Fractional Langevin Equation of Distributed Order

Distributed order fractional Langevin-like equations are introduced and applied to describe anomalous diffusion without unique diffusion or scaling exponent. It is shown that these fractional Langevin equations of distributed order can be used to model the kinetics of retarding subdiffusion whose scaling exponent decreases with time, and the strongly anomalous ultraslow diffusion with mean square displacement which varies asymptoically as a power of logarithm of time.Comment: 10 pages, 2 figure

Hadronic B Decays to Charmless VT Final States

Charmless hadronic decays of B mesons to a vector meson (V) and a tensor meson (T) are analyzed in the frameworks of both flavor SU(3) symmetry and generalized factorization. We also make comments on B decays to two tensor mesons in the final states. Certain ways to test validity of the generalized factorization are proposed, using $B \to VT$ decays. We calculate the branching ratios and CP asymmetries using the full effective Hamiltonian including all the penguin operators and the form factors obtained in the non-relativistic quark model of Isgur, Scora, Grinstein and Wise.Comment: 27 pages, no figures, LaTe

Learning Points and Routes to Recommend Trajectories

The problem of recommending tours to travellers is an important and broadly studied area. Suggested solutions include various approaches of points-of-interest (POI) recommendation and route planning. We consider the task of recommending a sequence of POIs, that simultaneously uses information about POIs and routes. Our approach unifies the treatment of various sources of information by representing them as features in machine learning algorithms, enabling us to learn from past behaviour. Information about POIs are used to learn a POI ranking model that accounts for the start and end points of tours. Data about previous trajectories are used for learning transition patterns between POIs that enable us to recommend probable routes. In addition, a probabilistic model is proposed to combine the results of POI ranking and the POI to POI transitions. We propose a new F$_1$ score on pairs of POIs that capture the order of visits. Empirical results show that our approach improves on recent methods, and demonstrate that combining points and routes enables better trajectory recommendations

Quantum random number generation for 1.25 GHz quantum key distribution systems

Security proofs of quantum key distribution (QKD) systems usually assume that the users have access to source of perfect randomness. State-of-the-art QKD systems run at frequencies in the GHz range, requiring a sustained GHz rate of generation and acquisition of quantum random numbers. In this paper we demonstrate such a high speed random number generator. The entropy source is based on amplified spontaneous emission from an erbium-doped fibre, which is directly acquired using a standard small form-factor pluggable (SFP) module. The module connects to the Field Programmable Gate Array (FPGA) of a QKD system. A real-time randomness extractor is implemented in the FPGA and achieves a sustained rate of 1.25 Gbps of provably random bits.Comment: 6 pages, 8 figure

Spin filling of valley-orbit states in a silicon quantum dot

We report the demonstration of a low-disorder silicon metal-oxide-semiconductor (Si MOS) quantum dot containing a tunable number of electrons from zero to N=27. The observed evolution of addition energies with parallel magnetic field reveals the spin filling of electrons into valley-orbit states. We find a splitting of 0.10 meV between the ground and first excited states, consistent with theory and placing a lower bound on the valley splitting. Our results provide optimism for the realization in the near future of spin qubits based on silicon quantum dots.Comment: 6 pages, 4 figures, to appear in Nanotechnolog