Latest Research
An efficient preconditioner for mixed-dimensional contact poromechanics based on the fixed stress splitting scheme
The robustness and efficiency of the simulation heavily depends on a preconditioner for the linear solver, which addresses the Jacobian matrices arising from Newton's method in fully implicit time-stepping schemes.
Numerical Analysis Numerical Analysis
Critical $(P_5,W_4)$-Free Graphs
A graph $G$ is $k$-vertex-critical if $\chi(G) = k$ but $\chi(G-v)<k$ for all $v \in V(G)$.
Combinatorics
Computational Graph Decompositions I: Oriented Berge-Fulkerson Conjecture
Similarly to the case of oriented cycle double cover, we can always construct an orientable surface (possibly with boundary) from an o6c4c solution.
Combinatorics
Direct Sampling of Confined Polygons in Linear Time
We present an algorithm for sampling tightly confined random equilateral closed polygons in three-space which has runtime linear in the number of edges.
Geometric Topology Statistical Mechanics Computational Geometry Symplectic Geometry 57K10, 53A04, 53D30, 82D60, 05A05
Totally Concave Regression
However, most existing shape-constrained nonparametric regression methods, except additive models, impose too few restrictions on the regression functions.
Statistics Theory Methodology Statistics Theory 62G08
A Constructive Approach to Zauner's Conjecture via the Stark Conjectures
Specifically, we give an explicit expression for an object that we call a ghost SIC, which is constructed from the real multiplication values of a special function and which is Galois conjugate to a SIC.
Number Theory Combinatorics Metric Geometry Quantum Physics
Multiple testing in multi-stream sequential change detection
We point out that any algorithm with finite average run length (ARL) must have a trivial worst-case false detection rate (FDR), family-wise error rate (FWER), and per-family error rate (PFER); thus, any attempt to control these Type I error metrics is fundamentally in conflict with the desire for a finite ARL (which is typically necessary in order to have a small detection delay).
Statistics Theory Signal Processing Methodology Statistics Theory
Analysis of mean-field models arising from self-attention dynamics in transformer architectures with layer normalization
timroith/transformerdynamics
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The latter are related to stationary points of the interaction energy in the Wasserstein geometry, and we further discuss energy minimizers and maximizers in different parameter settings.
Analysis of PDEs 68Q32, 49Q20, 43A35
On the numerical evaluation of wall shear stress using the finite element method
This work aims to compare WSS results obtained from two different finite element discretizations, quantify the differences between continuous and discontinuous stresses, and introduce a novel method for WSS evaluation through the formulation of a boundary-flux problem.
Numerical Analysis Numerical Analysis
A uniform bound on the smallest surjective prime of an elliptic curve
Let $E/\mathbb{Q}$ be an elliptic curve without complex multiplication.
Number Theory 11G05 (Primary) 11F80 (Secondary)
