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.     

An Optimized Content-Aware Authentication Scheme for Streaming JPEG-2000 Images Over Lossy Networks

This paper proposes an optimized content-aware authentication scheme for JPEG-2000 streams over lossy networks, where a received packet is consumed only when it is both decodable and authenticated. In a JPEG-2000 codestream, some packets are more important than others in terms of coding dependency and image quality. This naturally motivates allocating more redundant authentication information for the more important packets in order to maximize their probability of authentication and thereby minimize the distortion at the receiver. Towards this goal, with the awareness of its corresponding image content, we formulate an optimization framework to compute an authentication graph to maximize the expected media quality at the receiver, given specific authentication overhead and knowledge of network loss rate. System analysis and experimental results demonstrate that the proposed scheme achieves our design goal in that the rate-distortion (R-D) curve of the authenticated image is very close to the R-D curve when no authentication is required     

Domain-Driven, Actionable Knowledge Discovery

Data mining increasingly faces complex challenges in the real-life world of business problems and needs. The gap between business expectations and R&D results in this area involves key aspects of the field, such as methodologies, targeted problems, pattern interestingness, and infrastructure support. Both researchers and practitioners are realizing the importance of domain knowledge to close this gap and develop actionable knowledge for real user needs.     

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.