Related papers: Quantifying Symmetry: Transformation Information f…
We consider the geometrization of quantum mechanics. We then focus on the pull-back of the Fubini-Study metric tensor field from the projective Hibert space to the orbits of the local unitary groups. An inner product on these tensor fields…
Photometric classification of Type Ia supernovae is essential for modern time-domain surveys, where spectroscopic confirmation is not always feasible for the full transient sample. In this work, we investigate a compact and physically…
This paper develops information geometric representations for nonlinear filters in continuous time. The posterior distribution associated with an abstract nonlinear filtering problem is shown to satisfy a stochastic differential equation on…
High-dimensional astronomical data cubes provide a wealth of spectral and structural information that can be used to study astrophysical and chemical processes. The complexity and sheer size of these datasets pose significant challenges in…
We present bolometric and broadband light curves and spectra for a suite of core-collapse supernova models exploded self-consistently in spherical symmetry within the PUSH framework. We analyze broad trends in these light curves and…
Deep nonlinear models pose a challenge for fitting parameters due to lack of knowledge of the hidden layer and the potentially non-affine relation of the initial and observed layers. In the present work we investigate the use of information…
Symmetries impose structure on the Hilbert space of a quantum mechanical model. The mathematical units of this structure are the irreducible representations of symmetry groups and I consider how they function as conceptual units of…
This essay constitutes a review of the information geometric approach to renormalization developed in the recent works of B\'eny and Osborne as well as a detailed work-through of some of their contents. A noncommutative generalization of…
Emission-line regions are key to understanding the properties of galaxies, as they trace the exchange of matter and energy between stars and the interstellar medium (ISM). In nearby galaxies, individual nebulae can be identified as HII…
We estimate systematic errors due to K-corrections in standard photometric analyses of high redshift Type Ia supernovae. Errors due to K-correction occur when the spectral template model underlying the lightcurve fitter poorly represents…
Information theoretic measures (e.g. the Kullback Liebler divergence and Shannon mutual information) have been used for exploring possibly nonlinear multivariate dependencies in high dimension. If these dependencies are assumed to follow a…
Doppler reflectometry spatial and wavenumber resolution is analyzed within the framework of the linear Born approximation in slab plasma model. Explicit expression for its signal backscattering spectrum is obtained in terms of wavenumber…
We generalize the superposition principle for time-symmetric initial data of black hole spacetimes to (anti-)de Sitter cosmologies in terms of an eigenvalue problem $\Delta_g\phi={1/8}(R_g-2\Lambda)\phi$ for a conformal scale $\phi$ applied…
We introduce Locally Linear Embedding (LLE) to the astronomical community as a new classification technique, using SDSS spectra as an example data set. LLE is a nonlinear dimensionality reduction technique which has been studied in the…
Symmetry detection and discrimination are of fundamental meaning in science, technology, and engineering. This paper introduces reflection invariants and defines the directional moment to detect symmetry for shape analysis and object…
There are now hundreds of publicly available supernova spectral time series. Radiative transfer modeling of this data gives insights into the physical properties of these explosions such as the composition, the density structure, or the…
We investigate the consistency of visual morphological classifications of galaxies by comparing classifications for 831 galaxies from six independent observers. The galaxies were classified on laser print copy images or on computer screen…
This manuscript details and extends the SIMBa toolbox (System Identification Methods leveraging Backpropagation) presented in previous work, which uses well-established Machine Learning tools for discrete-time linear multi-step-ahead…
We review a geometric approach to classification and examination of quantum correlations in composite systems. Since quantum information tasks are usually achieved by manipulating spin and alike systems or, in general, systems with a finite…
Topology is a central notion in the classification of band insulators and characterization of entangled many-body quantum states. In some cases, it manifests as quantized observables such as quantum Hall conductance. However, being…