Fragment-based {sup 13}C nuclear magnetic resonance chemical shift predictions in molecular crystals: An alternative to planewave methods

Energy Technology Data Exchange (ETDEWEB)

Hartman, Joshua D.; Beran, Gregory J. O., E-mail: gregory.beran@ucr.edu [Department of Chemistry, University of California, Riverside, California 92521 (United States); Monaco, Stephen; Schatschneider, Bohdan [The Pennsylvania State University, The Eberly Campus, 2201 University Dr, Lemont Furnace, Pennsylvania 15456 (United States)

2015-09-14

We assess the quality of fragment-based ab initio isotropic {sup 13}C chemical shift predictions for a collection of 25 molecular crystals with eight different density functionals. We explore the relative performance of cluster, two-body fragment, combined cluster/fragment, and the planewave gauge-including projector augmented wave (GIPAW) models relative to experiment. When electrostatic embedding is employed to capture many-body polarization effects, the simple and computationally inexpensive two-body fragment model predicts both isotropic {sup 13}C chemical shifts and the chemical shielding tensors as well as both cluster models and the GIPAW approach. Unlike the GIPAW approach, hybrid density functionals can be used readily in a fragment model, and all four hybrid functionals tested here (PBE0, B3LYP, B3PW91, and B97-2) predict chemical shifts in noticeably better agreement with experiment than the four generalized gradient approximation (GGA) functionals considered (PBE, OPBE, BLYP, and BP86). A set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided based on these benchmark calculations. Statistical cross-validation procedures are used to demonstrate the robustness of these fits.

Nuclear spin relaxation due to chemical shift anisotropy of gas-phase 129Xe.

Science.gov (United States)

Hanni, Matti; Lantto, Perttu; Vaara, Juha

2011-08-14

Nuclear spin relaxation provides detailed dynamical information on molecular systems and materials. Here, first-principles modeling of the chemical shift anisotropy (CSA) relaxation time for the prototypic monoatomic (129)Xe gas is carried out, both complementing and predicting the results of NMR measurements. Our approach is based on molecular dynamics simulations combined with pre-parametrized ab initio binary nuclear shielding tensors, an "NMR force field". By using the Redfield relaxation formalism, the simulated CSA time correlation functions lead to spectral density functions that, for the first time, quantitatively determine the experimental spin-lattice relaxation times T(1). The quality requirements on both the Xe-Xe interaction potential and binary shielding tensor are investigated in the context of CSA T(1). Persistent dimers Xe(2) are found to be responsible for the CSA relaxation mechanism in the low-density limit of the gas, completely in line with the earlier experimental findings.

Numbat: an interactive software tool for fitting Δχ-tensors to molecular coordinates using pseudocontact shifts

International Nuclear Information System (INIS)

Schmitz, Christophe; Stanton-Cook, Mitchell J.; Su Xuncheng; Otting, Gottfried; Huber, Thomas

2008-01-01

Pseudocontact shift (PCS) effects induced by a paramagnetic lanthanide bound to a protein have become increasingly popular in NMR spectroscopy as they yield a complementary set of orientational and long-range structural restraints. PCS are a manifestation of the χ-tensor anisotropy, the Δχ-tensor, which in turn can be determined from the PCS. Once the Δχ-tensor has been determined, PCS become powerful long-range restraints for the study of protein structure and protein-ligand complexes. Here we present the newly developed package Numbat (New User-friendly Method Built for Automatic Δχ-Tensor determination). With a Graphical User Interface (GUI) that allows a high degree of interactivity, Numbat is specifically designed for the computation of the complete set of Δχ-tensor parameters (including shape, location and orientation with respect to the protein) from a set of experimentally measured PCS and the protein structure coordinates. Use of the program for Linux and Windows operating systems is illustrated by building a model of the complex between the E. coli DNA polymerase III subunits ε186 and θ using PCS

Chemical shift-dependent apparent scalar couplings: An alternative concept of chemical shift monitoring in multi-dimensional NMR experiments

International Nuclear Information System (INIS)

Kwiatkowski, Witek; Riek, Roland

2003-01-01

The paper presents an alternative technique for chemical shift monitoring in a multi-dimensional NMR experiment. The monitored chemical shift is coded in the line-shape of a cross-peak through an apparent residual scalar coupling active during an established evolution period or acquisition. The size of the apparent scalar coupling is manipulated with an off-resonance radio-frequency pulse in order to correlate the size of the coupling with the position of the additional chemical shift. The strength of this concept is that chemical shift information is added without an additional evolution period and accompanying polarization transfer periods. This concept was incorporated into the three-dimensional triple-resonance experiment HNCA, adding the information of 1 H α chemical shifts. The experiment is called HNCA coded HA, since the chemical shift of 1 H α is coded in the line-shape of the cross-peak along the 13 C α dimension

Metal alkyls programmed to generate metal alkylidenes by α-H abstraction: prognosis from NMR chemical shift† †Electronic supplementary information (ESI) available: Experimental and computational details, NMR spectra, results of NMR calculations and NCS analysis, graphical representation of shielding tensors, molecular orbital diagrams of selected compounds, optimized structures for all calculated species. See DOI: 10.1039/c7sc05039a

Science.gov (United States)

Gordon, Christopher P.; Yamamoto, Keishi; Searles, Keith; Shirase, Satoru

2018-01-01

Metal alkylidenes, which are key organometallic intermediates in reactions such as olefination or alkene and alkane metathesis, are typically generated from metal dialkyl compounds [M](CH2R)2 that show distinctively deshielded chemical shifts for their α-carbons. Experimental solid-state NMR measurements combined with DFT/ZORA calculations and a chemical shift tensor analysis reveal that this remarkable deshielding originates from an empty metal d-orbital oriented in the M–Cα–Cα′ plane, interacting with the Cα p-orbital lying in the same plane. This π-type interaction inscribes some alkylidene character into Cα that favors alkylidene generation via α-H abstraction. The extent of the deshielding and the anisotropy of the alkyl chemical shift tensors distinguishes [M](CH2R)2 compounds that form alkylidenes from those that do not, relating the reactivity to molecular orbitals of the respective molecules. The α-carbon chemical shifts and tensor orientations thus predict the reactivity of metal alkyl compounds towards alkylidene generation. PMID:29675237

Random coil chemical shift for intrinsically disordered proteins

DEFF Research Database (Denmark)

Kjærgaard, Magnus; Brander, Søren; Poulsen, Flemming Martin

2011-01-01

. Temperature has a non-negligible effect on the (13)C random coil chemical shifts, so temperature coefficients are reported for the random coil chemical shifts to allow extrapolation to other temperatures. The pH dependence of the histidine random coil chemical shifts is investigated in a titration series......, which allows the accurate random coil chemical shifts to be obtained at any pH. By correcting the random coil chemical shifts for the effects of temperature and pH, systematic biases of the secondary chemical shifts are minimized, which will improve the reliability of detection of transient secondary...

Using chemical shift perturbation to characterise ligand binding.

Science.gov (United States)

Williamson, Mike P

2013-08-01

Chemical shift perturbation (CSP, chemical shift mapping or complexation-induced changes in chemical shift, CIS) follows changes in the chemical shifts of a protein when a ligand is added, and uses these to determine the location of the binding site, the affinity of the ligand, and/or possibly the structure of the complex. A key factor in determining the appearance of spectra during a titration is the exchange rate between free and bound, or more specifically the off-rate koff. When koff is greater than the chemical shift difference between free and bound, which typically equates to an affinity Kd weaker than about 3μM, then exchange is fast on the chemical shift timescale. Under these circumstances, the observed shift is the population-weighted average of free and bound, which allows Kd to be determined from measurement of peak positions, provided the measurements are made appropriately. (1)H shifts are influenced to a large extent by through-space interactions, whereas (13)Cα and (13)Cβ shifts are influenced more by through-bond effects. (15)N and (13)C' shifts are influenced both by through-bond and by through-space (hydrogen bonding) interactions. For determining the location of a bound ligand on the basis of shift change, the most appropriate method is therefore usually to measure (15)N HSQC spectra, calculate the geometrical distance moved by the peak, weighting (15)N shifts by a factor of about 0.14 compared to (1)H shifts, and select those residues for which the weighted shift change is larger than the standard deviation of the shift for all residues. Other methods are discussed, in particular the measurement of (13)CH3 signals. Slow to intermediate exchange rates lead to line broadening, and make Kd values very difficult to obtain. There is no good way to distinguish changes in chemical shift due to direct binding of the ligand from changes in chemical shift due to allosteric change. Ligand binding at multiple sites can often be characterised, by

The calculation of proton chemical shifts in hydrocarbons

Energy Technology Data Exchange (ETDEWEB)

Abraham, Raymond J [Liverpool Univ. (United Kingdom). Dept. of Chemistry

1994-12-31

Novel extension of the CHARGE3 semi-empirical calculation of the partial atomic charges in molecules are described which allow the accurate calculation of the proton chemical shifts of a variety of acyclic alkanes. This simple scheme predicts the proton chemical shifts of all the simple alkanes, cyclohexane and methyl cyclohexanes, norbornane, trans-decalin and trans perhydrophenanthrene, comprising a range of chemical shifts from 0.3 to 2.2 {delta} with the known substituent chemical shifts of other functional groups this could allow the general prediction of proton chemical shifts in a simple and useful format. (author) 13 refs., 2 figs.

Comparison of Magnetic Susceptibility Tensor and Diffusion Tensor of the Brain.

Science.gov (United States)

Li, Wei; Liu, Chunlei

2013-10-01

Susceptibility tensor imaging (STI) provides a novel approach for noninvasive assessment of the white matter pathways of the brain. Using mouse brain ex vivo , we compared STI with diffusion tensor imaging (DTI), in terms of tensor values, principal tensor values, anisotropy values, and tensor orientations. Despite the completely different biophysical underpinnings, magnetic susceptibility tensors and diffusion tensors show many similarities in the tensor and principal tensor images, for example, the tensors perpendicular to the fiber direction have the highest gray-white matter contrast, and the largest principal tensor is along the fiber direction. Comparison to DTI fractional anisotropy, the susceptibility anisotropy provides much higher sensitivity to the chemical composition of the white matter, especially myelin. The high sensitivity can be further enhanced with the perfusion of ProHance, a gadolinium-based contrast agent. Regarding the tensor orientations, the direction of the largest principal susceptibility tensor agrees with that of diffusion tensors in major white matter fiber bundles. The STI fiber tractography can reconstruct the fiber pathways for the whole corpus callosum and for white matter fiber bundles that are in close contact but in different orientations. There are some differences between susceptibility and diffusion tensor orientations, which are likely due to the limitations in the current STI reconstruction. With the development of more accurate reconstruction methods, STI holds the promise for probing the white matter micro-architectures with more anatomical details and higher chemical sensitivity.

Validation of archived chemical shifts through atomic coordinates

Science.gov (United States)

Rieping, Wolfgang; Vranken, Wim F

2010-01-01

The public archives containing protein information in the form of NMR chemical shift data at the BioMagResBank (BMRB) and of 3D structure coordinates at the Protein Data Bank are continuously expanding. The quality of the data contained in these archives, however, varies. The main issue for chemical shift values is that they are determined relative to a reference frequency. When this reference frequency is set incorrectly, all related chemical shift values are systematically offset. Such wrongly referenced chemical shift values, as well as other problems such as chemical shift values that are assigned to the wrong atom, are not easily distinguished from correct values and effectively reduce the usefulness of the archive. We describe a new method to correct and validate protein chemical shift values in relation to their 3D structure coordinates. This method classifies atoms using two parameters: the per-atom solvent accessible surface area (as calculated from the coordinates) and the secondary structure of the parent amino acid. Through the use of Gaussian statistics based on a large database of 3220 BMRB entries, we obtain per-entry chemical shift corrections as well as Z scores for the individual chemical shift values. In addition, information on the error of the correction value itself is available, and the method can retain only dependable correction values. We provide an online resource with chemical shift, atom exposure, and secondary structure information for all relevant BMRB entries (http://www.ebi.ac.uk/pdbe/nmr/vasco) and hope this data will aid the development of new chemical shift-based methods in NMR. Proteins 2010. © 2010 Wiley-Liss, Inc. PMID:20602353

Ab Initio Calculations of 31P NMR Chemical Shielding Anisotropy Tensors in Phosphates: Variations Due to Ring Formation

Directory of Open Access Journals (Sweden)

Todd M. Alam

2002-08-01

Full Text Available Abstract: Ring formation in phosphate systems is expected to influence both the magnitude and orientation of the phosphorus (31P nuclear magnetic resonance (NMR chemical shielding anisotropy (CSA tensor. Ab initio calculations of the 31P CSA tensor in both cyclic and acyclic phosphate clusters were performed as a function of the number of phosphate tetrahedral in the system. The calculation of the 31P CSA tensors employed the GAUSSIAN 98 implementation of the gauge-including atomic orbital (GIAO method at the Hartree-Fock (HF level. It is shown that both the 31P CSA tensor anisotropy, and the isotropic chemical shielding can be used for the identification of cyclic phosphates. The differences between the 31P CSA tensor in acyclic and cyclic phosphate systems become less pronounced with increasing number of phosphate groups within the ring. The orientation of the principal components for the 31P CSA tensor shows some variation due to cyclization, most notably with the smaller, highly strained ring systems.

Combining the boundary shift integral and tensor-based morphometry for brain atrophy estimation

Science.gov (United States)

Michalkiewicz, Mateusz; Pai, Akshay; Leung, Kelvin K.; Sommer, Stefan; Darkner, Sune; Sørensen, Lauge; Sporring, Jon; Nielsen, Mads

2016-03-01

Brain atrophy from structural magnetic resonance images (MRIs) is widely used as an imaging surrogate marker for Alzheimers disease. Their utility has been limited due to the large degree of variance and subsequently high sample size estimates. The only consistent and reasonably powerful atrophy estimation methods has been the boundary shift integral (BSI). In this paper, we first propose a tensor-based morphometry (TBM) method to measure voxel-wise atrophy that we combine with BSI. The combined model decreases the sample size estimates significantly when compared to BSI and TBM alone.

De novo protein structure generation from incomplete chemical shift assignments

Energy Technology Data Exchange (ETDEWEB)

Shen Yang [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States); Vernon, Robert; Baker, David [University of Washington, Department of Biochemistry and Howard Hughes Medical Institute (United States); Bax, Ad [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States)], E-mail: bax@nih.gov

2009-02-15

NMR chemical shifts provide important local structural information for proteins. Consistent structure generation from NMR chemical shift data has recently become feasible for proteins with sizes of up to 130 residues, and such structures are of a quality comparable to those obtained with the standard NMR protocol. This study investigates the influence of the completeness of chemical shift assignments on structures generated from chemical shifts. The Chemical-Shift-Rosetta (CS-Rosetta) protocol was used for de novo protein structure generation with various degrees of completeness of the chemical shift assignment, simulated by omission of entries in the experimental chemical shift data previously used for the initial demonstration of the CS-Rosetta approach. In addition, a new CS-Rosetta protocol is described that improves robustness of the method for proteins with missing or erroneous NMR chemical shift input data. This strategy, which uses traditional Rosetta for pre-filtering of the fragment selection process, is demonstrated for two paramagnetic proteins and also for two proteins with solid-state NMR chemical shift assignments.

MR chemical shift imaging of human atheroma

International Nuclear Information System (INIS)

Mohiaddin, R.H.; Underwood, R.; Firmin, D.; Abdulla, A.K.; Rees, S.; Longmore, D.

1988-01-01

The lipid content of atheromatous plaques has been measured with chemical shift MR imaging by taking advantage of the different resonance frequencies of protons in lipid and water. Fifteen postmortem aortic specimens of the human descending aorta and the aortae of seven patients with documented peripheral vascular disease were studied at 0.5 T. Spin-echo images were used to localize the lesions before acquisition of the chemical shift images. The specimens were examined histologically, and the lipid distribution in the plaque showed good correlation with the chemical shift data. Validation in vivo and clinical applications remain to be established

Probabilistic validation of protein NMR chemical shift assignments

International Nuclear Information System (INIS)

Dashti, Hesam; Tonelli, Marco; Lee, Woonghee; Westler, William M.; Cornilescu, Gabriel; Ulrich, Eldon L.; Markley, John L.

2016-01-01

Data validation plays an important role in ensuring the reliability and reproducibility of studies. NMR investigations of the functional properties, dynamics, chemical kinetics, and structures of proteins depend critically on the correctness of chemical shift assignments. We present a novel probabilistic method named ARECA for validating chemical shift assignments that relies on the nuclear Overhauser effect data. ARECA has been evaluated through its application to 26 case studies and has been shown to be complementary to, and usually more reliable than, approaches based on chemical shift databases. ARECA is available online at http://areca.nmrfam.wisc.edu/ http://areca.nmrfam.wisc.edu/

Probabilistic validation of protein NMR chemical shift assignments

Energy Technology Data Exchange (ETDEWEB)

Dashti, Hesam [University of Wisconsin-Madison, Graduate Program in Biophysics, Biochemistry Department (United States); Tonelli, Marco; Lee, Woonghee; Westler, William M.; Cornilescu, Gabriel [University of Wisconsin-Madison, Biochemistry Department, National Magnetic Resonance Facility at Madison (United States); Ulrich, Eldon L. [University of Wisconsin-Madison, BioMagResBank, Biochemistry Department (United States); Markley, John L., E-mail: markley@nmrfam.wisc.edu, E-mail: jmarkley@wisc.edu [University of Wisconsin-Madison, Biochemistry Department, National Magnetic Resonance Facility at Madison (United States)

2016-01-15

Data validation plays an important role in ensuring the reliability and reproducibility of studies. NMR investigations of the functional properties, dynamics, chemical kinetics, and structures of proteins depend critically on the correctness of chemical shift assignments. We present a novel probabilistic method named ARECA for validating chemical shift assignments that relies on the nuclear Overhauser effect data. ARECA has been evaluated through its application to 26 case studies and has been shown to be complementary to, and usually more reliable than, approaches based on chemical shift databases. ARECA is available online at http://areca.nmrfam.wisc.edu/ http://areca.nmrfam.wisc.edu/.

Counterion influence on chemical shifts in strychnine salts

Energy Technology Data Exchange (ETDEWEB)

Metaxas, Athena E.; Cort, John R.

2013-05-01

The highly toxic plant alkaloid strychnine is often isolated in the form of the anion salt of its protonated tertiary amine. Here we characterize the relative influence of different counterions on 1H and 13C chemical shifts in several strychnine salts in D2O, methanol-d4 (CD3OD) and chloroform-d (CDCl3) solvents. In organic solvents, but not in water, substantial variation in chemical shifts of protons near the tertiary amine was observed among different salts. These secondary shifts reveal differences in the way each anion influences electronic structure within the protonated amine. The distributions of secondary shifts allow salts to be easily distinguished from each other as well as from the free base form. The observed effects are much greater in organic solvents than in water. Slight concentration-dependence in chemical shifts of some protons near the amine was observed for two salts in CDCl3, but this effect is small compared to the influence of the counterion. Distinct chemical shifts in different salt forms of the same compound may be useful as chemical forensic signatures for source attribution and sample matching of alkaloids such as strychnine and possibly other organic acid and base salts.

A probabilistic approach for validating protein NMR chemical shift assignments

International Nuclear Information System (INIS)

Wang Bowei; Wang, Yunjun; Wishart, David S.

2010-01-01

It has been estimated that more than 20% of the proteins in the BMRB are improperly referenced and that about 1% of all chemical shift assignments are mis-assigned. These statistics also reflect the likelihood that any newly assigned protein will have shift assignment or shift referencing errors. The relatively high frequency of these errors continues to be a concern for the biomolecular NMR community. While several programs do exist to detect and/or correct chemical shift mis-referencing or chemical shift mis-assignments, most can only do one, or the other. The one program (SHIFTCOR) that is capable of handling both chemical shift mis-referencing and mis-assignments, requires the 3D structure coordinates of the target protein. Given that chemical shift mis-assignments and chemical shift re-referencing issues should ideally be addressed prior to 3D structure determination, there is a clear need to develop a structure-independent approach. Here, we present a new structure-independent protocol, which is based on using residue-specific and secondary structure-specific chemical shift distributions calculated over small (3-6 residue) fragments to identify mis-assigned resonances. The method is also able to identify and re-reference mis-referenced chemical shift assignments. Comparisons against existing re-referencing or mis-assignment detection programs show that the method is as good or superior to existing approaches. The protocol described here has been implemented into a freely available Java program called 'Probabilistic Approach for protein Nmr Assignment Validation (PANAV)' and as a web server (http://redpoll.pharmacy.ualberta.ca/PANAVhttp://redpoll.pharmacy.ualberta.ca/PANAV) which can be used to validate and/or correct as well as re-reference assigned protein chemical shifts.

Rapid and reliable protein structure determination via chemical shift threading.

Science.gov (United States)

Hafsa, Noor E; Berjanskii, Mark V; Arndt, David; Wishart, David S

2018-01-01

Protein structure determination using nuclear magnetic resonance (NMR) spectroscopy can be both time-consuming and labor intensive. Here we demonstrate how chemical shift threading can permit rapid, robust, and accurate protein structure determination using only chemical shift data. Threading is a relatively old bioinformatics technique that uses a combination of sequence information and predicted (or experimentally acquired) low-resolution structural data to generate high-resolution 3D protein structures. The key motivations behind using NMR chemical shifts for protein threading lie in the fact that they are easy to measure, they are available prior to 3D structure determination, and they contain vital structural information. The method we have developed uses not only sequence and chemical shift similarity but also chemical shift-derived secondary structure, shift-derived super-secondary structure, and shift-derived accessible surface area to generate a high quality protein structure regardless of the sequence similarity (or lack thereof) to a known structure already in the PDB. The method (called E-Thrifty) was found to be very fast (often chemical shift refinement, these results suggest that protein structure determination, using only NMR chemical shifts, is becoming increasingly practical and reliable. E-Thrifty is available as a web server at http://ethrifty.ca .

Practical use of chemical shift databases for protein solid-state NMR: 2D chemical shift maps and amino-acid assignment with secondary-structure information

International Nuclear Information System (INIS)

Fritzsching, K. J.; Yang, Y.; Schmidt-Rohr, K.; Hong Mei

2013-01-01

We introduce a Python-based program that utilizes the large database of 13 C and 15 N chemical shifts in the Biological Magnetic Resonance Bank to rapidly predict the amino acid type and secondary structure from correlated chemical shifts. The program, called PACSYlite Unified Query (PLUQ), is designed to help assign peaks obtained from 2D 13 C– 13 C, 15 N– 13 C, or 3D 15 N– 13 C– 13 C magic-angle-spinning correlation spectra. We show secondary-structure specific 2D 13 C– 13 C correlation maps of all twenty amino acids, constructed from a chemical shift database of 262,209 residues. The maps reveal interesting conformation-dependent chemical shift distributions and facilitate searching of correlation peaks during amino-acid type assignment. Based on these correlations, PLUQ outputs the most likely amino acid types and the associated secondary structures from inputs of experimental chemical shifts. We test the assignment accuracy using four high-quality protein structures. Based on only the Cα and Cβ chemical shifts, the highest-ranked PLUQ assignments were 40–60 % correct in both the amino-acid type and the secondary structure. For three input chemical shifts (CO–Cα–Cβ or N–Cα–Cβ), the first-ranked assignments were correct for 60 % of the residues, while within the top three predictions, the correct assignments were found for 80 % of the residues. PLUQ and the chemical shift maps are expected to be useful at the first stage of sequential assignment, for combination with automated sequential assignment programs, and for highly disordered proteins for which secondary structure analysis is the main goal of structure determination.

TensorLy: Tensor Learning in Python

NARCIS (Netherlands)

Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

2016-01-01

Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning.

Practical use of chemical shift databases for protein solid-state NMR: 2D chemical shift maps and amino-acid assignment with secondary-structure information

Energy Technology Data Exchange (ETDEWEB)

Fritzsching, K. J.; Yang, Y.; Schmidt-Rohr, K.; Hong Mei, E-mail: mhong@iastate.edu [Iowa State University, Department of Chemistry (United States)

2013-06-15

We introduce a Python-based program that utilizes the large database of {sup 13}C and {sup 15}N chemical shifts in the Biological Magnetic Resonance Bank to rapidly predict the amino acid type and secondary structure from correlated chemical shifts. The program, called PACSYlite Unified Query (PLUQ), is designed to help assign peaks obtained from 2D {sup 13}C-{sup 13}C, {sup 15}N-{sup 13}C, or 3D {sup 15}N-{sup 13}C-{sup 13}C magic-angle-spinning correlation spectra. We show secondary-structure specific 2D {sup 13}C-{sup 13}C correlation maps of all twenty amino acids, constructed from a chemical shift database of 262,209 residues. The maps reveal interesting conformation-dependent chemical shift distributions and facilitate searching of correlation peaks during amino-acid type assignment. Based on these correlations, PLUQ outputs the most likely amino acid types and the associated secondary structures from inputs of experimental chemical shifts. We test the assignment accuracy using four high-quality protein structures. Based on only the C{alpha} and C{beta} chemical shifts, the highest-ranked PLUQ assignments were 40-60 % correct in both the amino-acid type and the secondary structure. For three input chemical shifts (CO-C{alpha}-C{beta} or N-C{alpha}-C{beta}), the first-ranked assignments were correct for 60 % of the residues, while within the top three predictions, the correct assignments were found for 80 % of the residues. PLUQ and the chemical shift maps are expected to be useful at the first stage of sequential assignment, for combination with automated sequential assignment programs, and for highly disordered proteins for which secondary structure analysis is the main goal of structure determination.

Empirical correlation between protein backbone {sup 15}N and {sup 13}C secondary chemical shifts and its application to nitrogen chemical shift re-referencing

Energy Technology Data Exchange (ETDEWEB)

Wang Liya [Cold Spring Harbor Laboratory (United States); Markley, John L. [University of Wisconsin, Biochemistry Department (United States)], E-mail: markley@nmrfam.wisc.edu

2009-06-15

The linear analysis of chemical shifts (LACS) has provided a robust method for identifying and correcting {sup 13}C chemical shift referencing problems in data from protein NMR spectroscopy. Unlike other approaches, LACS does not require prior knowledge of the three-dimensional structure or inference of the secondary structure of the protein. It also does not require extensive assignment of the NMR data. We report here a way of extending the LACS approach to {sup 15}N NMR data from proteins, so as to enable the detection and correction of inconsistencies in chemical shift referencing for this nucleus. The approach is based on our finding that the secondary {sup 15}N chemical shift of the backbone nitrogen atom of residue i is strongly correlated with the secondary chemical shift difference (experimental minus random coil) between the alpha and beta carbons of residue i - 1. Thus once alpha and beta {sup 13}C chemical shifts are available (their difference is referencing error-free), the {sup 15}N referencing can be validated, and an appropriate offset correction can be derived. This approach can be implemented prior to a structure determination and can be used to analyze potential referencing problems in database data not associated with three-dimensional structure. Application of the LACS algorithm to the current BMRB protein chemical shift database, revealed that nearly 35% of the BMRB entries have {delta}{sup 15}N values mis-referenced by over 0.7 ppm and over 25% of them have {delta}{sup 1}H{sup N} values mis-referenced by over 0.12 ppm. One implication of the findings reported here is that a backbone {sup 15}N chemical shift provides a better indicator of the conformation of the preceding residue than of the residue itself.

Unraveling the meaning of chemical shifts in protein NMR.

Science.gov (United States)

Berjanskii, Mark V; Wishart, David S

2017-11-01

Chemical shifts are among the most informative parameters in protein NMR. They provide wealth of information about protein secondary and tertiary structure, protein flexibility, and protein-ligand binding. In this report, we review the progress in interpreting and utilizing protein chemical shifts that has occurred over the past 25years, with a particular focus on the large body of work arising from our group and other Canadian NMR laboratories. More specifically, this review focuses on describing, assessing, and providing some historical context for various chemical shift-based methods to: (1) determine protein secondary and super-secondary structure; (2) derive protein torsion angles; (3) assess protein flexibility; (4) predict residue accessible surface area; (5) refine 3D protein structures; (6) determine 3D protein structures and (7) characterize intrinsically disordered proteins. This review also briefly covers some of the methods that we previously developed to predict chemical shifts from 3D protein structures and/or protein sequence data. It is hoped that this review will help to increase awareness of the considerable utility of NMR chemical shifts in structural biology and facilitate more widespread adoption of chemical-shift based methods by the NMR spectroscopists, structural biologists, protein biophysicists, and biochemists worldwide. This article is part of a Special Issue entitled: Biophysics in Canada, edited by Lewis Kay, John Baenziger, Albert Berghuis and Peter Tieleman. Copyright © 2017 Elsevier B.V. All rights reserved.

Evaluating amber force fields using computed NMR chemical shifts.

Science.gov (United States)

Koes, David R; Vries, John K

2017-10-01

NMR chemical shifts can be computed from molecular dynamics (MD) simulations using a template matching approach and a library of conformers containing chemical shifts generated from ab initio quantum calculations. This approach has potential utility for evaluating the force fields that underlie these simulations. Imperfections in force fields generate flawed atomic coordinates. Chemical shifts obtained from flawed coordinates have errors that can be traced back to these imperfections. We use this approach to evaluate a series of AMBER force fields that have been refined over the course of two decades (ff94, ff96, ff99SB, ff14SB, ff14ipq, and ff15ipq). For each force field a series of MD simulations are carried out for eight model proteins. The calculated chemical shifts for the 1 H, 15 N, and 13 C a atoms are compared with experimental values. Initial evaluations are based on root mean squared (RMS) errors at the protein level. These results are further refined based on secondary structure and the types of atoms involved in nonbonded interactions. The best chemical shift for identifying force field differences is the shift associated with peptide protons. Examination of the model proteins on a residue by residue basis reveals that force field performance is highly dependent on residue position. Examination of the time course of nonbonded interactions at these sites provides explanations for chemical shift differences at the atomic coordinate level. Results show that the newer ff14ipq and ff15ipq force fields developed with the implicitly polarized charge method perform better than the older force fields. © 2017 Wiley Periodicals, Inc.

TensorLy: Tensor Learning in Python

OpenAIRE

Kossaifi, Jean; Panagakis, Yannis; Pantic, Maja

2016-01-01

Tensors are higher-order extensions of matrices. While matrix methods form the cornerstone of machine learning and data analysis, tensor methods have been gaining increasing traction. However, software support for tensor operations is not on the same footing. In order to bridge this gap, we have developed \\emph{TensorLy}, a high-level API for tensor methods and deep tensorized neural networks in Python. TensorLy aims to follow the same standards adopted by the main projects of the Python scie...

Relative Configuration of Natural Products Using NMR Chemical Shifts

Science.gov (United States)

By comparing calculated with experimental NMR chemical shifts, we were able to determine the relative configurations of three monoterpene diastereomers produced by the walkingstick Anisomorpha buprestoides. The combined RMSDs of both 1H and 13C quantum chemically calculated shifts were able to predi...

SimShiftDB; local conformational restraints derived from chemical shift similarity searches on a large synthetic database

Energy Technology Data Exchange (ETDEWEB)

Ginzinger, Simon W. [Center of Applied Molecular Engineering, University of Salzburg, Department of Molecular Biology, Division of Bioinformatics (Austria)], E-mail: simon@came.sbg.ac.at; Coles, Murray [Max-Planck-Institute for Developmental Biology, Department of Protein Evolution (Germany)], E-mail: Murray.Coles@tuebingen.mpg.de

2009-03-15

We present SimShiftDB, a new program to extract conformational data from protein chemical shifts using structural alignments. The alignments are obtained in searches of a large database containing 13,000 structures and corresponding back-calculated chemical shifts. SimShiftDB makes use of chemical shift data to provide accurate results even in the case of low sequence similarity, and with even coverage of the conformational search space. We compare SimShiftDB to HHSearch, a state-of-the-art sequence-based search tool, and to TALOS, the current standard tool for the task. We show that for a significant fraction of the predicted similarities, SimShiftDB outperforms the other two methods. Particularly, the high coverage afforded by the larger database often allows predictions to be made for residues not involved in canonical secondary structure, where TALOS predictions are both less frequent and more error prone. Thus SimShiftDB can be seen as a complement to currently available methods.

SimShiftDB; local conformational restraints derived from chemical shift similarity searches on a large synthetic database

International Nuclear Information System (INIS)

Ginzinger, Simon W.; Coles, Murray

2009-01-01

We present SimShiftDB, a new program to extract conformational data from protein chemical shifts using structural alignments. The alignments are obtained in searches of a large database containing 13,000 structures and corresponding back-calculated chemical shifts. SimShiftDB makes use of chemical shift data to provide accurate results even in the case of low sequence similarity, and with even coverage of the conformational search space. We compare SimShiftDB to HHSearch, a state-of-the-art sequence-based search tool, and to TALOS, the current standard tool for the task. We show that for a significant fraction of the predicted similarities, SimShiftDB outperforms the other two methods. Particularly, the high coverage afforded by the larger database often allows predictions to be made for residues not involved in canonical secondary structure, where TALOS predictions are both less frequent and more error prone. Thus SimShiftDB can be seen as a complement to currently available methods

Direct solution of the Chemical Master Equation using quantized tensor trains.

Directory of Open Access Journals (Sweden)

Vladimir Kazeev

2014-03-01

Full Text Available The Chemical Master Equation (CME is a cornerstone of stochastic analysis and simulation of models of biochemical reaction networks. Yet direct solutions of the CME have remained elusive. Although several approaches overcome the infinite dimensional nature of the CME through projections or other means, a common feature of proposed approaches is their susceptibility to the curse of dimensionality, i.e. the exponential growth in memory and computational requirements in the number of problem dimensions. We present a novel approach that has the potential to "lift" this curse of dimensionality. The approach is based on the use of the recently proposed Quantized Tensor Train (QTT formatted numerical linear algebra for the low parametric, numerical representation of tensors. The QTT decomposition admits both, algorithms for basic tensor arithmetics with complexity scaling linearly in the dimension (number of species and sub-linearly in the mode size (maximum copy number, and a numerical tensor rounding procedure which is stable and quasi-optimal. We show how the CME can be represented in QTT format, then use the exponentially-converging hp-discontinuous Galerkin discretization in time to reduce the CME evolution problem to a set of QTT-structured linear equations to be solved at each time step using an algorithm based on Density Matrix Renormalization Group (DMRG methods from quantum chemistry. Our method automatically adapts the "basis" of the solution at every time step guaranteeing that it is large enough to capture the dynamics of interest but no larger than necessary, as this would increase the computational complexity. Our approach is demonstrated by applying it to three different examples from systems biology: independent birth-death process, an example of enzymatic futile cycle, and a stochastic switch model. The numerical results on these examples demonstrate that the proposed QTT method achieves dramatic speedups and several orders of

Role of quantitative chemical shift magnetic resonance imaging and chemical shift subtraction technique in discriminating adenomatous from non adenomatous adrenal solid lesions

Directory of Open Access Journals (Sweden)

Ahmed H. Afifi

2017-03-01

Conclusion: The signal intensity index and adrenal to spleen ratio are the most reliable quantitative chemical shift MRI methods in differentiation of adrenal adenomas from other non-adenomatous adrenal solid lesions. Chemical shift subtraction MRI is a recent technique that gives highly confident discrimination between two categories of pathology without using of any reference organ.

PPM-One: a static protein structure based chemical shift predictor

International Nuclear Information System (INIS)

Li, Dawei; Brüschweiler, Rafael

2015-01-01

We mined the most recent editions of the BioMagResDataBank and the protein data bank to parametrize a new empirical knowledge-based chemical shift predictor of protein backbone atoms using either a linear or an artificial neural network model. The resulting chemical shift predictor PPM-One accepts a single static 3D structure as input and emulates the effect of local protein dynamics via interatomic steric contacts. Furthermore, the chemical shift prediction was extended to most side-chain protons and it is found that the prediction accuracy is at a level allowing an independent assessment of stereospecific assignments. For a previously established set of test proteins some overall improvement was achieved over current top-performing chemical shift prediction programs

A robust algorithm for optimizing protein structures with NMR chemical shifts

Energy Technology Data Exchange (ETDEWEB)

Berjanskii, Mark; Arndt, David; Liang, Yongjie; Wishart, David S., E-mail: david.wishart@ualberta.ca [University of Alberta, Department of Computing Science (Canada)

2015-11-15

Over the past decade, a number of methods have been developed to determine the approximate structure of proteins using minimal NMR experimental information such as chemical shifts alone, sparse NOEs alone or a combination of comparative modeling data and chemical shifts. However, there have been relatively few methods that allow these approximate models to be substantively refined or improved using the available NMR chemical shift data. Here, we present a novel method, called Chemical Shift driven Genetic Algorithm for biased Molecular Dynamics (CS-GAMDy), for the robust optimization of protein structures using experimental NMR chemical shifts. The method incorporates knowledge-based scoring functions and structural information derived from NMR chemical shifts via a unique combination of multi-objective MD biasing, a genetic algorithm, and the widely used XPLOR molecular modelling language. Using this approach, we demonstrate that CS-GAMDy is able to refine and/or fold models that are as much as 10 Å (RMSD) away from the correct structure using only NMR chemical shift data. CS-GAMDy is also able to refine of a wide range of approximate or mildly erroneous protein structures to more closely match the known/correct structure and the known/correct chemical shifts. We believe CS-GAMDy will allow protein models generated by sparse restraint or chemical-shift-only methods to achieve sufficiently high quality to be considered fully refined and “PDB worthy”. The CS-GAMDy algorithm is explained in detail and its performance is compared over a range of refinement scenarios with several commonly used protein structure refinement protocols. The program has been designed to be easily installed and easily used and is available at http://www.gamdy.ca http://www.gamdy.ca.

The PROSECCO server for chemical shift predictions in ordered and disordered proteins.

Science.gov (United States)

Sanz-Hernández, Máximo; De Simone, Alfonso

2017-11-01

The chemical shifts measured in solution-state and solid-state nuclear magnetic resonance (NMR) are powerful probes of the structure and dynamics of protein molecules. The exploitation of chemical shifts requires methods to correlate these data with the protein structures and sequences. We present here an approach to calculate accurate chemical shifts in both ordered and disordered proteins using exclusively the information contained in their sequences. Our sequence-based approach, protein sequences and chemical shift correlations (PROSECCO), achieves the accuracy of the most advanced structure-based methods in the characterization of chemical shifts of folded proteins and improves the state of the art in the study of disordered proteins. Our analyses revealed fundamental insights on the structural information carried by NMR chemical shifts of structured and unstructured protein states.

Chemical Shift Imaging (CSI) by precise object displacement

OpenAIRE

Leclerc, Sebastien; Trausch, Gregory; Cordier, Benoit; Grandclaude, Denis; Retournard, Alain; Fraissard, Jacques; Canet, Daniel

2006-01-01

International audience; A mechanical device (NMR lift) has been built for displacing vertically an object (typically a NMR sample tube) inside the NMR probe with an accuracy of 1 Μm. A series of single pulse experiments are performed for incremented vertical positions of the sample. With a sufficiently spatially selective rf field, one obtains chemical shift information along the displacement direction (one dimensional Chemical Shift Imaging – CSI). Knowing the vertical radio-frequency (rf) f...

Chemical shifts of oxygen-17 NMR in polyoxotungstates

International Nuclear Information System (INIS)

Kazanskij, L.P.; Fedotov, M.A.; Spitsyn, V.I.

1977-01-01

17 O NMR spectra of aqueous solutions containing paratungstate BH 2 W 12 O 42 10- and metatungstate H 2 W 12 O 40 6- anions have been measured. On the basis of the obtained data a scale of chemical shifts for oxygen atoms connected by various bonds with tungsten atoms is suggested. The obtained data are compared with the Raman spectra of crystalline salts and their aqueous solutions. Chemical shifts of 17 O NMR spectra have been also measured in other heteropolyanions

Coupled Hartree-Fock calculation of {sup 13} C shielding tensors in acetylene clusters

Energy Technology Data Exchange (ETDEWEB)

Craw, John Simon; Nascimento, Marco Antonio Chaer [Universidade Federal, Rio de Janeiro, RJ (Brazil). Inst. de Quimica

1992-12-31

The coupled Hartree Fock method has been used to calculate ab-initio carbon magnetic shielding tensors for small clusters of acetylene molecules. The chemical shift increases from the monomer to the dimer and trimer. This is mainly due increased diamagnetism, which is imperfectly cancelled by increased paramagnetism due to loss of axial symmetry. Anisotropic effects are shown to be small in both the dimer the and trimer. (author) 21 refs., 2 tabs.

Correlation of chemical shifts predicted by molecular dynamics simulations for partially disordered proteins

Energy Technology Data Exchange (ETDEWEB)

Karp, Jerome M.; Erylimaz, Ertan; Cowburn, David, E-mail: cowburn@cowburnlab.org, E-mail: David.cowburn@einstein.yu.edu [Albert Einstein College of Medicine of Yeshiva University, Department of Biochemistry (United States)

2015-01-15

There has been a longstanding interest in being able to accurately predict NMR chemical shifts from structural data. Recent studies have focused on using molecular dynamics (MD) simulation data as input for improved prediction. Here we examine the accuracy of chemical shift prediction for intein systems, which have regions of intrinsic disorder. We find that using MD simulation data as input for chemical shift prediction does not consistently improve prediction accuracy over use of a static X-ray crystal structure. This appears to result from the complex conformational ensemble of the disordered protein segments. We show that using accelerated molecular dynamics (aMD) simulations improves chemical shift prediction, suggesting that methods which better sample the conformational ensemble like aMD are more appropriate tools for use in chemical shift prediction for proteins with disordered regions. Moreover, our study suggests that data accurately reflecting protein dynamics must be used as input for chemical shift prediction in order to correctly predict chemical shifts in systems with disorder.

Tensor Galileons and gravity

Energy Technology Data Exchange (ETDEWEB)

Chatzistavrakidis, Athanasios [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Khoo, Fech Scen [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany); Roest, Diederik [Van Swinderen Institute for Particle Physics and Gravity, University of Groningen,Nijenborgh 4, 9747 AG Groningen (Netherlands); Schupp, Peter [Department of Physics and Earth Sciences, Jacobs University Bremen,Campus Ring 1, 28759 Bremen (Germany)

2017-03-13

The particular structure of Galileon interactions allows for higher-derivative terms while retaining second order field equations for scalar fields and Abelian p-forms. In this work we introduce an index-free formulation of these interactions in terms of two sets of Grassmannian variables. We employ this to construct Galileon interactions for mixed-symmetry tensor fields and coupled systems thereof. We argue that these tensors are the natural generalization of scalars with Galileon symmetry, similar to p-forms and scalars with a shift-symmetry. The simplest case corresponds to linearised gravity with Lovelock invariants, relating the Galileon symmetry to diffeomorphisms. Finally, we examine the coupling of a mixed-symmetry tensor to gravity, and demonstrate in an explicit example that the inclusion of appropriate counterterms retains second order field equations.

Density functional calculations of backbone 15N shielding tensors in beta-sheet and turn residues of protein G

International Nuclear Information System (INIS)

Cai Ling; Kosov, Daniel S.; Fushman, David

2011-01-01

We performed density functional calculations of backbone 15 N shielding tensors in the regions of beta-sheet and turns of protein G. The calculations were carried out for all twenty-four beta-sheet residues and eight beta-turn residues in the protein GB3 and the results were compared with the available experimental data from solid-state and solution NMR measurements. Together with the alpha-helix data, our calculations cover 39 out of the 55 residues (or 71%) in GB3. The applicability of several computational models developed previously (Cai et al. in J Biomol NMR 45:245–253, 2009) to compute 15 N shielding tensors of alpha-helical residues is assessed. We show that the proposed quantum chemical computational model is capable of predicting isotropic 15 N chemical shifts for an entire protein that are in good correlation with experimental data. However, the individual components of the predicted 15 N shielding tensor agree with experiment less well: the computed values show much larger spread than the experimental data, and there is a profound difference in the behavior of the tensor components for alpha-helix/turns and beta-sheet residues. We discuss possible reasons for this.

Nucleic acid helix structure determination from NMR proton chemical shifts

Energy Technology Data Exchange (ETDEWEB)

Werf, Ramon M. van der; Tessari, Marco; Wijmenga, Sybren S., E-mail: S.Wijmenga@science.ru.nl [Radboud University Nijmegen, Department of Biophysical Chemistry, Institute of Molecules and Materials (Netherlands)

2013-06-15

We present a method for de novo derivation of the three-dimensional helix structure of nucleic acids using non-exchangeable proton chemical shifts as sole source of experimental restraints. The method is called chemical shift de novo structure derivation protocol employing singular value decomposition (CHEOPS) and uses iterative singular value decomposition to optimize the structure in helix parameter space. The correct performance of CHEOPS and its range of application are established via an extensive set of structure derivations using either simulated or experimental chemical shifts as input. The simulated input data are used to assess in a defined manner the effect of errors or limitations in the input data on the derived structures. We find that the RNA helix parameters can be determined with high accuracy. We finally demonstrate via three deposited RNA structures that experimental proton chemical shifts suffice to derive RNA helix structures with high precision and accuracy. CHEOPS provides, subject to further development, new directions for high-resolution NMR structure determination of nucleic acids.

Accessible surface area from NMR chemical shifts

Energy Technology Data Exchange (ETDEWEB)

Hafsa, Noor E.; Arndt, David; Wishart, David S., E-mail: david.wishart@ualberta.ca [University of Alberta, Department of Computing Science (Canada)

2015-07-15

Accessible surface area (ASA) is the surface area of an atom, amino acid or biomolecule that is exposed to solvent. The calculation of a molecule’s ASA requires three-dimensional coordinate data and the use of a “rolling ball” algorithm to both define and calculate the ASA. For polymers such as proteins, the ASA for individual amino acids is closely related to the hydrophobicity of the amino acid as well as its local secondary and tertiary structure. For proteins, ASA is a structural descriptor that can often be as informative as secondary structure. Consequently there has been considerable effort over the past two decades to try to predict ASA from protein sequence data and to use ASA information (derived from chemical modification studies) as a structure constraint. Recently it has become evident that protein chemical shifts are also sensitive to ASA. Given the potential utility of ASA estimates as structural constraints for NMR we decided to explore this relationship further. Using machine learning techniques (specifically a boosted tree regression model) we developed an algorithm called “ShiftASA” that combines chemical-shift and sequence derived features to accurately estimate per-residue fractional ASA values of water-soluble proteins. This method showed a correlation coefficient between predicted and experimental values of 0.79 when evaluated on a set of 65 independent test proteins, which was an 8.2 % improvement over the next best performing (sequence-only) method. On a separate test set of 92 proteins, ShiftASA reported a mean correlation coefficient of 0.82, which was 12.3 % better than the next best performing method. ShiftASA is available as a web server ( http://shiftasa.wishartlab.com http://shiftasa.wishartlab.com ) for submitting input queries for fractional ASA calculation.

Identifying secondary structures in proteins using NMR chemical shift 3D correlation maps

Science.gov (United States)

Kumari, Amrita; Dorai, Kavita

2013-06-01

NMR chemical shifts are accurate indicators of molecular environment and have been extensively used as aids in protein structure determination. This work focuses on creating empirical 3D correlation maps of backbone chemical shift nuclei for use as identifiers of secondary structure elements in proteins. A correlated database of backbone nuclei chemical shifts was constructed from experimental structural data gathered from entries in the Protein Data Bank (PDB) as well as isotropic chemical shift values from the RefDB database. Rigorous statistical analysis of the maps led to the conclusion that specific correlations between triplets of backbone chemical shifts are best able to differentiate between different secondary structures such as α-helices, β-strands and turns. The method is compared with similar techniques that use NMR chemical shift information as aids in biomolecular structure determination and performs well in tests done on experimental data determined for different types of proteins, including large multi-domain proteins and membrane proteins.

Prediction of Xaa-Pro peptide bond conformation from sequence and chemical shifts

Energy Technology Data Exchange (ETDEWEB)

Shen Yang; Bax, Ad, E-mail: bax@nih.go [National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Laboratory of Chemical Physics (United States)

2010-03-15

We present a program, named Promega, to predict the Xaa-Pro peptide bond conformation on the basis of backbone chemical shifts and the amino acid sequence. Using a chemical shift database of proteins of known structure together with the PDB-extracted amino acid preference of cis Xaa-Pro peptide bonds, a cis/trans probability score is calculated from the backbone and {sup 13}C{sup {beta}} chemical shifts of the proline and its neighboring residues. For an arbitrary number of input chemical shifts, which may include Pro-{sup 13}C{sup {gamma}}, Promega calculates the statistical probability that a Xaa-Pro peptide bond is cis. Besides its potential as a validation tool, Promega is particularly useful for studies of larger proteins where Pro-{sup 13}C{sup {gamma}} assignments can be challenging, and for on-going efforts to determine protein structures exclusively on the basis of backbone and {sup 13}C{sup {beta}} chemical shifts.

Protein Structure Determination Using Chemical Shifts

DEFF Research Database (Denmark)

Christensen, Anders Steen

is determined using only chemical shifts recorded and assigned through automated processes. The CARMSD to the experimental X-ray for this structure is 1.1. Å. Additionally, the method is combined with very sparse NOE-restraints and evolutionary distance restraints and tested on several protein structures >100...

Probing white-matter microstructure with higher-order diffusion tensors and susceptibility tensor MRI

Science.gov (United States)

Liu, Chunlei; Murphy, Nicole E.; Li, Wei

2012-01-01

Diffusion MRI has become an invaluable tool for studying white matter microstructure and brain connectivity. The emergence of quantitative susceptibility mapping and susceptibility tensor imaging (STI) has provided another unique tool for assessing the structure of white matter. In the highly ordered white matter structure, diffusion MRI measures hindered water mobility induced by various tissue and cell membranes, while susceptibility sensitizes to the molecular composition and axonal arrangement. Integrating these two methods may produce new insights into the complex physiology of white matter. In this study, we investigated the relationship between diffusion and magnetic susceptibility in the white matter. Experiments were conducted on phantoms and human brains in vivo. Diffusion properties were quantified with the diffusion tensor model and also with the higher order tensor model based on the cumulant expansion. Frequency shift and susceptibility tensor were measured with quantitative susceptibility mapping and susceptibility tensor imaging. These diffusion and susceptibility quantities were compared and correlated in regions of single fiber bundles and regions of multiple fiber orientations. Relationships were established with similarities and differences identified. It is believed that diffusion MRI and susceptibility MRI provide complementary information of the microstructure of white matter. Together, they allow a more complete assessment of healthy and diseased brains. PMID:23507987

Theoretical study of lithium clusters by electronic stress tensor

International Nuclear Information System (INIS)

Ichikawa, Kazuhide; Nozaki, Hiroo; Komazawa, Naoya; Tachibana, Akitomo

2012-01-01

We study the electronic structure of small lithium clusters Li_n (n = 2 ∼ 8) using the electronic stress tensor. We find that the three eigenvalues of the electronic stress tensor of the Li clusters are negative and degenerate, just like the stress tensor of liquid. This leads us to propose that we may characterize a metallic bond in terms of the electronic stress tensor. Our proposal is that in addition to the negativity of the three eigenvalues of the electronic stress tensor, their degeneracy characterizes some aspects of the metallic nature of chemical bonding. To quantify the degree of degeneracy, we use the differential eigenvalues of the electronic stress tensor. By comparing the Li clusters and hydrocarbon molecules, we show that the sign of the largest eigenvalue and the differential eigenvalues could be useful indices to evaluate the metallicity or covalency of a chemical bond.

Weyl curvature tensor in static spherical sources

International Nuclear Information System (INIS)

Ponce de Leon, J.

1988-01-01

The role of the Weyl curvature tensor in static sources of the Schwarzschild field is studied. It is shown that in general the contribution from the Weyl curvature tensor (the ''purely gravitational field energy'') to the mass-energy inside the body may be positive, negative, or zero. It is proved that a positive (negative) contribution from the Weyl tensor tends to increase (decrease) the effective gravitational mass, the red-shift (from a point in the sphere to infinity), as well as the gravitational force which acts on a constituent matter element of a body. It is also proved that the contribution from the Weyl tensor always is negative in sources with surface gravitational potential larger than (4/9. It is pointed out that large negative contributions from the Weyl tensor could give rise to the phenomenon of gravitational repulsion. A simple example which illustrates the results is discussed

The direct measurement of the heteronuclear chemical shifts relative to tetramethylsilane

International Nuclear Information System (INIS)

Moritz, A.G.

1988-12-01

The measurement of heteronuclear chemical shifts using absolute frequencies of the heteronucleus and the 1 H resonance of tetramethylsilane has been examined. This method avoids the problems associated with external standards and gives results which can be obtained quickly and with high precision. The method has a number of advantages in the accurate measurement of chemical shifts, as for example 31 P in chemical warfare agents and related chemicals and allows multinuclear data to be obtained without dynamic range or potential interference problems. 15 refs., 4 tabs

Temperature dependence of 1H NMR chemical shifts and its influence on estimated metabolite concentrations.

Science.gov (United States)

Wermter, Felizitas C; Mitschke, Nico; Bock, Christian; Dreher, Wolfgang

2017-12-01

Temperature dependent chemical shifts of important brain metabolites measured by localised 1 H MRS were investigated to test how the use of incorrect prior knowledge on chemical shifts impairs the quantification of metabolite concentrations. Phantom measurements on solutions containing 11 metabolites were performed on a 7 T scanner between 1 and 43 °C. The temperature dependence of the chemical shift differences was fitted by a linear model. Spectra were simulated for different temperatures and analysed by the AQSES program (jMRUI 5.2) using model functions with chemical shift values for 37 °C. Large differences in the temperature dependence of the chemical shift differences were determined with a maximum slope of about ±7.5 × 10 -4  ppm/K. For 32-40 °C, only minor quantification errors resulted from using incorrect chemical shifts, with the exception of Cr and PCr. For 1-10 °C considerable quantification errors occurred if the temperature dependence of the chemical shifts was neglected. If 1 H MRS measurements are not performed at 37 °C, for which the published chemical shift values have been determined, the temperature dependence of chemical shifts should be considered to avoid systematic quantification errors, particularly for measurements on animal models at lower temperatures.

Theoretical Study of the NMR Chemical Shift of Xe in Supercritical Condition

DEFF Research Database (Denmark)

Lacerda Junior, Evanildo Gomes; Sauer, Stephan P. A.; Mikkelsen, Kurt Valentin

2018-01-01

In this work we investigate the level of theory necessary for reproducing the non-linear variation of the 129Xe nuclear magnetic resonance (NMR) chemical shift with the density of Xe in supercritical conditions. In detail we study how the 129Xe chemical shift depends under these conditions...... on electron correlation, relativistic and many-body effects. The latter are included using a sequential-QM/MM methodology, in which a classical MD simulation is performed first and the chemical shift is then obtained as an average of quantum calculations of 250 MD snapshots conformations carried out for Xen...... this approach we obtain very good agreement with the experimental data, showing that the chemical shift of 129Xe in supercritical conditions is very well described by cluster calculations at the HF level, with small contributions from relativistic and electron correlation effects....

Degenerate Perturbation Theory for Electronic g Tensors: Leading-Order Relativistic Effects.

Science.gov (United States)

Rinkevicius, Zilvinas; de Almeida, Katia Julia; Oprea, Cornel I; Vahtras, Olav; Ågren, Hans; Ruud, Kenneth

2008-11-11

A new approach for the evaluation of the leading-order relativistic corrections to the electronic g tensors of molecules with a doublet ground state is presented. The methodology is based on degenerate perturbation theory and includes all relevant contributions to the g tensor shift up to order O(α(4)) originating from the one-electron part of the Breit-Pauli Hamiltonian-that is, it allows for the treatment of scalar relativistic, spin-orbit, and mixed corrections to the spin and orbital Zeeman effects. This approach has been implemented in the framework of spin-restricted density functional theory and is in the present paper, as a first illustration of the theory, applied to study relativistic effects on electronic g tensors of dihalogen anion radicals X2(-) (X = F, Cl, Br, I). The results indicate that the spin-orbit interaction is responsible for the large parallel component of the g tensor shift of Br2(-) and I2(-), and furthermore that both the leading-order scalar relativistic and spin-orbit corrections are of minor importance for the perpendicular component of the g tensor in these molecules since they effectively cancel each other. In addition to investigating the g tensors of dihalogen anion radicals, we also critically examine the importance of various relativistic corrections to the electronic g tensor of linear molecules with Σ-type ground states and present a two-state model suitable for an approximate estimation of the g tensor in such molecules.

29Si NMR Chemical Shift Calculation for Silicate Species by Gaussian Software

Science.gov (United States)

Azizi, S. N.; Rostami, A. A.; Godarzian, A.

2005-05-01

Hartree-Fock self-consistent-field (HF-SCF) theory and the Gauge-including atomic orbital (GIAO) methods are used in the calculation of 29Si NMR chemical shifts for ABOUT 90 units of 19 compounds of various silicate species of precursors for zeolites. Calculations have been performed at geometries optimized at the AM1 semi-empirical method. The GIAO-HF-SCF calculations were carried out with using three different basis sets: 6-31G*, 6-31+G** and 6-311+G(2d,p). To demonstrate the quality of the calculations the calculated chemical shifts, δ, were compared with the corresponding experimental values for the compounds in study. The results, especially with 6-31+g** are in excellent agreement with experimental values. The calculated chemical shifts, in practical point of view, appear to be accurate enough to aid in experimental peak assignments. The difference between the experimental and calculated 29Si chemical shift values not only depends on the Qn units but also it seems that basis set effects and the level of theory is more important. For the series of molecules studied here, the standard deviations and mean absolute errors for 29Si chemical shifts relative to TMS determined using Hartree--Fock 6-31+G** basis is nearly in all cases smaller than the errors for shifts determined using HF/6-311+G(2d,p).

Molecular and Silica-Supported Molybdenum Alkyne Metathesis Catalysts: Influence of Electronics and Dynamics on Activity Revealed by Kinetics, Solid-State NMR, and Chemical Shift Analysis.

Science.gov (United States)

Estes, Deven P; Gordon, Christopher P; Fedorov, Alexey; Liao, Wei-Chih; Ehrhorn, Henrike; Bittner, Celine; Zier, Manuel Luca; Bockfeld, Dirk; Chan, Ka Wing; Eisenstein, Odile; Raynaud, Christophe; Tamm, Matthias; Copéret, Christophe

2017-12-06

Molybdenum-based molecular alkylidyne complexes of the type [MesC≡Mo{OC(CH 3 ) 3-x (CF 3 ) x } 3 ] (MoF 0 , x = 0; MoF 3 , x = 1; MoF 6 , x = 2; MoF 9 , x = 3; Mes = 2,4,6-trimethylphenyl) and their silica-supported analogues are prepared and characterized at the molecular level, in particular by solid-state NMR, and their alkyne metathesis catalytic activity is evaluated. The 13 C NMR chemical shift of the alkylidyne carbon increases with increasing number of fluorine atoms on the alkoxide ligands for both molecular and supported catalysts but with more shielded values for the supported complexes. The activity of these catalysts increases in the order MoF 0 molecular and supported species. Detailed solid-state NMR analysis of molecular and silica-supported metal alkylidyne catalysts coupled with DFT/ZORA calculations rationalize the NMR spectroscopic signatures and discernible activity trends at the frontier orbital level: (1) increasing the number of fluorine atoms lowers the energy of the π*(M≡C) orbital, explaining the more deshielded chemical shift values; it also leads to an increased electrophilicity and higher reactivity for catalysts up to MoF 6 , prior to a sharp decrease in reactivity for MoF 9 due to the formation of stable metallacyclobutadiene intermediates; (2) the silica-supported catalysts are less active than their molecular analogues because they are less electrophilic and dynamic, as revealed by their 13 C NMR chemical shift tensors.

Composite antisymmetric tensor bosons in a four-fermion interaction model

International Nuclear Information System (INIS)

Dmitrasinovic, V.

2000-01-01

We discuss the phenomenological consequences of the U A (1) symmetry-breaking two-flavour four-fermion antisymmetric (AS) Lorentz tensor interaction Lagrangians. We use the recently developed methods that respect the 'duality' symmetry of this interaction. Starting from the Fierz transform of the two-flavour 't Hooft interaction (a four-fermion Lagrangian with AS tensor interaction terms augmented by Nambu and Jona-Lasinio (NJL)-type Lorentz scalar interaction responsible for dynamical symmetry breaking and quark mass generation), we find the following. (a) Four antisymmetric tensor and four AS pseudotensor bosons exist which satisfy a mass relation previously derived for scalar and pseudoscalar mesons from the 't Hooft interaction. (b) Antisymmetric tensor bosons mix with vector bosons via one-fermion-loop effective couplings so that both kinds of bosons have their masses shifted and the fermions (quarks) acquire anomalous magnetic moment form factors that explicitly violate chiral symmetry. (c) The mixing of massive AS tensor fields with vector fields leads to two sets of spin-1 states. The second set of spin-1 mesons is heavy and has not been observed. Moreover, at least one member of this second set is tachyonic, under standard assumptions about the source and strength of the AS tensor interaction. The tachyonic state also shows up as a pole in the space-like region of the electromagnetic form factors. (d) The mixing of axial-vector fields with antisymmetric tensor bosons is proportional to the (small) isospin-breaking up-down quark mass difference, so the mixing-induced mass shift is negligible. (e) The AS tensor version of the Veneziano-Witten U A (1) symmetry-breaking interaction does not lead to tachyons, or any AS tensor field propagation to leading order in N C . (author)

Resolution of NMR chemical shift images into real and imaginary components

International Nuclear Information System (INIS)

Yamamoto, E.; Kohno, H.

1986-01-01

Fast chemical shift imaging of two-line materials is described using a modified spin-echo sequence. The method resolves the two chemical shift images into real and imaginary components representing the reconstructed image. The measuring time is reduced to half of that for the conventional method proposed by Dixon et al, and quantitative evaluation of the images becomes possible. Reference material with a single resonant line is used to eliminate the phase error caused by static field inhomogeneity and the inherent apparatus offset phase. Experiments are conducted using acetone and benzene with a medium-bore superconductive magnet operating at 0.5T. From these experiments, two chemical shift images are obtained. These images are then superimposed to produce a conventional density image. (author)

Random coil chemical shifts in acidic 8 M urea: Implementation of random coil shift data in NMRView

International Nuclear Information System (INIS)

Schwarzinger, Stephan; Kroon, Gerard J.A.; Foss, Ted R.; Wright, Peter E.; Dyson, H. Jane

2000-01-01

Studies of proteins unfolded in acid or chemical denaturant can help in unraveling events during the earliest phases of protein folding. In order for meaningful comparisons to be made of residual structure in unfolded states, it is necessary to use random coil chemical shifts that are valid for the experimental system under study. We present a set of random coil chemical shifts obtained for model peptides under experimental conditions used in studies of denatured proteins. This new set, together with previously published data sets, has been incorporated into a software interface for NMRView, allowing selection of the random coil data set that fits the experimental conditions best

Prediction of proton chemical shifts in RNA - Their use in structure refinement and validation

International Nuclear Information System (INIS)

Cromsigt, Jenny A.M.T.C.; Hilbers, Cees W.; Wijmenga, Sybren S.

2001-01-01

An analysis is presented of experimental versus calculated chemical shifts of the non-exchangeable protons for 28 RNA structures deposited in the Protein Data Bank, covering a wide range of structural building blocks. We have used existing models for ring-current and magnetic-anisotropy contributions to calculate the proton chemical shifts from the structures. Two different parameter sets were tried: (i) parameters derived by Ribas-Prado and Giessner-Prettre (GP set) [(1981) J. Mol. Struct.,76, 81-92.]; (ii) parameters derived by Case [(1995) J. Biomol. NMR, 6, 341-346]. Both sets lead to similar results. The detailed analysis was carried using the GP set. The root-mean-square-deviation between the predicted and observed chemical shifts of the complete database is 0.16 ppm with a Pearson correlation coefficient of 0.79. For protons in the usually well-defined A-helix environment these numbers are, 0.08 ppm and 0.96, respectively. As a result of this good correspondence, a reliable analysis could be made of the structural dependencies of the 1 H chemical shifts revealing their physical origin. For example, a down-field shift of either H2' or H3' or both indicates a high-syn/syn χ-angle. In an A-helix it is essentially the 5'-neighbor that affects the chemical shifts of H5, H6 and H8 protons. The H5, H6 and H8 resonances can therefore be assigned in an A-helix on the basis of their observed chemical shifts. In general, the chemical shifts were found to be quite sensitive to structural changes. We therefore propose that a comparison between calculated and observed 1 H chemical shifts is a good tool for validation and refinement of structures derived from NOEs and J-couplings

A procedure to validate and correct the {sup 13}C chemical shift calibration of RNA datasets

Energy Technology Data Exchange (ETDEWEB)

Aeschbacher, Thomas; Schubert, Mario, E-mail: schubert@mol.biol.ethz.ch; Allain, Frederic H.-T., E-mail: allain@mol.biol.ethz.ch [ETH Zuerich, Institute for Molecular Biology and Biophysics (Switzerland)

2012-02-15

Chemical shifts reflect the structural environment of a certain nucleus and can be used to extract structural and dynamic information. Proper calibration is indispensable to extract such information from chemical shifts. Whereas a variety of procedures exist to verify the chemical shift calibration for proteins, no such procedure is available for RNAs to date. We present here a procedure to analyze and correct the calibration of {sup 13}C NMR data of RNAs. Our procedure uses five {sup 13}C chemical shifts as a reference, each of them found in a narrow shift range in most datasets deposited in the Biological Magnetic Resonance Bank. In 49 datasets we could evaluate the {sup 13}C calibration and detect errors or inconsistencies in RNA {sup 13}C chemical shifts based on these chemical shift reference values. More than half of the datasets (27 out of those 49) were found to be improperly referenced or contained inconsistencies. This large inconsistency rate possibly explains that no clear structure-{sup 13}C chemical shift relationship has emerged for RNA so far. We were able to recalibrate or correct 17 datasets resulting in 39 usable {sup 13}C datasets. 6 new datasets from our lab were used to verify our method increasing the database to 45 usable datasets. We can now search for structure-chemical shift relationships with this improved list of {sup 13}C chemical shift data. This is demonstrated by a clear relationship between ribose {sup 13}C shifts and the sugar pucker, which can be used to predict a C2 Prime - or C3 Prime -endo conformation of the ribose with high accuracy. The improved quality of the chemical shift data allows statistical analysis with the potential to facilitate assignment procedures, and the extraction of restraints for structure calculations of RNA.

Protein backbone angle restraints from searching a database for chemical shift and sequence homology

Energy Technology Data Exchange (ETDEWEB)

Cornilescu, Gabriel; Delaglio, Frank; Bax, Ad [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States)

1999-03-15

Chemical shifts of backbone atoms in proteins are exquisitely sensitive to local conformation, and homologous proteins show quite similar patterns of secondary chemical shifts. The inverse of this relation is used to search a database for triplets of adjacent residues with secondary chemical shifts and sequence similarity which provide the best match to the query triplet of interest. The database contains 13C{alpha}, 13C{beta}, 13C', 1H{alpha} and 15N chemical shifts for 20 proteins for which a high resolution X-ray structure is available. The computer program TALOS was developed to search this database for strings of residues with chemical shift and residue type homology. The relative importance of the weighting factors attached to the secondary chemical shifts of the five types of resonances relative to that of sequence similarity was optimized empirically. TALOS yields the 10 triplets which have the closest similarity in secondary chemical shift and amino acid sequence to those of the query sequence. If the central residues in these 10 triplets exhibit similar {phi} and {psi} backbone angles, their averages can reliably be used as angular restraints for the protein whose structure is being studied. Tests carried out for proteins of known structure indicate that the root-mean-square difference (rmsd) between the output of TALOS and the X-ray derived backbone angles is about 15 deg. Approximately 3% of the predictions made by TALOS are found to be in error.

Benchmarking quantum mechanical calculations with experimental NMR chemical shifts of 2-HADNT

Science.gov (United States)

Liu, Yuemin; Junk, Thomas; Liu, Yucheng; Tzeng, Nianfeng; Perkins, Richard

2015-04-01

In this study, both GIAO-DFT and GIAO-MP2 calculations of nuclear magnetic resonance (NMR) spectra were benchmarked with experimental chemical shifts. The experimental chemical shifts were determined experimentally for carbon-13 (C-13) of seven carbon atoms for the TNT degradation product 2-hydroxylamino-4,6-dinitrotoluene (2-HADNT). Quantum mechanics GIAO calculations were implemented using Becke-3-Lee-Yang-Parr (B3LYP) and other six hybrid DFT methods (Becke-1-Lee-Yang-Parr (B1LYP), Becke-half-and-half-Lee-Yang-Parr (BH and HLYP), Cohen-Handy-3-Lee-Yang-Parr (O3LYP), Coulomb-attenuating-B3LYP (CAM-B3LYP), modified-Perdew-Wang-91-Lee-Yang-Parr (mPW1LYP), and Xu-3-Lee-Yang-Parr (X3LYP)) which use the same correlation functional LYP. Calculation results showed that the GIAO-MP2 method gives the most accurate chemical shift values, and O3LYP method provides the best prediction of chemical shifts among the B3LYP and other five DFT methods. Three types of atomic partial charges, Mulliken (MK), electrostatic potential (ESP), and natural bond orbital (NBO), were also calculated using MP2/aug-cc-pVDZ method. A reasonable correlation was discovered between NBO partial charges and experimental chemical shifts of carbon-13 (C-13).

Relation between chemical shift artifact and infiltration on MR imaging of renal cell carcinoma

International Nuclear Information System (INIS)

Yoshigoe, Fukuo; Makino, Hideki; Yanada, Syuichi; Ohishi, Yukihiko; Mashima, Yasuoki; Yamada, Hideo.

1994-01-01

Retrospective study on the relation between existence of the interruption and disturbance of chemical shift artifact and tumor infiltration at the periphery of the kidney on MR imaging was evaluated in 28 cases with renal cell carcinoma. Judgement was possible in 9 out of the 11 cases with pathological stage below pT2 and 14 cases out of 17 pT3 cases. Judgement was impracticable in 5 cases because the peripheral fat tissue of the kidney was too less to observe chemical shift artifact and the tumor was spreading at the side opposite to the chemical shift artifact. Chemical shift artifact on MRI in this study correlated well with renal tumor infiltration. (author)

Database proton NMR chemical shifts for RNA signal assignment and validation

Energy Technology Data Exchange (ETDEWEB)

Barton, Shawn; Heng Xiao [University of Maryland, Baltimore County, Howard Hughes Medical Institute (United States); Johnson, Bruce A., E-mail: bruce@onemoonscientific.com [University of Maryland, Baltimore County, Department of Chemistry and Biochemistry (United States); Summers, Michael F., E-mail: summers@hhmi.umbc.edu [University of Maryland, Baltimore County, Howard Hughes Medical Institute (United States)

2013-01-15

The Biological Magnetic Resonance Data Bank contains NMR chemical shift depositions for 132 RNAs and RNA-containing complexes. We have analyzed the {sup 1}H NMR chemical shifts reported for non-exchangeable protons of residues that reside within A-form helical regions of these RNAs. The analysis focused on the central base pair within a stretch of three adjacent base pairs (BP triplets), and included both Watson-Crick (WC; G:C, A:U) and G:U wobble pairs. Chemical shift values were included for all 4{sup 3} possible WC-BP triplets, as well as 137 additional triplets that contain one or more G:U wobbles. Sequence-dependent chemical shift correlations were identified, including correlations involving terminating base pairs within the triplets and canonical and non-canonical structures adjacent to the BP triplets (i.e. bulges, loops, WC and non-WC BPs), despite the fact that the NMR data were obtained under different conditions of pH, buffer, ionic strength, and temperature. A computer program (RNAShifts) was developed that enables convenient comparison of RNA {sup 1}H NMR assignments with database predictions, which should facilitate future signal assignment/validation efforts and enable rapid identification of non-canonical RNA structures and RNA-ligand/protein interaction sites.

/sup 1/H-NMR chemical shift imaging suitable for low field systems

Energy Technology Data Exchange (ETDEWEB)

Yamamoto, Etsuji; Onodera, Takashi; Shiono, Hidemi; Kohno, Hideki

1986-12-01

An echo-time encoding proton NMR chemical shift imaging proposed by Dixon is extended to be applicable to low filed systems. The method utilizes the small phase angle between magnetic vectors of water and lipid protons to decrease the signal decays with spin-spin relaxation. The inevitable phase error caused by the static field inhomogeneity is corrected by using phase images of phantom measured under the same conditions as the actual measurements. The experiments were carried out using CuSO/sub 4/ doped water and vegetable oil at 0.5 T. Two chemical shift images could be clearly resolved with only one scan when the field inhomogeneity was larger than the chemical shift difference.

Equilibrium simulations of proteins using molecular fragment replacement and NMR chemical shifts.

Science.gov (United States)

Boomsma, Wouter; Tian, Pengfei; Frellsen, Jes; Ferkinghoff-Borg, Jesper; Hamelryck, Thomas; Lindorff-Larsen, Kresten; Vendruscolo, Michele

2014-09-23

Methods of protein structure determination based on NMR chemical shifts are becoming increasingly common. The most widely used approaches adopt the molecular fragment replacement strategy, in which structural fragments are repeatedly reassembled into different complete conformations in molecular simulations. Although these approaches are effective in generating individual structures consistent with the chemical shift data, they do not enable the sampling of the conformational space of proteins with correct statistical weights. Here, we present a method of molecular fragment replacement that makes it possible to perform equilibrium simulations of proteins, and hence to determine their free energy landscapes. This strategy is based on the encoding of the chemical shift information in a probabilistic model in Markov chain Monte Carlo simulations. First, we demonstrate that with this approach it is possible to fold proteins to their native states starting from extended structures. Second, we show that the method satisfies the detailed balance condition and hence it can be used to carry out an equilibrium sampling from the Boltzmann distribution corresponding to the force field used in the simulations. Third, by comparing the results of simulations carried out with and without chemical shift restraints we describe quantitatively the effects that these restraints have on the free energy landscapes of proteins. Taken together, these results demonstrate that the molecular fragment replacement strategy can be used in combination with chemical shift information to characterize not only the native structures of proteins but also their conformational fluctuations.

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)

2018-01-01

textabstractThe tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the

Tensor rank is not multiplicative under the tensor product

NARCIS (Netherlands)

M. Christandl (Matthias); A. K. Jensen (Asger Kjærulff); J. Zuiddam (Jeroen)

2017-01-01

textabstractThe tensor rank of a tensor is the smallest number r such that the tensor can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor (not to be confused with the "tensor Kronecker product" used in

Protein Structure Validation and Refinement Using Chemical Shifts Derived from Quantum Mechanics

DEFF Research Database (Denmark)

Bratholm, Lars Andersen

to within 3 A. Furthermore, a fast quantum mechanics based chemical shift predictor was developed together with methodology for using chemical shifts in structure simulations. The developed predictor was used for renement of several protein structures and for reducing the computational cost of quantum...... mechanics / molecular mechanics (QM/MM) computations of chemical shieldings. Several improvements to the predictor is ongoing, where among other things, kernel based machine learning techniques have successfully been used to improve the quantum mechanical level of theory used in the predictions....

Tensor rank is not multiplicative under the tensor product

OpenAIRE

Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen

2017-01-01

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an l-tensor. The tensor product of s and t is a (k + l)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection between restrictions and degenerations. A result of our study is that tensor rank is not in general multiplicative under the tensor product. This answers a question of Draisma and Saptharishi. Specif...

Tensor surgery and tensor rank

NARCIS (Netherlands)

M. Christandl (Matthias); J. Zuiddam (Jeroen)

2018-01-01

textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new vertices

Tensor surgery and tensor rank

NARCIS (Netherlands)

M. Christandl (Matthias); J. Zuiddam (Jeroen)

2016-01-01

textabstractWe introduce a method for transforming low-order tensors into higher-order tensors and apply it to tensors defined by graphs and hypergraphs. The transformation proceeds according to a surgery-like procedure that splits vertices, creates and absorbs virtual edges and inserts new

Improving 3D structure prediction from chemical shift data

Energy Technology Data Exchange (ETDEWEB)

Schot, Gijs van der [Utrecht University, Computational Structural Biology, Bijvoet Center for Biomolecular Research, Faculty of Science-Chemistry (Netherlands); Zhang, Zaiyong [Technische Universitaet Muenchen, Biomolecular NMR and Munich Center for Integrated Protein Science, Department Chemie (Germany); Vernon, Robert [University of Washington, Department of Biochemistry (United States); Shen, Yang [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States); Vranken, Wim F. [VIB, Department of Structural Biology (Belgium); Baker, David [University of Washington, Department of Biochemistry (United States); Bonvin, Alexandre M. J. J., E-mail: a.m.j.j.bonvin@uu.nl [Utrecht University, Computational Structural Biology, Bijvoet Center for Biomolecular Research, Faculty of Science-Chemistry (Netherlands); Lange, Oliver F., E-mail: oliver.lange@tum.de [Technische Universitaet Muenchen, Biomolecular NMR and Munich Center for Integrated Protein Science, Department Chemie (Germany)

2013-09-15

We report advances in the calculation of protein structures from chemical shift nuclear magnetic resonance data alone. Our previously developed method, CS-Rosetta, assembles structures from a library of short protein fragments picked from a large library of protein structures using chemical shifts and sequence information. Here we demonstrate that combination of a new and improved fragment picker and the iterative sampling algorithm RASREC yield significant improvements in convergence and accuracy. Moreover, we introduce improved criteria for assessing the accuracy of the models produced by the method. The method was tested on 39 proteins in the 50-100 residue size range and yields reliable structures in 70 % of the cases. All structures that passed the reliability filter were accurate (<2 A RMSD from the reference)

Effects of strain on Goos-Hänchen-like shifts of graphene

International Nuclear Information System (INIS)

Cao Zhenzhou; Cheng Yanfu; Li Guanqiang

2012-01-01

We have studied the Goos-Hänchen-like (GHL) shifts for massless Dirac electrons passing across a potential barrier in strained graphene. The analytical solutions of the transmission coefficient and the GHL shifts are obtained. The GHL shifts as the function of the strain tensor and direction, the incidence angle and the barrier's width are discussed. We also explore how critical angles change as the strain tensor and incidence electron energy change. Finally, we make a proposal of experimental measurement of the GHL shifts. The study of the GHL shifts will make for applications in graphene-based nano-electronics.

Tensor rank is not multiplicative under the tensor product

DEFF Research Database (Denmark)

Christandl, Matthias; Jensen, Asger Kjærulff; Zuiddam, Jeroen

2018-01-01

The tensor rank of a tensor t is the smallest number r such that t can be decomposed as a sum of r simple tensors. Let s be a k-tensor and let t be an ℓ-tensor. The tensor product of s and t is a (k+ℓ)-tensor. Tensor rank is sub-multiplicative under the tensor product. We revisit the connection b...

Chemical Mass Shifts in a Digital Linear Ion Trap as Analytical Identity of o-, m-, and p-Xylene

Science.gov (United States)

Sun, Lulu; Xue, Bing; Huang, Zhengxu; Cheng, Ping; Ma, Li; Ding, Li; Zhou, Zhen

2018-04-01

Chemical mass shifts between isomeric ions of o-, m-, and p-xylene were measured using a digital linear ion trap, and the directions and values of the shifts were found to be correlated to the collision cross sections of the isomers. Both forward and reverse scans were used and the chemical shifts for each pair of isomers in scans of opposite directions were in opposite signs. Using different voltage settings (namely the voltage dividing ratio-VDR) of the ion trap allows adding high order field components in the quadrupole field and results in larger chemical mass shifts. The differential chemical mass shift which combined the shifts from forward and reverse scans doubled the amount of chemical shift, e.g., 0.077 Th between o- and p-xylene, enough for identification of the type of isomer without using an additional ion mobility spectrometer. The feature of equal and opposite chemical mass shifts also allowed to null out the chemical mass shift by calculating the mean m/z value between the two opposite scans and remove or reduce the mass error caused by chemical mass shift. [Figure not available: see fulltext.

Chemical Mass Shifts in a Digital Linear Ion Trap as Analytical Identity of o-, m-, and p-Xylene.

Science.gov (United States)

Sun, Lulu; Xue, Bing; Huang, Zhengxu; Cheng, Ping; Ma, Li; Ding, Li; Zhou, Zhen

2018-07-01

Chemical mass shifts between isomeric ions of o-, m-, and p-xylene were measured using a digital linear ion trap, and the directions and values of the shifts were found to be correlated to the collision cross sections of the isomers. Both forward and reverse scans were used and the chemical shifts for each pair of isomers in scans of opposite directions were in opposite signs. Using different voltage settings (namely the voltage dividing ratio-VDR) of the ion trap allows adding high order field components in the quadrupole field and results in larger chemical mass shifts. The differential chemical mass shift which combined the shifts from forward and reverse scans doubled the amount of chemical shift, e.g., 0.077 Th between o- and p-xylene, enough for identification of the type of isomer without using an additional ion mobility spectrometer. The feature of equal and opposite chemical mass shifts also allowed to null out the chemical mass shift by calculating the mean m/z value between the two opposite scans and remove or reduce the mass error caused by chemical mass shift. Graphical Abstract ᅟ.

71Ga Chemical Shielding and Quadrupole Coupling Tensors of the Garnet Y(3)Ga(5)O(12) from Single-Crystal (71)Ga NMR

DEFF Research Database (Denmark)

Vosegaard, Thomas; Massiot, Dominique; Gautier, Nathalie

1997-01-01

A single-crystal (71)Ga NMR study of the garnet Y(3)Ga(5)O(12) (YGG) has resulted in the determination of the first chemical shielding tensors reported for the (71)Ga quadrupole. The single-crystal spectra are analyzed in terms of the combined effect of quadrupole coupling and chemical shielding ...

Stereospecific assignment of the asparagine and glutamine sidechain amide protons in proteins from chemical shift analysis

Energy Technology Data Exchange (ETDEWEB)

Harsch, Tobias; Schneider, Philipp; Kieninger, Bärbel; Donaubauer, Harald; Kalbitzer, Hans Robert, E-mail: hans-robert.kalbitzer@biologie.uni-regensburg.de [University of Regensburg, Institute of Biophysics and Physical Biochemistry and Centre of Magnetic Resonance in Chemistry and Biomedicine (Germany)

2017-02-15

Side chain amide protons of asparagine and glutamine residues in random-coil peptides are characterized by large chemical shift differences and can be stereospecifically assigned on the basis of their chemical shift values only. The bimodal chemical shift distributions stored in the biological magnetic resonance data bank (BMRB) do not allow such an assignment. However, an analysis of the BMRB shows, that a substantial part of all stored stereospecific assignments is not correct. We show here that in most cases stereospecific assignment can also be done for folded proteins using an unbiased artificial chemical shift data base (UACSB). For a separation of the chemical shifts of the two amide resonance lines with differences ≥0.40 ppm for asparagine and differences ≥0.42 ppm for glutamine, the downfield shifted resonance lines can be assigned to H{sup δ21} and H{sup ε21}, respectively, at a confidence level >95%. A classifier derived from UASCB can also be used to correct the BMRB data. The program tool AssignmentChecker implemented in AUREMOL calculates the Bayesian probability for a given stereospecific assignment and automatically corrects the assignments for a given list of chemical shifts.

Deuterium isotope effects on 13C chemical shifts of 10-Hydroxybenzo[h]quinolines

DEFF Research Database (Denmark)

Hansen, Poul Erik; Kamounah, Fadhil S.; Gryko, Daniel T.

2013-01-01

Deuterium isotope effects on 13C-NMR chemical shifts are investigated in a series of 10-hydroxybenzo[h]quinolines (HBQ’s) The OH proton is deuteriated. The isotope effects on 13C chemical shifts in these hydrogen bonded systems are rather unusual. The formal four-bond effects are found to be nega...

Tensor Factorization for Low-Rank Tensor Completion.

Science.gov (United States)

Zhou, Pan; Lu, Canyi; Lin, Zhouchen; Zhang, Chao

2018-03-01

Recently, a tensor nuclear norm (TNN) based method was proposed to solve the tensor completion problem, which has achieved state-of-the-art performance on image and video inpainting tasks. However, it requires computing tensor singular value decomposition (t-SVD), which costs much computation and thus cannot efficiently handle tensor data, due to its natural large scale. Motivated by TNN, we propose a novel low-rank tensor factorization method for efficiently solving the 3-way tensor completion problem. Our method preserves the low-rank structure of a tensor by factorizing it into the product of two tensors of smaller sizes. In the optimization process, our method only needs to update two smaller tensors, which can be more efficiently conducted than computing t-SVD. Furthermore, we prove that the proposed alternating minimization algorithm can converge to a Karush-Kuhn-Tucker point. Experimental results on the synthetic data recovery, image and video inpainting tasks clearly demonstrate the superior performance and efficiency of our developed method over state-of-the-arts including the TNN and matricization methods.

Solvent Effects on Oxygen-17 Chemical Shifts in Amides. Quantitative Linear Solvation Shift Relationships

Science.gov (United States)

Díez, Ernesto; Fabián, Jesús San; Gerothanassis, Ioannis P.; Esteban, Angel L.; Abboud, José-Luis M.; Contreras, Ruben H.; de Kowalewski, Dora G.

1997-01-01

A multiple-linear-regression analysis (MLRA) has been carried out using the Kamlet-Abboud-Taft (KAT) solvatochromic parameters in order to elucidate and quantify the solvent effects on the17O chemical shifts ofN-methylformamide (NMF),N,N-dimethylformamide (DMF),N-methylacetamide (NMA), andN,N-dimethylacetamide (DMA). The chemical shifts of the four molecules show the same dependence (in ppm) on the solvent polarity-polarizability, i.e., -22π*. The influence of the solvent hydrogen-bond-donor (HBD) acidities is slightly larger for the acetamides NMA and DMA, i.e., -48α, than for the formamides NMF and DMF, i.e., -42α. The influence of the solvent hydrogen-bond-acceptor (HBA) basicities is negligible for the nonprotic molecules DMF and DMA but significant for the protic molecules NMF and NMA, i.e., -9β. The effect of substituting the N-H hydrogen by a methyl group amounts to -5.9 ppm in NMF and 5.4 ppm in NMA. The effect of substituting the O=C-H hydrogen amounts to 5.5 ppm in NMF and 16.8 ppm in DMF. The model of specific hydration sites of amides by I. P. Gerothanassis and C. Vakka [J. Org. Chem.59,2341 (1994)] is settled in a more quantitative basis and the model by M. I. Burgar, T. E. St. Amour, and D. Fiat [J. Phys. Chem.85,502 (1981)] is critically evaluated.17O hydration shifts have been calculated for formamide (FOR) by the ab initio LORG method at the 6-31G* level. For a formamide surrounded by the four in-plane molecules of water in the first hydration shell, the calculated17O shift change due to the four hydrogen bonds, -83.2 ppm, is smaller than the empirical hydration shift, -100 ppm. The17O shift change from each out-of-plane water molecule hydrogen-bonded to the amide oxygen is -18.0 ppm. These LORG results support the conclusion that no more than four water molecules are hydrogen-bonded to the amide oxygen in formamide.

A Review of Tensors and Tensor Signal Processing

Science.gov (United States)

Cammoun, L.; Castaño-Moraga, C. A.; Muñoz-Moreno, E.; Sosa-Cabrera, D.; Acar, B.; Rodriguez-Florido, M. A.; Brun, A.; Knutsson, H.; Thiran, J. P.

Tensors have been broadly used in mathematics and physics, since they are a generalization of scalars or vectors and allow to represent more complex properties. In this chapter we present an overview of some tensor applications, especially those focused on the image processing field. From a mathematical point of view, a lot of work has been developed about tensor calculus, which obviously is more complex than scalar or vectorial calculus. Moreover, tensors can represent the metric of a vector space, which is very useful in the field of differential geometry. In physics, tensors have been used to describe several magnitudes, such as the strain or stress of materials. In solid mechanics, tensors are used to define the generalized Hooke’s law, where a fourth order tensor relates the strain and stress tensors. In fluid dynamics, the velocity gradient tensor provides information about the vorticity and the strain of the fluids. Also an electromagnetic tensor is defined, that simplifies the notation of the Maxwell equations. But tensors are not constrained to physics and mathematics. They have been used, for instance, in medical imaging, where we can highlight two applications: the diffusion tensor image, which represents how molecules diffuse inside the tissues and is broadly used for brain imaging; and the tensorial elastography, which computes the strain and vorticity tensor to analyze the tissues properties. Tensors have also been used in computer vision to provide information about the local structure or to define anisotropic image filters.

Identify Beta-Hairpin Motifs with Quadratic Discriminant Algorithm Based on the Chemical Shifts.

Directory of Open Access Journals (Sweden)

Feng YongE

Full Text Available Successful prediction of the beta-hairpin motif will be helpful for understanding the of the fold recognition. Some algorithms have been proposed for the prediction of beta-hairpin motifs. However, the parameters used by these methods were primarily based on the amino acid sequences. Here, we proposed a novel model for predicting beta-hairpin structure based on the chemical shift. Firstly, we analyzed the statistical distribution of chemical shifts of six nuclei in not beta-hairpin and beta-hairpin motifs. Secondly, we used these chemical shifts as features combined with three algorithms to predict beta-hairpin structure. Finally, we achieved the best prediction, namely sensitivity of 92%, the specificity of 94% with 0.85 of Mathew's correlation coefficient using quadratic discriminant analysis algorithm, which is clearly superior to the same method for the prediction of beta-hairpin structure from 20 amino acid compositions in the three-fold cross-validation. Our finding showed that the chemical shift is an effective parameter for beta-hairpin prediction, suggesting the quadratic discriminant analysis is a powerful algorithm for the prediction of beta-hairpin.

Identification of helix capping and {beta}-turn motifs from NMR chemical shifts

Energy Technology Data Exchange (ETDEWEB)

Shen Yang; Bax, Ad, E-mail: bax@nih.gov [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States)

2012-03-15

We present an empirical method for identification of distinct structural motifs in proteins on the basis of experimentally determined backbone and {sup 13}C{sup {beta}} chemical shifts. Elements identified include the N-terminal and C-terminal helix capping motifs and five types of {beta}-turns: I, II, I Prime , II Prime and VIII. Using a database of proteins of known structure, the NMR chemical shifts, together with the PDB-extracted amino acid preference of the helix capping and {beta}-turn motifs are used as input data for training an artificial neural network algorithm, which outputs the statistical probability of finding each motif at any given position in the protein. The trained neural networks, contained in the MICS (motif identification from chemical shifts) program, also provide a confidence level for each of their predictions, and values ranging from ca 0.7-0.9 for the Matthews correlation coefficient of its predictions far exceed those attainable by sequence analysis. MICS is anticipated to be useful both in the conventional NMR structure determination process and for enhancing on-going efforts to determine protein structures solely on the basis of chemical shift information, where it can aid in identifying protein database fragments suitable for use in building such structures.

Identification of helix capping and β-turn motifs from NMR chemical shifts

International Nuclear Information System (INIS)

Shen Yang; Bax, Ad

2012-01-01

We present an empirical method for identification of distinct structural motifs in proteins on the basis of experimentally determined backbone and 13 C β chemical shifts. Elements identified include the N-terminal and C-terminal helix capping motifs and five types of β-turns: I, II, I′, II′ and VIII. Using a database of proteins of known structure, the NMR chemical shifts, together with the PDB-extracted amino acid preference of the helix capping and β-turn motifs are used as input data for training an artificial neural network algorithm, which outputs the statistical probability of finding each motif at any given position in the protein. The trained neural networks, contained in the MICS (motif identification from chemical shifts) program, also provide a confidence level for each of their predictions, and values ranging from ca 0.7–0.9 for the Matthews correlation coefficient of its predictions far exceed those attainable by sequence analysis. MICS is anticipated to be useful both in the conventional NMR structure determination process and for enhancing on-going efforts to determine protein structures solely on the basis of chemical shift information, where it can aid in identifying protein database fragments suitable for use in building such structures.

Chemical shift MRI can aid in the diagnosis of indeterminate skeletal lesions of the spine

Energy Technology Data Exchange (ETDEWEB)

Douis, H. [University Hospital Birmingham, Department of Radiology, Birmingham (United Kingdom); Royal Orthopaedic Hospital, Department of Radiology, Birmingham (United Kingdom); Davies, A.M. [Royal Orthopaedic Hospital, Department of Radiology, Birmingham (United Kingdom); Jeys, L. [Royal Orthopaedic Hospital, Department of Orthopaedic Oncology, Birmingham (United Kingdom); Sian, P. [Royal Orthopaedic Hospital, Department of Spinal Surgery and Spinal Oncology, Birmingham (United Kingdom)

2016-04-15

To evaluate the role of chemical shift MRI in the characterisation of indeterminate skeletal lesions of the spine as benign or malignant. Fifty-five patients (mean age 54.7 years) with 57 indeterminate skeletal lesions of the spine were included in this retrospective study. In addition to conventional MRI at 3 T which included at least sagittal T1WI and T2WI/STIR sequences, patients underwent chemical shift MRI. A cut-off value with a signal drop-out of 20 % was used to differentiate benign lesions from malignant lesions (signal drop-out <20 % being malignant). There were 45 benign lesions and 12 malignant lesions. Chemical shift imaging correctly diagnosed 33 of 45 lesions as benign and 11 of 12 lesions as malignant. In contrast, there were 12 false positive cases and 1 false negative case based on chemical shift MRI. This yielded a sensitivity of 91.7 %, a specificity of 73.3 %, a negative predictive value of 97.1 %, a positive predictive value of 47.8 % and a diagnostic accuracy of 82.5 %. Chemical shift MRI can aid in the characterisation of indeterminate skeletal lesions of the spine in view of its high sensitivity in diagnosing malignant lesions. Chemical shift MRI can potentially avoid biopsy in a considerable percentage of patients with benign skeletal lesions of the spine. (orig.)

Sequence correction of random coil chemical shifts: correlation between neighbor correction factors and changes in the Ramachandran distribution

DEFF Research Database (Denmark)

Kjærgaard, Magnus; Poulsen, Flemming Martin

2011-01-01

Random coil chemical shifts are necessary for secondary chemical shift analysis, which is the main NMR method for identification of secondary structure in proteins. One of the largest challenges in the determination of random coil chemical shifts is accounting for the effect of neighboring residues....... The contributions from the neighboring residues are typically removed by using neighbor correction factors determined based on each residue's effect on glycine chemical shifts. Due to its unusual conformational freedom, glycine may be particularly unrepresentative for the remaining residue types. In this study, we...... in the conformational ensemble are an important source of neighbor effects in disordered proteins. Glutamine derived random coil chemical shifts and correction factors modestly improve our ability to predict (13)C chemical shifts of intrinsically disordered proteins compared to existing datasets, and may thus improve...

Conformationally selective multidimensional chemical shift ranges in proteins from a PACSY database purged using intrinsic quality criteria

International Nuclear Information System (INIS)

Fritzsching, Keith J.; Hong, Mei; Schmidt-Rohr, Klaus

2016-01-01

We have determined refined multidimensional chemical shift ranges for intra-residue correlations ( 13 C– 13 C, 15 N– 13 C, etc.) in proteins, which can be used to gain type-assignment and/or secondary-structure information from experimental NMR spectra. The chemical-shift ranges are the result of a statistical analysis of the PACSY database of >3000 proteins with 3D structures (1,200,207 13 C chemical shifts and >3 million chemical shifts in total); these data were originally derived from the Biological Magnetic Resonance Data Bank. Using relatively simple non-parametric statistics to find peak maxima in the distributions of helix, sheet, coil and turn chemical shifts, and without the use of limited “hand-picked” data sets, we show that ∼94 % of the 13 C NMR data and almost all 15 N data are quite accurately referenced and assigned, with smaller standard deviations (0.2 and 0.8 ppm, respectively) than recognized previously. On the other hand, approximately 6 % of the 13 C chemical shift data in the PACSY database are shown to be clearly misreferenced, mostly by ca. −2.4 ppm. The removal of the misreferenced data and other outliers by this purging by intrinsic quality criteria (PIQC) allows for reliable identification of secondary maxima in the two-dimensional chemical-shift distributions already pre-separated by secondary structure. We demonstrate that some of these correspond to specific regions in the Ramachandran plot, including left-handed helix dihedral angles, reflect unusual hydrogen bonding, or are due to the influence of a following proline residue. With appropriate smoothing, significantly more tightly defined chemical shift ranges are obtained for each amino acid type in the different secondary structures. These chemical shift ranges, which may be defined at any statistical threshold, can be used for amino-acid type assignment and secondary-structure analysis of chemical shifts from intra-residue cross peaks by inspection or by using a

Conformationally selective multidimensional chemical shift ranges in proteins from a PACSY database purged using intrinsic quality criteria

Energy Technology Data Exchange (ETDEWEB)

Fritzsching, Keith J., E-mail: kfritzsc@brandeis.edu [Brandeis University, Department of Chemistry (United States); Hong, Mei [Massachusetts Institute of Technology, Department of Chemistry (United States); Schmidt-Rohr, Klaus, E-mail: srohr@brandeis.edu [Brandeis University, Department of Chemistry (United States)

2016-02-15

We have determined refined multidimensional chemical shift ranges for intra-residue correlations ({sup 13}C–{sup 13}C, {sup 15}N–{sup 13}C, etc.) in proteins, which can be used to gain type-assignment and/or secondary-structure information from experimental NMR spectra. The chemical-shift ranges are the result of a statistical analysis of the PACSY database of >3000 proteins with 3D structures (1,200,207 {sup 13}C chemical shifts and >3 million chemical shifts in total); these data were originally derived from the Biological Magnetic Resonance Data Bank. Using relatively simple non-parametric statistics to find peak maxima in the distributions of helix, sheet, coil and turn chemical shifts, and without the use of limited “hand-picked” data sets, we show that ∼94 % of the {sup 13}C NMR data and almost all {sup 15}N data are quite accurately referenced and assigned, with smaller standard deviations (0.2 and 0.8 ppm, respectively) than recognized previously. On the other hand, approximately 6 % of the {sup 13}C chemical shift data in the PACSY database are shown to be clearly misreferenced, mostly by ca. −2.4 ppm. The removal of the misreferenced data and other outliers by this purging by intrinsic quality criteria (PIQC) allows for reliable identification of secondary maxima in the two-dimensional chemical-shift distributions already pre-separated by secondary structure. We demonstrate that some of these correspond to specific regions in the Ramachandran plot, including left-handed helix dihedral angles, reflect unusual hydrogen bonding, or are due to the influence of a following proline residue. With appropriate smoothing, significantly more tightly defined chemical shift ranges are obtained for each amino acid type in the different secondary structures. These chemical shift ranges, which may be defined at any statistical threshold, can be used for amino-acid type assignment and secondary-structure analysis of chemical shifts from intra

Tensor gauge condition and tensor field decomposition

Science.gov (United States)

Zhu, Ben-Chao; Chen, Xiang-Song

2015-10-01

We discuss various proposals of separating a tensor field into pure-gauge and gauge-invariant components. Such tensor field decomposition is intimately related to the effort of identifying the real gravitational degrees of freedom out of the metric tensor in Einstein’s general relativity. We show that as for a vector field, the tensor field decomposition has exact correspondence to and can be derived from the gauge-fixing approach. The complication for the tensor field, however, is that there are infinitely many complete gauge conditions in contrast to the uniqueness of Coulomb gauge for a vector field. The cause of such complication, as we reveal, is the emergence of a peculiar gauge-invariant pure-gauge construction for any gauge field of spin ≥ 2. We make an extensive exploration of the complete tensor gauge conditions and their corresponding tensor field decompositions, regarding mathematical structures, equations of motion for the fields and nonlinear properties. Apparently, no single choice is superior in all aspects, due to an awkward fact that no gauge-fixing can reduce a tensor field to be purely dynamical (i.e. transverse and traceless), as can the Coulomb gauge in a vector case.

Tensor spherical harmonics and tensor multipoles. II. Minkowski space

International Nuclear Information System (INIS)

Daumens, M.; Minnaert, P.

1976-01-01

The bases of tensor spherical harmonics and of tensor multipoles discussed in the preceding paper are generalized in the Hilbert space of Minkowski tensor fields. The transformation properties of the tensor multipoles under Lorentz transformation lead to the notion of irreducible tensor multipoles. We show that the usual 4-vector multipoles are themselves irreducible, and we build the irreducible tensor multipoles of the second order. We also give their relations with the symmetric tensor multipoles defined by Zerilli for application to the gravitational radiation

DFT/GIAO calculations of the relative contributions of hyperconjugation to the chemical shifts of ethanol

International Nuclear Information System (INIS)

Carneiro, J. Walkimar de M.; Dias, Jacques F.; Seidl, Peter R.; Tostes, J. Glauco R.

2002-01-01

Our previous DFT/GIAO calculations on different types of alcohols reveal that the rotation of the hydroxyl group can affect the chemical shift of carbons and hydrogens close to the substituent in different ways. Besides the steric and electrostatic effects that have been widely studied, hyperconjugation with the lone pairs on oxygen of the hydroxyl group leads to changes in bond lengths and angles as well as to different charge distributions. As all three of these factors also affect chemical shifts, we undertook a systematic investigation of their relative contributions to the chemical shifts of ethanol, a molecule in which there is minimum interference among these factors. Calculations by the B3LYP method at the 6-31G(d) level for ethanol conformers corresponding to a rotation around the carbon-oxygen bond at 30 dec increments are used to show how relative contributions vary with the dihedral angle formed between the carbon-carbon and oxygen-hydrogen bonds (C-C-O-H). Largest contributions to carbon chemical shifts can be attributed to changes in bond lengths while for hydrogen chemical shifts also contribute significantly differences in charge distribution. (author)

Prediction of hydrogen and carbon chemical shifts from RNA using database mining and support vector regression

Energy Technology Data Exchange (ETDEWEB)

Brown, Joshua D.; Summers, Michael F. [University of Maryland Baltimore County, Howard Hughes Medical Institute (United States); Johnson, Bruce A., E-mail: bruce.johnson@asrc.cuny.edu [University of Maryland Baltimore County, Department of Chemistry and Biochemistry (United States)

2015-09-15

The Biological Magnetic Resonance Data Bank (BMRB) contains NMR chemical shift depositions for over 200 RNAs and RNA-containing complexes. We have analyzed the {sup 1}H NMR and {sup 13}C chemical shifts reported for non-exchangeable protons of 187 of these RNAs. Software was developed that downloads BMRB datasets and corresponding PDB structure files, and then generates residue-specific attributes based on the calculated secondary structure. Attributes represent properties present in each sequential stretch of five adjacent residues and include variables such as nucleotide type, base-pair presence and type, and tetraloop types. Attributes and {sup 1}H and {sup 13}C NMR chemical shifts of the central nucleotide are then used as input to train a predictive model using support vector regression. These models can then be used to predict shifts for new sequences. The new software tools, available as stand-alone scripts or integrated into the NMR visualization and analysis program NMRViewJ, should facilitate NMR assignment and/or validation of RNA {sup 1}H and {sup 13}C chemical shifts. In addition, our findings enabled the re-calibration a ring-current shift model using published NMR chemical shifts and high-resolution X-ray structural data as guides.

Linear Invariant Tensor Interpolation Applied to Cardiac Diffusion Tensor MRI

Science.gov (United States)

Gahm, Jin Kyu; Wisniewski, Nicholas; Kindlmann, Gordon; Kung, Geoffrey L.; Klug, William S.; Garfinkel, Alan; Ennis, Daniel B.

2015-01-01

Purpose Various methods exist for interpolating diffusion tensor fields, but none of them linearly interpolate tensor shape attributes. Linear interpolation is expected not to introduce spurious changes in tensor shape. Methods Herein we define a new linear invariant (LI) tensor interpolation method that linearly interpolates components of tensor shape (tensor invariants) and recapitulates the interpolated tensor from the linearly interpolated tensor invariants and the eigenvectors of a linearly interpolated tensor. The LI tensor interpolation method is compared to the Euclidean (EU), affine-invariant Riemannian (AI), log-Euclidean (LE) and geodesic-loxodrome (GL) interpolation methods using both a synthetic tensor field and three experimentally measured cardiac DT-MRI datasets. Results EU, AI, and LE introduce significant microstructural bias, which can be avoided through the use of GL or LI. Conclusion GL introduces the least microstructural bias, but LI tensor interpolation performs very similarly and at substantially reduced computational cost. PMID:23286085

Effect of Tensor Correlations on Gamow-Teller States in 90Zr and 208Pb

International Nuclear Information System (INIS)

Bai, C. L.; Zhang, H. Q.; Zhang, X. Z.

2009-01-01

The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree-Fock plus Random Phase Approximation (HF-RPA) model. The Gamow-Teller (GT) strength functions of 9 0Z r and 2 08P b is calculated with and without the tensor terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcome of RPA. A microscopic origin of the quenching of GT sum rule due to the tensor force is discussed.(author)

Skeletal and chlorine effects on 13C-NMR chemical shifts of chlorinated polycyclic systems

Directory of Open Access Journals (Sweden)

Costa V.E.U.

1999-01-01

Full Text Available In order to establish a comparative analysis of chemical shifts caused by ring compression effects or by the presence of a chlorine atom on strained chlorinated carbons, a series of the chlorinated and dechlorinated polycyclic structures derived from "aldrin" (5 and "isodrin" (14 was studied. Compounds were classified in four different groups, according to their conformation and number of ring such as: endo-exo and endo-endo tetracyclics, pentacyclics and hexacyclics. The 13C chemical shift comparison between the chlorinated and dechlorinated compounds showed that when C-9 and C-10 are olefinic carbons, it occurs a shielding of 0.5-2.4 ppm for endo-endo tetracyclics and of 4.7-7.6 ppm for endo-exo tetracyclic. The chemical shift variation for C-11 reaches 49-53 ppm for endo-exo and endo-endo tetracyclics, 54 ppm for pentacyclic and 56-59 ppm for hexacyclic compounds. From these data, it was possible to observe the influence of ring compression on the chemical shifts.

SPARTA+: a modest improvement in empirical NMR chemical shift prediction by means of an artificial neural network

International Nuclear Information System (INIS)

Shen Yang; Bax, Ad

2010-01-01

NMR chemical shifts provide important local structural information for proteins and are key in recently described protein structure generation protocols. We describe a new chemical shift prediction program, SPARTA+, which is based on artificial neural networking. The neural network is trained on a large carefully pruned database, containing 580 proteins for which high-resolution X-ray structures and nearly complete backbone and 13 C β chemical shifts are available. The neural network is trained to establish quantitative relations between chemical shifts and protein structures, including backbone and side-chain conformation, H-bonding, electric fields and ring-current effects. The trained neural network yields rapid chemical shift prediction for backbone and 13 C β atoms, with standard deviations of 2.45, 1.09, 0.94, 1.14, 0.25 and 0.49 ppm for δ 15 N, δ 13 C', δ 13 C α , δ 13 C β , δ 1 H α and δ 1 H N , respectively, between the SPARTA+ predicted and experimental shifts for a set of eleven validation proteins. These results represent a modest but consistent improvement (2-10%) over the best programs available to date, and appear to be approaching the limit at which empirical approaches can predict chemical shifts.

Cyclohexanecarbonitriles: Assigning Configurations at Quaternary Centers From 13C NMR CN Chemical Shifts.1

Science.gov (United States)

Wei, Guoqing

2009-01-01

13C NMR chemical shifts of the nitrile carbon in cyclohexanecarbonitriles directly correlate with the configuration of the quaternary, nitrile-bearing stereocenter. Comparing 13C NMR chemical shifts for over 200 cyclohexanecarbonitriles reveals that equatorially oriented nitriles resonate 3.3 ppm downfield, on average, from their axial counterparts. Pairs of axial/equatorial diastereomers varying only at the nitrile-bearing carbon consistently exhibit downfield shifts of δ 0.4–7.2 for the equatorial nitrile carbon, even in angularly substituted decalins and hydrindanes. PMID:19348434

1H NMR spectra part 31: 1H chemical shifts of amides in DMSO solvent.

Science.gov (United States)

Abraham, Raymond J; Griffiths, Lee; Perez, Manuel

2014-07-01

The (1)H chemical shifts of 48 amides in DMSO solvent are assigned and presented. The solvent shifts Δδ (DMSO-CDCl3 ) are large (1-2 ppm) for the NH protons but smaller and negative (-0.1 to -0.2 ppm) for close range protons. A selection of the observed solvent shifts is compared with calculated shifts from the present model and from GIAO calculations. Those for the NH protons agree with both calculations, but other solvent shifts such as Δδ(CHO) are not well reproduced by the GIAO calculations. The (1)H chemical shifts of the amides in DMSO were analysed using a functional approach for near ( ≤ 3 bonds removed) protons and the electric field, magnetic anisotropy and steric effect of the amide group for more distant protons. The chemical shifts of the NH protons of acetanilide and benzamide vary linearly with the π density on the αN and βC atoms, respectively. The C=O anisotropy and steric effect are in general little changed from the values in CDCl3. The effects of substituents F, Cl, Me on the NH proton shifts are reproduced. The electric field coefficient for the protons in DMSO is 90% of that in CDCl3. There is no steric effect of the C=O oxygen on the NH proton in an NH…O=C hydrogen bond. The observed deshielding is due to the electric field effect. The calculated chemical shifts agree well with the observed shifts (RMS error of 0.106 ppm for the data set of 257 entries). Copyright © 2014 John Wiley & Sons, Ltd.

Correction for Eddy Current-Induced Echo-Shifting Effect in Partial-Fourier Diffusion Tensor Imaging.

Science.gov (United States)

Truong, Trong-Kha; Song, Allen W; Chen, Nan-Kuei

2015-01-01

In most diffusion tensor imaging (DTI) studies, images are acquired with either a partial-Fourier or a parallel partial-Fourier echo-planar imaging (EPI) sequence, in order to shorten the echo time and increase the signal-to-noise ratio (SNR). However, eddy currents induced by the diffusion-sensitizing gradients can often lead to a shift of the echo in k-space, resulting in three distinct types of artifacts in partial-Fourier DTI. Here, we present an improved DTI acquisition and reconstruction scheme, capable of generating high-quality and high-SNR DTI data without eddy current-induced artifacts. This new scheme consists of three components, respectively, addressing the three distinct types of artifacts. First, a k-space energy-anchored DTI sequence is designed to recover eddy current-induced signal loss (i.e., Type 1 artifact). Second, a multischeme partial-Fourier reconstruction is used to eliminate artificial signal elevation (i.e., Type 2 artifact) associated with the conventional partial-Fourier reconstruction. Third, a signal intensity correction is applied to remove artificial signal modulations due to eddy current-induced erroneous T2(∗) -weighting (i.e., Type 3 artifact). These systematic improvements will greatly increase the consistency and accuracy of DTI measurements, expanding the utility of DTI in translational applications where quantitative robustness is much needed.

Characterization of the conformational equilibrium between the two major substates of RNase A using NMR chemical shifts.

Science.gov (United States)

Camilloni, Carlo; Robustelli, Paul; De Simone, Alfonso; Cavalli, Andrea; Vendruscolo, Michele

2012-03-07

Following the recognition that NMR chemical shifts can be used for protein structure determination, rapid advances have recently been made in methods for extending this strategy for proteins and protein complexes of increasing size and complexity. A remaining major challenge is to develop approaches to exploit the information contained in the chemical shifts about conformational fluctuations in native states of proteins. In this work we show that it is possible to determine an ensemble of conformations representing the free energy surface of RNase A using chemical shifts as replica-averaged restraints in molecular dynamics simulations. Analysis of this surface indicates that chemical shifts can be used to characterize the conformational equilibrium between the two major substates of this protein. © 2012 American Chemical Society

Sequential nearest-neighbor effects on computed {sup 13}C{sup {alpha}} chemical shifts

Energy Technology Data Exchange (ETDEWEB)

Vila, Jorge A. [Cornell University, Baker Laboratory of Chemistry and Chemical Biology (United States); Serrano, Pedro; Wuethrich, Kurt [The Scripps Research Institute, Department of Molecular Biology (United States); Scheraga, Harold A., E-mail: has5@cornell.ed [Cornell University, Baker Laboratory of Chemistry and Chemical Biology (United States)

2010-09-15

To evaluate sequential nearest-neighbor effects on quantum-chemical calculations of {sup 13}C{sup {alpha}} chemical shifts, we selected the structure of the nucleic acid binding (NAB) protein from the SARS coronavirus determined by NMR in solution (PDB id 2K87). NAB is a 116-residue {alpha}/{beta} protein, which contains 9 prolines and has 50% of its residues located in loops and turns. Overall, the results presented here show that sizeable nearest-neighbor effects are seen only for residues preceding proline, where Pro introduces an overestimation, on average, of 1.73 ppm in the computed {sup 13}C{sup {alpha}} chemical shifts. A new ensemble of 20 conformers representing the NMR structure of the NAB, which was calculated with an input containing backbone torsion angle constraints derived from the theoretical {sup 13}C{sup {alpha}} chemical shifts as supplementary data to the NOE distance constraints, exhibits very similar topology and comparable agreement with the NOE constraints as the published NMR structure. However, the two structures differ in the patterns of differences between observed and computed {sup 13}C{sup {alpha}} chemical shifts, {Delta}{sub ca,i}, for the individual residues along the sequence. This indicates that the {Delta}{sub ca,i} -values for the NAB protein are primarily a consequence of the limited sampling by the bundles of 20 conformers used, as in common practice, to represent the two NMR structures, rather than of local flaws in the structures.

Effect on Tensor Correlations on Gamow- Teller States in 90Zr and 208Pb

International Nuclear Information System (INIS)

Bai, C. L.; Sagawa, H.; Zhang, H. Q.

2009-01-01

The tensor terms of the Skyrme effective interaction are included in the self-consistent Hartree-Fock plus Random Phase Approximation (HF-RPA) model. The Gamow-Teller (GT) strength function of 9 0Z r and 2 08P b are calculated with and without the tensor terms. The main peaks are moved downwards by about 2 MeV when including the tensor contribution. About 10% of the non-energy weighted sum rule is shifted to the excitation energy region above 30 MeV by the RPA tensor correlations. The contribution of the tensor terms to the energy weighted sum rule is given analytically, and compared to the outcome of RPA. A microscopic origin of the quenching of GT sum rule is discussed in relation with the coupling to giant spin-quadrupole excitations by the tensor interactions.(author)

Isotope effects on chemical shifts in tautomeric systems with double proton transfer. Citronin

International Nuclear Information System (INIS)

Hansen, P.E.; Langgard, M.; Bolvig, S.

1998-01-01

Primary and secondary deuterium isotope effects on 1 H and 13 C chemical shifts are measured in citrinin, a tautomeric compound with an unusual doubly intramolecularly hydrogen bonded structure. The isotope effects are to a large extent dominated by equilibrium contributions and deuteration leads to more of the deuterated enol forms rather than the deuterated acid form. 1 H 13 C and 17 O nuclear shieldings are calculated using density functional ab initio methods. A very good correlation between calculated nuclear shieldings and experimental 1 H and 13 C chemical shifts is obtained. The tautomeric equilibrium can be analyzed based on the isotope effects on B-6 and C-8 carbons and shows an increase in the o-quinone form on lowering the temperature. Furthermore, upon deuteration the largest equilibrium shift is found for deuteration at OH-8 and the shift in the tautomeric equilibrium upon deuteration at OH-8 and the shift in the tautomeric equilibrium upon deuteration is increasing at lower temperature. (author)

SPARTA+: a modest improvement in empirical NMR chemical shift prediction by means of an artificial neural network

Energy Technology Data Exchange (ETDEWEB)

Shen Yang; Bax, Ad, E-mail: bax@nih.go [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States)

2010-09-15

NMR chemical shifts provide important local structural information for proteins and are key in recently described protein structure generation protocols. We describe a new chemical shift prediction program, SPARTA+, which is based on artificial neural networking. The neural network is trained on a large carefully pruned database, containing 580 proteins for which high-resolution X-ray structures and nearly complete backbone and {sup 13}C{sup {beta}} chemical shifts are available. The neural network is trained to establish quantitative relations between chemical shifts and protein structures, including backbone and side-chain conformation, H-bonding, electric fields and ring-current effects. The trained neural network yields rapid chemical shift prediction for backbone and {sup 13}C{sup {beta}} atoms, with standard deviations of 2.45, 1.09, 0.94, 1.14, 0.25 and 0.49 ppm for {delta}{sup 15}N, {delta}{sup 13}C', {delta}{sup 13}C{sup {alpha}}, {delta}{sup 13}C{sup {beta}}, {delta}{sup 1}H{sup {alpha}} and {delta}{sup 1}H{sup N}, respectively, between the SPARTA+ predicted and experimental shifts for a set of eleven validation proteins. These results represent a modest but consistent improvement (2-10%) over the best programs available to date, and appear to be approaching the limit at which empirical approaches can predict chemical shifts.

The interplay between transient a-helix formation and side chain rotamer distributions in disordered proteins probed by methyl chemical shifts

DEFF Research Database (Denmark)

Kjærgaard, Magnus; Iesmantavicius, Vytautas; Poulsen, Flemming M

2011-01-01

and retinoid receptors (ACTR). We find that small differences in the methyl carbon chemical shifts due to the ¿-gauche effect may provide information about the side chain rotamer distributions. However, the effects of neighboring residues on the methyl group chemical shifts obscure the direct observation...... of ¿-gauche effect. To overcome this, we reference the chemical shifts to those in a more disordered state resulting in residue specific random coil chemical shifts. The (13)C secondary chemical shifts of the methyl groups of valine, leucine, and isoleucine show sequence specific effects, which allow...

What can we learn by computing 13Cα chemical shifts for X-ray protein models?

International Nuclear Information System (INIS)

Arnautova, Yelena A.; Vila, Jorge A.; Martin, Osvaldo A.; Scheraga, Harold A.

2009-01-01

The room-temperature X-ray structures of two proteins, solved at 1.8 and 1.9 Å resolution, are used to investigate whether a set of conformations, rather than a single X-ray structure, provides better agreement with both the X-ray data and the observed 13 C α chemical shifts in solution. The room-temperature X-ray structures of ubiquitin and of the RNA-binding domain of nonstructural protein 1 of influenza A virus solved at 1.8 and 1.9 Å resolution, respectively, were used to investigate whether a set of conformations rather than a single X-ray structure provides better agreement with both the X-ray data and the observed 13 C α chemical shifts in solution. For this purpose, a set of new conformations for each of these proteins was generated by fitting them to the experimental X-ray data deposited in the PDB. For each of the generated structures, which show R and R free factors similar to those of the deposited X-ray structure, the 13 C α chemical shifts of all residues in the sequence were computed at the DFT level of theory. The sets of conformations were then evaluated by their ability to reproduce the observed 13 C α chemical shifts by using the conformational average root-mean-square-deviation (ca-r.m.s.d.). For ubiquitin, the computed set of conformations is a better representation of the observed 13 C α chemical shifts in terms of the ca-r.m.s.d. than a single X-ray-derived structure. However, for the RNA-binding domain of nonstructural protein 1 of influenza A virus, consideration of an ensemble of conformations does not improve the agreement with the observed 13 C α chemical shifts. Whether an ensemble of conformations rather than any single structure is a more accurate representation of a protein structure in the crystal as well as of the observed 13 C α chemical shifts is determined by the dispersion of coordinates, in terms of the all-atom r.m.s.d. among the generated models; these generated models satisfy the experimental X-ray data with

Conformational analysis of the chemical shifts for molecules containing diastereotopic methylene protons

Science.gov (United States)

Borowski, Piotr

2012-01-01

Quantum chemistry SCF/GIAO calculations were carried out on a set of compounds containing diastereotopic protons. Five molecules, including recently synthesized 1,3-di(2,3-epoxypropoxy)benzene, containing the chiral or pro-chiral center and the neighboring methylene group, were chosen. The rotational averages (i.e. normalized averages with respect to the rotation about the torsional angle τ with the exponential energy weight at temperature T) calculated individually for each of the methylene protons in 1,3-di(2,3-epoxypropoxy)benzene differ by ca. 0.6 ppm, which is significantly less than the value calculated for the lowest energy conformer. This value turned out to be low enough to guarantee the proper ordering of theoretical chemical shifts, supporting the interpretation of the 1H NMR spectrum of this important compound. The rotational averages of chemical shifts for methylene protons for a given type of conformer are shown to be essentially equal to the Boltzmann averages (here, the population-weighted averages for the individual conformers representing minima on the E( τ) cross-section). The calculated Boltzmann averages in the representative conformational space may exhibit completely different ordering as compared to the chemical shifts calculated for the lowest-energy conformer. This is especially true in the case of molecules, for which no significant steric effects are present. In this case, only Boltzmann averages account for the experimental pattern of proton signals. In addition, better overall agreement with experiment (lower value of the root-mean-square deviation between calculated and measured chemical shifts) is typically obtained when Boltzmann averages are used.

Protein backbone chemical shifts predicted from searching a database for torsion angle and sequence homology

International Nuclear Information System (INIS)

Shen Yang; Bax, Ad

2007-01-01

Chemical shifts of nuclei in or attached to a protein backbone are exquisitely sensitive to their local environment. A computer program, SPARTA, is described that uses this correlation with local structure to predict protein backbone chemical shifts, given an input three-dimensional structure, by searching a newly generated database for triplets of adjacent residues that provide the best match in φ/ψ/χ 1 torsion angles and sequence similarity to the query triplet of interest. The database contains 15 N, 1 H N , 1 H α , 13 C α , 13 C β and 13 C' chemical shifts for 200 proteins for which a high resolution X-ray (≤2.4 A) structure is available. The relative importance of the weighting factors for the φ/ψ/χ 1 angles and sequence similarity was optimized empirically. The weighted, average secondary shifts of the central residues in the 20 best-matching triplets, after inclusion of nearest neighbor, ring current, and hydrogen bonding effects, are used to predict chemical shifts for the protein of known structure. Validation shows good agreement between the SPARTA-predicted and experimental shifts, with standard deviations of 2.52, 0.51, 0.27, 0.98, 1.07 and 1.08 ppm for 15 N, 1 H N , 1 H α , 13 C α , 13 C β and 13 C', respectively, including outliers

Influence of stacking interactions on NMR chemical shielding tensors in benzene and formamide homodimers as studied by HF, DFT and MP2 calculations

Czech Academy of Sciences Publication Activity Database

Czernek, Jiří

2003-01-01

Roč. 107, č. 19 (2003), s. 3952-3959 ISSN 1089-5639 R&D Projects: GA AV ČR KJB4050311 Institutional research plan: CEZ:AV0Z4050913 Keywords : NMR * chemical shielding tensor * ab initio Subject RIV: CD - Macromolecular Chemistry Impact factor: 2.792, year: 2003

Diffusion tensor image registration using hybrid connectivity and tensor features.

Science.gov (United States)

Wang, Qian; Yap, Pew-Thian; Wu, Guorong; Shen, Dinggang

2014-07-01

Most existing diffusion tensor imaging (DTI) registration methods estimate structural correspondences based on voxelwise matching of tensors. The rich connectivity information that is given by DTI, however, is often neglected. In this article, we propose to integrate complementary information given by connectivity features and tensor features for improved registration accuracy. To utilize connectivity information, we place multiple anchors representing different brain anatomies in the image space, and define the connectivity features for each voxel as the geodesic distances from all anchors to the voxel under consideration. The geodesic distance, which is computed in relation to the tensor field, encapsulates information of brain connectivity. We also extract tensor features for every voxel to reflect the local statistics of tensors in its neighborhood. We then combine both connectivity features and tensor features for registration of tensor images. From the images, landmarks are selected automatically and their correspondences are determined based on their connectivity and tensor feature vectors. The deformation field that deforms one tensor image to the other is iteratively estimated and optimized according to the landmarks and their associated correspondences. Experimental results show that, by using connectivity features and tensor features simultaneously, registration accuracy is increased substantially compared with the cases using either type of features alone. Copyright © 2013 Wiley Periodicals, Inc.

Implementation of the NMR CHEmical Shift Covariance Analysis (CHESCA): A Chemical Biologist's Approach to Allostery.

Science.gov (United States)

Boulton, Stephen; Selvaratnam, Rajeevan; Ahmed, Rashik; Melacini, Giuseppe

2018-01-01

Mapping allosteric sites is emerging as one of the central challenges in physiology, pathology, and pharmacology. Nuclear Magnetic Resonance (NMR) spectroscopy is ideally suited to map allosteric sites, given its ability to sense at atomic resolution the dynamics underlying allostery. Here, we focus specifically on the NMR CHEmical Shift Covariance Analysis (CHESCA), in which allosteric systems are interrogated through a targeted library of perturbations (e.g., mutations and/or analogs of the allosteric effector ligand). The atomic resolution readout for the response to such perturbation library is provided by NMR chemical shifts. These are then subject to statistical correlation and covariance analyses resulting in clusters of allosterically coupled residues that exhibit concerted responses to the common set of perturbations. This chapter provides a description of how each step in the CHESCA is implemented, starting from the selection of the perturbation library and ending with an overview of different clustering options.

Killing tensors and conformal Killing tensors from conformal Killing vectors

International Nuclear Information System (INIS)

Rani, Raffaele; Edgar, S Brian; Barnes, Alan

2003-01-01

Koutras has proposed some methods to construct reducible proper conformal Killing tensors and Killing tensors (which are, in general, irreducible) when a pair of orthogonal conformal Killing vectors exist in a given space. We give the completely general result demonstrating that this severe restriction of orthogonality is unnecessary. In addition, we correct and extend some results concerning Killing tensors constructed from a single conformal Killing vector. A number of examples demonstrate that it is possible to construct a much larger class of reducible proper conformal Killing tensors and Killing tensors than permitted by the Koutras algorithms. In particular, by showing that all conformal Killing tensors are reducible in conformally flat spaces, we have a method of constructing all conformal Killing tensors, and hence all the Killing tensors (which will in general be irreducible) of conformally flat spaces using their conformal Killing vectors

Tensors for physics

CERN Document Server

Hess, Siegfried

2015-01-01

This book presents the science of tensors in a didactic way. The various types and ranks of tensors and the physical basis is presented. Cartesian Tensors are needed for the description of directional phenomena in many branches of physics and for the characterization the anisotropy of material properties. The first sections of the book provide an introduction to the vector and tensor algebra and analysis, with applications to physics,  at undergraduate level. Second rank tensors, in particular their symmetries, are discussed in detail. Differentiation and integration of fields, including generalizations of the Stokes law and the Gauss theorem, are treated. The physics relevant for the applications in mechanics, quantum mechanics, electrodynamics and hydrodynamics is presented. The second part of the book is devoted to  tensors of any rank, at graduate level.  Special topics are irreducible, i.e. symmetric traceless tensors, isotropic tensors, multipole potential tensors, spin tensors, integration and spin-...

Proton chemical shift imaging after myocardial infarction

International Nuclear Information System (INIS)

Bouchard, A.; Doyle, M.; Pohost, G.M.

1989-01-01

The present study was undertaken to test whether chemical shift imaging could detect spatially the lipids known to accumulate in myocardium after an ischemic insult. Seven dogs underwent a 24-hour coronary artery occlusion. Hearts were removed and imaged ex vivo by the Dixon method (1.5 T), and myocardial samples were obtained for high-resolution H-1 spectroscopy. Lipid images revealed regions of increased signal intensity in the periphery f the myocardial infarction. The zones of high lipid signal corresponded to zones with elevated mobile lipids as detected by H-1 spectroscopy

Accuracy and precision of protein–ligand interaction kinetics determined from chemical shift titrations

International Nuclear Information System (INIS)

Markin, Craig J.; Spyracopoulos, Leo

2012-01-01

NMR-monitored chemical shift titrations for the study of weak protein–ligand interactions represent a rich source of information regarding thermodynamic parameters such as dissociation constants (K D ) in the micro- to millimolar range, populations for the free and ligand-bound states, and the kinetics of interconversion between states, which are typically within the fast exchange regime on the NMR timescale. We recently developed two chemical shift titration methods wherein co-variation of the total protein and ligand concentrations gives increased precision for the K D value of a 1:1 protein–ligand interaction (Markin and Spyracopoulos in J Biomol NMR 53: 125–138, 2012). In this study, we demonstrate that classical line shape analysis applied to a single set of 1 H– 15 N 2D HSQC NMR spectra acquired using precise protein–ligand chemical shift titration methods we developed, produces accurate and precise kinetic parameters such as the off-rate (k off ). For experimentally determined kinetics in the fast exchange regime on the NMR timescale, k off ∼ 3,000 s −1 in this work, the accuracy of classical line shape analysis was determined to be better than 5 % by conducting quantum mechanical NMR simulations of the chemical shift titration methods with the magnetic resonance toolkit GAMMA. Using Monte Carlo simulations, the experimental precision for k off from line shape analysis of NMR spectra was determined to be 13 %, in agreement with the theoretical precision of 12 % from line shape analysis of the GAMMA simulations in the presence of noise and protein concentration errors. In addition, GAMMA simulations were employed to demonstrate that line shape analysis has the potential to provide reasonably accurate and precise k off values over a wide range, from 100 to 15,000 s −1 . The validity of line shape analysis for k off values approaching intermediate exchange (∼100 s −1 ), may be facilitated by more accurate K D measurements from NMR

Accuracy and precision of protein-ligand interaction kinetics determined from chemical shift titrations.

Science.gov (United States)

Markin, Craig J; Spyracopoulos, Leo

2012-12-01

NMR-monitored chemical shift titrations for the study of weak protein-ligand interactions represent a rich source of information regarding thermodynamic parameters such as dissociation constants (K ( D )) in the micro- to millimolar range, populations for the free and ligand-bound states, and the kinetics of interconversion between states, which are typically within the fast exchange regime on the NMR timescale. We recently developed two chemical shift titration methods wherein co-variation of the total protein and ligand concentrations gives increased precision for the K ( D ) value of a 1:1 protein-ligand interaction (Markin and Spyracopoulos in J Biomol NMR 53: 125-138, 2012). In this study, we demonstrate that classical line shape analysis applied to a single set of (1)H-(15)N 2D HSQC NMR spectra acquired using precise protein-ligand chemical shift titration methods we developed, produces accurate and precise kinetic parameters such as the off-rate (k ( off )). For experimentally determined kinetics in the fast exchange regime on the NMR timescale, k ( off ) ~ 3,000 s(-1) in this work, the accuracy of classical line shape analysis was determined to be better than 5 % by conducting quantum mechanical NMR simulations of the chemical shift titration methods with the magnetic resonance toolkit GAMMA. Using Monte Carlo simulations, the experimental precision for k ( off ) from line shape analysis of NMR spectra was determined to be 13 %, in agreement with the theoretical precision of 12 % from line shape analysis of the GAMMA simulations in the presence of noise and protein concentration errors. In addition, GAMMA simulations were employed to demonstrate that line shape analysis has the potential to provide reasonably accurate and precise k ( off ) values over a wide range, from 100 to 15,000 s(-1). The validity of line shape analysis for k ( off ) values approaching intermediate exchange (~100 s(-1)), may be facilitated by more accurate K ( D ) measurements

Chemical shift-based identification of monosaccharide spin-systems with NMR spectroscopy to complement untargeted glycomics.

Science.gov (United States)

Klukowski, Piotr; Schubert, Mario

2018-06-15

A better understanding of oligosaccharides and their wide-ranging functions in almost every aspect of biology and medicine promises to uncover hidden layers of biology and will support the development of better therapies. Elucidating the chemical structure of an unknown oligosaccharide is still a challenge. Efficient tools are required for non-targeted glycomics. Chemical shifts are a rich source of information about the topology and configuration of biomolecules, whose potential is however not fully explored for oligosaccharides. We hypothesize that the chemical shifts of each monosaccharide are unique for each saccharide type with a certain linkage pattern, so that correlated data measured by NMR spectroscopy can be used to identify the chemical nature of a carbohydrate. We present here an efficient search algorithm, GlycoNMRSearch, that matches either a subset or the entire set of chemical shifts of an unidentified monosaccharide spin system to all spin systems in an NMR database. The search output is much more precise than earlier search functions and highly similar matches suggest the chemical structure of the spin system within the oligosaccharide. Thus searching for connected chemical shift correlations within all electronically available NMR data of oligosaccharides is a very efficient way of identifying the chemical structure of unknown oligosaccharides. With an improved database in the future, GlycoNMRSearch will be even more efficient deducing chemical structures of oligosaccharides and there is a high chance that it becomes an indispensable technique for glycomics. The search algorithm presented here, together with a graphical user interface, is available at http://glyconmrsearch.santos.pwr.edu.pl. Supplementary data are available at Bioinformatics online.

Repeatability of chemical-shift-encoded water-fat MRI and diffusion-tensor imaging in lower extremity muscles in children.

Science.gov (United States)

Ponrartana, Skorn; Andrade, Kristine E; Wren, Tishya A L; Ramos-Platt, Leigh; Hu, Houchun H; Bluml, Stefan; Gilsanz, Vicente

2014-06-01

The purpose of this study was to assess the repeatability of water-fat MRI and diffusion-tensor imaging (DTI) as quantitative biomarkers of pediatric lower extremity skeletal muscle. MRI at 3 T of a randomly selected thigh and lower leg of seven healthy children was studied using water-fat separation and DTI techniques. Muscle-fat fraction, apparent diffusion coefficient (ADC), and fractional anisotropy (FA) values were calculated. Test-retest and interrater repeatability were assessed by calculating the Pearson correlation coefficient, intraclass correlation coefficient, and Bland-Altman analysis. Bland-Altman plots show that the mean difference between test-retest and interrater measurements of muscle-fat fraction, ADC, and FA was near 0. The correlation coefficients and intraclass correlation coefficients were all between 0.88 and 0.99 (p DTI measurements in lower extremity skeletal muscles are objective repeatable biomarkers in children. This knowledge should aid in the understanding of the number of participants needed in clinical trials when using these determinations as an outcome measure to noninvasively monitor neuromuscular disease.

Elucidation of the substitution pattern of 9,10-anthraquinones through the chemical shifts of peri-hydroxyl protons

DEFF Research Database (Denmark)

Schripsema, Jan; Danigno, Denise

1996-01-01

In 9,10-anthraquinones the chemical shift of a peri-hydroxyl proton is affected by the substituents in the other benzenoid ring. These effects are additive. They are useful for the determination of substitution patterns and have been used to revise the structures of six previously reported...... anthraquinones containing methoxyl, hydroxyl, methylenedioxy and beta-methyl substituents. Because the chemical shifts of the other protons are hardly affected by substitutions in the other ring, the characteristic chemical shifts for a wide variety of substitution patterns could be derived....

The 1/ N Expansion of Tensor Models with Two Symmetric Tensors

Science.gov (United States)

Gurau, Razvan

2018-06-01

It is well known that tensor models for a tensor with no symmetry admit a 1/ N expansion dominated by melonic graphs. This result relies crucially on identifying jackets, which are globally defined ribbon graphs embedded in the tensor graph. In contrast, no result of this kind has so far been established for symmetric tensors because global jackets do not exist. In this paper we introduce a new approach to the 1/ N expansion in tensor models adapted to symmetric tensors. In particular we do not use any global structure like the jackets. We prove that, for any rank D, a tensor model with two symmetric tensors and interactions the complete graph K D+1 admits a 1/ N expansion dominated by melonic graphs.

Vanadium NMR Chemical Shifts of (Imido)vanadium(V) Dichloride Complexes with Imidazolin-2-iminato and Imidazolidin-2-iminato Ligands: Cooperation with Quantum-Chemical Calculations and Multiple Linear Regression Analyses.

Science.gov (United States)

Yi, Jun; Yang, Wenhong; Sun, Wen-Hua; Nomura, Kotohiro; Hada, Masahiko

2017-11-30

The NMR chemical shifts of vanadium ( 51 V) in (imido)vanadium(V) dichloride complexes with imidazolin-2-iminato and imidazolidin-2-iminato ligands were calculated by the density functional theory (DFT) method with GIAO. The calculated 51 V NMR chemical shifts were analyzed by the multiple linear regression (MLR) analysis (MLRA) method with a series of calculated molecular properties. Some of calculated NMR chemical shifts were incorrect using the optimized molecular geometries of the X-ray structures. After the global minimum geometries of all of the molecules were determined, the trend of the observed chemical shifts was well reproduced by the present DFT method. The MLRA method was performed to investigate the correlation between the 51 V NMR chemical shift and the natural charge, band energy gap, and Wiberg bond index of the V═N bond. The 51 V NMR chemical shifts obtained with the present MLR model were well reproduced with a correlation coefficient of 0.97.

Charged black holes in a generalized scalar–tensor gravity model

Directory of Open Access Journals (Sweden)

Yves Brihaye

2017-09-01

Full Text Available We study 4-dimensional charged and static black holes in a generalized scalar–tensor gravity model, in which a shift symmetry for the scalar field exists. For vanishing scalar field the solution corresponds to the Reissner–Nordström (RN solution, while solutions of the full scalar-gravity model have to be constructed numerically. We demonstrate that these black holes support Galilean scalar hair up to a maximal value of the scalar–tensor coupling that depends on the value of the charge and can be up to roughly twice as large as that for uncharged solutions. The Hawking temperature TH of the hairy black holes at maximal scalar–tensor coupling decreases continuously with the increase of the charge and reaches TH=0 for the highest possible charge that these solutions can carry. However, in this limit, the scalar–tensor coupling needs to vanish. The limiting solution hence corresponds to the extremal RN solution, which does not support regular Galilean scalar hair due to its AdS2×S2 near-horizon geometry.

Evaluation of the application of chemical shift for the detection of lipid in brain lesion

Energy Technology Data Exchange (ETDEWEB)

Lim, C.J. [Department of Biomedical Imaging, Faculty of Medicine, University of Malaya Medical Centre, Kuala Lumpur (Malaysia); Ng, K.H., E-mail: ngkh@um.edu.m [Department of Biomedical Imaging, Faculty of Medicine, University of Malaya Medical Centre, Kuala Lumpur (Malaysia); Ramli, N.; Azman, R.R. [Department of Biomedical Imaging, Faculty of Medicine, University of Malaya Medical Centre, Kuala Lumpur (Malaysia)

2011-02-15

Non-invasive detection of the presence of lipids is particularly important in staging of intracranial tumours. Presence of lipid peak in aggressive intracranial tumours has been reported widely using MR spectroscopy. However this method has limitation due to long imaging time and artefacts formed by adjacent bones. Chemical shift MR imaging (with has shorter imaging time) is an alternative method that had been used to detect presence of lipid in vivo by means of signal intensity loss. The purpose of this study was to evaluate gradient echo in- and opposed-phase chemical shift pulse sequences for detection of lipid elements in brain lesion. Ten cylindered phantoms measuring 3 x 3 cm were filled with various mixtures of lipid and water: 0-90% lipid, in 10% step by weight. The gradient echo in- and opposed-phase chemical shift sequences were performed using a 1.5 T MRI (Magnetom Vision, Siemens) with a head coil. In addition, we performed MRI and chemical shift studies on 32 patients with brain lesion. We then analysed the association between out of phase intensity value and classification of the lesions. For phantom containing 50% lipid, maximum signal loss on opposed-phase images was observed. There were significant differences between in- and opposed-phase lipid-water phantom images (P = 0.0054). Most of the benign lesions fall into the positive out of phase intensity value, and malignant lesions fall into negative out of phase intensity value. We conclude that chemical shift artefact can be applied in detecting and characterising lipid elements in brain lesion.

Evaluation of the application of chemical shift for the detection of lipid in brain lesion

International Nuclear Information System (INIS)

Lim, C.J.; Ng, K.H.; Ramli, N.; Azman, R.R.

2011-01-01

Non-invasive detection of the presence of lipids is particularly important in staging of intracranial tumours. Presence of lipid peak in aggressive intracranial tumours has been reported widely using MR spectroscopy. However this method has limitation due to long imaging time and artefacts formed by adjacent bones. Chemical shift MR imaging (with has shorter imaging time) is an alternative method that had been used to detect presence of lipid in vivo by means of signal intensity loss. The purpose of this study was to evaluate gradient echo in- and opposed-phase chemical shift pulse sequences for detection of lipid elements in brain lesion. Ten cylindered phantoms measuring 3 x 3 cm were filled with various mixtures of lipid and water: 0-90% lipid, in 10% step by weight. The gradient echo in- and opposed-phase chemical shift sequences were performed using a 1.5 T MRI (Magnetom Vision, Siemens) with a head coil. In addition, we performed MRI and chemical shift studies on 32 patients with brain lesion. We then analysed the association between out of phase intensity value and classification of the lesions. For phantom containing 50% lipid, maximum signal loss on opposed-phase images was observed. There were significant differences between in- and opposed-phase lipid-water phantom images (P = 0.0054). Most of the benign lesions fall into the positive out of phase intensity value, and malignant lesions fall into negative out of phase intensity value. We conclude that chemical shift artefact can be applied in detecting and characterising lipid elements in brain lesion.

Symmetry breaking nuclear quadrupole coupling tensor orientation for cesium-133 nuclei located in a mirror plane

Energy Technology Data Exchange (ETDEWEB)

Kim, Tae Ho; Kim, Jin Eun [Dept. of Chemistry (BK21 plus) and Research Institute of Natural Science, Gyeongsang National University, Jinju (Korea, Republic of); Lee, Kang Yeol [School of Mechanical Engineering, Korea University, Seoul (Korea, Republic of)

2016-11-15

Simultaneous multiple data set fits of all transition peaks of {sup 133}Cs nuclei enabled us to obtain accurate cesium-133 nuclear magnetic resonance (NMR) parameters and Euler angles between the principal axis systems of the chemical shift (CS) and quadrupole coupling (Q) tensors of {sup 133}Cs nuclei in Cs{sub 2}CrO{sub 4} . Although in a previous study of Cs{sub 2}CrO{sub 4} by Power et al. (W. P. Power, S. Mooibroek, R. E. Wasylishen, T. S. Cameron, J. Phys. Chem. 1994, 98, 1552), one central transition was observed for cesium sites 1 and 2 in the {sup 133}Cs NMR spectra and one Euler angle between the CS tensors and Q tensors was obtained as 52° and 7° for cesium sites 1 and 2, respectively, the present single-crystal {sup 133}Cs NMR measurements found two Euler angles (10(2)°, 51.9(1)°, 0°) for site 1 and two central transition peaks for site 2. Three principal components of the CS tensor for Cs1 are oriented along the crystallographic a, b, and c axes, whereas none of the principal components of the Q tensor for Cs1 are oriented along the crystal axes. The principal component V{sub 22} of the Q tensor for Cs1 is tilted 10° from the b axis in the bc plane, and the other two components are not located in the ac plane. Therefore, we have found that the requirement that “the quadrupole coupling tensor for a nucleus located in a mirror plane has one principal axis perpendicular to the mirror plane” cannot be applied to Cs1. On the other hand, δ{sub 11} and V{sub 22} for Cs2 are aligned along the b axis, and the other components of the CS and Q tensors deviate at an angle of 1.4(1)° and 10.1(1)°, respectively, from the a and c axes in the ac plane. A distortion-free powder {sup 133}Cs NMR spectrum of Cs{sub 2}CrO{sub 4} was measured using a solid-state spin echo technique.

Accuracy and precision of protein-ligand interaction kinetics determined from chemical shift titrations

Energy Technology Data Exchange (ETDEWEB)

Markin, Craig J.; Spyracopoulos, Leo, E-mail: leo.spyracopoulos@ualberta.ca [University of Alberta, Department of Biochemistry (Canada)

2012-12-15

NMR-monitored chemical shift titrations for the study of weak protein-ligand interactions represent a rich source of information regarding thermodynamic parameters such as dissociation constants (K{sub D}) in the micro- to millimolar range, populations for the free and ligand-bound states, and the kinetics of interconversion between states, which are typically within the fast exchange regime on the NMR timescale. We recently developed two chemical shift titration methods wherein co-variation of the total protein and ligand concentrations gives increased precision for the K{sub D} value of a 1:1 protein-ligand interaction (Markin and Spyracopoulos in J Biomol NMR 53: 125-138, 2012). In this study, we demonstrate that classical line shape analysis applied to a single set of {sup 1}H-{sup 15}N 2D HSQC NMR spectra acquired using precise protein-ligand chemical shift titration methods we developed, produces accurate and precise kinetic parameters such as the off-rate (k{sub off}). For experimentally determined kinetics in the fast exchange regime on the NMR timescale, k{sub off} {approx} 3,000 s{sup -1} in this work, the accuracy of classical line shape analysis was determined to be better than 5 % by conducting quantum mechanical NMR simulations of the chemical shift titration methods with the magnetic resonance toolkit GAMMA. Using Monte Carlo simulations, the experimental precision for k{sub off} from line shape analysis of NMR spectra was determined to be 13 %, in agreement with the theoretical precision of 12 % from line shape analysis of the GAMMA simulations in the presence of noise and protein concentration errors. In addition, GAMMA simulations were employed to demonstrate that line shape analysis has the potential to provide reasonably accurate and precise k{sub off} values over a wide range, from 100 to 15,000 s{sup -1}. The validity of line shape analysis for k{sub off} values approaching intermediate exchange ({approx}100 s{sup -1}), may be facilitated by

An extrapolation scheme for solid-state NMR chemical shift calculations

Science.gov (United States)

Nakajima, Takahito

2017-06-01

Conventional quantum chemical and solid-state physical approaches include several problems to accurately calculate solid-state nuclear magnetic resonance (NMR) properties. We propose a reliable computational scheme for solid-state NMR chemical shifts using an extrapolation scheme that retains the advantages of these approaches but reduces their disadvantages. Our scheme can satisfactorily yield solid-state NMR magnetic shielding constants. The estimated values have only a small dependence on the low-level density functional theory calculation with the extrapolation scheme. Thus, our approach is efficient because the rough calculation can be performed in the extrapolation scheme.

The energy–momentum tensor(s in classical gauge theories

Directory of Open Access Journals (Sweden)

Daniel N. Blaschke

2016-11-01

Full Text Available We give an introduction to, and review of, the energy–momentum tensors in classical gauge field theories in Minkowski space, and to some extent also in curved space–time. For the canonical energy–momentum tensor of non-Abelian gauge fields and of matter fields coupled to such fields, we present a new and simple improvement procedure based on gauge invariance for constructing a gauge invariant, symmetric energy–momentum tensor. The relationship with the Einstein–Hilbert tensor following from the coupling to a gravitational field is also discussed.

Experimental and DFT evaluation of the 1H and 13C NMR chemical shifts for calix[4]arenes

Science.gov (United States)

Guzzo, Rodrigo N.; Rezende, Michelle Jakeline Cunha; Kartnaller, Vinicius; Carneiro, José Walkimar de M.; Stoyanov, Stanislav R.; Costa, Leonardo Moreira da

2018-04-01

The density functional theory is employed to determine the efficiency of 11 exchange-correlation (XC) functionals to compute the 1H and 13C NMR chemical shifts of p-tert-butylcalix[4]arene (ptcx4, R1 = C(CH3)3) and congeners using the 6-31G(d,p) basis set. The statistical analysis shows that B3LYP, B3PW91 and PBE1PBE are the best XC functionals for the calculation of 1H chemical shifts. Moreover, the best results for the 13C chemical shifts are obtained using the LC-WPBE, M06-2X and wB97X-D functionals. The performance of these XC functionals is tested for three other calix[4]arenes: p-sulfonic acid calix[4]arene (sfxcx4 - R1 = SO3H), p-nitro-calix[4]arene (ncx4, R1 = NO2) and calix[4]arene (cx4 - R1 = H). For 1H chemical shifts B3LYP, B3PW91 and PBE1PBE yield similar results, although B3PW91 shows more consistency in the calculated error for the different structures. For 13C NMR chemical shifts, the XC functional that stood out as best is LC-WPBE. Indeed, the three functionals selected for each of 1H and 13C show good accuracy and can be used in future studies involving the prediction of 1H and 13C chemical shifts for this type of compounds.

Efficient tensor completion for color image and video recovery: Low-rank tensor train

OpenAIRE

Bengua, Johann A.; Phien, Ho N.; Tuan, Hoang D.; Do, Minh N.

2016-01-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via tensor tra...

Investigation of DOTA-Metal Chelation Effects on the Chemical Shift of ¹²⁹ Xe

Energy Technology Data Exchange (ETDEWEB)

Jeong, K; Slack, CC; Vassiliou, CC; Dao, P; Gomes, MD; Kennedy, DJ; Truxal, AE; Sperling, LJ; Francis, MB; Wemmer, DE; Pines, A

2015-09-17

Recent work has shown that xenon chemical shifts in cryptophane-cage sensors are affected when tethered chelators bind to metals. Here in this paper, we explore the xenon shifts in response to a wide range of metal ions binding to diastereomeric forms of 1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid (DOTA) linked to cryptophane-A. The shifts induced by the binding of Ca²⁺, Cu²⁺, Ce³⁺, Zn²⁺, Cd²⁺, Ni²⁺, Co²⁺, Cr²⁺, Fe³⁺, and Hg²⁺ are distinct. In addition, the different responses of the diastereomers for the same metal ion indicate that shifts are affected by partial folding with a correlation between the expected coordination number of the metal in the DOTA complex and the chemical shift of ¹²⁹Xe. Lastly, these sensors may be used to detect and quantify many important metal ions, and a better understanding of the basis for the induced shifts could enhance future designs.

Tensor completion and low-n-rank tensor recovery via convex optimization

International Nuclear Information System (INIS)

Gandy, Silvia; Yamada, Isao; Recht, Benjamin

2011-01-01

In this paper we consider sparsity on a tensor level, as given by the n-rank of a tensor. In an important sparse-vector approximation problem (compressed sensing) and the low-rank matrix recovery problem, using a convex relaxation technique proved to be a valuable solution strategy. Here, we will adapt these techniques to the tensor setting. We use the n-rank of a tensor as a sparsity measure and consider the low-n-rank tensor recovery problem, i.e. the problem of finding the tensor of the lowest n-rank that fulfills some linear constraints. We introduce a tractable convex relaxation of the n-rank and propose efficient algorithms to solve the low-n-rank tensor recovery problem numerically. The algorithms are based on the Douglas–Rachford splitting technique and its dual variant, the alternating direction method of multipliers

Tensor eigenvalues and their applications

CERN Document Server

Qi, Liqun; Chen, Yannan

2018-01-01

This book offers an introduction to applications prompted by tensor analysis, especially by the spectral tensor theory developed in recent years. It covers applications of tensor eigenvalues in multilinear systems, exponential data fitting, tensor complementarity problems, and tensor eigenvalue complementarity problems. It also addresses higher-order diffusion tensor imaging, third-order symmetric and traceless tensors in liquid crystals, piezoelectric tensors, strong ellipticity for elasticity tensors, and higher-order tensors in quantum physics. This book is a valuable reference resource for researchers and graduate students who are interested in applications of tensor eigenvalues.

Pressure-dependent {sup 13}C chemical shifts in proteins: origins and applications

Energy Technology Data Exchange (ETDEWEB)

Wilton, David J. [University of Sheffield, Department of Molecular Biology and Biotechnology (United Kingdom); Kitahara, Ryo [Ritsumeikan University, College of Pharmaceutical Sciences (Japan); Akasaka, Kazuyuki [Kinki University, Department of Biotechnological Science, School of Biology-Oriented Science and Technology (Japan); Williamson, Mike P. [University of Sheffield, Department of Molecular Biology and Biotechnology (United Kingdom)], E-mail: m.williamson@sheffield.ac.uk

2009-05-15

Pressure-dependent {sup 13}C chemical shifts have been measured for aliphatic carbons in barnase and Protein G. Up to 200 MPa (2 kbar), most shift changes are linear, demonstrating pressure-independent compressibilities. CH{sub 3}, CH{sub 2} and CH carbon shifts change on average by +0.23, -0.09 and -0.18 ppm, respectively, due to a combination of bond shortening and changes in bond angles, the latter matching one explanation for the {gamma}-gauche effect. In addition, there is a residue-specific component, arising from both local compression and conformational change. To assess the relative magnitudes of these effects, residue-specific shift changes for protein G were converted into structural restraints and used to calculate the change in structure with pressure, using a genetic algorithm to convert shift changes into dihedral angle restraints. The results demonstrate that residual {sup 13}C{alpha} shifts are dominated by dihedral angle changes and can be used to calculate structural change, whereas {sup 13}C{beta} shifts retain significant dependence on local compression, making them less useful as structural restraints.

Tensor Transpose and Its Properties

OpenAIRE

Pan, Ran

2014-01-01

Tensor transpose is a higher order generalization of matrix transpose. In this paper, we use permutations and symmetry group to define? the tensor transpose. Then we discuss the classification and composition of tensor transposes. Properties of tensor transpose are studied in relation to tensor multiplication, tensor eigenvalues, tensor decompositions and tensor rank.

Spin-echo based diagonal peak suppression in solid-state MAS NMR homonuclear chemical shift correlation spectra

Science.gov (United States)

Wang, Kaiyu; Zhang, Zhiyong; Ding, Xiaoyan; Tian, Fang; Huang, Yuqing; Chen, Zhong; Fu, Riqiang

2018-02-01

The feasibility of using the spin-echo based diagonal peak suppression method in solid-state MAS NMR homonuclear chemical shift correlation experiments is demonstrated. A complete phase cycling is designed in such a way that in the indirect dimension only the spin diffused signals are evolved, while all signals not involved in polarization transfer are refocused for cancellation. A data processing procedure is further introduced to reconstruct this acquired spectrum into a conventional two-dimensional homonuclear chemical shift correlation spectrum. A uniformly 13C, 15N labeled Fmoc-valine sample and the transmembrane domain of a human protein, LR11 (sorLA), in native Escherichia coli membranes have been used to illustrate the capability of the proposed method in comparison with standard 13C-13C chemical shift correlation experiments.

Physical basis of the effect of hemoglobin on the 31P NMR chemical shifts of various phosphoryl compounds

International Nuclear Information System (INIS)

Kirk, K.; Kuchel, P.W.

1988-01-01

The marked difference between the intra- and extracellular 31 P NMR chemical shifts of various phosphoryl compounds when added to a red cell suspension may be largely understood in terms of the effects of hemoglobin on the 31 P NMR chemical shifts. The presence of [oxy- or (carbonmonoxy)-] hemoglobin inside the red cell causes the bulk magnetic susceptibility of the cell cytoplasm to be significantly less than that of the external solution. This difference is sufficient to account for the difference in the intra- and extracellular chemical shifts of the two phosphate esters trimethyl phosphate and triethyl phosphate. However, in the case of the compounds dimethyl methylphosphonate, diethyl methylphosphonate, and trimethylphosphine oxide as well as the hypophosphite, phenylphosphinate, and diphenylphosphinate ions, hemoglobin exerts an additional, much larger, effect, causing the 31 P NMR resonances to shift to lower frequency in a manner that cannot be accounted for in terms of magnetic susceptibility. Lysozyme is a protein structurally unrelated to hemoglobin and was shown to cause similar shifts to lower frequency of the resonances of these six compounds; this suggests that the mechanism may involve a property of proteins in general and not a specific property of hemoglobin. The effect of different solvents on the chemical shifts of the eight phosphoryl compounds provided an insight into the possible physical basis of the effect. It is proposed that, in addition to magnetic susceptibility effects, hemoglobin exerts its influence on phosphoryl chemical shifts by disrupting the hydrogen bonding of the phosphoryl group to solvent water

The tensor rank of tensor product of two three-qubit W states is eight

OpenAIRE

Chen, Lin; Friedland, Shmuel

2017-01-01

We show that the tensor rank of tensor product of two three-qubit W states is not less than eight. Combining this result with the recent result of M. Christandl, A. K. Jensen, and J. Zuiddam that the tensor rank of tensor product of two three-qubit W states is at most eight, we deduce that the tensor rank of tensor product of two three-qubit W states is eight. We also construct the upper bound of the tensor rank of tensor product of many three-qubit W states.

Efficient Tensor Completion for Color Image and Video Recovery: Low-Rank Tensor Train.

Science.gov (United States)

Bengua, Johann A; Phien, Ho N; Tuan, Hoang Duong; Do, Minh N

2017-05-01

This paper proposes a novel approach to tensor completion, which recovers missing entries of data represented by tensors. The approach is based on the tensor train (TT) rank, which is able to capture hidden information from tensors thanks to its definition from a well-balanced matricization scheme. Accordingly, new optimization formulations for tensor completion are proposed as well as two new algorithms for their solution. The first one called simple low-rank tensor completion via TT (SiLRTC-TT) is intimately related to minimizing a nuclear norm based on TT rank. The second one is from a multilinear matrix factorization model to approximate the TT rank of a tensor, and is called tensor completion by parallel matrix factorization via TT (TMac-TT). A tensor augmentation scheme of transforming a low-order tensor to higher orders is also proposed to enhance the effectiveness of SiLRTC-TT and TMac-TT. Simulation results for color image and video recovery show the clear advantage of our method over all other methods.

Bowen-York tensors

International Nuclear Information System (INIS)

Beig, Robert; Krammer, Werner

2004-01-01

For a conformally flat 3-space, we derive a family of linear second-order partial differential operators which sends vectors into trace-free, symmetric 2-tensors. These maps, which are parametrized by conformal Killing vectors on the 3-space, are such that the divergence of the resulting tensor field depends only on the divergence of the original vector field. In particular, these maps send source-free electric fields into TT tensors. Moreover, if the original vector field is the Coulomb field on R 3 {0}, the resulting tensor fields on R 3 {0} are nothing but the family of TT tensors originally written by Bowen and York

Binding energies and chemical shifts of least bound core electron excitations in cubic Asub(N)Bsub(8-N) semiconductors

International Nuclear Information System (INIS)

Bechstedt, F.; Enderlein, R.; Wischnewski, R.

1981-01-01

Core electron binding energies Esup(B) with respect to the vacuum level and their chemical shifts are calculated for the least bound core levels of cations and anions of cubic Asub(N)Bsub(8-N) semiconductors. Starting from the HF-binding energy of the free atom absolute values of Esup(B) are obtained by adding core level shifts and relaxation energies. Core level shifts are calculated by means of an electrostatic model with ionic and bond charges according to Phillips' bond charge model. For the calculation of relaxation energies the linear dielectric theory of electronic polarization is applied. Valence and core electrons, and diagonal and non-diagonal screening are taken into account. The theoretical results for chemical shifts of binding energies are compared with experimental values from XPS-measurements corrected by work function data. Good agreement is obtained in all cases within the error limit of about one eV. Chemical and atomic trends of core level shifts, relaxation energies, and binding energies are discussed in terms of changes of atomic and solid state parameters. Chemical shifts and relaxation energies are predicted for various ternary Asub(N)Bsub(8-N) compounds. (author)

Rationalization of Anomalous Pseudocontact Shifts and Their Solvent Dependence in a Series of C3-Symmetric Lanthanide Complexes.

Science.gov (United States)

Vonci, Michele; Mason, Kevin; Suturina, Elizaveta A; Frawley, Andrew T; Worswick, Steven G; Kuprov, Ilya; Parker, David; McInnes, Eric J L; Chilton, Nicholas F

2017-10-11

Bleaney's long-standing theory of magnetic anisotropy has been employed with some success for many decades to explain paramagnetic NMR pseudocontact shifts, and has been the subject of many subsequent approximations. Here, we present a detailed experimental and theoretical investigation accounting for the anomalous solvent dependence of NMR shifts for a series of lanthanide(III) complexes, namely [LnL 1 ] (Ln = Eu, Tb, Dy, Ho, Er, Tm, and Yb; L 1 : 1,4,7-tris[(6-carboxypyridin-2-yl)methyl]-1,4,7-triazacyclononane), taking into account the effect of subtle ligand flexibility on the electronic structure. We show that the anisotropy of the room temperature magnetic susceptibility tensor, which in turn affects the sign and magnitude of the pseudocontact chemical shift, is extremely sensitive to minimal structural changes in the first coordination sphere of L 1 . We show that DFT structural optimizations do not give accurate structural models, as assessed by the experimental chemical shifts, and thus we determine a magnetostructural correlation and employ this to evaluate the accurate solution structure for each [LnL 1 ]. This approach allows us to explain the counterintuitive pseudocontact shift behavior, as well as a striking solvent dependence. These results have important consequences for the analysis and design of novel magnetic resonance shift and optical emission probes that are sensitive to the local solution environment and polarity.

Harmonic d-tensors

Energy Technology Data Exchange (ETDEWEB)

Hohmann, Manuel [Physikalisches Institut, Universitaet Tartu (Estonia)

2016-07-01

Tensor harmonics are a useful mathematical tool for finding solutions to differential equations which transform under a particular representation of the rotation group SO(3). In order to make use of this tool also in the setting of Finsler geometry, where the objects of relevance are d-tensors instead of tensors, we construct a set of d-tensor harmonics for both SO(3) and SO(4) symmetries and show how these can be used for calculations in Finsler geometry and gravity.

Current density tensors

Science.gov (United States)

Lazzeretti, Paolo

2018-04-01

It is shown that nonsymmetric second-rank current density tensors, related to the current densities induced by magnetic fields and nuclear magnetic dipole moments, are fundamental properties of a molecule. Together with magnetizability, nuclear magnetic shielding, and nuclear spin-spin coupling, they completely characterize its response to magnetic perturbations. Gauge invariance, resolution into isotropic, deviatoric, and antisymmetric parts, and contributions of current density tensors to magnetic properties are discussed. The components of the second-rank tensor properties are rationalized via relationships explicitly connecting them to the direction of the induced current density vectors and to the components of the current density tensors. The contribution of the deviatoric part to the average value of magnetizability, nuclear shielding, and nuclear spin-spin coupling, uniquely determined by the antisymmetric part of current density tensors, vanishes identically. The physical meaning of isotropic and anisotropic invariants of current density tensors has been investigated, and the connection between anisotropy magnitude and electron delocalization has been discussed.

Carbon 13 nuclear magnetic resonance chemical shifts empiric calculations of polymers by multi linear regression and molecular modeling

International Nuclear Information System (INIS)

Da Silva Pinto, P.S.; Eustache, R.P.; Audenaert, M.; Bernassau, J.M.

1996-01-01

This work deals with carbon 13 nuclear magnetic resonance chemical shifts empiric calculations by multi linear regression and molecular modeling. The multi linear regression is indeed one way to obtain an equation able to describe the behaviour of the chemical shift for some molecules which are in the data base (rigid molecules with carbons). The methodology consists of structures describer parameters definition which can be bound to carbon 13 chemical shift known for these molecules. Then, the linear regression is used to determine the equation significant parameters. This one can be extrapolated to molecules which presents some resemblances with those of the data base. (O.L.). 20 refs., 4 figs., 1 tab

Cα and Cβ Carbon-13 Chemical Shifts in Proteins From an Empirical Database

International Nuclear Information System (INIS)

Iwadate, Mitsuo; Asakura, Tetsuo; Williamson, Michael P.

1999-01-01

We have constructed an extensive database of 13C Cα and Cβ chemical shifts in proteins of solution, for proteins of which a high-resolution crystal structure exists, and for which the crystal structure has been shown to be essentially identical to the solution structure. There is no systematic effect of temperature, reference compound, or pH on reported shifts, but there appear to be differences in reported shifts arising from referencing differences of up to 4.2 ppm. The major factor affecting chemical shifts is the backbone geometry, which causes differences of ca. 4 ppm between typical α- helix and β-sheet geometries for Cα, and of ca. 2 ppm for Cβ. The side-chain dihedral angle χ1 has an effect of up to 0.5 ppm on the Cα shift, particularly for amino acids with branched side-chains at Cβ. Hydrogen bonding to main-chain atoms has an effect of up to 0.9 ppm, which depends on the main- chain conformation. The sequence of the protein and ring-current shifts from aromatic rings have an insignificant effect (except for residues following proline). There are significant differences between different amino acid types in the backbone geometry dependence; the amino acids can be grouped together into five different groups with different φ,ψ shielding surfaces. The overall fit of individual residues to a single non-residue-specific surface, incorporating the effects of hydrogen bonding and χ1 angle, is 0.96 ppm for both Cα and Cβ. The results from this study are broadly similar to those from ab initio studies, but there are some differences which could merit further attention

Short-ranged radial and tensor correlations in nuclear many-body systems

International Nuclear Information System (INIS)

Neff, T.; Feldmeier, H.

2003-01-01

The unitary correlation operator method (UCOM) is applied to realistic potentials. The effects of tensor correlations are investigated. The resulting phase shift equivalent correlated interactions are used in the no-core shell model for light nuclei and for mean-field calculations in the Fermionic Molecular Dynamics model for nuclei up to mass A=48. (orig.)

Iterative tensor voting for perceptual grouping of ill-defined curvilinear structures.

Science.gov (United States)

Loss, Leandro A; Bebis, George; Parvin, Bahram

2011-08-01

In this paper, a novel approach is proposed for perceptual grouping and localization of ill-defined curvilinear structures. Our approach builds upon the tensor voting and the iterative voting frameworks. Its efficacy lies on iterative refinements of curvilinear structures by gradually shifting from an exploratory to an exploitative mode. Such a mode shifting is achieved by reducing the aperture of the tensor voting fields, which is shown to improve curve grouping and inference by enhancing the concentration of the votes over promising, salient structures. The proposed technique is validated on delineating adherens junctions that are imaged through fluorescence microscopy. However, the method is also applicable for screening other organisms based on characteristics of their cell wall structures. Adherens junctions maintain tissue structural integrity and cell-cell interactions. Visually, they exhibit fibrous patterns that may be diffused, heterogeneous in fluorescence intensity, or punctate and frequently perceptual. Besides the application to real data, the proposed method is compared to prior methods on synthetic and annotated real data, showing high precision rates.

TensorFlow Agents: Efficient Batched Reinforcement Learning in TensorFlow

OpenAIRE

Hafner, Danijar; Davidson, James; Vanhoucke, Vincent

2017-01-01

We introduce TensorFlow Agents, an efficient infrastructure paradigm for building parallel reinforcement learning algorithms in TensorFlow. We simulate multiple environments in parallel, and group them to perform the neural network computation on a batch rather than individual observations. This allows the TensorFlow execution engine to parallelize computation, without the need for manual synchronization. Environments are stepped in separate Python processes to progress them in parallel witho...

A RENORMALIZATION PROCEDURE FOR TENSOR MODELS AND SCALAR-TENSOR THEORIES OF GRAVITY

OpenAIRE

SASAKURA, NAOKI

2010-01-01

Tensor models are more-index generalizations of the so-called matrix models, and provide models of quantum gravity with the idea that spaces and general relativity are emergent phenomena. In this paper, a renormalization procedure for the tensor models whose dynamical variable is a totally symmetric real three-tensor is discussed. It is proven that configurations with certain Gaussian forms are the attractors of the three-tensor under the renormalization procedure. Since these Gaussian config...

The 40th anniversary of the discovery of NMR-chemical shift and nuclear spin-spin coupling

International Nuclear Information System (INIS)

Zhu Zhenghe; Gou Qingquan

1989-01-01

After the discovery of NMR Phenomenon in the physics laboratories of E.M.Purcell at Harvard and F.Bloch at Stanford in 1946, W.G.Proctor and F.C.Yu made the successful discovery of NMR-chemical shift and nuclear spin-spin coupling at Stanford in 1950, Which brought NMR spectroscopy from the physics laboratory to the laboratories of many different fields. This is worth memorizing. Retrospecting the past 40 years, it is sure that chemical shift theory will be much more prosperous prospects

Time integration of tensor trains

OpenAIRE

Lubich, Christian; Oseledets, Ivan; Vandereycken, Bart

2014-01-01

A robust and efficient time integrator for dynamical tensor approximation in the tensor train or matrix product state format is presented. The method is based on splitting the projector onto the tangent space of the tensor manifold. The algorithm can be used for updating time-dependent tensors in the given data-sparse tensor train / matrix product state format and for computing an approximate solution to high-dimensional tensor differential equations within this data-sparse format. The formul...

Tensor spaces and exterior algebra

CERN Document Server

Yokonuma, Takeo

1992-01-01

This book explains, as clearly as possible, tensors and such related topics as tensor products of vector spaces, tensor algebras, and exterior algebras. You will appreciate Yokonuma's lucid and methodical treatment of the subject. This book is useful in undergraduate and graduate courses in multilinear algebra. Tensor Spaces and Exterior Algebra begins with basic notions associated with tensors. To facilitate understanding of the definitions, Yokonuma often presents two or more different ways of describing one object. Next, the properties and applications of tensors are developed, including the classical definition of tensors and the description of relative tensors. Also discussed are the algebraic foundations of tensor calculus and applications of exterior algebra to determinants and to geometry. This book closes with an examination of algebraic systems with bilinear multiplication. In particular, Yokonuma discusses the theory of replicas of Chevalley and several properties of Lie algebras deduced from them.

Chemical Shifts of the Carbohydrate Binding Domain of Galectin-3 from Magic Angle Spinning NMR and Hybrid Quantum Mechanics/Molecular Mechanics Calculations.

Science.gov (United States)

Kraus, Jodi; Gupta, Rupal; Yehl, Jenna; Lu, Manman; Case, David A; Gronenborn, Angela M; Akke, Mikael; Polenova, Tatyana

2018-03-22

Magic angle spinning NMR spectroscopy is uniquely suited to probe the structure and dynamics of insoluble proteins and protein assemblies at atomic resolution, with NMR chemical shifts containing rich information about biomolecular structure. Access to this information, however, is problematic, since accurate quantum mechanical calculation of chemical shifts in proteins remains challenging, particularly for 15 N H . Here we report on isotropic chemical shift predictions for the carbohydrate recognition domain of microcrystalline galectin-3, obtained from using hybrid quantum mechanics/molecular mechanics (QM/MM) calculations, implemented using an automated fragmentation approach, and using very high resolution (0.86 Å lactose-bound and 1.25 Å apo form) X-ray crystal structures. The resolution of the X-ray crystal structure used as an input into the AF-NMR program did not affect the accuracy of the chemical shift calculations to any significant extent. Excellent agreement between experimental and computed shifts is obtained for 13 C α , while larger scatter is observed for 15 N H chemical shifts, which are influenced to a greater extent by electrostatic interactions, hydrogen bonding, and solvation.

The direct tensor solution and higher-order acquisition schemes for generalized diffusion tensor imaging

NARCIS (Netherlands)

Akkerman, Erik M.

2010-01-01

Both in diffusion tensor imaging (DTI) and in generalized diffusion tensor imaging (GDTI) the relation between the diffusion tensor and the measured apparent diffusion coefficients is given by a tensorial equation, which needs to be inverted in order to solve the diffusion tensor. The traditional

H-1 chemical shift imaging characterization of human brain tumor and edema

NARCIS (Netherlands)

Sijens, PE; Oudkerk, M

Longitudinal (T1) and transverse (T2) relaxation times of metabolites in human brain tumor, peritumoral edema, and unaffected brain tissue were assessed from point resolved spectroscopy (PRESS) H-1 chemical shift imaging results at different repetition times (TR = 1500 and 5000 ms; T1: n = 19) and

PACSY, a relational database management system for protein structure and chemical shift analysis.

Science.gov (United States)

Lee, Woonghee; Yu, Wookyung; Kim, Suhkmann; Chang, Iksoo; Lee, Weontae; Markley, John L

2012-10-01

PACSY (Protein structure And Chemical Shift NMR spectroscopY) is a relational database management system that integrates information from the Protein Data Bank, the Biological Magnetic Resonance Data Bank, and the Structural Classification of Proteins database. PACSY provides three-dimensional coordinates and chemical shifts of atoms along with derived information such as torsion angles, solvent accessible surface areas, and hydrophobicity scales. PACSY consists of six relational table types linked to one another for coherence by key identification numbers. Database queries are enabled by advanced search functions supported by an RDBMS server such as MySQL or PostgreSQL. PACSY enables users to search for combinations of information from different database sources in support of their research. Two software packages, PACSY Maker for database creation and PACSY Analyzer for database analysis, are available from http://pacsy.nmrfam.wisc.edu.

PACSY, a relational database management system for protein structure and chemical shift analysis

Energy Technology Data Exchange (ETDEWEB)

Lee, Woonghee, E-mail: whlee@nmrfam.wisc.edu [University of Wisconsin-Madison, National Magnetic Resonance Facility at Madison, and Biochemistry Department (United States); Yu, Wookyung [Center for Proteome Biophysics, Pusan National University, Department of Physics (Korea, Republic of); Kim, Suhkmann [Pusan National University, Department of Chemistry and Chemistry Institute for Functional Materials (Korea, Republic of); Chang, Iksoo [Center for Proteome Biophysics, Pusan National University, Department of Physics (Korea, Republic of); Lee, Weontae, E-mail: wlee@spin.yonsei.ac.kr [Yonsei University, Structural Biochemistry and Molecular Biophysics Laboratory, Department of Biochemistry (Korea, Republic of); Markley, John L., E-mail: markley@nmrfam.wisc.edu [University of Wisconsin-Madison, National Magnetic Resonance Facility at Madison, and Biochemistry Department (United States)

2012-10-15

PACSY (Protein structure And Chemical Shift NMR spectroscopY) is a relational database management system that integrates information from the Protein Data Bank, the Biological Magnetic Resonance Data Bank, and the Structural Classification of Proteins database. PACSY provides three-dimensional coordinates and chemical shifts of atoms along with derived information such as torsion angles, solvent accessible surface areas, and hydrophobicity scales. PACSY consists of six relational table types linked to one another for coherence by key identification numbers. Database queries are enabled by advanced search functions supported by an RDBMS server such as MySQL or PostgreSQL. PACSY enables users to search for combinations of information from different database sources in support of their research. Two software packages, PACSY Maker for database creation and PACSY Analyzer for database analysis, are available from http://pacsy.nmrfam.wisc.eduhttp://pacsy.nmrfam.wisc.edu.

PACSY, a relational database management system for protein structure and chemical shift analysis

Science.gov (United States)

Lee, Woonghee; Yu, Wookyung; Kim, Suhkmann; Chang, Iksoo

2012-01-01

PACSY (Protein structure And Chemical Shift NMR spectroscopY) is a relational database management system that integrates information from the Protein Data Bank, the Biological Magnetic Resonance Data Bank, and the Structural Classification of Proteins database. PACSY provides three-dimensional coordinates and chemical shifts of atoms along with derived information such as torsion angles, solvent accessible surface areas, and hydrophobicity scales. PACSY consists of six relational table types linked to one another for coherence by key identification numbers. Database queries are enabled by advanced search functions supported by an RDBMS server such as MySQL or PostgreSQL. PACSY enables users to search for combinations of information from different database sources in support of their research. Two software packages, PACSY Maker for database creation and PACSY Analyzer for database analysis, are available from http://pacsy.nmrfam.wisc.edu. PMID:22903636

PACSY, a relational database management system for protein structure and chemical shift analysis

International Nuclear Information System (INIS)

Lee, Woonghee; Yu, Wookyung; Kim, Suhkmann; Chang, Iksoo; Lee, Weontae; Markley, John L.

2012-01-01

PACSY (Protein structure And Chemical Shift NMR spectroscopY) is a relational database management system that integrates information from the Protein Data Bank, the Biological Magnetic Resonance Data Bank, and the Structural Classification of Proteins database. PACSY provides three-dimensional coordinates and chemical shifts of atoms along with derived information such as torsion angles, solvent accessible surface areas, and hydrophobicity scales. PACSY consists of six relational table types linked to one another for coherence by key identification numbers. Database queries are enabled by advanced search functions supported by an RDBMS server such as MySQL or PostgreSQL. PACSY enables users to search for combinations of information from different database sources in support of their research. Two software packages, PACSY Maker for database creation and PACSY Analyzer for database analysis, are available from http://pacsy.nmrfam.wisc.eduhttp://pacsy.nmrfam.wisc.edu.

Determination of 13C CSA Tensors: Extension of the Model-independent Approach to an RNA Kissing Complex Undergoing Anisotropic Rotational Diffusion in Solution

International Nuclear Information System (INIS)

Ravindranathan, Sapna; Kim, Chul-Hyun; Bodenhausen, Geoffrey

2005-01-01

Chemical shift anisotropy (CSA) tensor parameters have been determined for the protonated carbons of the purine bases in an RNA kissing complex in solution by extending the model-independent approach [Fushman, D., Cowburn, D. (1998) J. Am. Chem. Soc. 120, 7109-7110]. A strategy for determining CSA tensor parameters of heteronuclei in isolated X-H two-spin systems (X = 13 C or 15 N) in molecules undergoing anisotropic rotational diffusion is presented. The original method relies on the fact that the ratio κ 2 =R 2 auto /R 2 cross of the transverse auto- and cross-correlated relaxation rates involving the X CSA and the X-H dipolar interaction is independent of parameters related to molecular motion, provided rotational diffusion is isotropic. However, if the overall motion is anisotropic κ 2 depends on the anisotropy D parallel /D -perpendicular of rotational diffusion. In this paper, the field dependence of both κ 2 and its longitudinal counterpart κ 1 =R 1 auto /R 1 cross are determined. For anisotropic rotational diffusion, our calculations show that the average κ av = 1/2 (κ 1 +κ 2 ), of the ratios is largely independent of the anisotropy parameter D parallel /D -perpendicular . The field dependence of the average ratio κ av may thus be utilized to determine CSA tensor parameters by a generalized model-independent approach in the case of molecules with an overall motion described by an axially symmetric rotational diffusion tensor

Gogny interactions with tensor terms

Energy Technology Data Exchange (ETDEWEB)

Anguiano, M.; Lallena, A.M.; Bernard, R.N. [Universidad de Granada, Departamento de Fisica Atomica, Molecular y Nuclear, Granada (Spain); Co' , G. [INFN, Lecce (Italy); De Donno, V. [Universita del Salento, Dipartimento di Matematica e Fisica ' ' E. De Giorgi' ' , Lecce (Italy); Grasso, M. [Universite Paris-Sud, Institut de Physique Nucleaire, IN2P3-CNRS, Orsay (France)

2016-07-15

We present a perturbative approach to include tensor terms in the Gogny interaction. We do not change the values of the usual parameterisations, with the only exception of the spin-orbit term, and we add tensor terms whose only free parameters are the strengths of the interactions. We identify observables sensitive to the presence of the tensor force in Hartree-Fock, Hartree-Fock-Bogoliubov and random phase approximation calculations. We show the need of including two tensor contributions, at least: a pure tensor term and a tensor-isospin term. We show results relevant for the inclusion of the tensor term for single-particle energies, charge-conserving magnetic excitations and Gamow-Teller excitations. (orig.)

Sensitivity of ab Initio vs Empirical Methods in Computing Structural Effects on NMR Chemical Shifts for the Example of Peptides.

Science.gov (United States)

Sumowski, Chris Vanessa; Hanni, Matti; Schweizer, Sabine; Ochsenfeld, Christian

2014-01-14

The structural sensitivity of NMR chemical shifts as computed by quantum chemical methods is compared to a variety of empirical approaches for the example of a prototypical peptide, the 38-residue kaliotoxin KTX comprising 573 atoms. Despite the simplicity of empirical chemical shift prediction programs, the agreement with experimental results is rather good, underlining their usefulness. However, we show in our present work that they are highly insensitive to structural changes, which renders their use for validating predicted structures questionable. In contrast, quantum chemical methods show the expected high sensitivity to structural and electronic changes. This appears to be independent of the quantum chemical approach or the inclusion of solvent effects. For the latter, explicit solvent simulations with increasing number of snapshots were performed for two conformers of an eight amino acid sequence. In conclusion, the empirical approaches neither provide the expected magnitude nor the patterns of NMR chemical shifts determined by the clearly more costly ab initio methods upon structural changes. This restricts the use of empirical prediction programs in studies where peptide and protein structures are utilized for the NMR chemical shift evaluation such as in NMR refinement processes, structural model verifications, or calculations of NMR nuclear spin relaxation rates.

Tensor structure for Nori motives

OpenAIRE

Barbieri-Viale, Luca; Huber, Annette; Prest, Mike

2018-01-01

We construct a tensor product on Freyd's universal abelian category attached to an additive tensor category or a tensor quiver and establish a universal property. This is used to give an alternative construction for the tensor product on Nori motives.

Tensor SOM and tensor GTM: Nonlinear tensor analysis by topographic mappings.

Science.gov (United States)

Iwasaki, Tohru; Furukawa, Tetsuo

2016-05-01

In this paper, we propose nonlinear tensor analysis methods: the tensor self-organizing map (TSOM) and the tensor generative topographic mapping (TGTM). TSOM is a straightforward extension of the self-organizing map from high-dimensional data to tensorial data, and TGTM is an extension of the generative topographic map, which provides a theoretical background for TSOM using a probabilistic generative model. These methods are useful tools for analyzing and visualizing tensorial data, especially multimodal relational data. For given n-mode relational data, TSOM and TGTM can simultaneously organize a set of n-topographic maps. Furthermore, they can be used to explore the tensorial data space by interactively visualizing the relationships between modes. We present the TSOM algorithm and a theoretical description from the viewpoint of TGTM. Various TSOM variations and visualization techniques are also described, along with some applications to real relational datasets. Additionally, we attempt to build a comprehensive description of the TSOM family by adapting various data structures. Copyright © 2016 Elsevier Ltd. All rights reserved.

Modelling the acid/base 1H NMR chemical shift limits of metabolites in human urine.

Science.gov (United States)

Tredwell, Gregory D; Bundy, Jacob G; De Iorio, Maria; Ebbels, Timothy M D

2016-01-01

Despite the use of buffering agents the 1 H NMR spectra of biofluid samples in metabolic profiling investigations typically suffer from extensive peak frequency shifting between spectra. These chemical shift changes are mainly due to differences in pH and divalent metal ion concentrations between the samples. This frequency shifting results in a correspondence problem: it can be hard to register the same peak as belonging to the same molecule across multiple samples. The problem is especially acute for urine, which can have a wide range of ionic concentrations between different samples. To investigate the acid, base and metal ion dependent 1 H NMR chemical shift variations and limits of the main metabolites in a complex biological mixture. Urine samples from five different individuals were collected and pooled, and pre-treated with Chelex-100 ion exchange resin. Urine samples were either treated with either HCl or NaOH, or were supplemented with various concentrations of CaCl 2 , MgCl 2 , NaCl or KCl, and their 1 H NMR spectra were acquired. Nonlinear fitting was used to derive acid dissociation constants and acid and base chemical shift limits for peaks from 33 identified metabolites. Peak pH titration curves for a further 65 unidentified peaks were also obtained for future reference. Furthermore, the peak variations induced by the main metal ions present in urine, Na + , K + , Ca 2+ and Mg 2+ , were also measured. These data will be a valuable resource for 1 H NMR metabolite profiling experiments and for the development of automated metabolite alignment and identification algorithms for 1 H NMR spectra.

Physical and Geometric Interpretations of the Riemann Tensor, Ricci Tensor, and Scalar Curvature

OpenAIRE

Loveridge, Lee C.

2004-01-01

Various interpretations of the Riemann Curvature Tensor, Ricci Tensor, and Scalar Curvature are described. Also, the physical meanings of the Einstein Tensor and Einstein's Equations are discussed. Finally a derivation of Newtonian Gravity from Einstein's Equations is given.

Generalized tensor-based morphometry of HIV/AIDS using multivariate statistics on deformation tensors.

Science.gov (United States)

Lepore, N; Brun, C; Chou, Y Y; Chiang, M C; Dutton, R A; Hayashi, K M; Luders, E; Lopez, O L; Aizenstein, H J; Toga, A W; Becker, J T; Thompson, P M

2008-01-01

This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor) of these deformations, as is common, we retain the full deformation tensors and apply a manifold version of Hotelling's $T(2) test to them, in a Log-Euclidean domain. In 2-D and 3-D magnetic resonance imaging (MRI) data from 26 HIV/AIDS patients and 14 matched healthy subjects, we compared multivariate tensor analysis versus univariate tests of simpler tensor-derived indices: the Jacobian determinant, the trace, geodesic anisotropy, and eigenvalues of the deformation tensor, and the angle of rotation of its eigenvectors. We detected consistent, but more extensive patterns of structural abnormalities, with multivariate tests on the full tensor manifold. Their improved power was established by analyzing cumulative p-value plots using false discovery rate (FDR) methods, appropriately controlling for false positives. This increased detection sensitivity may empower drug trials and large-scale studies of disease that use tensor-based morphometry.

Development of the Tensoral Computer Language

Science.gov (United States)

Ferziger, Joel; Dresselhaus, Eliot

1996-01-01

The research scientist or engineer wishing to perform large scale simulations or to extract useful information from existing databases is required to have expertise in the details of the particular database, the numerical methods and the computer architecture to be used. This poses a significant practical barrier to the use of simulation data. The goal of this research was to develop a high-level computer language called Tensoral, designed to remove this barrier. The Tensoral language provides a framework in which efficient generic data manipulations can be easily coded and implemented. First of all, Tensoral is general. The fundamental objects in Tensoral represent tensor fields and the operators that act on them. The numerical implementation of these tensors and operators is completely and flexibly programmable. New mathematical constructs and operators can be easily added to the Tensoral system. Tensoral is compatible with existing languages. Tensoral tensor operations co-exist in a natural way with a host language, which may be any sufficiently powerful computer language such as Fortran, C, or Vectoral. Tensoral is very-high-level. Tensor operations in Tensoral typically act on entire databases (i.e., arrays) at one time and may, therefore, correspond to many lines of code in a conventional language. Tensoral is efficient. Tensoral is a compiled language. Database manipulations are simplified optimized and scheduled by the compiler eventually resulting in efficient machine code to implement them.

Kronecker-Basis-Representation Based Tensor Sparsity and Its Applications to Tensor Recovery.

Science.gov (United States)

Xie, Qi; Zhao, Qian; Meng, Deyu; Xu, Zongben

2017-08-02

It is well known that the sparsity/low-rank of a vector/matrix can be rationally measured by nonzero-entries-number ($l_0$ norm)/nonzero- singular-values-number (rank), respectively. However, data from real applications are often generated by the interaction of multiple factors, which obviously cannot be sufficiently represented by a vector/matrix, while a high order tensor is expected to provide more faithful representation to deliver the intrinsic structure underlying such data ensembles. Unlike the vector/matrix case, constructing a rational high order sparsity measure for tensor is a relatively harder task. To this aim, in this paper we propose a measure for tensor sparsity, called Kronecker-basis-representation based tensor sparsity measure (KBR briefly), which encodes both sparsity insights delivered by Tucker and CANDECOMP/PARAFAC (CP) low-rank decompositions for a general tensor. Then we study the KBR regularization minimization (KBRM) problem, and design an effective ADMM algorithm for solving it, where each involved parameter can be updated with closed-form equations. Such an efficient solver makes it possible to extend KBR to various tasks like tensor completion and tensor robust principal component analysis. A series of experiments, including multispectral image (MSI) denoising, MSI completion and background subtraction, substantiate the superiority of the proposed methods beyond state-of-the-arts.

Phase-shift calculation using continuum-discretized states

International Nuclear Information System (INIS)

Suzuki, Y.; Horiuchi, W.; Arai, K.

2009-01-01

We present a method for calculating scattering phase shifts which utilizes continuum-discretized states obtained in a bound-state type calculation. The wrong asymptotic behavior of the discretized state is remedied by means of the Green's function formalism. Test examples confirm the accuracy of the method. The α+n scattering is described using realistic nucleon-nucleon potentials. The 3/2 - and 1/2 - phase shifts obtained in a single-channel calculation are too small in comparison with experiment. The 1/2 + phase shifts are in reasonable agreement with experiment, and gain contributions both from the tensor and central components of the nucleon-nucleon potential.

Killing-Yano tensors and Nambu mechanics

International Nuclear Information System (INIS)

Baleanu, D.

1998-01-01

Killing-Yano tensors were introduced in 1952 by Kentaro-Yano from mathematical point of view. The physical interpretation of Killing-Yano tensors of rank higher than two was unclear. We found that all Killing-Yano tensors η i 1 i 2 . .. i n with covariant derivative zero are Nambu tensors. We found that in the case of flat space case all Killing-Yano tensors are Nambu tensors. In the case of Taub-NUT and Kerr-Newmann metric Killing-Yano tensors of order two generate Nambu tensors of rank 3

Relativistic Spin-Orbit Heavy Atom on the Light Atom NMR Chemical Shifts: General Trends Across the Periodic Table Explained.

Science.gov (United States)

Vícha, Jan; Komorovsky, Stanislav; Repisky, Michal; Marek, Radek; Straka, Michal

2018-05-10

The importance of relativistic effects on the NMR parameters in heavy-atom (HA) compounds, particularly the SO-HALA (Spin-Orbit Heavy Atom on the Light Atom) effect on NMR chemical shifts, has been known for about 40 years. Yet, a general correlation between the electronic structure and SO-HALA effect has been missing. By analyzing 1 H NMR chemical shifts of the sixth-period hydrides (Cs-At), we discovered general electronic-structure principles and mechanisms that dictate the size and sign of the SO-HALA NMR chemical shifts. In brief, partially occupied HA valence shells induce relativistic shielding at the light atom (LA) nuclei, while empty HA valence shells induce relativistic deshielding. In particular, the LA nucleus is relativistically shielded in 5d 2 -5d 8 and 6p 4 HA hydrides and deshielded in 4f 0 , 5d 0 , 6s 0 , and 6p 0 HA hydrides. This general and intuitive concept explains periodic trends in the 1 H NMR chemical shifts along the sixth-period hydrides (Cs-At) studied in this work. We present substantial evidence that the introduced principles have a general validity across the periodic table and can be extended to nonhydride LAs. The decades-old question of why compounds with occupied frontier π molecular orbitals (MOs) cause SO-HALA shielding at the LA nuclei, while the frontier σ MOs cause deshielding is answered. We further derive connection between the SO-HALA NMR chemical shifts and Spin-Orbit-induced Electron Deformation Density (SO-EDD), a property that can be obtained easily from differential electron densities and can be represented graphically. SO-EDD provides an intuitive understanding of the SO-HALA effect in terms of the depletion/concentration of the electron density at LA nuclei caused by spin-orbit coupling due to HA in the presence of a magnetic field. Using an analogy between the SO-EDD concept and arguments from classic NMR theory, the complex question of the SO-HALA NMR chemical shifts becomes easily understandable for a wide

Pulse EPR-enabled interpretation of scarce pseudocontact shifts induced by lanthanide binding tags

Energy Technology Data Exchange (ETDEWEB)

Abdelkader, Elwy H.; Yao, Xuejun [Australian National University, Research School of Chemistry (Australia); Feintuch, Akiva [Weizmann Institute of Science, Department of Chemical Physics (Israel); Adams, Luke A.; Aurelio, Luigi; Graham, Bim [Monash University, Monash Institute of Pharmaceutical Sciences (Australia); Goldfarb, Daniella [Weizmann Institute of Science, Department of Chemical Physics (Israel); Otting, Gottfried, E-mail: gottfried.otting@anu.edu.au [Australian National University, Research School of Chemistry (Australia)

2016-01-15

Pseudocontact shifts (PCS) induced by tags loaded with paramagnetic lanthanide ions provide powerful long-range structure information, provided the location of the metal ion relative to the target protein is known. Usually, the metal position is determined by fitting the magnetic susceptibility anisotropy (Δχ) tensor to the 3D structure of the protein in an 8-parameter fit, which requires a large set of PCSs to be reliable. In an alternative approach, we used multiple Gd{sup 3+}-Gd{sup 3+} distances measured by double electron–electron resonance (DEER) experiments to define the metal position, allowing Δχ-tensor determinations from more robust 5-parameter fits that can be performed with a relatively sparse set of PCSs. Using this approach with the 32 kDa E. coli aspartate/glutamate binding protein (DEBP), we demonstrate a structural transition between substrate-bound and substrate-free DEBP, supported by PCSs generated by C3-Tm{sup 3+} and C3-Tb{sup 3+} tags attached to a genetically encoded p-azidophenylalanine residue. The significance of small PCSs was magnified by considering the difference between the chemical shifts measured with Tb{sup 3+} and Tm{sup 3+} rather than involving a diamagnetic reference. The integrative sparse data approach developed in this work makes poorly soluble proteins of limited stability amenable to structural studies in solution, without having to rely on cysteine mutations for tag attachment.

TALOS+: a hybrid method for predicting protein backbone torsion angles from NMR chemical shifts

Energy Technology Data Exchange (ETDEWEB)

Shen Yang; Delaglio, Frank [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States); Cornilescu, Gabriel [National Magnetic Resonance Facility (United States); Bax, Ad [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States)], E-mail: bax@nih.gov

2009-08-15

NMR chemical shifts in proteins depend strongly on local structure. The program TALOS establishes an empirical relation between {sup 13}C, {sup 15}N and {sup 1}H chemical shifts and backbone torsion angles {phi} and {psi} (Cornilescu et al. J Biomol NMR 13 289-302, 1999). Extension of the original 20-protein database to 200 proteins increased the fraction of residues for which backbone angles could be predicted from 65 to 74%, while reducing the error rate from 3 to 2.5%. Addition of a two-layer neural network filter to the database fragment selection process forms the basis for a new program, TALOS+, which further enhances the prediction rate to 88.5%, without increasing the error rate. Excluding the 2.5% of residues for which TALOS+ makes predictions that strongly differ from those observed in the crystalline state, the accuracy of predicted {phi} and {psi} angles, equals {+-}13{sup o}. Large discrepancies between predictions and crystal structures are primarily limited to loop regions, and for the few cases where multiple X-ray structures are available such residues are often found in different states in the different structures. The TALOS+ output includes predictions for individual residues with missing chemical shifts, and the neural network component of the program also predicts secondary structure with good accuracy.

A comparison of chemical shift sensitivity of trifluoromethyl tags: optimizing resolution in {sup 19}F NMR studies of proteins

Energy Technology Data Exchange (ETDEWEB)

Ye, Libin; Larda, Sacha Thierry; Frank Li, Yi Feng [University of Toronto, UTM, Department of Chemistry (Canada); Manglik, Aashish [Stanford University School of Medicine, Department of Molecular and Cellular Physiology (United States); Prosser, R. Scott, E-mail: scott.prosser@utoronto.ca [University of Toronto, UTM, Department of Chemistry (Canada)

2015-05-15

The elucidation of distinct protein conformers or states by fluorine ({sup 19}F) NMR requires fluorinated moieties whose chemical shifts are most sensitive to subtle changes in the local dielectric and magnetic shielding environment. In this study we evaluate the effective chemical shift dispersion of a number of thiol-reactive trifluoromethyl probes [i.e. 2-bromo-N-(4-(trifluoromethyl)phenyl)acetamide (BTFMA), N-(4-bromo-3-(trifluoromethyl)phenyl)acetamide (3-BTFMA), 3-bromo-1,1,1-trifluoropropan-2-ol (BTFP), 1-bromo-3,3,4,4,4-pentafluorobutan-2-one (BPFB), 3-bromo-1,1,1-trifluoropropan-2-one (BTFA), and 2,2,2-trifluoroethyl-1-thiol (TFET)] under conditions of varying polarity. In considering the sensitivity of the {sup 19}F NMR chemical shift to the local environment, a series of methanol/water mixtures were prepared, ranging from relatively non-polar (MeOH:H{sub 2}O = 4) to polar (MeOH:H{sub 2}O = 0.25). {sup 19}F NMR spectra of the tripeptide, glutathione ((2S)-2-amino-4-{[(1R)-1-[(carboxymethyl)carbamoyl] -2-sulfanylethyl]carbamoyl}butanoic acid), conjugated to each of the above trifluoromethyl probes, revealed that the BTFMA tag exhibited a significantly greater range of chemical shift as a function of solvent polarity than did either BTFA or TFET. DFT calculations using the B3LYP hybrid functional and the 6-31G(d,p) basis set, confirmed the observed trend in chemical shift dispersion with solvent polarity.

Quantitative chemical shift-encoded MRI is an accurate method to quantify hepatic steatosis.

Science.gov (United States)

Kühn, Jens-Peter; Hernando, Diego; Mensel, Birger; Krüger, Paul C; Ittermann, Till; Mayerle, Julia; Hosten, Norbert; Reeder, Scott B

2014-06-01

To compare the accuracy of liver fat quantification using a three-echo chemical shift-encoded magnetic resonance imaging (MRI) technique without and with correction for confounders with spectroscopy (MRS) as the reference standard. Fifty patients (23 women, mean age 56.6 ± 13.2 years) with fatty liver disease were enrolled. Patients underwent T2-corrected single-voxel MRS and a three-echo chemical shift-encoded gradient echo (GRE) sequence at 3.0T. MRI fat fraction (FF) was calculated without and with T2* and T1 correction and multispectral modeling of fat and compared with MRS-FF using linear regression. The spectroscopic range of liver fat was 0.11%-38.7%. Excellent correlation between MRS-FF and MRI-FF was observed when using T2* correction (R(2)  = 0.96). With use of T2* correction alone, the slope was significantly different from 1 (1.16 ± 0.03, P fat were addressed, the results showed equivalence between fat quantification using MRI and MRS (slope: 1.02 ± 0.03, P = 0.528; intercept: 0.26% ± 0.46%, P = 0.572). Complex three-echo chemical shift-encoded MRI is equivalent to MRS for quantifying liver fat, but only with correction for T2* decay and T1 recovery and use of spectral modeling of fat. This is necessary because T2* decay, T1 recovery, and multispectral complexity of fat are processes which may otherwise bias the measurements. Copyright © 2013 Wiley Periodicals, Inc.

Categorical Tensor Network States

Directory of Open Access Journals (Sweden)

Jacob D. Biamonte

2011-12-01

Full Text Available We examine the use of string diagrams and the mathematics of category theory in the description of quantum states by tensor networks. This approach lead to a unification of several ideas, as well as several results and methods that have not previously appeared in either side of the literature. Our approach enabled the development of a tensor network framework allowing a solution to the quantum decomposition problem which has several appealing features. Specifically, given an n-body quantum state |ψ〉, we present a new and general method to factor |ψ〉 into a tensor network of clearly defined building blocks. We use the solution to expose a previously unknown and large class of quantum states which we prove can be sampled efficiently and exactly. This general framework of categorical tensor network states, where a combination of generic and algebraically defined tensors appear, enhances the theory of tensor network states.

Chemical shift of Mn and Cr K-edges in X-ray absorption

Indian Academy of Sciences (India)

... Lecture Workshops · Refresher Courses · Symposia · Live Streaming. Home; Journals; Bulletin of Materials Science; Volume 36; Issue 6. Chemical shift of Mn and Cr K-edges in X-ray absorption spectroscopy with synchrotron radiation. D Joseph A K Yadav S N Jha D Bhattacharyya. Volume 36 Issue 6 November 2013 pp ...

Tensor Permutation Matrices in Finite Dimensions

OpenAIRE

Christian, Rakotonirina

2005-01-01

We have generalised the properties with the tensor product, of one 4x4 matrix which is a permutation matrix, and we call a tensor commutation matrix. Tensor commutation matrices can be constructed with or without calculus. A formula allows us to construct a tensor permutation matrix, which is a generalisation of tensor commutation matrix, has been established. The expression of an element of a tensor commutation matrix has been generalised in the case of any element of a tensor permutation ma...

Assignment of protein backbone resonances using connectivity, torsion angles and 13Cα chemical shifts

International Nuclear Information System (INIS)

Morris, Laura C.; Valafar, Homayoun; Prestegard, James H.

2004-01-01

A program is presented which will return the most probable sequence location for a short connected set of residues in a protein given just 13 C α chemical shifts (δ( 13 C α )) and data restricting the φ and ψ backbone angles. Data taken from both the BioMagResBank and the Protein Data Bank were used to create a probability density function (PDF) using a multivariate normal distribution in δ( 13 C α ), φ, and ψ space for each amino acid residue. Extracting and combining probabilities for particular amino acid residues in a short proposed sequence yields a score indicative of the correctness of the proposed assignment. The program is illustrated using several proteins for which structure and 13 C α chemical shift data are available

Iterative Tensor Voting for Perceptual Grouping of Ill-Defined Curvilinear Structures: Application to Adherens Junctions

Science.gov (United States)

Loss, Leandro A.; Bebis, George; Parvin, Bahram

2012-01-01

In this paper, a novel approach is proposed for perceptual grouping and localization of ill-defined curvilinear structures. Our approach builds upon the tensor voting and the iterative voting frameworks. Its efficacy lies on iterative refinements of curvilinear structures by gradually shifting from an exploratory to an exploitative mode. Such a mode shifting is achieved by reducing the aperture of the tensor voting fields, which is shown to improve curve grouping and inference by enhancing the concentration of the votes over promising, salient structures. The proposed technique is applied to delineation of adherens junctions imaged through fluorescence microscopy. This class of membrane-bound macromolecules maintains tissue structural integrity and cell-cell interactions. Visually, it exhibits fibrous patterns that may be diffused, punctate and frequently perceptual. Besides the application to real data, the proposed method is compared to prior methods on synthetic and annotated real data, showing high precision rates. PMID:21421432

The geomagnetic field gradient tensor

DEFF Research Database (Denmark)

Kotsiaros, Stavros; Olsen, Nils

2012-01-01

We develop the general mathematical basis for space magnetic gradiometry in spherical coordinates. The magnetic gradient tensor is a second rank tensor consisting of 3 × 3 = 9 spatial derivatives. Since the geomagnetic field vector B is always solenoidal (∇ · B = 0) there are only eight independent...... tensor elements. Furthermore, in current free regions the magnetic gradient tensor becomes symmetric, further reducing the number of independent elements to five. In that case B is a Laplacian potential field and the gradient tensor can be expressed in series of spherical harmonics. We present properties...... of the magnetic gradient tensor and provide explicit expressions of its elements in terms of spherical harmonics. Finally we discuss the benefit of using gradient measurements for exploring the Earth’s magnetic field from space, in particular the advantage of the various tensor elements for a better determination...

Algebraic classification of the Weyl tensor in higher dimensions based on its 'superenergy' tensor

International Nuclear Information System (INIS)

Senovilla, Jose M M

2010-01-01

The algebraic classification of the Weyl tensor in the arbitrary dimension n is recovered by means of the principal directions of its 'superenergy' tensor. This point of view can be helpful in order to compute the Weyl aligned null directions explicitly, and permits one to obtain the algebraic type of the Weyl tensor by computing the principal eigenvalue of rank-2 symmetric future tensors. The algebraic types compatible with states of intrinsic gravitational radiation can then be explored. The underlying ideas are general, so that a classification of arbitrary tensors in the general dimension can be achieved. (fast track communication)

Stereoelectronic effects on 1H nuclear magnetic resonance chemical shifts in methoxybenzenes

DEFF Research Database (Denmark)

Lambert, Maja; Olsen, Lars; Jaroszewski, Jerzy W

2006-01-01

the Ar-OCH3 torsion out of the ring plane, resulting in large stereoelectronic effects on the chemical shift of Hpara. Conformational searches and geometry optimizations for 3-16 at the B3LYP/6-31G** level, followed by B3LYP/6-311++G(2d,2p) calculations for all low-energy conformers, gave excellent...

Symmetric Tensor Decomposition

DEFF Research Database (Denmark)

Brachat, Jerome; Comon, Pierre; Mourrain, Bernard

2010-01-01

We present an algorithm for decomposing a symmetric tensor, of dimension n and order d, as a sum of rank-1 symmetric tensors, extending the algorithm of Sylvester devised in 1886 for binary forms. We recall the correspondence between the decomposition of a homogeneous polynomial in n variables...... of polynomial equations of small degree in non-generic cases. We propose a new algorithm for symmetric tensor decomposition, based on this characterization and on linear algebra computations with Hankel matrices. The impact of this contribution is two-fold. First it permits an efficient computation...... of the decomposition of any tensor of sub-generic rank, as opposed to widely used iterative algorithms with unproved global convergence (e.g. Alternate Least Squares or gradient descents). Second, it gives tools for understanding uniqueness conditions and for detecting the rank....

Chemical shift-selective snapshot FLASH MR imaging in combination with inversion-recovery T1 contrast at different field strengths

International Nuclear Information System (INIS)

Matthaei, D.; Haase, A.; Henrich, D.; Duhmke, E.

1991-01-01

With fast MR imaging, chemical shift contract becomes available to the clinician in seconds. The purpose of this paper is to evaluate the combination of chemical shift selective (CHESS) MR imaging using the snapshot FLASH MR method with the inversion-recovery technique and to obtain information concerning the signal-to-noise and chemical shift with the presaturation method at different field strengths. Investigations with volunteers and experimental animals were done at 2 and 3 T (whole body) and in a 4.7-T animal image. For the inversion-recovery experiments, saturation was done before every snapshot FLASH image. With increasing field strength due to signal-to-noise and chemical shift advantages, the method performs better. Increasing T1 values are also important at high field strengths. The combined technique is useful only for T1 water images with fat saturation. It also allows fast quantification of T1 in water-containing organs and pathologic processes. At high field strengths, fast CHESS and T1 imaging promise fast quantitative information. This is a possible argument for clinical high-field-strength MR imagining along with MR spectroscopy

Calculation of NMR chemical shifts. 7. Gauge-invariant INDO method

Science.gov (United States)

Fukui, H.; Miura, K.; Hirai, A.

A gauge-invariant INDO method based on the coupled Hartree-Fuck perturbation theory is presented and applied to the calculation of 1H and 13C chemical shifts of hydrocarbons including ring compounds. Invariance of the diamagnetic and paramagnetic shieldings with respect to displacement of the coordinate origin is discussed. Comparison between calculated and experimental results exhibits fairly good agreement, provided that the INDO parameters of Ellis et al. (J. Am. Chem. Soc.94, 4069 (1972)) are used with the inclusion of all multicenter one-electron integrals.

Determination of the bonding of alkyl monolayers to the Si(111) surface using chemical-shift, scanned-energy photoelectron diffraction

Energy Technology Data Exchange (ETDEWEB)

Terry, J.; Linford, M.R.; Wigren, C.; Cao, R.; Pianetta, P.; Chidsey, C.E. [Stanford University, Stanford, California 94309 (United States)

1997-08-01

The bonding of alkyl monolayers to Si(111) surfaces has been studied by conventional x-ray photoelectron spectroscopy (XPS) and chemical-shift, scanned-energy photoelectron diffraction (PED) using synchrotron radiation. Two very different wet-chemical methods have been used to prepare the alkyl monolayers: (i) olefin insertion into the H{endash}Si bond on the H{endash}Si(111) surface, and (ii) replacement of Cl on the Cl{endash}Si(111) surface by an alkyl group from an alkyllithium reagent. In both cases, XPS has revealed a C 1s signal chemically shifted to lower binding energy, which we have assigned to carbon bonded to silicon. PED has shown that both preparative methods result in carbon bonded in an atop site with the expected C{endash}Si bond length of 1.85{plus_minus}0.05{Angstrom}. Chemical-shift, scanned-energy photoelectron diffraction is a particularly valuable probe of local structure at surfaces that contain the same element in multiple, chemically distinct environments. {copyright} {ital 1997 American Institute of Physics.}

Determination of the bonding of alkyl monolayers to the Si(111) surface using chemical-shift, scanned-energy photoelectron diffraction

International Nuclear Information System (INIS)

Terry, J.; Linford, M.R.; Wigren, C.; Cao, R.; Pianetta, P.; Chidsey, C.E.

1997-01-01

The bonding of alkyl monolayers to Si(111) surfaces has been studied by conventional x-ray photoelectron spectroscopy (XPS) and chemical-shift, scanned-energy photoelectron diffraction (PED) using synchrotron radiation. Two very different wet-chemical methods have been used to prepare the alkyl monolayers: (i) olefin insertion into the H endash Si bond on the H endash Si(111) surface, and (ii) replacement of Cl on the Cl endash Si(111) surface by an alkyl group from an alkyllithium reagent. In both cases, XPS has revealed a C 1s signal chemically shifted to lower binding energy, which we have assigned to carbon bonded to silicon. PED has shown that both preparative methods result in carbon bonded in an atop site with the expected C endash Si bond length of 1.85±0.05 Angstrom. Chemical-shift, scanned-energy photoelectron diffraction is a particularly valuable probe of local structure at surfaces that contain the same element in multiple, chemically distinct environments. copyright 1997 American Institute of Physics

Solvation effects on chemical shifts by embedded cluster integral equation theory.

Science.gov (United States)

Frach, Roland; Kast, Stefan M

2014-12-11

The accurate computational prediction of nuclear magnetic resonance (NMR) parameters like chemical shifts represents a challenge if the species studied is immersed in strongly polarizing environments such as water. Common approaches to treating a solvent in the form of, e.g., the polarizable continuum model (PCM) ignore strong directional interactions such as H-bonds to the solvent which can have substantial impact on magnetic shieldings. We here present a computational methodology that accounts for atomic-level solvent effects on NMR parameters by extending the embedded cluster reference interaction site model (EC-RISM) integral equation theory to the prediction of chemical shifts of N-methylacetamide (NMA) in aqueous solution. We examine the influence of various so-called closure approximations of the underlying three-dimensional RISM theory as well as the impact of basis set size and different treatment of electrostatic solute-solvent interactions. We find considerable and systematic improvement over reference PCM and gas phase calculations. A smaller basis set in combination with a simple point charge model already yields good performance which can be further improved by employing exact electrostatic quantum-mechanical solute-solvent interaction energies. A larger basis set benefits more significantly from exact over point charge electrostatics, which can be related to differences of the solvent's charge distribution.

Monograph On Tensor Notations

Science.gov (United States)

Sirlin, Samuel W.

1993-01-01

Eight-page report describes systems of notation used most commonly to represent tensors of various ranks, with emphasis on tensors in Cartesian coordinate systems. Serves as introductory or refresher text for scientists, engineers, and others familiar with basic concepts of coordinate systems, vectors, and partial derivatives. Indicial tensor, vector, dyadic, and matrix notations, and relationships among them described.

Gamow-Teller resonances and a separable approximation for Skyrme tensor interactions

Directory of Open Access Journals (Sweden)

Severyukhin A. P.

2012-12-01

Full Text Available A finite rank separable approximation for the quasiparticle random phase approximation (QRPA with Skyrme interactions is applied to study properties of the Gamow-Teller (GT resonances in the neutron-rich Cd isotopes. This approximation enables one to reduce considerably the dimension of matrix that must be diagonalized to perform QRPA calculations in a very large configuration space. Our results from the SGII Skyrme interaction with the tensor interactions and the density-dependent zero-range pairing interaction show that the GT distribution is noticeably modified when the tensor correlations are taken into account. In particular, for 130Cd the dominant peak is moved 3.6 MeV downward and 10% of the GT distribution is shifted to the high excitation energy region near E=50MeV.

Benchmark fragment-based 1H, 13C, 15N and 17O chemical shift predictions in molecular crystals†

Science.gov (United States)

Hartman, Joshua D.; Kudla, Ryan A.; Day, Graeme M.; Mueller, Leonard J.; Beran, Gregory J. O.

2016-01-01

The performance of fragment-based ab initio 1H, 13C, 15N and 17O chemical shift predictions is assessed against experimental NMR chemical shift data in four benchmark sets of molecular crystals. Employing a variety of commonly used density functionals (PBE0, B3LYP, TPSSh, OPBE, PBE, TPSS), we explore the relative performance of cluster, two-body fragment, and combined cluster/fragment models. The hybrid density functionals (PBE0, B3LYP and TPSSh) generally out-perform their generalized gradient approximation (GGA)-based counterparts. 1H, 13C, 15N, and 17O isotropic chemical shifts can be predicted with root-mean-square errors of 0.3, 1.5, 4.2, and 9.8 ppm, respectively, using a computationally inexpensive electrostatically embedded two-body PBE0 fragment model. Oxygen chemical shieldings prove particularly sensitive to local many-body effects, and using a combined cluster/fragment model instead of the simple two-body fragment model decreases the root-mean-square errors to 7.6 ppm. These fragment-based model errors compare favorably with GIPAW PBE ones of 0.4, 2.2, 5.4, and 7.2 ppm for the same 1H, 13C, 15N, and 17O test sets. Using these benchmark calculations, a set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided and their robustness assessed using statistical cross-validation. We demonstrate the utility of these approaches and the reported scaling parameters on applications to 9-tertbutyl anthracene, several histidine co-crystals, benzoic acid and the C-nitrosoarene SnCl2(CH3)2(NODMA)2. PMID:27431490

Benchmark fragment-based (1)H, (13)C, (15)N and (17)O chemical shift predictions in molecular crystals.

Science.gov (United States)

Hartman, Joshua D; Kudla, Ryan A; Day, Graeme M; Mueller, Leonard J; Beran, Gregory J O

2016-08-21

The performance of fragment-based ab initio(1)H, (13)C, (15)N and (17)O chemical shift predictions is assessed against experimental NMR chemical shift data in four benchmark sets of molecular crystals. Employing a variety of commonly used density functionals (PBE0, B3LYP, TPSSh, OPBE, PBE, TPSS), we explore the relative performance of cluster, two-body fragment, and combined cluster/fragment models. The hybrid density functionals (PBE0, B3LYP and TPSSh) generally out-perform their generalized gradient approximation (GGA)-based counterparts. (1)H, (13)C, (15)N, and (17)O isotropic chemical shifts can be predicted with root-mean-square errors of 0.3, 1.5, 4.2, and 9.8 ppm, respectively, using a computationally inexpensive electrostatically embedded two-body PBE0 fragment model. Oxygen chemical shieldings prove particularly sensitive to local many-body effects, and using a combined cluster/fragment model instead of the simple two-body fragment model decreases the root-mean-square errors to 7.6 ppm. These fragment-based model errors compare favorably with GIPAW PBE ones of 0.4, 2.2, 5.4, and 7.2 ppm for the same (1)H, (13)C, (15)N, and (17)O test sets. Using these benchmark calculations, a set of recommended linear regression parameters for mapping between calculated chemical shieldings and observed chemical shifts are provided and their robustness assessed using statistical cross-validation. We demonstrate the utility of these approaches and the reported scaling parameters on applications to 9-tert-butyl anthracene, several histidine co-crystals, benzoic acid and the C-nitrosoarene SnCl2(CH3)2(NODMA)2.

Cartesian tensors an introduction

CERN Document Server

Temple, G

2004-01-01

This undergraduate text provides an introduction to the theory of Cartesian tensors, defining tensors as multilinear functions of direction, and simplifying many theorems in a manner that lends unity to the subject. The author notes the importance of the analysis of the structure of tensors in terms of spectral sets of projection operators as part of the very substance of quantum theory. He therefore provides an elementary discussion of the subject, in addition to a view of isotropic tensors and spinor analysis within the confines of Euclidean space. The text concludes with an examination of t

MATLAB tensor classes for fast algorithm prototyping.

Energy Technology Data Exchange (ETDEWEB)

Bader, Brett William; Kolda, Tamara Gibson (Sandia National Laboratories, Livermore, CA)

2004-10-01

Tensors (also known as mutidimensional arrays or N-way arrays) are used in a variety of applications ranging from chemometrics to psychometrics. We describe four MATLAB classes for tensor manipulations that can be used for fast algorithm prototyping. The tensor class extends the functionality of MATLAB's multidimensional arrays by supporting additional operations such as tensor multiplication. The tensor as matrix class supports the 'matricization' of a tensor, i.e., the conversion of a tensor to a matrix (and vice versa), a commonly used operation in many algorithms. Two additional classes represent tensors stored in decomposed formats: cp tensor and tucker tensor. We descibe all of these classes and then demonstrate their use by showing how to implement several tensor algorithms that have appeared in the literature.

Uncertainties for seismic moment tensors and applications to nuclear explosions, volcanic events, and earthquakes

Science.gov (United States)

Tape, C.; Alvizuri, C. R.; Silwal, V.; Tape, W.

2017-12-01

When considered as a point source, a seismic source can be characterized in terms of its origin time, hypocenter, moment tensor, and source time function. The seismologist's task is to estimate these parameters--and their uncertainties--from three-component ground motion recorded at irregularly spaced stations. We will focus on one portion of this problem: the estimation of the moment tensor and its uncertainties. With magnitude estimated separately, we are left with five parameters describing the normalized moment tensor. A lune of normalized eigenvalue triples can be used to visualize the two parameters (lune longitude and lune latitude) describing the source type, while the conventional strike, dip, and rake angles can be used to characterize the orientation. Slight modifications of these five parameters lead to a uniform parameterization of moment tensors--uniform in the sense that equal volumes in the coordinate domain of the parameterization correspond to equal volumes of moment tensors. For a moment tensor m that we have inferred from seismic data for an earthquake, we define P(V) to be the probability that the true moment tensor for the earthquake lies in the neighborhood of m that has fractional volume V. The average value of P(V) is then a measure of our confidence in our inference of m. The calculation of P(V) requires knowing both the probability P(w) and the fractional volume V(w) of the set of moment tensors within a given angular radius w of m. We apply this approach to several different data sets, including nuclear explosions from the Nevada Test Site, volcanic events from Uturuncu (Bolivia), and earthquakes. Several challenges remain: choosing an appropriate misfit function, handling time shifts between data and synthetic waveforms, and extending the uncertainty estimation to include more source parameters (e.g., hypocenter and source time function).

Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

Energy Technology Data Exchange (ETDEWEB)

Krtous, Pavel [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Kubiznak, David [Institute of Theoretical Physics, Charles University, V Holesovickach 2, Prague (Czech Republic); Page, Don N. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada); Frolov, Valeri P. [Theoretical Physics Institute, University of Alberta, Edmonton T6G 2G7, Alberta (Canada)

2007-02-15

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 {<=} j {<=} k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)

Killing-Yano tensors, rank-2 Killing tensors, and conserved quantities in higher dimensions

International Nuclear Information System (INIS)

Krtous, Pavel; Kubiznak, David; Page, Don N.; Frolov, Valeri P.

2007-01-01

From the metric and one Killing-Yano tensor of rank D-2 in any D-dimensional spacetime with such a principal Killing-Yano tensor, we show how to generate k = [(D+1)/2] Killing-Yano tensors, of rank D-2j for all 0 ≤ j ≤ k-1, and k rank-2 Killing tensors, giving k constants of geodesic motion that are in involution. For the example of the Kerr-NUT-AdS spacetime (hep-th/0604125) with its principal Killing-Yano tensor (gr-qc/0610144), these constants and the constants from the k Killing vectors give D independent constants in involution, making the geodesic motion completely integrable (hep-th/0611083). The constants of motion are also related to the constants recently obtained in the separation of the Hamilton-Jacobi and Klein-Gordon equations (hep-th/0611245)

Orientation-dependent surface core-level shifts and chemical shifts on clean and H 2S-covered GaAs

Science.gov (United States)

Ranke, W.; Finster, J.; Kuhr, H. J.

1987-08-01

Photoelectron spectra of the As 3d and Ga 3d core levels were studied in situ on a cylindrically shaped GaAs single crystal for the six inequivalent orientations (001), (113), (111), (110), (11¯1) and (11¯3). On the clean surface, prepared by molecular beam epitaxy (MBE), surface core levels are shifted by 0.25 to 0.55 eV towards smaller binding energy (BE) for As 3d and -0.25 to -0.35 eV towards higher BE for Ga, depending on orientation. Additional As causes As 3d contributions shifted between -0.45 and -0.7 eV towards higher BE. The position and intensity of them is influenced by H 2S adsorption. At 150 K, H 2S adsorbs preferentially on As sites. As chemical shifts appear at -0.6 to -0.9 eV towards higher BE. Simultaneously, As accumulation occurs on all orientations with the exception of (110). High temperature adsorption (550 K, 720 K) influences mainly the Ga 3d peaks. Two peaks shifted by about -0.45 and -0.8 eV towards higher Be were found which are attributed to Ga atoms with one or two sulfur ligands, respectively. At 720 K, also As depletion is observed. The compatibility of surface core-level positions and intensities with recent structural models for the (111) and (11¯1) surfaces is discussed.

Four-component relativistic density functional theory calculations of NMR shielding tensors for paramagnetic systems.

Science.gov (United States)

Komorovsky, Stanislav; Repisky, Michal; Ruud, Kenneth; Malkina, Olga L; Malkin, Vladimir G

2013-12-27

A four-component relativistic method for the calculation of NMR shielding constants of paramagnetic doublet systems has been developed and implemented in the ReSpect program package. The method uses a Kramer unrestricted noncollinear formulation of density functional theory (DFT), providing the best DFT framework for property calculations of open-shell species. The evaluation of paramagnetic nuclear magnetic resonance (pNMR) tensors reduces to the calculation of electronic g tensors, hyperfine coupling tensors, and NMR shielding tensors. For all properties, modern four-component formulations were adopted. The use of both restricted kinetically and magnetically balanced basis sets along with gauge-including atomic orbitals ensures rapid basis-set convergence. These approaches are exact in the framework of the Dirac-Coulomb Hamiltonian, thus providing useful reference data for more approximate methods. Benchmark calculations on Ru(III) complexes demonstrate good performance of the method in reproducing experimental data and also its applicability to chemically relevant medium-sized systems. Decomposition of the temperature-dependent part of the pNMR tensor into the traditional contact and pseudocontact terms is proposed.

Tensor-based spatiotemporal saliency detection

Science.gov (United States)

Dou, Hao; Li, Bin; Deng, Qianqian; Zhang, LiRui; Pan, Zhihong; Tian, Jinwen

2018-03-01

This paper proposes an effective tensor-based spatiotemporal saliency computation model for saliency detection in videos. First, we construct the tensor representation of video frames. Then, the spatiotemporal saliency can be directly computed by the tensor distance between different tensors, which can preserve the complete temporal and spatial structure information of object in the spatiotemporal domain. Experimental results demonstrate that our method can achieve encouraging performance in comparison with the state-of-the-art methods.

Criteria to average out the chemical shift anisotropy in solid-state NMR when irradiated with BABA I, BABA II, and C7 radiofrequency pulse sequences.

Science.gov (United States)

Stephane Mananga, Eugene

2013-01-01

Floquet-Magnus expansion is used to study the effect of chemical shift anisotropy in solid-state NMR of rotating solids. The chemical shift interaction is irradiated with two types of radiofrequency pulse sequences: BABA and C7. The criteria for the chemical shift anisotropy to be averaged out in each rotor period are obtained. Copyright © 2013 Elsevier Inc. All rights reserved.

Generalized dielectric permittivity tensor

International Nuclear Information System (INIS)

Borzdov, G.N.; Barkovskii, L.M.; Fedorov, F.I.

1986-01-01

The authors deal with the question of what is to be done with the formalism of the electrodynamics of dispersive media based on the introduction of dielectric-permittivity tensors for purely harmonic fields when Voigt waves and waves of more general form exist. An attempt is made to broaden and generalize the formalism to take into account dispersion of waves of the given type. In dispersive media, the polarization, magnetization, and conduction current-density vectors of point and time are determined by the values of the electromagnetic field vectors in the vicinity of this point (spatial dispersion) in the preceding instants of time (time dispersion). The dielectric-permittivity tensor and other tensors of electrodynamic parameters of the medium are introduced in terms of a set of evolution operators and not the set of harmonic function. It is noted that a magnetic-permeability tensor and an elastic-modulus tensor may be introduced for an acoustic field in dispersive anisotropic media with coupling equations of general form

Tensor analysis for physicists

CERN Document Server

Schouten, J A

1989-01-01

This brilliant study by a famed mathematical scholar and former professor of mathematics at the University of Amsterdam integrates a concise exposition of the mathematical basis of tensor analysis with admirably chosen physical examples of the theory. The first five chapters incisively set out the mathematical theory underlying the use of tensors. The tensor algebra in EN and RN is developed in Chapters I and II. Chapter II introduces a sub-group of the affine group, then deals with the identification of quantities in EN. The tensor analysis in XN is developed in Chapter IV. In chapters VI through IX, Professor Schouten presents applications of the theory that are both intrinsically interesting and good examples of the use and advantages of the calculus. Chapter VI, intimately connected with Chapter III, shows that the dimensions of physical quantities depend upon the choice of the underlying group, and that tensor calculus is the best instrument for dealing with the properties of anisotropic media. In Chapte...

Sparse alignment for robust tensor learning.

Science.gov (United States)

Lai, Zhihui; Wong, Wai Keung; Xu, Yong; Zhao, Cairong; Sun, Mingming

2014-10-01

Multilinear/tensor extensions of manifold learning based algorithms have been widely used in computer vision and pattern recognition. This paper first provides a systematic analysis of the multilinear extensions for the most popular methods by using alignment techniques, thereby obtaining a general tensor alignment framework. From this framework, it is easy to show that the manifold learning based tensor learning methods are intrinsically different from the alignment techniques. Based on the alignment framework, a robust tensor learning method called sparse tensor alignment (STA) is then proposed for unsupervised tensor feature extraction. Different from the existing tensor learning methods, L1- and L2-norms are introduced to enhance the robustness in the alignment step of the STA. The advantage of the proposed technique is that the difficulty in selecting the size of the local neighborhood can be avoided in the manifold learning based tensor feature extraction algorithms. Although STA is an unsupervised learning method, the sparsity encodes the discriminative information in the alignment step and provides the robustness of STA. Extensive experiments on the well-known image databases as well as action and hand gesture databases by encoding object images as tensors demonstrate that the proposed STA algorithm gives the most competitive performance when compared with the tensor-based unsupervised learning methods.

TensorPack: a Maple-based software package for the manipulation of algebraic expressions of tensors in general relativity

International Nuclear Information System (INIS)

Huf, P A; Carminati, J

2015-01-01

In this paper we: (1) introduce TensorPack, a software package for the algebraic manipulation of tensors in covariant index format in Maple; (2) briefly demonstrate the use of the package with an orthonormal tensor proof of the shearfree conjecture for dust. TensorPack is based on the Riemann and Canon tensor software packages and uses their functions to express tensors in an indexed covariant format. TensorPack uses a string representation as input and provides functions for output in index form. It extends the functionality to basic algebra of tensors, substitution, covariant differentiation, contraction, raising/lowering indices, symmetry functions and other accessory functions. The output can be merged with text in the Maple environment to create a full working document with embedded dynamic functionality. The package offers potential for manipulation of indexed algebraic tensor expressions in a flexible software environment. (paper)

Grid-based lattice summation of electrostatic potentials by assembled rank-structured tensor approximation

Science.gov (United States)

Khoromskaia, Venera; Khoromskij, Boris N.

2014-12-01

Our recent method for low-rank tensor representation of sums of the arbitrarily positioned electrostatic potentials discretized on a 3D Cartesian grid reduces the 3D tensor summation to operations involving only 1D vectors however retaining the linear complexity scaling in the number of potentials. Here, we introduce and study a novel tensor approach for fast and accurate assembled summation of a large number of lattice-allocated potentials represented on 3D N × N × N grid with the computational requirements only weakly dependent on the number of summed potentials. It is based on the assembled low-rank canonical tensor representations of the collected potentials using pointwise sums of shifted canonical vectors representing the single generating function, say the Newton kernel. For a sum of electrostatic potentials over L × L × L lattice embedded in a box the required storage scales linearly in the 1D grid-size, O(N) , while the numerical cost is estimated by O(NL) . For periodic boundary conditions, the storage demand remains proportional to the 1D grid-size of a unit cell, n = N / L, while the numerical cost reduces to O(N) , that outperforms the FFT-based Ewald-type summation algorithms of complexity O(N3 log N) . The complexity in the grid parameter N can be reduced even to the logarithmic scale O(log N) by using data-sparse representation of canonical N-vectors via the quantics tensor approximation. For justification, we prove an upper bound on the quantics ranks for the canonical vectors in the overall lattice sum. The presented approach is beneficial in applications which require further functional calculus with the lattice potential, say, scalar product with a function, integration or differentiation, which can be performed easily in tensor arithmetics on large 3D grids with 1D cost. Numerical tests illustrate the performance of the tensor summation method and confirm the estimated bounds on the tensor ranks.

Protein structure validation and refinement using amide proton chemical shifts derived from quantum mechanics

DEFF Research Database (Denmark)

Christensen, Anders Steen; Linnet, Troels Emtekær; Borg, Mikael

2013-01-01

We present the ProCS method for the rapid and accurate prediction of protein backbone amide proton chemical shifts - sensitive probes of the geometry of key hydrogen bonds that determine protein structure. ProCS is parameterized against quantum mechanical (QM) calculations and reproduces high level...

Differentiation of osteoporotic and neoplastic vertebral fractures by chemical shift {in-phase and out-of phase} MR imaging

International Nuclear Information System (INIS)

Ragab, Yasser; Emad, Yasser; Gheita, Tamer; Mansour, Maged; Abou-Zeid, A.; Ferrari, Serge; Rasker, Johannes J.

2009-01-01

Objective: The objective of this study was to establish the cut-off value of the signal intensity drop on chemical shift magnetic resonance imaging (MRI) with appropriate sensitivity and specificity to differentiate osteoporotic from neoplastic wedging of the spine. Patients and methods: All patients with wedging of vertebral bodies were included consecutively between February 2006 and January 2007. A chemical shift MRI was performed and signal intensity after (in-phase and out-phase) images were obtained. A DXA was performed in all. Results: A total of 40 patients were included, 20 with osteoporotic wedging (group 1) and 20 neoplastic (group 2). They were 21 males and 19 females. Acute vertebral collapse was observed in 15 patients in group 1 and subacute collapse in another 5 patients, while in group 2, 11 patients showed acute collapse and 9 patients (45%) showed subacute vertebral collapse. On the chemical shift MRI a substantial reduction in signal intensity was found in all lesions in both groups. The proportional changes observed in signal intensity of bone marrow lesions on in-phase compared with out-of-phase images showed significant differences in both groups (P < 0.05). At a cut-off value of 35%, the observed sensitivity of out-of-phase images was 95%, specificity was 100%, positive predictive value was 100% and negative predictive value was 95.2%. Conclusion: A chemical shift MRI is useful in order to differentiate patients with vertebral collapse due to underlying osteoporosis or neoplastic process.

Measuring 13Cβ chemical shifts of invisible excited states in proteins by relaxation dispersion NMR spectroscopy

International Nuclear Information System (INIS)

Lundstroem, Patrik; Lin Hong; Kay, Lewis E.

2009-01-01

A labeling scheme is introduced that facilitates the measurement of accurate 13 C β chemical shifts of invisible, excited states of proteins by relaxation dispersion NMR spectroscopy. The approach makes use of protein over-expression in a strain of E. coli in which the TCA cycle enzyme succinate dehydrogenase is knocked out, leading to the production of samples with high levels of 13 C enrichment (30-40%) at C β side-chain carbon positions for 15 of the amino acids with little 13 C label at positions one bond removed (∼5%). A pair of samples are produced using [1- 13 C]-glucose/NaH 12 CO 3 or [2- 13 C]-glucose as carbon sources with isolated and enriched (>30%) 13 C β positions for 11 and 4 residues, respectively. The efficacy of the labeling procedure is established by NMR spectroscopy. The utility of such samples for measurement of 13 C β chemical shifts of invisible, excited states in exchange with visible, ground conformations is confirmed by relaxation dispersion studies of a protein-ligand binding exchange reaction in which the extracted chemical shift differences from dispersion profiles compare favorably with those obtained directly from measurements on ligand free and fully bound protein samples

Unique characterization of the Bel-Robinson tensor

International Nuclear Information System (INIS)

Bergqvist, G; Lankinen, P

2004-01-01

We prove that a completely symmetric and trace-free rank-4 tensor is, up to sign, a Bel-Robinson-type tensor, i.e., the superenergy tensor of a tensor with the same algebraic symmetries as the Weyl tensor, if and only if it satisfies a certain quadratic identity. This may be seen as the first Rainich theory result for rank-4 tensors

Empirical isotropic chemical shift surfaces

International Nuclear Information System (INIS)

Czinki, Eszter; Csaszar, Attila G.

2007-01-01

A list of proteins is given for which spatial structures, with a resolution better than 2.5 A, are known from entries in the Protein Data Bank (PDB) and isotropic chemical shift (ICS) values are known from the RefDB database related to the Biological Magnetic Resonance Bank (BMRB) database. The structures chosen provide, with unknown uncertainties, dihedral angles φ and ψ characterizing the backbone structure of the residues. The joint use of experimental ICSs of the same residues within the proteins, again with mostly unknown uncertainties, and ab initio ICS(φ,ψ) surfaces obtained for the model peptides For-(l-Ala) n -NH 2 , with n = 1, 3, and 5, resulted in so-called empirical ICS(φ,ψ) surfaces for all major nuclei of the 20 naturally occurring α-amino acids. Out of the many empirical surfaces determined, it is the 13C α ICS(φ,ψ) surface which seems to be most promising for identifying major secondary structure types, α-helix, β-strand, left-handed helix (α D ), and polyproline-II. Detailed tests suggest that Ala is a good model for many naturally occurring α-amino acids. Two-dimensional empirical 13C α - 1 H α ICS(φ,ψ) correlation plots, obtained so far only from computations on small peptide models, suggest the utility of the experimental information contained therein and thus they should provide useful constraints for structure determinations of proteins

Lanthanide shift reagents, binding, shift mechanisms and exchange

International Nuclear Information System (INIS)

Boer, J.W.M. de

1977-01-01

Paramagnetic lanthanide shift reagents, when added to a solution of a substrate, induce shifts in the nuclear magnetic resonance (NMR) spectrum of the substrate molecules. The induced shifts contain information about the structure of the shift reagent substrate complex. The structural information, however, may be difficult to extract because of the following effects: (1) different complexes between shift reagent and substrate may be present in solution, e.g. 1:1 and 1:2 complexes, and the shift observed is a weighed average of the shifts of the substrate nuclei in the different complexes; (2) the Fermi contact interaction, arising from the spin density at the nucleus, contributes to the induced shift; (3) chemical exchange effects may complicate the NMR spectrum. In this thesis, the results of an investigation into the influence of these effects on the NMR spectra of solutions containing a substrate and LSR are presented. The equations describing the pseudo contact and the Fermi contact shift are derived. In addition, it is shown how the modified Bloch equations describing the effect of the chemical exchange processes occurring in the systems studied can be reduced to the familiar equations for a two-site exchange case. The binding of mono- and bifunctional ethers to the shift reagent are reported. An analysis of the induced shifts is given. Finally, the results of the experiments performed to study the exchange behavior of dimethoxyethane and heptafluorodimethyloctanedionato ligands are presented

Tensor Product of Polygonal Cell Complexes

OpenAIRE

Chien, Yu-Yen

2017-01-01

We introduce the tensor product of polygonal cell complexes, which interacts nicely with the tensor product of link graphs of complexes. We also develop the unique factorization property of polygonal cell complexes with respect to the tensor product, and study the symmetries of tensor products of polygonal cell complexes.

Mean template for tensor-based morphometry using deformation tensors.

Science.gov (United States)

Leporé, Natasha; Brun, Caroline; Pennec, Xavier; Chou, Yi-Yu; Lopez, Oscar L; Aizenstein, Howard J; Becker, James T; Toga, Arthur W; Thompson, Paul M

2007-01-01

Tensor-based morphometry (TBM) studies anatomical differences between brain images statistically, to identify regions that differ between groups, over time, or correlate with cognitive or clinical measures. Using a nonlinear registration algorithm, all images are mapped to a common space, and statistics are most commonly performed on the Jacobian determinant (local expansion factor) of the deformation fields. In, it was shown that the detection sensitivity of the standard TBM approach could be increased by using the full deformation tensors in a multivariate statistical analysis. Here we set out to improve the common space itself, by choosing the shape that minimizes a natural metric on the deformation tensors from that space to the population of control subjects. This method avoids statistical bias and should ease nonlinear registration of new subjects data to a template that is 'closest' to all subjects' anatomies. As deformation tensors are symmetric positive-definite matrices and do not form a vector space, all computations are performed in the log-Euclidean framework. The control brain B that is already the closest to 'average' is found. A gradient descent algorithm is then used to perform the minimization that iteratively deforms this template and obtains the mean shape. We apply our method to map the profile of anatomical differences in a dataset of 26 HIV/AIDS patients and 14 controls, via a log-Euclidean Hotelling's T2 test on the deformation tensors. These results are compared to the ones found using the 'best' control, B. Statistics on both shapes are evaluated using cumulative distribution functions of the p-values in maps of inter-group differences.

Notes on super Killing tensors

Energy Technology Data Exchange (ETDEWEB)

Howe, P.S. [Department of Mathematics, King’s College London,The Strand, London WC2R 2LS (United Kingdom); Lindström, University [Department of Physics and Astronomy, Theoretical Physics, Uppsala University,SE-751 20 Uppsala (Sweden); Theoretical Physics, Imperial College London,Prince Consort Road, London SW7 2AZ (United Kingdom)

2016-03-14

The notion of a Killing tensor is generalised to a superspace setting. Conserved quantities associated with these are defined for superparticles and Poisson brackets are used to define a supersymmetric version of the even Schouten-Nijenhuis bracket. Superconformal Killing tensors in flat superspaces are studied for spacetime dimensions 3,4,5,6 and 10. These tensors are also presented in analytic superspaces and super-twistor spaces for 3,4 and 6 dimensions. Algebraic structures associated with superconformal Killing tensors are also briefly discussed.

Extended nonnegative tensor factorisation models for musical sound source separation.

Science.gov (United States)

FitzGerald, Derry; Cranitch, Matt; Coyle, Eugene

2008-01-01

Recently, shift-invariant tensor factorisation algorithms have been proposed for the purposes of sound source separation of pitched musical instruments. However, in practice, existing algorithms require the use of log-frequency spectrograms to allow shift invariance in frequency which causes problems when attempting to resynthesise the separated sources. Further, it is difficult to impose harmonicity constraints on the recovered basis functions. This paper proposes a new additive synthesis-based approach which allows the use of linear-frequency spectrograms as well as imposing strict harmonic constraints, resulting in an improved model. Further, these additional constraints allow the addition of a source filter model to the factorisation framework, and an extended model which is capable of separating mixtures of pitched and percussive instruments simultaneously.

Extended Nonnegative Tensor Factorisation Models for Musical Sound Source Separation

Directory of Open Access Journals (Sweden)

Derry FitzGerald

2008-01-01

Full Text Available Recently, shift-invariant tensor factorisation algorithms have been proposed for the purposes of sound source separation of pitched musical instruments. However, in practice, existing algorithms require the use of log-frequency spectrograms to allow shift invariance in frequency which causes problems when attempting to resynthesise the separated sources. Further, it is difficult to impose harmonicity constraints on the recovered basis functions. This paper proposes a new additive synthesis-based approach which allows the use of linear-frequency spectrograms as well as imposing strict harmonic constraints, resulting in an improved model. Further, these additional constraints allow the addition of a source filter model to the factorisation framework, and an extended model which is capable of separating mixtures of pitched and percussive instruments simultaneously.

Pressure dependence of side chain 13C chemical shifts in model peptides Ac-Gly-Gly-Xxx-Ala-NH2.

Science.gov (United States)

Beck Erlach, Markus; Koehler, Joerg; Crusca, Edson; Munte, Claudia E; Kainosho, Masatsune; Kremer, Werner; Kalbitzer, Hans Robert

2017-10-01

For evaluating the pressure responses of folded as well as intrinsically unfolded proteins detectable by NMR spectroscopy the availability of data from well-defined model systems is indispensable. In this work we report the pressure dependence of 13 C chemical shifts of the side chain atoms in the protected tetrapeptides Ac-Gly-Gly-Xxx-Ala-NH 2 (Xxx, one of the 20 canonical amino acids). Contrary to expectation the chemical shifts of a number of nuclei have a nonlinear dependence on pressure in the range from 0.1 to 200 MPa. The size of the polynomial pressure coefficients B 1 and B 2 is dependent on the type of atom and amino acid studied. For H N , N and C α the first order pressure coefficient B 1 is also correlated to the chemical shift at atmospheric pressure. The first and second order pressure coefficients of a given type of carbon atom show significant linear correlations suggesting that the NMR observable pressure effects in the different amino acids have at least partly the same physical cause. In line with this observation the magnitude of the second order coefficients of nuclei being direct neighbors in the chemical structure also are weakly correlated. The downfield shifts of the methyl resonances suggest that gauche conformers of the side chains are not preferred with pressure. The valine and leucine methyl groups in the model peptides were assigned using stereospecifically 13 C enriched amino acids with the pro-R carbons downfield shifted relative to the pro-S carbons.

Reassigning the Structures of Natural Products Using NMR Chemical Shifts Computed with Quantum Mechanics: A Laboratory Exercise

Science.gov (United States)

Palazzo, Teresa A.; Truong, Tiana T.; Wong, Shirley M. T.; Mack, Emma T.; Lodewyk, Michael W.; Harrison, Jason G.; Gamage, R. Alan; Siegel, Justin B.; Kurth, Mark J.; Tantillo, Dean J.

2015-01-01

An applied computational chemistry laboratory exercise is described in which students use modern quantum chemical calculations of chemical shifts to assign the structure of a recently isolated natural product. A pre/post assessment was used to measure student learning gains and verify that students demonstrated proficiency of key learning…

Identifying Stereoisomers by ab-initio Calculation of Secondary Isotope Shifts on NMR Chemical Shieldings

Directory of Open Access Journals (Sweden)

Karl-Heinz Böhm

2014-04-01

Full Text Available We present ab-initio calculations of secondary isotope effects on NMR chemical shieldings. The change of the NMR chemical shift of a certain nucleus that is observed if another nucleus is replaced by a different isotope can be calculated by computing vibrational corrections on the NMR parameters using electronic structure methods. We demonstrate that the accuracy of the computational results is sufficient to even distinguish different conformers. For this purpose, benchmark calculations for fluoro(2-2Hethane in gauche and antiperiplanar conformation are carried out at the HF, MP2 and CCSD(T level of theory using basis sets ranging from double- to quadruple-zeta quality. The methodology is applied to the secondary isotope shifts for 2-fluoronorbornane in order to resolve an ambiguity in the literature on the assignment of endo- and exo-2-fluoronorbornanes with deuterium substituents in endo-3 and exo-3 positions, also yielding insight into mechanistic details of the corresponding synthesis.

Identifying stereoisomers by ab-initio calculation of secondary isotope shifts on NMR chemical shieldings.

Science.gov (United States)

Böhm, Karl-Heinz; Banert, Klaus; Auer, Alexander A

2014-04-23

We present ab-initio calculations of secondary isotope effects on NMR chemical shieldings. The change of the NMR chemical shift of a certain nucleus that is observed if another nucleus is replaced by a different isotope can be calculated by computing vibrational corrections on the NMR parameters using electronic structure methods. We demonstrate that the accuracy of the computational results is sufficient to even distinguish different conformers. For this purpose, benchmark calculations for fluoro(2-2H)ethane in gauche and antiperiplanar conformation are carried out at the HF, MP2 and CCSD(T) level of theory using basis sets ranging from double- to quadruple-zeta quality. The methodology is applied to the secondary isotope shifts for 2-fluoronorbornane in order to resolve an ambiguity in the literature on the assignment of endo- and exo-2-fluoronorbornanes with deuterium substituents in endo-3 and exo-3 positions, also yielding insight into mechanistic details of the corresponding synthesis.

Hairy black hole solutions in U(1) gauge-invariant scalar-vector-tensor theories

Science.gov (United States)

Heisenberg, Lavinia; Tsujikawa, Shinji

2018-05-01

In U (1) gauge-invariant scalar-vector-tensor theories with second-order equations of motion, we study the properties of black holes (BH) on a static and spherically symmetric background. In shift-symmetric theories invariant under the shift of scalar ϕ → ϕ + c, we show the existence of new hairy BH solutions where a cubic-order scalar-vector interaction gives rise to a scalar hair manifesting itself around the event horizon. In the presence of a quartic-order interaction besides the cubic coupling, there are also regular BH solutions endowed with scalar and vector hairs.

Tensor Train Neighborhood Preserving Embedding

Science.gov (United States)

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2018-05-01

In this paper, we propose a Tensor Train Neighborhood Preserving Embedding (TTNPE) to embed multi-dimensional tensor data into low dimensional tensor subspace. Novel approaches to solve the optimization problem in TTNPE are proposed. For this embedding, we evaluate novel trade-off gain among classification, computation, and dimensionality reduction (storage) for supervised learning. It is shown that compared to the state-of-the-arts tensor embedding methods, TTNPE achieves superior trade-off in classification, computation, and dimensionality reduction in MNIST handwritten digits and Weizmann face datasets.

Tensor network states in time-bin quantum optics

Science.gov (United States)

Lubasch, Michael; Valido, Antonio A.; Renema, Jelmer J.; Kolthammer, W. Steven; Jaksch, Dieter; Kim, M. S.; Walmsley, Ian; García-Patrón, Raúl

2018-06-01

The current shift in the quantum optics community towards experiments with many modes and photons necessitates new classical simulation techniques that efficiently encode many-body quantum correlations and go beyond the usual phase-space formulation. To address this pressing demand we formulate linear quantum optics in the language of tensor network states. We extensively analyze the quantum and classical correlations of time-bin interference in a single fiber loop. We then generalize our results to more complex time-bin quantum setups and identify different classes of architectures for high-complexity and low-overhead boson sampling experiments.

The Topology of Symmetric Tensor Fields

Science.gov (United States)

Levin, Yingmei; Batra, Rajesh; Hesselink, Lambertus; Levy, Yuval

1997-01-01

Combinatorial topology, also known as "rubber sheet geometry", has extensive applications in geometry and analysis, many of which result from connections with the theory of differential equations. A link between topology and differential equations is vector fields. Recent developments in scientific visualization have shown that vector fields also play an important role in the analysis of second-order tensor fields. A second-order tensor field can be transformed into its eigensystem, namely, eigenvalues and their associated eigenvectors without loss of information content. Eigenvectors behave in a similar fashion to ordinary vectors with even simpler topological structures due to their sign indeterminacy. Incorporating information about eigenvectors and eigenvalues in a display technique known as hyperstreamlines reveals the structure of a tensor field. The simplify and often complex tensor field and to capture its important features, the tensor is decomposed into an isotopic tensor and a deviator. A tensor field and its deviator share the same set of eigenvectors, and therefore they have a similar topological structure. A a deviator determines the properties of a tensor field, while the isotopic part provides a uniform bias. Degenerate points are basic constituents of tensor fields. In 2-D tensor fields, there are only two types of degenerate points; while in 3-D, the degenerate points can be characterized in a Q'-R' plane. Compressible and incompressible flows share similar topological feature due to the similarity of their deviators. In the case of the deformation tensor, the singularities of its deviator represent the area of vortex core in the field. In turbulent flows, the similarities and differences of the topology of the deformation and the Reynolds stress tensors reveal that the basic addie-viscosity assuptions have their validity in turbulence modeling under certain conditions.

Towards overcoming the Monte Carlo sign problem with tensor networks

Directory of Open Access Journals (Sweden)

Bañuls Mari Carmen

2017-01-01

Full Text Available The study of lattice gauge theories with Monte Carlo simulations is hindered by the infamous sign problem that appears under certain circumstances, in particular at non-zero chemical potential. So far, there is no universal method to overcome this problem. However, recent years brought a new class of non-perturbative Hamiltonian techniques named tensor networks, where the sign problem is absent. In previous work, we have demonstrated that this approach, in particular matrix product states in 1+1 dimensions, can be used to perform precise calculations in a lattice gauge theory, the massless and massive Schwinger model. We have computed the mass spectrum of this theory, its thermal properties and real-time dynamics. In this work, we review these results and we extend our calculations to the case of two flavours and non-zero chemical potential. We are able to reliably reproduce known analytical results for this model, thus demonstrating that tensor networks can tackle the sign problem of a lattice gauge theory at finite density.

Calculation of the NMR chemical shift for a 4d1 system in a strong crystal field environment of trigonal symmetry with a threefold axis of quantization

International Nuclear Information System (INIS)

Ahn, Sang Woon; Oh, Se Woung; Ro, Seung Woo

1986-01-01

The NMR chemical shift arising from 4d electron angular momentum and 4d electron angular momentum and 4d electron spin dipolar-nuclear spin angular momentum interactions for a 4d 1 system in a strong crystal field environment of trigonal symmetry, where the threefold axis is chosen to be the axis of quantization axis, has been examined. A general expression using the nonmultipole expansion method (exact method) is derived for the NMR chemical shift. From this expression all the multipolar terms are determined. we observe that along the (100), (010), (110), and (111) axes the NMR chemical shifts are positive while along the (001) axis, it is negative. We observe that the dipolar term (1/R 3 ) is the dominant contribution to the NMR chemical shift except for along the (111) axis. A comparison of the multipolar terms with the exact values shows also that the multipolar results are exactly in agreement with the exact values around R≥0.2 nm. The temperature dependence analysis on the NMR chemical shifts may imply that along the (111) axis the contribution to the NMR chemical shift is dominantly pseudo contact interaction. Separation of the contributions of the Fermi and the pseudo contact interactions would correctly imply that the dipolar interaction is the dominant contribution to the NMR chemical shifts along the (100), (010), (001), and (110) axes, but along the (111) axis the Fermi contact interaction is incorrectly the dominant contribution to the NMR chemical shift. (Author)

Protein backbone and sidechain torsion angles predicted from NMR chemical shifts using artificial neural networks

Energy Technology Data Exchange (ETDEWEB)

Shen Yang; Bax, Ad, E-mail: bax@nih.gov [National Institutes of Health, Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases (United States)

2013-07-15

A new program, TALOS-N, is introduced for predicting protein backbone torsion angles from NMR chemical shifts. The program relies far more extensively on the use of trained artificial neural networks than its predecessor, TALOS+. Validation on an independent set of proteins indicates that backbone torsion angles can be predicted for a larger, {>=}90 % fraction of the residues, with an error rate smaller than ca 3.5 %, using an acceptance criterion that is nearly two-fold tighter than that used previously, and a root mean square difference between predicted and crystallographically observed ({phi}, {psi}) torsion angles of ca 12 Masculine-Ordinal-Indicator . TALOS-N also reports sidechain {chi}{sup 1} rotameric states for about 50 % of the residues, and a consistency with reference structures of 89 %. The program includes a neural network trained to identify secondary structure from residue sequence and chemical shifts.

Random SU(2) invariant tensors

Science.gov (United States)

Li, Youning; Han, Muxin; Ruan, Dong; Zeng, Bei

2018-04-01

SU(2) invariant tensors are states in the (local) SU(2) tensor product representation but invariant under the global group action. They are of importance in the study of loop quantum gravity. A random tensor is an ensemble of tensor states. An average over the ensemble is carried out when computing any physical quantities. The random tensor exhibits a phenomenon known as ‘concentration of measure’, which states that for any bipartition the average value of entanglement entropy of its reduced density matrix is asymptotically the maximal possible as the local dimensions go to infinity. We show that this phenomenon is also true when the average is over the SU(2) invariant subspace instead of the entire space for rank-n tensors in general. It is shown in our earlier work Li et al (2017 New J. Phys. 19 063029) that the subleading correction of the entanglement entropy has a mild logarithmic divergence when n  =  4. In this paper, we show that for n  >  4 the subleading correction is not divergent but a finite number. In some special situation, the number could be even smaller than 1/2, which is the subleading correction of random state over the entire Hilbert space of tensors.

Spherical Tensor Calculus for Local Adaptive Filtering

Science.gov (United States)

Reisert, Marco; Burkhardt, Hans

In 3D image processing tensors play an important role. While rank-1 and rank-2 tensors are well understood and commonly used, higher rank tensors are rare. This is probably due to their cumbersome rotation behavior which prevents a computationally efficient use. In this chapter we want to introduce the notion of a spherical tensor which is based on the irreducible representations of the 3D rotation group. In fact, any ordinary cartesian tensor can be decomposed into a sum of spherical tensors, while each spherical tensor has a quite simple rotation behavior. We introduce so called tensorial harmonics that provide an orthogonal basis for spherical tensor fields of any rank. It is just a generalization of the well known spherical harmonics. Additionally we propose a spherical derivative which connects spherical tensor fields of different degree by differentiation. Based on the proposed theory we present two applications. We propose an efficient algorithm for dense tensor voting in 3D, which makes use of tensorial harmonics decomposition of the tensor-valued voting field. In this way it is possible to perform tensor voting by linear-combinations of convolutions in an efficient way. Secondly, we propose an anisotropic smoothing filter that uses a local shape and orientation adaptive filter kernel which can be computed efficiently by the use spherical derivatives.

Improved tensor multiplets

International Nuclear Information System (INIS)

Wit, B. de; Rocek, M.

1982-01-01

We construct a conformally invariant theory of the N = 1 supersymmetric tensor gauge multiplet and discuss the situation in N = 2. We show that our results give rise to the recently proposed variant of Poincare supergravity, and provide the complete tensor calculus for the theory. Finally, we argue that this theory cannot be quantized sensibly. (orig.)

The evolution of tensor polarization

International Nuclear Information System (INIS)

Huang, H.; Lee, S.Y.; Ratner, L.

1993-01-01

By using the equation of motion for the vector polarization, the spin transfer matrix for spin tensor polarization, the spin transfer matrix for spin tensor polarization is derived. The evolution equation for the tensor polarization is studied in the presence of an isolate spin resonance and in the presence of a spin rotor, or snake

Tensor algebra and tensor analysis for engineers with applications to continuum mechanics

CERN Document Server

Itskov, Mikhail

2015-01-01

This is the fourth and revised edition of a well-received book that aims at bridging the gap between the engineering course of tensor algebra on the one side and the mathematical course of classical linear algebra on the other side. In accordance with the contemporary way of scientific publications, a modern absolute tensor notation is preferred throughout. The book provides a comprehensible exposition of the fundamental mathematical concepts of tensor calculus and enriches the presented material with many illustrative examples. In addition, the book also includes advanced chapters dealing with recent developments in the theory of isotropic and anisotropic tensor functions and their applications to continuum mechanics. Hence, this monograph addresses graduate students as well as scientists working in this field. In each chapter numerous exercises are included, allowing for self-study and intense practice. Solutions to the exercises are also provided.

Tensor Calculus: Unlearning Vector Calculus

Science.gov (United States)

Lee, Wha-Suck; Engelbrecht, Johann; Moller, Rita

2018-01-01

Tensor calculus is critical in the study of the vector calculus of the surface of a body. Indeed, tensor calculus is a natural step-up for vector calculus. This paper presents some pitfalls of a traditional course in vector calculus in transitioning to tensor calculus. We show how a deeper emphasis on traditional topics such as the Jacobian can…

Terahertz spectroscopy of shift currents resulting from asymmetric (110)-oriented GaAs/AlGaAs quantum wells

International Nuclear Information System (INIS)

Priyadarshi, Shekhar; Leidinger, Markus; Pierz, Klaus; Racu, Ana M.; Siegner, Uwe; Bieler, Mark; Dawson, Philip

2009-01-01

We report the observation and the study of an additional shift current tensor element in (110)-oriented GaAs quantum wells, which arises from an out-of-plane asymmetry of the quantum well structure. The current resulting from this tensor element is optically induced with 150 fs laser pulses and detected by measuring the simultaneously emitted terahertz radiation. This terahertz spectroscopy of shift currents is a powerful technique for symmetry investigations, which shows, for example, that our nominally symmetric (110)-oriented GaAs/AlGaAs quantum wells grown by molecular beam epitaxy are in reality asymmetric structures with different right and left interfaces.

Link prediction via generalized coupled tensor factorisation

DEFF Research Database (Denmark)

Ermiş, Beyza; Evrim, Acar Ataman; Taylan Cemgil, A.

2012-01-01

and higher-order tensors. We propose to use an approach based on probabilistic interpretation of tensor factorisation models, i.e., Generalised Coupled Tensor Factorisation, which can simultaneously fit a large class of tensor models to higher-order tensors/matrices with com- mon latent factors using...... different loss functions. Numerical experiments demonstrate that joint analysis of data from multiple sources via coupled factorisation improves the link prediction performance and the selection of right loss function and tensor model is crucial for accurately predicting missing links....

Accuracy of chemical shift MR imaging in diagnosing indeterminate bone marrow lesions in the pelvis: review of a single institution's experience

International Nuclear Information System (INIS)

Kohl, Chad A.; Chivers, F.S.; Lorans, Roxanne; Roberts, Catherine C.; Kransdorf, Mark J.

2014-01-01

To re-assess the accuracy of chemical shift imaging in diagnosing indeterminate bone marrow lesions as benign or malignant. We retrospectively reviewed our experience with MR imaging of the pelvis to assess the accuracy of chemical shift imaging in distinguishing benign from malignant bone lesions. Two musculoskeletal radiologists retrospectively reviewed all osseous lesions biopsied since 2006, when chemical shift imaging was added to our routine pelvic imaging protocol. Study inclusion criteria required (1) MR imaging of an indeterminate bone marrow lesion about the pelvis and (2) subsequent histologic confirmation. The study group included 50 patients (29 male, 21 female) with an average age of 67 years (range, 41-89 years). MR imaging results were evaluated using biopsy results as the ''gold standard.'' There were 27 malignant and 23 benign lesions. Chemical shift imaging using an opposed-phase signal loss criteria of less than 20 % to indicate a malignant lesion, correctly diagnosed 27/27 malignant lesions and 14/23 benign lesions, yielding a 100 % sensitivity, 61 % specificity, 75 % PPV, 100 % NPV, and 82 % accuracy. The area under the receiver operator characteristic (ROC) curve was 0.88. The inter-rater and intra-rater agreement K values were both 1.0. Chemical shift imaging is a useful adjunct MR technique to characterize focal and diffuse marrow abnormalities on routine non-contrast pelvic imaging. It is highly sensitive in identifying malignant disease. Despite its lower specificity, the need for biopsy could be eliminated in more than 60 % of patients with benign disease. (orig.)

Comparison of experimental and DFT-calculated NMR chemical shifts of 2-amino and 2-hydroxyl substituted phenyl benzimidazoles, benzoxazoles and benzothiazoles in four solvents using the IEF-PCM solvation model.

Science.gov (United States)

Pierens, Gregory K; Venkatachalam, T K; Reutens, David C

2016-04-01

A comparative study of experimental and calculated NMR chemical shifts of six compounds comprising 2-amino and 2-hydroxy phenyl benzoxazoles/benzothiazoles/benzimidazoles in four solvents is reported. The benzimidazoles showed interesting spectral characteristics, which are discussed. The proton and carbon chemical shifts were similar for all solvents. The largest chemical shift deviations were observed in benzene. The chemical shifts were calculated with density functional theory using a suite of four functionals and basis set combinations. The calculated chemical shifts revealed a good match to the experimentally observed values in most of the solvents. The mean absolute error was used as the primary metric. The use of an additional metric is suggested, which is based on the order of chemical shifts. The DP4 probability measures were also used to compare the experimental and calculated chemical shifts for each compound in the four solvents. Copyright © 2015 John Wiley & Sons, Ltd. Copyright © 2015 John Wiley & Sons, Ltd.

Energy-momentum tensor of the electromagnetic field

International Nuclear Information System (INIS)

Horndeski, G.W.; Wainwright, J.

1977-01-01

In this paper we investigate the energy-momentum tensor of the most general second-order vector-tensor theory of gravitation and electromagnetism which has field equations which are (i) derivable from a variational principle, (ii) consistent with the notion of conservation of charge, and (iii) compatible with Maxwell's equations in a flat space. This energy-momentum tensor turns out to be quadratic in the first partial derivatives of the electromagnetic field tensor and depends upon the curvature tensor. The asymptotic behavior of this energy-momentum tensor is examined for solutions to Maxwell's equations in Minkowski space, and it is demonstrated that this energy-momentum tensor predicts regions of negative energy density in the vicinity of point sources

Protein energetic conformational analysis from NMR chemical shifts (PECAN) and its use in determining secondary structural elements

Energy Technology Data Exchange (ETDEWEB)

Eghbalnia, Hamid R.; Wang Liya; Bahrami, Arash [National Magnetic Resonance Facility at Madison, Biochemistry Department (United States); Assadi, Amir [University of Wisconsin-Madison, Mathematics Department (United States); Markley, John L. [National Magnetic Resonance Facility at Madison, Biochemistry Department (United States)], E-mail: eghbalni@nmrfam.wisc.edu

2005-05-15

We present an energy model that combines information from the amino acid sequence of a protein and available NMR chemical shifts for the purposes of identifying low energy conformations and determining elements of secondary structure. The model ('PECAN', Protein Energetic Conformational Analysis from NMR chemical shifts) optimizes a combination of sequence information and residue-specific statistical energy function to yield energetic descriptions most favorable to predicting secondary structure. Compared to prior methods for secondary structure determination, PECAN provides increased accuracy and range, particularly in regions of extended structure. Moreover, PECAN uses the energetics to identify residues located at the boundaries between regions of predicted secondary structure that may not fit the stringent secondary structure class definitions. The energy model offers insights into the local energetic patterns that underlie conformational preferences. For example, it shows that the information content for defining secondary structure is localized about a residue and reaches a maximum when two residues on either side are considered. The current release of the PECAN software determines the well-defined regions of secondary structure in novel proteins with assigned chemical shifts with an overall accuracy of 90%, which is close to the practical limit of achievable accuracy in classifying the states.

Protein energetic conformational analysis from NMR chemical shifts (PECAN) and its use in determining secondary structural elements

International Nuclear Information System (INIS)

Eghbalnia, Hamid R.; Wang Liya; Bahrami, Arash; Assadi, Amir; Markley, John L.

2005-01-01

We present an energy model that combines information from the amino acid sequence of a protein and available NMR chemical shifts for the purposes of identifying low energy conformations and determining elements of secondary structure. The model ('PECAN', Protein Energetic Conformational Analysis from NMR chemical shifts) optimizes a combination of sequence information and residue-specific statistical energy function to yield energetic descriptions most favorable to predicting secondary structure. Compared to prior methods for secondary structure determination, PECAN provides increased accuracy and range, particularly in regions of extended structure. Moreover, PECAN uses the energetics to identify residues located at the boundaries between regions of predicted secondary structure that may not fit the stringent secondary structure class definitions. The energy model offers insights into the local energetic patterns that underlie conformational preferences. For example, it shows that the information content for defining secondary structure is localized about a residue and reaches a maximum when two residues on either side are considered. The current release of the PECAN software determines the well-defined regions of secondary structure in novel proteins with assigned chemical shifts with an overall accuracy of 90%, which is close to the practical limit of achievable accuracy in classifying the states

Dynamic Stark shift and alignment-to-orientation conversion

International Nuclear Information System (INIS)

Kuntz, Matthew C.; Hilborn, Robert C.; Spencer, Alison M.

2002-01-01

We have observed alignment-to-orientation conversion in the (5d6p) 1 P state of atomic barium due to the combined effects of a static Zeeman shift and a dynamic Stark shift associated with the electric field of a pulsed laser beam. The measurements yield a value for the frequency-dependent tensor polarizability of the state in reasonable agreement with a simple perturbation theory calculation. With a tunable laser producing the dynamic Stark shift, we can both enhance the magnitude of the effect by tuning close to a resonance and reverse the sign of the orientation by tuning above or below the resonance. This method of producing an oriented atomic state is quite general, and with easily available field strengths can produce large orientations

15N NMR studies of layered nitride superconductor LixZrNCl

International Nuclear Information System (INIS)

Tou, H.; Oshiro, S.; Kotegawa, H.; Taguchi, Y.; Kishiume, Y.; Kasahara, Y.; Iwasa, Y.

2010-01-01

NMR measurements were carried out on pristine ZrNCl and Li x ZrNCl. From the 15 N-Knight shift study, the isotropic Knight shift, the traceless chemical (orbital) shift tensor and the traceless Knight shift tensor were determined as K iso = -71 ppm, (σ 1 , σ 2 , σ 3 ) = (-55, -55, 110) ppm and (K 1 , K 2 , K 3 ) = (48, 48, -96) ppm, respectively. In the superconducting state, the fractional change of the 15 N NMR shift for H-parallel ab was observed, evidencing that the pairing symmetry is a spin-singlet state.

A new Weyl-like tensor of geometric origin

Science.gov (United States)

Vishwakarma, Ram Gopal

2018-04-01

A set of new tensors of purely geometric origin have been investigated, which form a hierarchy. A tensor of a lower rank plays the role of the potential for the tensor of one rank higher. The tensors have interesting mathematical and physical properties. The highest rank tensor of the hierarchy possesses all the geometrical properties of the Weyl tensor.

Tensor calculus for physics a concise guide

CERN Document Server

Neuenschwander, Dwight E

2015-01-01

Understanding tensors is essential for any physics student dealing with phenomena where causes and effects have different directions. A horizontal electric field producing vertical polarization in dielectrics; an unbalanced car wheel wobbling in the vertical plane while spinning about a horizontal axis; an electrostatic field on Earth observed to be a magnetic field by orbiting astronauts—these are some situations where physicists employ tensors. But the true beauty of tensors lies in this fact: When coordinates are transformed from one system to another, tensors change according to the same rules as the coordinates. Tensors, therefore, allow for the convenience of coordinates while also transcending them. This makes tensors the gold standard for expressing physical relationships in physics and geometry. Undergraduate physics majors are typically introduced to tensors in special-case applications. For example, in a classical mechanics course, they meet the "inertia tensor," and in electricity and magnetism...

Seamless warping of diffusion tensor fields

DEFF Research Database (Denmark)

Xu, Dongrong; Hao, Xuejun; Bansal, Ravi

2008-01-01

To warp diffusion tensor fields accurately, tensors must be reoriented in the space to which the tensors are warped based on both the local deformation field and the orientation of the underlying fibers in the original image. Existing algorithms for warping tensors typically use forward mapping...... of seams, including voxels in which the deformation is extensive. Backward mapping, however, cannot reorient tensors in the template space because information about the directional orientation of fiber tracts is contained in the original, unwarped imaging space only, and backward mapping alone cannot...... transfer that information to the template space. To combine the advantages of forward and backward mapping, we propose a novel method for the spatial normalization of diffusion tensor (DT) fields that uses a bijection (a bidirectional mapping with one-to-one correspondences between image spaces) to warp DT...

207Pb and 205Tl NMR on Perovskite Type Crystals APbX3 (A = Cs, Tl, X = Br, I)

Science.gov (United States)

Sharma, Surendra; Weiden, Norbert; Weiss, Alarich

1987-11-01

By 205Tl and 207Pb NM R the chemical shift in polycrystalline samples of binary halides AX, BX2 and ternary halides ABX3 (A = Cs, Tl; B = Pb; X = Br, I) was studied at room temperature. The chemical shift tensors δ ( 205Tl) and δ (207Pb) were determined in magnitude and orientation on single crystals of the orthorhombic TlPbI3. The components of the δ(205Tl) tensor are δx (205Tl) || a = 611ppm; δy (205Tl) || b = 680 ppm; δZ(205Tl) || c = 1329 ppm; δiso(205Tl) = 873.3 ppm (with respect to 3.4 molar aqueous solution of TlOOCCH3). The chemical shift tensor of 207Pb in TlPbI3 shows two orientations. One of them is: δx (207Pb) = 3760 ppm, inclined 30° from b towards c, δy(207Pb) || a = 3485 ppm, δz(207Pb) = 2639 ppm inclined 120° from b towards c. δiso(207Pb) = 3295 ppm (with respect to saturated aqueous solution of Pb(NO3)2). The results are discussed with respect to the crystal structure and a model to explain orientation and anisotropy of the tensors δ(205Tl) and δ(207Pb) in TlPbI3 is proposed. In the system CsPbBr3-x Ix δ(207Pb) was studied on polycrystalline samples. The chemical shift increases with increasing x and negative excess shift is observed.

Application of diffusion tensor imaging in neurosurgery; Anwendung der Diffusions-Tensor-Bildgebung in der Neurochirurgie

Energy Technology Data Exchange (ETDEWEB)

Saur, R. [Sektion fuer Experimentelle Kernspinresonanz des ZNS, Abt. Neuroradiologie, Universitaetsklinikum Tuebingen (Germany); Augenklinik des Universitaetsklinikums Tuebingen (Germany); Klinik fuer Psychiatrie und Psychotherapie des Universitaetsklinikums Tuebingen (Germany); Gharabaghi, A. [Klinik fuer Neurochirurgie des Universitaetsklinikums Tuebingen (Germany); Erb, M. [Sektion fuer Experimentelle Kernspinresonanz des ZNS, Abt. Neuroradiologie, Universitaetsklinikum Tuebingen (Germany)

2007-07-01

Knowledge about integrity and location of fibre tracts arising from eloquent cortical areas is important to plan neurosurgical interventions and to allow maximization of resection of pathological tissue while preserving vital white matter tracts. Diffusion Tensor Imaging (DTI) is so far the only method to get preoperatively an impression of the individual complexity of nerve bundles. Thereby nerve fibres are not mapped directly. They are derived indirectly by analysis of the directional distribution of diffusion of water molecules which is influenced mainly by large fibre tracts. From acquisition to reconstruction and visualisation of the fibre tracts many representational stages and working steps have to be passed. Exact knowledge about problems of Diffusion Imaging is important for interpretation of the results. Particularly, brain tumor edema, intraoperative brain shift, MR-artefacts and limitations of the mathematical models and algorithms challenge DTI-developers and applicants. (orig.)

Tensor norms and operator ideals

CERN Document Server

Defant, A; Floret, K

1992-01-01

The three chapters of this book are entitled Basic Concepts, Tensor Norms, and Special Topics. The first may serve as part of an introductory course in Functional Analysis since it shows the powerful use of the projective and injective tensor norms, as well as the basics of the theory of operator ideals. The second chapter is the main part of the book: it presents the theory of tensor norms as designed by Grothendieck in the Resumé and deals with the relation between tensor norms and operator ideals. The last chapter deals with special questions. Each section is accompanied by a series of exer

pH-Dependent spin state population and 19F NMR chemical shift via remote ligand protonation in an iron(ii) complex.

Science.gov (United States)

Gaudette, Alexandra I; Thorarinsdottir, Agnes E; Harris, T David

2017-11-30

An Fe II complex that features a pH-dependent spin state population, by virtue of a variable ligand protonation state, is described. This behavior leads to a highly pH-dependent 19 F NMR chemical shift with a sensitivity of 13.9(5) ppm per pH unit at 37 °C, thereby demonstrating the potential utility of the complex as a 19 F chemical shift-based pH sensor.

Shape anisotropy: tensor distance to anisotropy measure

Science.gov (United States)

Weldeselassie, Yonas T.; El-Hilo, Saba; Atkins, M. S.

2011-03-01

Fractional anisotropy, defined as the distance of a diffusion tensor from its closest isotropic tensor, has been extensively studied as quantitative anisotropy measure for diffusion tensor magnetic resonance images (DT-MRI). It has been used to reveal the white matter profile of brain images, as guiding feature for seeding and stopping in fiber tractography and for the diagnosis and assessment of degenerative brain diseases. Despite its extensive use in DT-MRI community, however, not much attention has been given to the mathematical correctness of its derivation from diffusion tensors which is achieved using Euclidean dot product in 9D space. But, recent progress in DT-MRI has shown that the space of diffusion tensors does not form a Euclidean vector space and thus Euclidean dot product is not appropriate for tensors. In this paper, we propose a novel and robust rotationally invariant diffusion anisotropy measure derived using the recently proposed Log-Euclidean and J-divergence tensor distance measures. An interesting finding of our work is that given a diffusion tensor, its closest isotropic tensor is different for different tensor distance metrics used. We demonstrate qualitatively that our new anisotropy measure reveals superior white matter profile of DT-MR brain images and analytically show that it has a higher signal to noise ratio than fractional anisotropy.

Tensors and their applications

CERN Document Server

Islam, Nazrul

2006-01-01

About the Book: The book is written is in easy-to-read style with corresponding examples. The main aim of this book is to precisely explain the fundamentals of Tensors and their applications to Mechanics, Elasticity, Theory of Relativity, Electromagnetic, Riemannian Geometry and many other disciplines of science and engineering, in a lucid manner. The text has been explained section wise, every concept has been narrated in the form of definition, examples and questions related to the concept taught. The overall package of the book is highly useful and interesting for the people associated with the field. Contents: Preliminaries Tensor Algebra Metric Tensor and Riemannian Metric Christoffel`s Symbols and Covariant Differentiation Riemann-Christoffel Tensor The e-Systems and the Generalized Krönecker Deltas Geometry Analytical Mechanics Curvature of a Curve, Geodesic Parallelism of Vectors Ricci`s Coefficients of Rotation and Congruence Hyper Surfaces

Tensor Completion Algorithms in Big Data Analytics

OpenAIRE

Song, Qingquan; Ge, Hancheng; Caverlee, James; Hu, Xia

2017-01-01

Tensor completion is a problem of filling the missing or unobserved entries of partially observed tensors. Due to the multidimensional character of tensors in describing complex datasets, tensor completion algorithms and their applications have received wide attention and achievement in areas like data mining, computer vision, signal processing, and neuroscience. In this survey, we provide a modern overview of recent advances in tensor completion algorithms from the perspective of big data an...

Efficient MATLAB computations with sparse and factored tensors.

Energy Technology Data Exchange (ETDEWEB)

Bader, Brett William; Kolda, Tamara Gibson (Sandia National Lab, Livermore, CA)

2006-12-01

In this paper, the term tensor refers simply to a multidimensional or N-way array, and we consider how specially structured tensors allow for efficient storage and computation. First, we study sparse tensors, which have the property that the vast majority of the elements are zero. We propose storing sparse tensors using coordinate format and describe the computational efficiency of this scheme for various mathematical operations, including those typical to tensor decomposition algorithms. Second, we study factored tensors, which have the property that they can be assembled from more basic components. We consider two specific types: a Tucker tensor can be expressed as the product of a core tensor (which itself may be dense, sparse, or factored) and a matrix along each mode, and a Kruskal tensor can be expressed as the sum of rank-1 tensors. We are interested in the case where the storage of the components is less than the storage of the full tensor, and we demonstrate that many elementary operations can be computed using only the components. All of the efficiencies described in this paper are implemented in the Tensor Toolbox for MATLAB.

Reciprocal mass tensor : a general form

International Nuclear Information System (INIS)

Roy, C.L.

1978-01-01

Using the results of earlier treatment of wave packets, a general form of reciprocal mass tensor has been obtained. The elements of this tensor are seen to be dependent on momentum as well as space coordinates of the particle under consideration. The conditions under which the tensor would reduce to the usual space-independent form, are discussed and the impact of the space-dependence of this tensor on the motion of Bloch electrons, is examined. (author)

A new deteriorated energy-momentum tensor

International Nuclear Information System (INIS)

Duff, M.J.

1982-01-01

The stress-tensor of a scalar field theory is not unique because of the possibility of adding an 'improvement term'. In supersymmetric field theories the stress-tensor will appear in a super-current multiplet along with the sypersymmetry current. The general question of the supercurrent multiplet for arbitrary deteriorated stress tensors and their relationship to supercurrent multiplets for models with gauge antisymmetric tensors is answered for various models of N = 1, 2 and 4 supersymmetry. (U.K.)

Antisymmetric tensor generalizations of affine vector fields.

Science.gov (United States)

Houri, Tsuyoshi; Morisawa, Yoshiyuki; Tomoda, Kentaro

2016-02-01

Tensor generalizations of affine vector fields called symmetric and antisymmetric affine tensor fields are discussed as symmetry of spacetimes. We review the properties of the symmetric ones, which have been studied in earlier works, and investigate the properties of the antisymmetric ones, which are the main theme in this paper. It is shown that antisymmetric affine tensor fields are closely related to one-lower-rank antisymmetric tensor fields which are parallelly transported along geodesics. It is also shown that the number of linear independent rank- p antisymmetric affine tensor fields in n -dimensions is bounded by ( n + 1)!/ p !( n - p )!. We also derive the integrability conditions for antisymmetric affine tensor fields. Using the integrability conditions, we discuss the existence of antisymmetric affine tensor fields on various spacetimes.

(Ln-bar, g)-spaces. Special tensor fields

International Nuclear Information System (INIS)

Manoff, S.; Dimitrov, B.

1998-01-01

The Kronecker tensor field, the contraction tensor field, as well as the multi-Kronecker and multi-contraction tensor fields are determined and the action of the covariant differential operator, the Lie differential operator, the curvature operator, and the deviation operator on these tensor fields is established. The commutation relations between the operators Sym and Asym and the covariant and Lie differential operators are considered acting on symmetric and antisymmetric tensor fields over (L n bar, g)-spaces

The Riemann-Lovelock Curvature Tensor

OpenAIRE

Kastor, David

2012-01-01

In order to study the properties of Lovelock gravity theories in low dimensions, we define the kth-order Riemann-Lovelock tensor as a certain quantity having a total 4k-indices, which is kth-order in the Riemann curvature tensor and shares its basic algebraic and differential properties. We show that the kth-order Riemann-Lovelock tensor is determined by its traces in dimensions 2k \\le D

The Physical Interpretation of the Lanczos Tensor

OpenAIRE

Roberts, Mark D.

1999-01-01

The field equations of general relativity can be written as first order differential equations in the Weyl tensor, the Weyl tensor in turn can be written as a first order differential equation in a three index tensor called the Lanczos tensor. The Lanczos tensor plays a similar role in general relativity to that of the vector potential in electro-magnetic theory. The Aharonov-Bohm effect shows that when quantum mechanics is applied to electro-magnetic theory the vector potential is dynamicall...

Real-time object recognition in multidimensional images based on joined extended structural tensor and higher-order tensor decomposition methods

Science.gov (United States)

Cyganek, Boguslaw; Smolka, Bogdan

2015-02-01

In this paper a system for real-time recognition of objects in multidimensional video signals is proposed. Object recognition is done by pattern projection into the tensor subspaces obtained from the factorization of the signal tensors representing the input signal. However, instead of taking only the intensity signal the novelty of this paper is first to build the Extended Structural Tensor representation from the intensity signal that conveys information on signal intensities, as well as on higher-order statistics of the input signals. This way the higher-order input pattern tensors are built from the training samples. Then, the tensor subspaces are built based on the Higher-Order Singular Value Decomposition of the prototype pattern tensors. Finally, recognition relies on measurements of the distance of a test pattern projected into the tensor subspaces obtained from the training tensors. Due to high-dimensionality of the input data, tensor based methods require high memory and computational resources. However, recent achievements in the technology of the multi-core microprocessors and graphic cards allows real-time operation of the multidimensional methods as is shown and analyzed in this paper based on real examples of object detection in digital images.

3D reconstruction of tensors and vectors

International Nuclear Information System (INIS)

Defrise, Michel; Gullberg, Grant T.

2005-01-01

Here we have developed formulations for the reconstruction of 3D tensor fields from planar (Radon) and line-integral (X-ray) projections of 3D vector and tensor fields. Much of the motivation for this work is the potential application of MRI to perform diffusion tensor tomography. The goal is to develop a theory for the reconstruction of both Radon planar and X-ray or line-integral projections because of the flexibility of MRI to obtain both of these type of projections in 3D. The development presented here for the linear tensor tomography problem provides insight into the structure of the nonlinear MRI diffusion tensor inverse problem. A particular application of tensor imaging in MRI is the potential application of cardiac diffusion tensor tomography for determining in vivo cardiac fiber structure. One difficulty in the cardiac application is the motion of the heart. This presents a need for developing future theory for tensor tomography in a motion field. This means developing a better understanding of the MRI signal for diffusion processes in a deforming media. The techniques developed may allow the application of MRI tensor tomography for the study of structure of fiber tracts in the brain, atherosclerotic plaque, and spine in addition to fiber structure in the heart. However, the relations presented are also applicable to other fields in medical imaging such as diffraction tomography using ultrasound. The mathematics presented can also be extended to exponential Radon transform of tensor fields and to other geometric acquisitions such as cone beam tomography of tensor fields

Non-Newtonian stress tensor and thermal conductivity tensor in granular plane shear flow

Science.gov (United States)

Alam, Meheboob; Saha, Saikat

2014-11-01

The non-Newtonian stress tensor and the heat flux in the plane shear flow of smooth inelastic disks are analysed from the Grad-level moment equations using the anisotropic Gaussian as a reference. Closed-form expressions for shear viscosity, pressure, first normal stress difference (N1) and the dissipation rate are given as functions of (i) the density or the area fraction (ν), (ii) the restitution coefficient (e), (iii) the dimensionless shear rate (R), (iv) the temperature anisotropy [ η, the difference between the principal eigenvalues of the second moment tensor] and (v) the angle (ϕ) between the principal directions of the shear tensor and the second moment tensor. Particle simulation data for a sheared hard-disk system is compared with theoretical results, with good agreement for p, μ and N1 over a large range of density. In contrast, the predictions from a Navier-Stokes order constitutive model are found to deviate significantly from both the simulation and the moment theory even at moderate values of e. We show that the gradient of the deviatoric part of the kinetic stress drives a heat current and the thermal conductivity is characterized by an anisotropic 2nd rank tensor for which explicit expressions are derived.

NMR chemical shift and J coupling parameterization and quantum mechanical reference spectrum simulation for selected nerve agent degradation products in aqueous conditions.

Science.gov (United States)

Koskela, Harri; Anđelković, Boban

2017-10-01

The spectral parameters of selected nerve agent degradation products relevant to the Chemical Weapons Convention, namely, ethyl methylphosphonate, isopropyl methylphosphonate, pinacolyl methylphosphonate and methylphosphonic acid, were studied in wide range of pH conditions and selected temperatures. The pH and temperature dependence of chemical shifts and J couplings was parameterized using Henderson-Hasselbalch-based functions. The obtained parameters allowed calculation of precise chemical shifts and J coupling constants in arbitrary pH conditions and typical measurement temperatures, thus facilitating quantum mechanical simulation of reference spectra in the chosen magnetic field strength for chemical verification. Copyright © 2017 John Wiley & Sons, Ltd. Copyright © 2017 John Wiley & Sons, Ltd.

Weyl tensors for asymmetric complex curvatures

International Nuclear Information System (INIS)

Oliveira, C.G.

Considering a second rank Hermitian field tensor and a general Hermitian connection the associated complex curvature tensor is constructed. The Weyl tensor that corresponds to this complex curvature is determined. The formalism is applied to the Weyl unitary field theory and to the Moffat gravitational theory. (Author) [pt

Tensor voting for robust color edge detection

OpenAIRE

Moreno, Rodrigo; García, Miguel Ángel; Puig, Domenec

2014-01-01

The final publication is available at Springer via http://dx.doi.org/10.1007/978-94-007-7584-8_9 This chapter proposes two robust color edge detection methods based on tensor voting. The first method is a direct adaptation of the classical tensor voting to color images where tensors are initialized with either the gradient or the local color structure tensor. The second method is based on an extension of tensor voting in which the encoding and voting processes are specifically tailored to ...

Should I use TensorFlow

OpenAIRE

Schrimpf, Martin

2016-01-01

Google's Machine Learning framework TensorFlow was open-sourced in November 2015 [1] and has since built a growing community around it. TensorFlow is supposed to be flexible for research purposes while also allowing its models to be deployed productively. This work is aimed towards people with experience in Machine Learning considering whether they should use TensorFlow in their environment. Several aspects of the framework important for such a decision are examined, such as the heterogenity,...

Dictionary-Based Tensor Canonical Polyadic Decomposition

Science.gov (United States)

Cohen, Jeremy Emile; Gillis, Nicolas

2018-04-01

To ensure interpretability of extracted sources in tensor decomposition, we introduce in this paper a dictionary-based tensor canonical polyadic decomposition which enforces one factor to belong exactly to a known dictionary. A new formulation of sparse coding is proposed which enables high dimensional tensors dictionary-based canonical polyadic decomposition. The benefits of using a dictionary in tensor decomposition models are explored both in terms of parameter identifiability and estimation accuracy. Performances of the proposed algorithms are evaluated on the decomposition of simulated data and the unmixing of hyperspectral images.

Bayesian regularization of diffusion tensor images

DEFF Research Database (Denmark)

Frandsen, Jesper; Hobolth, Asger; Østergaard, Leif

2007-01-01

Diffusion tensor imaging (DTI) is a powerful tool in the study of the course of nerve fibre bundles in the human brain. Using DTI, the local fibre orientation in each image voxel can be described by a diffusion tensor which is constructed from local measurements of diffusion coefficients along...... several directions. The measured diffusion coefficients and thereby the diffusion tensors are subject to noise, leading to possibly flawed representations of the three dimensional fibre bundles. In this paper we develop a Bayesian procedure for regularizing the diffusion tensor field, fully utilizing...

Energy-momentum tensor in the fermion-pairing model

International Nuclear Information System (INIS)

Kawati, S.; Miyata, H.

1980-01-01

The symmetric energy-momentum tensor for the self-interacting fermion theory (psi-barpsi) 2 is expressed in terms of the collective mode within the Hartree approximation. The divergent part of the energy-momentum tensor for the fermion theory induces an effective energy-momentum tensor for the collective mode, and this effective energy-momentum tensor automatically has the Callan-Coleman-Jackiw improved form. The renormalized energy-momentum tensor is structurally equivalent to the Callan-Coleman-Jackiw improved tensor for the Yukawa theory

Diffusion tensor imaging tensor shape analysis for assessment of regional white matter differences.

Science.gov (United States)

Middleton, Dana M; Li, Jonathan Y; Lee, Hui J; Chen, Steven; Dickson, Patricia I; Ellinwood, N Matthew; White, Leonard E; Provenzale, James M

2017-08-01

Purpose The purpose of this study was to investigate a novel tensor shape plot analysis technique of diffusion tensor imaging data as a means to assess microstructural differences in brain tissue. We hypothesized that this technique could distinguish white matter regions with different microstructural compositions. Methods Three normal canines were euthanized at seven weeks old. Their brains were imaged using identical diffusion tensor imaging protocols on a 7T small-animal magnetic resonance imaging system. We examined two white matter regions, the internal capsule and the centrum semiovale, each subdivided into an anterior and posterior region. We placed 100 regions of interest in each of the four brain regions. Eigenvalues for each region of interest triangulated onto tensor shape plots as the weighted average of three shape metrics at the plot's vertices: CS, CL, and CP. Results The distribution of data on the plots for the internal capsule differed markedly from the centrum semiovale data, thus confirming our hypothesis. Furthermore, data for the internal capsule were distributed in a relatively tight cluster, possibly reflecting the compact and parallel nature of its fibers, while data for the centrum semiovale were more widely distributed, consistent with the less compact and often crossing pattern of its fibers. This indicates that the tensor shape plot technique can depict data in similar regions as being alike. Conclusion Tensor shape plots successfully depicted differences in tissue microstructure and reflected the microstructure of individual brain regions. This proof of principle study suggests that if our findings are reproduced in larger samples, including abnormal white matter states, the technique may be useful in assessment of white matter diseases.

Level shift and charm mass: a test of asymptotic planarity

International Nuclear Information System (INIS)

Palmer, W.F.; Pinsky, S.S.; Shi, C.C.

1976-01-01

Level shifts and mixings away from exact exchange degeneracy are examined with respect to the ''asymptotic planarity'' predictions of Chew and Rosenzweig. It is found that the data in the J/sup P/ = 0 - , 1 - , and 2 + multiplets support neither the general shape nor the special relation proposed by Chew and Rosenzweig for the tensor and vector ''cylinder'' corrections

The Einstein tensor characterizing some Riemann spaces

International Nuclear Information System (INIS)

Rahman, M.S.

1993-07-01

A formal definition of the Einstein tensor is given. Mention is made of how this tensor plays a role of expressing certain conditions in a precise form. The cases of reducing the Einstein tensor to a zero tensor are studied on its merit. A lucid account of results, formulated as theorems, on Einstein symmetric and Einstein recurrent spaces is then presented. (author). 5 refs

Radiative corrections in a vector-tensor model

International Nuclear Information System (INIS)

Chishtie, F.; Gagne-Portelance, M.; Hanif, T.; Homayouni, S.; McKeon, D.G.C.

2006-01-01

In a recently proposed model in which a vector non-Abelian gauge field interacts with an antisymmetric tensor field, it has been shown that the tensor field possesses no physical degrees of freedom. This formal demonstration is tested by computing the one-loop contributions of the tensor field to the self-energy of the vector field. It is shown that despite the large number of Feynman diagrams in which the tensor field contributes, the sum of these diagrams vanishes, confirming that it is not physical. Furthermore, if the tensor field were to couple with a spinor field, it is shown at one-loop order that the spinor self-energy is not renormalizable, and hence this coupling must be excluded. In principle though, this tensor field does couple to the gravitational field

Transposes, L-Eigenvalues and Invariants of Third Order Tensors

OpenAIRE

Qi, Liqun

2017-01-01

Third order tensors have wide applications in mechanics, physics and engineering. The most famous and useful third order tensor is the piezoelectric tensor, which plays a key role in the piezoelectric effect, first discovered by Curie brothers. On the other hand, the Levi-Civita tensor is famous in tensor calculus. In this paper, we study third order tensors and (third order) hypermatrices systematically, by regarding a third order tensor as a linear operator which transforms a second order t...

Pressure dependence of backbone chemical shifts in the model peptides Ac-Gly-Gly-Xxx-Ala-NH2.

Science.gov (United States)

Erlach, Markus Beck; Koehler, Joerg; Crusca, Edson; Kremer, Werner; Munte, Claudia E; Kalbitzer, Hans Robert

2016-06-01

For a better understanding of nuclear magnetic resonance (NMR) detected pressure responses of folded as well as unstructured proteins the availability of data from well-defined model systems are indispensable. In this work we report the pressure dependence of chemical shifts of the backbone atoms (1)H(α), (13)C(α) and (13)C' in the protected tetrapeptides Ac-Gly-Gly-Xxx-Ala-NH2 (Xxx one of the 20 canonical amino acids). Contrary to expectation the chemical shifts of these nuclei have a nonlinear dependence on pressure in the range from 0.1 to 200 MPa. The polynomial pressure coefficients B 1 and B 2 are dependent on the type of amino acid studied. The coefficients of a given nucleus show significant linear correlations suggesting that the NMR observable pressure effects in the different amino acids have at least partly the same physical cause. In line with this observation the magnitude of the second order coefficients of nuclei being direct neighbors in the chemical structure are also weakly correlated.

Joint Tensor Feature Analysis For Visual Object Recognition.

Science.gov (United States)

Wong, Wai Keung; Lai, Zhihui; Xu, Yong; Wen, Jiajun; Ho, Chu Po

2015-11-01

Tensor-based object recognition has been widely studied in the past several years. This paper focuses on the issue of joint feature selection from the tensor data and proposes a novel method called joint tensor feature analysis (JTFA) for tensor feature extraction and recognition. In order to obtain a set of jointly sparse projections for tensor feature extraction, we define the modified within-class tensor scatter value and the modified between-class tensor scatter value for regression. The k-mode optimization technique and the L(2,1)-norm jointly sparse regression are combined together to compute the optimal solutions. The convergent analysis, computational complexity analysis and the essence of the proposed method/model are also presented. It is interesting to show that the proposed method is very similar to singular value decomposition on the scatter matrix but with sparsity constraint on the right singular value matrix or eigen-decomposition on the scatter matrix with sparse manner. Experimental results on some tensor datasets indicate that JTFA outperforms some well-known tensor feature extraction and selection algorithms.

Graded tensor calculus

International Nuclear Information System (INIS)

Scheunert, M.

1982-10-01

We develop a graded tensor calculus corresponding to arbitrary Abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the transpose, adjoint, and trace of a linear mapping, are generalized to the graded case and a multitude of canonical isomorphisms is presented. Moreover, the graded versions of the classical Lie algebras are introduced and some of their basic properties are described. (orig.)

Convenient method for resolving degeneracies due to symmetry of the magnetic susceptibility tensor and its application to pseudo contact shift-based protein-protein complex structure determination

Energy Technology Data Exchange (ETDEWEB)

Kobashigawa, Yoshihiro; Saio, Tomohide [Hokkaido University, Department of Structural Biology, Faculty of Advanced Life Science (Japan); Ushio, Masahiro [Hokkaido University, Graduate School of Life Science (Japan); Sekiguchi, Mitsuhiro [Astellas Pharma Inc., Analysis and Pharmacokinetics Research Labs, Department of Drug Discovery (Japan); Yokochi, Masashi; Ogura, Kenji; Inagaki, Fuyuhiko, E-mail: finagaki@pharm.hokudai.ac.jp [Hokkaido University, Department of Structural Biology, Faculty of Advanced Life Science (Japan)

2012-05-15

Pseudo contact shifts (PCSs) induced by paramagnetic lanthanide ions fixed in a protein frame provide long-range distance and angular information, and are valuable for the structure determination of protein-protein and protein-ligand complexes. We have been developing a lanthanide-binding peptide tag (hereafter LBT) anchored at two points via a peptide bond and a disulfide bond to the target proteins. However, the magnetic susceptibility tensor displays symmetry, which can cause multiple degenerated solutions in a structure calculation based solely on PCSs. Here we show a convenient method for resolving this degeneracy by changing the spacer length between the LBT and target protein. We applied this approach to PCS-based rigid body docking between the FKBP12-rapamycin complex and the mTOR FRB domain, and demonstrated that degeneracy could be resolved using the PCS restraints obtained from two-point anchored LBT with two different spacer lengths. The present strategy will markedly increase the usefulness of two-point anchored LBT for protein complex structure determination.

Convenient method for resolving degeneracies due to symmetry of the magnetic susceptibility tensor and its application to pseudo contact shift-based protein–protein complex structure determination

International Nuclear Information System (INIS)

Kobashigawa, Yoshihiro; Saio, Tomohide; Ushio, Masahiro; Sekiguchi, Mitsuhiro; Yokochi, Masashi; Ogura, Kenji; Inagaki, Fuyuhiko

2012-01-01

Pseudo contact shifts (PCSs) induced by paramagnetic lanthanide ions fixed in a protein frame provide long-range distance and angular information, and are valuable for the structure determination of protein–protein and protein–ligand complexes. We have been developing a lanthanide-binding peptide tag (hereafter LBT) anchored at two points via a peptide bond and a disulfide bond to the target proteins. However, the magnetic susceptibility tensor displays symmetry, which can cause multiple degenerated solutions in a structure calculation based solely on PCSs. Here we show a convenient method for resolving this degeneracy by changing the spacer length between the LBT and target protein. We applied this approach to PCS-based rigid body docking between the FKBP12-rapamycin complex and the mTOR FRB domain, and demonstrated that degeneracy could be resolved using the PCS restraints obtained from two-point anchored LBT with two different spacer lengths. The present strategy will markedly increase the usefulness of two-point anchored LBT for protein complex structure determination.

(Ln-bar, g)-spaces. Ordinary and tensor differentials

International Nuclear Information System (INIS)

Manoff, S.; Dimitrov, B.

1998-01-01

Different types of differentials as special cases of differential operators acting on tensor fields over (L n bar, g)-spaces are considered. The ordinary differential, the covariant differential as a special case of the covariant differential operator, and the Lie differential as a special case of the Lie differential operator are investigated. The tensor differential and its special types (Covariant tensor differential, and Lie tensor differential) are determined and their properties are discussed. Covariant symmetric and antisymmetric (external) tensor differentials, Lie symmetric, and Lie antisymmetric (external) tensor differentials are determined and considered over (L n bar, g)-spaces

Tensor network method for reversible classical computation

Science.gov (United States)

Yang, Zhi-Cheng; Kourtis, Stefanos; Chamon, Claudio; Mucciolo, Eduardo R.; Ruckenstein, Andrei E.

2018-03-01

We develop a tensor network technique that can solve universal reversible classical computational problems, formulated as vertex models on a square lattice [Nat. Commun. 8, 15303 (2017), 10.1038/ncomms15303]. By encoding the truth table of each vertex constraint in a tensor, the total number of solutions compatible with partial inputs and outputs at the boundary can be represented as the full contraction of a tensor network. We introduce an iterative compression-decimation (ICD) scheme that performs this contraction efficiently. The ICD algorithm first propagates local constraints to longer ranges via repeated contraction-decomposition sweeps over all lattice bonds, thus achieving compression on a given length scale. It then decimates the lattice via coarse-graining tensor contractions. Repeated iterations of these two steps gradually collapse the tensor network and ultimately yield the exact tensor trace for large systems, without the need for manual control of tensor dimensions. Our protocol allows us to obtain the exact number of solutions for computations where a naive enumeration would take astronomically long times.

Benchmarking Hydrogen and Carbon NMR Chemical Shifts at HF, DFT, and MP2 Levels.

Science.gov (United States)

Flaig, Denis; Maurer, Marina; Hanni, Matti; Braunger, Katharina; Kick, Leonhard; Thubauville, Matthias; Ochsenfeld, Christian

2014-02-11

An extensive study of error distributions for calculating hydrogen and carbon NMR chemical shifts at Hartree-Fock (HF), density functional theory (DFT), and Møller-Plesset second-order perturbation theory (MP2) levels is presented. Our investigation employs accurate CCSD(T)/cc-pVQZ calculations for providing reference data for 48 hydrogen and 40 carbon nuclei within an extended set of chemical compounds covering a broad range of the NMR scale with high relevance to chemical applications, especially in organic chemistry. Besides the approximations of HF, a variety of DFT functionals, and conventional MP2, we also present results with respect to a spin component-scaled MP2 (GIAO-SCS-MP2) approach. For each method, the accuracy is analyzed in detail for various basis sets, allowing identification of efficient combinations of method and basis set approximations.

Robust estimation of adaptive tensors of curvature by tensor voting.

Science.gov (United States)

Tong, Wai-Shun; Tang, Chi-Keung

2005-03-01

Although curvature estimation from a given mesh or regularly sampled point set is a well-studied problem, it is still challenging when the input consists of a cloud of unstructured points corrupted by misalignment error and outlier noise. Such input is ubiquitous in computer vision. In this paper, we propose a three-pass tensor voting algorithm to robustly estimate curvature tensors, from which accurate principal curvatures and directions can be calculated. Our quantitative estimation is an improvement over the previous two-pass algorithm, where only qualitative curvature estimation (sign of Gaussian curvature) is performed. To overcome misalignment errors, our improved method automatically corrects input point locations at subvoxel precision, which also rejects outliers that are uncorrectable. To adapt to different scales locally, we define the RadiusHit of a curvature tensor to quantify estimation accuracy and applicability. Our curvature estimation algorithm has been proven with detailed quantitative experiments, performing better in a variety of standard error metrics (percentage error in curvature magnitudes, absolute angle difference in curvature direction) in the presence of a large amount of misalignment noise.

On the concircular curvature tensor of Riemannian manifolds

International Nuclear Information System (INIS)

Rahman, M.S.; Lal, S.

1990-06-01

Definition of the concircular curvature tensor, Z hijk , along with Z-tensor, Z ij , is given and some properties of Z hijk are described. Tensors identical with Z hijk are shown. A necessary and sufficient condition that a Riemannian V n has zero Z-tensor is found. A number of theorems on concircular symmetric space, concircular recurrent space (Z n -space) and Z n -space with zero Z-tensor are deduced. (author). 6 refs

Glyph-Based Comparative Visualization for Diffusion Tensor Fields.

Science.gov (United States)

Zhang, Changgong; Schultz, Thomas; Lawonn, Kai; Eisemann, Elmar; Vilanova, Anna

2016-01-01

Diffusion Tensor Imaging (DTI) is a magnetic resonance imaging modality that enables the in-vivo reconstruction and visualization of fibrous structures. To inspect the local and individual diffusion tensors, glyph-based visualizations are commonly used since they are able to effectively convey full aspects of the diffusion tensor. For several applications it is necessary to compare tensor fields, e.g., to study the effects of acquisition parameters, or to investigate the influence of pathologies on white matter structures. This comparison is commonly done by extracting scalar information out of the tensor fields and then comparing these scalar fields, which leads to a loss of information. If the glyph representation is kept, simple juxtaposition or superposition can be used. However, neither facilitates the identification and interpretation of the differences between the tensor fields. Inspired by the checkerboard style visualization and the superquadric tensor glyph, we design a new glyph to locally visualize differences between two diffusion tensors by combining juxtaposition and explicit encoding. Because tensor scale, anisotropy type, and orientation are related to anatomical information relevant for DTI applications, we focus on visualizing tensor differences in these three aspects. As demonstrated in a user study, our new glyph design allows users to efficiently and effectively identify the tensor differences. We also apply our new glyphs to investigate the differences between DTI datasets of the human brain in two different contexts using different b-values, and to compare datasets from a healthy and HIV-infected subject.

Tensoral for post-processing users and simulation authors

Science.gov (United States)

Dresselhaus, Eliot

1993-01-01

The CTR post-processing effort aims to make turbulence simulations and data more readily and usefully available to the research and industrial communities. The Tensoral language, which provides the foundation for this effort, is introduced here in the form of a user's guide. The Tensoral user's guide is presented in two main sections. Section one acts as a general introduction and guides database users who wish to post-process simulation databases. Section two gives a brief description of how database authors and other advanced users can make simulation codes and/or the databases they generate available to the user community via Tensoral database back ends. The two-part structure of this document conforms to the two-level design structure of the Tensoral language. Tensoral has been designed to be a general computer language for performing tensor calculus and statistics on numerical data. Tensoral's generality allows it to be used for stand-alone native coding of high-level post-processing tasks (as described in section one of this guide). At the same time, Tensoral's specialization to a minute task (namely, to numerical tensor calculus and statistics) allows it to be easily embedded into applications written partly in Tensoral and partly in other computer languages (here, C and Vectoral). Embedded Tensoral, aimed at advanced users for more general coding (e.g. of efficient simulations, for interfacing with pre-existing software, for visualization, etc.), is described in section two of this guide.

Geometric decomposition of the conformation tensor in viscoelastic turbulence

Science.gov (United States)

Hameduddin, Ismail; Meneveau, Charles; Zaki, Tamer A.; Gayme, Dennice F.

2018-05-01

This work introduces a mathematical approach to analysing the polymer dynamics in turbulent viscoelastic flows that uses a new geometric decomposition of the conformation tensor, along with associated scalar measures of the polymer fluctuations. The approach circumvents an inherent difficulty in traditional Reynolds decompositions of the conformation tensor: the fluctuating tensor fields are not positive-definite and so do not retain the physical meaning of the tensor. The geometric decomposition of the conformation tensor yields both mean and fluctuating tensor fields that are positive-definite. The fluctuating tensor in the present decomposition has a clear physical interpretation as a polymer deformation relative to the mean configuration. Scalar measures of this fluctuating conformation tensor are developed based on the non-Euclidean geometry of the set of positive-definite tensors. Drag-reduced viscoelastic turbulent channel flow is then used an example case study. The conformation tensor field, obtained using direct numerical simulations, is analysed using the proposed framework.

Applications of tensor functions in creep mechanics

International Nuclear Information System (INIS)

Betten, J.

1991-01-01

Within this contribution a short survey is given of some recent advances in the mathematical modelling of materials behaviour under creep conditions. The mechanical behaviour of anisotropic solids requires a suitable mathematical modelling. The properties of tensor functions with several argument tensors constitute a rational basis for a consistent mathematical modelling of complex material behaviour. This paper presents certain principles, methods, and recent successfull applications of tensor functions in solid mechanics. The rules for specifying irreducible sets of tensor invariants and tensor generators for material tensors of rank two and four are also discussed. Furthermore, it is very important that the scalar coefficients in constitutive and evolutional equations are determined as functions of the integrity basis and experimental data. It is explained in detail that these coefficients can be determined by using tensorial interpolation methods. Some examples for practical use are discussed. (orig./RHM)

Tensor interaction in heavy-ion scattering. Pt. 1

International Nuclear Information System (INIS)

Nishioka, H.; Johnson, R.C.

1985-01-01

The Heidelberg shape-effect model for heavy-ion tensor interactions is reformulated and generalized using the Hooton-Johnson formulation. The generalized semiclassical model (the turning-point model) predicts that the components of the tensor analysing power anti Tsub(2q) have certain relations with each other for each type of tensor interaction (Tsub(R), Tsub(P) and Tsub(L) types). The predicted relations between the anti Tsub(2q) are very simple and have a direct connection with the properties of the tensor interaction at the turning point. The model predictions are satisfied in quantum-mechanical calculations for 7 Li and 23 Na elastic scattering from 58 Ni in the Fresnel-diffraction energy region. As a consequence of this model, it becomes possible to single out effects from a Tsub(P)- or Tsub(L)-type tensor interaction in polarized heavy-ion scattering. The presence of a Tsub(P)-type tensor interaction is suggested by measured anti T 20 /anti T 22 ratios for 7 Li + 58 Ni scattering. In the turning-point model the three types of tensor operator are not independent, and this is found to be true also in a quantum-mechanical calculation. The model also predicts relations between the components of higher-rank tensor analysing power in the presence of a higher-rank tensor interaction. The rank-3 tensor case is discussed in detail. (orig.)

On Lovelock analogs of the Riemann tensor

Science.gov (United States)

Camanho, Xián O.; Dadhich, Naresh

2016-03-01

It is possible to define an analog of the Riemann tensor for Nth order Lovelock gravity, its characterizing property being that the trace of its Bianchi derivative yields the corresponding analog of the Einstein tensor. Interestingly there exist two parallel but distinct such analogs and the main purpose of this note is to reconcile both formulations. In addition we will introduce a simple tensor identity and use it to show that any pure Lovelock vacuum in odd d=2N+1 dimensions is Lovelock flat, i.e. any vacuum solution of the theory has vanishing Lovelock-Riemann tensor. Further, in the presence of cosmological constant it is the Lovelock-Weyl tensor that vanishes.

The simplicial Ricci tensor

International Nuclear Information System (INIS)

Alsing, Paul M; McDonald, Jonathan R; Miller, Warner A

2011-01-01

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincare conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area-an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.

The simplicial Ricci tensor

Science.gov (United States)

Alsing, Paul M.; McDonald, Jonathan R.; Miller, Warner A.

2011-08-01

The Ricci tensor (Ric) is fundamental to Einstein's geometric theory of gravitation. The three-dimensional Ric of a spacelike surface vanishes at the moment of time symmetry for vacuum spacetimes. The four-dimensional Ric is the Einstein tensor for such spacetimes. More recently, the Ric was used by Hamilton to define a nonlinear, diffusive Ricci flow (RF) that was fundamental to Perelman's proof of the Poincarè conjecture. Analytic applications of RF can be found in many fields including general relativity and mathematics. Numerically it has been applied broadly to communication networks, medical physics, computer design and more. In this paper, we use Regge calculus (RC) to provide the first geometric discretization of the Ric. This result is fundamental for higher dimensional generalizations of discrete RF. We construct this tensor on both the simplicial lattice and its dual and prove their equivalence. We show that the Ric is an edge-based weighted average of deficit divided by an edge-based weighted average of dual area—an expression similar to the vertex-based weighted average of the scalar curvature reported recently. We use this Ric in a third and independent geometric derivation of the RC Einstein tensor in arbitrary dimensions.

Optimal voxel size for measuring global gray and white matter proton metabolite concentrations using chemical shift imaging

DEFF Research Database (Denmark)

Hanson, Lars Peter Grüner; Adalsteinsson, E; Pfefferbaum, A

2000-01-01

Quantification of gray and white matter levels of spectroscopically visible metabolites can provide important insights into brain development and pathological conditions. Chemical shift imaging offers a gain in efficiency for estimation of global gray and white matter metabolite concentrations co...

Beyond Low Rank: A Data-Adaptive Tensor Completion Method

OpenAIRE

Zhang, Lei; Wei, Wei; Shi, Qinfeng; Shen, Chunhua; Hengel, Anton van den; Zhang, Yanning

2017-01-01

Low rank tensor representation underpins much of recent progress in tensor completion. In real applications, however, this approach is confronted with two challenging problems, namely (1) tensor rank determination; (2) handling real tensor data which only approximately fulfils the low-rank requirement. To address these two issues, we develop a data-adaptive tensor completion model which explicitly represents both the low-rank and non-low-rank structures in a latent tensor. Representing the no...

Exploring the tensor networks/AdS correspondence

Energy Technology Data Exchange (ETDEWEB)

Bhattacharyya, Arpan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Centre For High Energy Physics, Indian Institute of Science,560012 Bangalore (India); Gao, Zhe-Shen [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Hung, Ling-Yan [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); State Key Laboratory of Surface Physics and Department of Physics, Fudan University,220 Handan Road, 200433 Shanghai (China); Collaborative Innovation Center of Advanced Microstructures, Nanjing University,Nanjing, 210093 (China); Liu, Si-Nong [Department of Physics and Center for Field Theory and Particle Physics, Fudan University,220 Handan Road, 200433 Shanghai (China)

2016-08-11

In this paper we study the recently proposed tensor networks/AdS correspondence. We found that the Coxeter group is a useful tool to describe tensor networks in a negatively curved space. Studying generic tensor network populated by perfect tensors, we find that the physical wave function generically do not admit any connected correlation functions of local operators. To remedy the problem, we assume that wavefunctions admitting such semi-classical gravitational interpretation are composed of tensors close to, but not exactly perfect tensors. Computing corrections to the connected two point correlation functions, we find that the leading contribution is given by structures related to geodesics connecting the operators inserted at the boundary physical dofs. Such considerations admit generalizations at least to three point functions. This is highly suggestive of the emergence of the analogues of Witten diagrams in the tensor network. The perturbations alone however do not give the right entanglement spectrum. Using the Coxeter construction, we also constructed the tensor network counterpart of the BTZ black hole, by orbifolding the discrete lattice on which the network resides. We found that the construction naturally reproduces some of the salient features of the BTZ black hole, such as the appearance of RT surfaces that could wrap the horizon, depending on the size of the entanglement region A.

Precise determination of lattice phase shifts and mixing angles

Energy Technology Data Exchange (ETDEWEB)

Lu, Bing-Nan, E-mail: b.lu@fz-juelich.de [Institute for Advanced Simulation, Institut für Kernphysik, and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich (Germany); Lähde, Timo A. [Institute for Advanced Simulation, Institut für Kernphysik, and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich (Germany); Lee, Dean [Department of Physics, North Carolina State University, Raleigh, NC 27695 (United States); Meißner, Ulf-G. [Helmholtz-Institut für Strahlen- und Kernphysik and Bethe Center for Theoretical Physics, Universität Bonn, D-53115 Bonn (Germany); Institute for Advanced Simulation, Institut für Kernphysik, and Jülich Center for Hadron Physics, Forschungszentrum Jülich, D-52425 Jülich (Germany); JARA – High Performance Computing, Forschungszentrum Jülich, D-52425 Jülich (Germany)

2016-09-10

We introduce a general and accurate method for determining lattice phase shifts and mixing angles, which is applicable to arbitrary, non-cubic lattices. Our method combines angular momentum projection, spherical wall boundaries and an adjustable auxiliary potential. This allows us to construct radial lattice wave functions and to determine phase shifts at arbitrary energies. For coupled partial waves, we use a complex-valued auxiliary potential that breaks time-reversal invariance. We benchmark our method using a system of two spin-1/2 particles interacting through a finite-range potential with a strong tensor component. We are able to extract phase shifts and mixing angles for all angular momenta and energies, with precision greater than that of extant methods. We discuss a wide range of applications from nuclear lattice simulations to optical lattice experiments.

Study of chemical shifts of the chloroform complexes with cyclic donors of electrons

International Nuclear Information System (INIS)

Blaszkiewicz, B.; Pajak, Z.

1973-01-01

Chemical shifts of chloroform complexes with the heterocyclic electron donors: pyridine, piperidine, alpha-picoline and gamma-picoline have been studied using the high resolution (5.10 -9 ) spectrometer operating at 80 MHz. An attempt has also been made to study the three - component solutions of : chloroform, a heterocyclic donor of electrons and carbon tetrachloride. The results, which have been obtained, indicate that the complex-forming power of pyridine and other electron donors is greater in carbon tetrachloride than in other solvents. (S.B.)

Coronary artery atherosclerosis associated with shift work in chemical plant workers by using coronary CT angiography.

Science.gov (United States)

Kang, WonYang; Park, Won-Ju; Jang, Keun-Ho; Kim, Soo-Hyeon; Gwon, Do-Hyeong; Lim, Hyeong-Min; Ahn, Ji-Sung; Moon, Jai-Dong

2016-08-01

The aim of this study was to investigate whether shift work is related to elevated risk of coronary artery disease (CAD) by determining the coronary artery calcium (CAC) score and the presence of coronary artery stenosis by using coronary artery CT angiography (CCTA). In this study, 110 male workers participated and underwent a CCTA examination for CAC scoring, which represents coronary artery plaque, and were evaluated for luminal stenosis. All of the participants were working in the same chemical plant, of whom 70 worked day shifts and 40 worked rotating shifts. In a multivariate logistic regression analysis, including age, smoking status, alcohol consumption, regular exercise and waist circumference, shift work was associated with a 2.89-fold increase in the odds of developing coronary plaque compared with day work (OR, 2.89; 95% CI 1.07 to 7.82). The association between shift work and coronary plaque was strong after adjustment for age, low-density lipoprotein cholesterol, hypertension and diabetes mellitus (OR, 2.92; 95% CI 1.02 to 8.33). In addition, the number of years of shift work employment was associated with coronary plaque. However, no association was found between shift work and coronary artery stenosis. Shift work could induce CAD onset via the atherosclerotic process, and shift work employment duration was associated with an increased risk of atherosclerosis in male workers. Published by the BMJ Publishing Group Limited. For permission to use (where not already granted under a licence) please go to http://www.bmj.com/company/products-services/rights-and-licensing/

STRUCTURAL STUDY AND INVESTIGATION OF NMR TENSORS ...

African Journals Online (AJOL)

NBO studies were performed to the second-order and perturbative estimates of donor-acceptor interaction have been done. The procedures of gauge-invariant atomic orbital (GIAO) and continuous-set-of-gauge-transformation (CSGT) were employed to calculate isotropic shielding, chemical shifts anisotropy and chemical ...

Using 1H and 13C NMR chemical shifts to determine cyclic peptide conformations: a combined molecular dynamics and quantum mechanics approach.

Science.gov (United States)

Nguyen, Q Nhu N; Schwochert, Joshua; Tantillo, Dean J; Lokey, R Scott

2018-05-10

Solving conformations of cyclic peptides can provide insight into structure-activity and structure-property relationships, which can help in the design of compounds with improved bioactivity and/or ADME characteristics. The most common approaches for determining the structures of cyclic peptides are based on NMR-derived distance restraints obtained from NOESY or ROESY cross-peak intensities, and 3J-based dihedral restraints using the Karplus relationship. Unfortunately, these observables are often too weak, sparse, or degenerate to provide unequivocal, high-confidence solution structures, prompting us to investigate an alternative approach that relies only on 1H and 13C chemical shifts as experimental observables. This method, which we call conformational analysis from NMR and density-functional prediction of low-energy ensembles (CANDLE), uses molecular dynamics (MD) simulations to generate conformer families and density functional theory (DFT) calculations to predict their 1H and 13C chemical shifts. Iterative conformer searches and DFT energy calculations on a cyclic peptide-peptoid hybrid yielded Boltzmann ensembles whose predicted chemical shifts matched the experimental values better than any single conformer. For these compounds, CANDLE outperformed the classic NOE- and 3J-coupling-based approach by disambiguating similar β-turn types and also enabled the structural elucidation of the minor conformer. Through the use of chemical shifts, in conjunction with DFT and MD calculations, CANDLE can help illuminate conformational ensembles of cyclic peptides in solution.

p-Norm SDD tensors and eigenvalue localization

Directory of Open Access Journals (Sweden)

Qilong Liu

2016-07-01

Full Text Available Abstract We present a new class of nonsingular tensors (p-norm strictly diagonally dominant tensors, which is a subclass of strong H $\\mathcal{H}$ -tensors. As applications of the results, we give a new eigenvalue inclusion set, which is tighter than those provided by Li et al. (Linear Multilinear Algebra 64:727-736, 2016 in some case. Based on this set, we give a checkable sufficient condition for the positive (semidefiniteness of an even-order symmetric tensor.

Is the Lamb shift chemically significant?

Science.gov (United States)

Dyall, Kenneth G.; Bauschlicher, Charles W., Jr.; Schwenke, David W.; Pyykko, Pekka; Arnold, James (Technical Monitor)

2001-01-01

The contribution of the Lamb shift to the atomization energies of some prototype molecules, BF3, AlF3, and GaF3, is estimated by a perturbation procedure. It is found to be in the range of 3-5% of the one-electron scalar relativistic contribution to the atomization energy. The maximum absolute value is 0.2 kcal/mol for GaF3. These sample calculations indicate that the Lamb shift is probably small enough to be neglected for energetics of molecules containing light atoms if the target accuracy is 1 kcal/mol, but for higher accuracy calculations and for molecules containing heavy elements it must be considered.

The effect of noncollinearity of 15N-1H dipolar and 15N CSA tensors and rotational anisotropy on 15N relaxation, CSA/dipolar cross correlation, and TROSY

International Nuclear Information System (INIS)

Fushman, David; Cowburn, David

1999-01-01

Current approaches to 15N relaxation in proteins assume that the 15N-1H dipolar and 15N CSA tensors are collinear. We show theoretically that, when there is significant anisotropy of molecular rotation, different orientations of the two tensors, experimentally observed in proteins, nucleic acids, and small peptides, will result in differences in site- specific correlation functions and spectral densities. The standard treatments of the rates of longitudinal and transverse relaxation of amide 15N nuclei, of the 15N CSA/15N-1H dipolar cross correlation, and of the TROSY experiment are extended to account for the effect of noncollinearity of the 15N-1H dipolar and 15N CSA (chemical shift anisotropy) tensors. This effect, proportional to the degree of anisotropy of the overall motion, (D-parallel /D-perpendicular -1), is sensitive to the relative orientation of the two tensors and to the orientation of the peptide plane with respect to the diffusion coordinate frame. The effect is negligible at small degrees of anisotropy, but is predicted to become significant for D-parallel /D-perpendicular ≥1.5, and at high magnetic fields. The effect of noncollinearity of 15N CSA and 15N-1H dipolar interaction is sensitive to both gross (hydrodynamic) properties and atomic-level details of protein structure. Incorporation of this effect into relaxation data analysis is likely to improve both precision and accuracy of the derived characteristics of protein dynamics, especially at high magnetic fields and for molecules with a high degree of anisotropy of the overall motion. The effect will also make TROSY efficiency dependent on local orientation in moderately anisotropic systems

Differential invariants for higher-rank tensors. A progress report

International Nuclear Information System (INIS)

Tapial, V.

2004-07-01

We outline the construction of differential invariants for higher-rank tensors. In section 2 we outline the general method for the construction of differential invariants. A first result is that the simplest tensor differential invariant contains derivatives of the same order as the rank of the tensor. In section 3 we review the construction for the first-rank tensors (vectors) and second-rank tensors (metrics). In section 4 we outline the same construction for higher-rank tensors. (author)

Energy-momentum tensor in scalar QED

International Nuclear Information System (INIS)

Joglekar, S.D.; Misra, A.

1988-01-01

We consider the renormalization of the energy-momentum tensor in scalar quantum electrodynamics. We show the need for adding an improvement term to the conventional energy-momentum tensor. We consider two possible forms for the improvement term: (i) one in which the improvement coefficient is a finite function of bare parameters of the theory (so that the energy-momentum tensor can be obtained from an action that is a finite function of bare quantities); (ii) one in which the improvement coefficient is a finite quantity, i.e., a finite function of renormalized parameters. We establish a negative result; viz., neither form leads to a finite energy-momentum tensor to O(e 2 λ/sup n/). .AE

Calculus of tensors and differential forms

CERN Document Server

Sinha, Rajnikant

2014-01-01

Calculus of tensors and differential forms is an introductory-level textbook. Through this book, students will familiarize themselves with tools they need in order to use for further study on general relativity and research, such as affine tensors, tensor calculus on manifolds, relative tensors, Lie derivatives, wedge products, differential forms, and Stokes' theorem. The treatment is concrete and in detail, so that abstract concepts do not deter even physics and engineering students. This self contained book requires undergraduate-level calculus of several variables and linear algebra as prerequisite. Fubini's theorem in real analysis, to be used in Stokes' theorem, has been proved earlier than Stokes' theorem so that students don't have to search elsewhere.

Diffusion-weighted imaging of the liver at 3 T using section-selection gradient reversal: emphasis on chemical shift artefacts and lesion conspicuity

International Nuclear Information System (INIS)

Lee, J.S.; Kim, Y.K.; Jeong, W.K.; Choi, D.; Lee, W.J.

2015-01-01

Aim: To assess the value of section-selection gradient reversal (SSGR) in liver diffusion-weighted imaging (DWI) by comparing it to conventional DWI with an emphasis on chemical shift artefacts and lesion conspicuity. Materials and methods: Forty-eight patients (29 men and 19 women; age range 33–80 years) with 48 liver lesions underwent two DWI examinations using spectral presaturation with inversion recovery fat suppression with and without SSGR at 3 T. Two reviewers evaluated each DWI (b = 100 and b = 800 image) with respect to chemical shift artefacts and liver lesion conspicuity using five-point scales and performed pairwise comparisons between the two DWIs. The signal-to-noise ratio (SNR) of the liver and the lesion and the lesion–liver contrast-to-noise ratio (CNR) were also calculated. Results: SSGR-DWI was significantly better than conventional DWI with respect to chemical shift artefacts and lesion conspicuity in both separate reviews and pairwise comparisons (p < 0.05). There were significant differences in the SNR of the liver (b = 100 and b = 800 images) and lesion (b = 800) between SSGR-DWI and conventional DWI (p < 0.05). Conclusion: Applying the SSGR method to DWI using SPIR fat suppression at 3 T could significantly reduce chemical shift artefacts without incurring additional acquisition time or SNR penalties, which leads to increased conspicuity of focal liver lesions. - Highlights: • Chemical shift artefact in liver DWI is markedly decreased by applying SSGR. • Liver lesion conspicuity is improved by applying SSGR to DWI. • In SNR of the liver, SSGR-DWI is better than conventional DWI

Combining NMR ensembles and molecular dynamics simulations provides more realistic models of protein structures in solution and leads to better chemical shift prediction

International Nuclear Information System (INIS)

Lehtivarjo, Juuso; Tuppurainen, Kari; Hassinen, Tommi; Laatikainen, Reino; Peräkylä, Mikael

2012-01-01

While chemical shifts are invaluable for obtaining structural information from proteins, they also offer one of the rare ways to obtain information about protein dynamics. A necessary tool in transforming chemical shifts into structural and dynamic information is chemical shift prediction. In our previous work we developed a method for 4D prediction of protein 1 H chemical shifts in which molecular motions, the 4th dimension, were modeled using molecular dynamics (MD) simulations. Although the approach clearly improved the prediction, the X-ray structures and single NMR conformers used in the model cannot be considered fully realistic models of protein in solution. In this work, NMR ensembles (NMRE) were used to expand the conformational space of proteins (e.g. side chains, flexible loops, termini), followed by MD simulations for each conformer to map the local fluctuations. Compared with the non-dynamic model, the NMRE+MD model gave 6–17% lower root-mean-square (RMS) errors for different backbone nuclei. The improved prediction indicates that NMR ensembles with MD simulations can be used to obtain a more realistic picture of protein structures in solutions and moreover underlines the importance of short and long time-scale dynamics for the prediction. The RMS errors of the NMRE+MD model were 0.24, 0.43, 0.98, 1.03, 1.16 and 2.39 ppm for 1 Hα, 1 HN, 13 Cα, 13 Cβ, 13 CO and backbone 15 N chemical shifts, respectively. The model is implemented in the prediction program 4DSPOT, available at http://www.uef.fi/4dspothttp://www.uef.fi/4dspot.

Combining NMR ensembles and molecular dynamics simulations provides more realistic models of protein structures in solution and leads to better chemical shift prediction

Energy Technology Data Exchange (ETDEWEB)

Lehtivarjo, Juuso, E-mail: juuso.lehtivarjo@uef.fi; Tuppurainen, Kari; Hassinen, Tommi; Laatikainen, Reino [University of Eastern Finland, School of Pharmacy (Finland); Peraekylae, Mikael [University of Eastern Finland, Institute of Biomedicine (Finland)

2012-03-15

While chemical shifts are invaluable for obtaining structural information from proteins, they also offer one of the rare ways to obtain information about protein dynamics. A necessary tool in transforming chemical shifts into structural and dynamic information is chemical shift prediction. In our previous work we developed a method for 4D prediction of protein {sup 1}H chemical shifts in which molecular motions, the 4th dimension, were modeled using molecular dynamics (MD) simulations. Although the approach clearly improved the prediction, the X-ray structures and single NMR conformers used in the model cannot be considered fully realistic models of protein in solution. In this work, NMR ensembles (NMRE) were used to expand the conformational space of proteins (e.g. side chains, flexible loops, termini), followed by MD simulations for each conformer to map the local fluctuations. Compared with the non-dynamic model, the NMRE+MD model gave 6-17% lower root-mean-square (RMS) errors for different backbone nuclei. The improved prediction indicates that NMR ensembles with MD simulations can be used to obtain a more realistic picture of protein structures in solutions and moreover underlines the importance of short and long time-scale dynamics for the prediction. The RMS errors of the NMRE+MD model were 0.24, 0.43, 0.98, 1.03, 1.16 and 2.39 ppm for {sup 1}H{alpha}, {sup 1}HN, {sup 13}C{alpha}, {sup 13}C{beta}, {sup 13}CO and backbone {sup 15}N chemical shifts, respectively. The model is implemented in the prediction program 4DSPOT, available at http://www.uef.fi/4dspothttp://www.uef.fi/4dspot.

Algebraic and computational aspects of real tensor ranks

CERN Document Server

Sakata, Toshio; Miyazaki, Mitsuhiro

2016-01-01

This book provides comprehensive summaries of theoretical (algebraic) and computational aspects of tensor ranks, maximal ranks, and typical ranks, over the real number field. Although tensor ranks have been often argued in the complex number field, it should be emphasized that this book treats real tensor ranks, which have direct applications in statistics. The book provides several interesting ideas, including determinant polynomials, determinantal ideals, absolutely nonsingular tensors, absolutely full column rank tensors, and their connection to bilinear maps and Hurwitz-Radon numbers. In addition to reviews of methods to determine real tensor ranks in details, global theories such as the Jacobian method are also reviewed in details. The book includes as well an accessible and comprehensive introduction of mathematical backgrounds, with basics of positive polynomials and calculations by using the Groebner basis. Furthermore, this book provides insights into numerical methods of finding tensor ranks through...

Decomposition of a symmetric second-order tensor

Science.gov (United States)

Heras, José A.

2018-05-01

In the three-dimensional space there are different definitions for the dot and cross products of a vector with a second-order tensor. In this paper we show how these products can uniquely be defined for the case of symmetric tensors. We then decompose a symmetric second-order tensor into its ‘dot’ part, which involves the dot product, and the ‘cross’ part, which involves the cross product. For some physical applications, this decomposition can be interpreted as one in which the dot part identifies with the ‘parallel’ part of the tensor and the cross part identifies with the ‘perpendicular’ part. This decomposition of a symmetric second-order tensor may be suitable for undergraduate courses of vector calculus, mechanics and electrodynamics.

Efficient Low Rank Tensor Ring Completion

OpenAIRE

Wang, Wenqi; Aggarwal, Vaneet; Aeron, Shuchin

2017-01-01

Using the matrix product state (MPS) representation of the recently proposed tensor ring decompositions, in this paper we propose a tensor completion algorithm, which is an alternating minimization algorithm that alternates over the factors in the MPS representation. This development is motivated in part by the success of matrix completion algorithms that alternate over the (low-rank) factors. In this paper, we propose a spectral initialization for the tensor ring completion algorithm and ana...

Colored Tensor Models - a Review

Directory of Open Access Journals (Sweden)

Razvan Gurau

2012-04-01

Full Text Available Colored tensor models have recently burst onto the scene as a promising conceptual and computational tool in the investigation of problems of random geometry in dimension three and higher. We present a snapshot of the cutting edge in this rapidly expanding research field. Colored tensor models have been shown to share many of the properties of their direct ancestor, matrix models, which encode a theory of fluctuating two-dimensional surfaces. These features include the possession of Feynman graphs encoding topological spaces, a 1/N expansion of graph amplitudes, embedded matrix models inside the tensor structure, a resumable leading order with critical behavior and a continuum large volume limit, Schwinger-Dyson equations satisfying a Lie algebra (akin to the Virasoro algebra in two dimensions, non-trivial classical solutions and so on. In this review, we give a detailed introduction of colored tensor models and pointers to current and future research directions.

Efficient Tensor Strategy for Recommendation

Directory of Open Access Journals (Sweden)

Aboagye Emelia Opoku

2017-07-01

Full Text Available The era of big data has witnessed the explosion of tensor datasets, and large scale Probabilistic Tensor Factorization (PTF analysis is important to accommodate such increasing trend of data. Sparsity, and Cold-Start are some of the inherent problems of recommender systems in the era of big data. This paper proposes a novel Sentiment-Based Probabilistic Tensor Analysis technique senti-PTF to address the problems. The propose framework first applies a Natural Language Processing technique to perform sentiment analysis taking advantage of the huge sums of textual data generated available from the social media which are predominantly left untouched. Although some current studies do employ review texts, many of them do not consider how sentiments in reviews influence recommendation algorithm for prediction. There is therefore this big data text analytics gap whose modeling is computationally expensive. From our experiments, our novel machine learning sentiment-based tensor analysis is computationally less expensive, and addresses the cold-start problem, for optimal recommendation prediction.

Spectral Method with the Tensor-Product Nodal Basis for the Steklov Eigenvalue Problem

Directory of Open Access Journals (Sweden)

Xuqing Zhang

2013-01-01

Full Text Available This paper discusses spectral method with the tensor-product nodal basis at the Legendre-Gauss-Lobatto points for solving the Steklov eigenvalue problem. A priori error estimates of spectral method are discussed, and based on the work of Melenk and Wohlmuth (2001, a posterior error estimator of the residual type is given and analyzed. In addition, this paper combines the shifted-inverse iterative method and spectral method to establish an efficient scheme. Finally, numerical experiments with MATLAB program are reported.

Chemical shift of U L3 edges in different uranium compounds obtained by X-ray absorption spectroscopy with synchrotron radiation

International Nuclear Information System (INIS)

Joseph, D.; Jha, S.N.; Nayak, C.; Bhattacharyya, D.; Babu, P. Venu

2014-01-01

Uranium L 3 X-ray absorption edge was measured in various compounds containing uranium in U 4+ , U 5+ and U 5+ oxidation states. The measurements have been carried out at the Energy Dispersive EXAFS beamline (BL-08) at INDUS-2 synchrotron radiation source at RRCAT, Indore. Energy shifts of ∼ 2-3 eV were observed for U L 3 edge in the U-compounds compared to their value in elemental U. The different chemical shifts observed for the compounds having the same oxidation state of the cation but different anions or ligands show the effect of different chemical environments surrounding the cations in determining their X-ray absorption edges in the above compounds. The above chemical effect has been quantitatively described by determining the effective charges on U cation in the above compounds. (author)

Conformal field theories and tensor categories. Proceedings

Energy Technology Data Exchange (ETDEWEB)

Bai, Chengming [Nankai Univ., Tianjin (China). Chern Institute of Mathematics; Fuchs, Juergen [Karlstad Univ. (Sweden). Theoretical Physics; Huang, Yi-Zhi [Rutgers Univ., Piscataway, NJ (United States). Dept. of Mathematics; Kong, Liang [Tsinghua Univ., Beijing (China). Inst. for Advanced Study; Runkel, Ingo; Schweigert, Christoph (eds.) [Hamburg Univ. (Germany). Dept. of Mathematics

2014-08-01

First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

On improving the efficiency of tensor voting.

Science.gov (United States)

Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim

2011-11-01

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor voting and the stick component of the plate tensor voting must reinforce surfaceness, the plate components of both the plate and ball tensor voting must boost curveness, whereas junctionness must be strengthened by the ball component of the ball tensor voting. Two new parameters have been proposed for the second formulation in order to control the potentially conflictive influence of the stick component of the plate vote and the ball component of the ball vote. Results show that the proposed formulations can be used in applications where efficiency is an issue since they have a complexity of order O(1). Moreover, the second proposed formulation has been shown to be more appropriate than the original tensor voting for estimating saliencies by appropriately setting the two new parameters.

Reduction schemes for one-loop tensor integrals

International Nuclear Information System (INIS)

Denner, A.; Dittmaier, S.

2006-01-01

We present new methods for the evaluation of one-loop tensor integrals which have been used in the calculation of the complete electroweak one-loop corrections to e + e - ->4 fermions. The described methods for 3-point and 4-point integrals are, in particular, applicable in the case where the conventional Passarino-Veltman reduction breaks down owing to the appearance of Gram determinants in the denominator. One method consists of different variants for expanding tensor coefficients about limits of vanishing Gram determinants or other kinematical determinants, thereby reducing all tensor coefficients to the usual scalar integrals. In a second method a specific tensor coefficient with a logarithmic integrand is evaluated numerically, and the remaining coefficients as well as the standard scalar integral are algebraically derived from this coefficient. For 5-point tensor integrals, we give explicit formulas that reduce the corresponding tensor coefficients to coefficients of 4-point integrals with tensor rank reduced by one. Similar formulas are provided for 6-point functions, and the generalization to functions with more internal propagators is straightforward. All the presented methods are also applicable if infrared (soft or collinear) divergences are treated in dimensional regularization or if mass parameters (for unstable particles) become complex

Conformal field theories and tensor categories. Proceedings

International Nuclear Information System (INIS)

Bai, Chengming; Fuchs, Juergen; Huang, Yi-Zhi; Kong, Liang; Runkel, Ingo; Schweigert, Christoph

2014-01-01

First book devoted completely to the mathematics of conformal field theories, tensor categories and their applications. Contributors include both mathematicians and physicists. Some long expository articles are especially suitable for beginners. The present volume is a collection of seven papers that are either based on the talks presented at the workshop ''Conformal field theories and tensor categories'' held June 13 to June 17, 2011 at the Beijing International Center for Mathematical Research, Peking University, or are extensions of the material presented in the talks at the workshop. These papers present new developments beyond rational conformal field theories and modular tensor categories and new applications in mathematics and physics. The topics covered include tensor categories from representation categories of Hopf algebras, applications of conformal field theories and tensor categories to topological phases and gapped systems, logarithmic conformal field theories and the corresponding non-semisimple tensor categories, and new developments in the representation theory of vertex operator algebras. Some of the papers contain detailed introductory material that is helpful for graduate students and researchers looking for an introduction to these research directions. The papers also discuss exciting recent developments in the area of conformal field theories, tensor categories and their applications and will be extremely useful for researchers working in these areas.

Loop optimization for tensor network renormalization

Science.gov (United States)

Yang, Shuo; Gu, Zheng-Cheng; Wen, Xiao-Gang

We introduce a tensor renormalization group scheme for coarse-graining a two-dimensional tensor network, which can be successfully applied to both classical and quantum systems on and off criticality. The key idea of our scheme is to deform a 2D tensor network into small loops and then optimize tensors on each loop. In this way we remove short-range entanglement at each iteration step, and significantly improve the accuracy and stability of the renormalization flow. We demonstrate our algorithm in the classical Ising model and a frustrated 2D quantum model. NSF Grant No. DMR-1005541 and NSFC 11274192, BMO Financial Group, John Templeton Foundation, Government of Canada through Industry Canada, Province of Ontario through the Ministry of Economic Development & Innovation.

Pressure dependence of backbone chemical shifts in the model peptides Ac-Gly-Gly-Xxx-Ala-NH{sub 2}

Energy Technology Data Exchange (ETDEWEB)

Erlach, Markus Beck; Koehler, Joerg [University of Regensburg, Institute of Biophysics and Physical Biochemistry and Centre of Magnetic Resonance in Chemistry and Biomedicine (Germany); Crusca, Edson [University of São Paulo, Physics Institute of São Carlos (Brazil); Kremer, Werner [University of Regensburg, Institute of Biophysics and Physical Biochemistry and Centre of Magnetic Resonance in Chemistry and Biomedicine (Germany); Munte, Claudia E. [University of São Paulo, Physics Institute of São Carlos (Brazil); Kalbitzer, Hans Robert, E-mail: hans-robert.kalbitzer@biologie.uni-regensburg.de [University of Regensburg, Institute of Biophysics and Physical Biochemistry and Centre of Magnetic Resonance in Chemistry and Biomedicine (Germany)

2016-06-15

For a better understanding of nuclear magnetic resonance (NMR) detected pressure responses of folded as well as unstructured proteins the availability of data from well-defined model systems are indispensable. In this work we report the pressure dependence of chemical shifts of the backbone atoms {sup 1}H{sup α}, {sup 13}C{sup α} and {sup 13}C′ in the protected tetrapeptides Ac-Gly-Gly-Xxx-Ala-NH{sub 2} (Xxx one of the 20 canonical amino acids). Contrary to expectation the chemical shifts of these nuclei have a nonlinear dependence on pressure in the range from 0.1 to 200 MPa. The polynomial pressure coefficients B{sub 1} and B{sub 2} are dependent on the type of amino acid studied. The coefficients of a given nucleus show significant linear correlations suggesting that the NMR observable pressure effects in the different amino acids have at least partly the same physical cause. In line with this observation the magnitude of the second order coefficients of nuclei being direct neighbors in the chemical structure are also weakly correlated.Graphical Abstract.

The Twist Tensor Nuclear Norm for Video Completion.

Science.gov (United States)

Hu, Wenrui; Tao, Dacheng; Zhang, Wensheng; Xie, Yuan; Yang, Yehui

2017-12-01

In this paper, we propose a new low-rank tensor model based on the circulant algebra, namely, twist tensor nuclear norm (t-TNN). The twist tensor denotes a three-way tensor representation to laterally store 2-D data slices in order. On one hand, t-TNN convexly relaxes the tensor multirank of the twist tensor in the Fourier domain, which allows an efficient computation using fast Fourier transform. On the other, t-TNN is equal to the nuclear norm of block circulant matricization of the twist tensor in the original domain, which extends the traditional matrix nuclear norm in a block circulant way. We test the t-TNN model on a video completion application that aims to fill missing values and the experiment results validate its effectiveness, especially when dealing with video recorded by a nonstationary panning camera. The block circulant matricization of the twist tensor can be transformed into a circulant block representation with nuclear norm invariance. This representation, after transformation, exploits the horizontal translation relationship between the frames in a video, and endows the t-TNN model with a more powerful ability to reconstruct panning videos than the existing state-of-the-art low-rank models.

Application of the Fenske-Hall molecular orbital method to the calculation of 11B NMR chemical shifts. Antipodal substituent effects in deltahedral clusters

International Nuclear Information System (INIS)

Fehlner, T.P.; Czech, P.T.; Fenske, R.F.

1990-01-01

Utilizing Fenske-Hall wave functions and eigenvalues combined with the Ramsey sum over states (SOS) approximation, it is demonstrated that the sign and magnitude of the paramagnetic contribution to the shielding correlates well with the observed 11 B chemical shifts of a substantial variety of boron- and metal-containing compounds. Analysis of the molecular orbital (MO) contributions in the SOS approximation leads to an explanation of the large downfield shifts associated with metal-rich metallaboranes. A similar analysis demonstrates the importance of selected cluster occupied and unoccupied MO's in explaining both exo-cage substituent effects in which the antipodal boron resonance is shifted upfield and endo-cage substituent effects (interchange of isolobal fragments within the cage framework) in which the antipodal boron resonance is shifted downfield. Exo- and endo-cage substitution perturbs these MO's in an understandable fashion, leading to an internally consistent explanation of the observed chemical shift changes. 36 refs., 8 figs., 4 tabs

Off-shell N = 2 tensor supermultiplets

International Nuclear Information System (INIS)

Wit, Bernard de; Saueressig, Frank

2006-01-01

A multiplet calculus is presented for an arbitrary number n of N = 2 tensor supermultiplets. For rigid supersymmetry the known couplings are reproduced. In the superconformal case the target spaces parametrized by the scalar fields are cones over (3n-1)-dimensional spaces encoded in homogeneous SU(2) invariant potentials, subject to certain constraints. The coupling to conformal supergravity enables the derivation of a large class of supergravity Lagrangians with vector and tensor multiplets and hypermultiplets. Dualizing the tensor fields into scalars leads to hypermultiplets with hyperkaehler or quaternion-Kaehler target spaces with at least n abelian isometries. It is demonstrated how to use the calculus for the construction of Lagrangians containing higher-derivative couplings of tensor multiplets. For the application of the c-map between vector and tensor supermultiplets to Lagrangians with higher-order derivatives, an off-shell version of this map is proposed. Various other implications of the results are discussed. As an example an elegant derivation of the classification of 4-dimensional quaternion-Kaehler manifolds with two commuting isometries is given

Dissecting CFT Correlators and String Amplitudes. Conformal Blocks and On-Shell Recursion for General Tensor Fields

International Nuclear Information System (INIS)

Hansen, Tobias

2015-07-01

This thesis covers two main topics: the tensorial structure of quantum field theory correlators in general spacetime dimensions and a method for computing string theory scattering amplitudes directly in target space. In the first part tensor structures in generic bosonic CFT correlators and scattering amplitudes are studied. To this end arbitrary irreducible tensor representations of SO(d) (traceless mixed-symmetry tensors) are encoded in group invariant polynomials, by contracting with sets of commuting and anticommuting polarization vectors which implement the index symmetries of the tensors. The tensor structures appearing in CFT d correlators can then be inferred by studying these polynomials in a d + 2 dimensional embedding space. It is shown with an example how these correlators can be used to compute general conformal blocks describing the exchange of mixed-symmetry tensors in four-point functions, which are crucial for advancing the conformal bootstrap program to correlators of operators with spin. Bosonic string theory lends itself as an ideal example for applying the same methods to scattering amplitudes, due to its particle spectrum of arbitrary mixed-symmetry tensors. This allows in principle the definition of on-shell recursion relations for string theory amplitudes. A further chapter introduces a different target space definition of string scattering amplitudes. As in the case of on-shell recursion relations, the amplitudes are expressed in terms of their residues via BCFW shifts. The new idea here is that the residues are determined by use of the monodromy relations for open string theory, avoiding the infinite sums over the spectrum arising in on-shell recursion relations. Several checks of the method are presented, including a derivation of the Koba-Nielsen amplitude in the bosonic string. It is argued that this method provides a target space definition of the complete S-matrix of string theory at tree-level in a at background in terms of a small

A partial differential equation for pseudocontact shift.

Science.gov (United States)

Charnock, G T P; Kuprov, Ilya

2014-10-07

It is demonstrated that pseudocontact shift (PCS), viewed as a scalar or a tensor field in three dimensions, obeys an elliptic partial differential equation with a source term that depends on the Hessian of the unpaired electron probability density. The equation enables straightforward PCS prediction and analysis in systems with delocalized unpaired electrons, particularly for the nuclei located in their immediate vicinity. It is also shown that the probability density of the unpaired electron may be extracted, using a regularization procedure, from PCS data.

Generalized Tensor-Based Morphometry of HIV/AIDS Using Multivariate Statistics on Deformation Tensors

OpenAIRE

Lepore, Natasha; Brun, Caroline; Chou, Yi-Yu; Chiang, Ming-Chang; Dutton, Rebecca A.; Hayashi, Kiralee M.; Luders, Eileen; Lopez, Oscar L.; Aizenstein, Howard J.; Toga, Arthur W.; Becker, James T.; Thompson, Paul M.

2008-01-01

This paper investigates the performance of a new multivariate method for tensor-based morphometry (TBM). Statistics on Riemannian manifolds are developed that exploit the full information in deformation tensor fields. In TBM, multiple brain images are warped to a common neuroanatomical template via 3-D nonlinear registration; the resulting deformation fields are analyzed statistically to identify group differences in anatomy. Rather than study the Jacobian determinant (volume expansion factor...

Tensors, relativity, and cosmology

CERN Document Server

Dalarsson, Mirjana

2015-01-01

Tensors, Relativity, and Cosmology, Second Edition, combines relativity, astrophysics, and cosmology in a single volume, providing a simplified introduction to each subject that is followed by detailed mathematical derivations. The book includes a section on general relativity that gives the case for a curved space-time, presents the mathematical background (tensor calculus, Riemannian geometry), discusses the Einstein equation and its solutions (including black holes and Penrose processes), and considers the energy-momentum tensor for various solutions. In addition, a section on relativistic astrophysics discusses stellar contraction and collapse, neutron stars and their equations of state, black holes, and accretion onto collapsed objects, with a final section on cosmology discussing cosmological models, observational tests, and scenarios for the early universe. This fully revised and updated second edition includes new material on relativistic effects, such as the behavior of clocks and measuring rods in m...

Combined Tensor Fitting and TV Regularization in Diffusion Tensor Imaging Based on a Riemannian Manifold Approach.

Science.gov (United States)

Baust, Maximilian; Weinmann, Andreas; Wieczorek, Matthias; Lasser, Tobias; Storath, Martin; Navab, Nassir

2016-08-01

In this paper, we consider combined TV denoising and diffusion tensor fitting in DTI using the affine-invariant Riemannian metric on the space of diffusion tensors. Instead of first fitting the diffusion tensors, and then denoising them, we define a suitable TV type energy functional which incorporates the measured DWIs (using an inverse problem setup) and which measures the nearness of neighboring tensors in the manifold. To approach this functional, we propose generalized forward- backward splitting algorithms which combine an explicit and several implicit steps performed on a decomposition of the functional. We validate the performance of the derived algorithms on synthetic and real DTI data. In particular, we work on real 3D data. To our knowledge, the present paper describes the first approach to TV regularization in a combined manifold and inverse problem setup.

Measuring Nematic Susceptibilities from the Elastoresistivity Tensor

Science.gov (United States)

Hristov, A. T.; Shapiro, M. C.; Hlobil, Patrick; Maharaj, Akash; Chu, Jiun-Haw; Fisher, Ian

The elastoresistivity tensor mijkl relates changes in resistivity to the strain on a material. As a fourth-rank tensor, it contains considerably more information about the material than the simpler (second-rank) resistivity tensor; in particular, certain elastoresistivity coefficients can be related to thermodynamic susceptibilities and serve as a direct probe of symmetry breaking at a phase transition. The aim of this talk is twofold. First, we enumerate how symmetry both constrains the structure of the elastoresistivity tensor into an easy-to-understand form and connects tensor elements to thermodynamic susceptibilities. In the process, we generalize previous studies of elastoresistivity to include the effects of magnetic field. Second, we describe an approach to measuring quantities in the elastoresistivity tensor with a novel transverse measurement, which is immune to relative strain offsets. These techniques are then applied to BaFe2As2 in a proof of principle measurement. This work is supported by the Department of Energy, Office of Science, Basic Energy Sciences, Materials Sciences and Engineering Division, under Contract DE-AC02-76SF00515.

Unusually large chemical potential shift in a degenerate semiconductor: Angle-resolved photoemission study of SnSe and Na-doped SnSe

Science.gov (United States)

Maeda, M.; Yamamoto, K.; Mizokawa, T.; Saini, N. L.; Arita, M.; Namatame, H.; Taniguchi, M.; Tan, G.; Zhao, L. D.; Kanatzidis, M. G.

2018-03-01

We have studied the electronic structure of SnSe and Na-doped SnSe by means of angle-resolved photoemission spectroscopy. The valence-band top reaches the Fermi level by the Na doping, indicating that Na-doped SnSe can be viewed as a degenerate semiconductor. However, in the Na-doped system, the chemical potential shift with temperature is unexpectedly large and is apparently inconsistent with the degenerate semiconductor picture. The large chemical potential shift and anomalous spectral shape are key ingredients for an understanding of the novel metallic state with the large thermoelectric performance in Na-doped SnSe.

Tucker tensor analysis of Matern functions in spatial statistics

KAUST Repository

Litvinenko, Alexander

2018-04-20

Low-rank Tucker tensor methods in spatial statistics 1. Motivation: improve statistical models 2. Motivation: disadvantages of matrices 3. Tools: Tucker tensor format 4. Tensor approximation of Matern covariance function via FFT 5. Typical statistical operations in Tucker tensor format 6. Numerical experiments

Differentiation of osteoporotic and neoplastic vertebral fractures by chemical shift {l_brace}in-phase and out-of phase{r_brace} MR imaging

Energy Technology Data Exchange (ETDEWEB)

Ragab, Yasser [Radiology Department, Faculty of Medicine, Cairo University (Egypt); Radiology Department, Dr Erfan and Bagedo General Hospital (Saudi Arabia)], E-mail: yragab61@hotmail.com; Emad, Yasser [Rheumatology and Rehabilitation Department, Faculty of Medicine, Cairo University (Egypt); Rheumatology and Rehabilitation Department, Dr Erfan and Bagedo General Hospital (Saudi Arabia)], E-mail: yasseremad68@yahoo.com; Gheita, Tamer [Rheumatology and Rehabilitation Department, Faculty of Medicine, Cairo University (Egypt)], E-mail: gheitamer@yahoo.com; Mansour, Maged [Oncology Department, Faculty of Medicine, Cairo University (Egypt); Oncology Department, Dr Erfan and Bagedo General Hospital (Saudi Arabia)], E-mail: magedmansour@yahoo.com; Abou-Zeid, A. [Public Health Department, Faculty of Medicine, Cairo University, Cairo (Egypt)], E-mail: alaabouzeid@yahoo.com; Ferrari, Serge [Division of Bone Diseases, Department of Rehabilitation and Geriatrics, and WHO, Collaborating Center for Osteoporosis Prevention, Geneva University Hospital (Switzerland)], E-mail: serge.ferrari@medecine.unige.ch; Rasker, Johannes J. [Rheumatologist University of Twente, Enschede (Netherlands)], E-mail: j.j.rasker@utwente.nl

2009-10-15

Objective: The objective of this study was to establish the cut-off value of the signal intensity drop on chemical shift magnetic resonance imaging (MRI) with appropriate sensitivity and specificity to differentiate osteoporotic from neoplastic wedging of the spine. Patients and methods: All patients with wedging of vertebral bodies were included consecutively between February 2006 and January 2007. A chemical shift MRI was performed and signal intensity after (in-phase and out-phase) images were obtained. A DXA was performed in all. Results: A total of 40 patients were included, 20 with osteoporotic wedging (group 1) and 20 neoplastic (group 2). They were 21 males and 19 females. Acute vertebral collapse was observed in 15 patients in group 1 and subacute collapse in another 5 patients, while in group 2, 11 patients showed acute collapse and 9 patients (45%) showed subacute vertebral collapse. On the chemical shift MRI a substantial reduction in signal intensity was found in all lesions in both groups. The proportional changes observed in signal intensity of bone marrow lesions on in-phase compared with out-of-phase images showed significant differences in both groups (P < 0.05). At a cut-off value of 35%, the observed sensitivity of out-of-phase images was 95%, specificity was 100%, positive predictive value was 100% and negative predictive value was 95.2%. Conclusion: A chemical shift MRI is useful in order to differentiate patients with vertebral collapse due to underlying osteoporosis or neoplastic process.

Surface tensor estimation from linear sections

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel

From Crofton's formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....

Surface tensor estimation from linear sections

DEFF Research Database (Denmark)

Kousholt, Astrid; Kiderlen, Markus; Hug, Daniel

2015-01-01

From Crofton’s formula for Minkowski tensors we derive stereological estimators of translation invariant surface tensors of convex bodies in the n-dimensional Euclidean space. The estimators are based on one-dimensional linear sections. In a design based setting we suggest three types of estimators....... These are based on isotropic uniform random lines, vertical sections, and non-isotropic random lines, respectively. Further, we derive estimators of the specific surface tensors associated with a stationary process of convex particles in the model based setting....

[An Improved Spectral Quaternion Interpolation Method of Diffusion Tensor Imaging].

Science.gov (United States)

Xu, Yonghong; Gao, Shangce; Hao, Xiaofei

2016-04-01

Diffusion tensor imaging(DTI)is a rapid development technology in recent years of magnetic resonance imaging.The diffusion tensor interpolation is a very important procedure in DTI image processing.The traditional spectral quaternion interpolation method revises the direction of the interpolation tensor and can preserve tensors anisotropy,but the method does not revise the size of tensors.The present study puts forward an improved spectral quaternion interpolation method on the basis of traditional spectral quaternion interpolation.Firstly,we decomposed diffusion tensors with the direction of tensors being represented by quaternion.Then we revised the size and direction of the tensor respectively according to different situations.Finally,we acquired the tensor of interpolation point by calculating the weighted average.We compared the improved method with the spectral quaternion method and the Log-Euclidean method by the simulation data and the real data.The results showed that the improved method could not only keep the monotonicity of the fractional anisotropy(FA)and the determinant of tensors,but also preserve the tensor anisotropy at the same time.In conclusion,the improved method provides a kind of important interpolation method for diffusion tensor image processing.

Correlations of the chemical shift on fasly rotating biological solids by means of NMR spectroscopy

International Nuclear Information System (INIS)

Herbst, Christian

2010-01-01

The basic aim of the thesis was the development and improvement of homo- and heteronuclear feedback sequences for the generation of correlation spectra of the chemical shift. In a first step the possibility of the acquisition of 13 C- 13 correlation spectra of the chemical shift by means of inversion pulses with low RF power factor was studied. Furthermore it was shown that broad-band phase-modulated inversion and universal rotational pulses can be constructed by means of global optimization procedures like the genetic algorithms under regardment of the available RF field strength. By inversion, universal rotational, and 360 pulses as starting values of the optimization efficient homonuclear CN n ν and RN n ν mixing sequences as well as heteronuclear RN n ν s ,ν k feedback sequences were generated. The satisfactory power of the numerically optimized sequences was shown by means of the simulation as well by means of correlation experiments of the chemical shift of L-histidine, L-arginine, and the (CUG) 97 -RNA. This thesis deals furthermore with the possibility to acquire simultaneously different signals with several receivers. By means of numerically optimized RN n ν s ,ν k pulse sequences both 15 N- 13 C and 13 C- 15 N correlation spectra were simultaneously generated. Furthermore it could be shown that the simultaneous acquisition of 3D- 15 N- 13 C- 13 C and 13 C- 15 N-( 1 H)- 1 H correlation spectra is possible. By this in only one measurement process resonance assignments can be met and studies of the global folding performed. A further application of several receivers is the simultaneous acquisition of CHHC, NHHN, NHHC, as well as CHHN spectra. By such experiments it is possible to characterize the hydrogen-bonding pattern and the glycosidic torsion angle χ in RNA. This was demonstrated by means of the (CUG) 97 -RNA. The simultaneous acquisition of all relevant crossing signals of the correlation spectra leads not only to an essential time saving, but

Determination of hydration numbers of electrolytes from temperature dependence of PMR chemical shifts

International Nuclear Information System (INIS)

Subramanian, N.

1979-01-01

The method proposed by Malinowski et al. for the determination of effective hydration numbers (h) of electrolytes leads to a consistent incrrease in the observed values of 'h' with increase in solution concentration. An attempt is made to rationalize the experimental results by cosidering the simultaneous effects of temperature and concentration on the proton chemical shift. It is suggested that Malinowski's technique might yeld 'h' values very close to the true value for those ions for which there is a fortuitous cancellation of structure-making and structure-breaking properties. (Author) [pt

A recursive reduction of tensor Feynman integrals

International Nuclear Information System (INIS)

Diakonidis, T.; Riemann, T.; Tausk, J.B.; Fleischer, J.

2009-07-01

We perform a recursive reduction of one-loop n-point rank R tensor Feynman integrals [in short: (n,R)-integrals] for n≤6 with R≤n by representing (n,R)-integrals in terms of (n,R-1)- and (n-1,R-1)-integrals. We use the known representation of tensor integrals in terms of scalar integrals in higher dimension, which are then reduced by recurrence relations to integrals in generic dimension. With a systematic application of metric tensor representations in terms of chords, and by decomposing and recombining these representations, we find the recursive reduction for the tensors. The procedure represents a compact, sequential algorithm for numerical evaluations of tensor Feynman integrals appearing in next-to-leading order contributions to massless and massive three- and four-particle production at LHC and ILC, as well as at meson factories. (orig.)

Joint eigenvector estimation from mutually anisotropic tensors improves susceptibility tensor imaging of the brain, kidney, and heart.

Science.gov (United States)

Dibb, Russell; Liu, Chunlei

2017-06-01

To develop a susceptibility-based MRI technique for probing microstructure and fiber architecture of magnetically anisotropic tissues-such as central nervous system white matter, renal tubules, and myocardial fibers-in three dimensions using susceptibility tensor imaging (STI) tools. STI can probe tissue microstructure, but is limited by reconstruction artifacts because of absent phase information outside the tissue and noise. STI accuracy may be improved by estimating a joint eigenvector from mutually anisotropic susceptibility and relaxation tensors. Gradient-recalled echo image data were simulated using a numerical phantom and acquired from the ex vivo mouse brain, kidney, and heart. Susceptibility tensor data were reconstructed using STI, regularized STI, and the proposed algorithm of mutually anisotropic and joint eigenvector STI (MAJESTI). Fiber map and tractography results from each technique were compared with diffusion tensor data. MAJESTI reduced the estimated susceptibility tensor orientation error by 30% in the phantom, 36% in brain white matter, 40% in the inner medulla of the kidney, and 45% in myocardium. This improved the continuity and consistency of susceptibility-based fiber tractography in each tissue. MAJESTI estimation of the susceptibility tensors yields lower orientation errors for susceptibility-based fiber mapping and tractography in the intact brain, kidney, and heart. Magn Reson Med 77:2331-2346, 2017. © 2016 International Society for Magnetic Resonance in Medicine. © 2016 International Society for Magnetic Resonance in Medicine.

Tensor-based Dictionary Learning for Spectral CT Reconstruction

Science.gov (United States)

Zhang, Yanbo; Wang, Ge

2016-01-01

Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods. PMID:27541628

Tensor-Based Dictionary Learning for Spectral CT Reconstruction.

Science.gov (United States)

Zhang, Yanbo; Mou, Xuanqin; Wang, Ge; Yu, Hengyong

2017-01-01

Spectral computed tomography (CT) produces an energy-discriminative attenuation map of an object, extending a conventional image volume with a spectral dimension. In spectral CT, an image can be sparsely represented in each of multiple energy channels, and are highly correlated among energy channels. According to this characteristics, we propose a tensor-based dictionary learning method for spectral CT reconstruction. In our method, tensor patches are extracted from an image tensor, which is reconstructed using the filtered backprojection (FBP), to form a training dataset. With the Candecomp/Parafac decomposition, a tensor-based dictionary is trained, in which each atom is a rank-one tensor. Then, the trained dictionary is used to sparsely represent image tensor patches during an iterative reconstruction process, and the alternating minimization scheme is adapted for optimization. The effectiveness of our proposed method is validated with both numerically simulated and real preclinical mouse datasets. The results demonstrate that the proposed tensor-based method generally produces superior image quality, and leads to more accurate material decomposition than the currently popular popular methods.

Typesafe Abstractions for Tensor Operations

OpenAIRE

Chen, Tongfei

2017-01-01

We propose a typesafe abstraction to tensors (i.e. multidimensional arrays) exploiting the type-level programming capabilities of Scala through heterogeneous lists (HList), and showcase typesafe abstractions of common tensor operations and various neural layers such as convolution or recurrent neural networks. This abstraction could lay the foundation of future typesafe deep learning frameworks that runs on Scala/JVM.

Tensor network state correspondence and holography

Science.gov (United States)

Singh, Sukhwinder

2018-01-01

In recent years, tensor network states have emerged as a very useful conceptual and simulation framework to study quantum many-body systems at low energies. In this paper, we describe a particular way in which any given tensor network can be viewed as a representation of two different quantum many-body states. The two quantum many-body states are said to correspond to each other by means of the tensor network. We apply this "tensor network state correspondence"—a correspondence between quantum many-body states mediated by tensor networks as we describe—to the multi-scale entanglement renormalization ansatz (MERA) representation of ground states of one dimensional (1D) quantum many-body systems. Since the MERA is a 2D hyperbolic tensor network (the extra dimension is identified as the length scale of the 1D system), the two quantum many-body states obtained from the MERA, via tensor network state correspondence, are seen to live in the bulk and on the boundary of a discrete hyperbolic geometry. The bulk state so obtained from a MERA exhibits interesting features, some of which caricature known features of the holographic correspondence of String theory. We show how (i) the bulk state admits a description in terms of "holographic screens", (ii) the conformal field theory data associated with a critical ground state can be obtained from the corresponding bulk state, in particular, how pointlike boundary operators are identified with extended bulk operators. (iii) We also present numerical results to illustrate that bulk states, dual to ground states of several critical spin chains, have exponentially decaying correlations, and that the bulk correlation length generally decreases with increase in central charge for these spin chains.

Concatenated image completion via tensor augmentation and completion

OpenAIRE

Bengua, Johann A.; Tuan, Hoang D.; Phien, Ho N.; Do, Minh N.

2016-01-01

This paper proposes a novel framework called concatenated image completion via tensor augmentation and completion (ICTAC), which recovers missing entries of color images with high accuracy. Typical images are second- or third-order tensors (2D/3D) depending if they are grayscale or color, hence tensor completion algorithms are ideal for their recovery. The proposed framework performs image completion by concatenating copies of a single image that has missing entries into a third-order tensor,...

Fiber orientation measurements by diffusion tensor imaging improve hydrogen-1 magnetic resonance spectroscopy of intramyocellular lipids in human leg muscles.

Science.gov (United States)

Valaparla, Sunil K; Gao, Feng; Daniele, Giuseppe; Abdul-Ghani, Muhammad; Clarke, Geoffrey D

2015-04-01

Twelve healthy subjects underwent hydrogen-1 magnetic resonance spectroscopy ([Formula: see text]) acquisition ([Formula: see text]), diffusion tensor imaging (DTI) with a [Formula: see text]-value of [Formula: see text], and fat-water magnetic resonance imaging (MRI) using the Dixon method. Subject-specific muscle fiber orientation, derived from DTI, was used to estimate the lipid proton spectral chemical shift. Pennation angles were measured as 23.78 deg in vastus lateralis (VL), 17.06 deg in soleus (SO), and 8.49 deg in tibialis anterior (TA) resulting in a chemical shift between extramyocellular lipids (EMCL) and intramyocellular lipids (IMCL) of 0.15, 0.17, and 0.19 ppm, respectively. IMCL concentrations were [Formula: see text], [Formula: see text], and [Formula: see text] in SO, VL, and TA, respectively. Significant differences were observed in IMCL and EMCL pairwise comparisons in SO, VL, and TA ([Formula: see text]). Strong correlations were observed between total fat fractions from [Formula: see text] and Dixon MRI for VL ([Formula: see text]), SO ([Formula: see text]), and TA ([Formula: see text]). Bland-Altman analysis between fat fractions (FFMRS and FFMRI) showed good agreement with small limits of agreement (LoA): [Formula: see text] (LoA: [Formula: see text] to 0.69%) in VL, [Formula: see text] (LoA: [Formula: see text] to 1.33%) in SO, and [Formula: see text] (LoA: [Formula: see text] to 0.47%) in TA. The results of this study demonstrate the variation in muscle fiber orientation and lipid concentrations in these three skeletal muscle types.

General projective relativity and the vector-tensor gravitational field

International Nuclear Information System (INIS)

Arcidiacono, G.

1986-01-01

In the general projective relativity, the induced 4-dimensional metric is symmetric in three cases, and we obtain the vector-tensor, the scalar-tensor, and the scalar-vector-tensor theories of gravitation. In this work we examine the vector-tensor theory, similar to the Veblen's theory, but with a different physical interpretation

Tensor harmonic analysis on homogenous space

International Nuclear Information System (INIS)

Wrobel, G.

1997-01-01

The Hilbert space of tensor functions on a homogenous space with the compact stability group is considered. The functions are decomposed onto a sum of tensor plane waves (defined in the text), components of which are transformed by irreducible representations of the appropriate transformation group. The orthogonality relation and the completeness relation for tensor plane waves are found. The decomposition constitutes a unitary transformation, which allows to obtain the Parseval equality. The Fourier components can be calculated by means of the Fourier transformation, the form of which is given explicitly. (author)

Tensor estimation for double-pulsed diffusional kurtosis imaging.

Science.gov (United States)

Shaw, Calvin B; Hui, Edward S; Helpern, Joseph A; Jensen, Jens H

2017-07-01

Double-pulsed diffusional kurtosis imaging (DP-DKI) represents the double diffusion encoding (DDE) MRI signal in terms of six-dimensional (6D) diffusion and kurtosis tensors. Here a method for estimating these tensors from experimental data is described. A standard numerical algorithm for tensor estimation from conventional (i.e. single diffusion encoding) diffusional kurtosis imaging (DKI) data is generalized to DP-DKI. This algorithm is based on a weighted least squares (WLS) fit of the signal model to the data combined with constraints designed to minimize unphysical parameter estimates. The numerical algorithm then takes the form of a quadratic programming problem. The principal change required to adapt the conventional DKI fitting algorithm to DP-DKI is replacing the three-dimensional diffusion and kurtosis tensors with the 6D tensors needed for DP-DKI. In this way, the 6D diffusion and kurtosis tensors for DP-DKI can be conveniently estimated from DDE data by using constrained WLS, providing a practical means for condensing DDE measurements into well-defined mathematical constructs that may be useful for interpreting and applying DDE MRI. Data from healthy volunteers for brain are used to demonstrate the DP-DKI tensor estimation algorithm. In particular, representative parametric maps of selected tensor-derived rotational invariants are presented. Copyright © 2017 John Wiley & Sons, Ltd.

Tensor network decompositions in the presence of a global symmetry

International Nuclear Information System (INIS)

Singh, Sukhwinder; Pfeifer, Robert N. C.; Vidal, Guifre

2010-01-01

Tensor network decompositions offer an efficient description of certain many-body states of a lattice system and are the basis of a wealth of numerical simulation algorithms. We discuss how to incorporate a global symmetry, given by a compact, completely reducible group G, in tensor network decompositions and algorithms. This is achieved by considering tensors that are invariant under the action of the group G. Each symmetric tensor decomposes into two types of tensors: degeneracy tensors, containing all the degrees of freedom, and structural tensors, which only depend on the symmetry group. In numerical calculations, the use of symmetric tensors ensures the preservation of the symmetry, allows selection of a specific symmetry sector, and significantly reduces computational costs. On the other hand, the resulting tensor network can be interpreted as a superposition of exponentially many spin networks. Spin networks are used extensively in loop quantum gravity, where they represent states of quantum geometry. Our work highlights their importance in the context of tensor network algorithms as well, thus setting the stage for cross-fertilization between these two areas of research.

An Adaptive Spectrally Weighted Structure Tensor Applied to Tensor Anisotropic Nonlinear Diffusion for Hyperspectral Images

Science.gov (United States)

Marin Quintero, Maider J.

2013-01-01

The structure tensor for vector valued images is most often defined as the average of the scalar structure tensors in each band. The problem with this definition is the assumption that all bands provide the same amount of edge information giving them the same weights. As a result non-edge pixels can be reinforced and edges can be weakened…

Characterizing the magnetic susceptibility tensor of lanthanide-containing polymethylated-DOTA complexes

Energy Technology Data Exchange (ETDEWEB)

Strickland, Madeleine [National Institutes of Health, Laboratory of Molecular Biophysics, Biochemistry and Biophysics Center, National Heart, Lung, and Blood Institute (United States); Schwieters, Charles D. [National Institutes of Health, Office of Intramural Research, Center for Information Technology (United States); Göbl, Christoph [Technische Universität München, Department of Chemistry (Germany); Opina, Ana C. L. [National Institutes of Health, Imaging Probe Development Center, National Heart, Lung, and Blood Institute (United States); Strub, Marie-Paule [National Institutes of Health, Laboratory of Molecular Biophysics, Biochemistry and Biophysics Center, National Heart, Lung, and Blood Institute (United States); Swenson, Rolf E.; Vasalatiy, Olga [National Institutes of Health, Imaging Probe Development Center, National Heart, Lung, and Blood Institute (United States); Tjandra, Nico, E-mail: tjandran@nhlbi.nih.gov [National Institutes of Health, Laboratory of Molecular Biophysics, Biochemistry and Biophysics Center, National Heart, Lung, and Blood Institute (United States)

2016-10-15

Lanthanide complexes based on the DOTA (1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid) cage are commonly used as phase contrast agents in magnetic resonance imaging, but can also be utilized in structural NMR applications due to their ability to induce either paramagnetic relaxation enhancement or a pseudocontact shift (PCS) depending on the choice of the lanthanide. The size and sign of the PCS for any given atom is determined by its coordinates relative to the metal center, and the characteristics of the lanthanide’s magnetic susceptibility tensor. Using a polymethylated DOTA tag (Ln-M8-SPy) conjugated to ubiquitin, we calculated the position of the metal center and characterized the susceptibility tensor for a number of lanthanides (dysprosium, thulium, and ytterbium) under a range of pH and temperature conditions. We found that there was a difference in temperature sensitivity for each of the complexes studied, which depended on the size of the lanthanide ion as well as the isomeric state of the cage. Using {sup 17}O-NMR, we confirmed that the temperature sensitivity of the compounds was enhanced by the presence of an apically bound water molecule. Since amide-containing lanthanide complexes are known to be pH sensitive and can be used as probes of physiological pH, we also investigated the effect of pH on the Ln-M8-SPy susceptibility tensor, but we found that the changes in this pH range (5.0–7.4) were not significant.

Characterizing the magnetic susceptibility tensor of lanthanide-containing polymethylated-DOTA complexes

International Nuclear Information System (INIS)

Strickland, Madeleine; Schwieters, Charles D.; Göbl, Christoph; Opina, Ana C. L.; Strub, Marie-Paule; Swenson, Rolf E.; Vasalatiy, Olga; Tjandra, Nico

2016-01-01

Lanthanide complexes based on the DOTA (1,4,7,10-tetraazacyclododecane-1,4,7,10-tetraacetic acid) cage are commonly used as phase contrast agents in magnetic resonance imaging, but can also be utilized in structural NMR applications due to their ability to induce either paramagnetic relaxation enhancement or a pseudocontact shift (PCS) depending on the choice of the lanthanide. The size and sign of the PCS for any given atom is determined by its coordinates relative to the metal center, and the characteristics of the lanthanide’s magnetic susceptibility tensor. Using a polymethylated DOTA tag (Ln-M8-SPy) conjugated to ubiquitin, we calculated the position of the metal center and characterized the susceptibility tensor for a number of lanthanides (dysprosium, thulium, and ytterbium) under a range of pH and temperature conditions. We found that there was a difference in temperature sensitivity for each of the complexes studied, which depended on the size of the lanthanide ion as well as the isomeric state of the cage. Using "1"7O-NMR, we confirmed that the temperature sensitivity of the compounds was enhanced by the presence of an apically bound water molecule. Since amide-containing lanthanide complexes are known to be pH sensitive and can be used as probes of physiological pH, we also investigated the effect of pH on the Ln-M8-SPy susceptibility tensor, but we found that the changes in this pH range (5.0–7.4) were not significant.

Indicial tensor manipulation on MACSYMA

International Nuclear Information System (INIS)

Bogen, R.A.; Pavelle, R.

1977-01-01

A new computational tool for physical calculations is described. It is the first computer system capable of performing indicial tensor calculus (as opposed to component tensor calculus). It is now operational on the symbolic manipulation system MACSYMA. The authors outline the capabilities of the system and describe some of the physical problems considered as well as others being examined at this time. (Auth.)

Tensor based structure estimation in multi-channel images

DEFF Research Database (Denmark)

Schou, Jesper; Dierking, Wolfgang; Skriver, Henning

2000-01-01

. In the second part tensors are used for representing the structure information. This approach has the advantage, that tensors can be averaged either spatially or by applying several images, and the resulting tensor provides information of the average strength as well as orientation of the structure...

On energy-momentum tensors of gravitational field

International Nuclear Information System (INIS)

Nikishov, A.I.

2001-01-01

The phenomenological approach to gravitation is discussed in which the 3-graviton interaction is reduced to the interaction of each graviton with the energy-momentum tensor of two others. If this is so, (and in general relativity this is not so), then the problem of choosing the correct energy-momentum tensor comes to finding the right 3-graviton vertex. Several energy-momentum tensors od gravitational field are considered and compared in the lowest approximation. Each of them together with the energy-momentum tensor of point-like particles satisfies the conservation laws when equations of motion of particles are the same as in general relativity. It is shown that in Newtonian approximation the considered tensors differ one from other in the way their energy density is distributed between energy density of interaction (nonzero only at locations of particles) and energy density of gravitational field. Stating from Lorentz invariance, the Lagrangians for spin-2, mass-0 field are considered [ru

Chemical constituents of Ottonia corcovadensis Miq. from Amazon forest: 1H and 13C chemical shift assignments

International Nuclear Information System (INIS)

Facundo, Valdir A.; Morais, Selene M.; Braz Filho, Raimundo

2004-01-01

In an ethanolic extract of leaves of Ottonia corcovadensis (Piperaceae) were identified sixteen terpenoids of essential oil and the three flavonoids 3',4',5,5',7-penta methoxyflavone (1), 3',4',5,7-tetra methoxyflavone (2) and 5-hydroxy-3',4',5',7-tetra methoxyflavone (3) and cafeic acid (4). Two amides (5 and 6) were isolated from an ethanolic extract of the roots. The structures were established by spectral analysis, meanly NMR (1D and 2D) and mass spectra. Extensive NMR analysis was also used to complete 1 H and 13 C chemical shift assignments of the flavonoids and amides. The components of the essential oil were identified by computer library search, retention indices and visual interpretation of mass spectra. (author)

Thalassiosira spp. community composition shifts in response to chemical and physical forcing in the northeast Pacific Ocean.

Directory of Open Access Journals (Sweden)

Phoebe Dreux Chappell

2013-09-01

Full Text Available Diatoms are genetically diverse unicellular photosynthetic eukaryotes that are key primary producers in the ocean. Many of the over 100 extant diatom species in the cosmopolitan genus Thalassiosira are difficult to distinguish in mixed populations using light microscopy. Here we examine shifts in Thalassiosira spp. composition along a coastal to open ocean transect that encountered a three-month-old Haida eddy in the northeast Pacific Ocean. To quantify shifts in Thalassiosira species composition, we developed a targeted automated ribosomal intergenic spacer analysis (ARISA method to identify Thalassiosira spp. in environmental samples. As many specific fragment lengths are indicative of individual Thalassiosira spp., the ARISA method is a useful screening tool to identify changes in the relative abundance and distribution of specific species. The method also enabled us to assess changes in Thalassiosira community composition in response to chemical and physical forcing. Thalassiosira spp. community composition in the core of a three-month-old Haida eddy remained largely (>80% similar over a two-week period, despite moving 24 km southwestward. Shifts in Thalassiosira species correlated with changes in dissolved iron (Fe and temperature throughout the sampling period. Simultaneously tracking community composition and relative abundance of Thalassiosira species within the physical and chemical context they occurred allowed us to identify quantitative linkages between environmental conditions and community response.

Effects of tensor forces in nuclei

International Nuclear Information System (INIS)

Tanihata, Isao

2013-01-01

Recent studies of nuclei far from the stability line have revealed drastic changes in nuclear orbitals and reported the appearance of new magic numbers and the disappearance of magic numbers observed at the stability line. One of the important reasons for such changes is considered to be because of the effect of tensor forces on nuclear structure. Although the role of tensor forces in binding very light nuclei such as deuterons and 4 He has been known, direct experimental evidence for the effect on nuclear structure is scarce. In this paper, I review known effects of tensor forces in nuclei and then discuss the recently raised question of s–p wave mixing in a halo nucleus of 11 Li. Following these reviews, the development of a new experiment to see the high-momentum components due to the tensor forces is discussed and some of the new data are presented. (paper)

Spectral Tensor-Train Decomposition

DEFF Research Database (Denmark)

Bigoni, Daniele; Engsig-Karup, Allan Peter; Marzouk, Youssef M.

2016-01-01

The accurate approximation of high-dimensional functions is an essential task in uncertainty quantification and many other fields. We propose a new function approximation scheme based on a spectral extension of the tensor-train (TT) decomposition. We first define a functional version of the TT...... adaptive Smolyak approach. The method is also used to approximate the solution of an elliptic PDE with random input data. The open source software and examples presented in this work are available online (http://pypi.python.org/pypi/TensorToolbox/)....

Applications of Chemical Shift Imaging to Marine Sciences

Directory of Open Access Journals (Sweden)

Haakil Lee

2010-08-01

Full Text Available The successful applications of magnetic resonance imaging (MRI in medicine are mostly due to the non-invasive and non-destructive nature of MRI techniques. Longitudinal studies of humans and animals are easily accomplished, taking advantage of the fact that MRI does not use harmful radiation that would be needed for plain film radiographic, computerized tomography (CT or positron emission (PET scans. Routine anatomic and functional studies using the strong signal from the most abundant magnetic nucleus, the proton, can also provide metabolic information when combined with in vivo magnetic resonance spectroscopy (MRS. MRS can be performed using either protons or hetero-nuclei (meaning any magnetic nuclei other than protons or 1H including carbon (13C or phosphorus (31P. In vivo MR spectra can be obtained from single region ofinterest (ROI or voxel or multiple ROIs simultaneously using the technique typically called chemical shift imaging (CSI. Here we report applications of CSI to marine samples and describe a technique to study in vivo glycine metabolism in oysters using 13C MRS 12 h after immersion in a sea water chamber dosed with [2-13C]-glycine. This is the first report of 13C CSI in a marine organism.

Improvement of chemical shift selective saturation (CHESS) pulse for MR angiography

International Nuclear Information System (INIS)

Ishimori, Yoshiyuki; Sashie, Hiroyuki; Hiraga, Akira; Matsuda, Tsuyoshi

2000-01-01

We improved the fat suppression technique based on chemical shift selective saturation (CHESS). To do this, we shortened the duration of the CHESS pulse to achieve a short repetition time (TR) for MR angiography (MRA). A short-duration CHESS pulse causes broad frequency band saturation, creating extensive offset from the resonance frequency of water. In our phantom experiment, the best parameters of the short-duration CHESS pulse were 3.84 ms in duration, -650 Hz in offset frequency from water resonance, and had a 130-degree flip angle. With this technique, MRA will be able to be carried out without a significant increase in TR. Thus, better vessel contrast will be maintained in time-of-flight (TOF) MRA or contrast-enhanced MRA when using the maximum intensity projection (MIP) method. (author)

Isomer shifts and chemical bonding in crystalline Sn(II) and Sn(IV) compounds

International Nuclear Information System (INIS)

Terra, J.; Guenzburger, D.

1991-01-01

First-principles self-consistent Local Density calculations of the electronic structure of clusters representing Sn(II) (SnO, SnF 2 , SnS, SnSe) and Sn(IV) (SnO 2 , SnF 4 ) crystalline compounds were performed. Values of the electron density at the Sn nucleus were obtained and related to measured values of the Moessbauer Isomer Shifts reported in the literature. The nuclear parameter of 119 Sn derived was ΔR/R=(1.58±0.14)x10 -4 . The chemical bonding in the solids was analysed and related to the electron densities obtained. (author)

Scalable Tensor Factorizations with Missing Data

DEFF Research Database (Denmark)

Acar, Evrim; Dunlavy, Daniel M.; Kolda, Tamara G.

2010-01-01

of missing data, many important data sets will be discarded or improperly analyzed. Therefore, we need a robust and scalable approach for factorizing multi-way arrays (i.e., tensors) in the presence of missing data. We focus on one of the most well-known tensor factorizations, CANDECOMP/PARAFAC (CP...... is shown to successfully factor tensors with noise and up to 70% missing data. Moreover, our approach is significantly faster than the leading alternative and scales to larger problems. To show the real-world usefulness of CP-WOPT, we illustrate its applicability on a novel EEG (electroencephalogram...

Scalable tensor factorizations for incomplete data

DEFF Research Database (Denmark)

Acar, Evrim; Dunlavy, Daniel M.; KOlda, Tamara G.

2011-01-01

to factorize data sets with missing values with the goal of capturing the underlying latent structure of the data and possibly reconstructing missing values (i.e., tensor completion). We focus on one of the most well-known tensor factorizations that captures multi-linear structure, CANDECOMP/PARAFAC (CP...... experiments, our algorithm is shown to successfully factorize tensors with noise and up to 99% missing data. A unique aspect of our approach is that it scales to sparse large-scale data, e.g., 1000 × 1000 × 1000 with five million known entries (0.5% dense). We further demonstrate the usefulness of CP...

On improving the efficiency of tensor voting

OpenAIRE

Moreno, Rodrigo; Garcia, Miguel Angel; Puig, Domenec; Pizarro, Luis; Burgeth, Bernhard; Weickert, Joachim

2011-01-01

This paper proposes two alternative formulations to reduce the high computational complexity of tensor voting, a robust perceptual grouping technique used to extract salient information from noisy data. The first scheme consists of numerical approximations of the votes, which have been derived from an in-depth analysis of the plate and ball voting processes. The second scheme simplifies the formulation while keeping the same perceptual meaning of the original tensor voting: The stick tensor v...

Predicting Heats of Explosion of Nitroaromatic Compounds through NBO Charges and 15N NMR Chemical Shifts of Nitro Groups

Directory of Open Access Journals (Sweden)

Ricardo Infante-Castillo

2012-01-01

Full Text Available This work presents a new quantitative model to predict the heat of explosion of nitroaromatic compounds using the natural bond orbital (NBO charge and 15N NMR chemical shifts of the nitro groups (15NNitro as structural parameters. The values of the heat of explosion predicted for 21 nitroaromatic compounds using the model described here were compared with experimental data. The prediction ability of the model was assessed by the leave-one-out cross-validation method. The cross-validation results show that the model is significant and stable and that the predicted accuracy is within 0.146 MJ kg−1, with an overall root mean squared error of prediction (RMSEP below 0.183 MJ kg−1. Strong correlations were observed between the heat of explosion and the charges (R2 = 0.9533 and 15N NMR chemical shifts (R2 = 0.9531 of the studied compounds. In addition, the dependence of the heat of explosion on the presence of activating or deactivating groups of nitroaromatic explosives was analyzed. All calculations, including optimizations, NBO charges, and 15NNitro NMR chemical shifts analyses, were performed using density functional theory (DFT and a 6-311+G(2d,p basis set. Based on these results, this practical quantitative model can be used as a tool in the design and development of highly energetic materials (HEM based on nitroaromatic compounds.

CSI 3.0: a web server for identifying secondary and super-secondary structure in proteins using NMR chemical shifts.

Science.gov (United States)

Hafsa, Noor E; Arndt, David; Wishart, David S

2015-07-01

The Chemical Shift Index or CSI 3.0 (http://csi3.wishartlab.com) is a web server designed to accurately identify the location of secondary and super-secondary structures in protein chains using only nuclear magnetic resonance (NMR) backbone chemical shifts and their corresponding protein sequence data. Unlike earlier versions of CSI, which only identified three types of secondary structure (helix, β-strand and coil), CSI 3.0 now identifies total of 11 types of secondary and super-secondary structures, including helices, β-strands, coil regions, five common β-turns (type I, II, I', II' and VIII), β hairpins as well as interior and edge β-strands. CSI 3.0 accepts experimental NMR chemical shift data in multiple formats (NMR Star 2.1, NMR Star 3.1 and SHIFTY) and generates colorful CSI plots (bar graphs) and secondary/super-secondary structure assignments. The output can be readily used as constraints for structure determination and refinement or the images may be used for presentations and publications. CSI 3.0 uses a pipeline of several well-tested, previously published programs to identify the secondary and super-secondary structures in protein chains. Comparisons with secondary and super-secondary structure assignments made via standard coordinate analysis programs such as DSSP, STRIDE and VADAR on high-resolution protein structures solved by X-ray and NMR show >90% agreement between those made with CSI 3.0. © The Author(s) 2015. Published by Oxford University Press on behalf of Nucleic Acids Research.

The effects of noise over the complete space of diffusion tensor shape.

Science.gov (United States)

Gahm, Jin Kyu; Kindlmann, Gordon; Ennis, Daniel B

2014-01-01

Diffusion tensor magnetic resonance imaging (DT-MRI) is a technique used to quantify the microstructural organization of biological tissues. Multiple images are necessary to reconstruct the tensor data and each acquisition is subject to complex thermal noise. As such, measures of tensor invariants, which characterize components of tensor shape, derived from the tensor data will be biased from their true values. Previous work has examined this bias, but over a narrow range of tensor shape. Herein, we define the mathematics for constructing a tensor from tensor invariants, which permits an intuitive and principled means for building tensors with a complete range of tensor shape and salient microstructural properties. Thereafter, we use this development to evaluate by simulation the effects of noise on characterizing tensor shape over the complete space of tensor shape for three encoding schemes with different SNR and gradient directions. We also define a new framework for determining the distribution of the true values of tensor invariants given their measures, which provides guidance about the confidence the observer should have in the measures. Finally, we present the statistics of tensor invariant estimates over the complete space of tensor shape to demonstrate how the noise sensitivity of tensor invariants varies across the space of tensor shape as well as how the imaging protocol impacts measures of tensor invariants. Copyright © 2013 Elsevier B.V. All rights reserved.

3D Inversion of SQUID Magnetic Tensor Data

DEFF Research Database (Denmark)

Zhdanov, Michael; Cai, Hongzhu; Wilson, Glenn

2012-01-01

Developments in SQUID-based technology have enabled direct measurement of magnetic tensor data for geophysical exploration. For quantitative interpretation, we introduce 3D regularized inversion for magnetic tensor data. For mineral exploration-scale targets, our model studies show that magnetic...... tensor data have significantly improved resolution compared to magnetic vector data for the same model. We present a case study for the 3D regularized inversion of magnetic tensor data acquired over a magnetite skarn at Tallawang, Australia. The results obtained from our 3D regularized inversion agree...

Parameter-free calculation of K alpha chemical shifts for Al, Si, and Ge oxides

DEFF Research Database (Denmark)

Lægsgaard, Jesper

2001-01-01

The chemical shifts of the K alpha radiation line from Al, Si, and Ge ions between their elemental and oxide forms are calculated within the framework of density functional theory using ultrasoft pseudopotentials. It is demonstrated that this theoretical approach yields quantitatively accurate...... results fur the systems investigated, provided that relaxations of the valence electrons upon the core-hole transition are properly accounted for. Therefore, such calculations provide a powerful tool for identification of impurity states based on x-ray fluorescence data. Results for an Al impurity...

Tensor Rank Preserving Discriminant Analysis for Facial Recognition.

Science.gov (United States)

Tao, Dapeng; Guo, Yanan; Li, Yaotang; Gao, Xinbo

2017-10-12

Facial recognition, one of the basic topics in computer vision and pattern recognition, has received substantial attention in recent years. However, for those traditional facial recognition algorithms, the facial images are reshaped to a long vector, thereby losing part of the original spatial constraints of each pixel. In this paper, a new tensor-based feature extraction algorithm termed tensor rank preserving discriminant analysis (TRPDA) for facial image recognition is proposed; the proposed method involves two stages: in the first stage, the low-dimensional tensor subspace of the original input tensor samples was obtained; in the second stage, discriminative locality alignment was utilized to obtain the ultimate vector feature representation for subsequent facial recognition. On the one hand, the proposed TRPDA algorithm fully utilizes the natural structure of the input samples, and it applies an optimization criterion that can directly handle the tensor spectral analysis problem, thereby decreasing the computation cost compared those traditional tensor-based feature selection algorithms. On the other hand, the proposed TRPDA algorithm extracts feature by finding a tensor subspace that preserves most of the rank order information of the intra-class input samples. Experiments on the three facial databases are performed here to determine the effectiveness of the proposed TRPDA algorithm.

The tensor bi-spectrum in a matter bounce

Energy Technology Data Exchange (ETDEWEB)

Chowdhury, Debika; Sreenath, V.; Sriramkumar, L., E-mail: debika@physics.iitm.ac.in, E-mail: sreenath@lsu.edu, E-mail: sriram@physics.iitm.ac.in [Department of Physics, Indian Institute of Technology Madras, Chennai 600036 (India)

2015-11-01

Matter bounces are bouncing scenarios wherein the universe contracts as in a matter dominated phase at early times. Such scenarios are known to lead to a scale invariant spectrum of tensor perturbations, just as de Sitter inflation does. In this work, we examine if the tensor bi-spectrum can discriminate between the inflationary and the bouncing scenarios. Using the Maldacena formalism, we analytically evaluate the tensor bi-spectrum in a matter bounce for an arbitrary triangular configuration of the wavevectors. We show that, over scales of cosmological interest, the non-Gaussianity parameter h{sub NL} that characterizes the amplitude of the tensor bi-spectrum is quite small when compared to the corresponding values in de Sitter inflation. During inflation, the amplitude of the tensor perturbations freeze on super-Hubble scales, a behavior that results in the so-called consistency condition relating the tensor bi-spectrum and the power spectrum in the squeezed limit. In contrast, in the bouncing scenarios, the amplitude of the tensor perturbations grow strongly as one approaches the bounce, which suggests that the consistency condition will not be valid in such situations. We explicitly show that the consistency relation is indeed violated in the matter bounce. We discuss the implications of the results.

Endoscopic Anatomy of the Tensor Fold and Anterior Attic.

Science.gov (United States)

Li, Bin; Doan, Phi; Gruhl, Robert R; Rubini, Alessia; Marchioni, Daniele; Fina, Manuela

2018-02-01

Objectives The objectives of the study were to (1) study the anatomical variations of the tensor fold and its anatomic relation with transverse crest, supratubal recess, and anterior epitympanic space and (2) explore the most appropriate endoscopic surgical approach to each type of the tensor fold variants. Study Design Cadaver dissection study. Setting Temporal bone dissection laboratory. Subjects and Methods Twenty-eight human temporal bones (26 preserved and 2 fresh) were dissected through an endoscopic transcanal approach between September 2016 and June 2017. The anatomical variations of the tensor fold, transverse crest, supratubal recess, and anterior epitympanic space were studied before and after removing ossicles. Results Three different tensor fold orientations were observed: vertical (type A, 11/28, 39.3%) with attachment to the transverse crest, oblique (type B, 13/28, 46.4%) with attachment to the anterior tegmen tympani, and horizontal (type C, 4/28, 14.3%) with attachment to the tensor tympani canal. The tensor fold was a complete membrane in 20 of 28 (71.4%) specimens, preventing direct ventilation between the supratubal recess and anterior epitympanic space. We identified 3 surgical endoscopic approaches, which allowed visualization of the tensor fold without removing the ossicles. Conclusions The orientation of the tensor fold is the determining structure that dictates the conformation and limits of the epitympanic space. We propose a classification of the tensor fold based on 3 anatomical variants. We also describe 3 different minimally invasive endoscopic approaches to identify the orientation of the tensor fold while maintaining ossicular chain continuity.

Potentials for transverse trace-free tensors

International Nuclear Information System (INIS)

Conboye, Rory; Murchadha, Niall Ó

2014-01-01

In constructing and understanding initial conditions in the 3 + 1 formalism for numerical relativity, the transverse and trace-free (TT) part of the extrinsic curvature plays a key role. We know that TT tensors possess two degrees of freedom per space point. However, finding an expression for a TT tensor depending on only two scalar functions is a non-trivial task. Assuming either axial or translational symmetry, expressions depending on two scalar potentials alone are derived here for all TT tensors in flat 3-space. In a more general spatial slice, only one of these potentials is found, the same potential given in (Baker and Puzio 1999 Phys. Rev. D 59 044030) and (Dain 2001 Phys. Rev. D 64 124002), with the remaining equations reduced to a partial differential equation, depending on boundary conditions for a solution. As an exercise, we also derive the potentials which give the Bowen-York curvature tensor in flat space. (paper)

Gauge theories, duality relations and the tensor hierarchy

International Nuclear Information System (INIS)

Bergshoeff, Eric A.; Hohm, Olaf; Hartong, Jelle; Huebscher, Mechthild; OrtIn, Tomas

2009-01-01

We compute the complete 3- and 4-dimensional tensor hierarchies, i.e. sets of p-form fields, with 1 ≤ p ≤ D, which realize an off-shell algebra of bosonic gauge transformations. We show how these tensor hierarchies can be put on-shell by introducing a set of duality relations, thereby introducing additional scalars and a metric tensor. These so-called duality hierarchies encode the equations of motion of the bosonic part of the most general gauged supergravity theories in those dimensions, including the (projected) scalar equations of motion. We construct gauge-invariant actions that include all the fields in the tensor hierarchies. We elucidate the relation between the gauge transformations of the p-form fields in the action and those of the same fields in the tensor hierarchy.

A Bayesian-probability-based method for assigning protein backbone dihedral angles based on chemical shifts and local sequences

Energy Technology Data Exchange (ETDEWEB)

Wang Jun; Liu Haiyan [University of Science and Technology of China, Hefei National Laboratory for Physical Sciences at the Microscale, and Key Laboratory of Structural Biology, School of Life Sciences (China)], E-mail: hyliu@ustc.edu.cn

2007-01-15

Chemical shifts contain substantial information about protein local conformations. We present a method to assign individual protein backbone dihedral angles into specific regions on the Ramachandran map based on the amino acid sequences and the chemical shifts of backbone atoms of tripeptide segments. The method uses a scoring function derived from the Bayesian probability for the central residue of a query tripeptide segment to have a particular conformation. The Ramachandran map is partitioned into representative regions at two levels of resolution. The lower resolution partitioning is equivalent to the conventional definitions of different secondary structure regions on the map. At the higher resolution level, the {alpha} and {beta} regions are further divided into subregions. Predictions are attempted at both levels of resolution. We compared our method with TALOS using the original TALOS database, and obtained comparable results. Although TALOS may produce the best results with currently available databases which are much enlarged, the Bayesian-probability-based approach can provide a quantitative measure for the reliability of predictions.

Reconstruction of convex bodies from surface tensors