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Details the use of a custom embedding model on knowledge graphs to aid in downstream natural language processing (NLP) models for Derivative Classification Assist. Motivations, algorithms, and results were discussed.
Graph neural networks (GNNs) have been employed in materials research to predict physical and functional properties, and have achieved superior performance in several application domains over prior machine learning approaches. Recent studies incorporate features of increasing complexity such as Gaussian radial functions, plane wave functions, and angular terms to augment the neural network models, with the expectation that these features are critical for achieving a high performance. Here, we propose a GNN that adopts edge convolution where hidden edge features evolve during training and extensive attention mechanisms, and operates on simple graphs with atoms as nodes and distances between them as edges. As a result, the same model can be used for very different tasks as no other domain-specific features are used. With a model that uses no feature engineering, we achieve performance comparable with state-of-the-art models with elaborate features for formation energy and band gap prediction with standard benchmarks; we achieve even better performance when the dataset size increases. Although some domain-specific datasets still require hand-crafted features to achieve state-of-the-art results, our selected architecture choices greatly reduce the need for elaborate feature engineering and still maintain predictive power in comparison.
The emergent practical applicability of the Quantum Approximate Optimization Algorithm (QAOA) for approximate combinatorial optimization is a subject of considerable interest. One of the primary limitations of QAOA is the task of finding a set of good parameters, which is usually done using a variational optimization loop. Parameter transfer, or parameter concentration, is a phenomenon where QAOA angles trained on problem instances that are self-similar tend to perform well for other problem instances from that similar class. This suggests a potentially highly efficient and scalable non-variational learning method for QAOA angle finding. In this work, we systematically study QAOA parameter transferability from small problem sizes (16 and 27 decision variables) onto large problem instances (up to 156 qubits) for heavy-hex graph Ising models with geometrically local higher order terms using the Julia based QAOA simulation tool \texttt{JuliQAOA} to perform classical angle finding for up to $49$ QAOA layers ($p$). Parameter transfer of the fixed angles is validated using a combination of full statevector, Projected Entangled Pair States (PEPS), Matrix Product State (MPS), and LOWESA numerical simulations. We find that the QAOA parameter transfer from single instances applied to other (unseen) problem instances does not in general provide monotonically improving performance as a function of $p$ - there are many cases where the performance temporarily decreases as a function of $p$ - but despite this the transferred angles have a general trend of improved expectation value as the QAOA depth increases, in many cases converging close to the true ground-state energy of the $100+$ qubit instances. We also sample the hardware-compatible Ising models using the ensemble of transfer-learned QAOA parameters on several superconducting qubit IBM Quantum processors with 127, 133, and 156 qubits. We find continuous solution quality improvement of the hardware-compatible QAOA circuits run on the IBM NISQ processors up to $p=5$ on \texttt{ibm\_fez}, up to $p=9$ on \texttt{ibm\_torino}, and up to $p=10$ on \texttt{ibm\_pittsburgh}.
The role of rotation in the collisional quenching of the A2Sigma(+) v' = 0 states of OH and OD is investigated experimentally by laser-induced-fluorescence measurements in a two-chamber differentially pumped flow chamber similar to that of McDermid and Laudenslager (1982). The experimental apparatus is described in detail, and the results are presented in extensive tables and graphs. Collisional-quenching rate constants are determined for 21 different quenchers at various specific N' rotational levels and shown to decrease as the rotational quantum number increases, with no significant role for the internal levels of the colliding pairs and reasonable agreement with theoretical calculations incorporating attractive forces.
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.
A novel method for pairwise graph comparison that includes both the graph structure and applicable metadata. The resulting visual component allows a greater and more interpretable understanding of the comparison than current methods
The boundaries of the various regions of the magnetospheric plasma are considered, taking into account the bow shock, the magnetopause, the outer boundary of the plasma sheet, the inner boundary of the plasma sheet, and the trapping boundary for energetic particles. Attention is given to the steady state, or quasi-steady state, to substorm effects in which temporal changes are important, and to primary auroral processes. A description is presented of the high latitude lobes of the magnetotail. The characteristics of magnetic field topology associated with interconnected interplanetary and geomagnetic field lines are illustrated with the aid of a graph.
An integrated flight/aeroelastic control law is developed analytically for a hypothetical large supersonic transport aircraft in which the first aeroelastic mode frequency of the fuselage (6 rad/sec) is near the short-period mode (2 rad/sec). The approach employed is based on a linear-quadratic-regulator (LQR) formulation (yielding model-following state-feedback gains), followed by asymptotic loop-transfer recovery of LQR robustness (to produce an output-feedback control law). The derivation is outlined, and numerical results comparing the performance and multivariate stability robustness of the present controller with those of a classical controller are presented in graphs. The two controllers are shown to have similar characteristics, even with respect to the sources of limitations on robustness.
For zero energy, E = 0, we derive exact, classical and quantum solutions for all power-law oscillators with potentials V(r) = -gamma/r(exp nu), gamma greater than 0 and -infinity less than nu less than infinity. When the angular momentum is non-zero, these solutions lead to the classical orbits (p(t) = (cos mu(phi(t) - phi(sub 0)t))(exp 1/mu) with mu = nu/2 - 1 does not equal 0. For nu greater than 2, the orbits are bound and go through the origin. We calculate the periods and precessions of these bound orbits, and graph a number of specific examples. The unbound orbits are also discussed in detail. Quantum mechanically, this system is also exactly solvable. We find that when nu is greater than 2 the solutions are normalizable (bound), as in the classical case. Further, there are normalizable discrete, yet unbound, states. They correspond to unbound classical particles which reach infinity in a finite time. Finally, the number of space dimensions of the system can determine whether or not an E = 0 state is bound. These and other interesting comparisons to the classical system will be discussed.
Spatial search is the problem of finding a marked vertex in a graph. A continuous-time quantum walk in the single-excitation subspace of an $n$ spin system solves the problem of spatial search by finding the marked vertex in $O(\sqrt{n})$ time. Here, we investigate a natural extension of the spatial search problem, marking multiple vertices of a graph, which are still marked with local fields. We prove that a continuous-time quantum walk in the $k$-excitation subspace of $n$ spins can determine the binary string of $k$ marked vertices with an asymptotic fidelity in time $O(\sqrt{n})$, despite the size of the state space growing as $O(n^k)$. Numerically, we show that this algorithm can be implemented with interactions that decay as $1/r^\alpha$, where $r$ is the distance between spins, and an $\alpha$ that is readily available in current ion trap systems.
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.
Many applications from precision agriculture, environmental monitoring and transportation networks rely on data collected across space and time over a large geographic area. Missing data poses a significant challenge for any data-driven inference and control tasks. Data imputation or the estimation of missing data can help fill these gaps by utilizing inherent spatial relationships and temporal patterns. A variety of spatiotemporal imputation models have been developed to address missing data in spatiotemporal datasets. However, these classical methods rely on the assumption that the underlying data follows a smooth trend and fail to provide accurate estimates when there is a large number of missing points in the data. Even though there are machine learning driven tensor completion approaches such as convolutional neural network based tensor completion (CoSTCo) that capture the non-linear relationships in the dataset, the transductive nature makes the algorithm less scalable. Thus, existing approaches for estimating the missing information do not effectively capture all dimensions of the spatiotemporal data structure, resulting in erroneous predictions and poor performance. The main contributions of this paper are: (1) We propose a novel inductive framework (G-LSTM) for missing data imputation that integrates a graph neural network with LSTMs to effectively capture both spatial and temporal dependencies. (2) Experimental results on a traffic dataset demonstrate that the proposed GNN integrated with an LSTM framework achieves improved imputation and maintains steady performance even when there are extreme missing conditions in comparison with the state-of-the-art imputation framework (i.e, CoSTCo). (3) The simulation results on a traffic network show up to 69% reduction in mean absolute error and 61% reduction in root mean square error when compared to CoSTCo.
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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.
A general survey of the progress made in the areas of mathematical modelling of the system dynamics, structural analysis, development of control algorithms, and simulation of environmental disturbances is presented. The use of graph theory techniques is employed to examine the effects of inherent damping associated with LSST systems on the number and locations of the required control actuators. A mathematical model of the forces and moments induced on a flexible orbiting beam due to solar radiation pressure is developed and typical steady state open loop responses obtained for the case when rotations and vibrations are limited to occur within the orbit plane. A preliminary controls analysis based on a truncated (13 mode) finite element model of the 122m. Hoop/Column antenna indicates that a minimum of six appropriately placed actuators is required for controllability. An algorithm to evaluate the coefficients which describe coupling between the rigid rotational and flexible modes and also intramodal coupling was developed and numerical evaluation based on the finite element model of Hoop/Column system is currently in progress.
Results are reported from airborne measurements of NO, NO2, O3, and CO obtained in the free troposphere (FT) and boundary layer (BL) over the western U.S. and eastern Pacific during the NASA Global Tropospheric Experiment Chemical Instrumentation Test and Evaluation 2 (CITE 2) in summer 1986. The aircraft instrumentation and the CITE 2 flight protocols are described, and the results are presented in extensive tables and graphs. Over the ocean the median mixing ratios for NO and NO2 were found to be 4.0 and 10.4 parts per trillion by volume (pptv), respectively, in the BL and 12.4 and 18.0 pptv in the FT; the corresponding values over land were 34.5 and 75.0 pptv in the BL and 13.0 and 36.0 pptv in the FT. in continental air masses. NO(x) is shown to be positively correlated with O3 and CO and negatively correlated with dewpoint over the ocean, whereas over land NO(x) was positively correlated with O3, CO, and dewpoint.
Perturbative calculations involving fermion loops in quantum field theories require tracing over Dirac matrices. A simple way to regulate the divergences that generically appear in these calculations is dimensional regularisation, which has the consequence of replacing 4-dimensional Dirac matrices with d-dimensional counterparts for arbitrary complex values of d. In this work, a connection between traces of d-dimensional Dirac matrices and computations of the Tutte polynomial of associated graphs is proven. The time complexity of computing Dirac traces is analysed by this connection, and improvements to algorithms for computing Dirac traces are proposed.
Gas-rich impact-melt (GRIM) glasses in SNC meteorites are very rich in Martian atmospheric noble gases and sulfur suggesting a possible occurrence of regolith-derived secondary mineral assemblages in these samples. Previously, we have studied two GRIM glasses, 506 and 507, from EET79001 Lith A and Lith B, respectively, for elemental abundances and spatial distribution of sulfur using EMPA (WDS) and FE-SEM (EDS) techniques and for sulfur-speciation using K-edge XANES techniques. These elemental and FE-SEM micro-graph data at several locations in the GRIM glasses from Shergotty (DBS), Zagami 994 and EET79001, Lith B showed that FeO and SO3 are positively correlated (SO3 represents a mixture of sulfide and sulfate). FE-SEM (EDS) study revealed that the sulfur-rich pockets in these glasses contain numerous micron-sized iron-sulfide (Fe-S) globules sequestered throughout the volume. However, in some areas (though less frequently), we detected significant Fe-S-O signals suggesting the occurrence of iron sulfate. These GRIM glasses were studied by K-edge microXANES techniques for sulfur speciation in association with iron in sulfur-rich areas. In both samples, we found the sulfur speciation dominated by sulfide with minor oxidized sulfur mixed in with various proportions. The abundance of oxidized sulfur was greater in 506 than in 507. Based on these results, we hypothesize that sulfur initially existed as sulfate in the glass precursor materials and, on shock-impact melting of the precursor materials producing these glasses, the oxidized sulfur was reduced to predominately sulfide. In order to further test this hypothesis, we have used microXANES to measure the valence states of vanadium in GRIM glasses from Lith A and Lith B to complement and compare with previous analogous measurements on Lith C (note: 506 and 507 contain the largest amounts of martian atmospheric gases but the gas-contents in Lith C measured by are unknown). Vanadium is ideal for addressing this re-dox issue because it has multiple valence states and is a well-studied element. Ferrous-dominated iron valences determined by microXANES on the Lith A and Lith B glasses provide little redox sensitivity. Vanadium valence measurements for impact glass in Lith C at three different locations yielded valence values of 3.1, 3.2 and 3.4 with inferred fO2 values of IW-0.7, IW-0.1 and IW+0.7, respectively. This range of oxygen-fugacity values is understandable because the glasses are shock-molten impact glasses which are heterogeneous in nature. Oxygen fugacity values obtained from the analysis of Fe-Ti oxides and Eu partitioning in pyroxenes from EET79001 Lith A and Lith B (host lithologies) were in the range of IW+0.3 to IW+1.9 suggesting that V in the Lith C impact glass was reduced in the impact process. Here, we examine whether the 506 from Lith A and 507 from Lith B GRIM glasses yield similar or different fO2 values from those of Lith C using the vanadium K-edge microXANES technique.