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In the context of phase-space quantization, matrix elements and observables result from integration of c-number functions over phase space, with Wigner functions serving as the quasi-probability measure. The complete sets of Wigner…
Analytic distribution functions (DFs) for the Galactic disc are discussed. The DFs depend on action variables and their predictions for observable quantities are explored under the assumption that the motion perpendicular to the Galactic…
We use the Bradlow parameter expansion to construct the metric tensor in the space of solutions of the Bogomolny equations for the Abelian Higgs model on a two-dimensional torus. Using this metric we study the dynamics and scattering of…
We develop a method for constructing tolerance bounds for functional data with random warping variability. In particular, we define a generative, probabilistic model for the amplitude and phase components of such observations, which…
We investigate the influence of the star formation rate on the Tully-Fisher relation. We find that a simple model which combines the empirically-determined star-formation rate with the expected properties of galaxy halos provides a…
We present a method for fitting orbit-superposition models to the kinematics of discrete stellar systems when the available stellar sample has been filtered by a known selection function. The fitting method can be applied to any model in…
We propose Functional Flow Matching (FFM), a function-space generative model that generalizes the recently-introduced Flow Matching model to operate in infinite-dimensional spaces. Our approach works by first defining a path of probability…
The orbit distribution of young stars in the Galactic disk is highly structured, from well-defined clusters to streams of stars that may be widely dispersed across the sky, but are compact in orbital action-angle space. The age distribution…
Schulz (2017) galactic scaling rules, which include baryonic Tully-Fisher relation, have been surveyed in this work within the context of a modified dynamical model. These scaling relations are derived by employing the virial theorem and…
A particle method for reproducing the phase space of collisionless stellar systems is described. The key idea originates in Liouville's theorem which states that the distribution function (DF) at time t can be derived from tracing necessary…
Using the radiative transfer code Torus, we produce spectral-line cubes of the predicted HI profile from global SPH simulations of spiral galaxies. Torus grids the SPH galaxy using Adaptive Mesh Refinement, then applies a ray-tracing method…
In recent years, generative models have shown remarkable capabilities across diverse fields, including images, videos, language, and decision-making. By applying powerful generative models such as flow-based models to reinforcement…
Understanding $\textit{galaxy bias}$ -- that is the statistical relation between matter and galaxies -- is of key importance for extracting cosmological information from galaxy surveys. While the bias function $f$ -- that is the probability…
We study in detail the structure of phase space in the neighborhood of stable periodic orbits in a rotating 3D potential of galactic type. We have used the color and rotation method to investigate the properties of the invariant tori in the…
We adapt the Kolmogorov's normalization algorithm (which is the key element of the original proof scheme of the KAM theorem) to the construction of a suitable normal form related to an invariant elliptic torus. As a byproduct, our procedure…
The classical representation of Hamiltonian systems in terms of action-angle variables are defined for simply connected domains such as an interior of a homoclinic orbit. On this basis methods of (local) perturbations leading, in…
Understanding how galaxies obtain baryons, their stars and gas, over cosmic time is traditionally approached in two different ways - theoretically and observationally. In general, observational approaches to galaxy formation include…
(abridged) The large-scale distribution of galaxies is generally analyzed using the two-point correlation function. However, this statistic does not capture the topology of the distribution, and it is necessary to resort to higher order…
Traditional galaxy-galaxy lensing is a well-established method of probing the statistical properties of the Universe's matter and galaxy distribution. However, this measure does not carry all the statistical information, provided the matter…
Estimating stellar masses for billions of galaxies in upcoming surveys requires methods that are both accurate and computationally efficient. We present a new approach using symbolic regression trained on a simulation to derive simple,…