The symmetries of octupolar tensors

Octupolar tensors are third order, completely symmetric and traceless tensors. Whereas in 2D an octupolar tensor has the same symmetries as an equilateral triangle and can ultimately be identified with a vector in the plane, the symmetries that it enjoys in 3D are quite different, and only exceptionally reduce to those of a regular tetrahedron. By use of the octupolar potential that is, the cubic form associated on the unit sphere with an octupolar tensor, we shall classify all inequivalent octupolar symmetries. This is a mathematical study which also reviews and incorporates some previous, less systematic attempts

Deterministic Plug-and-Play for Quantum Communication

We present a scheme for secure deterministic quantum communication without using entanglement, in a Plug-and-Play fashion. The protocol is completely deterministic, both in the encoding procedure and in the control one, thus doubling the communication rate with respect to other setups; moreover, deterministic nature of transmission, apart from rendering unnecessary bases revelation on the public channel, allows the realization of protocols like `direct communication' and `quantum dialogue'. The encoding exploits the phase degree of freedom of a photon, thus paving the way to an optical fiber implementation, feasible with present day technology.Comment: 4 pages, 2 figures; one reference update

Random bits, true and unbiased, from atmospheric turbulence

Random numbers represent a fundamental ingredient for numerical simulation, games, informa- tion science and secure communication. Algorithmic and deterministic generators are affected by insufficient information entropy. On the other hand, suitable physical processes manifest intrinsic unpredictability that may be exploited for generating genuine random numbers with an entropy reaching the ideal limit. In this work, we present a method to extract genuine random bits by using the atmospheric turbulence: by sending a laser beam along a 143Km free-space link, we took advantage of the chaotic behavior of air refractive index in the optical propagation. Random numbers are then obtained by converting in digital units the aberrations and distortions of the received laser wave-front. The generated numbers, obtained without any post-processing, pass the most selective randomness tests. The core of our extracting algorithm can be easily generalized for other physical processes

Finite-Blocklength Bounds on the Maximum Coding Rate of Rician Fading Channels with Applications to Pilot-Assisted Transmission

We present nonasymptotic bounds on the maximum coding rate achievable over a Rician block-fading channel for a fixed packet size and a fixed packet error probability. Our bounds, which apply to the scenario where no a priori channel state information is available at the receiver, allow one to quantify the tradeoff between the rate gains resulting from the exploitation of time-frequency diversity and the rate loss resulting from fast channel variations and pilot-symbol overhead

An analysis of feature relevance in the classification of astronomical transients with machine learning methods

The exploitation of present and future synoptic (multi-band and multi-epoch) surveys requires an extensive use of automatic methods for data processing and data interpretation. In this work, using data extracted from the Catalina Real Time Transient Survey (CRTS), we investigate the classification performance of some well tested methods: Random Forest, MLPQNA (Multi Layer Perceptron with Quasi Newton Algorithm) and K-Nearest Neighbors, paying special attention to the feature selection phase. In order to do so, several classification experiments were performed. Namely: identification of cataclysmic variables, separation between galactic and extra-galactic objects and identification of supernovae.Comment: Accepted by MNRAS, 11 figures, 18 page

(1+1)-dimensional separation of variables

In this paper we explore general conditions which guarantee that the geodesic flow on a 2-dimensional manifold with indefinite signature is locally separable. This is equivalent to showing that a 2-dimensional natural Hamiltonian system on the hyperbolic plane possesses a second integral of motion which is a quadratic polynomial in the momenta associated with a 2nd-rank Killing tensor. We examine the possibility that the integral is preserved by the Hamiltonian flow on a given energy hypersurface only (weak integrability) and derive the additional requirement necessary to have conservation at arbitrary values of the Hamiltonian (strong integrability). Using null coordinates, we show that the leading-order coefficients of the invariant are arbitrary functions of one variable in the case of weak integrability. These functions are quadratic polynomials in the coordinates in the case of strong integrability. We show that for $(1+1)$-dimensional systems there are three possible types of conformal Killing tensors, and therefore, three distinct separability structures in contrast to the single standard Hamilton-Jacobi type separation in the positive definite case. One of the new separability structures is the complex/harmonic type which is characterized by complex separation variables. The other new type is the linear/null separation which occurs when the conformal Killing tensor has a null eigenvector.Comment: To appear on Journal of Mathematical Physic

Profiling Power Consumption on Mobile Devices

The proliferation of mobile devices, and the migration of the information access paradigm to mobile platforms, motivate studies of power consumption behaviors with the purpose of increasing the device battery life. The aim of this work is to profile the power consumption of a Samsung Galaxy I7500 and a Samsung Nexus S, in order to understand how such feature has evolved over the years. We performed two experiments: the first one measures consumption for a set of usage scenarios, which represent common daily user activities, while the second one analyzes a context-aware application with a known source code. The first experiment shows that the most recent device in terms of OS and hardware components shows significantly lower consumption than the least recent one. The second experiment shows that the impact of different configurations of the same application causes a different power consumption behavior on both smartphones. Our results show that hardware improvements and energy-aware software applications greatly impact the energy efficiency of mobile device