Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Level Set Method”

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 523 records · Page 29
All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Combining diagnostics, modeling, and control systems for automated alignment of the TES beamline

X-ray beamlines are essential components of all synchrotron light sources. Practical operations involve frequent variation in beamline component positions and orientation, particularly when photon beam parameters shift due to experimental needs, or due to variations in the incoming photon beam. The alignment process can be time consuming and takes away from valuable beam time for experimental data collection. We describe progress in the automation of certain alignment tasks on the tender-energy X-ray spectroscopy (TES) beamline at the National Synchrotron Light Source II (NSLS-II). The beamline is controlled using the BlueSky software in which high level experimental plans guide the beamline components during an experiment. Numerous software packages exist for beamline modeling, and they may be tied to the beamline control system using a package we are continuing to develop called Sirepo-Bluesky. The photon beam distribution may be measured with fluorescent screens, and a relation between beam and machine state can be found by varying the mirror and aperture settings over a multi-dimensional range. We describe the results of such parameter varying measurements and how we are combining Sirepo-Bluesky with machine learning methods and reduced models to automate mirror alignment on the TES beamline.

36 MATERIALS SCIENCE↗
DOE OSTI2024

Enhancing Photosynthesis Simulation Performance in ESMs with Machine Learning-Assisted Solvers

When simulating vegetation dynamics, photosynthesis accounts for a large fraction of the computational cost in most Earth System Models (ESMs). This is largely since photosynthesis is represented as a system of nonlinear equations, and the solution requires the use of an initial guess followed by many iterations of the numerical solver to obtain a solution. We use machine learning (ML) to replicate the response surface of the model’s numerical solver to improve the choice of initial guess, therefore requiring fewer iterations to obtain a final solution. We implemented this test on the leaf-level calculations as well as at the canopy scale, and for both we observed fewer iterations of the photosynthesis solver when a ML-based initial guess was implemented. The model tested here is the Energy Exascale Earth System Model - Land Model (ELM). The ML-based algorithms used here are trained on simulations from the model itself and used only to improve the initial guess for the solver; therefore, the model maintains its own set of physics to obtain the final solution. This work shows novel ways to utilize ML-based methods to improve the performance of numerical solvers in ESMs.

Massoud, Elias [ORNL] (ORCID:0000000217725361)↗
DOE OSTI2024

Verification of Adaptive Protection in Hardware in the Loop for Coordination with Solar Variability

As inverter-based resources continue to be installed at all levels of the electric grid, the fixed protection schemes used at the distribution level will continue to be stressed until they no longer ensure the protection of the grid. Adaptive protection has been proposed as a solution with the ability to update the protection schemes in near real-time to ensure reliability and increase the resilience of the grid. However, weather variability poses a significant challenge to the ability of these methods to keep the selectivity and reliability of these schemes coordinated. If the ramp rates, due to solar variability, of the inverter-based resources change faster than the adaptive protection can issue new settings, the protection system could be uncoordinated, with the wrong device responding to a system fault. The proposed adaptive protection method ensures that due to solar variability, communication, and protection calculation latency, it can issu e coordinated protection settings promptly, in one minute or less. The hardware-in-the-loop results show the protection settings being issued and maintaining system coordination in under a minute.

Summers, Adam↗
DOE OSTI2024

Assessing thermal comfort and participation in residential demand flexibility programs

Residential space-conditioning-based demand flexibility (DF) has become an increasingly sought-after method for demand-side load management to enhance grid reliability and facilitate integration of renewable energy generation. However, predicting the effectiveness and flexibility of residential DF resources is challenging due to the variability in household energy use behaviors. Current estimates show that only 50 % of projected savings from DF resources are actualized due to regulatory, technological, and social barriers. From a household perspective, concerns over thermal comfort during space conditioning-based DF events significantly impact participation decisions. Currently, there is a very limited understanding of how thermal comfort during space-conditioning-based DF events in real-world settings impacts household energy use behaviors and, consequently, the success of DF programs in achieving targeted savings. This paper proposes a method to comprehensively assess the thermal comfort implications of DF strategies and presents results of their impacts on DF event participation decisions and demand savings. Here, the proposed method was applied to a heat pump DF field study in Cordova, Alaska. The study’s key findings are: 1) DF event setpoint offsets that maintain indoor operative temperatures between 18 to 22 °C (65 to 71°F) may be preferred in Cordova, Alaska; 2) Household-level thermal comfort is more sensitive to the duration of the DF event than to the degree of temperature offset from baseline conditions; 3) The delayed impact of changes in indoor operative temperature in response to setpoint offsets, both during and after a DF event, influences occupants’ thermal comfort perceptions and willingness to persistently participate in events. The findings from application of the proposed method can help inform future larger-scale occupant-centric DF programs as it can capture information not readily available through utility and device-level energy use data. Thus, it can supplement these sources and help program administrators develop occupant-centric DF strategies, enabling more accurate predictions of participation rates and savings estimates for space-conditioning-based DF programs.

Demand side management↗
DOE OSTI2024

A static quantum embedding scheme based on coupled cluster theory

Here, we develop a static quantum embedding scheme that utilizes different levels of approximations to coupled cluster (CC) theory for an active fragment region and its environment. To reduce the computational cost, we solve the local fragment problem using a high-level CC method and address the environment problem with a lower-level Møller–Plesset (MP) perturbative method. This embedding approach inherits many conceptual developments from the hybrid second-order Møller–Plesset (MP2) and CC works by Nooijen [J. Chem. Phys. 111, 10815 (1999)] and Bochevarov and Sherrill [J. Chem. Phys. 122, 234110 (2005)]. We go beyond those works here by primarily targeting a specific localized fragment of a molecule and also introducing an alternative mechanism to relax the environment within this framework. We will call this approach MP-CC. We demonstrate the effectiveness of MP-CC on several potential energy curves and a set of thermochemical reaction energies, using CC with singles and doubles as the fragment solver, and MP2-like treatments of the environment. The results are substantially improved by the inclusion of orbital relaxation in the environment. Using localized bonds as the active fragment, we also report results for N=N bond breaking in azomethane and for the central C–C bond torsion in butadiene. We find that when the fragment Hilbert space size remains fixed (e.g., when determined by an intrinsic atomic orbital approach), the method achieves comparable accuracy with both a small and a large basis set. Additionally, our results indicate that increasing the fragment Hilbert space size systematically enhances the accuracy of observables, approaching the precision of the full CC solver.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Reference document for LANL stack sampling and ANSI N13.1 (Article) Gielow RL and McNamee MR 1993. Numerical Flue Gas Flow Modeling for Continuous Emissions Monitoring Applications. EPRI CEM Users Group Meeting. Baltimore. RP1961-13

American National Standard N13.1 “sets forth guidelines and performance criteria for sampling the emissions of airborne radioactive substances in the air discharge ducts and stacks of nuclear facilities. Emphasis is on extractive sampling from a location in a stack or duct where the contaminant is well mixed. At such a location, sampling may be conducted at a single point. This standard provides performance-based criteria for the use of air sampling probes, transport lines, sample collectors, sample monitoring instruments, and gas flow measuring methods. This standard also covers sampling program objectives, quality assurance issues, developing air sampling action levels, system optimization, and system performance verification. Workplace, containment, and environmental air monitoring are not addressed. Specific sample analysis methods and the reporting or interpreting of results are also not addressed.” (HPS 2011).

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2024

Engineered living materials for capture, conversion, and recycling technologies

Continued dependence on crude oil and natural gas resources for fossil fuels has caused global atmospheric carbon dioxide (CO 2 ) emissions to increase to record-setting proportions. There is an urgent need for efficient and inexpensive carbon sequestration systems to mitigate large-scale CO 2 emissions from industrial flue gas. Carbonic anhydrase (CA) has shown high potential for enhanced CO 2 capture applications compared to conventional absorption-based methods currently utilized in various industrial settings. This study aims to understand structural aspects that contribute to the stability of CA enzymes critical for their applications in industrial processes, which require the ability to withstand conditions different from their native environments. Here, we evaluated the thermostability and enzyme activity of mesophilic and thermophilic CA variants at different temperature conditions and in the presence of atmospheric gas pollutants like nitrogen oxides (NO x ) and sulphur oxides (SO x ). Based on our enzyme activity assays and molecular dynamics simulations, we see increased conformational stability and CA activity levels in thermostable CA variants incubated week-long at different temperature conditions. The thermostable CA variants also retained high levels of CA activity despite changes in solution pH due to increasing NO x and SO x concentrations. Furthermore, a loss of CA activity was observed only at high concentrations of NO x /SO x that possibly can be minimized with appropriate buffered solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

First M87 Event Horizon Telescope Results. VII. Polarization of the Ring

In 2017 April, the Event Horizon Telescope (EHT) observed the near-horizon region around the supermassive black hole at the core of the M87 galaxy. These 1.3 mm wavelength observations revealed a compact asymmetric ring-like source morphology. This structure originates from synchrotron emission produced by relativistic plasma located in the immediate vicinity of the black hole. Here we present the corresponding linear-polarimetric EHT images of the center of M87. We find that only a part of the ring is significantly polarized. The resolved fractional linear polarization has a maximum located in the southwest part of the ring, where it rises to the level of ~15%. The polarization position angles are arranged in a nearly azimuthal pattern. We perform quantitative measurements of relevant polarimetric properties of the compact emission and find evidence for the temporal evolution of the polarized source structure over one week of EHT observations. The details of the polarimetric data reduction and calibration methodology are provided. We carry out the data analysis using multiple independent imaging and modeling techniques, each of which is validated against a suite of synthetic data sets. The gross polarimetric structure and its apparent evolution with time are insensitive to the method used to reconstruct the image. These polarimetric images carry information about the structure of the magnetic fields responsible for the synchrotron emission. Their physical interpretation is discussed in an accompanying publication.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2022

Evaluating fast methods for static polarizabilities on extended conjugated oligomers

Given the importance of accurate polarizability calculations to many chemical applications, coupled with the need for efficiency when calculating the properties of sets of molecules or large oligomers, we present a benchmark study examining possible calculation methods for polarizable materials. We first investigate the accuracy of the additive model used in GFN2, a highly-efficient semi-empirical tight-binding method, and the D4 dispersion model, comparing its predicted additive polarizabilities to ωB97XD results for a subset of PubChemQC and a compiled benchmark set of molecules spanning polarizabilities from approximately 3 Å 3 to 600 Å 3 , with some compounds in the range of approximately 1200–1400 Å 3 . Although we find additive GFN2 polarizabilities, and thus D4, to have large errors with polarizability calculations on large conjugated oligomers, it would appear an empirical quadratic correction can largely remedy this. We also compare the accuracy of DFT polarizability calculations run using basis sets of varying size and level of augmentation, determining that a non-augmented basis set may be used for large, highly polarizable species in conjunction with a linear correction factor to achieve accuracy extremely close to that of aug-cc-pVTZ.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Glass Property-Composition Models Update for use in Direct Feed High-Level Waste Flowsheet Development: EWG3.0

A set of preliminary glass property models and constraints were developed and augmented by models from literature for use in design of Direct Feed High-Level Waste glasses for flowsheet evaluation, testing, and design of the High-Level Waste Facility at the Hanford Waste Treatment and Immobilization Plant. These models and constraints are meant to be used as a placeholder while glass property-composition data gaps are filled and final plant operating models are developed. This report describes the motivation and intended use of the models, the compilation of data, model fitting and selection, and methods to apply the models and constraints in glass design, and offers example calculations demonstrating their intended use.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2023

High-Nickel Cathode Materials for High-Energy, Long-Life, Low-Cost Lithium-Ion Batteries (Final Report)

The overall goal of this project is to produce Li-ion cells, which deliver at least 600 Wh kg -1 at the cathode level with usable lifetimes of at least 1,000 cycles or 15 years of storage (calendar life). A secondary goal of this project is to minimize the use of cobalt in the cathode, with the ultimate goal of eliminating cobalt entirely. To develop such a cathode, the University of Texas at Austin (UT Austin) team extensively investigated the structural, physical, and chemical properties of layered oxide materials. A panel of dopant elements were surveyed with an emphasis on identifying those, which impart electrochemical and thermal stability. Of those tested, Al and Mg showed the greatest performance improvements while still being easily incorporated into the cathode through simple alterations of the precursor coprecipitation method. Other dopants, such as Ta, Nb, B, and F significantly improved cathode performance, yet their mode of incorporation required additional processing which negated their use under scaled-up conditions. From this work, a first-generation cathode LiNi 0.85 Mn 0.075 Co 0.05 Al 0.02 Mg 0.005 O 2 (NMCAM-85) was produced and an initial set of 2 Ah cells was fabricated by Tesla Inc. These cells delivered 650 Wh kg -1 and a cycle life of just over 700 cycles. Further improvements were garnered through careful study of electrolyte additives. A tailored, ethylene carbonate (EC)-free electrolyte was developed, which improved capacity retention from 60% to 82% after 500 cycles in model LiNi 0.9 Mn 0.05 Al 0.05 O 2 (NMA-90) full cells. This study identified the additives fluoroethylene carbonate (FEC) and lithium difluorophosphate (LiPO 2 F 2 ) as beneficial additives, which were included in the electrolyte for the end-of-project cells. The UT Austin team developed a high-Ni layered oxide cathode LiNi 0.85 Mn 0.1 Al 0.05 Mg 0.005 O 2 (NMAM-85) capable of meeting the project goals. This cathode was synthesized in kilogram quantities and delivered to Tesla for fabrication into 2 Ah pouch cells for DOE testing. These large-format cells achieved 630 Wh kg -1 at the cathode level under the designated testing parameters, meeting the project goal with a completely cobalt-free cathode. The large-format cells are currently undergoing cycle life and calendar life evaluation at Idaho National Lab.

25 ENERGY STORAGE↗
DOE OSTI2025

Global bases for nonplanar loop integrands, generalized unitarity, and the double copy to all loop orders

We introduce a constructive method for defining a global loop-integrand basis for scattering amplitudes, encompassing both planar and nonplanar contributions. Our approach utilizes a graph-based framework to establish a well-defined, non-redundant basis of integrands. This basis, constructed from a chosen set of non-redundant graphs together with a selection of irreducible scalar products, provides clear insights into various physical properties of scattering amplitudes and proves useful in multiple contexts, such as on-shell Ward identities and manifesting gauge-choice independence. A key advantage of our integrand basis is its ability to streamline the generalized unitarity method. Specifically, we can directly read off the coefficients of basis elements without resorting to ansätze or solving linear equations. This novel approach allows us to lift generalized unitarity cuts — expressed as products of tree amplitudes — to loop-level integrands, facilitating the use of the tree-level double copy to generate complete gravitational integrands at any loop order. This method circumvents the difficulties in identifying complete higher-loop-order gauge-theory integrands that adhere to the color-kinematics duality. Additionally, our cut-based organization is well-suited for expansion in hard or soft limits, aiding in the exploration of ultraviolet or classical limits of scattering amplitudes.

Effective Field Theories↗
DOE OSTI2024

Direct Feed High-Level Waste APPS Model Glass Testing (DFHLW APPS) Matrix

This report summarizes the data collected during the batching and melting of the Direct Feed High-Level Waste APPS Model Glass Matrix (DFHLW APPS) to serve as a quality-assured validation of the Aspen Process Performance Simulation (APPS) formulation method. Of 15 glasses tested, 12 satisfied all target property constraints. Two glasses, APPS-05 and -06, formed nepheline on canister centerline cooling heat-treatment and failed the Product Consistency Test response limits. Glass APPS-07-2 formed unacceptably high concentrations of crystals (primarily Na3Nd(PO4)2) when heat treated at 950 °C. All other glasses were found to be satisfactory. The measured property values were compared to predicted values from a set of current models. In many cases the current models were found to be inadequate for design of DFHLW glasses. These models are being adjusted to correct for mispredictions. Other models, e.g., density, toxicity characteristic leaching procedure, and sulfur solubility, are adequate for formulation of DFHLW glasses.

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2020

Using Digital and Web-Based Platforms to Enhance Nuclear Power Plant Knowledge Transfer - 20203

As the workforce ages, the loss of experienced personnel can result in a loss of important knowledge. Updating Electric Power Research Institute (EPRI) research and guidance with the latest technology developments and operating experience is an important method to transfer knowledge between the retiring and incoming workforce. Studies suggest that the incoming workforce is accustomed to using digital and/or internet-based platforms to find information and may have a higher comfort with these types of platforms than they have with static, written reports. Additionally, the ease and speed of updating and delivering content through digital formats may offer an effective method for knowledge transfer and combining information from multiple reports into a single access point. EPRI has recently produced an online Decommissioning Hub available to members and is working on replicating the effort in the area of radioactive waste management called the Radwaste Web References. EPRI has extensive guidance in both disciplines. The Decommissioning Hub uses a wiki format to provide a platform that allows for both the updating of that guidance resulting from new research and new operating experiences, and combining related topical information from multiple reports. It also allows users to access the information based on key words and topical searches, and can be a tool for users to input experience to share with others. The Decommissioning Hub is accessed via a web-based portal and includes topical pages; experience summaries; a question and answer capability; and a smart search function of all EPRI decommissioning reports. Use of a wiki format allows users to input new experiences or modify existing experience summaries to add additional detail. EPRI moderates all content. The experience data base has been initially populated with information available in published EPRI reports and unpublished information currently available within EPRI. Moving forward, population of the database will continue with information available within the open literature, new information developed from current decommissioning projects, and user inputs. The web site became active in late 2017, and a major update will be issued in early 2020. Larger scale updates are planned biannually, and smaller-scale updates will occur continuously. Capturing and applying lessons learned from industry experiences is a hallmark of the global nuclear industry. This is even more important in the decommissioning technology area since very few plant staff have relevant experience and thus there is a steep learning curve. Moreover, decommissioning involves a number of complex, non-routine and specialized tasks. The web-accessible and searchable experience database provides an easy-to-use resource for capturing and disseminating practical experiences from completed and ongoing decommissioning projects. The EPRI Radwaste Web References will build upon the philosophy and objectives of the Radwaste Desk References that were published in the 1990's. The purpose of the original Radwaste Desk References was to provide nuclear power plant professionals with a how-to manual for managing radioactive waste. The Radwaste Web References will adopt this original purpose and will be a wiki type web site that provide fundamental practical and theoretical information, operating experience (OE), and information about advanced technologies and methods. As much as practicable, features that allow for interaction between users to share OE, best practices, and benchmarking will be added. Where they exist and are appropriate, the various EPRI Guidelines documents on radwaste topics will be updated and incorporated into the Radwaste Web References. The first Radwaste Web Reference will be on Low Level Waste Characterization and will build upon the EPRI Low Level Waste Characterization Guidelines (EPRI Report TR-107201, 1996) and will be available in 2020. The next Radwaste Web Reference will be on the topic of liquid radioactive waste processing and management, tentatively set for unveiling in 2021. This paper summarizes the EPRI's previous experiences with web-based platforms and future plans in this area. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2026

Continual Learning for Production-Level Machine Learning in Particle Accelerators

Particle accelerators operate in complex environments where data distribution can change dynamically, leading to data drifts that significantly challenge Machine Learning (ML) models. These non-stationary conditions often cause ML models to deteriorate in performance, making it difficult to maintain reliable predictions in operation. The primary sources of data drifts are changes in accelerator settings and changes in equipment performance which cannot be measured directly. To bridge this gap between ML development and long-term deployment in operational settings, we identify key areas within particle accelerators where continual learning can help mitigate drift-induced performance degradation. We will provide a practical guide on selecting the appropriate method given resource constraints and desired stability plasticity trade offs. As a concrete example, we will present a real-world use case for anomaly detection to predict errant beams at the Spallation Neutron Source accelerator, where continual learning has been employed to demonstrate stable performance on drifting data streams. We will present practical challenges, lessons learned, and the results from the deployed ML model.

Rajput, Kishansingh [Thomas Jefferson National Acc↗
DOE OSTI2022

Operational Probabilistic Tools for Solar Uncertainty (OPTSUN) (Final Project Report for DOE Solar Forecasting II Project)

Increasing levels of solar PV can challenge system operations and may require novel methods to operate the power system reliably and efficiently. Power system operating plans generally use deterministic forecasts, in which the variable energy resources are represented by the expected value for each interval of the decision horizon. Probabilistic forecasts are relatively new but have the potential to address the shortfalls of deterministic forecasts. However, understanding how best to use such forecasts is still a key gap in industry and was the focus of this project. The project had three workstreams. In a forecasting workstream, improvements were made to baseline probabilistic forecasts using a number of new approaches such as machine learning methods and improved input data. In a design workstream, advanced simulation tools used these forecasts to investigate newly proposed reserve determination methods. Lastly, in a demonstration workstream a scheduling management platform (SMP) was developed to leverage probabilistic forecasts in a modular and customizable manner. In order to study the benefits that could be accrued, the project team collaborated with three utility partners (Duke Energy, Southern Company and Hawaiian Electric) to deliver improved probabilistic forecasts for each region and to model each region in case studies using advanced production cost modeling tools. Different methods to determine operating reserve requirements from probabilistic forecasts were developed, simulated, and tested across each region. The benefits of using these newly proposed methods varied by utility, but, in general, using probabilistic forecasts as well as historical data to set the reserve requirements seems to improve reliability related results, with less risk of reserve or supply shortfalls. The cost implications were not always straightforward; in some cases the new methods could show a reduction in expected operating costs, but often the increase in reserves associated with better risk mitigation using probabilistic forecasts could result in an increase in operating costs in the simulations. The SMP tool was developed to process probabilistic forecasts from their initial receipt through to scheduling decisions. This open-source tool consists of several modules for scenario development, reserve requirements calculation, and visualization. The SMP tool was demonstrated to a wide range of operators and stakeholders at all three utilities and further improved based on their feedback. The tool will be available on www.epri.com/optsun. The proposed probabilistic information-based reserve determination approaches have the potential to be implemented by different regions to ensure an economic and reliable power system operation on power systems integrating increasing levels of variable renewable resources. The innovative yet practical methods developed in this project demonstrated tangible benefits from using probabilistic forecasts beyond just study-based assessments to include three unique balancing areas. The demonstrated benefits across the multiple utility environments, are expected to provide system operators in all regions the confidence required and a platform to adopt the new forecasting and operating methods.

14 SOLAR ENERGY↗
DOE OSTI2025

Full event particle-level unfolding with variable-length latent variational diffusion

The measurements performed by particle physics experiments must account for the imperfect response of the detectors used to observe the interactions. One approach, unfolding, statistically adjusts the experimental data for detector effects. Recently, generative machine learning models have shown promise for performing unbinned unfolding in a high number of dimensions. However, all current generative approaches are limited to unfolding a fixed set of observables, making them unable to perform full-event unfolding in the variable dimensional environment of collider data. A novel modification to the variational latent diffusion model (VLD) approach to generative unfolding is presented, which allows for unfolding of high- and variable-dimensional feature spaces. The performance of this method is evaluated in the context of semi-leptonic t\bar{t} t t ‾ production at the Large Hadron Collider.

Shmakov, Alexander↗
DOE OSTI2023

Topological structure of complex predictions

Abstract Current complex prediction models are the result of fitting deep neural networks, graph convolutional networks or transducers to a set of training data. A key challenge with these models is that they are highly parameterized, which makes describing and interpreting the prediction strategies difficult. We use topological data analysis to transform these complex prediction models into a simplified topological view of the prediction landscape. The result is a map of the predictions that enables inspection of the model results with more specificity than dimensionality-reduction methods such as tSNE and UMAP. The methods scale up to large datasets across different domains. We present a case study of a transformer-based model previously designed to predict expression levels of a piece of DNA in thousands of genomic tracks. When the model is used to study mutations in the BRCA1 gene, our topological analysis shows that it is sensitive to the location of a mutation and the exon structure of BRCA1 in ways that cannot be found with tools based on dimensionality reduction. Moreover, the topological framework offers multiple ways to inspect results, including an error estimate that is more accurate than model uncertainty. Further studies show how these ideas produce useful results in graph-based learning and image classification.

Computer Science↗