Finite-dimensional models for equations of mathematical physics
Finite dimensional models for obtaining finite difference methods with same properties
FINITE DIFFERENCE METHOD↗
SEARCH · Search NASA
Results for “mathematics and 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.
Volume-rendering on a 3D hyperwall: A molecular visualization platform for research, education and outreach
Not provided.
Biochemistry & Molecular Biology↗
Linking metabolic phenotypes to pathogenic traits among “ Candidatus Liberibacter asiaticus” and its hosts
Candidatus Liberibacter asiaticus (CLas) has been associated with Huanglongbing, a lethal vector-borne disease affecting citrus crops worldwide. While comparative genomics has provided preliminary insights into the metabolic capabilities of this uncultured microorganism, a comprehensive functional characterization is currently lacking. Here, we reconstructed and manually curated genome-scale metabolic models for the six CLas strains A4, FL17, gxpsy, Ishi-1, psy62, and YCPsy, in addition to a model of the closest related culturable microorganism, L. crescens BT-1. Predictions about nutrient requirements and changes in growth phenotypes of CLas were confirmed using in vitro hairy root-based assays, while the L. crescens BT-1 model was validated using cultivation assays. Host-dependent metabolic phenotypes were revealed using expression data obtained from CLas-infected citrus trees and from the CLas-harboring psyllid Diaphorina citri Kuwayama. These results identified conserved and unique metabolic traits, as well as strain-specific interactions between CLas and its hosts, laying the foundation for the development of model-driven Huanglongbing management strategies.
59 BASIC BIOLOGICAL SCIENCES↗
Model-based iterative reconstruction with adaptive regularization for artifact reduction in electron tomography
Obtaining high-quality 3D reconstructions from electron tomography of crystalline particles embedded in lighter support elements is crucial for various material systems such as catalysts for fuel cell applications. However, significant challenges arise due to the limited tilt range, sparse and low signal-to-noise ratio of the measurements. In addition, small metal particles can cause strong streaking and shading artifacts in the 3D reconstructions when using conventional reconstruction algorithms due to the presence of Bragg diffraction and the large scattering cross-section difference between the materials of the particles and the background support regions. These artifacts lead to errors in the downstream characterization affecting extraction of critical features such as the size of the metal particles, their distribution and the volume of the lighter support regions. In this paper, we present a two-stage algorithm based on metal artifact reduction, utilizing model-based iterative reconstruction methods with adaptive adjustment of regularization parameters. Our approach yields high-quality 3D reconstructions compared to traditional algorithms, accurately capturing both the metal particles as well as the background support. We demonstrate the effectiveness of our algorithm through simulated and experimental bright-field electron tomography data, showing significant improvements in reconstruction quality compared to traditional methods.
97 MATHEMATICS AND COMPUTING↗
Bigpicc: a graph-based approach to identifying carcinogenic gene combinations from mutation data
Abstract Genome data from cancer patients represents relationships between the presence of a gene mutation and cancer occurrence in a patient. Different types of cancer in human are thought to be caused by combinations of two to nine gene mutations. Identifying these combinations through traditional exhaustive search requires the amount of computation that scales exponentially with the combination size and in most cases is intractable even for cutting-edge supercomputers. We propose a parameter-free heuristic approach that leverages the intrinsic topology of gene-patient mutations to identify carcinogenic combinations. The biological relevance of the identified combinations is measured by using them to predict the presence of tumor in previously unseen samples. The resulting classifiers for 16 cancer types perform on par with exhaustive search results, and score the average of 80.1% sensitivity and 91.6% specificity for the best choice of hit range per cancer type. Our approach is able to find higher-hit carcinogenic combinations targeting which would take years of computations using exhaustive search.
Biochemistry & Molecular Biology↗
Networks of neuroinjury semantic predications to identify biomarkers for mild traumatic brain injury
Objective: Mild traumatic brain injury (mTBI) has high prevalence in the military, among athletes, and in the general population worldwide (largely due to falls). Consequences can include a range of neuropsychological disorders. Unfortunately, such neural injury often goes undiagnosed due to the difficulty in identifying symptoms, so the discovery of an effective biomarker would greatly assist diagnosis; however, no single biomarker has been identified. We identify several body substances as potential components of a panel of biomarkers to support the diagnosis of mild traumatic brain injury. Methods: Our approach to diagnostic biomarker discovery combines ideas and techniques from systems medicine, natural language processing, and graph theory. We create a molecular interaction network that represents neural injury and is composed of relationships automatically extracted from the literature. We retrieve citations related to neurological injury and extract relationships (semantic predications) that contain potential biomarkers. After linking all relationships together to create a network representing neural injury, we filter the network by relationship frequency and concept connectivity to reduce the set to a manageable size of higher interest substances. Results: 99,437 relevant citations yielded 26,441 unique relations. 18,085 of these contained a potential biomarker as subject or object with a total of 6246 unique concepts. After filtering by graph metrics, the set was reduced to 1021 relationships with 49 unique concepts, including 17 potential biomarkers. Conclusion: We created a network of relationships containing substances derived from 99,437 citations and filtered using graph metrics to provide a set of 17 potential biomarkers. We discuss the interaction of several of these (glutamate, glucose, and lactate) as the basis for more effective diagnosis than is currently possible. This method provides an opportunity to focus the effort of wet bench research on those substances with the highest potential as biomarkers for mTBI.
59 BASIC BIOLOGICAL SCIENCES↗
Weighting and Bayes Nets for Rollup of Surveillance Metrics
The LANL IKE team proposes that the surveillance metrics for several data stream that are used to detect the same failure mode be weighted. Similarly, the failure mode metrics are weighted to obtain a subsystem metric.
97 MATHEMATICS AND COMPUTING↗
The dynamic sphere test problem
In this manuscript we define the dynamic sphere problem as a spherical shell composed of a homogeneous, linearly elastic material. The material exhibits either isotropic or transverse isotropic symmetry. When the problem is formulated in material coordinates, the balance of mass equation is satisfied automatically. Also, the material is assumed to be kept at constant temperature, so the only relevant equation is the equation of motion. The shell has inner radius r i and outer radius r o . Initially, the shell is at rest. We assume that the interior of the shell is a void and we apply a time-varying radial stress on the outer surface.
97 MATHEMATICS AND COMPUTING↗
Uncertainty Quantification of Hypothesis Testing for the Integrated Knowledge Engine
The Integrated Knowledge Engine (IKE) is a tool of Bayesian analysis, based on Bayesian Belief Networks or Bayesian networks for short. A Bayesian network is a graphical model (directed acyclic graph) that allows representing the probabilistic structure of many variables assuming a localized type of dependency called the Markov property. The Markov property in this instance makes any node or random variable to be independent of any non-descendant node given information about its parent. A direct consequence of this property is that it is relatively easy to incorporate new evidence and derive the appropriate consequences, which in general is not an easy or feasible task. Typically we use Bayesian networks as predictive models for a small subset of the variables, either the leave nodes or the root nodes. In IKE, since most applications deal with diagnostics, we are interested in predicting the likelihood of the root nodes given new observations on any of the children nodes. The root nodes represent the various possible outcomes of the analysis, and an important problem is to determine when we have gathered enough evidence to lean toward one of these particular outcomes. This document presents criteria to decide when the evidence gathered is sufficient to draw a particular conclusion or decide in favor of a particular outcome by quantifying the uncertainty in the conclusions that are drawn from the data. The material in this document is organized as follows: Section 2 presents briefly a forensics Bayesian network, and we explore evaluating the information provided by new evidence by looking first at the posterior distribution of the nodes of interest, and then at the corresponding posterior odds ratios. Section 3 presents a third alternative: Bayes Factors. In section 4 we finalize by showing the relation between the posterior odds ratios and Bayes factors and showing examples these cases, and in section 5 we conclude by providing clear guidelines of how to use these for the type of Bayesian networks used in IKE.
97 MATHEMATICS AND COMPUTING↗
Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?
The power iteration method is the standard Monte Carlo approach for obtaining the eigenfunctions of a nuclear system, but the power method sometimes converges very slowly. Most discussions give a mathematical reason for the slow convergence of the Monte Carlo power method using the same concepts and terminology as when the power method is applied to a deterministic problem. This note first looks at why the convergence is slow from an intuitive Monte Carlo neutron perspective. Second, this note proposes building an eigenfunction intuitively in a cumulative (and noniterative) neutron by neutron manner that tends to better direct neutrons to where the neutrons need to be. Third, a very similar method for building the second eigenfunction is speculatively proposed.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Fast 3D Surface Extraction
Ocean scientists searching for isosurfaces and/or thresholds of interest in high resolution 3D datasets required a tedious and time-consuming interactive exploration experience. PISTON research and development activities are enabling ocean scientists to rapidly and interactively explore isosurfaces and thresholds in their large data sets using a simple slider with real time calculation and visualization of these features. Ocean Scientists can now visualize more features in less time, helping them gain a better understanding of the high resolution data sets they work with on a daily basis. Isosurface timings (512 3 grid): VTK 7.7 s, Parallel VTK (48-core) 1.3 s, PISTON OpenMP (48-core) 0.2 s, PISTON CUDA (Quadro 6000) 0.1 s.
97 MATHEMATICS AND COMPUTING↗
Image processing and reconstruction [Slides]
This talk will examine some mathematical methods for image processing and the solution of underdetermined, linear inverse problems. The talk will have a tutorial flavor, mostly accessible to undergraduates, while still presenting research results. The primary approach is the use of optimization problems. We will find that relaxing the usual assumption of convexity will give us much better results.
97 MATHEMATICS AND COMPUTING↗
Simulation and Analysis of Converging Shock Wave Test Problems
Results and analysis pertaining to the simulation of the Guderley converging shock wave test problem (and associated code verification hydrodynamics test problems involving converging shock waves) in the LANL ASC radiation-hydrodynamics code xRAGE are presented. One-dimensional (1D) spherical and two-dimensional (2D) axi-symmetric geometric setups are utilized and evaluated in this study, as is an instantiation of the xRAGE adaptive mesh refinement capability. For the 2D simulations, a 'Surrogate Guderley' test problem is developed and used to obviate subtleties inherent to the true Guderley solution's initialization on a square grid, while still maintaining a high degree of fidelity to the original problem, and minimally straining the general credibility of associated analysis and conclusions.
97 MATHEMATICS AND COMPUTING↗
Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach? Part 2
The recent work 'Is the Standard Monte Carlo Power Iteration Approach the Wrong Approach?' speculated that the second eigenfunction could be built using essentially the same 'building brick' approach that obtained the first eigenfunction in LA-UR-12-21928. This note shows that the speculation was at least partially correct, but not complete.
97 MATHEMATICS AND COMPUTING↗
MCMini: Monte Carlo on GPGPU
MCMini is a proof of concept that demonstrates the possibility for Monte Carlo neutron transport using OpenCL with a focus on performance. This implementation, written in C, shows that tracing particles and calculating reactions on a 3D mesh can be done in a highly scalable fashion. These results demonstrate a potential path forward for MCNP or other Monte Carlo codes.
97 MATHEMATICS AND COMPUTING↗
Moment of Fluid Interface Reconstruction with Filaments [Slides]
A moving system made up of multiple fluids (e.g. air and water) may be defined by an evolving interface with a changing topology. MOF uses a piecewise linear interface reconstruction to numerically model deforming boundaries. Given a volume fraction V and reference centroid x for a material in cell Ω, we seek to find an interface Γ that exactly captures V and minimizes error in x. This differs from Volume of Fluid methods.
97 MATHEMATICS AND COMPUTING↗
Role of the site of synaptic competition and the balance of learning forces for Hebbian encoding of probabilistic Markov sequences
The majority of distinct sensory and motor events occur as temporally ordered sequences with rich probabilistic structure. Sequences can be characterized by the probability of transitioning from the current state to upcoming states (forward probability), as well as the probability of having transitioned to the current state from previous states (backward probability). Despite the prevalence of probabilistic sequencing of both sensory and motor events, the Hebbian mechanisms that mold synapses to reflect the statistics of experienced probabilistic sequences are not well understood. Here, we show through analytic calculations and numerical simulations that Hebbian plasticity (correlation, covariance, and STDP) with pre-synaptic competition can develop synaptic weights equal to the conditional forward transition probabilities present in the input sequence. In contrast, post-synaptic competition can develop synaptic weights proportional to the conditional backward probabilities of the same input sequence. We demonstrate that to stably reflect the conditional probability of a neuron’s inputs and outputs, local Hebbian plasticity requires balance between competitive learning forces that promote synaptic differentiation and homogenizing learning forces that promote synaptic stabilization. The balance between these forces dictates a prior over the distribution of learned synaptic weights, strongly influencing both the rate at which structure emerges and the entropy of the final distribution of synaptic weights. Together, these results demonstrate a simple correspondence between the biophysical organization of neurons, the site of synaptic competition, and the temporal flow of information encoded in synaptic weights by Hebbian plasticity while highlighting the utility of balancing learning forces to accurately encode probability distributions, and prior expectations over such probability distributions.
59 BASIC BIOLOGICAL SCIENCES↗
Motivating the sure bounds
Motivation is provided for a theorem that provides upper and lower bounds for the reliability of reconfigurable digital control systems. The reliability goals for these systems are too high to be established by natural life testing, which means the probability of system failure must be computed from mathematical models that capture the essential elements of fault occurence and system fault recovery. The upper and lower bound theorem shows that system recovery can be adequately described by its first two moments, provided component failure rate is low and system recovery is fast. This result greatly simplifies both the fault injection experiments that study system recovery and the numerical computations that estimate the probability of system failure from a mathematical model.
White, Allan L.↗