Quasi-isometric groups with no common model geometry

A simple surface amalgam is the union of a finite collection of surfaces with precisely one boundary component each and which have their boundary curves identified. We prove if two fundamental groups of simple surface amalgams act properly and cocompactly by isometries on the same proper geodesic metric space, then the groups are commensurable. Consequently, there are infinitely many fundamental groups of simple surface amalgams that are quasi-isometric, but which do not act properly and cocompactly on the same proper geodesic metric space.Comment: v2: 19 pages, 6 figures; minor changes. To appear in Journal of the London Mathematical Societ

Quadratic equations over free groups are NP-complete

We prove that the problems of deciding whether a quadratic equation over a free group has a solution is NP-complete

Acceleration of the retrieval of past experiences in Case Based Reasoning : application for preliminary design in Chemical Engineering

The way to manage knowledge accumulated is one of the firm’s trends, in order to capitalize and to transmit this knowledge. Some Artificial Intelligence methods are devoted to preserve and to reuse past experiences. Case Based Reasoning (CBR) is one of these methods dedicated to problem solving, new knowledge acquisition and knowledge management. CBR is a cyclic method where the central notion is a case which represents an earlier experience. Several cases are collected and stored in a memory: the case base. The goal of this paper is to soften the way to describe problem and to increase the effectiveness of the system during the retrieval of relevant case

Case Based Reasoning for Chemical Engineering Design

With current industrial environment (competition, lower profit margin, reduced time to market, decreased product life cycle, environmental constraints, sustainable development, reactivity, innovation…), we must decrease the time for design of new products or processes. While the design activity is marked out by several steps, this article proposed a decision support tool for the preliminary design step. This tool is based on the Case Based Reasoning (CBR) method. This method has demonstrated its effectiveness in other domains (medical, architecture…) and more recently in chemical engineering. This method, coming from Artificial Intelligence, is based on the reusing of earlier experiences to solve new problems. The goal of this article is to show the utility of such method for unit operation (for example) pre-design but also to propose several evolutions for CBR through a domain as complex as the chemical engineering is (because of its interactions, non linearity, intensification problems…). During the pre-design step, some parameters like operating conditions are not precisely known but we have an interval of possible values, worse we only have a partial description of the problem.. To take into account this imprecision in the problem description, the CBR method is coupled with the fuzzy sets theory. After a mere presentation of the CBR method, a practical implementation is described with the choice and the pre-design of packing for separation columns