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About

I am a Ph.D. fellow studying computer science at the University of Utah School of Computing within the Scientific Computing Institute. My focuses are the derivation and/or application of machine learning, with weighted interest in neural networks and graphical models, and topological computing algorithms-both independently and in novel combinations.

Other interests include the theoretical foundation and capabilities of quantum computing from a categorical or functional perspective.

Research

I have had the fortune of working with Stephan LeBohec on a derivation of the quantum postulates using scale relativity as well as a search for quantum like structuring in celestial systems, Jeff Phillips in constructing an effecient geometric algorithm used for determining the extent of multi-dimensional data sets under the strict turnstile model, Benoit Valiron in extending the quantum functional programming language Quipper to include callcc, and Bei Wang developing a topologicaly based quality measure for dimension reduction of high dimensional data. Currently, under the advisement of Valerio Pascucci , my interests focus on topological computation and/or deep learning in design and application.

Abstracts

(.) Modeling Hierarchical Topological Structure in Scientific Images with Graph Neural Networks

Topological analysis reveals meaningful structure in data from a variety of domains. Tasks such as image segmentation can be effectively performed on the network structure of an image’s topological complex using graph neural networks (GNNs). We propose two methods for using GNNs to learn from the hierarchical information captured by complexes at multiple levels of topological persistence: one modifies the training procedure of an existing GNN, while one extends the message passing across all levels of the complex. Experiments on real-world data from three different domains shows the performance benefits to GNNs from using a hierarchical topological structure.

Modeling hierarchical topological structure in scientific images with graph neural networks. S. Leventhal, A. Gyulassy, V. Pascucci, and M. Heimann. “Modeling hierarchical topological structure in scientific images with graph neural networks.” In NeurIPS 2022 Workshop: New Frontiers in Graph Learning, 2022.

(.) Exploring Classification of Topological Priors with Machine Learning for Feature Extraction

In this paper, we describe an approach to creating learnable topological elements, explore the application of ML techniques to classification tasks in a number of areas, and demonstrate this approach as a viable alternative to pixel-level classification, with similar accuracy, improved execution time and requiring marginal training data. In this manuscript, we also introduce a tool allowing users to easily label topological priors of the Morse-Smale Complex to use for training downstream learning models in an active learning setting.

S. Leventhal, A. Gyulassy, M. Heimann, and V. Pascucci, Exploring Classification of Topological Priors with Machine Learning for Feature Extraction, To appear in: Transactions on Visualization

(.) PAVE: An In Situ Framework for Scientific Visualization and Machine Learning Coupling

Machine learning (ML) has emerged as a tool for understanding data at scale. However, this new methodology comes at a cost because even more HPC resources are required to generate ML algorithms. In addition to the compute resources required to develop ML algorithms, ML does not sidestep one of the biggest challenges on leading-edge HPC systems: the increasing gap between compute performance and I/O bandwidth. This has led to a strong push towards in situ designs by processing data as it is generated and developing strategies to mitigate the I/O bottleneck. Unfortunately, there are no in situ frameworks dedicated to coupling scientific visualization and ML at scale to develop ML algorithms for scientific visualization.

To address the ML and in situ visualization gap, we introduce PAVE. PAVE is an in situ framework which addresses the data management needs between visualisation and machine learning tasks. We demonstrate our framework with a case study that accelerates physically-based light rendering, path-tracing, through the use of a conditional Generative Adversarial neural Network (cGAN). PAVE couples the training over path-traced images resulting in a generative model able to produce scene renderings with accurate light transport and global illumination of a quality comparable to offline approaches in a more efficient manner.

The International Conference for High Performance Computing, Networking, Storage, and Analysis Workshop DRBSD-5

(.) High-throughput Feature Extraction for Measuring Attributes of Deforming Open-Cell Foams

Metallic open-cell foams are promising structural materials with applications in multifunctional systems such as biomedical implants, energy absorbers in impact, noise mitigation, and batteries. There is a high demand for means to understand and correlate the design space of material performance metrics to the material structure in terms of attributes such as density, ligament and node properties, void sizes, and alignments. Currently, X-ray Computed Tomography (CT) scans of these materials are segmented either manually or with skeletonization approaches that may not accurately model the variety of shapes present in nodes and ligaments, especially irregularities that arise from manufacturing, image artifacts, or deterioration due to compression. In this paper, we present a new workflow for analysis of open-cell foams that combines a new density measurement to identify nodal structures, and topological approaches to identify ligament structures between them. Additionally, we provide automated measurement of foam properties. We demonstrate stable extraction of features and time-tracking in an image sequence of a foam being compressed. Our approach allows researchers to study larger and more complex foams than could previously be segmented only manually, and enables the high-throughput analysis needed to predict future foam performance.

Petruzza, S., Gyulassy, A., Leventhal, S., Baglino, J. J., Czabaj, M., Spear, A. D., & Pascucci, V. (2019). High-throughput feature extraction for measuring attributes of deforming open-cell foams. IEEE transactions on visualization and computer graphics.

(.) Application of a Convolutional Neural Network to Distinguish Burkitt Lymphoma From Diffuse Large B-Cell Lymphoma. Authors J. Mohlman, S. Leventhal, A. Venkat, A. Gyulassy, V. Pascucci, M. Salama.

Burkitt lymphoma (BL) and diffuse large B-cell lymphoma (DLBCL) are entities that can present a diagnostic challenge due to overlapping morphological features and often require exhaustive phenotypic and often expensive ancillary testing to yield a final diagnosis. On occasion, even with extensive testing and depending on the cytogenetic or molecular findings, the final diagnosis can be challenging. Convolutional neural networks (CNNs) are a popular machine-learning method for object recognition. The objective of this study was to evaluate if a CNN could reliably differentiate between images of BL and DLBCL. American Journal of Clinical Pathology

(.) Topological Distortion From Dimension Reduction

Bei Wang and I tackle the problem of reducing high dimensional data such that information loss is minimized by preserving similarity between persistence diagrams between high dimensional data and its projected equivilent following principle component analysis. We are then able to project large scale data along the sub-planes which preserve the structure of first degree homological features. Using topological measures such as bottleneck and p-Wasserstein distances we can then identify optimal projection of high dimensional data which preserve general topological structures. https://github.com/sam-lev/topologicaldistortionofdimensionreduction

(.) A Deterministic Sketch for Geometric Extents. Authors Sam Leventhal and Jeff M. Phillips.

We consider a point set P in a d-dimensional space of size u. Our goal is to contuct a sketch of order log(u) which can approximate the extents of P along any direction. The algorithm presented amounts to a turnstile model where elements of P are associated to an array of counters. The array of counters takes the form of a square lattice defined by a modular relation dependent on length with each counter associated to an equivilence class. The approximate extent in our query direction is found by continually reducing the length up to some minimum resolution parameter.

(.) Search For Quantum Like Structuring In Keplerian Systems. Authors: Sam Leventhal, Stephan LeBohec.

Various approaches have bee used with some success and some limitations to provide mathematical derivations of the axioms of quantum mechanics (QM) which otherwise are only justified by the predictive power they provide. All of these approaches involve stochastic mechanics with brownian like trajectories. One such approach is known as the theory of Scale Relativity (SR). In the development of SR, it was suggested that quantum like behavior may appear on macroscopic scales in chaotic systems. Here we engage in a search for signatures of SR and quantum like structure that maybe expected to arrise during the formation of some systems. Indeed, SR suggests that for example, solar systems may form along probability distributions predicted by the square magnitude of the Schrodinger-Keplerian wave equation.

In search for some SR signature, we use our own solar system as a reference to establish a scaling parameter used to define orbital ranks to be assimilated to the principal quantum number. Similar to the principle quantum number for electron orbitals, the orbital rank of celestial bodies correlates to the probability distribution described by the Schrodinger-Keplerian equation. This scaling parameter is then used with extrasolar planets to see if their orbital configuration tend to fall near integer orbital ranks.

For an analysis through spectral graphs and set similarity: https://github.com/sam- lev/SpectralGraphSetSimilarityAnalysisForQuantumStructuringInKeplerianSystems

Presentation on research given at UROP: Search for Quantum Like Structuring in Keplerian Systems

Recent Projects

(.) Classification of Songs via Homology of Chroma Features

Topological Similarity Classification of Music

Majority of methods for song recommendation are based on a co-similarity defined by the degrees of separation between listener's interests, formally called collaborative filtering recommendation. This project attempts to propose a topological based filtering method where similar songs are identified by compositional structures such as pitch, timing, and intensity. We show homological features within a musical composition, as identified through persistence of chroma features, serve as a unique signature to the compositional style of an artist. github

(.) Stochastic Nondeterministic Automaton and Applications

Literature Replicator with Markov Chains

Given a file the program will record word frequencies to generate text files in a similar voice to that of the input file using Markov chains. The code is written in C#. https://github.com/sam-lev/MarkovChainBasedFileReplicator

(.) Protein Family Classification

A classifier trains to label proteins by family in two manners: First, supervised learning with a support vector machine and decision trees given amino acid chains labeled by protein family. Secondly, supervised learning for a convolutional neural net (CNN) with example inputs as snapshot images taken from 3D model renderings of proteins labeled by family. The CNN then labels proteins of an undefined family given image renderings of the protein.

https://github.com/sam- lev/ConvolutionalNueralNetFor3DProteinRenderings

Other Interests

(.) Collection of random drawings.
(.) Collection of random writings.