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Bella Finkel

Publications and source records attributed to Bella Finkel.

5 recordsLinked to original sources

The Euclidean distance degree of one-parameter anchored multiview varieties

Multiview varieties are mathematical models for the set of image feature correspondences that can be produced by a given camera arrangement. They possess an invariant known as their Euclidean distance (ED) degree, which measures the algebraic complexity of determining the 3D features that minimize the reprojection error when computing the scene structure by triangulation. In this article, we prove a formula for the ED degree of curves parameterized by rational functions with mild genericity assumptions. We apply our results to resolve conjectures on one-dimensional line multiview varieties from computer vision proposed by Duff and Rydell.

math.AG

Graphical Scattering Equations

The CHY scattering equations on the moduli space $M_{0,n}$ play a prominent role at the interface of particle physics and algebraic statistics. We study the scattering correspondence when the Mandelstam invariants are restricted to a fixed graph on $n$ vertices.

math.CO

Assessing a Template-Based Approach for Core-Collapse Supernova Gravitational-Wave Detection

Gravitational waves from core-collapse supernovae are a promising yet challenging target for detection due to the stochastic and complex nature of these signals. Conventional detection methods for core-collapse supernovae rely on excess energy searches because matched filtering has been hindered by the lack of well-defined waveform templates. However, numerical simulations of core-collapse supernovae have improved our understanding of the gravitational wave signals they emit, which enables us, for the first time, to construct a set of templates that closely resemble predictions from numerical simulations. In this study, we investigate the possibility of detecting gravitational waves from core-collapse supernovae using template-based methods. We construct a theoretically-informed template bank and use it to recover core-collapse supernova signals injected into real LIGO-Virgo-KAGRA detector data. We consider the signals from three state-of-the-art numerical models, simulated with three different codes. We evaluate the detection efficiency of the template-filtering approach and how well the injected signal is reconstructed. For signals whose structure is well captured by our template bank, we recover ~90% of injections at a distance of 1 kpc and ~30-60% at 2 kpc. In contrast, a model whose signal differs significantly from the templates is recovered less efficiently. For many of the recovered events, the underlying signal characteristics can be reconstructed with an accuracy of ~10-20%. We discuss the strengths and limitations of this approach and identify areas for further improvements for template-based methods for supernova gravitational-wave detection. We also present the open-source Python package SynthGrav used to generate the template bank.

astro-ph.HE

Activation degree thresholds and expressiveness of polynomial neural networks

We study the expressive power of deep polynomial neural networks through the geometry of their neurovariety. We introduce the notion of the activation degree threshold of a network architecture to express when the dimension of the neurovariety achieves its theoretical maximum. We prove the existence of the activation degree threshold for all polynomial neural networks without width-one bottlenecks and demonstrate a universal upper bound that is quadratic in the width of largest size. In doing so, we prove the high activation degree conjecture of Kileel, Trager, and Bruna. Certain structured architectures have exceptional activation degree thresholds, making them especially expressive in the sense of their neurovariety dimension. In this direction, we prove that polynomial neural networks with equi-width architectures are maximally expressive by showing their activation degree threshold is one.

cs.LG

Stochastic Gravitational-Wave Background from Stellar Core-Collapse Events

We estimate the stochastic gravitational-wave background arising from all stellar core-collapse events in the universe based on the gravitational-wave signal predictions of recent numerical simulations. We focus on waveforms from slowly or non-rotating stars and include rapidly rotating, highly massive progenitors as extreme case limits. Our most realistic estimates are more than one hundred times below the sensitivity of third-generation terrestrial gravitational-wave detectors and likely weaker than cosmological contributions to the stochastic gravitational-wave background.

gr-qc