arXiv subjects

Ilya Grigoriev

Publications and source records attributed to Ilya Grigoriev.

4 recordsLinked to original sources

arXiv2024

Deep Joint Denoising and Detection for Enhanced Intracellular Particle Analysis

Reliable analysis of intracellular dynamic processes in time-lapse fluorescence microscopy images requires complete and accurate tracking of all small particles in all time frames of the image sequences. A fundamental first step towards this goal is particle detection. Given the small size of the particles, their detection is greatly affected by image noise. Recent studies have shown that applying image denoising as a preprocessing step indeed improves particle detection and their subsequent tracking. Deep learning based particle detection methods have shown superior results compared to traditional detection methods. However, they do not explicitly aim to remove noise from the images to facilitate detection. Thus we hypothesize that their performance could be further improved. In this paper, we propose a new deep neural network, called DENODET (denoising-detection network), which performs image denoising and particle detection simultaneously. We show that integrative denoising and detection yields more accurate detection results. Our method achieves superior results compared to state-of-the-art particle detection methods on the particle tracking challenge dataset and our own real fluorescence microscopy image data.

eess.IV↗

arXiv2016

Relations among characteristic classes of manifold bundles

We study relations among characteristic classes of smooth manifold bundles with highly-connected fibers. For bundles with fiber the connected sum of $g$ copies of a product of spheres $S^d \times S^d$ and an odd $d$, we find numerous algebraic relations among the so-called "generalized Miller-Morita-Mumford classes". For all $g > 1$, we show that these infinitely many classes are algebraically generated by a finite subset. Our results contrast with the fact that there are no algebraic relations among these classes in a range of cohomological degrees that grows linearly with $g$, according to recent homological stability results. In the case of surface bundles ($d=1$), our approach recovers some previously known results about the structure of the classical "tautological ring", as introduced by Mumford, using only the tools of algebraic topology.

math.AT↗

arXiv2015

Tautological rings for high dimensional manifolds

We study tautological rings for high dimensional manifolds, that is, for each smooth manifold $M$ the ring $R^*(M)$ of those of characteristic classes of smooth fibre bundles with fibre $M$ which is generated by generalised Miller--Morita--Mumford classes. We completely describe these rings modulo nilpotent elements, when $M$ is a connected sum of copies of $S^n \times S^n$ for $n$ odd.

math.AT↗

arXiv2011

On μ-Compatible Metrics and Measurable Sensitivity

We introduce the notion of W-measurable sensitivity, which extends and strictly implies canonical measurable sensitivity, a measure- theoretic version of sensitive dependence on initial conditions. This notion also implies pairwise sensitivity with respect to a large class of metrics. We show that nonsingular ergodic and conservative dynamical systems on standard spaces must be either W-measurably sensitive, or isomorphic mod 0 to a minimal uniformly rigid isometry. In the finite measure-preserving case they are W-measurably sensitive or measurably isomorphic to an ergodic isometry on a compact metric space.

math.DS↗