Open Access. Powered by Scholars. Published by Universities.®
Physical Sciences and Mathematics Commons™
Open Access. Powered by Scholars. Published by Universities.®
- Keyword
-
- Advection-diffusion (1)
- BRC (1)
- CGISS (1)
- Context directed swap (1)
- Cosmic microwave background radiation (1)
-
- Determinants (1)
- Double Fourier sphere (1)
- Factorization into cycles (1)
- Fast spherical harmonic transform (1)
- HEALPix (1)
- High-order methods (1)
- Infinite game (1)
- Manifolds (1)
- Meager set (1)
- Non-uniform fast Fourier transform (1)
- Nowhere dense set (1)
- Permanents (1)
- Permutation sorting (1)
- Radial basis functions (1)
- Singular cardinal hypothesis (1)
- Strategic pile (1)
- Symmetric cactus rank (1)
- Symmetric rank (1)
- Syzygies (1)
- Transport (1)
- Waring rank (1)
- Winning strategy (1)
Articles 1 - 6 of 6
Full-Text Articles in Physical Sciences and Mathematics
A Fast And Accurate Algorithm For Spherical Harmonic Analysis On Healpix Grids With Applications To The Cosmic Microwave Background Radiation, Kathryn P. Drake, Grady B. Wright
A Fast And Accurate Algorithm For Spherical Harmonic Analysis On Healpix Grids With Applications To The Cosmic Microwave Background Radiation, Kathryn P. Drake, Grady B. Wright
Mathematics Faculty Publications and Presentations
The Hierarchical Equal Area isoLatitude Pixelation (HEALPix) scheme is used extensively in astrophysics for data collection and analysis on the sphere. The scheme was originally designed for studying the Cosmic Microwave Background (CMB) radiation, which represents the first light to travel during the early stages of the universe's development and gives the strongest evidence for the Big Bang theory to date. Refined analysis of the CMB angular power spectrum can lead to revolutionary developments in understanding the nature of dark matter and dark energy. In this paper, we present a new method for performing spherical harmonic analysis for HEALPix data, …
Meager Sets, Games And Singular Cardinals, Liljana Babinkostova, Marion Scheepers
Meager Sets, Games And Singular Cardinals, Liljana Babinkostova, Marion Scheepers
Mathematics Faculty Publications and Presentations
We show that a statement concerning the existence of winning strategies of limited memory in an infinite two-person topological game is equivalent to a weak version of the Singular Cardinals Hypothesis.
The Classification Of Countable Models Of Set Theory, John Clemens, Samuel Coskey, Samuel Dworetzky
The Classification Of Countable Models Of Set Theory, John Clemens, Samuel Coskey, Samuel Dworetzky
Mathematics Faculty Publications and Presentations
We study the complexity of the classification problem for countable models of set theory (ZFC). We prove that the classification of arbitrary countable models of ZFC is Borel complete, meaning that it is as complex as it can conceivably be. We then give partial results concerning the classification of countable well‐founded models of ZFC.
A Bound For The Waring Rank Of The Determinant Via Syzygies, Mats Boij, Zach Teitler
A Bound For The Waring Rank Of The Determinant Via Syzygies, Mats Boij, Zach Teitler
Mathematics Faculty Publications and Presentations
We show that the Waring rank of the 3 × 3 determinant, previously known to be between 14 and 18, is at least 15. We use syzygies of the apolar ideal, which have not been used in this way before. Additionally, we show that the symmetric cactus rank of the 3 × 3 permanent is at least 14.
Quantifying Cds Sortability Of Permutations By Strategic Pile Size, Marisa Gaetz, Bethany Flanagan, Marion Scheepers, Meghan Shanks
Quantifying Cds Sortability Of Permutations By Strategic Pile Size, Marisa Gaetz, Bethany Flanagan, Marion Scheepers, Meghan Shanks
Mathematics Faculty Publications and Presentations
The special purpose sorting operation, context directed swap (CDS), is an example of the block interchange sorting operation studied in prior work on permutation sorting. CDS has been postulated to model certain molecular sorting events that occur in the genome maintenance program of some species of ciliates. We investigate the mathematical structure of permutations not sortable by the CDS sorting operation. In particular, we present substantial progress towards quantifying permutations with a given strategic pile size, which can be understood as a measure of CDS non-sortability. Our main results include formulas for the number of permutations in Sn with …
A Robust Hyperviscosity Formulation For Stable Rbf-Fd Discretizations Of Advection-Diffusion-Reaction Equations On Manifolds, Varun Shankar, Grady B. Wright, Akil Narayan
A Robust Hyperviscosity Formulation For Stable Rbf-Fd Discretizations Of Advection-Diffusion-Reaction Equations On Manifolds, Varun Shankar, Grady B. Wright, Akil Narayan
Mathematics Faculty Publications and Presentations
We present a new hyperviscosity formulation for stabilizing radial basis function-finite difference (RBF-FD) discretizations of advection-diffusion-reaction equations on manifolds �� ⊂ ℝ3 of codimension 1. Our technique involves automatic addition of artificial hyperviscosity to damp out spurious modes in the differentiation matrices corresponding to surface gradients, in the process overcoming a technical limitation of a recently developed Euclidean formulation. Like the Euclidean formulation, the manifold formulation relies on von Neumann stability analysis performed on auxiliary differential operators that mimic the spurious solution growth induced by RBF-FD differentiation matrices. We demonstrate high-order convergence rates on problems involving surface advection and …