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A formal theory of cubical complexes Formal report, 1 Sep. 1968 - 30 Apr. 1969
Algorithm for computation of test failures in cyclic circuits
A formal theory of cubical complexes Final report
Logic minimization and description of IBM 7094 program MIN6
Design of automata theory of cubical complexes with applications to diagnosis and algorithmic description
The following problems are considered: (1) methods for development of logic design together with algorithms, so that it is possible to compute a test for any failure in the logic design, if such a test exists, and developing algorithms and heuristics for the purpose of minimizing the computation for tests; and (2) a method of design of logic for ultra LSI (large scale integration). It was discovered that the so-called quantum calculus can be extended to render it possible: (1) to describe the functional behavior of a mechanism component by component, and (2) to compute tests for failures, in the mechanism, using the diagnosis algorithm. The development of an algorithm for the multioutput two-level minimization problem is presented and the program MIN 360 was written for this algorithm. The program has options of mode (exact minimum or various approximations), cost function, cost bound, etc., providing flexibility.
Design of automata theory of cubical complexes with applications to diagnosis and algorithmic description
Methods for development of logic design together with algorithms for failure testing, a method for design of logic for ultra-large-scale integration, extension of quantum calculus to describe the functional behavior of a mechanism component-by-component and to computer tests for failures in the mechanism using the diagnosis algorithm, and the development of an algorithm for the multi-output 2-level minimization problem are discussed.
Non-linear dynamics for clinicians: chaos theory, fractals, and complexity at the bedside
No abstract available
Using Systems Theory to Address Complex Challenges to International Spent Nuclear Fuel Transportation (Slides).
Abstract not provided.
Accurate Thermochemistry of Complex Lignin Structures via Density Functional Theory, Group Additivity, and Machine Learning
A molecular-level understanding of lignin structures and bond dissociation energies could facilitate depolymerization technologies. Still, this information is currently limited due to the lack of databases and the simplification of surrogate models. Here, substitution effects on seven common linkages in lignin polymers are systematically investigated. An automated reaction network generator is employed to create a database of structures. A new group additivity (GA) model based on principal component analysis (PCA) descriptors is introduced and trained on gas-phase density functional theory data of 4100 species at the M06-2X/6-311++G(d,p) level. Hydrogen bonds, local steric, and nonaromatic ring contributions are also incorporated. Lastly, we improve the accuracy of the group additivity model to reach the G4 theory by computing a data set of 770 species at this level and using a data fusion approach.
On the shell equations in complex form.
Linear thin shell theory in complex dependent variable form for determining fourth order partial differential equations, considering elastic shells with edge loads
Kohn–Sham calculations of NMR shifts for paramagnetic 3d metal complexes: protocols, delocalization error, and the curious amide proton shifts of a high-spin iron(ii) macrocycle complex
A theory for the nuclear chemical shifts of molecules in arbitrary spin states is applied to a set of paramagnetic organometallic complexes of 3d metals. Ligand chemical shifts are calculated and analyzed using Kohn–Sham (KS) density functional theory with and without relativistic corrections. The roles of the KS delocalization error, Gaussian-type versus Slater-type basis sets, relativistic effects (scalar and spin–orbit), and zero field splitting (ZFS) are investigated. A strong functional dependence of the chemical shifts is apparent and correlated with the delocalization error. Here, the functional dependence is between one and two orders of magnitude larger than variations of the NMR shifts due the other influences that are investigated. ZFS effects are negligible in the determination of the NMR chemical shifts of the complexes except at very low temperatures. The DFT calculated shifts agree reasonably well with experiment. A 73 ppm difference in the NMR shifts of the two protons in the amide groups of a high-spin Fe(II) macrocycle complex arises from selective O → Fe dative bonding that only involves the transfer of β spin density, along with orbital delocalization throughout the ligand bonding framework which electronically couples the coordinating oxygen lone pair orbitals directly to the amide trans proton.
Autonomous Energy Grids
Current frameworks to monitor, control, and optimize large-scale energy systems are becoming increasingly inadequate because of significantly high penetration levels of variable generation and distributed energy resources being integrated into electric power systems; the deluge of data from pervasive metering of energy grids; and a variety of new market mechanisms, including multilevel ancillary services. This paper outlines the concept of autonomous energy grids (AEGs). These systems are supported by a scalable, reconfigurable, and self-organizing information and control infrastructure, are extremely secure and resilient (self-healing), and can self-optimize in real time to ensure economic and reliable performance while systematically integrating energy in all forms. AEGs rely on cellular building blocks that can self-optimize when isolated from a larger grid and participate in optimal operation when interconnected to a larger grid. This paper describes the key concepts and research necessary in the broad domains of optimization theory, control theory, big data analytics, and complex system theory and modeling to realize the AEG vision.
Cation-π Bonding in Actinides: UO x + (Benzene) ( x = 0, 1, 2) Complexes Studied with Threshold Photodissociation Spectroscopy and Theory
Cation-π complexes of the form UO x + (benzene) (x = 0, 1, 2) are produced by laser vaporization and cooled in a supersonic molecular beam. These ions are mass selected and studied with UV–visible laser photodissociation spectroscopy. Each of these complexes photodissociates by elimination of the benzene ligand. Above an energetic threshold, the absorption and photodissociation are continuous, indicating a high density of strongly coupled electronic states. The thresholds for the dissociation of each of these three complexes are measured and assigned as their respective bond dissociation energies. The bond energies determined [U + –(benzene): 42.5 ± 0.3 kcal/mol; UO + –(benzene): 41.0 ± 0.3 kcal/mol; UO 2 + –(benzene): 39.7 ± 0.3 kcal/mol] are comparable to those of transition metal ion-benzene complexes. Computational studies at the DFT/B3LYP level complement the experiments, predicting dissociation energies in reasonably good agreement with the experiments. Experiments and theory agree that the U+(benzene) complex is more strongly bound than its corresponding oxide ions. This new thermochemistry on actinide cation-π bonding should stimulate higher-level computational studies on these systems.
Predicting Stability Constants for Uranyl Complexes Using Density Functional Theory
The ability to predict the equilibrium constants for the formation of 1:1 uranyl:ligand complexes (log K 1 values) provides the essential foundation for the rational design of ligands with enhanced uranyl affinity and selectivity. We also use density functional theory (B3LYP) and the IEFPCM continuum solvation model to compute aqueous stability constants for UO 2 2+ complexes with 18 donor ligands. Theoretical calculations permit reasonably good estimates of relative binding strengths, while the absolute log K 1 values are significantly overestimated. Accurate predictions of the absolute log K 1 values (root mean square deviation from experiment < 1.0 for log K 1 values ranging from 0 to 16.8) can be obtained by fitting the experimental data for two groups of mono and divalent negative oxygen donor ligands. The utility of correlations is demonstrated for amidoxime and imide dioxime ligands, providing a useful means of screening for new ligands with strong chelate capability to uranyl.
Free Energy Calculations of Crystalline Hard Sphere Complexes Using Density Functional Theory
Recently developed fundamental measure density functional theory (FMT) is used to study binary hard sphere (HS) complexes in crystalline phases. By comparing the excess free energy, pressure and phase diagram, we show that the fundamental measure functional yields good agreements to the available simulation results of AB, AB 2 and AB 13 crystals. Additionally, we use this functional to study the HS models of five binary crystals, Cu 5 Zr(C15 b ), Cu 51 Zr 14 (β), Cu 10 Zr 7 (φ), CuZr(B2) and CuZr 2 (C11 b ), which are observed in the Cu-Zr system. The FMT functional gives well behaved minimum for most of the hard sphere crystal complexes in the two dimensional Gaussian space, namely a crystalline phase. However, the current version of FMT functional (white Bear) fails to give a stable minimum for the structure Cu 10 Zr 7 (φ). We argue that the observed solid phases for the HS models of the Cu-Zr system are true thermodynamic stable phases and can be used as a reference system in perturbation calculations.
Equivariant Verlinde Formula from Fivebranes and Vortices
We study complex Chern–Simons theory on a Seifert manifold M 3 by embedding it into string theory. We show that complex Chern–Simons theory on M 3 is equivalent to a topologically twisted supersymmetric theory and its partition function can be naturally regularized by turning on a mass parameter. We find that the dimensional reduction of this theory to 2d gives the low energy dynamics of vortices in fourdimensional gauge theory, the fact apparently overlooked in the vortex literature. We also generalize the relations between (1) the Verlinde algebra, (2) quantum cohomology of the Grassmannian, (3) Chern–Simons theory on Σ × S 1 and (4) index of a spin c Dirac operator on the moduli space of flat connections to a new set of relations between (1) the “equivariant Verlinde algebra” for a complex group, (2) the equivariant quantum K-theory of the vortex moduli space, (3) complex Chern–Simons theory on Σ × S 1 and (4) the equivariant index of a spinc Dirac operator on the moduli space of Higgs bundles.
Impact Testing Theories and Techniques Employed at the TA-III Mechanical Shock Complex
We present theories and techniques to support safe, predictable, and efficient impact testing at the Sandia National Laboratories TA-III Mechanical Shock Complex (MSC), located in Building 6570. The two testing instruments used at the MSC are the 20-inch actuator, which is a launcher that propels sleds down an indoor track, and an indoor 6-in bore compressed-gas powered cannon. The theories and techniques presented derive from basic mechanical engineering principles but are significantly informed and validated by testing experience at the MSC.
Information transfer in complex systems, with applications to regulation
Information theory of complex systems
Operator origin of anomalous dimensions in de Sitter space
The late-time limit of the power spectrum for heavy (principal series) fields in de Sitter (dS) space yields a series of polynomial terms with complex scaling dimensions. Such scaling behavior is expected to result from an associated operator with a complex dimension. In a free theory, these complex dimensions are known to match the constraints imposed by unitarity on the space of states. Yet, perturbative corrections to the scaling behavior of operators are naively inconsistent with unitary evolution of the quantum fields in dS space. This paper demonstrates how to compute one-loop corrections to the scaling dimensions that appear in the two-point function from the field theory description in terms of local operators. We first show how to evaluate these anomalous dimensions using Mellin space, which has the feature that it naturally accommodates a scaleless regulator. We then explore the consequences for the soft de Sitter effective theory (SdSET) description that emerges in the long wavelength limit. Carefully matching between the UV and SdSET descriptions requires the introduction of novel nondynamical “operators” in the effective theory. This is not only necessary to reproduce results extracted from the Källén-Lehmann representation (that use the space of unitary states directly), but it is also required by general arguments that invoke positivity. Published by the American Physical Society 2025