Search NASA⌕ Search

SEARCH · Search NASA

Results for “Mathematical Computing”

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 73 records · Page 4
All sourcesNASA NTRSDOE OSTI
DOE OSTI2019

PHANOTATE: a novel approach to gene identification in phage genomes

Motivation: Currently there are no tools specifically designed for annotating genes in phages. Several tools are available that have been adapted to run on phage genomes, but due to their underlying design, they are unable to capture the full complexity of phage genomes. Phages have adapted their genomes to be extremely compact, having adjacent genes that overlap and genes completely inside of other longer genes. This non-delineated genome structure makes it difficult for gene prediction using the currently available gene annotators. Here we present PHANOTATE, a novel method for gene calling specifically designed for phage genomes. Although the compact nature of genes in phages is a problem for current gene annotators, we exploit this property by treating a phage genome as a network of paths: where open reading frames are favorable, and overlaps and gaps are less favorable, but still possible. We represent this network of connections as a weighted graph, and use dynamic programing to find the optimal path. Results: We compare PHANOTATE to other gene callers by annotating a set of 2133 complete phage genomes from GenBank, using PHANOTATE and the three most popular gene callers. We found that the four programs agree on 82% of the total predicted genes, with PHANOTATE predicting more genes than the other three. We searched for these extra genes in both GenBank’s non-redundant protein database and all of the metagenomes in the sequence read archive, and found that they are present at levels that suggest that these are functional protein-coding genes. Availability and implementation: https://github.com/deprekate/PHANOTATE. Supplementary information: Supplementary data are available at Bioinformatics online.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2019

Identifying emerging phenomenon in long temporal phenotyping experiments

Abstract Motivation The rapid improvement of phenotyping capability, accuracy and throughput have greatly increased the volume and diversity of phenomics data. A remaining challenge is an efficient way to identify phenotypic patterns to improve our understanding of the quantitative variation of complex phenotypes, and to attribute gene functions. To address this challenge, we developed a new algorithm to identify emerging phenomena from large-scale temporal plant phenotyping experiments. An emerging phenomenon is defined as a group of genotypes who exhibit a coherent phenotype pattern during a relatively short time. Emerging phenomena are highly transient and diverse, and are dependent in complex ways on both environmental conditions and development. Identifying emerging phenomena may help biologists to examine potential relationships among phenotypes and genotypes in a genetically diverse population and to associate such relationships with the change of environments or development. Results We present an emerging phenomenon identification tool called Temporal Emerging Phenomenon Finder (TEP-Finder). Using large-scale longitudinal phenomics data as input, TEP-Finder first encodes the complicated phenotypic patterns into a dynamic phenotype network. Then, emerging phenomena in different temporal scales are identified from dynamic phenotype network using a maximal clique based approach. Meanwhile, a directed acyclic network of emerging phenomena is composed to model the relationships among the emerging phenomena. The experiment that compares TEP-Finder with two state-of-art algorithms shows that the emerging phenomena identified by TEP-Finder are more functionally specific, robust and biologically significant. Availability and implementation The source code, manual and sample data of TEP-Finder are all available at: http://phenomics.uky.edu/TEP-Finder/. Supplementary information Supplementary data are available at Bioinformatics online.

Biochemistry & Molecular Biology↗
DOE OSTI2019

ACTINN: automated identification of cell types in single cell RNA sequencing

Abstract Motivation Cell type identification is one of the major goals in single cell RNA sequencing (scRNA-seq). Current methods for assigning cell types typically involve the use of unsupervised clustering, the identification of signature genes in each cluster, followed by a manual lookup of these genes in the literature and databases to assign cell types. However, there are several limitations associated with these approaches, such as unwanted sources of variation that influence clustering and a lack of canonical markers for certain cell types. Here, we present ACTINN (Automated Cell Type Identification using Neural Networks), which employs a neural network with three hidden layers, trains on datasets with predefined cell types and predicts cell types for other datasets based on the trained parameters. Results We trained the neural network on a mouse cell type atlas (Tabula Muris Atlas) and a human immune cell dataset, and used it to predict cell types for mouse leukocytes, human PBMCs and human T cell sub types. The results showed that our neural network is fast and accurate, and should therefore be a useful tool to complement existing scRNA-seq pipelines. Availability and implementation The codes and datasets are available at https://figshare.com/articles/ACTINN/8967116. Tutorial is available at https://github.com/mafeiyang/ACTINN. All codes are implemented in python. Supplementary information Supplementary data are available at Bioinformatics online.

Ma, Feiyang (ORCID:0000000262600787)↗
DOE OSTI2024

SRBench++: Principled Benchmarking of Symbolic Regression With Domain-Expert Interpretation

Symbolic regression searches for analytic expressions that accurately describe studied phenomena. The main promise of this approach is that it may return an interpretable model that can be insightful to users, while maintaining high accuracy. The current standard for benchmarking these algorithms is SRBench, which evaluates methods on hundreds of datasets that are a mix of real-world and simulated processes spanning multiple domains. At present, the ability of SRBench to evaluate interpretability is limited to measuring the size of expressions on real-world data, and the exactness of model forms on synthetic data. In practice, model size is only one of many factors used by subject experts to determine how interpretable a model truly is. Furthermore, SRBench does not characterize algorithm performance on specific, challenging sub-tasks of regression such as feature selection and evasion of local minima. In this work, we propose and evaluate an approach to benchmarking SR algorithms that addresses these limitations of SRBench by 1) incorporating expert evaluations of interpretability on a domain-specific task, and 2) evaluating algorithms over distinct properties of data science tasks. We evaluate 12 modern symbolic regression algorithms on these benchmarks and present an in-depth analysis of the results, discuss current challenges of symbolic regression algorithms and highlight possible improvements for the benchmark itself.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Integrated Framework of Multisource Data Fusion for Outage Location in Looped Distribution Systems

Accurate outage location is essential for expediting post-outage power restoration, minimizing outage duration, and enhancing the resilience of distribution networks. With the advent of advanced metering infrastructure, data-driven outage location methods have significantly advanced beyond traditional approaches that rely on manual inspections. However, existing methods still face critical challenges, like reliance on single-source data, limited ability to handle partially observable systems or difficulties with loop networks. To the best of our knowledge, no single approach has comprehensively addressed all of these challenges at once. To this end, this paper proposes a comprehensive multisource data fusion framework for outage locations via probabilistic graph networks. The framework consists of three key phases. First, a novel method for reconstituting distribution networks with loops is developed, transforming looped networks into multiple radial subnetworks that retain all outage causalities of the original network. Second, Bayesian network (BN) models are established for each subnetwork, integrating multiple data sources and network structures. Finally, a joint Gibbs sampling mechanism, featuring forward and backward information flow, is designed to merge data from separate BN models and maximize the utilization of limited evidence, ensuring accurate outage location identification. In conclusion, the framework was validated on two modified public test systems, and comparative studies confirmed its effectiveness.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2021

The Eight Levers of Coercive Conflict: No More, No Less

Few concepts are more important to our nation than the principle of deterrence. It is at the very core of our national security strategy. Despite its lasting import to our nation, and the rest of the world, we still lack a complete and explicit formulation of the calculus of deterrence. This has, at times, resulted in failed policies costing the Nation lives and wealth. With the ultimate objective of making the Nation more secure, we establish a complete and explicit formulation of deterrence calculus, which consists of eight levers. As it turns out this formulation also applies to the calculus of compellence, and is thus a unifying model of coercive conflict.

45 MILITARY TECHNOLOGY, WEAPONRY, AND NATIONAL DEF↗
DOE OSTI2026

A mathematical framework for thermodynamic computing with applications to chemical reaction networks

The widespread adoption of energy-intensive computing applications has led to a growing need for energy-efficient computing approaches. Thermodynamic computing offers a promising approach for low-energy computation by leveraging the intrinsic computational capabilities of physical, chemical, or biological systems. However, the mathematical foundations of thermodynamic computing require further development to fully realize the potential energy efficiencies, as well as to assess factors like noise and operational speed. In this paper, we establish a mathematical framework for utilizing thermodynamic processes to perform fundamental operations, including addition, subtraction, multiplication, and division. We highlight the use of chemical reactions as potential computational units and explore synthetic chemical and biochemical systems as practical implementations. Additionally, we demonstrate how these principles can be applied to solving complex mathematical problems, such as ordinary differential equations (ODEs) and suggest the necessary components to implement the thermodynamic computing framework using chemical reactions based in a microfluidic device. This work enhances our understanding of thermodynamic processes for natural computing as a basis for scalable, energy-efficient computation in paradigm disruptive next-generation systems.

Cannon, William R. [Pacific Northwest National Lab↗
DOE OSTI2022

Likelihood Maximization and Moment Matching in Low SNR Gaussian Mixture Models

We derive an asymptotic expansion for the log-likelihood of Gaussian mixture models (GMMs) with equal covariance matrices in the low signal-to-noise regime. The expansion reveals an intimate connection between two types of algorithms for parameter estimation: the method of moments and likelihood optimizing algorithms such as Expectation-Maximization (EM). We show that likelihood optimization in the low SNR regime reduces to a sequence of least squares optimization problems that match the moments of the estimate to the ground truth moments one by one. This connection is a stepping stone towards the analysis of EM and maximum likelihood estimation in a wide range of models. A motivating application for the study of low SNR mixture models is cryo-electron microscopy data, which can be modeled as a GMM with algebraic constraints imposed on the mixture centers. We discuss the application of our expansion to algebraically constrained GMMs, among other example models of interest. © 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Estimating posterior quantity of interest expectations in a multilevel scalable framework

Scalable approaches for uncertainty quantification are necessary for characterizing prediction confidence in large-scale subsurface flow simulations with uncertain permeability. To this end we explore a multilevel Monte Carlo approach for estimating posterior moments of a particular quantity of interest, where we employ an element-agglomerated algebraic multigrid (AMG) technique to generate the hierarchy of coarse spaces with guaranteed approximation properties for both the generation of spatially correlated random fields and the forward simulation of Darcy's law to model subsurface flow. In both these components (sampling and forward solves), we exploit solvers that rely on state-of-the-art scalable AMG. To illustrate the applicability of this approach, numerical tests are performed on two 3D examples-a unit cube and an egg-shaped domain with an irregular boundary-where the scalability of each simulation as well as the scalability of the overall algorithm are demonstrated.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Convergence analysis of single rate and multirate fixed stress split iterative coupling schemes in heterogeneous poroelastic media

Recently, the accurate modeling of flow–structure interactions has gained more attention and importance for both petroleum and environmental engineering applications. Of particular interest is the coupling between subsurface flow and reservoir geomechanics. Different single rate and multirate iterative and explicit coupling schemes have been proposed and analyzed in the past. In addition, Banach fixed point contraction results were obtained for iterative coupling schemes, and conditionally stable results were obtained for explicit coupling schemes. In this work, we will consider the mathematical analysis of the single rate and multirate fixed stress split iterative coupling schemes for spatially heterogeneous poroelastic media. We will re–establish the contractivity for both schemes in the localized case, and we will show that heterogeneities come at the expense of imposing more restricted conditions on the number of fine flow time steps that can be taken within one coarse mechanics time step in the multirate case. Our mathematical analysis is supplemented by numerical simulations validating our derived upper bounds. Finally, to the best of our knowledge, this is the first rigorous mathematical analysis of the multirate fixed–stress split iterative coupling scheme in heterogeneous poroelastic media.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Selecting a near-optimal design for multiple criteria with improved robustness to different user priorities

In a decision-making process, relying on only one objective can often lead to oversimplified decisions that ignore important considerations. Incorporating multiple, and likely competing, objectives is critical for balancing trade-offs on different aspects of performance. When multiple objectives are considered, it is often hard to make a precise decision on how to weight the different objectives when combining their performance for ranking and selecting designs. We show that there are situations when selecting a design with near-optimality for a broad range of weight combinations of the criteria is a better test selection strategy compared with choosing a design that is strictly optimal under very restricted conditions. Here, we propose a new design selection strategy that identifies several top-ranked solutions across broad weight combinations using layered Pareto fronts and then selects the final design that offers the best robustness to different user priorities. This method involves identifying multiple leading solutions based on the primary objectives and comparing the alternatives using secondary objectives to make the final decision. We focus on the selection of screening designs because they are widely used both in industrial research, development, and operational testing. The method is illustrated with an example of selecting a single design from a catalog of designs of a fixed size. However, the method can be adapted to more general designed experiment selection problems that involve searching through a large design space.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

Nearly Periodic Maps and Geometric Integration of Noncanonical Hamiltonian Systems

Abstract M. Kruskal showed that each continuous-time nearly periodic dynamical system admits a formal U (1)-symmetry, generated by the so-called roto-rate. When the nearly periodic system is also Hamiltonian, Noether’s theorem implies the existence of a corresponding adiabatic invariant. We develop a discrete-time analog of Kruskal’s theory. Nearly periodic maps are defined as parameter-dependent diffeomorphisms that limit to rotations along a U (1)-action. When the limiting rotation is non-resonant, these maps admit formal U (1)-symmetries to all orders in perturbation theory. For Hamiltonian nearly periodic maps on exact presymplectic manifolds, we prove that the formal U (1)-symmetry gives rise to a discrete-time adiabatic invariant using a discrete-time extension of Noether’s theorem. When the unperturbed U (1)-orbits are contractible, we also find a discrete-time adiabatic invariant for mappings that are merely presymplectic, rather than Hamiltonian. As an application of the theory, we use it to develop a novel technique for geometric integration of non-canonical Hamiltonian systems on exact symplectic manifolds.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

On Properties of Adjoint Systems for Evolutionary PDEs

We investigate the geometric structure of adjoint systems associated with evolutionary partial differential equations at the fully continuous, semi-discrete, and fully discrete levels and the relations between these levels. We show that the adjoint system associated with an evolutionary partial differential equation has an infinite-dimensional Hamiltonian structure, which is useful for connecting the fully continuous, semi-discrete, and fully discrete levels. We subsequently address the question of discretize-then-optimize versus optimize-then-discrete for both semi-discretization and time integration, by characterizing the commutativity of discretize-then-optimize methods versus optimize-then-discretize methods uniquely in terms of an adjoint-variational quadratic conservation law. For Galerkin semi-discretizations and one-step time integration methods in particular, we explicitly construct these commuting methods by using structure-preserving discretization techniques.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

A Type II Hamiltonian Variational Principle and Adjoint Systems for Lie Groups

We present a novel Type II variational principle on the cotangent bundle of a Lie group which enforces Type II boundary conditions, i.e., fixed initial position and final momentum. In general, such Type II variational principles are only globally defined on vector spaces or locally defined on general manifolds; however, by left translation, we are able to define this variational principle globally on cotangent bundles of Lie groups. Type II boundary conditions are particularly important for adjoint sensitivity analysis, which is our motivating application. As such, we additionally discuss adjoint systems on Lie groups, their properties, and how they can be used to solve optimization problems subject to dynamics on Lie groups.

97 MATHEMATICS AND COMPUTING↗