Mapping of Cosmic Dark Matter with Gravitational Lensing Analyses and Applications of Deep Neural Networks
An array of large-scale astronomical observations has firmly confirmed the existence of invisible mass components in the universe. Such invisible materials are referred to as cosmic dark matter. Although the observational studies have indicated that dark matter can exist anywhere from the past to the present, its existence cannot be explained by the Standard Model of particle physics. Mapping of spatial distribution in dark matter density plays a critical role in identifying the nature of cosmic dark matter. Gravitational lensing analyses are among the most powerful approaches to provide a large-scale map of cosmic dark matter from observations. General relativity predicts that intervening cosmic matter distribution causes a coherent distortion of images of background galaxies at large separation. This interesting phenomenon is known as the gravitational lensing effect. Modern galaxy imaging surveys aim to infer the dark matter density in dierent line-of-sight directions through precise measurement of gravitational lensing effects of billions of galaxies in a wide sky coverage. In this article, we begin with a brief summary of modern cosmology and summarize the basics of gravitational lensing analyses. We then describe recent progress in applications of deep learning to the gravitational-lensing-based mapping of dark matter, including our latest analysis.
Key words: Cosmic dark matter, gravitational lensing, deep learning, generative models, Generative Adversarial Networks.
Statistical Analysis of Time-series Data Using the Projection Operator Method and Its Application
The projection operator method is a mathematical method developed in nonequilibrium statistical physics, where the time evolution of the response variable is split into correlated and uncorrelated terms for the explanatory variables and are described as a generalized Langevin equation. The projection operator method is practically applicable for the statistical analysis of time-series data. In the present study, we revisited its formulation and extended it to arbitrary explanatory and response variables in continuous and discrete-time systems. We also compared the method with a structural vector auto-regressive (SVAR) model as a time-series analysis having similar structures. The projection operator method has a wider application range than the SVAR model and can extract equivalent correlations with the SVAR model when auto-regressive explanatory and response variables are employed. As an application example, we applied the projection operator method to plasma turbulence phenomena and explained zonal-flow generation/maintenance processes in a generalized Langevin description. These examples demonstrate the validity of the projection operator method in data analysis for physics interpretation and modeling for reproducing statistical time-series data. We provide the developed method in this study as an open-source Python code, allowing readers to use it by calling a simple function.
Key words: Projection operator method, continuous/discrete-time system, turbulence, time series analysis.
Development of Data Assimilation System for Fusion Plasma Control
We developed a data assimilation system, named ASTI, to analyze and control fusion plasma behavior. Although the goal of ASTI is to control fusion plasmas with high accuracy, existing data assimilation frameworks do not include control processes. We therefore developed a data assimilation framework that integrates system model updates and optimal control-input estimation. The proposed framework provides model predictive control even when the system model has large uncertainties. In this article, we provide an overview of ASTI and show the proposed data assimilation framework. We demonstrate the effectiveness of the framework through a numerical experiment to control virtual fusion plasma.
Key words: Data assimilation, model predictive control, fusion plasma.
Mathematical Foundation of Detrending-operation-based Fractal Scaling Analysis
To characterize long-range correlation, 1/fβ fluctuation, and self-affine fractal properties embedded in nonstationary time series, detrended fluctuation analysis (DFA) has become widely used in the fields of physics and biomedical time series analysis. In DFA, a detrending operation with piecewise regression is included in the scaling analysis procedure. Such detrending operations have the advantages of avoiding a false estimate of the scaling exponent induced by nonstationary trend components and expanding the range of the detectable scaling exponent. DFA has recently been implemented as a package in R and Python and is often used instead of conventional power spectral analysis. In this paper, we provide the mathematical basis for the detrending-operation-based scaling analysis methods, focusing on DFA and its variant, the detrending moving average (DMA) algorithm.
Key words: Long-range correlation, fractal, long memory, 1/f fluctuation, time series analysis.
Recent Studies of Human Resting-state Brain Activity Using a Public Open Database
The human brain exhibits resting brain activity, defined as spontaneous activity in the absence of volitional movements or external sensory inputs. In recent years, the neuroscience community has been constructing large-scale brain activity databases, such as a database of the resting brain activity of more than 1,000 participants. These public databases are beginning to be used not only by neuroscientists but also by experts in mathematical statistics. Such collaborations are revealing new aspects of resting brain activity. In this paper, we introduce recent studies focusing on the spatiotemporal dynamics of resting brain activity. Traditionally, in psychology and neuroscience, resting brain activity has been regarded as a transition between multiple states. However, detailed statistical investigations using public databases have revealed that this assumption may be incorrect. Public databases will promote this type of collaboration between neuroscientists and statisticians and are therefore likely to play an important role across the field of neuroscience.
Key words: Neuroscience, fMRI (functional magnetic resonance imaging), spontaneous activity, public database, time-series modeling, non-stationarity.