The integrated perturbation theory for cosmological tensor fields I: Basic formulation

In order to extract maximal information about cosmology from the large-scale structure of the Universe, one needs to use every bit of signals that can be observed. Beyond the spatial distributions of astronomical objects, the spatial correlations of tensor fields, such as galaxy spins and shapes, are ones of promising sources that one can access in the era of large surveys in near future. The perturbation theory is a powerful tool to analytically describe the behaviors and evolutions of correlation statistics on large scales for a given cosmology. In this paper, we formulate a nonlinear perturbation theory of tensor fields in general, based on the formulation of integrated perturbation theory for the scalar-valued bias, generalizing it to include the tensor-valued bias. To take advantage of rotational symmetry, the formalism is constructed on the basis of irreducible decomposition of tensors, identifying physical variables which are invariant under the rotation of the coordinates system.Comment: 39 pages, no figure; made significant changes of notations and normalizations of various quantities; this paper is followed by the second and third of a series, arXiv:2210.11085 and arXiv:2304.133

Evolving Graphs by Graph Programming

Graphs are a ubiquitous data structure in computer science and can be used to represent solutions to difficult problems in many distinct domains. This motivates the use of Evolutionary Algorithms to search over graphs and efficiently find approximate solutions. However, existing techniques often represent and manipulate graphs in an ad-hoc manner. In contrast, rule-based graph programming offers a formal mechanism for describing relations over graphs. This thesis proposes the use of rule-based graph programming for representing and implementing genetic operators over graphs. We present the Evolutionary Algorithm Evolving Graphs by Graph Programming and a number of its extensions which are capable of learning stateful and stateless digital circuits, symbolic expressions and Artificial Neural Networks. We demonstrate that rule-based graph programming may be used to implement new and effective constraint-respecting mutation operators and show that these operators may strictly generalise others found in the literature. Through our proposal of Semantic Neutral Drift, we accelerate the search process by building plateaus into the fitness landscape using domain knowledge of equivalence. We also present Horizontal Gene Transfer, a mechanism whereby graphs may be passively recombined without disrupting their fitness. Through rigorous evaluation and analysis of over 20,000 independent executions of Evolutionary Algorithms, we establish numerous benefits of our approach. We find that on many problems, Evolving Graphs by Graph Programming and its variants may significantly outperform other approaches from the literature. Additionally, our empirical results provide further evidence that neutral drift aids the efficiency of evolutionary search

A Regularization Technique for the Analysis of Photographic Data Used in Chemical Release Wind Measurements

The neutral winds are a key parameter in the electrodynamics of the ionosphere. The available techniques for measuring vertical neutral wind profiles, especially with good height resolution, are extremely limited. This is especially true with sounding rocket flights as it is not practical to take direct measurements of neutral winds with onboard instruments. Chemical releases from sounding rockets, however, allow such measurements by providing a tracer of the motion of the neutral atmosphere at altitudes in the mesosphere and lower thermosphere (MLT). The resulting chemiluminescent trail is typically photographed from two or more locations to track neutral motions. Triangulation based on these photographs then yields position information at each instant when simultaneous photographs are available from different locations. The resulting time series of position information can then be used to obtain a neutral wind profile. A technique is presented that improves this existing triangulation procedure by implementing computer vision-based automation techniques and an improved tracking algorithm that can accommodate non-simultaneous image data more easily and can provide better continuity in the motions inferred from consecutive images. Neutral wind profiles from the Joule II and HEX II sounding rocket experiments are presented and compared with results from the previous method

Applications of Modern Statistical Methods to Analysis of Data in Physical Science

Modern methods of statistical and computational analysis offer solutions to dilemmas confronting researchers in physical science. Although the ideas behind modern statistical and computational analysis methods were originally introduced in the 1970’s, most scientists still rely on methods written during the early era of computing. These researchers, who analyze increasingly voluminous and multivariate data sets, need modern analysis methods to extract the best results from their studies. The first section of this work showcases applications of modern linear regression. Since the 1960’s, many researchers in spectroscopy have used classical stepwise regression techniques to derive molecular constants. However, problems with thresholds of entry and exit for model variables plagues this analysis method. Other criticisms of this kind of stepwise procedure include its inefficient searching method, the order in which variables enter or leave the model and problems with overfitting data. We implement an information scoring technique that overcomes the assumptions inherent in the stepwise regression process to calculate molecular model parameters. We believe that this kind of information based model evaluation can be applied to more general analysis situations in physical science. The second section proposes new methods of multivariate cluster analysis. The K-means algorithm and the EM algorithm, introduced in the 1960’s and 1970’s respectively, formed the basis of multivariate cluster analysis methodology for many years. However, several shortcomings of these methods include strong dependence on initial seed values and inaccurate results when the data seriously depart from hypersphericity. We propose new cluster analysis methods based on genetic algorithms that overcomes the strong dependence on initial seed values. In addition, we propose a generalization of the Genetic K-means algorithm which can accurately identify clusters with complex hyperellipsoidal covariance structures. We then use this new algorithm in a genetic algorithm based Expectation-Maximization process that can accurately calculate parameters describing complex clusters in a mixture model routine. Using the accuracy of this GEM algorithm, we assign information scores to cluster calculations in order to best identify the number of mixture components in a multivariate data set. We will showcase how these algorithms can be used to process multivariate data from astronomical observations

Examining the Coupling of the Mechanical and Chemical Functions of Myosin Family Members Using Single Molecule and Bulk Solution Techniques

Myosins are actin-activated ATPases that convert the chemical energy stored in ATP into the mechanical swing of its lever-arm. The members of the myosin family exhibit a wide range of cellular functions. Myosin Ib (myo1b) is single-headed and may link the cell membrane to the actin network acting as a tension sensor; while myosin V (myoV) is double-headed and can act as a cargo transporter in cells. The very different functions of myo1b and myoV arise from differences in their chemical and mechanical activities. We examined the chemomechanical properties of myo1b using stopped flow and optical trap experiments, from which were determined mechanical step sizes and kinetic rates associated with the chemomechanical steps of the myo1b crossbridge cycle. Most importantly, we found that the rates are slow and the rate associated with ADP release during actin attachment is greatly decreased by force, which could allow it to act as a tension sensor. These kinetic rates and force sensitivity of myo1b are strongly regulated by the signaling molecule, calcium. MyoV steps along actin in a complex and dense cellular environment; how this is done can be understood from its intrinsic stepping behavior as measured from the changes in lever-arm conformation as it steps along actin using single molecule techniques and a novel analytic tool I developed. From this we find that myoV mainly walks straight along actin, but can take steps around the long axis of actin. The frequency of these azimuthal steps depends on the length of the myoV lever-arm

Muscle activation mapping of skeletal hand motion: an evolutionary approach.

Creating controlled dynamic character animation consists of mathe- matical modelling of muscles and solving the activation dynamics that form the key to coordination. But biomechanical simulation and control is com- putationally expensive involving complex di erential equations and is not suitable for real-time platforms like games. Performing such computations at every time-step reduces frame rate. Modern games use generic soft- ware packages called physics engines to perform a wide variety of in-game physical e ects. The physics engines are optimized for gaming platforms. Therefore, a physics engine compatible model of anatomical muscles and an alternative control architecture is essential to create biomechanical charac- ters in games. This thesis presents a system that generates muscle activations from captured motion by borrowing principles from biomechanics and neural con- trol. A generic physics engine compliant muscle model primitive is also de- veloped. The muscle model primitive forms the motion actuator and is an integral part of the physical model used in the simulation. This thesis investigates a stochastic solution to create a controller that mimics the neural control system employed in the human body. The control system uses evolutionary neural networks that evolve its weights using genetic algorithms. Examples and guidance often act as templates in muscle training during all stages of human life. Similarly, the neural con- troller attempts to learn muscle coordination through input motion samples. The thesis also explores the objective functions developed that aids in the genetic evolution of the neural network. Character interaction with the game world is still a pre-animated behaviour in most current games. Physically-based procedural hand ani- mation is a step towards autonomous interaction of game characters with the game world. The neural controller and the muscle primitive developed are used to animate a dynamic model of a human hand within a real-time physics engine environment