Lagrangian Data-Driven Reduced Order Modeling of Finite Time Lyapunov Exponents

There are two main strategies for improving the projection-based reduced order model (ROM) accuracy: (i) improving the ROM, i.e., adding new terms to the standard ROM; and (ii) improving the ROM basis, i.e., constructing ROM bases that yield more accurate ROMs. In this paper, we use the latter. We propose new Lagrangian inner products that we use together with Eulerian and Lagrangian data to construct new Lagrangian ROMs. We show that the new Lagrangian ROMs are orders of magnitude more accurate than the standard Eulerian ROMs, i.e., ROMs that use standard Eulerian inner product and data to construct the ROM basis. Specifically, for the quasi-geostrophic equations, we show that the new Lagrangian ROMs are more accurate than the standard Eulerian ROMs in approximating not only Lagrangian fields (e.g., the finite time Lyapunov exponent (FTLE)), but also Eulerian fields (e.g., the streamfunction). We emphasize that the new Lagrangian ROMs do not employ any closure modeling to model the effect of discarded modes (which is standard procedure for low-dimensional ROMs of complex nonlinear systems). Thus, the dramatic increase in the new Lagrangian ROMs' accuracy is entirely due to the novel Lagrangian inner products used to build the Lagrangian ROM basis

Neighboring Extremal Optimal Control Theory for Parameter-Dependent Closed-loop Laws

This study introduces an approach to obtain a neighboring extremal optimal control (NEOC) solution for a closed-loop optimal control problem, applicable to a wide array of nonlinear systems and not necessarily quadratic performance indices. The approach involves investigating the variation incurred in the functional form of a known closed-loop optimal control law due to small, known parameter variations in the system equations or the performance index. The NEOC solution can formally be obtained by solving a linear partial differential equation, akin to those encountered in the iterative solution of a nonlinear Hamilton-Jacobi equation. Motivated by numerical procedures for solving these latter equations, we also propose a numerical algorithm based on the Galerkin algorithm, leveraging the use of basis functions to solve the underlying Hamilton-Jacobi equation of the original optimal control problem. The proposed approach simplifies the NEOC problem by reducing it to the solution of a simple set of linear equations, thereby eliminating the need for a full re-solution of the adjusted optimal control problem. Furthermore, the variation to the optimal performance index can be obtained as a function of both the system state and small changes in parameters, allowing the determination of the adjustment to an optimal control law given a small adjustment of parameters in the system or the performance index. Moreover, in order to handle large known parameter perturbations, we propose a homotopic approach that breaks down the single calculation of NEOC into a finite set of multiple steps. Finally, the validity of the claims and theory is supported by theoretical analysis and numerical simulations

Use of suggestion as a classroom learning strategy in China and Australia : an assessment scale with structural equation explanatory models in terms of stress, depression, learning styles and academic grades

This study is innovative in that it draws together the concepts of suggestion from several cultural groups and develops an inventory to account for variations the occurrence of scale to studies the relatively new area of the effects of suggestion in classrooms and compares effect on personality and academic variables. As new ideas and knowledge become more widespread and accepted by the community and teaching profession, precision in the applications of suggestion in the classroom is being seen as more important. Although new to education, suggestion and similar variations has always been central to influencing behaviour and learning among pastoral, counseling and hypnotherapy fields. Teachers who had experience or influence from those fields or the ideas of Lozanov (1978) or accelerated learning groups were and are more the exception than the rule. However, as new ideas become more influential, the influence of suggestion in is becoming increasingly important in progressive, modern education. A major goal of the study was to provide a valid instrument to compare Chinese and Australian differences and similarities in use of suggestion in learning. It was hoped that such a comparison would provide increased mutual understanding of values, strategies, practices and preferences by teachers and students. A second goal was to develop a causative model that explained the relationships between the measured variables of personality and learning behaviour and suggestion in teaching and learning.. A third aim was to make a comparison on effects and performance of suggestion in teaching and learning in Australian, Chinese and Australian accelerative learning classes. This study examined differences between Australian and Chinese high school Science classrooms in their use of suggestion in teaching and learning. To ascertain the prevalence and types of suggestion in the classroom the 39-item suggestion in teaching and learning (STL) scale was developed and validated v in Year 7, 9, and 11 high school classes in China and Australia. The STL scale categorized suggestion into the following types or subscales: Selfsuggestion, metaphor, indirect non-verbal suggestion, general spoken suggestion, negative suggestion, intuitive suggestion, direct verbal suggestion, relaxation, and de-suggestion. The study involved surveying 344 participants (n=182 female, n=162 male) from four high schools in Australia and China. A further 374 participants (n=108 teachers, n=266 students) from six high schools were surveyed for selecting a Chinese sample in a pilot study. About 284 participants (China: 200 students; Australia: 84 students [includes 8 adults]) were observed for validation of the STL instrument. All subjects and classes were randomly selected and were surveyed and observed for the purpose of scale and model development. The STL scale was found to be capable of distinguishing different types of suggestion within Chinese, Australian, and Australian Accelerative Learning classes. The STL scale was significant as a first scale to measure suggestion in teaching and learning in Australian and Chinese classrooms. Items in the scale were strongly and significantly correlated with other items within the subscales and with the overall scale. Path analytic techniques were used to explain relationships between the STL scale, its subscales, nation, gender and high school students profiles on stress, depression, learning styles and academic grades. Limitations of the study included problems arising from language and cultural differences as well as newness of the scale and the field of study. Recommendations for further study included strengthening aspects of the scale with new items and further qualitative and quantitative studies on the uses of suggestion in academic learning and other forms of change in childhood and adolescence

Knowledge Rich Natural Language Queries over Structured Biological Databases

Increasingly, keyword, natural language and NoSQL queries are being used for information retrieval from traditional as well as non-traditional databases such as web, document, image, GIS, legal, and health databases. While their popularity are undeniable for obvious reasons, their engineering is far from simple. In most part, semantics and intent preserving mapping of a well understood natural language query expressed over a structured database schema to a structured query language is still a difficult task, and research to tame the complexity is intense. In this paper, we propose a multi-level knowledge-based middleware to facilitate such mappings that separate the conceptual level from the physical level. We augment these multi-level abstractions with a concept reasoner and a query strategy engine to dynamically link arbitrary natural language querying to well defined structured queries. We demonstrate the feasibility of our approach by presenting a Datalog based prototype system, called BioSmart, that can compute responses to arbitrary natural language queries over arbitrary databases once a syntactic classification of the natural language query is made