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All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Mutually unbiased projectors and duality between lines and bases in finite quantum systems

Quantum systems with variables in the ring Z(d) are considered, and the concepts of weak mutually unbiased bases and mutually unbiased projectors are discussed. The lines through the origin in the Z(d)×Z(d) phase space, are classified into maximal lines (sets of d points), and sublines (sets of d{sub i} points where d{sub i}|d). The sublines are intersections of maximal lines. It is shown that there exists a duality between the properties of lines (resp., sublines), and the properties of weak mutually unbiased bases (resp., mutually unbiased projectors). -- Highlights: •Lines in discrete phase space. •Bases in finite quantum systems. •Duality between bases and lines. •Weak mutually unbiased bases.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
NASA NTRS1994

A new determination of radii and limb parameters for Pluto and Charon from mutual event lightcurves

Over the past several years Pluto-Charon mutual events have yielded progressively more accurate estimates of Charon's orbital elements and the radii of Pluto and Charon (e.g., Buie, Tholen, and Horne, 1992). Analysis of the 1988 stellar occultation by Pluto indicates a radius for Pluto that is about 4%, or 50 km, larger than the mutual event radius of 1151 km. One possible explanation for the discrepancy is that the mutual event modeling treats Pluto and Charon as uniformly bright disks. If they are limb-darkened, the mutual event fits could underestimate their radii. In this paper we use an independent mutual event data set (Young and Binzel, 1992) to fit for Pluto and Charon's radii in a manner independent of either object's limb profile or albedo distribution. Our least-squares solution indicates that Pluto's radius is 1164 +/- 22.9 km and Charon's radius is 621 +/- 20.6 km.

Young, Eliot F.↗
NASA NTRS2019

Mutual Orbit Orientations of Transneptunian Binaries

We present Keplerian orbit solutions for the mutual orbits of 17 transneptunian binary systems (TNBs). For ten of them, the orbit had not previously been known: 60458 2000 CM (sub 114), 119979 2002 WC (sub 19), 160091 2000 OL (sub 67), 160256 2002 PD (sub 149), 469514 2003 QA (sub 91), 469705 ǂKagara, 508788 2000 CQ (sub 114), 508869 2002 VT (sub 130), 1999 RT (sub 214), and 2002 XH (sub 91). Seven more are systems where the size, shape, and period of the orbit had been published, but new observations have now eliminated the sky plane mirror ambiguity in its orientation: 90482 Orcus, 120347 Salacia-Actaea, 1998 WW (sub 31), 1999 OJ (sub 4), 2000 QL (sub 251), 2001 XR (sub 254), and 2003 TJ (sub 58). The dynamical masses we obtain from TNB mutual orbits can be combined with estimates of the objects' sizes from thermal observations or stellar occultations to estimate their bulk densities. The ǂKagara system is currently undergoing mutual events in which one component casts its shadow upon the other and/or obstructs the view of the other. Such events provide valuable opportunities for further characterization of the system. Combining our new orbits with previously published orbits yields a sample of 35 binary orbits with known orientations that can provide important clues about the environment in which outer solar system planetesimals formed, as well as their subsequent evolutionary history. Among the relatively tight binaries, with semimajor axes less than about 5 percent of their Hill radii, prograde mutual orbits vastly outnumber retrograde orbits. This imbalance is not attributable to any known observational bias. We suggest that this distribution could be the signature of planetesimal formation through gravitational collapse of local density enhancements such as caused by the streaming instability. Wider binaries, with semimajor axes greater than 5 percent of their Hill radii, are somewhat more evenly distributed between prograde and retrograde orbits, but with mutual orbits that are aligned or anti-aligned with their heliocentric orbits. This pattern could perhaps result from Kozai-Lidov cycles coupled with tidal evolution eliminating high inclination wide binaries.

Grundy, W. M.↗
DOE OSTI2016

Exometabolomics Assisted Design and Validation of Synthetic Obligate Mutualism

Synthetic microbial ecology has the potential to enhance the productivity and resiliency of biotechnology processes compared to approaches using single isolates. Engineering microbial consortia is challenging; however, one approach that has attracted significant attention is the creation of synthetic obligate mutualism using auxotrophic mutants that depend on each other for exchange or cross-feeding of metabolites. In this paper, we describe the integration of mutant library fitness profiling with mass spectrometry based exometabolomics as a method for constructing synthetic mutualism based on cross-feeding. Two industrially important species lacking known ecological interactions, Zymomonas mobilis and Escherichia coli, were selected as the test species. Amino acid exometabolites identified in the spent medium of Z. mobilis were used to select three corresponding E. coli auxotrophs (proA, pheA and IlvA), as potential E. coli counterparts for the coculture. A pooled mutant fitness assay with a Z. mobilis transposon mutant library was used to identify mutants with improved growth in the presence of E. coli. An auxotroph mutant in a gene (ZMO0748) with sequence similarity to cysteine synthase A (cysK), was selected as the Z. mobilis counterpart for the coculture. Exometabolomic analysis of spent E. coli medium identified glutathione related metabolites as potentially available for rescue of the Z. mobilis cysteine synthase mutant. Three sets of cocultures between the Z. mobilis auxotroph and each of the three E. coli auxotrophs were monitored by optical density for growth and analyzed by flow cytometry to confirm high cell counts for each species. Taken together, our methods provide a technological framework for creating synthetic mutualisms combining existing screening based methods and exometabolomics for both the selection of obligate mutualism partners and elucidation of metabolites involved in auxotroph rescue.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2020

Mutualism increases diversity, stability, and function of multiplex networks that integrate pollinators into food webs

Ecosystems are composed of complex networks of many species interacting in different ways. While ecologists have long studied food webs of feeding interactions, recent studies increasingly focus on mutualistic networks including plants that exchange food for reproductive services provided by animals such as pollinators. Here, we synthesize both types of consumer-resource interactions to better understand the controversial effects of mutualism on ecosystems at the species, guild, and whole-community levels. We find that consumer-resource mechanisms underlying plant-pollinator mutualisms can increase persistence, productivity, abundance, and temporal stability of both mutualists and non-mutualists in food webs. These effects strongly increase with floral reward productivity and are qualitatively robust to variation in the prevalence of mutualism and pollinators feeding upon resources in addition to rewards. This work advances the ability of mechanistic network theory to synthesize different types of interactions and illustrates how mutualism can enhance the diversity, stability, and function of complex ecosystems.

54 ENVIRONMENTAL SCIENCES↗
DOE OSTI2016

INTEGRATION OF PARTICLE-GAS SYSTEMS WITH STIFF MUTUAL DRAG INTERACTION

Numerical simulation of numerous mm/cm-sized particles embedded in a gaseous disk has become an important tool in the study of planet formation and in understanding the dust distribution in observed protoplanetary disks. However, the mutual drag force between the gas and the particles can become so stiff—particularly because of small particles and/or strong local solid concentration—that an explicit integration of this system is computationally formidable. In this work, we consider the integration of the mutual drag force in a system of Eulerian gas and Lagrangian solid particles. Despite the entanglement between the gas and the particles under the particle-mesh construct, we are able to devise a numerical algorithm that effectively decomposes the globally coupled system of equations for the mutual drag force, and makes it possible to integrate this system on a cell-by-cell basis, which considerably reduces the computational task required. We use an analytical solution for the temporal evolution of each cell to relieve the time-step constraint posed by the mutual drag force, as well as to achieve the highest degree of accuracy. To validate our algorithm, we use an extensive suite of benchmarks with known solutions in one, two, and three dimensions, including the linear growth and the nonlinear saturation of the streaming instability. We demonstrate numerical convergence and satisfactory consistency in all cases. Our algorithm can, for example, be applied to model the evolution of the streaming instability with mm/cm-sized pebbles at high mass loading, which has important consequences for the formation scenarios of planetesimals.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1987

Mutual interactions of redox couples via electron exchange in silicate melts - Models for geochemical melt systems

The mutual interactions via electron exchange of redox couples in glass-forming melts were investigated both theoretically and experimentally. A thermodynamic approach for considering the mutual interactions leads to conclusion that the degree of mutual interaction in the melt should be proportional in part to the difference in relative reduction potentials of the interacting redox couples. Experimental studies verify this conclusion for numerous redox couples in several composition/temperature/oxygen fugacity regimes. Geochemical systems simultaneously possess many potentially multivalent elements; the stabilized redox states in the resulting magmas can be explained in part by mutual interactions and by redox buffering through the central Fe(III)- Fe(II) couples in the melts. The significance of these results for basaltic magmas of the earth, moon, and meteorites is addressed.

Schreiber, Henry D.↗
NASA NTRS1990

Mutual coupling between circular apertures on an infinite conducting ground plane and radiating into a finite width slab

The problem of electromagnetic coupling between two horns is of interest for the Microwave Reflectometer Ionization Sensor (MRIS) that will be used in the Aeroassist Flight Experiment (AFE). Laboratory measurements of mutual coupling between conical horns (using a flat metallic reflector to simulate a critically dense plasma outside) have shown a strong dependence on the finite dimensions of the shuttle tile over the apertures. Since both, the dielectric tile and the plasma outside the tile reflect microwaves, a study should be done to isolate the two mechanisms so that the MRIS reentry flight data can be interpreted correctly. Once the coupling due to the tile itself is determined then the location of the critial electron number density layers can be determined. As a first attempt to tackle this problem the Geometrical Theory of Diffraction was used to modify the existing solution to mutual coupling between apertures with infinite dielectric sheets. By using the equivalent current method, aperture theory to determine the radiated fields inside the dielectric tiles, and ray tracing the contributions to mutual coupling were determined. Results from two cases with different tile thicknesses have indicated that the main contribution to mutual coupling is due to diffraction from the bottom and top (back and front) wedges.

Christodoulou, Christos↗
NASA NTRS1997

Nonlinear pattern analysis of ventricular premature beats by mutual information

The frequency of ventricular premature beats (VPBs) has been related to the risk of mortality. However, little is known about the temporal pattern of occurrence of VPBs and its relationship to autonomic activity. Hence, we applied a general correlation measure, mutual information, to quantify how VPBs are generated over time. We also used mutual information to determine the correlation between VPB production and heart rate in order to evaluate effects of autonomic activity on VPB production. We examined twenty subjects with more than 3000 VPBs/day and simulated random time series of VPB occurrence. We found that mutual information values could be used to characterize quantitatively the temporal patterns of VPB generation. Our data suggest that VPB production is not random and VPBs generated with a higher value of mutual information may be more greatly affected by autonomic activity.

NASA Discipline Regulatory Physiology↗
NASA NTRS2007

On the Mutual Coupling Between Circular Resonant Slots

For near- and far-field microwave imaging purposes, array of circular resonant slots can be utilized to sample the electric field at a given reference plane. In general, the sensitivity of such array probes is impaired by the mutual coupling present between the radiating elements. The mutual coupling problem poses a design tradeoff between the resolution of the array and its sensitivity. In this paper, we investigate the mutual coupling between circular resonant slots in conducting ground plane both numerically and experimentally. Based on the analysis of the dominant coupling mechanism, i.e., the surface currents, various remedies to reduce the slots' mutual coupling are proposed and verified.

Abou-Khousa, M. A.↗
NASA NTRS2007

On the Mutual Coupling between Circular Resonant Slots

For near- and far-field microwave imaging purposes, array of circular resonant slots can be utilized to sample the electric field at a given reference plane. In general, the sensitivity of such an array is impaired by the existing mutual coupling between the radiating elements or in this case circular slots. The mutual coupling problem imposes a design tradeoff between the resolution of the array and the overall system sensitivity and dynamic range. In this paper, the mutual coupling between circular resonant slots in conducting ground plane is investigated both numerically and experimentally. In particular, the mutual coupling in the E- and H-plane configurations of two identical slots is studied.

Abou-Khousa, M. A.↗
DOE OSTI2021

Mutual Diffusion Coefficients of Na 2 SO 4 at C = 0.02989 mol·dm -3 and 298.15 K by Using Rayleigh Interferometry with Free Diffusion Boundary Conditions: Experimental Test of the Effect of the C 3/2 Concentration Dependence of Refractive Index at Low Concentration

Rayleigh interferometry is one of the most precise and accurate methods for the experimental determination of the mutual diffusion coefficients of both electrolytes and non-electrolytes in liquid solutions. For binary solutions at moderate and high concentrations where the concentration dependences of both diffusion coefficient and refractive index can be assumed to be linear or almost linear and the concentration difference ΔC between a pair of solutions undergoing free diffusion is not large compared to their average concentration, and by using proper combinations of the interference fringe positions as they vary with time, under these conditions diffusion coefficients are obtained that are independent of the size of ΔC. However, this situation becomes more complicated at low concentrations for electrolyte solutions where the concentration dependences of both the diffusion coefficient and refractive index are non-linear, with C 1/2 dependence for the diffusion coefficient and C 3/2 dependence for the refractive index. As a test of these effects on calculated mutual diffusion of electrolyte solutions at low concentrations as measured by Rayleigh interferometry, apparent mutual diffusion coefficients D v,a (volume-fixed reference frame) were measured for fixed average concentrations C=(0.02989 ± 0.00001) mol·dm –3 of Na 2 SO 4 (aq) at 298.15 K while varying ΔC/C from 0.66673 to 2, a threefold variation. The dependence of the diffusion coefficient on ΔC/C was found to be linear, yielding D v = 1.041 6 × 10 –9 m 2 ·s –1 for an infinitely small concentration difference between the diffusing solutions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Determination of the mutual orientation between proton CSA tensors mediated through band-selective 1 H– 1 H recoupling under fast MAS

We report the mutual orientation of nuclear spin interaction tensors provides critical information on the conformation and arrangement of molecules in chemicals, materials, and biological systems at an atomic level. Proton is a ubiquitous and important element in a variety of substances, and its NMR is highly sensitive due to their virtually 100% natural abundance and large gyromagnetic ratio. Nevertheless, the measurement of mutual orientation between the 1 H CSA tensors has remained largely untouched in the past due to strong 1 H– 1 H homonuclear interactions in a dense network of protons. In this study, we have developed a proton-detected 3D 1 H CSA/ 1 H CSA/ 1 H CS correlation method that utilizes three techniques to manage homonuclear interactions, namely fast magic-angle spinning, windowless C-symmetry-based CSA recoupling (windowless-ROCSA), and a band-selective 1 H– 1 H polarization transfer. The asymmetric 1 H CSA/ 1 H CSA correlated powder patterns produced by the C-symmetry-based methods are highly sensitive to the sign and asymmetry parameter of the 1 H CSA, and the Euler angle β as compared to the symmetric pattern obtained by the existing γ-encoded R-symmetry-based CSA/CSA correlation methods and allows a larger spectral area for data fitting. These features are beneficial for determining the mutual orientation between the nuclear spin interaction tensors with improved accuracy.

1H CSA↗
DOE OSTI2018

Evolution of bidirectional costly mutualism from byproduct consumption

Mutualisms are essential for life, yet it is unclear how they arise. A two-stage process has been proposed for the evolution of mutualisms that involve exchanges of two costly resources. First, costly provisioning by one species may be selected for if that species gains a benefit from costless byproducts generated by a second species, and cooperators get disproportionate access to byproducts. Selection could then drive the second species to provide costly resources in return. Previously, a synthetic consortium evolved the first stage of this scenario: Salmonella enterica evolved costly production of methionine in exchange for costless carbon byproducts generated by an auxotrophic Escherichia coli . Growth on agar plates localized the benefits of cooperation around methionine-secreting S. enterica . Here, we report that further evolution of these partners on plates led to hypercooperative E. coli that secrete the sugar galactose. Sugar secretion arose repeatedly across replicate communities and is costly to E. coli producers, but enhances the growth of S. enterica . The tradeoff between individual costs and group benefits led to maintenance of both cooperative and efficient E. coli genotypes in this spatially structured environment. This study provides an experimental example of de novo, bidirectional costly mutualism evolving from byproduct consumption. The results validate the plausibility of costly cooperation emerging from initially costless exchange, a scenario widely used to explain the origin of the mutualistic species interactions that are central to life on Earth.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2023

Improved quality metrics for association and reproducibility in chromatin accessibility data using mutual information

Correlation metrics are widely utilized in genomics analysis and often implemented with little regard to assumptions of normality, homoscedasticity, and independence of values. This is especially true when comparing values between replicated sequencing experiments that probe chromatin accessibility, such as assays for transposase-accessible chromatin via sequencing (ATAC-seq). Such data can possess several regions across the human genome with little to no sequencing depth and are thus non-normal with a large portion of zero values. Despite distributed use in the epigenomics field, few studies have evaluated and benchmarked how correlation and association statistics behave across ATAC-seq experiments with known differences or the effects of removing specific outliers from the data. Here, we developed a computational simulation of ATAC-seq data to elucidate the behavior of correlation statistics and to compare their accuracy under set conditions of reproducibility. Using these simulations, we monitored the behavior of several correlation statistics, including the Pearson’s R and Spearman’s ρ coefficients as well as Kendall’s τ and Top–Down correlation. We also test the behavior of association measures, including the coefficient of determination R 2 , Kendall’s W, and normalized mutual information. Our experiments reveal an insensitivity of most statistics, including Spear man’s ρ, Kendall’s τ, and Kendall’s W, to increasing differences between simulated ATAC-seq replicates. The removal of co-zeros (regions lacking mapped sequenced reads) between simulated experiments greatly improves the estimates of correlation and association. After removing co-zeros, the R 2 coefficient and normalized mutual information display the best performance, having a closer one-to-one relationship with the known portion of shared, enhanced loci between simulated replicates. When comparing values between experimental ATAC-seq data using a random forest model, mutual information best predicts ATAC-seq replicate relationships. Collectively, this study demonstrates how measures of correlation and association can behave in epigenomics experiments. We provide improved strategies for quantifying relationships in these increasingly prevalent and important chromatin accessibility assays.

59 BASIC BIOLOGICAL SCIENCES↗
DOE OSTI2021

Mutual information superadditivity and unitarity bounds

We derive the property of strong superadditivity of mutual information arising from the Markov property of the vacuum state in a conformal field theory and strong subadditivity of entanglement entropy. We show this inequality encodes unitarity bounds for different types of fields. These unitarity bounds are precisely the ones that saturate for free fields. This has a natural explanation in terms of the possibility of localizing algebras on null surfaces. A particular continuity property of mutual information characterizes free fields from the entropic point of view. We derive a general formula for the leading long distance term of the mutual information for regions of arbitrary shape which involves the modular flow of these regions. We obtain the general form of this leading term for two spheres with arbitrary orientations in spacetime, and for primary fields of any tensor representation. For free fields we further obtain the explicit form of the leading term for arbitrary regions with boundaries on null cones.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2023

Mutual-information based optimal experimental design for hyperpolarized $$^{13}$$C-pyruvate MRI

Abstract A key parameter of interest recovered from hyperpolarized (HP) MRI measurements is the apparent pyruvate-to-lactate exchange rate, $$k_{{\textrm PL}}$$ k P L , for measuring tumor metabolism. This manuscript presents an information-theory-based optimal experimental design approach that minimizes the uncertainty in the rate parameter, $$k_{{\textrm PL}}$$ k P L , recovered from HP-MRI measurements. Mutual information is employed to measure the information content of the HP measurements with respect to the first-order exchange kinetics of the pyruvate conversion to lactate. Flip angles of the pulse sequence acquisition are optimized with respect to the mutual information. A time-varying flip angle scheme leads to a higher parameter optimization that can further improve the quantitative value of mutual information over a constant flip angle scheme. However, the constant flip angle scheme, 35 and 28 degrees for pyruvate and lactate measurements, leads to an accuracy and precision comparable to the variable flip angle schemes obtained from our method. Combining the comparable performance and practical implementation, optimized pyruvate and lactate flip angles of 35 and 28 degrees, respectively, are recommended.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2014

Generalized mutual information and Tsirelson's bound

We introduce a generalization of the quantum mutual information between a classical system and a quantum system into the mutual information between a classical system and a system described by general probabilistic theories. We apply this generalized mutual information (GMI) to a derivation of Tsirelson's bound from information causality, and prove that Tsirelson's bound can be derived from the chain rule of the GMI. By using the GMI, we formulate the 'no-supersignalling condition' (NSS), that the assistance of correlations does not enhance the capability of classical communication. We prove that NSS is never violated in any no-signalling theory.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗