10 papers
Exact ReLU realization of affine one-dimensional refinement iterates via residual memory and offset frames
Boldsaikhan Bolorkhuu, Tsogtgerel Gantumur
We study vector-valued affine refinement operators of the form [ (Wγ)(t)=\sum_{j\in\mathbb{Z}} A_jγ(Mt-j)+B(t), ] with finitely supported matrix mask and compactly supported cont…
Neural network realization of binary refinement iterates via a two-chart atlas selector
Tsogtgerel Gantumur
Refinement operators generate many functions used in wavelet constructions, subdivision schemes, and geometric modeling. Their finite iterates can develop rapidly increasing number…
Projectional continuous data assimilation on the torus: Resonant and kernel-free regimes
Tsogtgerel Gantumur
We study continuous data assimilation for the two-dimensional incompressible Navier-Stokes equations on the periodic torus using a single signed scalar velocity projection in a pre…
Conditional Euclidean-Hamiltonian reductions for sign-problem toy models
Tsogtgerel Gantumur
Euclidean Monte Carlo methods are effective when the path-integral weight is real and nonnegative, but finite-density fermion systems often produce sign-changing or complex scalar…
Rotationally invariant dynamical lattice regulators for Euclidean quantum field theories
Tsogtgerel Gantumur
We introduce a dynamical lattice regulator for Euclidean quantum field theories on a fixed hypercubic graph , in which the embedding is…
Exact ReLU realization of tensor-product refinement iterates
Tsogtgerel Gantumur
We study scalar dyadic refinement operators on R^2 of the form (Vf)(x,y) = sum_{(j,k) in Z^2} c_{j,k} f(2x-j, 2y-k), where only finitely many mask coefficients c_{j,k} are nonzero.…