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All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

The SEMA3F-NRP1/NRP2 axis is a key factor in the acquisition of invasive traits in in situ breast ductal carcinoma

A better understanding of ductal carcinoma in situ (DCIS) is urgently needed to identify these preinvasive lesions as distinct clinical entities. Semaphorin 3F (SEMA3F) is a soluble axonal guidance molecule, and its coreceptors Neuropilin 1 (NRP1) and NRP2 are strongly expressed in invasive epithelial BC cells. We utilized two cell line models to represent the progression from a healthy state to the mild-aggressive or ductal carcinoma in situ (DCIS) stage and, ultimately, to invasive cell lines. Additionally, we employed in vivo models and conducted analyses on patient databases to ensure the translational relevance of our results. We revealed SEMA3F as a promoter of invasion during the DCIS-to-invasive ductal carcinoma transition in breast cancer (BC) through the action of NRP1 and NRP2. In epithelial cells, SEMA3F activates epithelialmesenchymal transition, whereas it promotes extracellular matrix degradation and basal membrane and myoepithelial cell layer breakdown. Together with our patient database data, these proof-of-concept results reveal new SEMA3F-mediated mechanisms occurring in the most common preinvasive BC lesion, DCIS, and represent potent and direct activation of its transition to invasion. Moreover, and of clinical and therapeutic relevance, the effects of SEMA3F can be blocked directly through its coreceptors, thus preventing invasion and keeping DCIS lesions in the preinvasive state.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Transverse Momentum at Work in High-Energy Scattering Experiments

I will review some aspects of the definition and the phenomenology of Transverse-Momentum-Dependent distributions (TMDs) which are potentially interesting for the physics program at several current and future experimental facilities. First of all, I will review the definition of quark, gluon and Wilson loop TMDs based on gauge invariant hadronic matrix elements. Looking at the phenomenology of quarks, I will address the flavor dependence of the intrinsic transverse momentum in unpolarized TMDs, focusing on its extraction from Semi-Inclusive Deep-Inelastic Scattering. I will also present an estimate of its impact on the transverse momentum spectrum of W and Z bosons produced in unpolarized hadronic collisions and on the determination of the W boson mass. Moreover, the combined effect of the flavor dependence and the evolution of TMDs with the energy scale will be discussed for electron-positron annihilation. Concerning gluons, I will present from an effective theory point of view the TMD factorization theorem for the transverse momentum spectrum of pseudoscalar quarkonium produced in hadronic collisions. Relying on this, I will discuss the possibility of extracting precise information on (un)polarized gluon TMDs at a future Fixed Target Experiment at the LHC (AFTER@LHC).

Signori, Andrea↗
NASA NTRS1989

A comparison of various micromechanics models for metal matrix composites

Four micromechanics models currently used in the analysis of metal matrix composites are reviewed. The four models are the vanishing fiber diameter model, the Aboudi model, the multicell model, and discrete fiber-matrix model. Results predicted by computer programs based on each of the models are compared. Comparisons are made for the laminate properties and laminate stress-strain behavior for boron/aluminum and silicon-carbide/titanium composites. The predictions of constituent stresses are also compared. The predictions are compared to experimental data. Each of the models did a reasonably good job predicting laminate properties and stress-strain behavior. Thus, the discriminator between the models is a question of what type of results are required, the capabilities of the model and program, or the ease of operation. The choice of a model and program depends on several factors and the same program may not be the best choice for all analysis needs. The descriptions and comparisons made in this paper should aid in the choice of a model and program.

Bigelow, C. A.↗
DOE OSTI2017

Wound healing potential of adipose tissue stem cell extract

Adipose tissue stem cells (ATSCs) are considered as a promising source in the field of cell therapy and regenerative medicine. In addition to direct cell replacement using stem cells, intercellular molecule exchange by stem cell secretory factors showed beneficial effects by reducing tissue damage and augmentation of endogenous repair. Delayed cutaneous wound healing is implicated in many conditions such as diabetes, aging, stress and alcohol consumption. However, the effects of cell-free extract of ATSCs (ATSC-Ex) containing secretome on wound healing process have not been investigated. In this study, ATSC-Ex was topically applied on the cutaneous wound and healing speed was examined. As a result, wound closure was much faster in the cell-free extract treated wound than control wound at 4, 6, 8 days after application of ATSC-Ex. Dermal fibroblast proliferation, migration and extracellular matrix (ECM) production are critical aspects of wound healing, and the effects of ATSC-Ex on human dermal fibroblast (HDF) was examined. ATSC-Ex augmented HDF proliferation in a dose-dependent manner and migration ability was enhanced by extract treatment. Representative ECM proteins, collagen type I and matrix metalloproteinase-1, are significantly up-regulated by treatment of ATSC-Ex. Our results suggest that the ATSC-Ex have improving effect of wound healing and can be the potential therapeutic candidate for cutaneous wound healing. - Highlights: • Topical application of ATSC-Ex results in faster wound closure than normal wound in vivo. • ATSC-Ex enhances dermal fibroblast proliferation, migration and extracellular matrix production. • This study suggests that ATSC-Ex is an effective source to augment wound healing.

60 APPLIED LIFE SCIENCES↗
NASA NTRS1986

Models of polarized infrared emission from bipolar nebulae

Many stars with circumstellar dust shells show a high degree of linear polarization (Sato et al. 1985). We are developing a model which assumes that the polarization arises from scattering by circumstellar dust. Our model assumes a geometry in which the star is surrounded by an optically thin spherical dust shell and embedded within an optically thick disk. This geometry is consistent with that proposed for objects with bipolar molecular outflow. This is important because many bipolar flow objects have also been observed to be highly polarized. The high degree of linear polarization is produced because the disk differentially attenuates the light from the star. The light incident from the point source is attenuated by a factor of exp(-tau/cos theta) where theta is the angle between a ray from the point source to the scatterer and a ray normal to the disk; tau is the optical depth at the wavelength of interest. Hence, the light scattered from the regions directly above and below the disk give the largest contribution to the total flux. The scattering angle for light from these regions is near 90 deg., so the light is strongly polarized and, in the Rayleigh scattering regime, is polarized parallel to the disk. The Stokes parameters for the scattered light from each particle in the shell are calculated by using the scattering matrix elements generated by a Mie scattering program. After the Stokes parameters for each particle are computed they are summed to give the Stokes parameters for the entire shell. Two graphs are presented which show the intensity and polarization spectrum generated by our model using the optical constants for astronomical silicates as defined by Draine and Lee (1984).

Burns, M. S.↗
NASA NTRS2003

The ATIC Long Duration Balloon Project

Long Duration Balloon (LDB) scientific experiments, launched to circumnavigate the south pole over Antarctica, have particular advantages compared to Shuttle or other Low Earth Orbit (LEO) missions in terms of cost, weight, scientific 'duty factor' and work force development. The Advanced Thin Ionization Calorimeter (ATIC) cosmic ray astrophysics experiment is a good example of a university-based project that takes full advantage of current LDB capability. The ATIC experiment is currently being prepared for its first LDB science flight that will investigate the charge composition and energy spectra of primary cosmic rays over the energy range from about 10(exp 10) to 10(exp 14) eV. The instrument is built around a fully active, Bismuth Germanate (BGO) ionization calorimeter to measure the energy deposited by the cascades formed by particles interacting in a thick carbon target. A highly segmented silicon matrix, located above the target, provides good incident charge resolution plus rejection of the 'backscattered' particles from the interaction. Trajectory reconstruction is based on the cascade profile in the BGO calorimeter, plus information from the three pairs of scintillator hodoscope layers in the target section above it. A full evaluation of the experiment was performed during a test flight occurring between 28 December 2000 and 13 January 2001 where ATIC was carried to an altitude of approx. 37 km above Antarctica by an approx. 850,000 cu m helium filled balloon for one circumnavigation of the continent. All systems behaved well, the detectors performed as expected, more than 43 gigabytes of engineering and cosmic ray event data was returned and these data are now undergoing preliminary data analysis. During the coming 2002-2003 Antarctica summer season, we are preparing for a ATIC science flight with approx. 15 to 30 days of continuous data collection in the near-space environment of LDB float altitudes.

Guzik, T. G.↗
DOE OSTI2025

Calculation of ion–ion mutual neutralization rate constants using Landau–Zener theory coupled with trajectory simulations for Ar + –Cl − , Br − , I −

In this computational study, we self-consistently calculate the rate constants of mutual neutralization reactions by incorporating the electron transfer probability, using Landau–Zener state transition theory with inputs derived from ab initio quantum chemistry calculations, into classical trajectory simulations. Electronic structure calculations are done using correlation consistent basis sets with multi-reference configuration interaction to map all the molecular electronic states below the ion-dissociation limit as a function of the distance between the reacting species. Our electronic structure calculations have been significantly improved from our previous work through improved selection of molecular electronic configurations maintaining a fine grid of 1a 0 over a wide range of bond lengths and accurate treatment of spin–orbit couplings. Non-adiabatic coupling matrix elements are calculated with the three-point central difference method near each avoided crossing to estimate the exact crossing point R x and coupling parameter H if , which are inputs to the multi-channel Landau–Zener theory to calculate the electron transition probability. Our approach is applied to estimate the mutual neutralization rate constants for the following ion pairs: Ar + –Cl − , Ar + –Br − , Ar + –I − at ∼133 Pa. Furthermore, our predictions are compared against the experimental data reported. It is seen that the improvement in the electronic structure calculation results in excellent agreement between the simulation results and the available experimental data to within a factor of ∼2 or ∼±50%.

Complete-active space self-consistent field↗
DOE OSTI2024

Designing Ti-6Al-4V microstructure for strain delocalization using neural networks

Abstract The deformation behavior of Ti-6Al-4V titanium alloy is significantly influenced by slip localized within crystallographic slip bands. Experimental observations reveal that intense slip bands in Ti-6Al-4V form at strains well below the macroscopic yield strain and may serially propagate across grain boundaries, resulting in long-range localization that percolates through the microstructure. These connected, localized slip bands serve as potential sites for crack initiation. Although slip localization in Ti-6Al-4V is known to be influenced by various factors, an investigation of optimal microstructures that limit localization remains lacking. In this work, we develop a novel strategy that integrates an explicit slip band crystal plasticity technique, graph networks, and neural network models to identify Ti-6Al-4V microstructures that reduce the propensity for strain localization. Simulations are conducted on a dataset of 3D polycrystals, each represented as a graph to account for grain neighborhood and connectivity. The results are then used to train neural network surrogate models that accurately predict localization-based properties of a polycrystal, given its microstructure. These properties include the ratio of slip accumulated in the band to that in the matrix, fraction of total applied strain accommodated by slip bands, and spatial connectivity of slip bands throughout the microstructure. The initial dataset is enriched by synthetic data generated by the surrogate models, and a grid search optimization is subsequently performed to find optimal microstructures. Describing a 3D polycrystal with only a few features and a combination of graph and neural network models offer robustness compared to the alternative approaches without compromising accuracy. We show that while each material property is optimized through a unique microstructure solution, elongated grain shape emerges as a recurring feature among all optimal microstructures. This finding suggests that designing microstructures with elongated grains could potentially mitigate strain localization without compromising strength.

Ahmadikia, Behnam↗
DOE OSTI2024

O-GlcNAc transferase regulates collagen deposition and fibrosis resolution in idiopathic pulmonary fibrosis

Idiopathic pulmonary fibrosis (IPF) is a chronic pulmonary disease that is characterized by an excessive accumulation of extracellular matrix (ECM) proteins (e.g. collagens) in the parenchyma, which ultimately leads to respiratory failure and death. While current therapies exist to slow the progression, no therapies are available to resolve fibrosis. We characterized the O-linked N-Acetylglucosamine (O-GlcNAc) transferase (OGT)/O-GlcNAc axis in IPF using single-cell RNA-sequencing (scRNA-seq) data and human lung sections and isolated fibroblasts from IPF and non-IPF donors. The underlying mechanism(s) of IPF were further investigated using multiple experimental models to modulate collagen expression and accumulation by genetically and pharmacologically targeting OGT. Furthermore, we hone in on the transforming growth factor-beta (TGF-β) effector molecule, Smad3, by co-expressing it with OGT to determine if it is modified and its subsequent effect on Smad3 activation. We found that OGT and O-GlcNAc levels are upregulated in patients with IPF compared to non-IPF. We report that the OGT regulates collagen deposition and fibrosis resolution, which is an evolutionarily conserved process demonstrated across multiple species. Co-expression of OGT and Smad3 showed that Smad3 is O-GlcNAc modified. Blocking OGT activity resulted in decreased phosphorylation at Ser-423/425 of Smad3 attenuating the effects of TGF-β1 induced collagen expression/deposition. OGT inhibition or knockdown successfully blocked and reversed collagen expression and accumulation, respectively. Smad3 is discovered to be a substrate of OGT and its O-GlcNAc modification(s) directly affects its phosphorylation state. These data identify OGT as a potential target in pulmonary fibrosis resolution, as well as other diseases that might have aberrant ECM/collagen accumulation.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1989

On polynomial preconditioning for indefinite Hermitian matrices

The minimal residual method is studied combined with polynomial preconditioning for solving large linear systems (Ax = b) with indefinite Hermitian coefficient matrices (A). The standard approach for choosing the polynomial preconditioners leads to preconditioned systems which are positive definite. Here, a different strategy is studied which leaves the preconditioned coefficient matrix indefinite. More precisely, the polynomial preconditioner is designed to cluster the positive, resp. negative eigenvalues of A around 1, resp. around some negative constant. In particular, it is shown that such indefinite polynomial preconditioners can be obtained as the optimal solutions of a certain two parameter family of Chebyshev approximation problems. Some basic results are established for these approximation problems and a Remez type algorithm is sketched for their numerical solution. The problem of selecting the parameters such that the resulting indefinite polynomial preconditioners speeds up the convergence of minimal residual method optimally is also addressed. An approach is proposed based on the concept of asymptotic convergence factors. Finally, some numerical examples of indefinite polynomial preconditioners are given.

Freund, Roland W.↗
NASA NTRS1994

Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres

Although neglecting polarization and replacing the rigorous vector radiative transfer equation by its approximate scalar counterpart has no physical background, it is a widely used simplification when the incident light is unpolarized and only the intensity of the reflected light is to be computed. We employ accurate vector and scalar multiple-scattering calculations to perform a systematic study of the errors induced by the neglect of polarization in radiance calculations for a homogeneous, plane-parallel Rayleigh-scattering atmosphere (with and without depolarization) above a Lambertian surface. Specifically, we calculate percent errors in the reflected intensity for various directions of light incidence and reflection, optical thicknesses of the atmosphere, single-scattering albedos, depolarization factors, and surface albedos. The numerical data displayed can be used to decide whether or not the scalar approximation may be employed depending on the parameters of the problem. We show that the errors decrease with increasing depolarization factor and/or increasing surface albedo. For conservative or nearly conservative scattering and small surface albedos, the errors are maximum at optical thicknesses of about 1. The calculated errors may be too large for some practical applications, and, therefore, rigorous vector calculations should be employed whenever possible. However, if approximate scalar calculations are used, we recommend to avoid geometries involving phase angles equal or close to 0 deg and 90 deg, where the errors are especially significant. We propose a theoretical explanation of the large vector/scalar differences in the case of Rayleigh scattering. According to this explanation, the differences are caused by the particular structure of the Rayleigh scattering matrix and come from lower-order (except first-order) light scattering paths involving right scattering angles and right-angle rotations of the scattering plane.

Mishchenko, M. I.↗
NASA NTRS1996

Methodology for Sensitivity Analysis, Approximate Analysis, and Design Optimization in CFD for Multidisciplinary Applications

An incremental iterative formulation together with the well-known spatially split approximate-factorization algorithm, is presented for solving the large, sparse systems of linear equations that are associated with aerodynamic sensitivity analysis. This formulation is also known as the 'delta' or 'correction' form. For the smaller two dimensional problems, a direct method can be applied to solve these linear equations in either the standard or the incremental form, in which case the two are equivalent. However, iterative methods are needed for larger two-dimensional and three dimensional applications because direct methods require more computer memory than is currently available. Iterative methods for solving these equations in the standard form are generally unsatisfactory due to an ill-conditioned coefficient matrix; this problem is overcome when these equations are cast in the incremental form. The methodology is successfully implemented and tested using an upwind cell-centered finite-volume formulation applied in two dimensions to the thin-layer Navier-Stokes equations for external flow over an airfoil. In three dimensions this methodology is demonstrated with a marching-solution algorithm for the Euler equations to calculate supersonic flow over the High-Speed Civil Transport configuration (HSCT 24E). The sensitivity derivatives obtained with the incremental iterative method from a marching Euler code are used in a design-improvement study of the HSCT configuration that involves thickness. camber, and planform design variables.

Taylor, Arthur C., III↗
DOE OSTI2019

The effects of soil phosphorus content on plant microbiota are driven by the plant phosphate starvation response

Phosphate starvation response (PSR) in nonmycorrhizal plants comprises transcriptional reprogramming resulting in severe physiological changes to the roots and shoots and repression of plant immunity. Thus, plant-colonizing microorganisms—the plant microbiota—are exposed to direct influence by the soil’s phosphorus (P) content itself as well as to the indirect effects of soil P on the microbial niches shaped by the plant. The individual contribution of these factors to plant microbiota assembly remains unknown. To disentangle these direct and indirect effects, we planted PSR-deficient Arabidopsis mutants in a long-term managed soil P gradient and compared the composition of their shoot and root microbiota to wild-type plants across different P concentrations. PSR-deficiency had a larger effect on the composition of both bacterial and fungal plant-associated microbiota than soil P concentrations in both roots and shoots. To dissect plant–microbe interactions under variable P conditions, we conducted a microbiota reconstitution experiment. Using a 185-member bacterial synthetic community (SynCom) across a wide P concentration gradient in an agar matrix, we demonstrated a shift in the effect of bacteria on the plant from a neutral or positive interaction to a negative one, as measured by rosette size. This phenotypic shift was accompanied by changes in microbiota composition: the genus Burkholderia was specifically enriched in plant tissue under P starvation. Through a community drop-out experiment, we demonstrated that in the absence of Burkholderia from the SynCom, plant shoots accumulated higher ortophosphate (Pi) levels than shoots colonized with the full SynCom but only under Pi starvation conditions. Therefore, Pi-stressed plants are susceptible to colonization by latent opportunistic competitors found within their microbiome, thus exacerbating the plant’s Pi starvation.

59 BASIC BIOLOGICAL SCIENCES↗
NASA NTRS1993

Programmable display pushbuttons on the Space Station's telerobot control panel

The Man-Systems Telerobotics Laboratory at NASA's Johnson Space Center and supported by Lockheed, is working to ensure that the Flight Telerobotic Servicer (FTS) to be used on the Space Shuttle (Orbiter) and the Space Station has a well designed user interface from a Human Factors perspective. The FTS, which is a project led by NASA's Goddard Space Flight Center, will be a telerobot used for Space Station construction, maintenance, and satellite repair. It will be directly controlled from workstations on the Orbiter and the Space Station and monitored from a ground workstation. The FTS will eventually evolve into a more autonomous system, but in the short-term the system will be manually operated (teleoperated) for many tasks. This emphasizes the importance of the human/telerobot interface on this system. This phase of the FTS workstation evaluation covers a preliminary study of programmable display pushbuttons (PDP's). The PDP is constructed of a matrix of directly addressable electroluminescent (EL) pixels which can be used to form dot-matrix characters. PDP's can be used to display more than one message and to control more than one function. Since the PDP's have these features, then a single PDP may possibly replace the use of many single-function pushbuttons, rotary switches, and toggle switches, thus using less panel space. It is of interest to determine if PDP's can be used to adequately perform complex hierarchically structured task sequences. The objective of this investigation was to compare the performance of experienced and inexperienced Remote Manipulator System (RMS) operators while performing an RMS like task on simulated PDP and non-PDP computer prototypes so that guidelines governing the use of programmable display pushbuttons on the FTS workstation could be created. The functionality of the RMS on the Orbiter was used as a model for this evaluation since the functionality of the FTS at the time of this writing has not been solidified.

Stuart, Mark A.↗
NASA NTRS2001

Modulation of lens cell adhesion molecules by particle beams

Cell adhesion molecules (CAMs) are proteins which anchor cells to each other and to the extracellular matrix (ECM), but whose functions also include signal transduction, differentiation, and apoptosis. We are testing a hypothesis that particle radiations modulate CAM expression and this contributes to radiation-induced lens opacification. We observed dose-dependent changes in the expression of beta 1-integrin and ICAM-1 in exponentially-growing and confluent cells of a differentiating human lens epithelial cell model after exposure to particle beams. Human lens epithelial (HLE) cells, less than 10 passages after their initial culture from fetal tissue, were grown on bovine corneal endothelial cell-derived ECM in medium containing 15% fetal bovine serum and supplemented with 5 ng/ml basic fibroblast growth factor (FGF-2). Multiple cell populations at three different stages of differentiation were prepared for experiment: cells in exponential growth, and cells at 5 and 10 days post-confluence. The differentiation status of cells was characterized morphologically by digital image analysis, and biochemically by Western blotting using lens epithelial and fiber cell-specific markers. Cultures were irradiated with single doses (4, 8 or 12 Gy) of 55 MeV protons and, along with unirradiated control samples, were fixed using -20 degrees C methanol at 6 hours after exposure. Replicate experiments and similar experiments with helium ions are in progress. The intracellular localization of beta 1-integrin and ICAM-1 was detected by immunofluorescence using monoclonal antibodies specific for each CAM. Cells known to express each CAM were also processed as positive controls. Both exponentially-growing and confluent, differentiating cells demonstrated a dramatic proton-dose-dependent modulation (upregulation for exponential cells, downregulation for confluent cells) and a change in the intracellular distribution of the beta 1-integrin, compared to unirradiated controls. In contrast, there was a dose-dependent increase in ICAM-1 immunofluorescence in confluent, but not exponentially-growing cells. These results suggest that proton irradiation downregulates beta 1-integrin and upregulates ICAM-1, potentially contributing to cell death or to aberrant differentiation via modulation of anchorage and/or signal transduction functions. Quantification of the expression levels of the CAMs by Western analysis is in progress.

NASA Discipline Radiation Health↗
NASA NTRS2019

TURBOMAT: A Probabilistic Turbomachinery Aeroelastic Analysis Tool

An integration of aeroelastic analysis procedures with probabilistic analysis methods enables us to design safe reliable engines with quantified reliability. Towards this goal, a graphical user interface (GUI) based tool that integrates the codes Aeroelastic analysis of propfans (ASTROP2) and Numerical Evaluation of Stochastic Structures Under Stress (NESSUS) is developed. The tool entitled TURBOMachinery Aeroelastic Analysis Tool (TURBOMAT), is developed utilizing the MATrix Laboratory (Matlab) Guide (Graphical User Interface Development) tool box. TURBOMAT provides a user friendly computational environment for rapid assessment of Turbomachinery blades flutter characteristics, subjected to uncertain loading conditions with variability in material and aerodynamic properties. The tool is seen as an education tool for new students and young engineers starting their careers in structural Aeroelasticity who want to learn and understand aeroelastic aspects of turbomachinery components, fans, compressors and turbines, including uncertainties in loading and material properties.A typical fan blade configuration geometry was chosen to demonstrate the tool. The results are presented in the form of probabilistic density function (PDF), the cumulative distribution function (CDF) and sensitivity factors. Both first order fast probability integration (FPI) and the Monto Carlo (MC) techniques are used in the analysis and compared. The tool enabled us to quantify blade flutter reliability as well as the ranking of uncertain variables and their importance to blade flutter response.

Aeroelastic Analysis↗
DOE OSTI2024

Hybrid analysis of radiative corrections to neutron decay with current algebra and effective field theory

We introduce a useful framework for high-precision studies of the neutron beta decay by merging the current algebra description and the fixed-order effective field theory calculation of the electroweak radiative corrections to the neutron axial form factor. We discuss the advantages of this hybrid method and show that it only requires a minimal amount of lattice QCD inputs to achieve a 10 –4 theory accuracy for the Standard Model prediction of the neutron lifetime and the axial-to-vector coupling ratio λ, both important to the search for physics beyond the Standard Model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Systematic Generation of Moment Invariant Bases for 2D and 3D Tensor Fields

Moment invariants have been successfully applied to pattern detection tasks in 2D and 3D scalar, vector, and matrix valued data. However so far no flexible basis of invariants exists, i.e., no set that is optimal in the sense that it is complete and independent for every input pattern. Here, we prove that a basis of moment invariants can be generated that consists of tensor contractions of not more than two different moment tensors each under the conjecture of the set of all possible tensor contractions to be complete. This result allows us to derive the first generator algorithm that produces flexible bases of moment invariants with respect to orthogonal transformations by selecting a single non-zero moment to pair with all others in these two-factor products. Since at least one non-zero moment can be found in every non-zero pattern, this approach always generates a complete set of descriptors.

97 MATHEMATICS AND COMPUTING↗