arXiv subjects

Himani Sharma

Publications and source records attributed to Himani Sharma.

4 recordsLinked to original sources

arXiv2025

Conformational Rank Conditioned Committees for Machine Learning-Assisted Directed Evolution

Machine Learning-assisted directed evolution (MLDE) is a powerful tool for efficiently navigating antibody fitness landscapes. Many structure-aware MLDE pipelines rely on a single conformation or a single committee across all conformations, limiting their ability to separate conformational uncertainty from epistemic uncertainty. Here, we introduce a rank -conditioned committee (RCC) framework that leverages ranked conformations to assign a deep neural network committee per rank. This design enables a principled separation between epistemic uncertainty and conformational uncertainty. We validate our RCC-MLDE approach on SARS-CoV-2 antibody docking, demonstrating significant improvements over baseline strategies. Our results offer a scalable route for therapeutic antibody discovery while directly addressing the challenge of modeling conformational uncertainty.

cs.LG↗

arXiv2024

Vertical Maximal Functions on Manifolds with Ends

We consider the setting of manifolds with ends which are obtained by compact perturbation (gluing) of ends of the form $\mathbb{R}^{n_i}\times \mathcal{M}_i$. We investigate family of vertical resolvent $\{\sqrt{t}\nabla(1+tΔ)^{-m}\}_{t>0}$ where $m\geq1$. We show that the family is uniformly continuous on all $L^p$ for $1\le p \le \min_{i}n_i$. Interestingly this is a closed-end condition in the considered setting. We prove that the corresponding Maximal function is bounded in the same range except that it is only weak-type $(1,1)$ for $p=1$. The Fefferman-Stein vector-valued maximal function is again of weak-type $(1,1)$ but bounded if and only if $1<p<\min_{i}n_i$, and not at $p=\min_{i}n_i$.

math.AP↗

arXiv2022

Spectral multiplier theorems for abstract harmonic oscillators on UMD lattices

We consider operators acting on a UMD Banach lattice $X$ that have the same algebraic structure as the position and momentum operators associated with the harmonic oscillator $-\frac12Δ+ \frac12|x|^{2} $ acting on $L^{2}(\mathbb{R}^{d})$. More precisely, we consider abstract harmonic oscillators of the form $\frac12 \sum _{j=1} ^{d}(A_{j}^{2}+B_{j}^{2})$ for tuples of operators $A=(A_{j})_{j=1} ^{d}$ and $B=(B_{k})_{k=1} ^{d}$, where $iA_j$ and $iB_k$ are assumed to generate $C_{0}$ groups and to satisfy the canonical commutator relations. We prove functional calculus results for these abstract harmonic oscillators that match classical Hörmander spectral multiplier estimates for the harmonic oscillator $-\frac12Δ+ \frac12|x|^{2}$ on $L^{p}(\mathbb{R}^{d})$. This covers situations where the underlying metric measure space is not doubling and the use of function spaces that are not particularly well suited to extrapolation arguments. For instance, as an application we treat the harmonic oscillator on mixed norm Bargmann-Fock spaces. Our approach is based on a transference principle for the Schrödinger representation of the Heisenberg group that allows us to reduce the problem to the study of the twisted Laplacian on the Bochner spaces $L^{2}(\mathbb{R}^{2d};X)$. This can be seen as a generalisation of the Stone-von Neumann theorem to UMD lattices $X$ that are not Hilbert spaces.

math.FA↗

arXiv2021

Bounds on the Phillips calculus of abstract first order differential operators

For an operator generating a group on $L^p$ spaces transference results give bounds on the Phillips functional calculus also known as spectral multiplier estimates. In this paper we consider specific group generators which are abstraction of first order differential operators and prove similar spectral multiplier estimates assuming only that the group is bounded on $L^2$ rather than $L^p$. We also prove an R-bounded Hörmander calculus result by assuming an abstract Sobolev embedding property and show that the square of a perturbed Hodge-Dirac operator has such calculus.

math.FA↗