Research
Research
Research
Research
2,619+ open-access research outputs.
Submersions with definite folds are submersions on manifolds with boundary whose restrictions to the boundary are definite fold maps. In this paper, we study the properties from the viewpoint of diffe…
In this paper, we study the moduli space of Higgs pairs, which can be considered as a generalization of holomorphic pairs. Higgs pairs are an example of quiver bundles. We introduce the notion of $\ta…
This paper presents a high-order accurate Continuous Galerkin Finite Element Method (CGFEM) for solving the initial boundary value problems governed by the Incompressible Navier-Stokes (INS) equations…
We derive a topological decoupling of the equations of modified nodal analysis (MNA) to a semi-explicit index one differential-algebraic equation. The decoupling explicitly allows for controlled sourc…
This thesis generalizes the study of $C\cap(C + \alpha)$ where $C$ is the middle third Cantor set to self-affine sets in $\mathbb{R}^{n}$. We present sufficient and necessary conditions for when the t…
Low-rank matrix recovery can be solved to statistical optimality by convex matrix optimization under the classical assumption of restricted isometry property (RIP). However, for large problems, the co…
Linek's 1989 problem asks whether the numbers of independent sets of trees avoid infinitely many positive integers. We show that the set of natural numbers realized as the number of independent sets o…
We show that the category of (right-)preordered groups is a quasivariety of universal algebras by giving explicit axioms. We then look at lattices of effective equivalence relations, which turn out to…
In this paper, we consider the design of Model Predictive Control (MPC) algorithms based on Mamba neural networks. Mamba is a neural network architecture capable of sub-quadratic computational scaling…
Monotone variational inequalities (VIs) provide a unifying framework for convex minimization, equilibrium computation, and convex-concave saddle-point problems. Extragradient-type methods are among th…
We consider polynomial Bergman kernels with respect to exponentially varying weights $e^{-n \mathscr Q(z)}$ depending on a potential $\mathscr Q:\mathbb C^d\to\mathbb R$. We use these kernels to const…
Lasso problems arise in many areas, including signal processing, machine learning, and control, and are closely connected to sparse coding mechanisms observed in neuroscience. A continuous-time ordina…
We develop a novel framework for sparse multiscale kernel approximation of large scattered data problems based on a samplet representation. Samplets form a multiresolution analysis of localized discre…
We give a structure result on the set of locally constant stability conditions, $\operatorname{Stab}(\mathcal{D}/R)$, defined by Halpern-Leistner-Robotis showing that it has the structure of a complex…
In this paper, we study the tracking controllability of a 1D parabolic type equation. Notably, with controls acting on the boundary, we seek to approximately control the solution of the equation on sp…
We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the …
We consider the algebra of square matrices of bounded non-commutative (NC) functions over NC operator unit balls (unit balls corresponding to finite-dimensional operator spaces) and characterize cycli…
The secondary zeta function is defined as a generalized zeta series over the imaginary parts of non-trivial zeros assuming (RH). This function admits Laurent series expansion at the double pole at $s=…
In this paper, we study Clairaut generic Riemannian map from a nearly Kahler manifold to a Riemannian manifold. Further, we obtain a condition for a Clairaut generic Riemannian map to be a totally geo…
The Highly Adaptive Lasso (HAL) delivers unprecedented guarantees in nonparametric minimum loss estimation under minimal smoothness assumptions, such as dimension-free minimax optimal rates. However, …
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