Algorithms for detecting dependencies and rigid subsystems for CAD

Geometric constraint systems underly popular Computer Aided Design soft- ware. Automated approaches for detecting dependencies in a design are critical for developing robust solvers and providing informative user feedback, and we provide algorithms for two types of dependencies. First, we give a pebble game algorithm for detecting generic dependencies. Then, we focus on identifying the "special positions" of a design in which generically independent constraints become dependent. We present combinatorial algorithms for identifying subgraphs associated to factors of a particular polynomial, whose vanishing indicates a special position and resulting dependency. Further factoring in the Grassmann- Cayley algebra may allow a geometric interpretation giving conditions (e.g., "these two lines being parallel cause a dependency") determining the special position.Comment: 37 pages, 14 figures (v2 is an expanded version of an AGD'14 abstract based on v1

Geometric Over-Constraints Detection: A Survey

Currently, geometric over-constraints detection is of major interest in several diferent felds. In terms of product development process (PDP), many approaches exist to compare and detect geometric over-constraints, to decompose geometric systems, to solve geometric constraints systems. However, most approaches do not take into account the key characteristics of a geometric system, such as types of geometries, diferent levels at which a system can be decomposed e.g numerical or structural. For these reasons, geometric over-constraints detection still faces challenges to fully satisfy real needs of engineers. The aim of this paper is to review the state-of-the-art of works involving with geometric over-constraints detection and to identify pos sible research directions. Firstly, the paper highlights the user requirements for over-constraints detection when modeling geometric constraints systems in PDP and proposes a set of criteria to analyze the available methods classifed into four categories: level of detecting over-constraints, system decomposition, system modeling and results generation. Secondly, it introduces and analyzes the available methods by grouping them based on the introduced criteria. Finally, it discusses pos sible directions and future challenges

On the detection of over-constrained subparts of configurations when deforming free-form curves

Today, designers use CAD modelers to define and modify NURBS surfaces involved in the design of complex shapes like car bodies or turbine blades. The generated shapes often result from the use of variational modeling techniques where user-specified constraints define the shapes. However, for free-form curve/surfaces, if too much constraints are added to subparts of a configuration, the system will not be solvable even if it is globally well-/under-constrained. When this happens, it is useful to identify locally unsatisfiable subparts of configurations and provide the user feedback for adjustment. Currently, in the domain of geometric constraint solving, techniques are mainly developed for Euler geometries rather than parametric entities like free-form curves/surfaces. In this paper, we apply the Dulmage-Mendelsohn decomposition method to isolate structural over-constrained subparts of configurations. Since structural over-constraints do not necessarily mean unsatisfiable, a Jacobian matrix analysis approach is taken to further detect the inconsistent constraints. Indeed, these numerical methods can be generalized to detect overconstraints on free-form curves. We illustrate our approach on different examples where results show that Gauss elimination, though restricted to linear cases, is more relevant in our context than Dulmage-Mendelsohn decomposition

Towards a better integration of modelers and black box constraint solvers within the Product Design Process

This paper presents a new way of interaction between modelers and solvers to support the Product Development Process (PDP). The proposed approach extends the functionalities and the power of the solvers by taking into account procedural constraints. A procedural constraint requires calling a procedure or a function of the modeler. This procedure performs a series of actions and geometric computations in a certain order. The modeler calls the solver for solving a main problem, the solver calls the modeler’s procedures, and similarly procedures of the modeler can call the solver for solving sub-problems. The features, specificities, advantages and drawbacks of the proposed approach are presented and discussed. Several examples are also provided to illustrate this approach

Next Generation Very Large Array Memo No. 9 Science Working Group 4: Time Domain, Fundamental Physics, and Cosmology

We report here on key science topics for the Next Generation Very Large Array in the areas of time domain, fundamental physics, and cosmology. Key science cases considered are pulsars in orbit around the Galactic Center massive black hole, Sagittarius A*, electromagnetic counterparts to gravitational waves, and astrometric cosmology. These areas all have the potential for ground-breaking and transformative discovery. Numerous other topics were discussed during the preparation of this report and some of those discussions are summarized here, as well. There is no doubt that further investigation of the science case will reveal rich and compelling opportunities

Entanglement Distillation; A Discourse on Bound Entanglement in Quantum Information Theory

PhD thesis (University of York). The thesis covers in a unified way the material presented in quant-ph/0403073, quant-ph/0502040, quant-ph/0504160, quant-ph/0510035, quant-ph/0512012 and quant-ph/0603283. It includes two large review chapters on entanglement and distillation.Comment: 192 page

Railway Transport Planning and Management

Railway engineering is facing different and complex challenges due to the growing demand for travel, new technologies, and new mobility paradigms. All these issues require a clear understanding of the existing technologies, and it is crucial to identify the real opportunities that the current technological revolution may pose. As railway transportation planning processes change and pursue a multi-objective vision, diagnostic and maintenance issues are becoming even more crucial for overall system performances and alternative fuel solutions

Next Generation Very Large Array Memo No. 9 Science Working Group 4: Time Domain, Fundamental Physics, and Cosmology

We report here on key science topics for the Next Generation Very Large Array in the areas of time domain, fundamental physics, and cosmology. Key science cases considered are pulsars in orbit around the Galactic Center massive black hole, Sagittarius A*, electromagnetic counterparts to gravitational waves, and astrometric cosmology. These areas all have the potential for ground-breaking and transformative discovery. Numerous other topics were discussed during the preparation of this report and some of those discussions are summarized here, as well. There is no doubt that further investigation of the science case will reveal rich and compelling opportunities