The paper examines the problem of dynamic ship positioning with the use of Kalman Filter- and Particle Filter-based sensor fusion algorithms. The proposed approach enables to estimate accurately the ship's state vector by fusing the vessel's position and heading measurements coming from on-board sensors together with distance measurements coming from sensors located at the coast (e.g. radar). The estimated state vector is used in turn, in a control loop, to regulate the horizontal position and heading of the vessel. The performance of dynamic positioning of the ship based on Kalman and Particle Filtering is evaluated through simulation experiments.

We consider a mixture of one exponential distribution and one gamma distribution with increasing failure rate. For the right choice of parameters, it is shown that its failure rate has an upsidedown bathtub shape failure rate. We also consider a mixture of a family of exponentials and a family of gamma distributions and obtain a similar result.

Taking our inspiration from modal correspondence theory, we present the idea of correspondence analysis for many-valued logics. As a benchmark case, we study truth-functional extensions of the Logic of Paradox (LP). First, we characterize each of the possible truth table entries for unary and binary operators that could be added to LP by an inference scheme. Second, we define a class of natural deduction systems on the basis of these characterizing inference schemes and a natural deduction system for LP. Third, we show that each of the resulting natural deduction systems is sound and complete with respect to its particular semantics.

This paper introduces two statistics that assess whether (or not) a sequence sampled from a stationary time-homogeneous Markov chain on a finite state space is reversible. The test statistics are based on observed deviations of transition sample counts between each pair of states in the chain. First, the joint asymptotic normality of these sample counts is established. This result is then used to construct two chi-squared-based tests for reversibility. Simulations assess the power and type one error of the proposed tests.

A cascading failure is a failure in a system of interconnected parts, in which the breakdown of one element can lead to the subsequent collapse of the others. The aim of this paper is to introduce a simple combinatorial model for the study of cascading failures. In particular, having in mind particle systems and Markov random fields, we take into consideration a network of interacting urns displaced over a lattice. Every urn is Pólya-like and its reinforcement matrix is not only a function of time (time contagion) but also of the behavior of the neighboring urns (spatial contagion), and of a random component, which can represent either simple fate or the impact of exogenous factors. In this way a non-trivial dependence structure among the urns is built, and it is used to study default avalanches over the lattice. Thanks to its flexibility and its interesting probabilistic properties, the given construction may be used to model different phenomena characterized by cascading failures such as power grids and financial networks.

In this paper, we introduce generating networks of splicing processors (GNSP for short),a formal languages generating model related to networks of evolutionary processors and toaccepting networks of splicing processors. We show that all recursively enumerablelanguages can be generated by GNSPs with only nine processors. We also show, by directsimulation, that two other variants of this computing model, where the communicationbetween processors is conducted in different ways, have the same computational power.

We analyze the asymptotic number of items chosen in a selection procedure. The procedure selects items whose rank among all previous applicants is within the best 100p percent of the number of previously selected items. We use analytic methods to obtain a succinct formula for the first-order asymptotic growth of the expected number of items chosen by the procedure.

A class of Markov chains we call successively lumbaple is specified for which it is shown that the stationary probabilities can be obtained by successively computing the stationary probabilities of a propitiously constructed sequence of Markov chains. Each of the latter chains has a(typically much) smaller state space and this yields significant computational improvements. We discuss how the results for discrete time Markov chains extend to semi-Markov processes and continuous time Markov processes. Finally, we will study applications of successively lumbaple Markov chains to classical reliability and queueing models.

One of the most fundamental results in inventory theory is the optimality of (s, S) policy for inventory systems with setup cost. This result is established under a key assumption of infinite ordering/production capacity. Several studies have shown that, when the ordering/production capacity is finite, the optimal policy for the inventory system with setup cost is very complicated and indeed, only partial characterization for the optimal policy is possible. In this paper, we consider a continuous review production/inventory system with finite capacity and setup cost. The demand follows a Poisson process and a demand that cannot be satisfied upon arrival is backlogged. We show that the optimal control policy has a very simple structure when the holding/shortage cost rate is quasi-convex. We also develop efficient algorithms to compute the optimal control parameters.

We consider the problem of dynamic multi-skill routing in call centers. Calls from different customer classes are offered to the call center according to a Poisson process. The agents are grouped into pools according to their heterogeneous skill sets that determine the calls that they can handle. Each pool of agents serves calls with independent exponentially distributed service times. Arriving calls that cannot be served directly are placed in a buffer that is dedicated to the customer class. We obtain nearly optimal dynamic routing policies that are scalable with the problem instance and can be computed online. The algorithm is based on approximate dynamic programming techniques. In particular, we perform one-step policy improvement using a polynomial approximation to relative value functions. We compare the performance of this method with decomposition techniques. Numerical experiments demonstrate that our method outperforms leading routing policies and has close to optimal performance.

The purpose of this study is two-fold. First, we investigate further properties of the second-order regular variation (2RV). These properties include the preservation properties of 2RV under the composition operation and the generalized inverse transform, among others. Second, we derive second-order expansions of the tail probabilities of convolutions of non-independent and identically distributed (i.i.d.) heavy-tail random variables, and establish second-order expansions of risk concentration under mild assumptions. The main results extend some ones in the literature from the i.i.d. case to non-i.i.d. case.

A class of labelled graphs is bridge-addable if, for all graphs G in and all vertices u and v in distinct connected components of G, the graph obtained by adding an edge between u and v is also in ; the class is monotone if, for all G ∈ and all subgraphs H of G, we have H ∈ . We show that for any bridge-addable, monotone class whose elements have vertex set {1,. . .,n}, the probability that a graph chosen uniformly at random from is connected is at least (1−on(1))e−½, where on(1) → 0 as n → ∞. This establishes the special case of the conjecture of McDiarmid, Steger and Welsh when the condition of monotonicity is added. This result has also been obtained independently by Kang and Panagiotou.

The normalized importance sampling estimator allows the target density f to be known only up to a multiplicative constant. We indicate how it can be derived by a delta method-based approximation of a Rao–Blackwellized acceptance rejection estimator. Using additional terms in the delta method then results on a new estimator that also only requires f to be known only up to a multiplicative constant. Numerical examples indicate that the new estimator usually outperforms the normalized importance sampling estimator in terms of mean square error.

We introduce the notion of a stable instance for a discrete optimization problem, and argue that in many practical situations only sufficiently stable instances are of interest. The question then arises whether stable instances of NP-hard problems are easier to solve, and in particular, whether there exist algorithms that solve in polynomial time all sufficiently stable instances of some NP-hard problem. The paper focuses on the Max-Cut problem, for which we show that this is indeed the case.

The European air traffic flow management problem poses particular challenges on optimization technology as it requires detailed modelling and rapid online optimization capabilities. Constraint programming proved successful in addressing these challenges for departure time slot allocation by offering fine-grained modelling of resource constraints and fast allocation through heuristic-repair strategies.