The Quadratic Cycle Cover Problem: special cases and efficient bounds

The quadratic cycle cover problem is the problem of finding a set of node-disjoint cycles visiting all the nodes such that the total sum of interaction costs between consecutive arcs is minimized. In this paper we study the linearization problem for the quadratic cycle cover problem and related lower bounds. In particular, we derive various sufficient conditions for the quadratic cost matrix to be linearizable, and use these conditions to compute bounds. We also show how to use a sufficient condition for linearizability within an iterative bounding procedure. In each step, our algorithm computes the best equivalent representation of the quadratic cost matrix and its optimal linearizable matrix with respect to the given sufficient condition for linearizability. Further, we show that the classical Gilmore-Lawler type bound belongs to the family of linearization based bounds, and therefore apply the above mentioned iterative reformulation technique. We also prove that the linearization vectors resulting from this iterative approach satisfy the constant value property. The best among here introduced bounds outperform existing lower bounds when taking both quality and efficiency into account

Alternating-Gradient Focusing of the Benzonitrile-Argon Van der Waals Complex

We report on the focusing and guiding of the van der Waals complex formed between benzonitrile molecules (C$_6$H$_5$CN) and argon atoms in a cold molecular beam using an ac electric quadrupole guide. The distribution of quantum states in the guided beam is non-thermal, because the transmission efficiency depends on the state-dependent effective dipole moment in the applied electric fields. At a specific ac frequency, however, the excitation spectrum can be described by a thermal distribution at a rotational temperature of 0.8 K. From the observed transmission characteristics and a combination of trajectory and Stark-energy calculations we conclude that the permanent electric dipole moment of benzonitrile remains unchanged upon the attachment of the argon atom to within \pm5%. By exploiting the different dipole-moment-to-mass (\mu/m) ratios of the complex and the benzonitrile monomer, transmission can be selectively suppressed for or, in the limit of 0 K rotational temperature, restricted to the complex.Comment: to be published in JC

Spatial cognition in synthetic environments

The current dissertation discussed the use of Virtual Reality in product design, referred to as the use of Synthetic Environments (SEs). The research of two basic and two case studies focused on investigating the effectiveness of SEs for the users. We expected that the users’ insight in the possibilities and flaws in a product’s design would increase if design situations were visualized and interactions were made with virtual prototypes. As a result, designers receive more accurate feedback about a product’s design, which leads to more effective design solutions.\ud Two basic studies were conducted to determine the effect of interactivity on learning performance of virtual 3D objects. The results of these studies showed that interactively studied objects were memorized more accurately than passively studied objects. Moreover, the results revealed that interactivity is more effective for users with a low visual spatial ability (VSA) than for those with high VSA. The results also showed that interactivity affected visual related object representations, rather than action related representations. This implies that users were better able to memorize the visual appearance of virtual objects than performing imaginary actions with them.\ud In addition, two case studies were conducted. The first case study investigated the relevance of visually realistic SEs for the users. The results confirmed the hypothesis that users were better able to memorize the spatial lay-out of visually realistic SEs than of a non-realistic SE. A second case study examined the influence of interactivity on the users’ subjective experience of realism in SEs. The results revealed that the users experienced an interactive SE as more realistic than an animation of the same environment. These results suggest that extra investment in visual realism and interactivity in SEs is useful.\ud In conclusion, this dissertation showed that interactivity and visual realism are important characteristics of SEs, because it positively affects human memory. For the development of SEs it is therefore important to include these elements to ensure an effective application of SEs to product design. Furthermore, this dissertation emphasizes that designers should first define the users and their characteristics before they implement the technology of SEs

Integrality and cutting planes in semidefinite programming approaches for combinatorial optimization

Many real-life decision problems are discrete in nature. To solve such problems as mathematical optimization problems, integrality constraints are commonly incorporated in the model to reflect the choice of finitely many alternatives. At the same time, it is known that semidefinite programming is very suitable for obtaining strong relaxations of combinatorial optimization problems. In this dissertation, we study the interplay between semidefinite programming and integrality, where a special focus is put on the use of cutting-plane methods. Although the notions of integrality and cutting planes are well-studied in linear programming, integer semidefinite programs (ISDPs) are considered only recently. We show that manycombinatorial optimization problems can be modeled as ISDPs. Several theoretical concepts, such as the Chvátal-Gomory closure, total dual integrality and integer Lagrangian duality, are studied for the case of integer semidefinite programming. On the practical side, we introduce an improved branch-and-cut approach for ISDPs and a cutting-plane augmented Lagrangian method for solving semidefinite programs with a large number of cutting planes. Throughout the thesis, we apply our results to a wide range of combinatorial optimization problems, among which the quadratic cycle cover problem, the quadratic traveling salesman problem and the graph partition problem. Our approaches lead to novel, strong and efficient solution strategies for these problems, with the potential to be extended to other problem classes

Augmenting mental models

The complexity of conceptualizing mental models has made Virtual Reality an interesting way to enhance communication and understanding between individuals working together on a project or idea. Here, the authors discuss practical applications of using VR for this purpose

SDP-based bounds for the Quadratic Cycle Cover Problem via cutting plane augmented Lagrangian methods and reinforcement learning

We study the Quadratic Cycle Cover Problem (QCCP), which aims to find a node-disjoint cycle cover in a directed graph with minimum interaction cost between successive arcs. We derive several semidefinite programming (SDP) relaxations and use facial reduction to make these strictly feasible. We investigate a nontrivial relationship between the transformation matrix used in the reduction and the structure of the graph, which is exploited in an efficient algorithm that constructs this matrix for any instance of the problem. To solve our relaxations, we propose an algorithm that incorporates an augmented Lagrangian method into a cutting plane framework by utilizing Dykstra's projection algorithm. Our algorithm is suitable for solving SDP relaxations with a large number of cutting planes. Computational results show that our SDP bounds and our efficient cutting plane algorithm outperform other QCCP bounding approaches from the literature. Finally, we provide several SDP-based upper bounding techniques, among which a sequential Q-learning method that exploits a solution of our SDP relaxation within a reinforcement learning environment

Laser-induced 3D alignment and orientation of quantum-state-selected molecules

A strong inhomogeneous static electric field is used to spatially disperse a rotationally cold supersonic beam of 2,6-difluoroiodobenzene molecules according to their rotational quantum state. The molecules in the lowest lying rotational states are selected and used as targets for 3-dimensional alignment and orientation. The alignment is induced in the adiabatic regime with an elliptically polarized, intense laser pulse and the orientation is induced by the combined action of the laser pulse and a weak static electric field. We show that the degree of 3-dimensional alignment and orientation is strongly enhanced when rotationally state-selected molecules, rather than molecules in the original molecular beam, are used as targets.Comment: 8 pages, 7 figures; v2: minor update

The impact of interactive manipulation on the recognition of objects

A new application for VR has emerged: product development, in which several stakeholders (from engineers to end users) use the same VR for development and communicate purposes. Various characteristics among these stakeholders vary considerably, which imposes potential constraints to the VR. The current paper discusses the influence of three types of exploration of objects (i.e., none, passive, active) on one of these characteristics: the ability to form mental representations or visuo-spatial ability (VSA). Through an experiment we found that all users benefit from exploring objects. Moreover, people with low VSA (e.g., end users) benefit from an interactive exploration of objects opposed to people with a medium or high VSA (e.g. engineers), who are not sensitive for the type of exploration. Hence, for VR environments in which multiple stakeholders participate (e.g. for product development), differences among their cognitive abilities (e.g., VSA) have to be taken into account to enable an efficient usage of VR