A note on the variance of rank-based selection strategies for genetic algorithms and genetic programming

This paper evaluates different forms of rank-based selection that are used with genetic algorithms and genetic programming. Many types of rank based selection have exactly the same expected value in terms of the sampling rate allocated to each member of the population. However, the variance associated with that sampling rate can vary depending on how selection is implemented. We examine two forms of tournament selection and compare these to linear rank-based selection using an explicit formula. Because selective pressure has a direct impact on population diversity, we also examine the interaction between selective pressure and different mutation strategies.     

Computing Minimal Multi-Homogeneous Bezout Numbers Is Hard

The multi-homogeneous Bezout number is a bound for the number of solutions of a system of multi-homogeneous polynomial equations, in a suitable product of projective spaces. Given an arbitrary, not necessarily multi-homogeneous, system, one can ask for the optimal multi-homogenization that would minimize the Bezout number. In this paper it is proved that the problem of computing, or even estimating, the optimal multi-homogeneous Bezout number is actually NP-hard. In terms of approximation theory for combinatorial optimization, the problem of computing the best multi-homogeneous structure does not belong to APX, unless P = NP. Moreover, polynomial-time algorithms for estimating the minimal multi-homogeneous Bezout number up to a fixed factor cannot exist even in a randomized setting, unless BPP ⫆ NP.     

AssetCollector: a system for managing collections of cultural assets

In this paper, AssetCollector is presented, which is a system for managing collections of cultural assets. AssetCollector covers the needs of collection curators towards defining, populating and searching a collection in a flexible way, while supporting them in generating reports based on the collection’s assets and reusing them in order to build web sites and CD-ROMs. In order to support the above functionality, the system provides the content structuring subsystem, the content input subsystem, the search subsystem and the report subsystem. The use of the subsystems is straightforward and requires no technical skills from the curators. AssetCollector has been successfully applied for organizing various collections of cultural assets in Greece, such as archaeological sites, museums and published books. In the future, an evaluation procedure is planned in order to further refine the use of the system according to the targeted users’ needs. Furthermore, more import and export facilities will be provided, which will make the system compliant with widely accepted standards.     

VaR and ES for linear portfolios with mixture of elliptic distributions risk factors

In this paper, we generalize the Linear VaR method from portfolios with normally distributed risk factors to portfolios with mixture of elliptically distributed ones. We treat both the Expected Shortfall and the Value-at-Risk of such portfolios. Special attention is given to the particular case of a mixture of multivariate t-distributions. This is a part of J. SADEFO-KAMDEM PhD Thesis[12] of the Université de Reims, France . It has been presented at the workshop on modelling and computation in Financial Engineering at Bad Herrenalb, Germany May 6-8, 2003. The author is an associate professor at the Department of mathematics, université d’Evry Val d’Essonne.     

Applications of the discrete element method in mechanical engineering

Compared to other fields of engineering, in mechanical engineering, the Discrete Element Method (DEM) is not yet a well known method. Nevertheless, there is a variety of simulation problems where the method has obvious advantages due to its meshless nature. For problems where several free bodies can collide and break after having been largely deformed, the DEM is the method of choice. Neighborhood search and collision detection between bodies as well as the separation of large solids into smaller particles are naturally incorporated in the method. The main DEM algorithm consists of a relatively simple loop that basically contains the three substeps contact detection, force computation and integration. However, there exists a large variety of different algorithms to choose the substeps to compose the optimal method for a given problem. In this contribution, we describe the dynamics of particle systems together with appropriate numerical integration schemes and give an overview over different types of particle interactions that can be composed to adapt the method to fit to a given simulation problem. Surface triangulations are used to model complicated, non-convex bodies in contact with particle systems. The capabilities of the method are finally demonstrated by means of application examples. Commemorative Contribution.     

Simulation model of general human and humanoid motion

In the last decade we have witnessed a rapid growth of Humanoid Robotics, which has already constituted an autonomous research field. Humanoid robots (or simply humanoids) are expected in all situations of humans’ everyday life, “living” and cooperating with us. They will work in services, in homes, and hospitals, and they are even expected to get involved in sports. Hence, they will have to be capable of doing diverse kinds of tasks. This forces the researchers to develop an appropriate mathematical model to support simulation, design, and control of these systems. Another important fact is that today’s, and especially tomorrow’s, humanoid robots will be more and more humanlike in their shape and behavior. A dynamic model developed for an advanced humanoid robot may become a very useful tool for the dynamic analysis of human motion in different tasks (walking, running and jumping, manipulation, various sports, etc.). So, we derive a general model and talk about a human-and-humanoid simulation system. The basic idea is to start from a human/humanoid considered as a free spatial system (“flier”). Particular problems (walking, jumping, etc.) are then considered as different contact tasks – interaction between the flier and various objects (being either single bodies or separate dynamic systems).     

Mining process models with non-free-choice constructs

Process mining aims at extracting information from event logs to capture the business process as it is being executed. Process mining is particularly useful in situations where events are recorded but there is no system enforcing people to work in a particular way. Consider for example a hospital where the diagnosis and treatment activities are recorded in the hospital information system, but where health-care professionals determine the “careflow.” Many process mining approaches have been proposed in recent years. However, in spite of many researchers’ persistent efforts, there are still several challenging problems to be solved. In this paper, we focus on mining non-free-choice constructs, i.e., situations where there is a mixture of choice and synchronization. Although most real-life processes exhibit non-free-choice behavior, existing algorithms are unable to adequately deal with such constructs. Using a Petri-net-based representation, we will show that there are two kinds of causal dependencies between tasks, i.e., explicit and implicit ones. We propose an algorithm that is able to deal with both kinds of dependencies. The algorithm has been implemented in the ProM framework and experimental results shows that the algorithm indeed significantly improves existing process mining techniques.