Search NASA⌕ Search

SEARCH · Search NASA

Results for “Basis function”

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 685 records · Page 38
All sourcesNASA NTRSDOE OSTI
DOE OSTI2012

The Functional Requirements and Design Basis for Information Barriers

This report summarizes the results of the Information Barrier Working Group workshop held at Sandia National Laboratory in Albuquerque, NM, February 2-4, 1999. This workshop was convened to establish the functional requirements associated with warhead radiation signature information barriers, to identify the major design elements of any such system or approach, and to identify a design basis for each of these major elements. Such information forms the general design basis to be used in designing, fabricating, and evaluating the complete integrated systems developed for specific purposes.

Fuller, James L.↗
DOE OSTI2019

Heavy quarkonia production at energies available at the CERN Large Hadron Collider and future electron-ion colliding facilities using basis light-front quantization wave functions

We study here exclusive charmonium and bottomonium production in ultraperipheral heavy-ion collisions and electron-ion collisions within the dipole picture. We employ heavy quarkonium light-front wave functions obtained within the basis light-front quantization framework, which has some features of the light-front holographic QCD. We focus on comparison with measurements of exclusive charmonium and bottomonium production in ultraperipheral pp, pPb, and PbPb collisions at the CERN Large Hadron Collider and find reasonable agreement with the cross sections. We also discuss the coherent production cross-section ratios of excited states to the ground state for charmonium and bottomonium, which exhibit insensitivity to the dipole model parameters. We demonstrate that electron-ion collisions provide an opportunity for a quantitative study of heavy quarkonium structure.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2025

SineKAN: Kolmogorov-Arnold Networks using sinusoidal activation functions

Recent work has established an alternative to traditional multi-layer perceptron neural networks in the form of Kolmogorov-Arnold Networks (KAN). The general KAN framework uses learnable activation functions on the edges of the computational graph followed by summation on nodes. The learnable edge activation functions in the original implementation are basis spline functions (B-Spline). Here, we present a model in which learnable grids of B-Spline activation functions are replaced by grids of re-weighted sine functions (SineKAN). We evaluate numerical performance of our model on a benchmark vision task. We show that our model can perform better than or comparable to B-Spline KAN models and an alternative KAN implementation based on periodic cosine and sine functions representing a Fourier Series. Further, we show that SineKAN has numerical accuracy that could scale comparably to dense neural networks (DNNs). Compared to the two baseline KAN models, SineKAN achieves a substantial speed increase at all hidden layer sizes, batch sizes, and depths. Current advantage of DNNs due to hardware and software optimizations are discussed along with theoretical scaling. Additionally, properties of SineKAN compared to other KAN implementations and current limitations are also discussed.

Reinhardt, Eric↗
DOE OSTI2024

Permutation-adapted complete and independent basis for atomic cluster expansion descriptors

Atomic cluster expansion (ACE) methods provide a systematic way to describe particle local environments of arbitrary body order. For practical applications it is often required that the basis of cluster functions be symmetrized with respect to rotations and permutations. Existing methodologies yield sets of symmetrized functions that are over-complete. These methodologies thus require an additional numerical procedure, such as singular value decomposition (SVD), to eliminate redundant functions. In this work, it is shown that analytical linear relationships for subsets of cluster functions may be derived using recursion and permutation properties of generalized Wigner symbols. From these relationships, subsets (blocks) of cluster functions can be selected such that, within each block, functions are guaranteed to be linearly independent. It is conjectured that this block-wise independent set of permutation-adapted rotation and permutation invariant (PA-RPI) functions forms a complete, independent basis for ACE. Along with the first analytical proofs of block-wise linear dependence of ACE cluster functions and other theoretical arguments, numerical results are offered to demonstrate this. The utility of the method is demonstrated in the development of an ACE interatomic potential for tantalum. Using the new basis functions in combination with Bayesian compressive sensing sparse regression, some high degree descriptors are observed to persist and help achieve high-accuracy models.

Angular momentum↗
DOE OSTI2013

A basis in an invariant subspace of analytic functions

The existence problem for a basis in a differentiation-invariant subspace of analytic functions defined in a bounded convex domain in the complex plane is investigated. Conditions are found for the solvability of a certain special interpolation problem in the space of entire functions of exponential type with conjugate diagrams lying in a fixed convex domain. These underlie sufficient conditions for the existence of a basis in the invariant subspace. This basis consists of linear combinations of eigenfunctions and associated functions of the differentiation operator, whose exponents are combined into relatively small clusters. Necessary conditions for the existence of a basis are also found. Under a natural constraint on the number of points in the groups, these coincide with the sufficient conditions. That is, a criterion is found under this constraint that a basis constructed from relatively small clusters exists in an invariant subspace of analytic functions in a bounded convex domain in the complex plane. Bibliography: 25 titles.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2012

A new implementation of dynamic polarizability evaluation using a multi-resolution multi-wavelet basis set

An algorithm to evaluate the response function on the space spanned by Multiresolution Multi-wavelet (MRMW) basis functions is implemented in a new efficient quantum chemical program system. Dynamic electric dipole polarizability of a molecule is evaluated for a range of applied optical frequencies as a preliminary application of the implementation. The results obtained by the MRMW provide the one in near completeness limit. We also compare a few examples of the dynamic polarizabilities evaluated using conventional Gaussian basis set functions with the one evaluated by the MMMW basis functions. For small frequencies, there is no significant difference among them and large Gaussian results are close to the MRMW value, but they diverge from the MRMW value when the applied frequency approaches to the resonance region.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2017

Accelerated Time-Domain Modeling of Electromagnetic Pulse Excitation of Finite-Length Dissipative Conductors over a Ground Plane via Function Fitting and Recursive Convolution

In this report we overview the fundamental concepts for a pair of techniques which together greatly hasten computational predictions of electromagnetic pulse (EMP) excitation of finite-length dissipative conductors over a ground plane. In a time- domain, transmission line (TL) model implementation, predictions are computationally bottlenecked time-wise, either for late-time predictions (about 100ns-10000ns range) or predictions concerning EMP excitation of long TLs (order of kilometers or more ). This is because the method requires a temporal convolution to account for the losses in the ground. Addressing this to facilitate practical simulation of EMP excitation of TLs, we first apply a technique to extract an (approximate) complex exponential function basis-fit to the ground/Earth's impedance function, followed by incorporating this into a recursion-based convolution acceleration technique. Because the recursion-based method only requires the evaluation of the most recent voltage history data (versus the entire history in a "brute-force" convolution evaluation), we achieve necessary time speed- ups across a variety of TL/Earth geometry/material scenarios. Intentionally Left Blank

36 MATERIALS SCIENCE↗
DOE OSTI2017

Molecular basis of human CD22 function and therapeutic targeting

CD22 maintains a baseline level of B-cell inhibition to keep humoral immunity in check. As a B-cell-restricted antigen, CD22 is targeted in therapies against dysregulated B cells that cause autoimmune diseases and blood cancers. Here we report the crystal structure of human CD22 at 2.1 Å resolution, which reveals that specificity for α2-6 sialic acid ligands is dictated by a pre-formed β-hairpin as a unique mode of recognition across sialic acid-binding immunoglobulin-type lectins. The CD22 ectodomain adopts an extended conformation that facilitates concomitant CD22 nanocluster formation on B cells and binding to trans ligands to avert autoimmunity in mammals. We structurally delineate the CD22 site targeted by the therapeutic antibody epratuzumab at 3.1 Å resolution and determine a critical role for CD22 N-linked glycosylation in antibody engagement. Our studies provide molecular insights into mechanisms governing B-cell inhibition and valuable clues for the design of immune modulators in B-cell dysfunction.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Structural basis of impaired disaggregase function in the oxidation-sensitive SKD3 mutant causing 3-methylglutaconic aciduria

Abstract Mitochondria are critical to cellular and organismal health. To prevent damage, mitochondria have evolved protein quality control machines to survey and maintain the mitochondrial proteome. SKD3, also known as CLPB, is a ring-forming, ATP-fueled protein disaggregase essential for preserving mitochondrial integrity and structure. SKD3 deficiency causes 3-methylglutaconic aciduria type VII (MGCA7) and early death in infants, while mutations in the ATPase domain impair protein disaggregation with the observed loss-of-function correlating with disease severity. How mutations in the non-catalytic N-domain cause disease is unknown. Here, we show that the disease-associated N-domain mutation, Y272C, forms an intramolecular disulfide bond with Cys267 and severely impairs SKD3 Y272C function under oxidizing conditions and in living cells. While Cys267 and Tyr272 are found in all SKD3 isoforms, isoform-1 features an additional α-helix that may compete with substrate-binding as suggested by crystal structure analyses and in silico modeling, underscoring the importance of the N-domain to SKD3 function.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2012

Molecular basis of the fructose-2,6-bisphosphatase reaction of PFKFB3: Transition state and the C-terminal function

The molecular basis of fructose-2,6-bisphosphatase (F-2,6-P{sub 2}ase) of 6-phosphofructo-2-kinase/fructose-2,6-bisphosphatase (PFKFB) was investigated using the crystal structures of the human inducible form (PFKFB3) in a phospho-enzyme intermediate state (PFKFB3-P {center_dot} F-6-P), in a transition state-analogous complex (PFKFB3 {center_dot} AlF{sub 4}), and in a complex with pyrophosphate (PFKFB3 {center_dot} PP{sub i}) at resolutions of 2.45, 2.2, and 2.3 {angstrom}, respectively. Trapping the PFKFB3-P {center_dot} F-6-P intermediate was achieved by flash cooling the crystal during the reaction, and the PFKFB3 {center_dot} AlF{sub 4} and PFKFB3 {center_dot} PP{sub i} complexes were obtained by soaking. The PFKFB3 {center_dot} AlF{sub 4} and PFKFB3 {center_dot} PP{sub i} complexes resulted in removing F-6-P from the catalytic pocket. With these structures, the structures of the Michaelis complex and the transition state were extrapolated. For both the PFKFB3-P formation and break down, the phosphoryl donor and the acceptor are located within {approx}5.1 {angstrom}, and the pivotal point 2-P is on the same line, suggesting an 'in-line' transfer with a direct inversion of phosphate configuration. The geometry suggests that NE2 of His253 undergoes a nucleophilic attack to form a covalent N-P bond, breaking the 2O-P bond in the substrate. The resulting high reactivity of the leaving group, 2O of F-6-P, is neutralized by a proton donated by Glu322. Negative charges on the equatorial oxygen of the transient bipyramidal phosphorane formed during the transfer are stabilized by Arg252, His387, and Asn259. The C-terminal domain (residues 440-446) was rearranged in PFKFB3 {center_dot} PP{sub i}, implying that this domain plays a critical role in binding of substrate to and release of product from the F-2,6-P{sub 2}ase catalytic pocket. These findings provide a new insight into the understanding of the phosphoryl transfer reaction.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2016

A finite-temperature Hartree–Fock code for shell-model Hamiltonians

The codes HFgradZ.py and HFgradT.py find axially symmetric minima of a Hartree–Fock energy functional for a Hamiltonian supplied in a shell model basis. The functional to be minimized is the Hartree–Fock energy for zero-temperature properties or the Hartree–Fock grand potential for finite-temperature properties (thermal energy, entropy). The minimization may be subjected to additional constraints besides axial symmetry and nucleon numbers. A single-particle operator can be used to constrain the minimization by adding it to the single-particle Hamiltonian with a Lagrange multiplier. One can also constrain its expectation value in the zero-temperature code. Also the orbital filling can be constrained in the zero-temperature code, fixing the number of nucleons having given $K^π$ quantum numbers. So, this is particularly useful to resolve near-degeneracies among distinct minima.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Comparing event generator predictions and ab initio calculations of ν- 12 C neutral-current quasielastic scattering at 1 GeV

The measurement of neutrino oscillations and exotic physics searches are important parts of the physics program in the near future, with new state-of-the-art experiments planned within the next decade. Future and modern experiments in these fields will make use of nuclear targets. Event generators (EGs) are software used in the analysis of neutrino oscillation experiments. EGs are used to predict kinematic observables for a range of neutrino energies. These simulations make use of simple models of nucleon dynamics. As such, they may fail to capture features of more rigorous theoretical calculations. This work compares EG performance to nuclear theory calculations by comparing observables generated in the two frameworks. We provide a common set of definitions between theory and experiment and assess the adequacy of the implementation of two nuclear physics models in EG simulations. Neutral-current quasielastic (NCQE) scattering events for neutrinos and antineutrinos on a 12 C target are simulated with a specific EG, NEUT, used by the T2K experiment for its analysis. The simulated cross sections are compared to analytic calculations from nuclear theory within the factorization scheme. We compare the NEUT implementation of two different models on nuclear spectral functions: the relativistic Fermi gas (RFG) and the correlated basis spectral function (CBF) to analytic calculations of the same models in the factorization scheme. For both nuclear physics models, we compare the appearance of features in the distributions relevant to experimental analyses. The peak of the cross section dσ/(dΩ dω) is consistent in energy transfer, ω, for RFG and CBF simulations. Qualitatively, the shape of the simulated distribution is similar to the one obtained through theory calculations; however, there are some discrepancies between the theory calculations and the NEUT simulation. While the EG simulations and analytic calculations with the same model of nuclear dynamics show similar overall features, there are still differences between the two. These results demonstrate the importance of benchmarking EGs so their nuclear physics implementations can be improved for the analysis of future experiments.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Comparing event generator predictions and ab-initio calculations of $\nu$-$^{12}$C neutral current quasi-elastic scattering at 1 GeV

The measurement of neutrino oscillations and exotic physics searches are important parts of the physics program in the near future, with new state-of-the-art experiments planned within the next decade. Future and modern experiments in these fields will make use of nuclear targets. Event Generators (EGs) are software used in the analysis of neutrino oscillation experiments. EGs use to predict kinematic observables for a range of neutrino energies. These simulations may lack physics captured by more rigorous theoretical calculations. This work compares EG performance to nuclear theory calculations by comparing observables generated in the two frameworks. We provide a common set of definitions between theory and experiment and assess the physics contained in EG simulations. Neutral current quasi-elastic (NCQE) scattering events for neutrinos and anti-neutrinos on a $^{12}$C target are simulated with a specific EG, NEUT, used by the T2K experiment for its analysis. The simulated cross sections are compared to analytic calculations from nuclear theory within the factorization scheme. We compare the NEUT implementation of two different models on nuclear spectral functions: the Relativistic Fermi Gas (RFG) and the correlated basis spectral function (CBF) to analytic calculations of the same models in the factorization scheme. For both nuclear physics models, we compare the appearance of features in the distributions relevant to experimental analyses. Qualitatively, the shape of the simulated distribution is similar to the one obtained through theory calculations; however, there are some discrepancies between the theory calculations and the NEUT simulation. While the EG simulations and analytic calculations with the same model of nuclear dynamics show similar overall features, there are still differences between the two.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2014

Practical auxiliary basis implementation of Rung 3.5 functionals

Approximate exchange-correlation functionals for Kohn-Sham density functional theory often benefit from incorporating exact exchange. Exact exchange is constructed from the noninteracting reference system's nonlocal one-particle density matrix γ(r{sup -vector},r{sup -vector}′). Rung 3.5 functionals attempt to balance the strengths and limitations of exact exchange using a new ingredient, a projection of γ(r{sup -vector},r{sup -vector} ′) onto a semilocal model density matrix γ{sub SL}(ρ(r{sup -vector}),∇ρ(r{sup -vector}),r{sup -vector}−r{sup -vector} ′). γ{sub SL} depends on the electron density ρ(r{sup -vector}) at reference point r{sup -vector}, and is closely related to semilocal model exchange holes. We present a practical implementation of Rung 3.5 functionals, expanding the r{sup -vector}−r{sup -vector} ′ dependence of γ{sub SL} in an auxiliary basis set. Energies and energy derivatives are obtained from 3D numerical integration as in standard semilocal functionals. We also present numerical tests of a range of properties, including molecular thermochemistry and kinetics, geometries and vibrational frequencies, and bandgaps and excitation energies. Rung 3.5 functionals typically provide accuracy intermediate between semilocal and hybrid approximations. Nonlocal potential contributions from γ{sub SL} yield interesting successes and failures for band structures and excitation energies. The results enable and motivate continued exploration of Rung 3.5 functional forms.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗