Shape preserving approximation using least squares splines

Least squares polynomial splines are an effective tool for data fitting, but they may fail to preserve essential properties of the underlying function, such as monotonicity or convexity. The shape restrictions are translated into linear inequality conditions on spline coefficients. The basis functions are selected in such a way that these conditions take a simple form, and the problem becomes non-negative least squares problem, for which effecitive and robust methods of solution exist. Multidimensional monotone approximation is achieved by using tensor-product splines with the appropriate restrictions. Additional inter polation conditions can also be introduced. The conversion formulas to traditional B-spline representation are provided.

Review of applications of the Cutting Angle methods

The theory of abstract convexity provides us with the necessary tools for building accurate one-sided approximations of functions. Cutting angle methods have recently emerged as a tool for global optimization of families of abstract convex functions. Their applicability have been subsequently extended to other problems, such as scattered data interpolation. This paper reviews three different applications of cutting angle methods, namely global optimization, generation of nonuniform random variates and multivatiate interpolation.

Extended cutting angle method of global optimization

Methods of Lipschitz optimization allow one to find and confirm the global minimum of multivariate Lipschitz functions using a finite number of function evaluations. This paper extends the Cutting Angle method, in which the optimization problem is solved by building a sequence of piecewise linear underestimates of the objective function. We use a more flexible set of support functions, which yields a better underestimate of a Lipschitz objective function. An efficient algorithm for enumeration of all local minima of the underestimate is presented, along with the results of numerical experiments. One dimensional Pijavski-Shubert method arises as a special case of the proposed approach.

Partners in crime : collusive corruption and search

This paper analyzes corruption as a collusive act which requires the participation of two willing partners. An agent intending to engage in a corrupt act must search for a like-minded partner. When many people in the economy are corrupt, such a search is more likely to be fruitful. Thus when an agent engages in a search, he raises the net benefit of searching for other similar agents in the economy, creating an externality. This introduces a non-convexity in the model, which consequently has multiple equilibria. The economy can be in stable equilibrium with a high or low level of corruption.

Starting from the high-corruption equilibrium, a sufficient increase in vigilance triggers a negative cascade, leading the economy to a new equilibrium in which no agent finds it profitable to search for corrupt partners. The no-corruption equilibrium continues to be stable if vigilance is then relaxed. This suggests that the correct way to deal with corruption is to launch a ``big push'' with large amounts of resources. Once the level of corruption declines, these resources can be withdrawn.

Construction of k-Lipschitz triangular norms and conorms from empirical data

This paper examines the practical construction of k-Lipschitz triangular norms and conorms from empirical data. We apply a characterization of such functions based on k-convex additive generators and translate k-convexity of piecewise linear strictly decreasing functions into a simple set of linear inequalities on their coefficients. This is the basis of a simple linear spline-fitting algorithm, which guarantees k-Lipschitz property of the resulting triangular norms and conorms.

Bounded lower subdifferentiability optimization techniques : applications

In this article we develop a global optimization algorithm for quasiconvex programming where the objective function is a Lipschitz function which may have "flat parts". We adapt the Extended Cutting Angle method to quasiconvex functions, which reduces significantly the number of iterations and objective function evaluations, and consequently the total computing time. Applications of such an algorithm to mathematical programming problems inwhich the objective function is derived from economic systems and location problems are described. Computational results are presented.

Vehicle detection and classification by measuring and processing magnetic signal

This paper presents novel vehicle detection and classification method by measuring and processing magnetic signal based on single micro-electro- mechanical system (MEMS) magnetic sensor. When a vehicle moves over the ground, it generates a succession of impacts on the earth's magnetic field, which can be detected by single magnetic sensor. The magnetic signal measured by the magnetic sensor is related to the moving direction and the type of the vehicle. Generally, the recognition rate using single sensor detector is not high. In order to improve the recognition rate, a novel feature extraction algorithm and a novel vehicle classification and recognition algorithm are presented. The concavity and convexity areas, and the angles of concave and convex parts of the waveform are extracted. An improved support vector machine (ISVM) classifier is developed to perform vehicle classification and recognition. The effectiveness of the proposed approach is verified by outdoor experiments.

On the use of restricted dissimilarity and dissimilarity-like functions for defining penalty functions

In this work we study the relation between restricted dissimilarity functions-and, more generally, dissimilarity-like functions- and penalty functions and the possibility of building the latter using the former. Several results on convexity and quasiconvexity are also considered.

Synchronization of singular Markovian jumping complex networks with additive time-varying delays via pinning control

Abstract
This study examines the problem of synchronization for singular complex dynamical networks with Markovian jumping parameters and two additive time-varying delay components. The complex networks consist of m modes which switch from one mode to another according to a Markovian chain with known transition probability. Pinning control strategies are designed to make the singular complex networks synchronized. Based on the appropriate Lyapunov-Krasovskii functional, introducing some free weighting matrices and using convexity of matrix functions, a novel synchronization criterion is derived. The proposed sufficient conditions are established in the form of linear matrix inequalities. Finally, a numerical example is presented to illustrate the effectiveness of the obtained results.

A new industry concentration index

We propose and analyse a new concentration index alternative to the Herfindahl-Hirschman Index (HHI). This new index emphasises the concept of competitive balance. It is designed to preserve the convexity property of the HHI when a merger involves one of the m largest firms, but to decrease and thus to indicate an increase in competition when a merger is purely among the (n − m) smallest firms.

Non-linear observer design for a class of singular time-delay systems with Lipschitz non-linearities

In this paper, we consider a class of time-delay singular systems with Lipschitz non-linearities. A method of designing full-order observers for the systems is presented which can handle non-linearities with large-Lipschitz constants. The Lipschitz conditions are reformulated into linear parameter varying systems, then the Lyapunov–Krasovskii approach and the convexity principle are applied to study stability of the new systems. Furthermore, the observers design does not require the assumption of regularity for singular systems. In case the systems are non-singular, a reduced-order observers design is proposed instead. In both cases, synthesis conditions for the observers designs are derived in terms of linear matrix inequalities which can be solved efficiently by numerical methods. The efficiency of the obtained results is illustrated by two numerical examples.