Computing A Glimpse of Randomness

A Chaitin Omega number is the halting probability of a universal Chaitin (self-delimiting Turing) machine. Every Omega number is both computably enumerable (the limit of a computable, increasing, converging sequence of rationals) and random (its binary expansion is an algorithmic random sequence). In particular, every Omega number is strongly non-computable. The aim of this paper is to describe a procedure, which combines Java programming and mathematical proofs, for computing the exact values of the first 64 bits of a Chaitin Omega: 0000001000000100000110001000011010001111110010111011101000010000. Full description of programs and proofs will be given elsewhere.Comment: 16 pages; Experimental Mathematics (accepted

Context-awareness for mobile sensing: a survey and future directions

The evolution of smartphones together with increasing computational power have empowered developers to create innovative context-aware applications for recognizing user related social and cognitive activities in any situation and at any location. The existence and awareness of the context provides the capability of being conscious of physical environments or situations around mobile device users. This allows network services to respond proactively and intelligently based on such awareness. The key idea behind context-aware applications is to encourage users to collect, analyze and share local sensory knowledge in the purpose for a large scale community use by creating a smart network. The desired network is capable of making autonomous logical decisions to actuate environmental objects, and also assist individuals. However, many open challenges remain, which are mostly arisen due to the middleware services provided in mobile devices have limited resources in terms of power, memory and bandwidth. Thus, it becomes critically important to study how the drawbacks can be elaborated and resolved, and at the same time better understand the opportunities for the research community to contribute to the context-awareness. To this end, this paper surveys the literature over the period of 1991-2014 from the emerging concepts to applications of context-awareness in mobile platforms by providing up-to-date research and future research directions. Moreover, it points out the challenges faced in this regard and enlighten them by proposing possible solutions

Comment on ``A new efficient method for calculating perturbative energies using functions which are not square integrable'': regularization and justification

The method recently proposed by Skala and Cizek for calculating perturbation energies in a strict sense is ambiguous because it is expressed as a ratio of two quantities which are separately divergent. Even though this ratio comes out finite and gives the correct perturbation energies, the calculational process must be regularized to be justified. We examine one possible method of regularization and show that the proposed method gives traditional quantum mechanics results.Comment: 6 pages in REVTeX, no figure

Enhancement of the ν=5/2\nu = 5/2 Fractional Quantum Hall State in a Small In-Plane Magnetic Field

Using a 50-nm width, ultra-clean GaAs/AlGaAs quantum well, we have studied the Landau level filling factor $\nu = 5/2$ fractional quantum Hall effect in a perpendicular magnetic field $B \sim$ 1.7 T and determined its dependence on tilted magnetic fields. Contrary to all previous results, the 5/2 resistance minimum and the Hall plateau are found to strengthen continuously under an increasing tilt angle $0 < \theta < 25^\circ$ (corresponding to an in-plane magnetic field 0 $<$ $B_\parallel$ $< 0.8$ T). In the same range of $\theta$ the activation gaps of both the 7/3 and the 8/3 states are found to increase with tilt. The 5/2 state transforms into a compressible Fermi liquid upon tilt angle $\theta > 60^\circ$, and the composite fermion series [2+$p/(2p\pm1)$], $p =$ 1, 2 can be identified. Based on our results, we discuss the relevance of a Skyrmion spin texture at $\nu = 5/2$ associated with small Zeeman energy in wide quantum wells, as proposed by W$\acute{\text o}$js $et$ $al$., Phys. Rev. Lett. 104, 086801 (2010).Comment: 5+ pages, 3 figures, accepted for by Phy. Rev. Let

A General Phase Matching Condition for Quantum Searching Algorithm

A general consideration on the phase rotations in quantum searching algorithm is taken in this work. As four phase rotations on the initial state, the marked states, and the states orthogonal to them are taken account, we deduce a phase matching condition for a successful search. The optimal options for these phase are obtained consequently.Comment: 3 pages, 3 figure