A step by step Bogoliubov transformation method for diagonalising a kind of non Hermitian effective Hamiltonian

1 A Novel Interval Method for Validating State Enclosures of the Solution of Initial Value Problems Andreas Rauh 1 , Ekaterina Auer 2 , and Eberhard P. Hofer 1 1 Institute of Measurement, Control, and Microtechnology University of Ulm D-89069 Ulm, Germany {Andreas.Rauh, Eberhard.hofer}@uni-ulm.de 2 Ekaterina Auer Faculty of Engineering, IIIS University of Duisburg-Essen D-47048 Duisburg, Germany Auer@inf.uni-due.de Abstract In this paper, VALENCIA-IVP, a novel approach for VALidation of state ENClosures using Interval Arithmetic for Initial Value Problems, is presented to determine guaranteed state enclosures. The algorithm is based on the computation of non-validated approximate solutions followed by an interval arithmetic fixed-point iteration for enclosing the approximation error. The performance of VALENCIA-IVP is compared with other validated solvers for dynamical systems with uncertain but bounded initial states. I. INTRODUCTION The solution of initial value problems (IVPs) is of great importance in many different disciplines, for example, modeling of dynamical systems in engineering, biology, and economics. To analyze the dynamical behavior of parameterized models, numerical simulations have to be performed in almost all practical applications due to the lack of analytical solutions. If usual floating point techniques with inappropriate step-sizes are applied, the results are often erroneous, which, for example, lets instable systems seem stable or vice versa. Validated techniques, in contrast, are able to determine guaranteed enclosures of the exact solutions of IVPs even if the state equations are discretized for simulation purposes. Furthermore, they can also provide guaranteed enclosures of all possible states if the exact values of initial conditions or parameters are unknown. The uncertainties originate from the fact that in almost all practical situations only conservative bounds for the range of these values are available. Throughout this article, 2 the words validated, guaranteed, and verified are used interchangeably to denote that state enclosures are mathematically and not only empirically proven to be correct. Traditional validated techniques for the solution of IVPs are implemented in various software pack- ages. VNODE [1], [2] and COSY VI [3], [4] are probably two of the most representative tools, see Subsection II-C. Although they are fairly efficient for exactly known initial states and parameters, they are sometimes insufficient for practical scenarios with uncertain but bounded initial states and parameters which have to be considered in verification and design of robust control strategies for sensitivity analysis of the system w.r.t. all uncertainties. These uncertainties often lead to increased overestimation due to the wrapping effect and the dependency problem and therefore in many cases to higher computational effort for its reduction. In this article, a new algorithm implemented in the solver VALENCIA-IVP 1 is proposed. First, an approximate solution of an IVP similar to the considered one is calculated with exactly known initial states and parameters. Based on this approximate solution, an easy-to-implement fixed-point iteration scheme is derived to determine validated enclosures by evaluation of the set of state equations on a finite time interval. It is shown for two examples that these "A step-by-step Bogoliubov transformation method for diagonalising a kind of non-Hermitian effective Hamiltonian" "A step-by-step Bogoliubov transformation method for diagonalising a kind of nonHermitian effective Hamiltonian" Bởi: paulmandel Introduction Introduction From the microscopic description to macroscopic equations Steady-state bistability Analytic local treatment around the limit points Conclusion Read more 1/1 A Method for Word Sense Disambiguation of Unrestricted Text Rada Mihalcea and Dan I. Moldovan Department of Computer Science and Engineering Southern Methodist University Dallas, Texas, 75275-0122 (rada,moldovan}@seas.smu.edu Abstract Selecting the most appropriate sense for an am- biguous word in a sentence is a central prob- lem in Natural Language Processing. In this paper, we present a method that attempts to disambiguate all the nouns, verbs, adverbs and adjectives in a text, using the senses pro- vided in WordNet. The senses are ranked us- ing two sources of information: (1) the Inter- net for gathering statistics for word-word co- occurrences and (2)WordNet for measuring the semantic density for a pair of words. We report an average accuracy of 80% for the first ranked sense, and 91% for the first two ranked senses. Extensions of this method for larger windows of more than two words are considered. 1 Introduction Word Sense Disambiguation (WSD) is an open problem in Natural Language Processing. Its solution impacts other tasks such as discourse, reference resolution, coherence, inference and others. WSD methods can be broadly classified into three types: 1. WSD that make use of the information provided by machine readable dictionaries (Cowie et al., 1992), (Miller et al., 1994), (Agirre and Rigau, 1995), (Li et al., 1995), (McRoy, 1992); 2. WSD that use information gathered from training on a corpus that has already been semantically disambiguated (super- vised training methods) (Gale et al., 1992), (Ng and Lee, 1996); 3. WSD that use information gathered from raw corpora (unsupervised training meth- ods) (Yarowsky, 1995) (Resnik, 1997). There are also hybrid methods that combine several sources of knowledge such as lexicon in- formation, heuristics, collocations and others (McRoy, 1992) (Bruce and Wiebe, 1994) (Ng and Lee, 1996) (Rigau et al., 1997). Statistical methods produce high accuracy re- sults for small number of preselected words. A lack of widely available semantically tagged cor- pora almost excludes supervised learning meth- ods. A possible solution for automatic acqui- sition of sense tagged corpora has been pre- sented in (Mihalcea and Moldovan, 1999), but the corpora acquired with this method has not been yet tested for statistical disambiguation of words. On the other hand, the disambiguation using unsupervised methods has the disadvan- tage that the senses are not well defined. None of the statistical methods disambiguate adjec- tives or adverbs so far. In this paper, we introduce a method that at- tempts to disambiguate all the nouns, verbs, ad- jectives and adverbs in a text, using the senses provided in WordNet (Fellbaum, 1998). To our knowledge, there is only one other method, recently reported, that disambiguates unre- stricted words in texts (Stetina et al., 1998). 2 A word-word dependency approach The method presented here takes advantage of the sentence context. The words are paired and an attempt is made to disambiguate one word within the context of the other word. This is done by searching on Internet with queries formed using different senses of one word, while keeping the other word fixed. The senses are ranked simply by the order provided by the number VNU Journal of Science, Mathematics - Physics 23 (2007) 131-138 131 A combination of the identification algorithm and the modal superposition method for feedback active control of incomplete measured systems N.D. Anh * , L.D. Viet Institute of Mechanics, 264 Doi can, Hanoi, Vietnam Received 15 November 2006; received in revised form 12 September 2007 Abstract. In a previous paper [1], the identification algorithm is presented for feedback active controlled systems. However, this method can only be applied to complete measured systems. The aim of this paper is to present a combination of the identification algorithm and the modal superposition method to control the incomplete measured systems. The system response is expanded by modal eigenfunction technique. The external excitation acting on some first modes is identified with a time delay and with a small error depending on the locations of the sensors. Then the control forces will be generated to balance the identified excitations. A numerical simulation is applied to a building modeled as a cantilever beam subjected to base acceleration. 1. Introduction The active control method can be applied to many problems such as robot control, ship autopilot, airplane autopilot, vibration control of vehicles or structures Fig 1 provides a schematic diagram of an active control system. Fig. 1. Diagram of a structural control system. It consists of 3 main parts: sensors to measure either external excitations or system responses or both; computer controller to process the measured information and to compute necessary control force ______ * Corresponding author. Tel.: 84-4-8326134 E-mail: ndanh@imech.ac.vn  Actuators, Control forces Controlled system Excitations Responses Computer, control algorithm Sensors Sensors N.D. Anh, L.D. Viet / VNU Journal of Science, Mathematics - Physics 23 (2007) 131-138 132 based on a given control algorithm; actuators to produce the required forces. When only the responses can be measured, the method is called feedback active control. In recent years, the active control method has been widely used to reduce the excessive vibrations of civil structures due to environmental disturbances ([1-10]). One of the basic tasks of active structural control problem is to determine a control strategy that uses the measured structural responses to calculate an appropriate control signal to send to the actuator. Many control strategies have been proposed, such as LQR/LQG control [2,3], H 2 /H ∞ control [4,5], sliding mode control [6], saturation control [7], reliability-based control [8], fuzzy control [9], neural control [10] In fact, it is usually that one is unable to measure the external excitation while the structural response can often be measured. The identification algorithm presented in [1] is a method, which identifies the external excitation from the structural response measured. Although this version of identification algorithm can be applied even for the nonlinear structures, it requires knowledge of the entire state vector of the structure, which is not possible for VNU Journal of Science, Mathematics - Physics 23 (2007) 131-138 131 A combination of the identification algorithm and the modal superposition method for feedback active control of incomplete measured systems N.D. Anh * , L.D. Viet Institute of Mechanics, 264 Doi can, Hanoi, Vietnam Received 15 November 2006; received in revised form 12 September 2007 Abstract. In a previous paper [1], the identification algorithm is presented for feedback active controlled systems. However, this method can only be applied to complete measured systems. The aim of this paper is to present a combination of the identification algorithm and the modal superposition method to control the incomplete measured systems. The system response is expanded by modal eigenfunction technique. The external excitation acting on some first modes is identified with a time delay and with a small error depending on the locations of the sensors. Then the control forces will be generated to balance the identified excitations. A numerical simulation is applied to a building modeled as a cantilever beam subjected to base acceleration. 1. Introduction The active control method can be applied to many problems such as robot control, ship autopilot, airplane autopilot, vibration control of vehicles or structures Fig 1 provides a schematic diagram of an active control system. Fig. 1. Diagram of a structural control system. It consists of 3 main parts: sensors to measure either external excitations or system responses or both; computer controller to process the measured information and to compute necessary control force ______ * Corresponding author. Tel.: 84-4-8326134 E-mail: ndanh@imech.ac.vn  Actuators, Control forces Controlled system Excitations Responses Computer, control algorithm Sensors Sensors N.D. Anh, L.D. Viet / VNU Journal of Science, Mathematics - Physics 23 (2007) 131-138 132 based on a given control algorithm; actuators to produce the required forces. When only the responses can be measured, the method is called feedback active control. In recent years, the active control method has been widely used to reduce the excessive vibrations of civil structures due to environmental disturbances ([1-10]). One of the basic tasks of active structural control problem is to determine a control strategy that uses the measured structural responses to calculate an appropriate control signal to send to the actuator. Many control strategies have been proposed, such as LQR/LQG control [2,3], H 2 /H ∞ control [4,5], sliding mode control [6], saturation control [7], reliability-based control [8], fuzzy control [9], neural control [10] In fact, it is usually that one is unable to measure the external excitation while the structural response can often be measured. The identification algorithm presented in [1] is a method, which identifies the external excitation from the structural response measured. Although this version of identification algorithm can be applied even for the nonlinear structures, it requires knowledge of the entire state vector of the structure, which is not possible for large Hindawi Publishing Corporation EURASIP Journal on Image and Video Processing Volume 2011, Article ID 538294, 24 pages doi:10.1155/2011/538294 Research Ar ticle The Extended-OPQ Method for User-Centered Quality of Experience Evaluation: A Study for Mobile 3D Video Broadcasting over DVB-H Dominik Strohmeier, 1 Satu Jumisko-Pyykk ¨ o, 2 Kristina Kunze, 1 and Mehmet Oguz Bici 3 1 Institute for Media Technology, Ilmenau University of Technology, 98693 Ilmenau, Germany 2 Unit of Human-Centered Technology, Tampere University of Technology, 33101 Tampere, Finland 3 Department of Electrical and Electronics Engineering, Middle East Technical University, 06531 Ankara, Turkey Correspondence should be addressed to Dominik Strohmeier, dominik.strohmeier@tu-ilmenau.de Received 1 November 2010; Accepted 14 January 2011 Academic Editor: Vittorio Baroncini Copyright © 2011 Dominik Strohmeier et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The Open Profiling of Quality (OPQ) is a mixed methods a pproach combining a conventional quantitative psychoperceptual evaluation and qualitative descriptive quality evaluation based on na ¨ ıve participants’ individual vocabulary. The method targets evaluation of heterogeneous and multimodal stimulus material. The current OPQ data collection procedure provides a rich pool of data, but full benefit of it has neither been taken in the analysis to build up completeness in understanding the phenomenon under the study nor has the procedure in the analysis been probed with alternative methods. The goal of this paper is to extend the original OPQ method with advanced r esearc h methods that have become popular in related research and the component model to be able to generalize individual attributes into a terminology of Quality of Experience. We conduct an extensive subjective quality evaluation study for 3D video on mobile device with heterogeneous stimuli. We vary factors on content, media (coding, concealments, and slice modes), and transmission levels (channel loss rate). The results showed that advanced procedures in the analysis cannot only complement each other but also draw deeper understanding on Quality of Experience. 1. Introduction Meeting the requirements of consumers and providing them a greater quality of experience than existing systems do is a key issue for the success of modern multimedia systems. However, the question about an optimized quality of expe- rience becomes more and more complex as technological systems are evolving and several systems are merged into new ones. Mobile3DTV combines 3DTV and mobileTV, both being emerging technologies in the area of audiovisual multimedia systems. The term 3DTV thereby refers to the whole value chain from image capturing, encoding, broadcasting, reception, and display [1 , 2]. In our approach, we extend this chain with the users as the end consumers of the system. The user, his needs and expectations, and his perceptual abilities play a key role for optimizing t he quality of the system Mobile3DTV. The challenges for modern quality evaluations grow in parallel to the increasing complexity of