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All sourcesNASA NTRSDOE OSTI
DOE OSTI2022

Level density within a micro-macroscopic approach

Statistical level density $ρ$($E, A$) is derived for nucleonic system with a given energy $E$, particle number $A$ and other integrals of motion in the micro-macroscopic approximation beyond the standard saddle-point method of the Fermi gas model. This level density reaches the two limits; the well-known Fermi gas grand-canonical ensemble limit for a large entropy $S$ related to large excitation energies, and the finite micro-canonical limit for a small combinatorical entropy $S$ at low excitation energies. In conclusion, the inverse level density parameter $K$ as function of the particle number $A$ in the semiclassical periodic orbit theory, taking into account the extended Thomas-Fermi and Strutinsky shell corrections, is calculated and compared with experimental data.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Novel Strategy To Analyze Fourier Transform Ion Cyclotron Resonance Mass Spectrometry Data of Biomass Pyrolysis Oil for Oligomeric Structure Assignment

Among the most prominent challenges for the analysis of biomass pyrolysis products is the characterization of the abundant oligomer fraction of bio-oil. This fraction is principally made up of pyrolytic lignins and dehydrated, highly modified sugar oligomers, called humins, in liquid phase. An emerging technique for analysis of this oligomer fraction is high-resolution Fourier transform-ion cyclotron resonance mass spectrometry (FT-ICR MS), which allows for accurate determination of C x H y O z formulae for detected oligomers. Additionally, using simple dehydration and fragmentation reaction schemes, similar formulae can be developed from cellulose-, hemicellulose- and lignin-derived oligomers, which are primary depolymerization products. In this paper, FT-ICR MS analysis is coupled with combinatoric dehydration and fragmentation modeling in order to match experimentally detected bio-oil oligomers with hypothetical pathways for their formation during pyrolysis. In this way, we present a novel strategy by which oligomeric structures can be proposed for bio-oils. Using this approach, it becomes possible to advance the understanding of both the molecular structures comprising the bio-oil oligomer fraction and the pathways by which these structures form during biomass pyrolysis reactions.

09 BIOMASS FUELS↗
DOE OSTI2025

Efficient sparse state preparation via quantum walks

Continuous-time quantum walks (CTQWs) on dynamic graphs, referred to as dynamic CTQWs, are a recently introduced universal model of computation that offers a new paradigm in which to envision quantum algorithms. In this work, we develop an algorithm that converts single-edge and self-loop dynamic CTQWs to the gate model of computation. We use this mapping to introduce an efficient sparse quantum state preparation framework based on dynamic CTQWs. Our approach utilizes combinatorics techniques such as minimal hitting sets, minimum spanning trees, and shortest Hamiltonian paths to reduce the number of controlled gates required to prepare sparse states. We show that our framework encompasses the current state of the art ancilla-free sparse state preparation method by reformulating this method as a CTQW. This CTQW-based framework offers an alternative to the uniformly controlled rotation method used by Qiskit by requiring fewer CX gates when the target state has a polynomial number of non-zero amplitudes.

dynamic continuous time quantum walks↗
DOE OSTI2024

Efficient generation of grids and traversal graphs in compositional spaces towards exploration and path planning

Abstract Diverse disciplines across science and engineering deal with problems related to compositions, which exist in non-Euclidean simplex spaces, rendering many standard tools inaccurate or inefficient. This work explores such spaces conceptually in the context of materials discovery, quantifies their computational feasibility, and implements several essential methods specific to simplex spaces through a new high-performance open-source library . Most significantly, we derive and implement an algorithm for constructing a novel n-dimensional simplex graph data structure, containing all discretized compositions and possible neighbor-to-neighbor transitions. Critically, no distance or neighborhood calculations are performed, instead leveraging pure combinatorics and order in procedurally generated simplex grids, keeping the algorithm $${\mathcal{O}}(N)$$ O ( N ) , with minimal memory, enabling rapid construction of graphs with billions of transitions in seconds. Additionally, we demonstrate how such graph representations can be combined to homogeneously express complex path-planning problems, while facilitating efficient deployment of existing high-performance gradient descent, graph traversal, and other optimization algorithms.

Krajewski, Adam M. (ORCID:0000000222660099)↗
DOE OSTI2022

Microscopic-macroscopic level densities for low excitation energies

Level density ρ(E,Q) is derived within the micro-macroscopic approximation (MMA) for a system of strongly interacting Fermi particles with the energy E and additional integrals of motion Q , in line with several topics of the universal and fruitful activity of A. S. Davydov. Within the extended Thomas Fermi and semiclassical periodic orbit theory beyond the Fermi-gas saddle-point method, we obtain ρ ∝ I ν (S)/S ν , where I ν (S) is the modified Bessel function of the entropy S . For small shell-structure contribution, one finds ν = κ/2 + 1, where κ is the number of additional integrals of motion. This integer number is a dimension of Q, Q = { N, Z , …} for the case of two-component atomic nuclei, where N and Z are the numbers of neutrons and protons, respectively. For much larger shell structure contributions, one obtains ν = κ /2 + 2. The MMA level density ρ reaches the well-known Fermi gas asymptote for large excitation energies and the finite micro-canonical combinatoric limit for low excitation energies. Further, the additional integrals of motion can also be the projection of the angular momentum of a nuclear system for nuclear rotations of deformed nuclei, number of excitons for collective dynamics, and so on. Fitting the MMA total level density ρ( E , Q) for a set of the integrals of motion Q = { N, Z }, to experimental data on a long nuclear isotope chain for low excitation energies, one obtains the results for the inverse level-density parameter K , which differs significantly from those of neutron resonances due to shell, isotopic asymmetry, and pairing effects.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

Scalable generalized screening for high-order terms in the many-body expansion: Algorithm, open-source implementation, and demonstration

The many-body expansion lies at the heart of numerous fragment-based methods that are intended to sidestep the nonlinear scaling of ab initio quantum chemistry, making electronic structure calculations feasible in large systems. In principle, inclusion of higher-order n-body terms ought to improve the accuracy in a controllable way, but unfavorable combinatorics often defeats this in practice and applications with n ≥ 4 are rare. Here, we outline an algorithm to overcome this combinatorial bottleneck, based on a bottom-up approach to energy-based screening. This is implemented within a new open-source software application (“Fragme∩t”), which is integrated with a lightweight semi-empirical method that is used to cull subsystems, attenuating the combinatorial growth of higher-order terms in the graph that is used to manage the calculations. This facilitates applications of unprecedented size, and we report four-body calculations in (H2O)64 clusters that afford relative energies within 0.1 kcal/mol/monomer of the supersystem result using less than 10% of the unique subsystems. We also report n-body calculations in (H2O)20 clusters up to n = 8, at which point the expansion terminates naturally due to screening. These are the largest n-body calculations reported to date using ab initio electronic structure theory, and they confirm that high-order n-body terms are mostly artifacts of basis-set superposition error.

Chemistry↗
DOE OSTI2021

Beyond 4D tracking: using cluster shapes for track seeding

Tracking is one of the most time consuming aspects of event reconstruction at the Large Hadron Collider (LHC) and its high-luminosity upgrade (HL-LHC). Innovative detector technologies extend tracking to four-dimensions by including timing in the pattern recognition and parameter estimation. However, present and future hardware already have additional information that is largely unused by existing track seeding algorithms. The shape of pixel-clusters provides an additional dimension for track seeding that can significantly reduce the combinatorial challenge of track finding. We use neural networks to show that cluster shapes can reduce significantly the rate of fake combinatorical backgrounds while preserving a high efficiency. We demonstrate this using the information in cluster singlets, doublets and triplets. Numerical results are presented with simulations from the TrackML challenge.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2022

Discovering mechanisms for materials microstructure optimization via reinforcement learning of a generative model

Abstract The design of materials structure for optimizing functional properties and potentially, the discovery of novel behaviors is a keystone problem in materials science. In many cases microstructural models underpinning materials functionality are available and well understood. However, optimization of average properties via microstructural engineering often leads to combinatorically intractable problems. Here, we explore the use of the reinforcement learning (RL) for microstructure optimization targeting the discovery of the physical mechanisms behind enhanced functionalities. We illustrate that RL can provide insights into the mechanisms driving properties of interest in a 2D discrete Landau ferroelectrics simulator. Intriguingly, we find that non-trivial phenomena emerge if the rewards are assigned to favor physically impossible tasks, which we illustrate through rewarding RL agents to rotate polarization vectors to energetically unfavorable positions. We further find that strategies to induce polarization curl can be non-intuitive, based on analysis of learned agent policies. This study suggests that RL is a promising machine learning method for material design optimization tasks, and for better understanding the dynamics of microstructural simulations.

36 MATERIALS SCIENCE↗
DOE OSTI2025

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↗
DOE OSTI2024

Data-driven and model-agnostic approach to solving combinatorial assignment problems in searches for new physics

We present a novel approach to solving combinatorial assignment problems in particle physics. The correct assignment of decay products to parent particles is achieved in a model-agnostic fashion by introducing a neural network architecture, asswd-, which combines a custom layer based on attention mechanisms and dual autoencoders. We demonstrate how the network, trained purely on background events in an unsupervised setting, is capable of reconstructing correctly hypothetical new particles regardless of their mass, decay multiplicity, and substructure, and produces simultaneously an anomaly score that can be used to efficiently suppress the background. This model allows the extension of the suite of searches for localized excesses to include nonresonant particle pair production where the reconstruction of the two resonant masses is thwarted by combinatorics. Published by the American Physical Society 2024

Astronomy & Astrophysics↗
DOE OSTI2023

An over-approximation of entropy for elemental multiconfigurational ground state electronic structures

The ability to predict the chemical and physical properties of a material is directly related to the structure and interactions of its electrons. For materials comprised of f-block elements (the lanthanides and actinides found in the last two rows of the periodic table), the complexity of electronic structure has presented great difficulty in understanding, modeling, and predicting material properties. The complexity of multiconfigurational ground state electronic structures is illustrated herein by the combinatorics of electron permutations within individual and cumulative occupancy configurations. A non-integer orbital occupancy representation of multiconfigurational ground states is described for superposition mixing between multiple near-energy degenerate occupancy configurations and generalized in such a way that established ground states are returned by approximation for elements with less-complex electronic structures. By considering the occupancy configurations as statistical mechanics macrostates, and the permutations of electrons as statistical mechanics microstates within those macrostates, an over-approximation of entropy for multiconfigurational elemental ground state electronic structures has been calculated.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

A Unified Approach to Unimodality of Gaussian Polynomials

In 2013, Pak and Panova proved the strict unimodality property of q-binomial coefficients (as polynomials in q) based on the combinatorics of Young tableaux and the semigroup property of Kronecker coefficients. They showed it to be true for all ℓ, m ≥ 8 and a few other cases. We propose a different approach to this problem based on computer algebra, where we establish a closed form for the coefficients of these polynomials and then use cylindrical algebraic decomposition to identify exactly the range of coefficients where strict unimodality holds. This strategy allows us to tackle generalizations of the problem, e.g., to show unimodality with larger gaps or unimodality of related sequences. In particular, we present proofs of two additional cases of a conjecture by Stanley and Zanello.

Koutschan, Christoph↗
DOE OSTI2023

BARC Element Classifier (barc)

SAND2024-02120O This program enumerates and classifies all possible functional elements in several different categories within the Ballistic Asynchronous Reversible Computing (barc) model of computation. barc software is a research tool that is being used to help document the possible digital behaviors of primitive functional elements in the ABRC a.k.a. BARC model of computation. The method of operation of this software leverages elementary concepts and methods from discrete mathematics: combinatorics (permutations), partitions and equivalence classes, symmetry transformations, and the theory of finite groups. Implementation is in Python programming language. Sandia National Laboratories is a multimission laboratory managed and operated by National Technology & Engineering Solutions of Sandia, LLC, a wholly owned subsidiary of Honeywell International Inc., for the U.S. Department of Energy’s National Nuclear Security Administration under contract DE-NA0003525.

Frank, Michael↗
DOE OSTI2021

Data from: Learning coagulation processes with combinatorially-invariant neural networks

This dataset contains all the necessary information to recreate the study presented in the paper entitled "Learning coagulation processes with combinatorially-invariant neural networks". This consists of (1) the aggregated output files used for machine learning, (2) the machine learning codes used to learn the presented models, (3) the PartMC model source code that was used to generate the simulation data and (4) the Python scripts used construct the scenario library for training and testing simulations. This data was used to investigate a method (combinatorally-invariant neural network) for learning the aerosol process of coagulation. This data may be useful for application of other methods.

Atmospheric chemistry↗
DOE OSTI2024

Lorentzian contours for tree-level string amplitudes

We engineer compact contours on the moduli spaces of genus-zero Riemann surfaces that achieve analytic continuation from Euclidean to Lorentzian worldsheets. These generalized Pochhammer contours are based on the combinatorics of associahedra and make the analytic properties of tree-level amplitudes entirely manifest for any number and type of external strings. We use them in practice to perform first numerical computations of open and closed string amplitudes directly in the physical kinematics for n=4,5,6,7,8,9 n = 4 , 5 , 6 , 7 , 8 , 9 . We provide a code that allows anyone to do such computations.

Physics↗
DOE OSTI2023

Smart Pixels: towards on-sensor inference of charged particle track parameters and uncertainties

The combinatorics of track seeding has long been a computational bottleneck for triggering and offline computing in High Energy Physics (HEP), and remains so for the HL-LHC. Next-generation pixel sensors will be sufficiently fine-grained to determine angular information of the charged particle passing through from pixel-cluster properties. This detector technology immediately improves the situation for offline tracking, but any major improvements in physics reach are unrealized since they are dominated by lowest-level hardware trigger acceptance. We will demonstrate track angle and hit position prediction, including errors, using a mixture density network within a single layer of silicon as well as the progress towards and status of implementing the neural network in hardware on both FPGAs and ASICs.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Novel Mutant Alleles Reveal a Role of the Extra-Large G Protein in Rice Grain Filling, Panicle Architecture, Plant Growth, and Disease Resistance

Plant growth and grain filling are the key agronomical traits for grain weight and yield of rice. The continuous improvement in rice yield is required for a future sustainable global economy and food security. The heterotrimeric G protein complex containing a canonical α subunit (RGA1) couples extracellular signals perceived by receptors to modulate cell function including plant development and grain weight. We hypothesized that, besides RGA1, three atypical, extra-large GTP-binding protein (XLG) subunits also regulate panicle architecture, plant growth, development, grain weight, and disease resistance. Here, we identified a role of XLGs in agronomic traits and stress tolerance by genetically ablating all three rice XLGs individually and in combination using the CRISPR/Cas9 genome editing in rice. For this study, eight (three single, two double, and three triple) null mutants were selected. Three XLG proteins combinatorically regulate seed filling, because loss confers a decrease in grain weight from 14% with loss of one XLG and loss of three to 32% decrease in grain weight. Null mutations in XLG2 and XLG4 increase grain size. The mutants showed significantly reduced panicle length and number per plant including lesser number of grains per panicle compared to the controls. Loss-of-function of all individual XLGs contributed to 9% more aerial biomass compared to wild type (WT). The double mutant showed improved salinity tolerance. Moreover, loss of the XLG gene family confers hypersensitivity to pathogens. Our findings suggest that the non-canonical XLGs play important roles in regulating rice plant growth, grain filling, panicle phenotype, stress tolerance, and disease resistance. Genetic manipulation of XLG s has the potential to improve agronomic properties in rice.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2024

Estimation of the Chances to Find New Phenomena at the LHC in a Model-Agnostic Combinatorial Analysis

In this paper, we estimate the number of event topologies that have the potential to be produced in 𝑝𝑝 collisions at the Large Hadron Collider (LHC) without violating kinematic and other constraints. We use numerical calculations and combinatorics, guided by large-scale Monte Carlo simulations of Standard Model (SM) processes. Then, we set the upper limit on the probability that new physics may escape detection, assuming a model-agnostic approach. The calculated probability is unexpectedly large, and the fact that LHC has not found new physics until now is not entirely surprising. Theoretical limitations and experimental challenges in observing new physics within the studied exclusive event classes are examined.

BSM↗