Determining Principal Component Cardinality through the Principle of Minimum Description Length

PCA (Principal Component Analysis) and its variants areubiquitous techniques for matrix dimension reduction and reduced-dimensionlatent-factor extraction. One significant challenge in using PCA, is thechoice of the number of principal components. The information-theoreticMDL (Minimum Description Length) principle gives objective compression-based criteria for model selection, but it is difficult to analytically applyits modern definition - NML (Normalized Maximum Likelihood) - to theproblem of PCA. This work shows a general reduction of NML prob-lems to lower-dimension problems. Applying this reduction, it boundsthe NML of PCA, by terms of the NML of linear regression, which areknown.Comment: LOD 201

Microscopic activity patterns in the Naming Game

The models of statistical physics used to study collective phenomena in some interdisciplinary contexts, such as social dynamics and opinion spreading, do not consider the effects of the memory on individual decision processes. On the contrary, in the Naming Game, a recently proposed model of Language formation, each agent chooses a particular state, or opinion, by means of a memory-based negotiation process, during which a variable number of states is collected and kept in memory. In this perspective, the statistical features of the number of states collected by the agents becomes a relevant quantity to understand the dynamics of the model, and the influence of topological properties on memory-based models. By means of a master equation approach, we analyze the internal agent dynamics of Naming Game in populations embedded on networks, finding that it strongly depends on very general topological properties of the system (e.g. average and fluctuations of the degree). However, the influence of topological properties on the microscopic individual dynamics is a general phenomenon that should characterize all those social interactions that can be modeled by memory-based negotiation processes.Comment: submitted to J. Phys.

Recent activities within the Aeroservoelasticity Branch at the NASA Langley Research Center

The objective of research in aeroservoelasticity at the NASA Langley Research Center is to enhance the modeling, analysis, and multidisciplinary design methodologies for obtaining multifunction digital control systems for application to flexible flight vehicles. Recent accomplishments are discussed, and a status report on current activities within the Aeroservoelasticity Branch is presented. In the area of modeling, improvements to the Minimum-State Method of approximating unsteady aerodynamics are shown to provide precise, low-order aeroservoelastic models for design and simulation activities. Analytical methods based on Matched Filter Theory and Random Process Theory to provide efficient and direct predictions of the critical gust profile and the time-correlated gust loads for linear structural design considerations are also discussed. Two research projects leading towards improved design methodology are summarized. The first program is developing an integrated structure/control design capability based on hierarchical problem decomposition, multilevel optimization and analytical sensitivities. The second program provides procedures for obtaining low-order, robust digital control laws for aeroelastic applications. In terms of methodology validation and application the current activities associated with the Active Flexible Wing project are reviewed

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

Machine Learning for Observables: Reactant to Product State Distributions for Atom-Diatom Collisions

Machine learning-based models to predict product state distributions from a distribution of reactant conditions for atom-diatom collisions are presented and quantitatively tested. The models are based on function-, kernel- and grid-based representations of the reactant and product state distributions. While all three methods predict final state distributions from explicit quasi-classical trajectory simulations with R$^2$ > 0.998, the grid-based approach performs best. Although a function-based approach is found to be more than two times better in computational performance, the kernel- and grid-based approaches are preferred in terms of prediction accuracy, practicability and generality. The function-based approach also suffers from lacking a general set of model functions. Applications of the grid-based approach to nonequilibrium, multi-temperature initial state distributions are presented, a situation common to energy distributions in hypersonic flows. The role of such models in Direct Simulation Monte Carlo and computational fluid dynamics simulations is also discussed

Sonic Booms in Atmospheric Turbulence (SonicBAT): The Influence of Turbulence on Shaped Sonic Booms

The objectives of the Sonic Booms in Atmospheric Turbulence (SonicBAT) Program were to develop and validate, via research flight experiments under a range of realistic atmospheric conditions, one numeric turbulence model research code and one classic turbulence model research code using traditional N-wave booms in the presence of atmospheric turbulence, and to apply these models to assess the effects of turbulence on the levels of shaped sonic booms predicted from low boom aircraft designs. The SonicBAT program has successfully investigated sonic boom turbulence effects through the execution of flight experiments at two NASA centers, Armstrong Flight Research Center (AFRC) and Kennedy Space Center (KSC), collecting a comprehensive set of acoustic and atmospheric turbulence data that were used to validate the numeric and classic turbulence models developed. The validated codes were incorporated into the PCBoom sonic boom prediction software and used to estimate the effect of turbulence on the levels of shaped sonic booms associated with several low boom aircraft designs. The SonicBAT program was a four year effort that consisted of turbulence model development and refinement throughout the entire period as well as extensive flight test planning that culminated with the two research flight tests being conducted in the second and third years of the program. The SonicBAT team, led by Wyle, includes partners from the Pennsylvania State University, Lockheed Martin, Gulfstream Aerospace, Boeing, Eagle Aeronautics, Technical & Business Systems, and the Laboratory of Fluid Mechanics and Acoustics (France). A number of collaborators, including the Japan Aerospace Exploration Agency, also participated by supporting the experiments with human and equipment resources at their own expense. Three NASA centers, AFRC, Langley Research Center (LaRC), and KSC were essential to the planning and conduct of the experiments. The experiments involved precision flight of either an F-18A or F-18B executing steady, level passes at supersonic airspeeds in a turbulent atmosphere to create sonic boom signatures that had been distorted by turbulence. The flights spanned a range of atmospheric turbulence conditions at NASA Armstrong and Kennedy in order to provide a variety of conditions for code validations. The SonicBAT experiments at both sites were designed to capture simultaneous F-18A or F-18B onboard flight instrumentation data, high fidelity ground based and airborne acoustic data, surface and upper air meteorological data, and additional meteorological data from ultrasonic anemometers and SODARs to determine the local atmospheric turbulence and boundary layer height