Engineering topics

Joslyn, Cliff A.

Publications and source records attributed to Joslyn, Cliff A..

At least 19 records

DOE OSTI2024

Introducing Molecular Hypernetworks for Discovery in Multidimensional Metabolomics Data

Orthogonal separations of data from high-resolution mass spectrometry can provide insight into sample composition and address challenges of complete annotation of molecules in untargeted metabolomics. “Molecular networks” (MNs), as used in the Global Natural Products Social Molecular Networking platform, are a prominent strategy for exploring and visualizing molecular relationships and improving annotation. MNs are mathematical graphs showing the relationships between measured multidimensional data features. MNs also show promise for using network science algorithms to automatically identify targets for annotation candidates and to dereplicate features associated with a single molecular identity. Here, this paper introduces “molecular hypernetworks” (MHNs) as more complex MN models able to natively represent multiway relationships among observations. Compared to MNs, MHNs can more parsimoniously represent the inherent complexity present among groups of observations, initially supporting improved exploratory data analysis and visualization. MHNs also promise to increase confidence in annotation propagation, for both human and analytical processing. We first illustrate MHNs with simple examples, and build them from liquid chromatography- and ion mobility spectrometry-separated MS data. We then describe a method to construct MHNs directly from existing MNs as their “clique reconstructions”, demonstrating their utility by comparing examples of previously published graph-based MNs to their respective MHNs.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2023

Comparing Mapper Graphs of Artificial Neuron Activations

The mapper graph is a popular tool from topological data analysis that provides a graphical summary of point cloud data. It has been used to study data from cancer research, sports analytics, neurosciences, and machine learning. In particular, mapper graphs have been used recently to visualize the topology of high-dimensional artificial neural activations from convolutional neural networks and large language models. However, a key question that arises from using mapper graphs across applications is how to compare mapper graphs to study their structural differences. In this paper, we introduce a distance between mapper graphs using tools from optimal transport. We demonstrate the utility of such a distance by studying the topological changes of neural activations across convolutional layers in deep learning, as well as by capturing the loss of structural information for multiscale mapper.

mapper graphs, computational topology, machine lea↗

DOE OSTI2023

Malicious Cyber Activity Detection using Zigzag Persistence

In this study we synthesize zigzag persistence from topological data analysis with autoencoder-based approaches to detect malicious cyber activity, and derive analytic insights. Cybersecurity aims to safeguard computers, networks, and servers from various forms of malicious attacks, including network damage, data theft, and activity monitoring. We focus on the cybersecurity domain and investigate the detection of malicious activity using log data. We consider the dynamics of the log data and explore the changing topology of a hypergraph representation of this data to gain insights into the underlying activity. These hypergraphs capture complex interactions between processes, together with their temporal information. To study the changing topology we use zigzag persistence, which captures how topological features persist at multiple dimensions over time. We observe that this detects malicious activity in a cyber data set. To automate this detection we implement an autoencoder trained on a vectorization of the resulting zigzag persistence barcodes. Our experimental results demonstrate the effectiveness of the autoencoder in detecting malicious activity. Overall, this study highlights the potential of zigzag persistence and its combination with temporal hypergraphs for analyzing cybersecurity log data and detecting malicious behavior.

hypergraphs, temporal hypergraph, topological data↗

DOE OSTI2023

Molecular Hypernetworks for Exploration of Multi-Dimensional Metabolomics Data (Chyper)

Orthogonal separations of data from high-resolution mass spectrometry can provide insight into sample composition and help address the challenge of complete annotation of molecules in untargeted metabolomics. “Molecular networks” (MNs), as used, for example, in the Global Natural Products Social Molecular Networking platform, are an increasingly popular computational strategy for exploring and visualizing molecular relationships and improving annotation. MNs use graph representations to show the relationships between measured multidimensional data features. MNs also show promise for using network science algorithms to automatically identify targets for annotation candidates and to dereplicate features associated to a single molecular identity. However, more advanced methods may better represent the complexity present in samples. Our work aims to increase confidence in annotation propagation by extending molecular network methods to include “molecular hypernetworks” (MHNs), able to natively represent multiway relationships among observations supporting both human and analytical processing. In this paper we first introduce MHNs illustrated with simple examples, and demonstrate how to build them from liquid chromatography- and ion mobility spectrometry- separated MS data. We then describe a method to construct MHNs directly from existing MNs as their “clique reconstructions”, demonstrating their utility by comparing examples of previously published graph-based MNs to their respective MHNs.

59 BASIC BIOLOGICAL SCIENCES↗

DOE OSTI2023

Experimental Observations of the Topology of Convolutional Neural Network Activations

Topological data analysis (TDA) is a branch of computational mathematics, bridging algebraic topology and data science, that provides compact, noise-robust representations of complex structures. Deep neural networks (DNNs) learn millions of parameters associated with a series of transformations defined by the model architecture resulting in high-dimensional, difficult to interpret internal representations of input data. As DNNs become more ubiquitous across multiple sectors of our society, there is increasing recognition that mathematical methods are needed to aid analysts, researchers, and practitioners in understanding and interpreting how these models' internal representations relate to the final classification. In this paper we apply cutting edge techniques from TDA with the goal of gaining insight towards interpretability of convolutional neural networks used for image classification. We use two common TDA approaches to explore several methods for modeling hidden layer activations as high-dimensional point clouds, and provide experimental evidence that these point clouds capture valuable structural information about the model's process. First, we demonstrate that a distance metric based on persistent homology can be used to quantify meaningful differences between layers and discuss these distances in the broader context of existing representational similarity metrics for neural network interpretability. Second, we show that a mapper graph can provide semantic insight as to how these models organize hierarchical class knowledge at each layer. These observations demonstrate that TDA is a useful tool to help deep learning practitioners unlock the hidden structures of their models.

topological data analysis, deep learning↗

DOE OSTI2023

Topological Analysis of Temporal Hypergraphs

In this work we study the topological properties of temporal hypergraphs. Hypergraphs provide a higher dimensional generalization of a graph that is capable of capturing multi-way connections. As such, they have become an integral part of network science. A common use of hypergraphs is to model events as hyperedges in which the event can involve many elements as nodes. This provides a more complete picture of the event in comparison to the standard dyadic connection limitation of a graph. However, a common attribution to events is temporal information as an interval for when the event occurred. Consequently, a temporal hypergraph is born which accurately captures both the temporal information of events as well as their multi-way connections. Common tools for studying these temporal hypergraphs typically use summary statistics of snapshots from a sliding window procedure to capture changes in the underlying dynamics. However, these do not provide insight into how the changing structure of the hypergraph evolves and which components of the temporal hypergraph persist and are influential to the underlying system. To alleviate this need we leverage zigzag persistence from the field of Topological Data Analysis (TDA) to study the change in topological structure of time-evolving hypergraphs. We apply our pipeline to both a cyber security and social network dataset and show how the topological structure of their temporal hypergraphs change and can be used to understand the underlying dynamics.

hypergraphs, topological data analysis, zigzag per↗

DOE OSTI2023

Session Introduction: Graph Representations and Algorithms in Biomedicine

Connectivity is a fundamental property of biological systems: on the cellular level, proteins interact with each other to form protein-protein interaction networks (PPIs); on the organism level, neurons are arranged in a network; and on a community-level, species can have complex relationships with one another that drive the development and balance of an ecosystem. Graphs, representations of systems consisting of entities as vertices and their connections as edges, are a useful structure to characterize many such systems. Such models can be used to understand biological systems that naturally have a network structure, including PPIs, biological neurons, and ecosystems. In today’s information age, graph representations and algorithms (often in combination with machine learning techniques) are used to organize massive amounts of related data, much of which may be heterogeneous or unstructured, and identify patterns that represent novel biological insights. PSB’s 2023 session “Graph Representations and algorithms in Biomedicine,” encompasses modern developments in graph theory and its applications to various fields of biomedicine. This session includes a wide range of research - knowledge graphs built from text-mined health data, heterogeneous networks using multi-omic databases, and graphs refined to represent uncertainty or improve memory usage.

Chrisman, Brianna S.↗

DOE OSTI2022

Models and Methods for Sparse (Hyper)Network Science in Business, Industry, and Government

The authors are hosting an AMS sponsored Mathematics Research Community (MRC) focusing on two themes that have garnered intense attention in network models of complex relational data: (1) how to faithfully model multi-way relations in hypergraphs, rather than only pairwise interactions in graphs; and (2) challenges posed by modelling networks with extreme sparsity. Here we introduce and explore these two themes and their challenges. In this work, we hope to generate interest from researchers in pure and applied mathematics and computer science.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2021

Parallel Algorithms for Efficient Computation of High-Order Line Graphs of Hypergraphs

This paper considers structures of systems beyond dyadic (pairwise) interactions and investigates mathematical modeling of multi-way interactions and connections as hypergraphs, where captured relationships among system entities are set-valued. To date, in most situations, entities in a hypergraph are considered connected as long as there is at least one common ``neighbor''. However, minimal commonality sometimes discards the ``strength'' of connections and interactions among groups. To this end, considering the ``width'' of a connection, referred to as the \emph{$s$-overlap} of neighbors, provides more meaningful insights into how closely the communities or entities interact with each other. In addition, $s$-overlap computation is the fundamental kernel to construct the line graph of a hypergraph, a low-order approximation of the hypergraph which can carry significant information about the original hypergraph. Subsequent stages of a data analytics pipeline then can apply highly-tuned graph algorithms on the line graph to reveal important features. Given a hypergraph, computing the $s$-overlaps by exhaustively considering all pairwise entities can be computationally prohibitive. To tackle this challenge, we develop efficient algorithms to compute $s$-overlaps and the corresponding line graph of a hypergraph. We propose several heuristics to avoid execution of redundant work and improve performance of the $s$-overlap computation. Our parallel algorithm, combined with these heuristics, is orders of magnitude (more than $10\times$) faster than the naive algorithm in all cases and the SpGEMM algorithm with filtration in most cases (especially with large $s$ value).

hypergraph algorithms, graph algorithms, parallel ↗

DOE OSTI2021

Sheaves as a Framework for Understanding and Interpreting Model Fit

As data grows in size and complexity, finding frameworks which aid in interpretation and analysis has become critical. This is particularly true when data comes from complex systems where extensive structure is available, but must be drawn from peripheral sources. In this paper we argue that in such situations, sheaves can provide a natural framework to analyze how well a statistical model fits at the local level (that is, on subsets of related datapoints) vs the global level (on all the data). The sheaf-based approach that we propose is suitably general enough to be useful in a range of applications, from analyzing sensor networks to understanding the feature space of a deep learning model.

Kvinge, Henry J.↗

DOE OSTI2021

Hypernetwork Science: From Multidimensional Networks to Computational Topology

As data structures and mathematical objects used for complex systems modeling, hypergraphs sit nicely poised between on the one hand the world of network models, and on the other that of higher-order mathematical abstractions from algebra, lattice theory, and topology. They are able to represent complex systems interactions more faithfully than graphs and networks, while also being some of the simplest classes of systems representing topological structures as collections of multidimensional objects connected in a particular pattern. In this paper we discuss the role of (undirected) hypergraphs in the science of complex networks, and provide a mathematical overview of the core concepts needed for hypernetwork modeling, including duality and the relationship to bicolored graphs, quantitative adjacency and incidence, the nature of walks in hypergraphs, and available topological relationships and properties. We close with a brief discussion of two example applications: biomedical databases for disease analysis, and domain-name system (DNS) analysis of cyber data.

Joslyn, Cliff A.↗

DOE OSTI2021

Hypergraph Models of Biological Networks to Identify Genes Critical to Pathogenic Viral Response

Motivation: Representing biological networks as graphs is a powerful approach to reveal underlying patterns, signatures, and critical components from high-throughput biomolecular data. However, graphs do not natively capture the multi-way relationships present among genes and proteins in biological systems such as protein complexes, metabolic reactions, and signal transduction pathways. Hypergraphs are generalizations of graphs that naturally model multi-way interactions in data, and we therefore seek to understand how they can more faithfully identify, and potentially predict, complex relationships in genomic expression data sets. Results: We compiled a novel data set of transcriptional host response to pathogenic viral infections and formulated relationships between genes as a hypergraph where hyperedges are differentially expressed genes and vertices represent conditions. We find that hypergraph betweenness centrality is a superior method for identification of genes important to viral response when compared with graph centrality. Our results demonstrate the utility of using hypergraphs to represent complex biological systems, and highlight potentially interesting biological results about host response to highly pathogenic viruses.

systems biology, hypergraph, viral infection, biol↗

DOE OSTI2020

Exploration of Potential Application of Distributed Ledger Technology for Managing Transactions Under Joint Technology Development and Transfer Agreements

This document summarizes the findings from the team’s evaluation of applying DLT to transactions taking place inside and outside of a joint technology development and transfer agreement. As part of this examination, PNNL focused on addressing whether DLT could be used to promote civil nuclear cooperation without raising proliferation concerns.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Computing Hypergraph Homology in Chapel

In this paper, we discuss our experience in implementing homology computation, in particular Betti number calculation in Chapel hypergraph Library (CHGL). Given a dataset represented as a hypergraph, a Betti number for a particular dimension $k$ indicates how many $k$-dimensional `voids' are present in the dataset. Computing Betti number involves various array-centric and linear algebra operations. We demonstrate that implementing these operations in Chapel is both concise and intuitive. In addition, we show that Chapel provides language constructs for implementing parallel and distributed execution of the linear algebra kernels with minimal effort. Syntactically, Chapel provides succinctness of Python, while delivering comparable and better performance than C++-based and Julia-based packages for calculating Betti numbers respectively.

hypergraph, topological data analysis↗

DOE OSTI2020

A Sheaf Theoretical Approach to Uncertainty Quantification of Heterogeneous Geolocation Information

Integration of multiple, heterogeneous sensors is a challenging problem across a range of applications. Prominent among these are multi-target tracking, where one must combine observations from different sensor types in a meaningful and efficient way to track multiple targets. Because different sensors have differing error models, we seek a theoretically justified quantification of the agreement among ensembles of sensors, both overall for a sensor collection, and also at a fine-grained level specifying pairwise and multi-way interactions among sensors. We demonstrate that the theory of mathematical sheaves provides a unified answer to this need, supporting both quantitative and qualitative data. Furthermore, the theory provides algorithms to globalize data across the network of deployed sensors, and to diagnose issues when the data do not globalize cleanly. We demonstrate and illustrate the utility of sheaf-based tracking models based on experimental data of a wild population of black bears in Asheville, North Carolina. A measurement model involving four sensors deployed among the bears and the team of scientists charged with tracking their location is deployed. This provides a sheaf-based integration model which is small enough to fully interpret, but of sufficient complexity to demonstrate the sheaf’s ability to recover a holistic picture of the locations and behaviors of both individual bears and the bear-human tracking system. A statistical approach was developed in parallel for comparison, a dynamic linear model which was estimated using a Kalman filter. This approach also recovered bear and human locations and sensor accuracies. When the observations are normalized into a common coordinate system, the structure of the dynamic linear observation model recapitulates the structure of the sheaf model, demonstrating the canonicity of the sheaf-based approach. However, when the observations are not so normalized, the sheaf model still remains valid.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2020

Hypergraph Analytics of Domain Name System Relationships

We report on the use of novel mathematical methods in hypergraph analytice over a large quantity of DNS data. Hypergraphs generalize graphs, as used in network science, to better model complex multiway relations in cyber data. Specifically, casting DNS data from Georgia Tech's ActiveDNS repository as hypergraphs allows us to fully represent the interactions between {\em collections} of domains and IP addresses. To facilitate large-scale analytics, we fielded an analytical pipeline of two capabilities. HyperNetX (HNX) is a Python package for the exploration and visualization of hypergraphs, acting as a frontend. For the backend, the Chapel HyperGraph Library (CHGL) is a library for high performance hypergraph analytics written in the exascale programming language Chapel. CHGL was used to process gigascale DNS data, performing compute-intensive calculations for data reduction and segmentation. Identified portions are then sent to HNX for both exploratory analysis and knowledge discovery targeting known tactics, techniques, and procedures.

Joslyn, Cliff A.↗

DOE OSTI2019

Graph Algorithms in PGAS: Chapel and UPC++

The Partitioned Global Address Space (PGAS) programming model can be implemented «««< HEAD either with programming language features or with runtime library APIs, each implementation favoring different aspects (e.g., productivity, abstraction, flexibility, or performance). Certain language and runtime features, such as collectives, explicit and asynchronous communication primitives, and constructs facilitating overlap of communication and computation (such as futures and conjoined futures) can enable better performance and scaling for irregular applications, in particular for distributed graph analytics. We compare graph algorithms in one of each of these environments: the Chapel PGAS programming language and the UPC++ PGAS runtime library. We implement algorithms for breadth-first search and triangle counting graph kernels in both environments. We discuss the code in each of the environments, and compile performance data on a Cray Aries and an Infiniband platform. Our results show that the library-based approach of UPC++ currently provides strong performance while Chapel provides a high-level abstraction that, harder to optimize, still provides comparable performance. We argue that various language primitives and runtime library features should be considered in conjunction with each other to design future graph analytics libraries so as to incorporate the best of both worlds.

Distributed Algorithms, Graph algorithms, HPC↗

DOE OSTI2018

Chapel HyperGraph Library (CHGL)

We present the Chapel Hpergraph Library (CHGL), a library for hypergraph computation in the emerging Chapel language. Hypergraphs generalize graphs, where a hypergraph edge can connect any number of vertices. Thus, hypergraphs capture high-order, high-dimensional interactions between mulitple entities that are not directly expressible in graphs. CHGL is designed to provide HPC-class computation with high-level abstractions and modern language support for parallel comptuing on shared memory and distributed memory systems.

Jenkins, Louis P.↗