arXiv subjects

Nitya Gadhiwala

Publications and source records attributed to Nitya Gadhiwala.

5 recordsLinked to original sources

arXiv2026

Unbalanced Minimal Matchings for Measurable Scale Invariant Costs on $\mathbb{R}^d$

Given red and blue points drawn from Poisson point processes of equal intensities, we match them by locally minimizing a cost function. In our paper, we identify all possible measurable cost functions on $\mathbb{R}^d$ such that the resulting matching is scale invariant. Our cost functions can be asymmetrical, which we refer to as unbalanced cost functions. The investigation is motivated by arXiv:2012.07129 where the authors consider scale invariant cost functions with added regularity assumptions. Furthermore, we discuss how different the unbalanced matchings are compared to these more regular cost functions for points on $\mathbb{R}$.

math.PR↗

arXiv2025

The Triangle Friendship Paradox

We consider the generalised friendship paradox, focussing on the number of triangles at a vertex as the relevant attribute. We show that, contrary to the setting where the attribute is the number of edges at a vertex or the number of wedges at a vertex, the average friendship-bias of the number of triangles at a vertex is not always non-negative. We identify classes of finite deterministic graphs for which the bias is non-negative, and provide examples of finite deterministic graphs for which it is not. For certain classes of sparse and dense random graphs, we compute the scaling of the bias in the limit as the number of vertices tends to infinity.

math.PR↗

arXiv2024

Trajectory inference for a branching SDE model of cell differentiation

A core challenge for modern biology is how to infer the trajectories of individual cells from population-level time courses of high-dimensional gene expression data. Birth and death of cells present a particular difficulty: existing trajectory inference methods cannot distinguish variability in net proliferation from cell differentiation dynamics, and hence require accurate prior knowledge of the proliferation rate. Building on Global Waddington-OT (gWOT), which performs trajectory inference with rigorous theoretical guarantees when birth and death can be neglected, we show how to use lineage trees available with recently developed CRISPR-based measurement technologies to disentangle proliferation and differentiation. In particular, when there is neither death nor subsampling of cells, we show that we extend gWOT to the case with proliferation with similar theoretical guarantees and computational cost, without requiring any prior information. In the case of death and/or subsampling, our method introduces a bias, that we describe explicitly and argue to be inherent to these lineage tracing data. We demonstrate in both cases the ability of this method to reliably reconstruct the landscape of a branching SDE from time-courses of simulated datasets with lineage tracing, outperforming even a benchmark using the experimentally unavailable true branching rates.

q-bio.QM↗

arXiv2023

Controlled Martingale Problems And Their Markov Mimics

In this article we prove under suitable assumptions that the marginals of any solution to a relaxed controlled martingale problem on a Polish space $E$ can be mimicked by a Markovian solution of a Markov-relaxed controlled martingale problem. We also show how such `Markov mimics' can be obtained by relative entropy minimisation. We provide many examples where the above results can be applied.

math.PR↗

arXiv2022

Elliptic Harnack Inequality for ${\mathbb{Z}}^d$

We prove the scale invariant Elliptic Harnack Inequality (EHI) for non-negative harmonic functions on ${\mathbb{Z}}^d$. The purpose of this note is to provide a simplified self-contained probabilistic proof of EHI in ${\mathbb{Z}}^d$ that is accessible at the undergraduate level. We use the Local Central Limit Theorem for simple symmetric random walks on ${\mathbb{Z}}^d$ to establish Gaussian bounds for the $n$-step probability function. The uniform Green inequality and the classical Balayage formula then imply the EHI.

math.PR↗