Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Graph properties”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 127 records · Page 7
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

Algebraic Methods of the Study of Quantum Information Transfer Channels

Kraus representation of quantum information transfer channels is widely used in practice. We present examples of Kraus decompositions for channels that possess the covariance property with respect to the maximal commutative group of unitary operators. We show that in some problems (for example, the problem on the estimate of the minimal output entropy of the channel), the choice of a Kraus representation with nonminimal number of Kraus operators is relevant. We also present certain algebraic properties of noncommutative operator graphs generated by Kraus operators for the case of quantum channels that demonstrate the superactivation phenomenon.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Dirac cones in the spectrum of bond-decorated graphenes

We present a two-band model based on periodic Hückel theory, which is capable of predicting the existence and position of Dirac cones in the first Brillouin zone of an infinite class of two-dimensional periodic carbon networks, obtained by systematic perturbation of the graphene connectivity by bond decoration, that is by inclusion of arbitrary π-electron Hückel networks into each of the three carbon–carbon π-bonds within the graphene unit cell. The bond decoration process can fundamentally modify the graphene unit cell and honeycomb connectivity, representing a simple and general way to describe many cases of graphene chemical functionalization of experimental interest, such as graphyne, janusgraphenes, and chlorographenes. Exact mathematical conditions for the presence of Dirac cones in the spectrum of the resulting two-dimensional π-networks are formulated in terms of the spectral properties of the decorating graphs. Our method predicts the existence of Dirac cones in experimentally characterized janusgraphenes and chlorographenes, recently speculated on the basis of density functional theory calculations. For these cases, our approach provides a proof of the existence of Dirac cones, and can be carried out at the cost of a back of the envelope calculation, bypassing any diagonalization step, even within Hückel theory.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2016

An Exploration of Moving Target Efficacy and Application

Moving target defense (MTD) is an emerging paradigm in which system defenses dynamically mutate in order to decrease the overall system attack surface. Though the initial concept is promising, implementations have not been widely adopted. The field has been actively researched for over ten years, and has only produced a small amount of extensively adopted defenses, most notably, address space layout randomization (ASLR). This is despite the fact that there currently exist a variety of moving target implementations and proofs-of-concept. We suspect that this results from the moving target controls breaking critical system dependencies from the perspectives of users and administrators, as well as making things more difficult for attackers. As a result, the impact of the controls on overall system security is not sufficient to overcome the inconvenience imposed on legitimate system users. In this paper, we analyze a successful MTD approach. We study the control's dependency graphs, showing how we use graph theoretic and network properties to predict the effectiveness of the selected control. Then, with this framework in place, the dynamic nature of some Moving Target Defenses opens the possibility of modeling them with dynamic systems approaches, such as state space representations familiar from control and systems theory. We then use this approach to develop state space models for Moving Target Defenses, provide an analysis of their properties, and suggest approaches for using them.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2019

Ordering of Trotterization: Impact on Errors in Quantum Simulation of Electronic Structure

Trotter–Suzuki decompositions are frequently used in the quantum simulation of quantum chemistry. They transform the evolution operator into a form implementable on a quantum device, while incurring an error—the Trotter error. The Trotter error can be made arbitrarily small by increasing the Trotter number. However, this increases the length of the quantum circuits required, which may be impractical. It is therefore desirable to find methods of reducing the Trotter error through alternate means. The Trotter error is dependent on the order in which individual term unitaries are applied. Due to the factorial growth in the number of possible orderings with respect to the number of terms, finding an optimal strategy for ordering Trotter sequences is difficult. In this paper, we propose three ordering strategies, and assess their impact on the Trotter error incurred. Initially, we exhaustively examine the possible orderings for molecular hydrogen in a STO-3G basis. We demonstrate how the optimal ordering scheme depends on the compatibility graph of the Hamiltonian, and show how it varies with increasing bond length. We then use 44 molecular Hamiltonians to evaluate two strategies based on coloring their incompatibility graphs, while considering the properties of the obtained colorings. We find that the Trotter error for most systems involving heavy atoms, using a reference magnitude ordering, is less than 1 kcal/mol. Relative to this, the difference between ordering schemes can be substantial, being approximately on the order of millihartrees. The coloring-based ordering schemes are reasonably promising—particularly for systems involving heavy atoms—however further work is required to increase dependence on the magnitude of terms. Finally, we consider ordering strategies based on the norm of the Trotter error operator, including an iterative method for generating the new error operator terms added upon insertion of a term into an ordered Hamiltonian.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Data-Driven Template Discovery Using Graph Convolutional Neural Networks

Modeling adversarial activities is a critical component of developing high-con?dence indicators of efforts to acquire, fabricate, proliferate, and/or deploy weapons of mass terror (WMTs). Current approaches to generating representative patterns of interest (a.k.a templates) from the real-world domains involve a Subject Matter Expert (SME)-guided manual process. The goal of Data-Driven Template Discovery (DDTD) is to use a (potentially small) set of SME generated templates to discover other previously unknown and interesting templates in an attributed graph. A template is an activity pattern describing a set of interactions among a group of nodes in the graph. The motivation behind DDTD is to expand the original set of templates, without having SMEs craft all the templates by hand. DDTD also provides seed templates to SMEs, to help them construct larger, high-?delity, and scenario-oriented templates. In these cases, obtaining a larger set of templates that are related (contain similar signals) to the original set is of great value. In this work, we propose to use Graph Convolutional Neural Networks (GCNs) to discover new templates that are heavily related to the original set. GCNs are a family of Neural Network (NN) architectures especially designed to work directly on graphs. In contrast to the traditional NNs, that require considerable amounts of labeled data, GCNs do not require a big labeled training set because they can directly leverage the graph structure instead. This property makes GCNs the perfect tool for creating activity templates.

Joaristi, Mikel↗
DOE OSTI2024

Virtual node graph neural network for full phonon prediction

Understanding the structure-property relationship is crucial for designing materials with desired properties. The past few years have witnessed remarkable progress in machine-learning methods for this connection. However, substantial challenges remain, including the generalizability of models and prediction of properties with materials-dependent output dimensions. Here we present the virtual node graph neural network to address the challenges. By developing three virtual node approaches, we achieve Γ-phonon spectra and full phonon dispersion prediction from atomic coordinates. We show that, compared with the machine-learning interatomic potentials, our approach achieves orders-of-magnitude-higher efficiency with comparable to better accuracy. This allows us to generate databases for Γ-phonon containing over 146,000 materials and phonon band structures of zeolites. Additionally, our work provides an avenue for rapid and high-quality prediction of phonon band structures enabling materials design with desired phonon properties. The virtual node method also provides a generic method for machine-learning design with a high level of flexibility. In this study, the authors present a virtual node graph neural network to enable the prediction of material properties with variable output dimensions. This method offers fast and accurate predictions of phonon band structures in complex solids.

36 MATERIALS SCIENCE↗
DOE OSTI2013

The Component Slope Linear Model for Calculating Intensive Partial Molar Properties: Application to Waste Glasses and Aluminate Solutions - 13099

Partial molar properties are the changes occurring when the fraction of one component is varied while the fractions of all other component mole fractions change proportionally. They have many practical and theoretical applications in chemical thermodynamics. Partial molar properties of chemical mixtures are difficult to measure because the component mole fractions must sum to one, so a change in fraction of one component must be offset with a change in one or more other components. Given that more than one component fraction is changing at a time, it is difficult to assign a change in measured response to a change in a single component. In this study, the Component Slope Linear Model (CSLM), a model previously published in the statistics literature, is shown to have coefficients that correspond to the intensive partial molar properties. If a measured property is plotted against the mole fraction of a component while keeping the proportions of all other components constant, the slope at any given point on a graph of this curve is the partial molar property for that constituent. Actually plotting this graph has been used to determine partial molar properties for many years. The CSLM directly includes this slope in a model that predicts properties as a function of the component mole fractions. This model is demonstrated by applying it to the constant pressure heat capacity data from the NaOHNaAl(OH){sub 4}-H{sub 2}O system, a system that simplifies Hanford nuclear waste. The partial molar properties of H{sub 2}O, NaOH, and NaAl(OH){sub 4} are determined. The equivalence of the CSLM and the graphical method is verified by comparing results determined by the two methods. The CSLM model has been previously used to predict the liquidus temperature of spinel crystals precipitated from Hanford waste glass. Those model coefficients are re-interpreted here as the partial molar spinel liquidus temperature of the glass components. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2011

Multilevel Method for Modeling Large-Scale Networks

Understanding the behavior of real complex networks is of great theoretical and practical significance. It includes developing accurate artificial models whose topological properties are similar to the real networks, generating the artificial networks at different scales under special conditions, investigating a network dynamics, reconstructing missing data, predicting network response, detecting anomalies and other tasks. Network generation, reconstruction, and prediction of its future topology are central issues of this field. In this project, we address the questions related to the understanding of the network modeling, investigating its structure and properties, and generating artificial networks. Most of the modern network generation methods are based either on various random graph models (reinforced by a set of properties such as power law distribution of node degrees, graph diameter, and number of triangles) or on the principle of replicating an existing model with elements of randomization such as R-MAT generator and Kronecker product modeling. Hierarchical models operate at different levels of network hierarchy but with the same finest elements of the network. However, in many cases the methods that include randomization and replication elements on the finest relationships between network nodes and modeling that addresses the problem of preserving a set of simplified properties do not fit accurately enough the real networks. Among the unsatisfactory features are numerically inadequate results, non-stability of algorithms on real (artificial) data, that have been tested on artificial (real) data, and incorrect behavior at different scales. One reason is that randomization and replication of existing structures can create conflicts between fine and coarse scales of the real network geometry. Moreover, the randomization and satisfying of some attribute at the same time can abolish those topological attributes that have been undefined or hidden from researchers. We propose to develop multilevel methods to model complex networks. The key point of the proposed strategy is that it will help to preserve part of the unknown structural attributes by guaranteeing the similar behavior of the real and artificial model on different scales.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2013

The component slope linear model for calculating intensive partial molar properties /application to waste glasses and aluminate solutions

Partial molar properties are the changes occurring when the fraction of one component is varied while the fractions of all other component mole fractions change proportionally. They have many practical and theoretical applications in chemical thermodynamics. Partial molar properties of chemical mixtures are difficult to measure because the component mole fractions must sum to one, so a change in fraction of one component must be offset with a change in one or more other components. Given that more than one component fraction is changing at a time, it is difficult to assign a change in measured response to a change in a single component. In this study, the Component Slope Linear Model (CSLM), a model previously published in the statistics literature, is shown to have coefficients that correspond to the intensive partial molar properties. If a measured property is plotted against the mole fraction of a component while keeping the proportions of all other components constant, the slope at any given point on a graph of this curve is the partial molar property for that constituent. Actually plotting this graph has been used to determine partial molar properties for many years. The CSLM directly includes this slope in a model that predicts properties as a function of the component mole fractions. This model is demonstrated by applying it to the constant pressure heat capacity data from the NaOH-NaAl(OH){sub 4}-H{sub 2}O system, a system that simplifies Hanford nuclear waste. The partial molar properties of H{sub 2}O, NaOH, and NaAl(OH){sub 4} are determined. The equivalence of the CSLM and the graphical method is verified by comparing results determined by the two methods. The CSLM model has been previously used to predict the liquidus temperature of spinel crystals precipitated from Hanford waste glass. Those model coefficients are re-interpreted here as the partial molar spinel liquidus temperature of the glass components.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2013

The Component Slope Linear Model for Calculating Intensive Partial Molar Properties: Application to Waste Glasses

Partial molar properties are the changes occurring when the fraction of one component is varied while the fractions of all other component mole fractions change proportionally. They have many practical and theoretical applications in chemical thermodynamics. Partial molar properties of chemical mixtures are difficult to measure because the component mole fractions must sum to one, so a change in fraction of one component must be offset with a change in one or more other components. Given that more than one component fraction is changing at a time, it is difficult to assign a change in measured response to a change in a single component. In this study, the Component Slope Linear Model (CSLM), a model previously published in the statistics literature, is shown to have coefficients that correspond to the intensive partial molar properties. If a measured property is plotted against the mole fraction of a component while keeping the proportions of all other components constant, the slope at any given point on a graph of this curve is the partial molar property for that constituent. Actually plotting this graph has been used to determine partial molar properties for many years. The CSLM directly includes this slope in a model that predicts properties as a function of the component mole fractions. This model is demonstrated by applying it to the constant pressure heat capacity data from the NaOH-NaAl(OH{sub 4}H{sub 2}O system, a system that simplifies Hanford nuclear waste. The partial molar properties of H{sub 2}O, NaOH, and NaAl(OH){sub 4} are determined. The equivalence of the CSLM and the graphical method is verified by comparing results detennined by the two methods. The CSLM model has been previously used to predict the liquidus temperature of spinel crystals precipitated from Hanford waste glass. Those model coefficients are re-interpreted here as the partial molar spinel liquidus temperature of the glass components.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2012

A Space-Filling Visualization Technique for Multivariate Small World Graphs

We introduce an information visualization technique, known as GreenCurve, for large sparse graphs that exhibit small world properties. Our fractal-based design approach uses spatial cues to approximate the node connections and thus eliminates the links between the nodes in the visualization. The paper describes a sophisticated algorithm to order the neighboring nodes of a large sparse graph by solving the Fiedler vector of its graph Laplacian, and then fold the graph nodes into a space-filling fractal curve based on the Fiedler vector. The result is a highly compact visualization that gives a succinct overview of the graph with guaranteed visibility of every graph node. We show in the paper that the GreenCurve technology is (1) theoretically sustainable by introducing an error estimation metric to measure the fidelity of the new graph representation, (2) empirically rigorous by conducting a usability study to investigate its strengths and weaknesses against the traditional graph layout, and (3) pragmatically feasible by applying it to analyze stressed conditions of the large scale electric power grid on the west coast.

99 GENERAL AND MISCELLANEOUS↗
DOE OSTI2015

A new approach to the method of source-sink potentials for molecular conduction

We re-derive the tight-binding source-sink potential (SSP) equations for ballistic conduction through conjugated molecular structures in a form that avoids singularities. This enables derivation of new results for families of molecular devices in terms of eigenvectors and eigenvalues of the adjacency matrix of the molecular graph. In particular, we define the transmission of electrons through individual molecular orbitals (MO) and through MO shells. We make explicit the behaviour of the total current and individual MO and shell currents at molecular eigenvalues. A rich variety of behaviour is found. A SSP device has specific insulation or conduction at an eigenvalue of the molecular graph (a root of the characteristic polynomial) according to the multiplicities of that value in the spectra of four defined device polynomials. Conduction near eigenvalues is dominated by the transmission curves of nearby shells. A shell may be inert or active. An inert shell does not conduct at any energy, not even at its own eigenvalue. Conduction may occur at the eigenvalue of an inert shell, but is then carried entirely by other shells. If a shell is active, it carries all conduction at its own eigenvalue. For bipartite molecular graphs (alternant molecules), orbital conduction properties are governed by a pairing theorem. Inertness of shells for families such as chains and rings is predicted by selection rules based on node counting and degeneracy.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2012

Pure and entangled N=4 linear supermultiplets and their one-dimensional sigma-models

'Pure' homogeneous linear supermultiplets (minimal and non-minimal) of the N=4-extended one-dimensional supersymmetry algebra are classified. 'Pure' means that they admit at least one graphical presentation (the corresponding graph/graphs are known as 'Adinkras'). We further prove the existence of 'entangled' linear supermultiplets which do not admit a graphical presentation, by constructing an explicit example of an entangled N=4 supermultiplet with field content (3, 8, 5). It interpolates between two inequivalent pure N=4 supermultiplets with the same field content. The one-dimensional N=4 sigma-model with a three-dimensional target based on the entangled supermultiplet is presented. The distinction between the notion of equivalence for pure supermultiplets and the notion of equivalence for their associated graphs (Adinkras) is discussed. Discrete properties such as 'chirality' and 'coloring' can discriminate different supermultiplets. The tools used in our classification include, among others, the notion of field content, connectivity symbol, commuting group, node choice group, and so on.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Many-body expansion based machine learning models for octahedral transition metal complexes

Abstract Graph-based machine learning (ML) models for material properties show great potential to accelerate virtual high-throughput screening of large chemical spaces. However, in their simplest forms, graph-based models do not include any 3D information and are unable to distinguish stereoisomers such as those arising from different orderings of ligands around a metal center in coordination complexes. In this work we present a modification to revised autocorrelation descriptors, a molecular graph featurization method, for predicting spin state dependent properties of octahedral transition metal complexes (TMCs). Inspired by analytical semi-empirical models for TMCs, the new modeling strategy is based on the many-body expansion (MBE) and allows one to tune the captured stereoisomer information by changing the truncation order of the MBE. We present the necessary modifications to include this approach in two commonly used ML methods, kernel ridge regression and feed-forward neural networks. On a test set composed of all possible isomers of binary TMCs, the best MBE models achieve mean absolute errors (MAEs) of 2.75 kcal mol −1 on spin-splitting energies and 0.26 eV on frontier orbital energy gaps, a 30%–40% reduction in error compared to models based on our previous approach. We also observe improved generalization to previously unseen ligands where the best-performing models exhibit MAEs of 4.00 kcal mol −1 (i.e. a 0.73 kcal mol −1 reduction) on the spin-splitting energies and 0.53 eV (i.e. a 0.10 eV reduction) on the frontier orbital energy gaps. Because the new approach incorporates insights from electronic structure theory, such as ligand additivity relationships, these models exhibit systematic generalization from homoleptic to heteroleptic complexes, allowing for efficient screening of TMC search spaces.

Meyer, Ralf (ORCID:0000000322360261)↗
DOE OSTI2018

Identifying Backbones in Three-Dimensional Discrete Fracture Networks: A Bipartite Graph-Based Approach

In this paper, we present a graph-based method to identify primary flow and transport sub-networks in three-dimensional discrete fracture networks (DFNs). The structure of a DFN lends itself to the use of graphs as a coarse-scale representation that retains the multiscale nature of flow and transport through fracture media. We develop a bipartite graph representation that integrates fracture network topology, fracture geometry, and hydraulic properties. We show that the two most common graph-representations of DFNs, vertices representing intersections and vertices representing fractures, are projections of this bipartite graph thereby providing a generalization of previous DFN-graph frameworks. The primary subnetworks in each DFN are identified by running a heuristic algorithm that determines the edge-disjoint shortest paths through the graph which correspond to the regions where the fastest transport occurs. The method does not have any user-defined parameters and terminates in a finite number of steps. The quality of the method is demonstrated by comparing transport simulations on the identified primary subnetwork and full network, which are in good agreement for early and middle times. In conclusion, these estimates of the first passage times can be achieved with close to an order of magnitude reduction of computational expense using the proposed method.

58 GEOSCIENCES↗
DOE OSTI2014

Investigating the solid-liquid phase transition of water nanofilms using the generalized replica exchange method

The generalized Replica Exchange Method (gREM) was applied to study a solid-liquid phase transition in a nanoconfined bilayer water system using the monatomic water (mW) model. Exploiting optimally designed non-Boltzmann sampling weights with replica exchanges, gREM enables an effective sampling of configurations that are metastable or unstable in the canonical ensemble via successive unimodal energy distributions across phase transition regions, often characterized by S-loop or backbending in the statistical temperature. Extensive gREM simulations combined with Statistical Temperature Weighted Histogram Analysis Method (ST-WHAM) for nanoconfined mW water at various densities provide a comprehensive characterization of diverse thermodynamic and structural properties intrinsic to phase transitions. Graph representation of minimized structures of bilayer water systems determined by the basin-hopping global optimization revealed heterogeneous ice structures composed of pentagons, hexagons, and heptagons, consistent with an increasingly ordered solid phase with decreasing density. Apparent crossover from a first-order solid-liquid transition to a continuous one in nanoconfined mW water with increasing density of the system was observed in terms of a diminishing S-loop in the statistical temperature, smooth variation of internal energies and heat capacities, and a characteristic variation of lateral radial distribution functions, and transverse density profiles across transition regions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Trust based attachment

In social systems subject to indirect reciprocity, a positive reputation is key for increasing one’s likelihood of future positive interactions. The flow of gossip can amplify the impact of a person’s actions on their reputation depending on how widely it spreads across the social network, which leads to a percolation problem. To quantify this notion, we calculate the expected number of individuals, the “audience”, who find out about a particular interaction. For a potential donor, a larger audience constitutes higher reputational stakes, and thus a higher incentive, to perform “good” actions in line with current social norms. For a receiver, a larger audience therefore increases the trust that the partner will be cooperative. This idea can be used for an algorithm that generates social networks, which we call trust based attachment (TBA). TBA produces graphs that share crucial quantitative properties with real-world networks, such as high clustering, small-world behavior, and powerlaw degree distributions. We also show that TBA can be approximated by simple friend-of-friend routines based on triadic closure, which are known to be highly effective at generating realistic social network structures. Therefore, our work provides a new justification for triadic closure in social contexts based on notions of trust, gossip, and social information spread. These factors are thus identified as potential significant influences on how humans form social ties.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Application of Modified Meshgraphnets for Subsurface Prediction during CO2 Sequestration

In the face of the increasingly dire consequences of anthropogenic climate change, capturing and storing carbon dioxide is paramount. However, several impediments exist to the safe and effective subsurface storage of CO2, such as cost of transport, identification of suitable sites for subsurface storage, and assessment of long-term risk from storage in subsurface aquifers. Accurate subsurface modeling is necessary to ensure that CO2 storage is both safe and effective. Still, such modeling has traditionally required either substantial time and computational power (numerical simulation) or a substantial amount of pre-existing data for training (machine learning models). Additionally, these models lack flexibility in dealing with both changes in discretization of the input data and generalizability beyond the data on which they are trained. In order to address these issues, this research applies graph neural networks (GNNs) to predict subsurface saturation and pressure during CO₂ injection in a model of the Illinois Basin-Decatur Project (IBDP). GNNs provide a flexible, intuitive method for representing and manipulating complex unstructured data, which is often found in many practical domain problems such as fluid flow and subsurface characterization. These unstructured grids are easily represented in GNNs by representing spatially-localized features such as permeability, porosity, saturation, and pressure as nodes in a graph and relationships between these properties as edges connecting these nodes. This research applies a specific GNN model called MeshGraphNets (MGN) to model the change in CO2 saturation and pressure over a 50-month time period (36 months of injection, 14 months post-injection). The MGN model leverages a message passing process that allows the network to learn both the spatial and temporal dynamics of this system simultaneously. Additionally, training on a limited dataset (64 realizations, 20 time points each) resulted in a high degree of accuracy in saturation prediction both within the same timeframe as the training (20 months, 0.039 average RMSE) and when projecting out to the end of injection (36 months, 0.053 average RMSE). Temporal predictions such as those generated by MGNs and other similar models are prone to accumulated error over time; in order to address this, a multi-step rollout (MSR) training process was applied to calculate training loss. This method mimics the forward prediction during inference by “rolling out” multiple time points in a single training step using the previous prediction as input to the MGN model. By calculating the loss several time steps forward from the current prediction, the model is forced to find a more stable state over time. Application of MSR to the MGN model resulted in an average 15% reduction in inference error over time during forward prediction. This study showcases the immense potential of GNNs as a game-changing methodology for predicting pressure and saturation evolution in CCS projects, ultimately paving the way for more sustainable and effective carbon storage solutions. Presentation prepared for the 2024 AiChE Annual Meeting, October 27 to November 1 2024, San Diego, CA.

Holcomb, Paul↗