arXiv subjects

Allen R. Tannenbaum

Publications and source records attributed to Allen R. Tannenbaum.

5 recordsLinked to original sources

arXiv2023

Unbalanced Regularized Optimal Mass Transport with Applications to Fluid Flows in the Brain

As a generalization of the optimal mass transport (OMT) approach of Benamou and Brenier's, the regularized optimal mass transport (rOMT) formulates a transport problem from an initial mass configuration to another with the optimality defined by the total kinetic energy, but subject to an advection-diffusion constraint equation. Both rOMT and the Benamou and Brenier's formulation require the total initial and final masses to be equal; mass is preserved during the entire transport process. However, for many applications, e.g., in dynamic image tracking, this constraint is rarely if ever satisfied. Therefore, we propose to employ an unbalanced version of rOMT to remove this constraint together with a detailed numerical solution procedure and applications to analyzing fluid flows in the brain.

math.NA↗

arXiv2022

Visualizing fluid flows via regularized optimal mass transport with applications to neuroscience

Regularized optimal mass transport (rOMT) problem adds a diffusion term to the continuity equation in the original dynamic formulation of the optimal mass transport (OMT) problem proposed by Benamou and Brenier. We show that the rOMT model serves as a powerful tool in computational fluid dynamics (CFD) for visualizing fluid flows in the glymphatic system. In the present work, we describe how to modify the previous numerical method for efficient implementation, resulting in a significant reduction in computational runtime. Numerical results applied to synthetic and real-data are provided.

math.NA↗

arXiv2020

Probabilistic Kernel Support Vector Machines

We propose a probabilistic enhancement of standard kernel Support Vector Machines for binary classification, in order to address the case when, along with given data sets, a description of uncertainty (e.g., error bounds) may be available on each datum. In the present paper, we specifically consider Gaussian distributions to model uncertainty. Thereby, our data consist of pairs $(x_i,Σ_i)$, $i\in\{1,\ldots,N\}$, along with an indicator $y_i\in\{-1,1\}$ to declare membership in one of two categories for each pair. These pairs may be viewed to represent the mean and covariance, respectively, of random vectors $ξ_i$ taking values in a suitable linear space (typically $\mathbb R^n$). Thus, our setting may also be viewed as a modification of Support Vector Machines to classify distributions, albeit, at present, only Gaussian ones. We outline the formalism that allows computing suitable classifiers via a natural modification of the standard "kernel trick." The main contribution of this work is to point out a suitable kernel function for applying Support Vector techniques to the setting of uncertain data for which a detailed uncertainty description is also available (herein, "Gaussian points").

cs.LG↗

arXiv2019

Controlled and Uncontrolled Stochastic Norton-Simon-Massagué Tumor Growth Models

Tumorigenesis is a complex process that is heterogeneous and affected by numerous sources of variability. This study presents a stochastic extension of a biologically grounded tumor growth model, referred to as the Norton-Simon-Massagué (NSM) tumor growth model. We first study the uncontrolled version of the model where the effect of chemotherapeutic drug agent is absent. Conditions on the model's parameters are derived to guarantee the positivity of the tumor volume and hence the validity of the proposed stochastic NSM model. To calibrate the proposed model we utilize a maximum likelihood-based estimation algorithm and population mixed-effect modeling formulation. The algorithm is tested by fitting previously published tumor volume mice data. Then, we study the controlled version of the model which includes the effect of chemotherapy treatment. Analysis of the influence of adding the control drug agent into the model and how sensitive it is to the stochastic parameters is performed both in open-loop and closed-loop viewpoints through different numerical simulations.

q-bio.TO↗

arXiv2009

Segmentation of Facial Expressions Using Semi-Definite Programming and Generalized Principal Component Analysis

In this paper, we use semi-definite programming and generalized principal component analysis (GPCA) to distinguish between two or more different facial expressions. In the first step, semi-definite programming is used to reduce the dimension of the image data and "unfold" the manifold which the data points (corresponding to facial expressions) reside on. Next, GPCA is used to fit a series of subspaces to the data points and associate each data point with a subspace. Data points that belong to the same subspace are claimed to belong to the same facial expression category. An example is provided.

cs.CV↗