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- Borel equivalence relations (2)
- CGISS (2)
- Association test (1)
- Borel reducibility (1)
- CDR3 (1)
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- Clinical phenotypes (1)
- Curl-free (1)
- Electrical/resistivity (1)
- Ground-penetrating radar (1)
- Implicit surface reconstruction (1)
- Jump operators (1)
- Meshfree (1)
- Multiparameter (1)
- Multiphysics (1)
- Near surface (1)
- Partition of unity (1)
- Partition relations (1)
- Point clouds (1)
- Radial basis function (1)
- Scattered linear orders (1)
- T cell receptors (1)
- TCR homology (1)
- TCR repertoire (1)
Articles 1 - 5 of 5
Full-Text Articles in Mathematics
New Jump Operators On Equivalence Relations, John D. Clemens, Samuel Coskey
New Jump Operators On Equivalence Relations, John D. Clemens, Samuel Coskey
Mathematics Faculty Publications and Presentations
We introduce a new family of jump operators on Borel equivalence relations; specifically, for each countable group Γ we introduce the Γ-jump. We study the elementary properties of the Γ-jumps and compare them with other previously studied jump operators. One of our main results is to establish that for many groups Γ, the Γ-jump is proper in the sense that for any Borel equivalence relation E the Γ-jump of E is strictly higher than E in the Borel reducibility hierarchy. On the other hand, there are examples of groups Γ for which the Γ-jump is not proper. To establish properness, …
Implicit Surface Reconstruction With A Curl-Free Radial Basis Function Partition Of Unity Method, Kathryn P. Drake, Edward J. Fuselier, Grady B. Wright
Implicit Surface Reconstruction With A Curl-Free Radial Basis Function Partition Of Unity Method, Kathryn P. Drake, Edward J. Fuselier, Grady B. Wright
Mathematics Faculty Publications and Presentations
Surface reconstruction from a set of scattered points, or a point cloud, has many applications ranging from computer graphics to remote sensing. We present a new method for this task that produces an implicit surface (zero-level set) approximation for an oriented point cloud using only information about (approximate) normals to the surface. The technique exploits the fundamental result from vector calculus that the normals to an implicit surface are curl-free. By using curl-free radial basis function (RBF) interpolation of the normals, we can extract a potential for the vector field whose zero-level surface approximates the point cloud. We use curl-free …
Tcr-L: An Analysis Tool For Evaluating The Association Between The T-Cell Receptor Repertoire And Clinical Phenotypes, Meiling Liu, Juna Goo, Yang Liu, Wei Sun, Michael C. Wu, Li Hsu, Qianchuan He
Tcr-L: An Analysis Tool For Evaluating The Association Between The T-Cell Receptor Repertoire And Clinical Phenotypes, Meiling Liu, Juna Goo, Yang Liu, Wei Sun, Michael C. Wu, Li Hsu, Qianchuan He
Mathematics Faculty Publications and Presentations
Background: T cell receptors (TCRs) play critical roles in adaptive immune responses, and recent advances in genome technology have made it possible to examine the T cell receptor (TCR) repertoire at the individual sequence level. The analysis of the TCR repertoire with respect to clinical phenotypes can yield novel insights into the etiology and progression of immune-mediated diseases. However, methods for association analysis of the TCR repertoire have not been well developed.
Methods: We introduce an analysis tool, TCR-L, for evaluating the association between the TCR repertoire and disease outcomes. Our approach is developed under a mixed effect modeling, where …
Relative Primeness And Borel Partition Properties For Equivalence Relations, John D. Clemens
Relative Primeness And Borel Partition Properties For Equivalence Relations, John D. Clemens
Mathematics Faculty Publications and Presentations
We introduce a notion of relative primeness for equivalence relations, strengthening the notion of non-reducibility, and show for many standard benchmark equivalence relations that non-reducibility may be strengthened to relative primeness. We introduce several analogues of cardinal properties for Borel equivalence relations, including the notion of a prime equivalence relation and Borel partition properties on quotient spaces. In particular, we introduce a notion of Borel weak compactness, and characterize partition properties for the equivalence relations ��2 and ��1. We also discuss dichotomies related to primeness, and see that many natural questions related to Borel reducibility of equivalence …
Joint Full-Waveform Ground-Penetrating Radar And Electrical Resistivity Inversion Applied To Field Data Acquired On The Surface, Diego Domenzain, John Bradford, Jodi Mead
Joint Full-Waveform Ground-Penetrating Radar And Electrical Resistivity Inversion Applied To Field Data Acquired On The Surface, Diego Domenzain, John Bradford, Jodi Mead
Mathematics Faculty Publications and Presentations
We exploit the different but complementary data sensitivities of ground-penetrating radar (GPR) and electrical resistivity (ER) by applying a multiphysics, multiparameter, simultaneous 2.5D joint inversion without invoking petrophysical relationships. Our method joins full-waveform inversion (FWI) GPR with adjoint derived ER sensitivities on the same computational domain. We incorporate a stable source estimation routine into the FWI-GPR. We apply our method in a controlled alluvial aquifer using only surface-acquired data. The site exhibits a shallow groundwater boundary and unconsolidated heterogeneous alluvial deposits. We compare our recovered parameters to individual FWI-GPR and ER results, and we compare them to log measurements of …