Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “representation”

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 19 records

Higher-order particle representation for particle-in-cell simulations

In this paper we present an alternative approach to the representation of simulation particles for unstructured electrostatic and electromagnetic PIC simulations. In our modified PIC algorithm we represent particles as having a smooth shape function limited by some specified finite radius, r 0 . A unique feature of our approach is the representation of this shape by surrounding simulation particles with a set of virtual particles with delta shape, with fixed offsets and weights derived from Gaussian quadrature rules and the value of r 0 . As the virtual particles are purely computational, they provide the additional benefit of increasing the arithmetic intensity of traditionally memory bound particle kernels. The modified algorithm is implemented within Sandia National Laboratories' unstructured EMPIRE-PIC code, for electrostatic and electromagnetic simulations, using periodic boundary conditions. We show results for a representative set of benchmark problems, including electron orbit, a transverse electromagnetic wave propagating through a plasma, numerical heating, and a plasma slab expansion. In this work, good error reduction across all of the chosen problems is achieved as the particles are made progressively smoother, with the optimal particle radius appearing to be problem-dependent.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

Real-space representation of the quasiparticle self-consistent GW self-energy and its application to defect calculations

The quasiparticle self-consistent (QS) GW (G for Green's function, W for screened Coulomb interaction) approach incorporates the corrections of the quasiparticle energies from their Kohn-Sham density functional theory (DFT) eigenvalues by means of an energy-independent and Hermitian self-energy matrix usually given in the basis set of the DFT eigenstates. By expanding these into an atom-centered basis set (specifically here the linearized muffin-tin orbitals) a real space representation of the self-energy corrections becomes possible. In this work, We show that this representation is relatively short-ranged. This offers opportunities to construct the self-energy of a complex system from parts of the system by a cut-and-paste method. Specifically for a point defect, represented in a large supercell, the self-energy can be constructed from those of the host and a smaller defect-containing cell. The self-energy of the periodic host can be constructed simply from a GW calculation for the primitive cell. We show for the case of the As Ga in GaAs that the defect part can already be well represented by a minimal eight-atom cell and allows us to construct the self-energy for a 64-atom cell in good agreement with direct QSGW calculations for the large cell. Using this approach to an even larger 216-atom cell shows the defect band approaches an isolated defect level. The calculations also allow us to identify a second defect band which appears as a resonance near the conduction band minimum. The results on the extracted defect levels agree well with Green's function calculations for an isolated defect and with experimental data.

36 MATERIALS SCIENCE↗

Integrating Characteristic Arctic Vegetation in a Land Surface Model Improves Representation of Carbon Dynamics Across a Tundra Landscape: Modeling Archive

This modeling archive is in support of the Next-Generation Ecosystem Experiments in the Arctic (NGEE Arctic) publication "Integrating Characteristic Arctic Vegetation in a Land Surface Model Improves Representation of Carbon Dynamics Across a Tundra Landscape", by Murphy et al. (2025). This archive contains model input files and outputs from landscape-scale simulations conducted using ELM, the land model component of the Department of Energy’s Energy Exascale Earth System Model (E3SM), at the Council NGEE Arctic field site (Council Road mile marker 71) on Alaska’s Seward Peninsula. Input data and model output from two sets of ELM simulations are provided. The first set of simulations were conducted with the two default ELM Arctic plant functional types (PFTs; broadleaf deciduous boreal shrub and a C3 grass) and the second set of simulations were conducted with a set of nine Arctic-specific PFTs including nonvascular mosses and lichens, graminoids, forbs, evergreen dwarf shrubs, three height classes of deciduous shrubs (dwarf, low, and low to tall), and deciduous alder shrubs (Sulman et al., 2021). Parameter names and major parameter changes in the Arctic-specific PFT configuration are described in Sulman et al. (2021) and archived in the Sulman et al. (2021) dataset (see below). Simulations were spatially explicit, covering an approximately 6.4X3.3 km domain at the Council site with a spatial resolution of 100 m for a total of 2,112 simulated grid cells under each ELM PFT configuration. The modeling archive contains meteorological forcing (seven *.nc files and one *.txt file), a domain definition file (one *.nc files), land surface configuration files (two *.nc files), parameter files (two *.nc files), annual ELM output files spanning 1980-2014 (68 *.nc files), and a User’s Guide (*pdf file). Additional information on the provided files is in the “Modeling Archive Contents” section of the User’s Guide. Model outputs are aggregated to the column scale (i.e. PFT-specific outputs are not provided here).

Murphy, Bailey [ORNL] (ORCID:0000000203995221)↗

Quantifying structural errors in cloud condensation nuclei activity from reduced representation of aerosol size distributions

Aerosol effects on clouds and radiation are the dominant contribution to uncertainty in radiative forcing relative to the pre-industrial atmosphere. While previous studies have assessed the impact of parametric uncertainty on modeled forcing, structural errors from the numerical representation of particle distributions have not been well quantified. Here we present a framework for quantifying error in aerosol size distributions and cloud condensation nuclei activity, which we apply to the widely used 4-mode version of the Modal Aerosol Module (MAM4). Box model predictions from the MAM4 are evaluated against the Particle Monte Carlo Model for Simulating Aerosol Interactions and Chemistry (PartMC-MOSAIC), a benchmark model that tracks the evolution of individual particles. We show that size distributions simulated by MAM4 diverge from those simulated by PartMC-MOSAIC after only a few hours of aging by condensation and coagulation in polluted conditions, which leads to large errors in modeled cloud condensation nuclei concentrations. We find that differences between MAM4 and PartMC-MOSAIC are largest under polluted conditions, where the size distribution evolves rapidly though aging by condensation of semi-volatile substances and coagulation among particles. These findings suggest that structural error in modeled aerosol properties contributes to the large inter-model variability in aerosol radiative forcing.

Fierce, Laura M.↗

Real-Time Interactive 4D-STEM Phase-Contrast Imaging From Electron Event Representation Data: Less computation with the right representation

The arrival of direct electron detectors (DED) with high frame-rates in the field of scanning transmission electron microscopy has enabled many experimental techniques that require collection of a full diffraction pattern at each scan position, a field which is subsumed under the name four dimensional-scanning transmission electron microscopy (4D-STEM). DED frame rates approaching 100 kHz require data transmission rates and data storage capabilities that exceed commonly available computing infrastructure. Current commercial DEDs allow the user to make compromises in pixel bit depth, detector binning or windowing to reduce the per-frame file size and allow higher frame rates. This change in detector specifications requires decisions to be made before data acquisition that may reduce or lose information that could have been advantageous during data analysis. The 4D Camera, a DED with 87 kHz frame-rate developed at Lawrence Berkeley National Laboratory, reduces the raw data to a linear-index encoded electron event representation (EER). Here we show with experimental data from the 4D Camera that linear-index encoded EER and its direct use in 4D-STEM phase contrast imaging methods enables real-time, interactive phase-contrast from large-area 4D-STEM datasets. Furthermore, we detail the computational complexity advantages of the EER and the necessary computational steps to achieve real-time interactive ptychography and center-of-mass differential phase contrast using commonly available hardware accelerators.

4D-STEM↗

Efficient Four-Component Dirac–Coulomb–Gaunt Hartree–Fock in the Pauli Spinor Representation

Four-component Dirac Hartree--Fock is an accurate mean-field method for treating molecular systems where relativistic effects are important. However, the computational cost and complexity of the two-electron interaction makes this method less common, even though we can consider the Dirac Hartree--Fock Hamiltonian the ``ground truth" of electronic structure, barring explicit quantum-electrodynamical effects. Being able to calculate these effects is then vital to the design of lower scaling methods for accurate predictions in computational spectroscopy and properties of heavy element complexes that must include relativistic effects for even qualitative accuracy. In this work, we present a Pauli quaternion formalism of maximal component- and spin-separation for computing the Dirac-Coulomb-Gaunt Hartree-Fock ground state, with a minimal floating-point-operation count algorithm. Furthermore, this approach also allows one to explicitly separate different spin physics from the two-body interactions, such as spin-free, spin-orbit, and the spin-spin contributions. Additionally, we use this formalism to examine relativistic trends in the periodic table, and analyze the basis set dependence of atomic gold and gold dimer systems.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Consequences and benefits of utilizing continuous vibro-impact representations in constrained pipeline conveying fluid systems

Here, the effectiveness of continuous vibro-impact forcing representations for the cantilevered pipe that conveys fluid is explored and analyzed. The previously accepted forcing model utilizing a smoothened trilinear spring is estimated using three continuous forcing representations, namely, polynomial, rational polynomial, and hyperbolic tangent. The accuracy of the estimated forcing functions is investigated and analyzed by calculating the root mean square error, and bifurcation diagrams are generated and compared to the nominal system. Additionally, the dynamic response of the system is further characterized using Poincare maps, power spectra, and basins of attraction. Once all continuous forcing representations are analyzed and compared to the nominal system, the computational cost of each method is examined, and further limitations of the hyperbolic tangent method are discovered. It is proved that the hyperbolic tangent forcing representation most accurately captures the dynamic response of the pipeline, and the least accurate representation is the rational polynomial representation. Additionally, considerable computational cost is saved when employing the hyperbolic tangent representation compared to the discontinuous representation.

42 ENGINEERING↗

From Latent Dynamics to Meaningful Representations

While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learnt representations meaningful. For this the typical approach is to regularize the learned representation through prior probability distributions. However such priors are usually unavailable or are ad hoc. To deal with this, recent efforts have shifted towards leveraging the insights from physical principles to guide the learning process. In this spirit, we propose a purely dynamics-constrained representation learning framework. Instead of relying on predefined probabilities, we restrict the latent representation to follow overdamped Langevin dynamics with a learnable transition density — a prior driven by statistical mechanics. We show this is a more natural constraint for representation learning in stochastic dynamical systems, with the crucial ability to uniquely identify the ground truth representation. We validate our framework for different systems including a real-world fluorescent DNA movie dataset. Here, we show that our algorithm can uniquely identify orthogonal, isometric and meaningful latent representations.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Characterization of oceanic post-cold frontal clouds and their model representation. Final report

Low-level clouds are ubiquitous over the oceans, and their impact on the Earth’ radiative budget is important. However, general circulation models (GCMs) that are used to represent our climate and its evolution still experience problems to represent their correct amount and radiative impact. In the extratropical latitudes (~30-60 N/S), cloud properties are strongly modulated by the occurrence of anti-cyclones (high pressure systems) and cyclones (low pressure systems). While deep clouds dominate in cyclones near the center and along the cold and warm fronts, low-level clouds populate the colder regions of the cyclones, and more specifically the region in the wake of the cold fronts, the post-cold frontal region (PCF). The GCMs mentioned above were found to underestimate the amount of these PCF clouds, and this caused errors in their representation of the amount of solar radiation at the surface of the southern hemisphere oceans, causing an excess in absorption and errors in long-term predictions. To better understand which processes are ill-represented in the GCMs to cause such issues, we used ground-based observations from the Eastern North Atlantic (ENA) ARM site and a high resolution regional model (called WRF) to examine the properties of PCF clouds. With the WRF model, we simulated the passage of a cold front at the ENA site using theoretically distinct representations of convection and the physics of the boundary layer. While these physical representations had little impact on the timing, structure and circulation of the cold front, we found a high sensitivity to how the large scale information was fed into the model. Errors rapidly developed if the incoming flow information was injected too far from the site, but 1000 km was found to be an optimal distance between the outer boundary and the ENA site for a realistic cold front passage. With this model, we then conducted a series of experiment where convection and boundary layer schemes were changed, and revealed that 1) the clouds were more sensitive to the convection than boundary layer schemes and 2) the interaction between the two has a large impact. Furthermore, changing the representation of the physics in the model had greater impacts on PCF clouds than changing the initial conditions. As large-scale models increase their spatial resolution, convection will eventually be resolved but it remains that their representation of the physics of the boundary layer will matter for the correct representation of shallow (low-level) clouds. Observations were used to find which large-scale information had a clear relationship with PCF cloud and precipitation properties, in view of helping with GCM parameterizations and evaluation. Both lower troposphere stability and surface forcing were found to be important for PCF clouds that experience more vigorous dynamics than their tropical or subtropical counterparts. For cloud base and top heights, a simple measure of the change in potential temperature between the surface and the 800 hPa was found to be a good predictor. This relationship was found to hold as well when using data from campaigns recently conducted in the southern ocean south of Tasmania. A recent GCM was found to succeed in representing similar relations. For cloud depth, water content, and different characteristics of precipitation both the temperature contrast between the surface and near-air and the near-surface wind speed had a strong relationship. To summarize, through observational constraints and regional model experiments, the project has provided guidance to evaluate GCMs and tools to improve their representation of low-level clouds in the extratropics. It has also highlighted differences in behavior between these clouds and those typically found in the subtropics, thus opening new avenues of research for shallow clouds in general.

54 ENVIRONMENTAL SCIENCES↗

Learning energy-based representations of quantum many-body states

Efficient representation of quantum many-body states on classical computers is a problem of practical importance. An ideal representation of a quantum state combines a succinct characterization informed by the structure and symmetries of the system along with the ability to predict the physical observables of interest. Several machine-learning approaches have been recently used to construct such classical representations, which enable predictions of observables and account for physical symmetries. However, the structure of a quantum state typically gets lost unless a specialized is employed based on prior knowledge of the system. Moreover, most such approaches give no information about what states are easier to learn in comparison with others. Here, we propose a generative energy-based representation of quantum many-body states derived from Gibbs distributions used for modeling the thermal states of classical spin systems. Based on the prior information on a family of quantum states, the energy function can be specified by a small number of parameters using an explicit low-degree polynomial or a generic parametric family such as neural nets and can naturally include the known symmetries of the system. Our results show that such a representation can be efficiently learned from data using exact algorithms in a form that enables the prediction of expectation values of physical observables. Importantly, the structure of the learned energy function provides a natural explanation for the difficulty of learning an energy-based representation of a given class of quantum states when measured in a certain basis. Published by the American Physical Society 2024

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

LieART 2.0 – A Mathematica application for Lie Algebras and Representation Theory

In this paper, we present LieART 2.0 which contains substantial extensions to the Mathematica application LieART (Lie Algebras and Representation Theory) for computations frequently encountered in Lie algebras and representation theory, such as tensor product decomposition and subalgebra branching of irreducible representations. The basic procedure is unchanged—it computes root systems of Lie algebras, weight systems and several other properties of irreducible representations, but new features and procedures have been included to allow the extensions to be seamless. The new version of LieART continues to be user friendly. New extended tables of properties, tensor products and branching rules of irreducible representations are included in the supplementary material for use without Mathematica software. LieART 2.0 now includes the branching rules to special subalgebras for all classical and exceptional Lie algebras up to and including rank 15.

97 MATHEMATICS AND COMPUTING↗

Quantum Algorithms for Representation-Theoretic Multiplicities

Kostka, Littlewood-Richardson, Plethysm, and Kronecker coefficients are the multiplicities of irreducible representations in the decomposition of representations of the symmetric group that play an important role in representation theory, geometric complexity, and algebraic combinatorics. We give quantum algorithms for computing these coefficients whenever the ratio of dimensions of the representations is polynomial. We show that there is an efficient classical algorithm for computing the Kostka numbers under this restriction and conjecture the existence of an analogous algorithm for the Littlewood-Richardson coefficients. We argue why such classical algorithm does not straightforwardly work for the Plethysm and Kronecker coefficients and conjecture that our quantum algorithms lead to superpolynomial speedups. The conjecture about Kronecker coefficients was disproved by Panova [Polynomial time classical versus quantum algorithms for representation theoretic multiplicities, arXiv:2502.20253] with a classical algorithm which, if optimal, points to a 𝒪⁡(𝑛 4+2⁢𝑘 ) vs $\tilde{Ω}$⁡(𝑛 4⁢𝑘 2 +1 ) polynomial gap in quantum vs classical computational complexity for an integer parameter 𝑘.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

Enhancing occupant behavior representation for interoperability between building information modeling and building energy modeling

Building Performance Simulation (BPS) has been adopted as an essential tool for designing, operating, and retrofitting buildings to optimize energy efficiency throughout the building life cycle. The Green Building XML (gbXML) schema facilitates seamless data exchange between Building Information Modeling (BIM) and Building Energy Modeling (BEM) software tools. However, limited occupant behavior (OB) representation in BIM often leads to inconsistent and inaccurate energy simulation in BEM software. This paper presents 154 systematic enhancements to the existing occupant behavior XML (obXML) schema v1.3.4, initially developed for standardizing OB representation for BEM, to address existing limitations and improve interoperability with BIM models. The enhancements encompass improved integration with BIM models through extended building representations and system operations, expanded support for advanced OB models with additional environmental parameters and mathematical capabilities, and implementation of a standardized model documentation framework. To facilitate seamless data transformation between gbXML and obXML schemas, we developed a publicly available gb-obXML Schema Converter. Three case studies demonstrate the enhanced schema’s capabilities: representation of building information using a two-story office building model, documentation of a window operation behavior model, and validation of the schema converter’s functionality. The enhanced obXML schema v1.4 enables sophisticated modeling of occupant-building interactions while maintaining consistency with industry-standard BIM schemas. The standardized documentation framework facilitates reproducibility and knowledge sharing in the OB research community, while the schema converter automates the integration of building information into OB simulation workflows. These enhancements establish a foundation for more accurate building performance simulation by supporting sophisticated representation of occupant behavior within the BIM-to-BEM simulation workflows.

Chung, Jihoon↗

Importance of Engineered and Learned Molecular Representations in Predicting Organic Reactivity, Selectivity, and Chemical Properties

Machine-readable chemical structure representations are foundational in all attempts to harness machine learning for the prediction of reactivities, selectivities, and chemical properties directly from molecular structure. The featurization of discrete chemical structures into a continuous vector space is a critical phase undertaken before model selection, and the development of new ways to quantitatively encode molecules is an active area of research. Here, we highlight the application and suitability of different representations, from expert-guided “engineered” descriptors to automatically “learned” features, in different prediction tasks relevant to organic and organometallic chemistry, where differing amounts of training data are available. These tasks include statistical models of stereo- and enantioselectivity, thermochemistry, and kinetics developed using experimental and quantum chemical data. The use of expert-guided molecular descriptors provides an opportunity to incorporate chemical knowledge, domain expertise, and physical constraints into statistical modeling. In applications to stereoselective organic and organometallic catalysis, where data sets may be relatively small and 3D-geometries and conformations play an important role, mechanistically informed features can be used successfully to obtain predictive statistical models that are also chemically interpretable. We provide an overview of several recent applications of this approach to obtain quantitative models for reactivity and selectivity, where topological descriptors, quantum mechanical calculations of electronic and steric properties, along with conformational ensembles, all feature as essential ingredients of the molecular representations used. Alternatively, more flexible, general-purpose molecular representations such as attributed molecular graphs can be used with machine learning approaches to learn the complex relationship between a structure and prediction target. This approach has the potential to out-perform more traditional representation methods such as “hand-crafted” molecular descriptors, particularly as data set sizes grow. One area where this is particularly relevant is in the use of large sets of quantum mechanical data to train quantitative structure–property relationships. A general approach toward curating useful data sets and training highly accurate graph neural network models is discussed in the context of organic bond dissociation enthalpies, where this strategy outperforms regression using precomputed descriptors. Finally, we describe how graph neural network predictions can be incorporated into mechanistically informed statistical models of chemical reactivity and selectivity. Once trained, this approach avoids the expensive computational overhead associated with quantum mechanical calculations, while maintaining chemical interpretability. We illustrate examples for which fast predictions of bond dissociation enthalpy and of the identities of radicals formed through cleavage of a molecule’s weakest bond are used in simple physical models of site-selectivity and reactivity.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Invariant Molecular Representations for Heterogeneous Catalysis

Catalyst screening is a critical step in the discovery and development of heterogeneous catalysts, which are vital for a wide range of chemical processes. In recent years, computational catalyst screening, primarily through density functional theory (DFT), has gained significant attention as a method for identifying promising catalysts. However, the computation of adsorption energies for all likely chemical intermediates present in complex surface chemistries is computationally intensive and costly due to the expensive nature of these calculations and the intrinsic idiosyncrasies of the methods or data sets used. This study introduces a novel machine learning (ML) method to learn adsorption energies from multiple DFT functionals by using invariant molecular representations (IMRs). To do this, we first extract molecular fingerprints for the reaction intermediates and later use a Siamese-neural-network-based training strategy to learn invariant molecular representations or the IMR across all available functionals. Our Siamese network-based representations demonstrate superior performance in predicting adsorption energies compared with other molecular representations. Notably, when considering mean absolute values of adsorption energies as 0.43 eV (PBE-D3), 0.46 eV (BEEF-vdW), 0.81 eV (RPBE), and 0.37 eV (scan+rVV10), our IMR method has achieved the lowest mean absolute errors (MAEs) of 0.18 0.10, 0.16, and 0.18 eV, respectively. These results emphasize the superior predictive capacity of our Siamese network-based representations. The empirical findings in this study illuminate the efficacy, robustness, and dependability of our proposed ML paradigm in predicting adsorption energies, specifically for propane dehydrogenation on a platinum catalyst surface.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Determining the N -Representability of a Reduced Density Matrix via Unitary Evolution and Stochastic Sampling

The N-representability problem consists in determining whether, for a given p-body matrix, there exists at least one N-body density matrix from which the p-body matrix can be obtained by contraction, that is, if the given matrix is a p-body reduced density matrix (p-RDM). The knowledge of all necessary and sufficient conditions for a p-body matrix to be N-representable allows the constrained minimization of a many-body Hamiltonian expectation value with respect to the p-body density matrix and, thus, the determination of its exact ground state. However, the number of constraints that complete the N-representability conditions grows exponentially with system size, and hence, the procedure quickly becomes intractable for practical applications. This work introduces a hybrid quantum-stochastic algorithm to effectively replace the N-representability conditions. The algorithm consists of applying to an initial N-body density matrix a sequence of unitary evolution operators constructed from a stochastic process that successively approaches the reduced state of the density matrix on a p-body subsystem, represented by a p-RDM, to a target p-body matrix, potentially a p-RDM. The generators of the evolution operators follow the well-known adaptive derivative-assembled pseudo-Trotter method (ADAPT), while the stochastic component is implemented by using a simulated annealing process. The resulting algorithm is independent of any underlying Hamiltonian, and it can be used to decide whether a given p-body matrix is N-representable, establishing a criterion to determine its quality and correcting it. We apply the proposed hybrid ADAPT algorithm to alleged reduced density matrices from a quantum chemistry electronic Hamiltonian, from the reduced Bardeen–Cooper–Schrieffer model with constant pairing, and from the Heisenberg XXZ spin model. In all cases, the proposed method behaves as expected for 1-RDMs and 2-RDMs, evolving the initial matrices toward different targets.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Advancing molecular machine learning representations with stereoelectronics-infused molecular graphs

Molecular representation is a critical element in our understanding of the physical world and the foundation for modern molecular machine learning. Previous molecular machine learning models have used strings, fingerprints, global features and simple molecular graphs that are inherently information-sparse representations. However, as the complexity of prediction tasks increases, the molecular representation needs to encode higher fidelity information. This work introduces a new approach to infusing quantum-chemical-rich information into molecular graphs via stereoelectronic effects, enhancing expressivity and interpretability. Learning to predict the stereoelectronics-infused representation with a tailored double graph neural network workflow enables its application to any downstream molecular machine learning task without expensive quantum-chemical calculations. We show that the explicit addition of stereoelectronic information substantially improves the performance of message-passing two-dimensional machine learning models for molecular property prediction. We show that the learned representations trained on small molecules can accurately extrapolate to much larger molecular structures, yielding chemical insight into orbital interactions for previously intractable systems, such as entire proteins, opening new avenues of molecular design. Finally, we have developed a web application (simg.cheme.cmu.edu) where users can rapidly explore stereoelectronic information for their own molecular systems.

Boiko, Daniil A↗