Perturbed Laguerre unitary ensembles,Hankel determinants,and information theory

This article investigates a key information‐theoretic performance metric in multiple‐antenna wireless communications, the so‐called outage probability. The article is partly a review, with the methodology based mainly on [10], while also presenting some new results. The outage probability may be expressed in terms of a moment generating function, which involves a Hankel determinant generated from a perturbed Laguerre weight. For this Hankel determinant, we present two separate integral representations, both involving solutions to certain non‐linear differential equations. In the second case, this is identified with a particular σ‐form of Painlevé V. As an alternative to the Painlevé V, we show that this second integral representation may also be expressed in terms of a non‐linear second order difference equation. Copyright © 2014 John Wiley & Sons, Ltd.     

A novel mollifier inversion scheme for the Laplace transform

In this article we present a novel inversion method for the Laplace transform for non‐equidistant scanning points applying the approximate inverse to this transform. The approximate inverse is a regularization technique for inverse problems based on evaluations of scalar products of the given data with so called reconstruction kernels. Each kernel solves a system of linear equations defined by the adjoint of the Laplace transform and dilatation invariant mollifiers, which are designed articularly for this operator. The paper includes numerical results.     

ORCA: Outlier detection and Robust Clustering for Attributed graphs

A framework is proposed to simultaneously cluster objects and detect anomalies in attributed graph data. Our objective function along with the carefully constructed constraints promotes interpretability of both the clustering and anomaly detection components, as well as scalability of our method. In addition, we developed an algorithm called Outlier detection and Robust Clustering for Attributed graphs (ORCA) within this framework. ORCA is fast and convergent under mild conditions, produces high quality clustering results, and discovers anomalies that can be mapped back naturally to the features of the input data. The efficacy and efficiency of ORCA is demonstrated on real world datasets against multiple state-of-the-art techniques.

     

Weekday dependence of German stock market returns

The so‐called ‘Monday effect’ has been found for various stock markets of the world. The empirical finding that Monday returns are significantly smaller than returns measured for the remaining days of the week calls the efficiency hypothesis for pricing processes operating on stock markets into question. Investigating an index series measured at the Frankfurt stock exchange the paper compares estimation results of parametric and non‐parametric autoregressive models with respect to possible weekday dependence of return data. Allowing for heteroskedastic error distributions the wild bootstrap is used to infer against time‐varying means and correlation of return data in parametric models and to obtain confidence bands for non‐parametric estimates. It is shown that time dependence is an important feature describing the dynamics of German stock market returns in the period 1960–1979. Within two subsamples obtained from the period 1980–1997 the evidence in favour of such effects is mitigated substantially. Copyright © 2000 John Wiley & Sons, Ltd.     

High‐order split‐step theta methods for non‐autonomous stochastic differential equations with non‐globally Lipschitz continuous coefficients

In this paper, we first propose the so‐called improved split‐step theta methods for non‐autonomous stochastic differential equations driven by non‐commutative noise. Then, we prove that the improved split‐step theta method is convergent with strong order of one for stochastic differential equations with the drift coefficient satisfying a superlinearly growing condition and a one‐sided Lipschitz continuous condition. Finally, the obtained results are verified by numerical experiments. Copyright © 2016 John Wiley & Sons, Ltd.     

Modified Hermitian and skew‐Hermitian splitting methods for non‐Hermitian positive‐definite linear systems

To further study the Hermitian and non‐Hermitian splitting methods for a non‐Hermitian and positive‐definite matrix, we introduce a so‐called lopsided Hermitian and skew‐Hermitian splitting and then establish a class of lopsided Hermitian/skew‐Hermitian (LHSS) methods to solve the non‐Hermitian and positive‐definite systems of linear equations. These methods include a two‐step LHSS iteration and its inexact version, the inexact Hermitian/skew‐Hermitian (ILHSS) iteration, which employs some Krylov subspace methods as its inner process. We theoretically prove that the LHSS method converges to the unique solution of the linear system for a loose restriction on the parameter α. Moreover, the contraction factor of the LHSS iteration is derived. The presented numerical examples illustrate the effectiveness of both LHSS and ILHSS iterations. Copyright © 2007 John Wiley & Sons, Ltd.     

An adaptive neuro‐fuzzy inference system for islanding detection in wind turbine as distributed generation

This article proposes a new integrated diagnostic system for islanding detection by means of a neuro‐fuzzy approach. Islanding detection and prevention is a mandatory requirement for grid‐connected distributed generation (DG) systems. Several methods based on passive and active detection scheme have been proposed. Although passive schemes have a large non‐detection zone (NDZ), concern has been raised on active method due to its degrading power‐quality effect. Reliably detecting this condition is regarded by many as an ongoing challenge as existing methods are not entirely satisfactory. The main emphasis of the proposed scheme is to reduce the NDZ to as close as possible and to keep the output power quality unchanged. In addition, this technique can also overcome the problem of setting the detection thresholds inherent in the existing techniques. In this study, we propose to use a hybrid intelligent system called ANFIS (the adaptive neuro‐fuzzy inference system) for islanding detection. This approach utilizes rate of change of frequency (ROCOF) at the target DG location and used as the input sets for a neuro‐fuzzy inference system for intelligent islanding detection. This approach utilizes the ANFIS as a machine learning technology and fuzzy clustering for processing and analyzing the large data sets provided from network simulations using MATLAB software. To validate the feasibility of this approach, the method has been validated through several conditions and different loading, switching operation, and network conditions. The proposed algorithm is compared with the widely used ROCOF relays and found working effectively in the situations where ROCOF fails. Simulation studies showed that the ANFIS‐based algorithm detects islanding situation accurate than other islanding detection algorithms. © 2014 Wiley Periodicals, Inc. Complexity 21: 10–20, 2015     

The Asymptotic and Numerical Inversion of the Marcum Q‐Function

The generalized Marcum functions appear in problems of technical and scientific areas such as, for example, radar detection and communications. In mathematical statistics and probability theory these functions are called the noncentral gamma or the noncentral chi‐squared cumulative distribution functions. In this paper, we describe a new asymptotic method for inverting the generalized Marcum Q‐function and for the complementary Marcum P‐function. Also, we show how monotonicity and convexity properties of these functions can be used to find initial values for reliable Newton or secant methods to invert the function. We present details of numerical computations that show the reliability of the asymptotic approximations.     

On the potential in non‐Gaussian chain polymer models

In this paper, we investigate the potential for a class of non‐Gaussian processes so‐called generalized grey Brownian motion. We obtain a closed analytic form for the potential as an integral of the M‐Wright functions and the Green function. In particular, we recover the special cases of Brownian motion and fractional Brownian motion. In addition, we give the connection to a fractional partial differential equation and its the fundamental solution.     

Blended kernel approximation in the ℋ︁‐matrix techniques

Several types of ??‐matrices were shown to provide a data‐sparse approximation of non‐local (integral) operators in FEM and BEM applications. The general construction is applied to the operators with asymptotically smooth kernel function provided that the Galerkin ansatz space has a hierarchical structure. The new class of ??‐matrices is based on the so‐called blended FE and polynomial approximations of the kernel function and leads to matrix blocks with a tensor‐product of block‐Toeplitz (block‐circulant) and rank‐k matrices. This requires the translation (rotation) invariance of the kernel combined with the corresponding tensor‐product grids. The approach allows for the fast evaluation of volume/boundary integral operators with possibly non‐smooth kernels defined on canonical domains/manifolds in the FEM/BEM applications. (Here and in the following, we call domains canonical if they are obtained by translation or rotation of one of their parts, e.g. parallelepiped, cylinder, sphere, etc.) In particular, we provide the error and complexity analysis for blended expansions to the Helmholtz kernel. Copyright © 2002 John Wiley & Sons, Ltd.     

The tanh method: a tool for solving certain classes of non‐linear PDEs

The tanh (or hyperbolic tangent) method is a powerful technique to look for travelling waves when dealing with one‐dimensional non‐linear wave and evolution equations. In particular, this method is well suited for those problems where dispersion, convection and reaction–diffusion play an important role. To show the strength of this method we study a coupled set (the so‐called Boussinesq equations) which arises in the theory of non‐linear dispersive water waves. As a result, a solitary wave profile is found which generalizes an earlier result, the famous Korteweg‐de Vries solitary wave solution. Copyright © 2005 John Wiley & Sons, Ltd.     

A mathematical assessment of the isolation random forest method for anomaly detection in big data

We present the mathematical analysis of the Isolation Random Forest Method (IRF Method) for anomaly detection, proposed by Liu F.T., Ting K.M. and Zhou Z. H. in their seminal work as a heuristic method for anomaly detection in Big Data. We prove that the IRF space can be endowed with a probability induced by the Isolation Tree algorithm (iTree). In this setting, the convergence of the IRF method is proved, using the Law of Large Numbers. A couple of counterexamples are presented to show that the method is inconclusive and no certificate of quality can be given, when using it as a means to detect anomalies. Hence, an alternative version of the method is proposed whose mathematical foundation is fully justified. Furthermore, a criterion for choosing the number of sampled trees needed to guarantee confidence intervals of the numerical results is presented. Finally, numerical experiments are presented to compare the performance of the classic method with the proposed one.     

Phase‐field systems for multi‐dimensional Prandtl–Ishlinskii operators with non‐polyhedral characteristics

Hysteresis operators have recently proved to be a powerful tool in modelling phase transition phenomena which are accompanied by the occurrence of hysteresis effects. In a series of papers, the present authors have proposed phase‐field models in which hysteresis non‐linearities occur at several places. A very important class of hysteresis operators studied in this connection is formed by the so‐called Prandtl–Ishlinskii operators. For these operators, the corresponding phase‐field systems are in the multi‐dimensional case only known to admit unique solutions if the characteristic convex sets defining the operators are polyhedrons. In this paper, we use approximation techniques to extend the known results to multi‐dimensional Prandtl–Ishlinskii operators having non‐polyhedral convex characteristicsets. Copyright © 2002 John Wiley & Sons, Ltd.     

Numerical treatment of degenerate diffusion equations via Feller's boundary classification,and applications

A numerical method is devised to solve a class of linear boundary‐value problems for one‐dimensional parabolic equations degenerate at the boundaries. Feller theory, which classifies the nature of the boundary points, is used to decide whether boundary conditions are needed to ensure uniqueness, and, if so, which ones they are. The algorithm is based on a suitable preconditioned implicit finite‐difference scheme, grid, and treatment of the boundary data. Second‐order accuracy, unconditional stability, and unconditional convergence of solutions of the finite‐difference scheme to a constant as the time‐step index tends to infinity are further properties of the method. Several examples, pertaining to financial mathematics, physics, and genetics, are presented for the purpose of illustration. © 2011 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2011     

Minimum time‐step criteria for the Galerkin finite element methods applied to one‐dimensional parabolic partial differential equations

The finite element method has been well established for numerically solving parabolic partial differential equations (PDEs). Also it is well known that a too large time step should not be chosen in order to obtain a stable and accurate numerical solution. In this article, accuracy analysis shows that a too small time step should not be chosen either for some time‐stepping schemes. Otherwise, the accuracy of the numerical solution cannot be improved or can even be worsened in some cases. Furthermore, the so‐called minimum time step criteria are established for the Crank‐Nicolson scheme, the Galerkin‐time scheme, and the backward‐difference scheme used in the temporal discretization. For the forward‐difference scheme, no minimum time step exists as far as the accuracy is concerned. In the accuracy analysis, no specific initial and boundary conditions are invoked so that such established criteria can be applied to the parabolic PDEs subject to any initial and boundary conditions. These minimum time step criteria are verified in a series of numerical experiments for a one‐dimensional transient field problem with a known analytical solution. The minimum time step criteria developed in this study are useful for choosing appropriate time steps in numerical simulations of practical engineering problems. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006     

Traffic incident detection: Sensors and algorithms

Incident detection involves both the collection and analysis of traffic data. In this paper, we take a look at the various traffic flow sensing technologies, and discuss the effects that the environment has on each. We provide recommendations on the selection of sensors, and propose a mix of wide-area and single-lane sensors to ensure reliable performance. We touch upon the issue of sensor accuracy and identify the increased use of neural networks and fuzzy logic for incident detection.Specifically, this paper addresses a novel approach to use measurements from a single station to detect anomalies in traffic flow. Anomalies are ascertained from deviations from the expected norms of traffic patterns calibrated at each individual station.We use an extension to the McMaster incident detection algorithm as a baseline to detect traffic anomalies. The extensions allow the automatic field calibration of the sensor.The paper discusses the development of a new novel time indexed anomaly detection algorithm. We establish norms as a time dependent function for each station by integrating past “normal” traffic patterns for a given time period. Time indexing will include time of day, day of week, and season. Initial calibration will take place over the prior few weeks. Online background calibration continues after initial calibration to continually tune and build the global seasonal time index. We end with a discussion of fuzzy-neural implementations.     

Structural damage detection strategy using correlation functions under inconsistent excitation

Structural damage detection using vibration response signals is appealing in recent years since it does not require the identification of the modal parameters or building the structures' finite element model, among which the correlation-function-based damage detection methodologies is a novel topic [1]. Beginning with the introduction of the correlation function theory, this paper proposes a new damage detection strategy using the auto correlation function values of vibration response signals of the structure. The maximum value of the auto correlation functions of the vibration responses from different measurement points are used to form the damage index to locate the damage. Differences of the damage index are used to make the damage location more clearly. As in real world applications, structures may undergo different external excitations [2]. Different external excitations are input into the intact and damaged structure. The results from numerical simulation of stiffness reduction detection of a 12-story frame structure show that the proposed strategy can locate the damage correctly and has a very good anti-noise ability under inconsistent external excitations. As only the vibration responses before and after damage are used in this damage detection strategy, it can be a useful tool for structural health monitoring. (© 2014 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Categorical abstract algebraic logic: The categorical Suszko operator

Czelakowski introduced the Suszko operator as a basis for the development of a hierarchy of non‐protoalgebraic logics, paralleling the well‐known abstract algebraic hierarchy of protoalgebraic logics based on the Leibniz operator of Blok and Pigozzi. The scope of the theory of the Leibniz operator was recently extended to cover the case of, the so‐called, protoalgebraic π‐institutions. In the present work, following the lead of Czelakowski, an attempt is made at lifting parts of the theory of the Suszko operator to the π‐institution framework. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Nonequivalence transformation of λ‐matrix eigenproblems and model embedding approach to model tuning

In this paper we present some theory for a non‐equivalence transformation of matrix eigenvalues for λ‐matrix polynomials. Application of this transformation to eigenvalue embedding for model tuning on a realistic industry problem is illustrated. The new approach has several advantages such as flexibility, efficiency, and structure‐preservation. A numerical experiment on a pseudosimulation data set from The Boeing Company is reported. Copyright © 2001 John Wiley & Sons, Ltd.     

The estimation of the prevalence of delinquency: Two approaches and a correction of the literature†

The index “the proportion of a cohort that have become delinquent by a given age,” here called the “prevalence of delinquency,” is an important social indicator. In the present paper, we indicate methods by which this index can be estimated from data, and correct errors in previous sex‐ and race‐specific prevalence estimates published by Monahan (1960) for the city of Philadelphia. The difference between the sexes and between the races shown by these corrected prevalence estimates are of sufficient magnitude to render suspect any comparisons of prevalences of delinquency among cohorts which do not take account of the sex and race compositions of the cohorts to be compared.