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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.

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At least 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2015

On Bipartite Graphs Trees and Their Partial Vertex Covers.

Graphs can be used to model risk management in various systems. Particularly, Caskurlu et al. in [7] have considered a system, which has threats, vulnerabilities and assets, and which essentially represents a tripartite graph. The goal in this model is to reduce the risk in the system below a predefined risk threshold level. One can either restricting the permissions of the users, or encapsulating the system assets. The pointed out two strategies correspond to deleting minimum number of elements corresponding to vulnerabilities and assets, such that the flow between threats and assets is reduced below the predefined threshold level. It can be shown that the main goal in this risk management system can be formulated as a Partial Vertex Cover problem on bipartite graphs. It is well-known that the Vertex Cover problem is in P on bipartite graphs, however; the computational complexity of the Partial Vertex Cover problem on bipartite graphs has remained open. In this paper, we establish that the Partial Vertex Cover problem is NP-hard on bipartite graphs, which was also recently independently demonstrated [N. Apollonio and B. Simeone, Discrete Appl. Math., 165 (2014), pp. 37–48; G. Joret and A. Vetta, preprint, arXiv:1211.4853v1 [cs.DS], 2012]. We then identify interesting special cases of bipartite graphs, for which the Partial Vertex Cover problem, the closely related Budgeted Maximum Coverage problem, and their weighted extensions can be solved in polynomial time. We also present an 8/9-approximation algorithm for the Budgeted Maximum Coverage problem in the class of bipartite graphs. We show that this matches and resolves the integrality gap of the natural LP relaxation of the problem and improves upon a recent 4/5-approximation.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2018

Gibbs Measures Over Locally Tree-Like Graphs and Percolative Entropy Over Infinite Regular Trees

Consider a statistical physical model on the d-regular infinite tree T{sub d} described by a set of interactions Φ. Let {G_n} be a sequence of finite graphs with vertex sets V{sub n} that locally converge to T{sub d}. From Φ one can construct a sequence of corresponding models on the graphs G{sub n}. Let {μ_n} be the resulting Gibbs measures. Here we assume that {μ_n} converges to some limiting Gibbs measure μ on T{sub d} in the local weak{sup ∗} sense, and study the consequences of this convergence for the specific entropies |V{sub n}|{sup −1}H(μ{sub n}). We show that the limit supremum of |V{sub n}|{sup −1}H(μ{sub n}) is bounded above by the percolative entropyH{sub perc}(μ), a function of μ itself, and that |V{sub n}|{sup −1}H(μ{sub n}) actually converges to H{sub perc}(μ) in case Φ exhibits strong spatial mixing on T{sub d}. When it is known to exist, the limit of |V{sub n}|{sup −1}H(μ{sub n}) is most commonly shown to be given by the Bethe ansatz. Percolative entropy gives a different formula, and we do not know how to connect it to the Bethe ansatz directly. We discuss a few examples of well-known models for which the latter result holds in the high temperature regime.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Classical eikonal from Magnus expansion

In a classical scattering problem, the classical eikonal is defined as the generator of the canonical transformation that maps in-states to out-states. It can be regarded as the classical limit of the log of the quantum S-matrix. In a classical analog of the Born approximation in quantum mechanics, the classical eikonal admits an expansion in oriented tree graphs, where oriented edges denote retarded/advanced worldline propagators. The Magnus expansion, which takes the log of a time-ordered exponential integral, offers an efficient method to compute the coefficients of the tree graphs to all orders. We exploit a Hopf algebra structure behind the Magnus expansion to develop a fast algorithm which can compute the tree coefficients up to the 12th order (over half a million trees) in less than an hour. In a relativistic setting, our methods can be applied to the post-Minkowskian (PM) expansion for gravitational binaries in the worldline formalism. We demonstrate the methods by computing the 3PM eikonal and find agreement with previous results based on amplitude methods. Importantly, the Magnus expansion yields a finite eikonal, while the naïve eikonal based on the time-symmetric propagator is infrared-divergent from 3PM on.

Black Holes↗
DOE OSTI2025

Differential equations for cosmological correlators

Cosmological fluctuations retain a memory of the physics that generated them in their spatial correlations. The strength of correlations varies smoothly as a function of external kinematics, which is encoded in differential equations satisfied by cosmological correlation functions. In this work, we provide a broader perspective on the origin and structure of these differential equations. As a concrete example, we study conformally coupled scalar fields in a power-law cosmology. The wavefunction coefficients in this model have integral representations, with the integrands being the product of the corresponding flat-space results and “twist factors” that depend on the cosmological evolution. Similar twisted integrals arise for loop amplitudes in dimensional regularization, and their recent study has led to the discovery of rich mathematical structures and powerful new tools for computing multi-loop Feynman integrals in quantum field theory. The integrals of interest in cosmology are also part of a finite-dimensional basis of master integrals, which satisfy a system of first-order differential equations. We develop a formalism to derive these differential equations for arbitrary tree graphs. The results can be represented in graphical form by associating the singularities of the differential equations with a set of graph tubings. Upon differentiation, these tubings grow in a local and predictive fashion. In fact, a few remarkably simple rules allow us to predict — by hand — the equations for all tree graphs. While the rules of this “kinematic flow” are defined purely in terms of data on the boundary of the spacetime, they reflect the physics of bulk time evolution. We also study the analogous structures in tr ϕ 3 theory, and see some glimpses of hidden structure in the sum over planar graphs. This suggests that there is an autonomous combinatorial or geometric construction from which cosmological correlations, and the associated spacetime, emerge.

Cosmological models↗
DOE OSTI2016

CHSalign: A Web Server That Builds upon Junction-Explorer and RNAJAG for Pairwise Alignment of RNA Secondary Structures with Coaxial Helical Stacking

RNA junctions are important structural elements of RNA molecules. They are formed when three or more helices come together in three-dimensional space. Recent studies have focused on the annotation and prediction of coaxial helical stacking (CHS) motifs within junctions. Here we exploit such predictions to develop an efficient alignment tool to handle RNA secondary structures with CHS motifs. Specifically, we build upon our Junction-Explorer software for predicting coaxial stacking and RNAJAG for modelling junction topologies as tree graphs to incorporate constrained tree matching and dynamic programming algorithms into a new method, called CHSalign, for aligning the secondary structures of RNA molecules containing CHS motifs. Thus, CHSalign is intended to be an efficient alignment tool for RNAs containing similar junctions. Experimental results based on thousands of alignments demonstrate that CHSalign can align two RNA secondary structures containing CHS motifs more accurately than other RNA secondary structure alignment tools. CHSalign yields a high score when aligning two RNA secondary structures with similar CHS motifs or helical arrangement patterns, and a low score otherwise. This new method has been implemented in a web server, and the program is also made freely available, at http://bioinformatics.njit.edu/CHSalign/.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2018

Sparse Hardware Embedding of Spiking Neuron Systems for Community Detection

We study the applicability of spiking neural networks and neuromorphic hardware for solving general optimization problems without the use of adaptive training or learning algorithms. We leverage the dynamics of Hopfield networks and spin-glass systems to construct a fully connected spiking neural system to generate synchronous spike responses indicative of the underlying community structure in an undirected, unweighted graph. Mapping this fully connected system to current generation neuromorphic hardware is done by embedding sparse tree graphs to generate only the leading-order spiking dynamics. Here, we demonstrate that for a chosen set of benchmark graphs, the spike responses generated on a current generation neuromorphic processor can improve the stability of graph partitions and non-overlapping communities can be identified even with the loss of higher-order spiking behavior if the graphs are sufficiently dense. For sparse graphs, the loss of higher-order spiking behavior improves the stability of certain graph partitions but does not retrieve the known community memberships.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2025

Hidden zeros of the cosmological wavefunction

Motivated by the recent discovery of hidden zeros in particle and string amplitudes, we characterize zeros of individual graph contributions to the cosmological wavefunction of a scalar field theory. We demonstrate that these contributions factorize near these zeros for all tree graphs and provide evidence that this extends to loop graphs as well. We explicitly construct polytopal realizations of the relevant graph associahedra and show that the cosmological zeros have natural geometric and physical interpretations. As a byproduct, we establish an equivalence between the wavefunction coefficients of chain graphs and flat-space Tr(ϕ 3 ) amplitudes, enabling us to leverage the cosmological zeros to uncover the recently discovered hidden zeros of colored amplitudes.

Cosmological models↗
DOE OSTI2023

ExTreeM: Scalable Augmented Merge Tree Computation via Extremum Graphs

Over the last decade merge trees have been proven to support a plethora of visualization and analysis tasks since they effectively abstract complex datasets. Here, this paper describes the ExTreeM-Algorithm: A scalable algorithm for the computation of merge trees via extremum graphs. The core idea of ExTreeM is to first derive the extremum graph G of an input scalar field f defined on a cell complex K, and subsequently compute the unaugmented merge tree of f on G instead of K; which are equivalent. Any merge tree algorithm can be carried out significantly faster on G, since K in general contains substantially more cells than G. To further speed up computation, ExTreeM includes a tailored procedure to derive merge trees of extremum graphs. The computation of the fully augmented merge tree, i.e., a merge tree domain segmentation of K, can then be performed in an optional post-processing step. All steps of ExTreeM consist of procedures with high parallel efficiency, and we provide a formal proof of its correctness. Our experiments, performed on publicly available datasets, report a speedup of up to one order of magnitude over the state-of-the-art algorithms included in the TTK and VTK-m software libraries, while also requiring significantly less memory and exhibiting excellent scaling behavior.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Programmable interactions and emergent geometry in an array of atom clouds

Interactions govern the flow of information and the formation of correlations between constituents of many-body quantum systems, dictating phases of matter found in nature and forms of entanglement generated in the laboratory. Typical interactions decay with distance and thus produce a network of connectivity governed by geometry—such as the crystalline structure of a material or the trapping sites of atoms in a quantum simulator. However, many envisioned applications in quantum simulation and computation require more complex coupling graphs including non-local interactions, which feature in models of information scrambling in black hole, and mappings of hard optimization problems onto frustrated classical magnets. Here we describe the realization of programmable non-local interactions in an array of atomic ensembles within an optical cavity, in which photons carry information between atomic spins. By programming the distance dependence of the interactions, we access effective geometries for which the dimensionality, topology and metric are entirely distinct from the physical geometry of the array. As examples, we engineer an antiferromagnetic triangular ladder, a Möbius strip with sign-changing interactions and a treelike geometry inspired by concepts of quantum gravity. The tree graph constitutes a toy model of holographic duality, in which the quantum system lies on the boundary of a higher-dimensional geometry that emerges from measured correlations. Overall, our work provides broader prospects for simulating frustrated magnets and topological phases, investigating quantum optimization paradigms and engineering entangled resource states for sensing and computation.

74 ATOMIC AND MOLECULAR PHYSICS↗
DOE OSTI2015

Higgs constraints from vector boson fusion and scattering

We present results on 4-lepton + 2-jet production, the partonic processes most commonly described as vector boson pair production in the Vector Boson Fusion (VBF) mode. That final state contains diagrams that are mediated by Higgs boson exchange. We focus particularly on the high-mass behaviour of the Higgs boson mediated diagrams, which unlike on-shell production, gives information about the Higgs couplings without assumptions on the Higgs boson total width. We assess the sensitivity of the high-mass region to Higgs coupling strengths, considering all vector boson pair channels, W - W + , W ± W ± , W ± Z and ZZ. Because of the small background, the most promising mode is W + W + which has sensitivity to Higgs couplings because of Higgs boson exchange in the t-channel. Furthermore, using the Caola-Melnikov (CM) method, the off-shell couplings can be interpreted as bounds on the Higgs boson total width. We estimate the bound that can be obtained with current data, as well as the bounds that could be obtained at √s=13 TeV in the VBF channel for data samples of 100 and 300 fb -1 . The CM method has already been successfully applied in the gluon fusion (GGF) production channel. The VBF production channel gives important complementary information, because both production and decay of the Higgs boson occur already at tree graph level.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Loops of loops expansion in the amplituhedron

We study a novel geometric expansion for scattering amplitudes in the planar sector of $\mathcal{N}$ = 4 super Yang-Mills theory, in the context of the Amplituhedron which reproduces the all-loop integrand as a canonical differential form on the positive geometry. In a paper by Arkani-Hamed, Henn and one of the authors, it was shown that this result can be recast in terms of negative geometries with a certain hierarchy of loops (closed cycles) in the space of loop momenta, represented by lines in momentum twistor space. One can then calculate an all-loop order result in the approximation where only tree graphs in the space of all loops are considered. Furthermore, using differential equation methods, it is possible to calculate and resum integrated expressions and obtain strong coupling results. In this paper, we provide a more general framework for the ‘loops of loops’ expansion and outline a powerful method for the determination of differential forms for higher-order geometries. We solve the problem completely for graphs with one internal cycle, but the method can be used more generally for other geometries.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

EVI-EnSitePy (Electric Vehicle Infrastructure – Energy Estimation and Site Optimization Tool in Python) [EVI-X Modeling Suite] [SWR-25-07]

EVI-EnSitePy is a comprehensive agent-based tool designed for the analysis and design of high-power charging sites, encompassing a wide array of site agents including Electric Vehicles (EVs), chargers, energy storage units (ESS), renewable energy resources (DER), and loads. This versatile tool offers diverse functionalities and a modular modeling approach, allowing detailed configuration of agents based on power ratings, port numbers, energy capacities, demand requirements, charger interfaces, and flexibility to customize the tool for project specific goals. By simulating agent interactions and employing various metrics, EVI-EnSitePy enables the assessment of site performance, exploration of energy management systems (EMS), and implementation of innovative EV charging policies. Utilizing EV charge schedules and arrival states, the tool performs thorough charging site simulations, with outputs consisting of agent and site-level power profiles and statistical metrics. Employing a tree graph structure, EVI-EnSitePy supports nested site structures and power distribution modeling. The tool's ability to generate charging schedules deterministically or via stochastic analysis further enhances its versatility. Through its features and capabilities, EVI-EnSitePy offers a powerful platform for informed decision-making in the realm of high-power charging site design and operation.

Jackson, Derek [National Renewable Energy Laborato↗
DOE OSTI2018

The Local Limit of the Uniform Spanning Tree on Dense Graphs

Let G be a connected graph in which almost all vertices have linear degrees and let T be a uniform spanning tree of G. For any fixed rooted tree F of height r we compute the asymptotic density of vertices v for which the r-ball around v in T is isomorphic to F. We deduce from this that if {G_n} is a sequence of such graphs converging to a graphon W, then the uniform spanning tree of G{sub n} locally converges to a multi-type branching process defined in terms of W. As an application, we prove that in a graph with linear minimum degree, with high probability, the density of leaves in a uniform spanning tree is at least e{sup −1}−o(1), the density of vertices of degree 2 is at most e{sup −1}+o(1) and the density of vertices of degree k⩾3 is at most (((k−2){sup k−2})/((k−1)!e{sup k−2}))+o(1). These bounds are sharp.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2016

Computing Maximum Cardinality Matchings in Parallel on Bipartite Graphs via Tree-Grafting

It is difficult to obtain high performance when computing matchings on parallel processors because matching algorithms explicitly or implicitly search for paths in the graph, and when these paths become long, there is little concurrency. In spite of this limitation, we present a new algorithm and its shared-memory parallelization that achieves good performance and scalability in computing maximum cardinality matchings in bipartite graphs. This algorithm searches for augmenting paths via specialized breadth-first searches (BFS) from multiple source vertices, hence creating more parallelism than single source algorithms. Algorithms that employ multiple-source searches cannot discard a search tree once no augmenting path is discovered from the tree, unlike algorithms that rely on single-source searches. We describe a novel tree-grafting method that eliminates most of the redundant edge traversals resulting from this property of multiple-source searches. We also employ the recent direction-optimizing BFS algorithm as a subroutine to discover augmenting paths faster. Our algorithm compares favorably with the current best algorithms in terms of the number of edges traversed, the average augmenting path length, and the number of iterations. Here, we provide a proof of correctness for our algorithm. Our NUMA-aware implementation is scalable to 80 threads of an Intel multiprocessor and to 240 threads on an Intel Knights Corner coprocessor. On average, our parallel algorithm runs an order of magnitude faster than the fastest algorithms available. The performance improvement is more significant on graphs with small matching number.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2023

TDAG: Tree-based Directed Acyclic Graph Partitioning for Quantum Circuits

We propose the Tree-based Directed Acyclic Graph (TDAG) partitioning for quantum circuits, a novel quantum circuit partitioning method which partitions circuits by viewing them as a series of binary trees and selecting the tree containing the most gates. TDAG produces results of comparable quality (number of partitions) to an existing method called ScanPartitioner (an exhaustive search algorithm) with an 95% average reduction in execution time. Furthermore, TDAG improves compared to a faster partitioning method called QuickPartitioner by 38% in terms of quality of the results with minimal overhead in execution time.

Clark, Joseph↗
DOE OSTI2020

The matrix product approximation for the dynamic cavity method

Stochastic dynamics of classical degrees of freedom, defined on vertices of locally tree-like graphs, can be studied in the framework of the dynamic cavity method which is exact for tree graphs. Such models correspond for example to spin-glass systems, Boolean networks, neural networks, and other technical, biological, and social networks. The central objects in the cavity method are edge messages—conditional probabilities of two vertex variable trajectories. In this paper, we discuss a rather pedagogical derivation for the dynamic cavity method, give a detailed account of the novel matrix product edge message (MPEM) algorithm for the solution of the dynamic cavity equation as introduced, and present optimizations and extensions. Matrix product approximations of the edge messages are constructed recursively in an iteration over time. Computation costs and precision can be tuned by controlling the matrix dimensions of the MPEM in truncations. Without truncations, the dynamics is exact. Data for Glauber–Ising dynamics shows a linear growth of computation costs in time. In contrast to Monte Carlo simulations, the approach has a much better error scaling. Hence, it gives for example access to low probability events and decaying observables like temporal correlations. Here, we discuss optimized truncation schemes and an extension that allows to capture models which have a continuum time limit.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2014

Cloud computing method for dynamically scaling a process across physical machine boundaries

A cloud computing platform includes first device having a graph or tree structure with a node which receives data. The data is processed by the node or communicated to a child node for processing. A first node in the graph or tree structure determines the reconfiguration of a portion of the graph or tree structure on a second device. The reconfiguration may include moving a second node and some or all of its descendant nodes. The second and descendant nodes may be copied to the second device.

Gillen, Robert E.↗
DOE OSTI2017

Peculiar spectral statistics of ensembles of trees and star-like graphs

In this paper we investigate the eigenvalue statistics of exponentially weighted ensembles of full binary trees and p-branching star graphs. We show that spectral densities of corresponding adjacency matrices demonstrate peculiar ultrametric structure inherent to sparse systems. In particular, the tails of the distribution for binary trees share the \Lifshitz singularity" emerging in the onedimensional localization, while the spectral statistics of p-branching star-like graphs is less universal, being strongly dependent on p. The hierarchical structure of spectra of adjacency matrices is interpreted as sets of resonance frequencies, that emerge in ensembles of fully branched tree-like systems, known as dendrimers. However, the relaxational spectrum is not determined by the cluster topology, but has rather the number-theoretic origin, re ecting the peculiarities of the rare-event statistics typical for one-dimensional systems with a quenched structural disorder. The similarity of spectral densities of an individual dendrimer and of ensemble of linear chains with exponential distribution in lengths, demonstrates that dendrimers could be served as simple disorder-less toy models of one-dimensional systems with quenched disorder.

97 MATHEMATICS AND COMPUTING↗