Higher-dimensional open quantum walk in environment of quantum Bernoulli noises

Open quantum walks (OQWs) (also known as open quantum random walks) are quantum analogs of classical Markov chains in probability theory, and have potential application in quantum information and quantum computation. Quantum Bernoulli noises (QBNs) are annihilation and creation operators acting on Bernoulli functionals, and can be used as the environment of an open quantum system. In this paper, by using QBNs as the environment, we introduce an OQW on a general higher-dimensional integer lattice. We obtain a quantum channel representation of the walk, which shows that the walk is indeed an OQW. We prove that all the states of the walk are separable provided its initial state is separable. We also prove that, for some initial states, the walk has a limit probability distribution of higher-dimensional Gauss type. Finally, we show links between the walk and a unitary quantum walk recently introduced in terms of QBNs.

Higher-Dimensional Quantum Walk in Terms of Quantum Bernoulli Noises

As a discrete-time quantum walk model on the one-dimensional integer lattice Z , the quantum walk recently constructed by Wang and Ye [Caishi Wang and Xiaojuan Ye, Quantum walk in terms of quantum Bernoulli noises, Quantum Information Processing 15 (2016), 1897–1908] exhibits quite different features. In this paper, we extend this walk to a higher dimensional case. More precisely, for a general positive integer d ≥ 2 , by using quantum Bernoulli noises we introduce a model of discrete-time quantum walk on the d-dimensional integer lattice Z d , which we call the d-dimensional QBN walk. The d-dimensional QBN walk shares the same coin space with the quantum walk constructed by Wang and Ye, although it is a higher dimensional extension of the latter. Moreover we prove that, for a range of choices of its initial state, the d-dimensional QBN walk has a limit probability distribution of d-dimensional standard Gauss type, which is in sharp contrast with the case of the usual higher dimensional quantum walks. Some other results are also obtained.

A New Limit Theorem for Quantum Walk in Terms of Quantum Bernoulli Noises

In this paper, we consider limit probability distributions of the quantum walk recently introduced by Wang and Ye (C.S. Wang and X.J. Ye, Quantum walk in terms of quantum Bernoulli noises, Quantum Inf. Process. 15 (2016), no. 5, 1897–1908). We first establish several technical theorems, which themselves are also interesting. Then, by using these theorems, we prove that, for a wide range of choices of the initial state, the above-mentioned quantum walk has a limit probability distribution of standard Gauss type, which actually gives a new limit theorem for the walk.

Automatic Identification System (AIS) dynamic data estimation based on discrete Kalman Filter (KF) algorithm

Due to the safety reason, the ship movement on the littoral area should be monitored, tracked, recorded and stored. Automatic Identification System (AIS) is the perfect tool to ensure this requirement. The limit probability for the AIS dynamic data availability can be limited by the lack of Global Position System (GPS) signal, heading (HDG) and rate of turn (ROT) data in position report. Availability of data link is an additional limitation. For this purpose, it is possible to attach the Discrete Kalman filter (KF) for the position, and course estimation. Coordinate estimation in the absence of a transmission link can improve the quality of AIS service at Vessel Traffic Service (VTS) stations. This article presents Kalman filtering algorithm to improve the possibilities of ship motion tracking and monitoring in the TSS (Traffic Separation Scheme) and fairways area. Only 39 iterations were presented to familiarize how the Kalman filter algorithm works. The archival data from 2006 were used deliberately. During that time, there were problems with the AIS availability service. With the use of measurements series from those years, it is easier to observe the effectiveness of Kalman filter in absence of AIS data.

Characterization of sets of limit measures of a cellular automaton iterated on a random configuration

The asymptotic behaviour of a cellular automaton iterated on a random configuration is well described by its limit probability measure(s). In this paper, we characterize measures and sets of measures that can be reached as limit points after iterating a cellular automaton on a simple initial measure. In addition to classical topological constraints, we exhibit necessary computational obstructions. With an additional hypothesis of connectivity, we show these computability conditions are sufficient by constructing a cellular automaton realizing these sets, using auxiliary states in order to perform computations. Adapting this construction, we obtain a similar characterization for the Cesàro mean convergence, a Rice theorem on the sets of limit points, and we are able to perform computation on the set of measures, i.e. the cellular automaton converges towards a set of limit points that depends on the initial measure. Last, under non-surjective hypotheses, it is possible to remove auxiliary states from the construction.

On a Gauss-Kuzmin-Type Problem For a Generalized Gauss-Kuzmin Operator

A generalized limit probability measure associated with a random system with complete connections for a generalized Gauss-Kuzmin operator, only for a special case, is defined, and its behaviour is investigated. As a consequence a specific version of Gauss-Kuzmin-type problem for the above generalized operator is obtained.

ONLINE LEARNING WITH MARKOV SAMPLING

This paper attempts to give an extension of learning theory to a setting where the assumption of i.i.d. data is weakened by keeping the independence but abandoning the identical restriction. We hypothesize that a sequence of examples (xt, yt) in X × Y for t = 1, 2, 3,… is drawn from a probability distribution ρt on X × Y. The marginal probabilities on X are supposed to converge to a limit probability on X. Two main examples for this time process are discussed. The first is a stochastic one which in the special case of a finite space X is defined by a stochastic matrix and more generally by a stochastic kernel. The second is determined by an underlying discrete dynamical system on the space X. Our theoretical treatment requires that this dynamics be hyperbolic (or "Axiom A") which still permits a class of chaotic systems (with Sinai–Ruelle–Bowen attractors). Even in the case of a limit Dirac point probability, one needs the measure theory to be defined using Hölder spaces. Many implications of our work remain unexplored. These include, for example, the relation to Hidden Markov Models, as well as Markov Chain Monte Carlo methods. It seems reasonable that further work should consider the push forward of the process from X × Y by some kind of observable function to a data space.

Probabilistic Index for Increasing Hourly Transmission Line Ratings

The steady state thermal rating of overhead transmission lines is limited by the conductor`s maximum design temperature, which is related to the maximum sag and the loss of tensile strength of the conductors. Traditionally, this overhead transmission lines rating is computed using a deterministic approach, with reference to severe weather conditions. Thus, the application of this method leads to conservative results resulting in under-utilization of conductors. In this paper, a new method based on an hourly probabilistic index is proposed to predict the line thermal rating for each hour of the day; this index is evaluated using the conductor current limit probability density function (pdf). The method uses Bayesian time series models for the weather parameters (ambient temperature, wind speed and wind direction) and calculates the conductor current limit pdf using a Monte Carlo simulation. The probabilistic index is applied by considering measured weather data of both hot and cold seasons; the corresponding lines ratings are reported and analyzed.