ray images according to their experience and knowledge in bone fracture analysis. Manual examination of x-rays has multitude drawbacks. The process is time-consuming and subjective. Approach: Since detection of fractures is an important orthopedics and radiologic problem and therefore a Computer Aided Detection(CAD) system should be developed to improve the scenario. In this study, a fracture detection CAD based on GLCM recognition could improve the current manual inspection of x-ray images system. The GLCM for fracture and non-fracture bone is computed and analysis is made. Features of Homogeneity, contrast, energy, correlation are calculated to classify the fractured bone. Results: 30 images of femur fractures have been tested, the result shows that the CAD system can differentiate the x-ray bone into fractured and nonfractured femur. The accuracy obtained from the system is 86.67. Conclusion: The CAD system is proved to be effective in classifying the digital radiograph of bone fracture. However the accuracy rate is not perfect, the performance of this system can be further improved using multiple features of GLCM and future works can be done on classifying the bone into different degree of fracture specifically

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

A comprehensive study of Bluetooth signal parameters for localization

We provide an elaborate discussion on Bluetooth signal parameters with respect to localization, whereby we collectively designate all types of Bluetooth specification parameters that are related to signal strength - such as RSSI, Link Quality, Received and Transmit Power Level - as Bluetooth signal, parameters. According to our analysis and experimental results, "RSSI" and "Transmit Power Level" turn out to be poor candidates for localization, while "Link Quality" has its limitations. On the other hand, "Received Power Level" correlates nicely with distance, which makes it the most desirable Bluetooth signal parameter to be used in location systems. We contend that it is vital to choose the appropriate signal parameter in Bluetooth location systems, and we expect our work to provide useful pointers in any future design of such systems. Existing systems can also benefit by adopting the appropriate Bluetooth signal parameter in their systems, and thereby, improve their location accuracy