Loop Variables Research Articles

Loop variables and gauge invariant exact renormalization group equations for (open) string theory II

In arXiv:1202.4298 gauge invariant interacting equations were written down for the spin 2 and spin 3 massive modes using the exact renormalization group of a world sheet theory. This is generalized to all the higher levels in this paper. An interacting theory of an infinite tower of massive higher spins is obtained. They appear as a compactification of a massless theory in one higher dimension. The compactification and consequent mass is essential for writing the interaction terms. Just as for spin 2 and spin 3, the interactions are in terms of gauge invariant “field strengths” and the gauge transformations are the same as for the free theory. This theory can then be truncated in a gauge invariant way by removing one oscillator of the extra dimension to match the field content of BRST string (field) theory. The truncation has to be done level by level and results are given explicitly for level 4. At least up to level 5, the truncation can be done in a way that preserves the higher-dimensional structure. There is a relatively straightforward generalization of this construction to (arbitrary) curved space–time and this is also outlined.

Loop variables and gauge invariant exact renormalization group equations for (open) string theory

An exact renormalization group equation is written down for the world sheet theory describing the bosonic open string in general backgrounds. Loop variable techniques are used to make the equation gauge invariant. This is worked out explicitly up to level 3. The equation is quadratic in the fields and can be viewed as a proposal for a string field theory equation. As in the earlier loop variable approach, the theory has one extra space dimension and mass is obtained by dimensional reduction. Being based on the sigma model RG, it is background independent. It is intriguing that in contrast to BRST string field theory, the gauge transformations are not modified by the interactions up to the level calculated. The interactions can be written in terms of gauge invariant field strengths for the massive higher spin fields and the non-zero mass is essential for this. This is reminiscent of Abelian Born–Infeld action (along with derivative corrections) for the massless vector field, which is also written in terms of the field strength.

Modeling Structures and Motions of Loops in Protein Molecules

Unlike the secondary structure elements that connect in protein structures, loop fragments in protein chains are often highly mobile even in generally stable proteins. The structural variability of loops is often at the center of a protein’s stability, folding, and even biological function. Loops are found to mediate important biological processes, such as signaling, protein-ligand binding, and protein-protein interactions. Modeling conformations of a loop under physiological conditions remains an open problem in computational biology. This article reviews computational research in loop modeling, highlighting progress and challenges. Important insight is obtained on potential directions for future research.

An Integrated Approach to Oscillation Propagation Identification and Source Locating in Process Multi-loop Systems

An integrated method for identifying the propagation of multi-loop process oscillations and their source location is proposed in this paper. Oscillatory process loop variables are automatically selected based on the component-related ratio index and a mixing matrix, both of which are obtained in data preprocessing by spectral independent component analysis. The complex causality among oscillatory process variables is then revealed by Granger causality test and is visualized in the form of causality diagram. The simplification of causal connectivity in the diagram is performed according to the understanding of process knowledge and the final simplest causality diagram, which represents the main oscillation propagation paths, is achieved by the automated cutting-off threshold search, with which less significant causality pathways are filtered out. The source of the oscillation disturbance can be identified intuitively through the final causality diagram. Both simulated and real plant data tests are presented to demonstrate the effectiveness and feasibility of the proposed method.

Non-Abelian quantum holonomy of hydrogenlike atoms

We study the Uhlmann holonomy [Rep. Math. Phys. 24, 229 (1986)] of quantum states for hydrogenlike atoms where the intrinsic spin and orbital angular momentum are coupled by the spin-orbit interaction and are subject to a slowly varying magnetic field. We show that the holonomy for the orbital angular momentum and spin subsystems is non-Abelian while the holonomy of the whole system is Abelian. Quantum entanglement in the states of the whole system is crucially related to the non-Abelian gauge structure of the subsystems. We analyze the phase of the Wilson loop variable associated with the Uhlmann holonomy and find a relation between the phase of the whole system and corresponding marginal phases. Based on the results for the model system, we provide evidence that the phase of the Wilson loop variable and the mixed-state geometric phase [E. Sj\"oqvist et al., Phys. Rev. Lett. 85, 2845 (2000).] are generally inequivalent.

Exploring the Structure–Function Loop Adaptability of a (β/α)8-Barrel Enzyme through Loop Swapping and Hinge Variability

Evolution of proteins involves sequence changes that are frequently localized at loop regions, revealing their important role in natural evolution. However, the development of strategies to understand and imitate such events constitutes a challenge to design novel enzymes in the laboratory. In this study, we show how to adapt loop swapping as semiautonomous units of functional groups in an enzyme with the (β/α)8-barrel and how this functional adaptation can be measured in vivo. To mimic the natural mechanism providing loop variability in antibodies, we developed an overlap PCR strategy. This includes introduction of sequence diversity at two hinge residues, which connect the new loops with the rest of the protein scaffold, and we demonstrate that this is necessary for a successful exploration of functional sequence space. This design allowed us to explore the sequence requirements to functional adaptation of each loop replacement that may not be sampled otherwise. Libraries generated following this strategy were evaluated in terms of their folding competence and their functional proficiency, an observation that was formalized as a Structure–Function Loop Adaptability value. Molecular details about the function and structure of some variants were obtained by enzyme kinetics and circular dichroism. This strategy yields functional variants that retain the original activity at higher frequencies, suggesting a new strategy for protein engineering that incorporates a more divergent sequence exploration beyond that limited to point mutations. We discuss how this approach may provide insights into the mechanism of enzyme evolution and function.

Detection of control loop interactions and prioritization of control loop maintenance

Chemical processes with multiloop control configurations have significant amount of control loop interactions due to tight mass and heat integration. Change in set point and/or controller parameters of one control loop may affect the variables of other loops. The presence of loop interactions in a process plant can cause significant quality and production losses of the plant. It is challenging to measure the degree of interaction between control loops and rank the loops according to the extent of interactions. This paper presents two data driven techniques to quantify control loop interactions and rank the loops according to their importance. In the first approach, a novel method based on canonical correlation analysis has been developed to calculate interaction among the loops and then normalization is done with respect to the maximum canonical correlation to determine the rank of the loops. In another approach, two indices have been developed using integral of absolute or squared error criteria to quantify loop interaction and determine rank of the loops. Both methods require step test data of the plant. Simulation and experimental results show the validity and efficacy of the proposed methods.

Plantwide oscillations diagnosis—current state and future directions

AbstractThis paper describes the currently available techniques for root‐cause diagnosis of plantwide oscillation and future directions for research in this area. Plantwide oscillation arises mainly for three reasons: (1) tight controller tuning, (2) loop interactions and (3) presence of nonlinear faults such as valve stiction and sensor faults. Plantwide oscillation is detrimental for plant operation because it causes large variability in the control loops resulting in reduced profitability due to inferior quality products, larger rejection rates, reduction in average throughput and increase in energy requirements. Copyright © 2011 Curtin University of Technology and John Wiley & Sons, Ltd.

Integration of Design and Control using an MPC-based superstructure for control structure selection.

AbstractA MINLP framework is used to solve the simultaneous process design and control of a waste water treatment plant including the selection of the control structure. The novelties of the work are that MPC controllers with different interconnection structures are considered and that the resulting closed loop variability costs are calculated using analytical bounds derived from robust control tests. Both centralized and decentralized MPC controllers involving different combinations of manipulated and controlled variables are considered as candidates within the methodology. The proposed simultaneous design and control methodology was applied to a waste-water treatment industrial plant.

Experimental Characterization and Diagnosis of Different Problems in Control Valves

AbstractIn the perspective of developing an integrated system able to include loop performance assessment and early diagnosis of anomalies, an experimental characterization of more common problems encountered in industrial valves has been carried out on a pilot scale plant. The primary scope was to investigate the possibility of detecting different types of valve anomalies from the analysis of routine data, by taking into account additional variables made available by intelligent instrumentation and field bus communication systems. Experimental results show that different problems (as: stiction, change in valve dynamics, air leakage and periodic disturbances), cannot be easily detected by referring to classical loop variables. On the contrary, their presence can be promptly identified by means of Travel Deviation and Drive Signal values, made available by the valve positioner. A key role is plaid by the availability of the valve stem position.

Alternate States of Proteins Revealed by Detailed Energy Landscape Mapping

What conformations do protein molecules populate in solution? Crystallography provides a high-resolution description of protein structure in the crystal environment, while NMR describes structure in solution but using less data. NMR structures display more variability, but is this because crystal contacts are absent or because of fewer data constraints? Here we report unexpected insight into this issue obtained through analysis of detailed protein energy landscapes generated by large-scale, native-enhanced sampling of conformational space with Rosetta@home for 111 protein domains. In the absence of tightly associating binding partners or ligands, the lowest-energy Rosetta models were nearly all <2.5 Å CαRMSD from the experimental structure; this result demonstrates that structure prediction accuracy for globular proteins is limited mainly by the ability to sample close to the native structure. While the lowest-energy models are similar to deposited structures, they are not identical; the largest deviations are most often in regions involved in ligand, quaternary, or crystal contacts. For ligand binding proteins, the low energy models may resemble the apo structures, and for oligomeric proteins, the monomeric assembly intermediates. The deviations between the low energy models and crystal structures largely disappear when landscapes are computed in the context of the crystal lattice or multimer. The computed low-energy ensembles, with tight crystal-structure-like packing in the core, but more NMR-structure-like variability in loops, may in some cases resemble the native state ensembles of proteins better than individual crystal or NMR structures, and can suggest experimentally testable hypotheses relating alternative states and structural heterogeneity to function.

STRING THEORY AND TURBULENCE

We propose a string theory of turbulence that explains the Kolmogorov scaling in 3+1 dimensions and the Kraichnan and Kolmogorov scalings in 2+1 dimensions. This string theory of turbulence should be understood in light of the AdS/CFT dictionary. Our argument is crucially based on the use of Migdal's loop variables and the self-consistent solutions of Migdal's loop equations for turbulence. In particular, there is an area law for turbulence in 2+1 dimensions related to the Kraichnan scaling.

Casimir forces from a loop integral formulation

We reformulate the Casimir force between bodies in non-trivial background media. The force may be written in terms of loop variables, the loop being a curve around the scattering sites. A natural path ordering of exponentials takes place when a particular representation of the scattering centres is given. The basic object to be evaluated is a reduced (or abbreviated) classical pseudo-action that can be operator valued, and can be obtained from a classical path integral description.

BPS operators from the Wilson loop in the 3-dimensional supersymmetric Chern-Simons theory

We consider the small deformation of the point-like Wilson loop in the 3-dimensional $\mathcal{N}=6$ superconformal Chern-Simons theory. By Taylor expansion of the point-like Wilson loop in powers of the loop variables, we obtain the BPS operators that correspond to the excited string states of the dual IIA string theory on the pp wave background. The BPS conditions of the Wilson loop constrain both the loop variables and the forms of the operators obtained in the Taylor expansion.

On the Cuts of Scattering Amplitudes

The use of complex analysis for computing one-loop scattering amplitudes is naturally induced by generalised unitarity-cut conditions, fulfilled by complex values of the loop variable. We report on two techniques: the cut-integration with spinor-variables as contour integrals of rational functions; and the use of the Discrete Fourier Transform to optimize the reduction of tensor-integrals to master scalar integrals.

Botulinum neurotoxin interactions with substrate

The mechanism by which a CNT properly identifies and cleaves its target SNARE once inside the neuron involves one or more regions of enzyme–substrate interaction remote from the active site (so called exosites). We determined the structure of a CNT endopeptidase in complex with its target SNARE that illustrates the extensive enzyme–substrate interface and the basis of substrate selectivity. Our structure of BoNT/A, in complex with human SNAP-25, revealed multiple exosites, including several that are involved in substrate specificity, and one that likely functions as an allosteric activator of the toxin. Different crystal forms of wildtype BoNT/A revealed conformational variability of several loops near the active site. We also determined crystal structures of the apo form of the TeNT LC49 and that of the BoNT/C1 LC protease50. We found remarkable structural differences between the BoNT/C1 and BoNT/A LC proteases that may explain the dual substrate-binding ability of BoNT/C1.

An exact bosonization rule forc= 1 noncritical string theory

We construct a string field theory for c=1 noncritical strings using the loop variables as the string field. We show how one can express the nonrelativistic free fermions which describes the theory, in terms of these string fields.

A large data set comparison of protein structures determined by crystallography and NMR: Statistical test for structural differences and the effect of crystal packing

The existence of a large number of proteins for which both nuclear magnetic resonance (NMR) and X-ray crystallographic coordinates have been deposited into the Protein Data Bank (PDB) makes the statistical comparison of the corresponding crystal and NMR structural models over a large data set possible, and facilitates the study of the effect of the crystal environment and other factors on structure. We present an approach for detecting statistically significant structural differences between crystal and NMR structural models which is based on structural superposition and the analysis of the distributions of atomic positions relative to a mean structure. We apply this to a set of 148 protein structure pairs (crystal vs NMR), and analyze the results in terms of methodological and physical sources of structural difference. For every one of the 148 structure pairs, the backbone root-mean-square distance (RMSD) over core atoms of the crystal structure to the mean NMR structure is larger than the average RMSD of the members of the NMR ensemble to the mean, with 76% of the structure pairs having an RMSD of the crystal structure to the mean more than a factor of two larger than the average RMSD of the NMR ensemble. On average, the backbone RMSD over core atoms of crystal structure to the mean NMR is approximately 1 A. If non-core atoms are included, this increases to 1.4 A due to the presence of variability in loops and similar regions of the protein. The observed structural differences are only weakly correlated with the age and quality of the structural model and differences in conditions under which the models were determined. We examine steric clashes when a putative crystalline lattice is constructed using a representative NMR structure, and find that repulsive crystal packing plays a minor role in the observed differences between crystal and NMR structures. The observed structural differences likely have a combination of physical and methodological causes. Stabilizing attractive interactions arising from intermolecular crystal contacts which shift the equilibrium of the crystal structure relative to the NMR structure is a likely physical source which can account for some of the observed differences. Methodological sources of apparent structural difference include insufficient sampling or other issues which could give rise to errors in the estimates of the precision and/or accuracy.

Holonomy transformation in the FRW metric

In this work we investigate loop variables in Friedman-Robertson-Walker spacetime. We analyze the parallel transport of vectors and spinors along several paths in this spacetime in order to classify its global properties. Band holonomy invariance is analysed in this background.

The Barbero connection and its relation to the histories connection formalism without gauge fixing

We present a histories version of the connection formalism of general relativity. Such an approach introduces a spacetime description—a characteristic feature of the histories approach—and we discuss the extent to which the usual loop variables are compatible with a spacetime description. In particular, we discuss the definability of the Barbero connection without any gauge fixing. Although it is not the pullback of a spacetime connection onto the 3-surface and it does not have a natural spacetime interpretation, this does not mean that the Barbero connection is not a suitable variable for quantization; it appears naturally in the formalism even in the absence of gauge fixing. It may be employed therefore to define loop variables similar to those employed in loop quantum gravity. However, the loop algebra would have to be augmented by the introduction of additional variables.