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Context: The modelling of stationary galactic stellar populations can be performed using distribution functions. Aims: This paper aims to write explicit integrals of motion and distribution functions. Methods: We propose an analytic…
After deriving the classical Ward identity for the variation of the action under a change of the modulus of the torus we map the problem of the sphere with four sources to the torus. We extend the method previously developed for computing…
We present a method for recovering the distribution functions of edge-on thin axisymmetric disks directly from their observable kinematic properties. The most generally observable properties of such a stellar system are the line-of-sight…
We treat here general relativistically the issue of galaxy formation, which is a major problem in cosmology. While the current models use a top-hat collapse model, coupled with Newtonian virialization technique to balance the…
A topological computation method, called the MGSTD method, is applied to time-series data obtained from meteorological measurement. The method gives decomposition of the dynamics into invariant sets and gradient-like transitions between…
Statistical inference on large-dimensional tensor data has been extensively studied in the literature and widely used in economics, biology, machine learning, and other fields, but how to generate a structured tensor with a target…
The temporal lag between actions and their long-term consequences makes credit assignment a challenge when learning goal-directed behaviors from data. Generative world models capture the distribution of future states an agent may visit,…
We study the correlation functions of local operators in unitary $\textrm{T}\bar{\textrm{T}}$-deformed field theories defined on a torus, using their formulation in terms of Jackiw-Teitelboim gravity. We focus on the two-point correlation…
The velocity distributions of stellar tracers in general exhibit weak non-Gaussianity encoding information on the orbital composition of a galaxy and the underlying potential. The standard solution for measuring non-Gaussianity involves…
We construct time-evolving gravitational potential models for a Milky Way-mass galaxy from the FIRE-2 suite of cosmological-baryonic simulations using basis function expansions. These models capture the angular variation with spherical…
We determine the spatial distribution function of galaxies from a wide range of samples in the 2MASS survey. The results agree very well with the form of the distribution predicted by the theory of cosmological gravitational many-body…
Generative modeling of spatio-temporal fields is crucial for a variety of applications, including stochastic weather generators and climate-model surrogates. However, many such fields exhibit complex dependence structures that vary across…
Orbital-free density functional theory as an extension of traditional Thomas-Fermi theory has attracted a lot of interest in the past decade because of developments in both more accurate kinetic energy functionals and highly efficient…
We introduce a new family of metrics, called functional metrics, on noncommutative tori and study their spectral geometry. We define a class of Laplace type operators for these metrics and study their spectral invariants obtained from the…
We develop an analytical formalism to determine the statistical properties of a system consisting of an ensemble of vortices with random position in plane interacting with a turbulent field. We calculate the generating functional by…
Variability in the light curves of spotted, rotating stars is often non-sinusoidal and quasi-periodic --- spots move on the stellar surface and have finite lifetimes, causing stellar flux variations to slowly shift in phase. A strictly…
We present a new iterative method for constructing equilibrium phase models of stellar systems. Importantly, this method can provide phase models with arbitrary mass distributions. The method is based on the following principle. Our task is…
Joint analyses of the large-scale distribution of galaxies, and their motions under the gravitational influence of this density field, allow powerful tests of the cosmological model, including measurement of the growth rate of cosmic…
Observations of the interstellar medium are key to deciphering the physical processes regulating star formation in galaxies. However, observational uncertainties and detection limits can bias the interpretation unless carefully modeled.…
Human activity encompasses a series of complex spatiotemporal processes that are difficult to model, but represents an essential component of human exposure assessment. A significant empirical data source like the American Time Use Survey…