Phenomenological Analysis of the Decay $B^{\pm}\to K^{\pm} p {\bar p}

We propose a parametrization for intepreting some of the presently available data of the $B^{\pm} \to K^{\pm} p {\bar p}$ decay, in particular those by LHCb and Belle collaborations. The model is inspired by the well-known current and transition contributions, usually assumed in this kind of decay. However, in the light of considerations about the dominant graphs and about final state interactions, we modify some parameters of the model, determining them by means of a best fit to data. We show the results, which we discuss in some detail. Moreover we give some predictions on other observables relative to the decays.Comment: 19 pages, 5 figures in EPJC 201

An Analytical Solution for Probabilistic Guarantees of Reservation Based Soft Real-Time Systems

We show a methodology for the computation of the probability of deadline miss for a periodic real-time task scheduled by a resource reservation algorithm. We propose a modelling technique for the system that reduces the computation of such a probability to that of the steady state probability of an infinite state Discrete Time Markov Chain with a periodic structure. This structure is exploited to develop an efficient numeric solution where different accuracy/computation time trade-offs can be obtained by operating on the granularity of the model. More importantly we offer a closed form conservative bound for the probability of a deadline miss. Our experiments reveal that the bound remains reasonably close to the experimental probability in one real-time application of practical interest. When this bound is used for the optimisation of the overall Quality of Service for a set of tasks sharing the CPU, it produces a good sub-optimal solution in a small amount of time.Comment: IEEE Transactions on Parallel and Distributed Systems, Volume:27, Issue: 3, March 201

Bi-Hamiltonian Aspects of a Matrix Harry Dym Hierarchy

We study the Harry Dym hierarchy of nonlinear evolution equations from the bi-Hamiltonian view point. This is done by using the concept of an S-hierarchy. It allows us to define a matrix Harry Dym hierarchy of commuting Hamiltonian flows in two fields that projects onto the scalar Harry Dym hierarchy. We also show that the conserved densities of the matrix Harry Dym equation can be found by means of a Riccati-type equation.Comment: Revised version, 22 pages; a section on reciprocal transformations added. To appear in J. Math. Phys

A Software-based Low-Jitter Servo Clock for Inexpensive Phasor Measurement Units

This paper presents the design and the implementation of a servo-clock (SC) for low-cost Phasor Measurement Units (PMUs). The SC relies on a classic Proportional Integral (PI) controller, which has been properly tuned to minimize the synchronization error due to the local oscillator triggering the on-board timer. The SC has been implemented into a PMU prototype developed within the OpenPMU project using a BeagleBone Black (BBB) board. The distinctive feature of the proposed solution is its ability to track an input Pulse-Per-Second (PPS) reference with good long-term stability and with no need for specific on-board synchronization circuitry. Indeed, the SC implementation relies only on one co-processor for real-time application and requires just an input PPS signal that could be distributed from a single substation clock

Beyond Zipf's Law: The Lavalette Rank Function and its Properties

Although Zipf's law is widespread in natural and social data, one often encounters situations where one or both ends of the ranked data deviate from the power-law function. Previously we proposed the Beta rank function to improve the fitting of data which does not follow a perfect Zipf's law. Here we show that when the two parameters in the Beta rank function have the same value, the Lavalette rank function, the probability density function can be derived analytically. We also show both computationally and analytically that Lavalette distribution is approximately equal, though not identical, to the lognormal distribution. We illustrate the utility of Lavalette rank function in several datasets. We also address three analysis issues on the statistical testing of Lavalette fitting function, comparison between Zipf's law and lognormal distribution through Lavalette function, and comparison between lognormal distribution and Lavalette distribution.Comment: 15 pages, 4 figure