Results for “shared error” — Page 11

DOE OSTI2014

spammpack, Version 2013-06-18

This library is an implementation of the Sparse Approximate Matrix Multiplication (SpAMM) algorithm introduced. It provides a matrix data type, and an approximate matrix product, which exhibits linear scaling computational complexity for matrices with decay. The product error and the performance of the multiply can be tuned by choosing an appropriate tolerance. The library can be compiled for serial execution or parallel execution on shared memory systems with an OpenMP capable compiler

Source record↗

DOE OSTI2021

A Contrast Calibration Protocol for X-ray Speckle Visibility Spectroscopy

X-ray free electron lasers, with their ultrashort highly coherent pulses, opened up the opportunity of probing ultrafast nano- and atomic-scale dynamics in amorphous and disordered material systems via speckle visibility spectroscopy. However, the anticipated count rate in a typical experiment is usually low. Therefore, visibility needs to be extracted via photon statistics analysis, i.e., by estimating the probabilities of multiple photons per pixel events using pixelated detectors. Considering the realistic X-ray detector responses including charge cloud sharing between pixels, pixel readout noise, and gain non-uniformity, speckle visibility extraction relying on photon assignment algorithms are often computationally demanding and suffer from systematic errors. In this paper, we present a systematic study of the commonly-used algorithms by applying them to an experimental data set containing small-angle coherent scattering with visibility levels ranging from below 1% to ∼60%. We also propose a contrast calibration protocol and show that a computationally lightweight algorithm can be implemented for high-speed correlation evaluation.

47 OTHER INSTRUMENTATION↗

DOE OSTI2014

spammpack, Version 2013-06-18

This library is an implementation of the Sparse Approximate Matrix Multiplication (SpAMM) algorithm introduced. It provides a matrix data type, and an approximate matrix product, which exhibits linear scaling computational complexity for matrices with decay. The product error and the performance of the multiply can be tuned by choosing an appropriate tolerance. The library can be compiled for serial execution or parallel execution on shared memory systems with an OpenMP capable compiler

Source record↗

DOE OSTI2015

Scalable tuning of building models to hourly data

Energy models of existing buildings are unreliable unless calibrated so they correlate well with actual energy usage. Manual tuning requires a skilled professional, is prohibitively expensive for small projects, imperfect, non-repeatable, non-transferable, and not scalable to the dozens of sensor channels that smart meters, smart appliances, and cheap/ubiquitous sensors are beginning to make available today. A scalable, automated methodology is needed to quickly and intelligently calibrate building energy models to all available data, increase the usefulness of those models, and facilitate speed-and-scale penetration of simulation-based capabilities into the marketplace for actualized energy savings. The "Autotune'' project is a novel, model-agnostic methodology which leverages supercomputing, large simulation ensembles, and big data mining with multiple machine learning algorithms to allow automatic calibration of simulations that match measured experimental data in a way that is deployable on commodity hardware. This paper shares several methodologies employed to reduce the combinatorial complexity to a computationally tractable search problem for hundreds of input parameters. Furthermore, accuracy metrics are provided which quantify model error to measured data for either monthly or hourly electrical usage from a highly-instrumented, emulated-occupancy research home.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗

DOE OSTI2023

Outcomes of WPEC SG47 on "Use of Shielding Integral Benchmark Archive and Database for Nuclear Data Validation"

The Working Party on International Nuclear Data Evaluation Co-operation Subgroup 47 (WPECSG47) entitled "Use of Shielding Integral Benchmark Archive and Database for Nuclear Data Validation" was organised from 2019 and 2022 with the objectives to promote more systematic and wider use of shielding benchmark experiments in nuclear data (ND) and transport code validation and development, to provide feedback on the Shielding Integral Benchmark Archive and Database (SINBAD), and to promote its further development in coordination with the Expert Group on Physics of Reactor Systems (EGPRS). Altogether 9 meetings, the large majority (8) held remotely, were organised during the past 3 years to discuss the experience on the use of SINBAD, evaluation of new benchmarks and improvements to be contributed to the database which was severely neglected and lacking maintenance over the past ← 10+ years. Several proposals for new or updated benchmark evaluation were presented and discussed, such as FNG copper, LLNL pulsed spheres, CIAE iron sphere, KFK 1977 gamma measurements, Rez Fe sphere, ASPIS, ORNL Oxygen broomstick, TIARA and others. Complementing the database with new features was also discussed, for example providing the nuclear data sensitivity profiles more systematically would facilitate and better guide the use of data. Information on the geometry, (radiation source) and materials available in CAD format is expected to allow an easier and less error prone reference for computational model preparation and a potential input to CAD based workflows. Inputs for various transport codes and other benchmark data from participants have been shared via the NEA GitLab which could hopefully in the future evolve and form a bases for critically checked and validated benchmark data. Future development of SINBAD will be monitored by EGPRS and the newly created SINBAD Task Force.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗

DOE OSTI2014

MO-C-BRD-01: SBRT I: Overview of Simulation, Planning, and Delivery

SBRT is having a dramatic impact on radiation therapy of early-stage, locally advanced cancers. Treatment planning of SBRT is characterized by precise target volume delineation, highly conformal dose distribution, sharp dose gradient outside the target volume, and meticulous tumor motion management. Stringent dose volume constraints of SBRT require the treatment planning to be highly personalized. Not only the complete patient's medical information (anatomy, tumor size/shape/location/motion, breathing pattern, health status) should be taken into consideration during planning, but also a wide range of factors including imaging techniques (imaging modality, breathing control, immobilization, patient position, etc.), treatment planning techniques (3D-conformal, dynamic conformal arcs, IMRT, VMAT, etc.), image guidance techniques (CBCT, orthogonal X-Ray, fiducial marker tracking, fluoroscopy, etc.), and delivery techniques (FFF, gating, tracking, etc.). In addition, potential pitfalls may exist in SBRT techniques and processes, such as target volume error in 4DCT and image registration error in image guidance. How to manage these affecting factors to achieve optimal, personalized SBRT treatment plans remains a great challenge. In this proposal, we will review technologies, share experiences, and discuss strategies concerning SBRT simulation, planning, and delivery. Learning Objectives: Understand requirements and challenges of SBRT treatment planning Discuss information-driven strategies of developing optimal SBRT plans Discuss practical considerations and potential pitfalls of SBRT treatment planning.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2026

ObstacleSense: Low-Power Neuromorphic Vision for Corridor Obstacle Awareness in Low-Level ADAS

The automotive industry’s pursuit of Level 5 autonomy is constrained by substantial perception-compute power requirements, often reaching 1, 000 + watts in full autonomy stacks. Reducing this energy burden requires rethinking perception not only at the high-end autonomy level, but also at the foundational Advanced Driver Assistance Systems (ADAS) level where low-power, safety-critical sensing can have broad impact. Neuromorphic vision provides a promising starting point: HD Dynamic Vision Sensors (DVS) can operate below 100 mW at the sensor level by reporting only asynchronous brightness changes. However, low-power sensing alone is insufficient if downstream perception reintroduces dense, energy-intensive computation. In particular, many event-driven object-detection pipelines still rely on CNN backbones, while purely spiking alternatives often trade away accuracy or ignore deployment constraints. We introduce ObstacleSense, a highly compact, CNN-free hybrid ANN–SNN framework for Level 0–1 forward-corridor obstacle awareness. Instead of performing full-scene object detection with a convolutional feature backbone, ObstacleSense targets the safety-critical question of whether the ego corridor is occupied and how far the nearest obstacle is. The architecture combines polarity-conditioned event encoding, lightweight temporal spiking dynamics, axial spatial mixing, and coarse-to-fine range estimation within a regular fixed-grid compute pattern. This design avoids the dense CNN backbone commonly used in event-based detection while maintaining a small state footprint suitable for eventual small-FPGA deployment. Before hardware mapping, we evaluate the software implementation using a model-side power proxy derived from MACs, weight and activation traffic, and spiking state updates under shared FP16 assumptions. On simulated CARLA event corpora, the deployment-oriented model achieves 0.9464 objectness F1, 0.9978 grid-level mAP, and 0.8987 m distance Mean Absolute Error at an estimated 1.92 mW proxy cost, while maintaining performance on unseen generalization test sequences.

Johnson-Scott, Zac [ORNL]↗

DOE OSTI2015

TU-CD-BRD-00: Incident Learning / RO-ILS

It has long been standard practice in radiation oncology to report internally when a patient’s treatment has not gone as planned and to report events to regulatory agencies when legally required. Most potential errors are caught early and never affect the patient. Quality assurance steps routinely prevent errors from reaching the patient, and these “near misses” are much more frequent than treatment errors. A growing number of radiation oncology facilities have implemented incident learning systems to report and analyze both errors and near misses. Using the term “incident learning” instead of “event reporting” emphasizes the need to use these experiences to change the practice and make future errors less likely and promote an educational, non-punitive environment. There are challenges in making such a system practical and effective. Speakers from institutions of different sizes and practice environments will share their experiences on how to make such a system work and what benefits their clinics have accrued. Questions that will be addressed include: How to create a system that is easy for front line staff to access How to motivate staff to report How to promote the system as positive and educational and not punitive or demeaning How to organize the team for reviewing and responding to reports How to prioritize which reports to discuss in depth How not to dismiss the rest How to identify underlying causes How to design corrective actions and implement change How to develop useful statistics and analysis tools How to coordinate a departmental system with a larger risk management system How to do this without a dedicated quality manager Some speakers’ experience is with in-house systems and some will share experience with the AAPM/ASTRO national Radiation Oncology Incident Learning System (RO-ILS). Reports intended to be of value nationally need to be comprehensible to outsiders; examples of useful reports will be shown. There will be ample time set aside for audience members to contribute to the discussion. Learning Objectives: Learn how to promote the use of an incident learning system in a clinic. Learn how to convert “event reporting” into “incident learning”. See examples of practice changes that have come out of learning systems. Learn how the RO-ILS system can be used as a primary internal learning system. Learn how to create succinct, meaningful reports useful to outside readers. Gary Ezzell chairs the AAPM committee overseeing RO-ILS and has received an honorarium from ASTRO for working on the committee reviewing RO-ILS reports. Derek Brown is a director of http://TreatSafely.org . Brett Miller has previously received travel expenses and an honorarium from Varian. Phillip Beron has nothing to report.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1993

The ParaScope parallel programming environment

The ParaScope parallel programming environment, developed to support scientific programming of shared-memory multiprocessors, includes a collection of tools that use global program analysis to help users develop and debug parallel programs. This paper focuses on ParaScope's compilation system, its parallel program editor, and its parallel debugging system. The compilation system extends the traditional single-procedure compiler by providing a mechanism for managing the compilation of complete programs. Thus, ParaScope can support both traditional single-procedure optimization and optimization across procedure boundaries. The ParaScope editor brings both compiler analysis and user expertise to bear on program parallelization. It assists the knowledgeable user by displaying and managing analysis and by providing a variety of interactive program transformations that are effective in exposing parallelism. The debugging system detects and reports timing-dependent errors, called data races, in execution of parallel programs. The system combines static analysis, program instrumentation, and run-time reporting to provide a mechanical system for isolating errors in parallel program executions. Finally, we describe a new project to extend ParaScope to support programming in FORTRAN D, a machine-independent parallel programming language intended for use with both distributed-memory and shared-memory parallel computers.

Cooper, Keith D.↗

DOE OSTI2015

TU-CD-BRD-01: Making Incident Learning Practical and Useful: Challenges and Previous Experiences

It has long been standard practice in radiation oncology to report internally when a patient’s treatment has not gone as planned and to report events to regulatory agencies when legally required. Most potential errors are caught early and never affect the patient. Quality assurance steps routinely prevent errors from reaching the patient, and these “near misses” are much more frequent than treatment errors. A growing number of radiation oncology facilities have implemented incident learning systems to report and analyze both errors and near misses. Using the term “incident learning” instead of “event reporting” emphasizes the need to use these experiences to change the practice and make future errors less likely and promote an educational, non-punitive environment. There are challenges in making such a system practical and effective. Speakers from institutions of different sizes and practice environments will share their experiences on how to make such a system work and what benefits their clinics have accrued. Questions that will be addressed include: How to create a system that is easy for front line staff to access How to motivate staff to report How to promote the system as positive and educational and not punitive or demeaning How to organize the team for reviewing and responding to reports How to prioritize which reports to discuss in depth How not to dismiss the rest How to identify underlying causes How to design corrective actions and implement change How to develop useful statistics and analysis tools How to coordinate a departmental system with a larger risk management system How to do this without a dedicated quality manager Some speakers’ experience is with in-house systems and some will share experience with the AAPM/ASTRO national Radiation Oncology Incident Learning System (RO-ILS). Reports intended to be of value nationally need to be comprehensible to outsiders; examples of useful reports will be shown. There will be ample time set aside for audience members to contribute to the discussion. Learning Objectives: Learn how to promote the use of an incident learning system in a clinic. Learn how to convert “event reporting” into “incident learning”. See examples of practice changes that have come out of learning systems. Learn how the RO-ILS system can be used as a primary internal learning system. Learn how to create succinct, meaningful reports useful to outside readers. Gary Ezzell chairs the AAPM committee overseeing RO-ILS and has received an honorarium from ASTRO for working on the committee reviewing RO-ILS reports. Derek Brown is a director of http://TreatSafely.org . Brett Miller has previously received travel expenses and an honorarium from Varian. Phillip Beron has nothing to report.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

TU-CD-BRD-02: Henry Ford Hospital System Experience, with Focus On Motivating and Reviewing

It has long been standard practice in radiation oncology to report internally when a patient’s treatment has not gone as planned and to report events to regulatory agencies when legally required. Most potential errors are caught early and never affect the patient. Quality assurance steps routinely prevent errors from reaching the patient, and these “near misses” are much more frequent than treatment errors. A growing number of radiation oncology facilities have implemented incident learning systems to report and analyze both errors and near misses. Using the term “incident learning” instead of “event reporting” emphasizes the need to use these experiences to change the practice and make future errors less likely and promote an educational, non-punitive environment. There are challenges in making such a system practical and effective. Speakers from institutions of different sizes and practice environments will share their experiences on how to make such a system work and what benefits their clinics have accrued. Questions that will be addressed include: How to create a system that is easy for front line staff to access How to motivate staff to report How to promote the system as positive and educational and not punitive or demeaning How to organize the team for reviewing and responding to reports How to prioritize which reports to discuss in depth How not to dismiss the rest How to identify underlying causes How to design corrective actions and implement change How to develop useful statistics and analysis tools How to coordinate a departmental system with a larger risk management system How to do this without a dedicated quality manager Some speakers’ experience is with in-house systems and some will share experience with the AAPM/ASTRO national Radiation Oncology Incident Learning System (RO-ILS). Reports intended to be of value nationally need to be comprehensible to outsiders; examples of useful reports will be shown. There will be ample time set aside for audience members to contribute to the discussion. Learning Objectives: Learn how to promote the use of an incident learning system in a clinic. Learn how to convert “event reporting” into “incident learning”. See examples of practice changes that have come out of learning systems. Learn how the RO-ILS system can be used as a primary internal learning system. Learn how to create succinct, meaningful reports useful to outside readers. Gary Ezzell chairs the AAPM committee overseeing RO-ILS and has received an honorarium from ASTRO for working on the committee reviewing RO-ILS reports. Derek Brown is a director of http://TreatSafely.org . Brett Miller has previously received travel expenses and an honorarium from Varian. Phillip Beron has nothing to report.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

TU-CD-BRD-03: UCSD Experience, with Focus On Implementing Change

It has long been standard practice in radiation oncology to report internally when a patient’s treatment has not gone as planned and to report events to regulatory agencies when legally required. Most potential errors are caught early and never affect the patient. Quality assurance steps routinely prevent errors from reaching the patient, and these “near misses” are much more frequent than treatment errors. A growing number of radiation oncology facilities have implemented incident learning systems to report and analyze both errors and near misses. Using the term “incident learning” instead of “event reporting” emphasizes the need to use these experiences to change the practice and make future errors less likely and promote an educational, non-punitive environment. There are challenges in making such a system practical and effective. Speakers from institutions of different sizes and practice environments will share their experiences on how to make such a system work and what benefits their clinics have accrued. Questions that will be addressed include: How to create a system that is easy for front line staff to access How to motivate staff to report How to promote the system as positive and educational and not punitive or demeaning How to organize the team for reviewing and responding to reports How to prioritize which reports to discuss in depth How not to dismiss the rest How to identify underlying causes How to design corrective actions and implement change How to develop useful statistics and analysis tools How to coordinate a departmental system with a larger risk management system How to do this without a dedicated quality manager Some speakers’ experience is with in-house systems and some will share experience with the AAPM/ASTRO national Radiation Oncology Incident Learning System (RO-ILS). Reports intended to be of value nationally need to be comprehensible to outsiders; examples of useful reports will be shown. There will be ample time set aside for audience members to contribute to the discussion. Learning Objectives: Learn how to promote the use of an incident learning system in a clinic. Learn how to convert “event reporting” into “incident learning”. See examples of practice changes that have come out of learning systems. Learn how the RO-ILS system can be used as a primary internal learning system. Learn how to create succinct, meaningful reports useful to outside readers. Gary Ezzell chairs the AAPM committee overseeing RO-ILS and has received an honorarium from ASTRO for working on the committee reviewing RO-ILS reports. Derek Brown is a director of http://TreatSafely.org . Brett Miller has previously received travel expenses and an honorarium from Varian. Phillip Beron has nothing to report.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

TU-CD-BRD-04: UCLA Experience, with Focus On Developing Metrics and Using RO-ILS

It has long been standard practice in radiation oncology to report internally when a patient’s treatment has not gone as planned and to report events to regulatory agencies when legally required. Most potential errors are caught early and never affect the patient. Quality assurance steps routinely prevent errors from reaching the patient, and these “near misses” are much more frequent than treatment errors. A growing number of radiation oncology facilities have implemented incident learning systems to report and analyze both errors and near misses. Using the term “incident learning” instead of “event reporting” emphasizes the need to use these experiences to change the practice and make future errors less likely and promote an educational, non-punitive environment. There are challenges in making such a system practical and effective. Speakers from institutions of different sizes and practice environments will share their experiences on how to make such a system work and what benefits their clinics have accrued. Questions that will be addressed include: How to create a system that is easy for front line staff to access How to motivate staff to report How to promote the system as positive and educational and not punitive or demeaning How to organize the team for reviewing and responding to reports How to prioritize which reports to discuss in depth How not to dismiss the rest How to identify underlying causes How to design corrective actions and implement change How to develop useful statistics and analysis tools How to coordinate a departmental system with a larger risk management system How to do this without a dedicated quality manager Some speakers’ experience is with in-house systems and some will share experience with the AAPM/ASTRO national Radiation Oncology Incident Learning System (RO-ILS). Reports intended to be of value nationally need to be comprehensible to outsiders; examples of useful reports will be shown. There will be ample time set aside for audience members to contribute to the discussion. Learning Objectives: Learn how to promote the use of an incident learning system in a clinic. Learn how to convert “event reporting” into “incident learning”. See examples of practice changes that have come out of learning systems. Learn how the RO-ILS system can be used as a primary internal learning system. Learn how to create succinct, meaningful reports useful to outside readers. Gary Ezzell chairs the AAPM committee overseeing RO-ILS and has received an honorarium from ASTRO for working on the committee reviewing RO-ILS reports. Derek Brown is a director of http://TreatSafely.org . Brett Miller has previously received travel expenses and an honorarium from Varian. Phillip Beron has nothing to report.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2023

Analyzing Hardware and Software Common Cause Failures in Digital Instrumentation and Control Systems using Dual Error Propagation Method

This paper develops a methodology for quantifying software common cause failures (CCFs) in digital instrumentation and control (I&C) systems of nuclear power plants. To support the transition of analog I&C systems to digital in nuclear power plants, probabilistic risk assessment (PRA) techniques are used. The hardware components of the I&C systems have reliability databases that can be used in the PRA studies. However, the failure data for redundant software components of the systems is sparse. Failure of components constitutes a CCF, wherein two or more components or systems fail due to a single shared cause and coupling mechanism. This paper proposes a quantification approach that can simultaneously model hardware and software components, incorporate the CCFs of software systems in the models, and bridge the gap between the failure quantification of models and the development of CCF parametric databases. We demonstrate the dual error propagation method (DEPM) by developing I&C systems failure models for a representative digital reactor trip system. The DEPM models are built to simulate the control and data flows within the systems and can accommodate failure states. By expanding DEPM to software CCFs, we generated alpha factor parameter estimates for each of the modeled error propagation mechanisms.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

NASA NTRS2000

XTE J1906+09 Observations with RXTE

The 89 s pulsar XTE J1906+09 was serendipitously discovered in a 1996 observation of the soft gamma repeater SGR 1900+14. Two outbursts, in 1996 September and 1998 September have been reported to date. Since this system appears to be transient, it is likely in a Be/X-ray binary, accreting material from a circumstellar disk around its companion. Preliminary pulse timing analyses of RXTE data from the 1998 September outburst revealed an orbital signature consistent with either (i) a low-eccentricity, short period orbit, similar to OAO 1657-415 or (ii) periastron passage in a longer orbital period, higher eccentricity Be/X-ray binary system. No companion has been identified to date due to the large 2 feet error radius of the current best position. SGR 1900+14 has been regularly monitored with RXTE since 1998. Because XTE J1906+09 is only 33 feet away, it often shares the RXTE/PCA field of view with SGR 1900+14, giving us a large number of archival PCA observations. We will present results of a search of RXTE data for outbursts of XTE 1906+09, including histories of pulse frequency, 2-30 keV intensity, pulse profiles, and energy spectra. Results of a pulse timing analysis of the detected outbursts will also be presented.

Wilson, Colleen A.↗

NASA NTRSDate not supplied

US-EUSST SSA Data Exchange for Improved Orbital Safety

Data sharing and exchange among different Space Situational Awareness (SSA) data collectors/providers is frequently discussed as a mechanism to improve the accuracy and precision of orbital safety products. Indeed, at the conceptual level this claim is quite sensible: objects with more tracking, and thus presumably better distribution of that tracking about their orbit, should produce updates with smaller epoch errors and more realistic covariances at epoch, which should then translate into better performance in prediction and thus improved close approach calculations. However, this thesis has not been verified with any large study involving two different data providers, through which the amount of realized improvement can be quantified and, perhaps more importantly, the logistics of effecting observation data sharing in a regularized way can be established and circulated to assist others. To create rubrics for helpful data sharing for conjunction assessment applications, and to collect empirical data on the improvements achieved through sharing of measurement data, the US Office of Space Commerce and the European Union Space Surveillance and Tracking (EUSST) Support Framework have embarked on a joint experiment to collect and exchange satellite metric observations on selected satellites of interest over an experimental period. Each entity will perform orbit determination with their own observations, the other entity’s observations, and with both observation data sets combined. The product results will be compared with each other, showing differences attributable both to the three different data groups and to the two entities’ different approaches to orbit determination. The exemplar satellites include both objects that have external precision reference ephemerides and those that do not, allowing the experiment to exercise both precision-comparison and assimilative-comparison techniques. The present reporting will give preliminary results and a set of lessons learned for data sharing; a second presentation later in 2023 will provide a full accounting of the experiment’s results. The hope is that, through this work, a pathway can be established for the expeditious and fruitful sharing among collection entities, both commercial and governmental.

space situational awareness↗

DOE OSTI2022

Waveform Data Quality Assessment

Healthy seismoacoustic sensors and accurate metadata are critical to all the science objectives of both the Source Physics Experiment (SPE) Rock Valley Direct Comparison (RV/DC) and LowYield Physics Experiment-1 (LYNM PE-1). Both projects share similar seismoacoustic stations. We provide a plan on how to move forward with waveform data quality assessments (QA) to the working groups. The identification of stations with instrument response errors will be useful to researchers using amplitudes to study source effects and Earth attenuation. The data QA can also be useful for field technicians to help identify and correct problem sites.

47 OTHER INSTRUMENTATION↗

NASA NTRS1989

Ground-state coding in partially connected neural networks

Patterns over (-1,0,1) define, by their outer products, partially connected neural networks, consisting of internally strongly connected, externally weakly connected subnetworks. The connectivity patterns may have highly organized structures, such as lattices and fractal trees or nests. Subpatterns over (-1,1) define the subcodes stored in the subnetwork, that agree in their common bits. It is first shown that the code words are locally stable stares of the network, provided that each of the subcodes consists of mutually orthogonal words or of, at most, two words. Then it is shown that if each of the subcodes consists of two orthogonal words, the code words are the unique ground states (absolute minima) of the Hamiltonian associated with the network. The regions of attraction associated with the code words are shown to grow with the number of subnetworks sharing each of the neurons. Depending on the particular network architecture, the code sizes of partially connected networks can be vastly greater than those of fully connected ones and their error correction capabilities can be significantly greater than those of the disconnected subnetworks. The codes associated with lattice-structured and hierarchical networks are discussed in some detail.

Baram, Yoram↗