arXiv subjects

Andrew Swift

Publications and source records attributed to Andrew Swift.

6 recordsLinked to original sources

arXiv2023

Noninvasive Estimation of Mean Pulmonary Artery Pressure Using MRI, Computer Models, and Machine Learning

Pulmonary Hypertension (PH) is a severe disease characterized by an elevated pulmonary artery pressure. The gold standard for PH diagnosis is measurement of mean Pulmonary Artery Pressure (mPAP) during an invasive Right Heart Catheterization. In this paper, we investigate noninvasive approach to PH detection utilizing Magnetic Resonance Imaging, Computer Models and Machine Learning. We show using the ablation study, that physics-informed feature engineering based on models of blood circulation increases the performance of Gradient Boosting Decision Trees-based algorithms for classification of PH and regression of values of mPAP. We compare results of regression (with thresholding of estimated mPAP) and classification and demonstrate that metrics achieved in both experiments are comparable. The predicted mPAP values are more informative to the physicians than the probability of PH returned by classification models. They provide the intuitive explanation of the outcome of the machine learning model (clinicians are accustomed to the mPAP metric, contrary to the PH probability).

eess.IV↗

arXiv2021

No dimension reduction for doubling subsets of $\ell_q$ when $q>2$ revisited

We revisit the main results from \cites{BGN_SoCG14,BGN_SIAM15} and \cite{LafforgueNaor14_GD} about the impossibility of dimension reduction for doubling subsets of $\ell_q$ for $q>2$. We provide an alternative elementary proof of this impossibility result that combines the simplicity of the construction in \cites{BGN_SoCG14,BGN_SIAM15} with the generality of the approach in \cite{LafforgueNaor14_GD} (except for $L_1$ targets). One advantage of this different approach is that it can be naturally generalized to obtain embeddability obstructions into non-positively curved spaces or asymptotically uniformly convex Banach spaces.

math.MG↗

arXiv2020

Utilizing Transfer Learning and a Customized Loss Function for Optic Disc Segmentation from Retinal Images

Accurate segmentation of the optic disc from a retinal image is vital to extracting retinal features that may be highly correlated with retinal conditions such as glaucoma. In this paper, we propose a deep-learning based approach capable of segmenting the optic disc given a high-precision retinal fundus image. Our approach utilizes a UNET-based model with a VGG16 encoder trained on the ImageNet dataset. This study can be distinguished from other studies in the customization made for the VGG16 model, the diversity of the datasets adopted, the duration of disc segmentation, the loss function utilized, and the number of parameters required to train our model. Our approach was tested on seven publicly available datasets augmented by a dataset from a private clinic that was annotated by two Doctors of Optometry through a web portal built for this purpose. We achieved an accuracy of 99.78\% and a Dice coefficient of 94.73\% for a disc segmentation from a retinal image in 0.03 seconds. The results obtained from comprehensive experiments demonstrate the robustness of our approach to disc segmentation of retinal images obtained from different sources.

eess.IV↗

arXiv2018

Coarse embeddings into superstable spaces

Krivine and Maurey proved in 1981 that every stable Banach space contains almost isometric copies of $\ell_p$, for some $p\in[1,\infty)$. In 1983, Raynaud showed that if a Banach space uniformly embeds into a superstable Banach space, then $X$ must contain an isomorphic copy of $\ell_p$, for some $p\in[1,\infty)$. In these notes, we show that if a Banach space coarsely embeds into a superstable Banach space, then $X$ has a spreading model isomorphic to $\ell_p$, for some $p\in[1,\infty)$. In particular, we obtain that there exist reflexive Banach spaces which do not coarsely embed into any superstable Banach space.

math.FA↗

arXiv2017

A coding of bundle graphs and their embeddings into Banach spaces

The purpose of this article is to generalize some known characterizations of Banach space properties in terms of graph preclusion. In particular, it is shown that superreflexivity can be characterized by the non-equi-bi-Lipschitz embeddability of any family of bundle graphs generated by a nontrivial finitely-branching bundle graph. It is likewise shown that asymptotic uniform convexifiability can be characterized within the class of reflexive Banach spaces with an unconditional asymptotic structure by the non-equi-bi-Lipschitz embeddability of any family of bundle graphs generated by a nontrivial $\aleph_0$-branching bundle graph. The best known distortions are recovered. For the specific case of $L_1$, it is shown that every countably-branching bundle graph bi-Lipschitzly embeds into $L_1$ with distortion no worse than $2$.

math.FA↗

arXiv2017

On coarse Lipschitz embeddability into $c_0(κ)$

In 1994, Jan Pelant proved that a metric property related to the notion of paracompactness called the uniform Stone property characterizes a metric space's uniform embeddability into $c_0(κ)$ for some cardinality $κ$. In this paper it is shown that coarse Lipschitz embeddability of a metric space into $c_0(κ)$ can be characterized in a similar manner. It is also shown that coarse, uniform, and bi-Lipschitz embeddability into $c_0(κ)$ are equivalent notions for normed linear spaces.

math.FA↗