Dipolar cross-correlation effects in the nuclear overhauser experiments of weakly and strongly coupled spins

The effect of dipolar cross correlation in 1H---1H nuclear Overhauser effect experiments is investigated by detailed calculation in an ABX spin system. It is found that in weakly coupled spin systems, the cross-correlation effects are limited to single-quantum transition probabilities and decrease in magnitude as ωτc increases. Strong coupling, however, mixes the states and the cross correlations affect the zero-quantum and double-quantum transition probabilities as well. The effect of cross correlation in steady-state and transient NOE experiments is studied as a function of strong coupling and ωτc. The results for steady-state NOE experiments are calculated analytically and those for transient NOE experiments are calculated numerically. The NOE values for the A and B spins have been calculated by assuming nonselective perturbation of all the transitions of the X spin. A significant effect of cross correlation is found in transient NOE experiments of weakly as well as strongly coupled spins when the multiplets are resolved. Cross correlation manifests itself largely as a multiplet effect in the transient NOE of weakly coupled spins for nonselective perturbation of all X transitions. This effect disappears for a measuring pulse of 90° or when the multiplets are not resolved. For steady-state experiments, the effect of cross correlation is analytically zero for weakly coupled spins and small for strongly coupled spins.

Influence of cross-correlation between dipolar and chemical shift anisotropy relaxation mechanisms upon the transverse relaxation rates of 15N in macromolecules

Heteronuclear multiple-quantum coherence relaxation rate are calculated for the individual transitions of the S spin in an AIS nuclear spin system assuming that the heteronucleus (S spin) has relaxation contributions from both intramolecular dipole-dipole and chemical shift anisotropy relaxation. The individual multiplet components of the heteronuclear zero- and double-quantum coherences are shown to have different transverse relaxation rates. The cross-correlation between the two relaxation mechanisms is shown to be the dominant cause of the calculated differential line broadening. Experimental data are presented using as an example a uniformly 15N labelled sample of human epidermal growth factor.

Cross-correlation-aided transport in stochastically driven accretion flows

The origin of linear instability resulting in rotating sheared accretion flows has remained a controversial subject for a long time. While some explanations of such non-normal transient growth of disturbances in the Rayleigh stable limit were available for magnetized accretion flows, similar instabilities in the absence of magnetic perturbations remained unexplained. This dichotomy was resolved in two recent publications by Chattopadhyay and co-workers Mukhopadhyay and Chattopadhyay, J. Phys. A 46, 035501 (2013); Nath et al., Phys. Rev. E 88, 013010 (2013)] where it was shown that such instabilities, especially for nonmagnetized accretion flows, were introduced through interaction of the inherent stochastic noise in the system (even a ``cold'' accretion flow at 3000Kis too ``hot'' in the statistical parlance and is capable of inducing strong thermal modes) with the underlying Taylor-Couette flow profiles. Both studies, however, excluded the additional energy influx (or efflux) that could result from nonzero cross correlation of a noise perturbing the velocity flow, say, with the noise that is driving the vorticity flow (or equivalently the magnetic field and magnetic vorticity flow dynamics). Through the introduction of such a time symmetry violating effect, in this article we show that nonzero noise cross correlations essentially renormalize the strength of temporal correlations. Apart from an overall boost in the energy rate (both for spatial and temporal correlations, and hence in the ensemble averaged energy spectra), this results in mutual competition in growth rates of affected variables often resulting in suppression of oscillating Alfven waves at small times while leading to faster saturations at relatively longer time scales. The effects are seen to be more pronounced with magnetic field fluxes where the noise cross correlation magnifies the strength of the field concerned. Another remarkable feature noted specifically for the autocorrelation functions is the removal of energy degeneracy in the temporal profiles of fast growing non-normal modes leading to faster saturation with minimum oscillations. These results, including those presented in the previous two publications, now convincingly explain subcritical transition to turbulence in the linear limit for all possible situations that could now serve as the benchmark for nonlinear stability studies in Keplerian accretion disks.

Vibrational phase relaxation of O–H stretch in bulk water: Role of large amplitude angular jumps and negative cross-correlations among the forces on the O–H bond

The ultrafast vibrational phase relaxation of O–H stretch in bulk water is investigated in molecular dynamics simulations. The dephasing time (T2) of the O–H stretch in bulk water calculated from the frequency fluctuation time correlation function (Cω(t)) is in the range of 70–80 femtosecond (fs), which is comparable to the characteristic timescale obtained from the vibrational echo peak shift measurements using infrared photon echo [W.P. de Boeij, M.S. Pshenichnikov, D.A. Wiersma, Ann. Rev. Phys. Chem. 49 (1998) 99]. The ultrafast decay of Cω(t) is found to be responsible for the ultrashort T2 in bulk water. Careful analysis reveals the following two interesting reasons for the ultrafast decay of Cω(t). (A) The large amplitude angular jumps of water molecules (within 30–40 fs time duration) provide a large scale contribution to the mean square vibrational frequency fluctuation and gives rise to the rapid spectral diffusion on 100 fs time scale. (B) The projected force, due to all the atoms of the solvent molecules on the oxygen (FO(t)) and hydrogen (FH(t)) atom of the O–H bond exhibit a large negative cross-correlation (NCC). We further find that this NCC is partly responsible for a weak, non-Arrhenius temperature dependence of the dephasing rate.

Universality of scaling laws in correlation between velocity and shear stress in turbulent boundary layers

In this study, we analyse simultaneous measurements (at 50 Hz) of velocity at several heights and shear stress at the surface made during the Utah field campaign for the presence of ranges of scales, where distinct scale-to-scale interactions between velocity and shear stress can be identified. We find that our results are similar to those obtained in a previous study [Venugopal et al., 2003] (contrary to the claim in V2003, that the scaling relations might be dependent on Reynolds number) where wind tunnel measurements of velocity and shear stress were analysed. We use a wavelet-based scale-to-scale cross-correlation to detect three ranges of scales of interaction between velocity and shear stress, namely, (a) inertial subrange, where the correlation is negligible; (b) energy production range, where the correlation follows a logarithmic law; and (c) for scales larger than the boundary layer height, the correlation reaches a plateau.

Allostery in tRNA Synthetases Elucidated from MD Simulations and Protein Structure Networks

tRNA synthetases (aaRS) are enzymes crucial in the translation of genetic code. The enzyme accylates the acceptor stem of tRNA by the congnate amino acid bound at the active site, when the anti-codon is recognized by the anti-codon site of aaRS. In a typical aaRS, the distance between the anti-codon region and the amino accylation site is approximately 70 Å. We have investigated this allosteric phenomenon at molecular level by MD simulations followed by the analysis of protein structure networks (PSN) of non-covalent interactions. Specifically, we have generated conformational ensembles by performing MD simulations on different liganded states of methionyl tRNA synthetase (MetRS) from Escherichia coli and tryptophenyl tRNA synthetase (TrpRS) from Human. The correlated residues during the MD simulations are identified by cross correlation maps. We have identified the amino acids connecting the correlated residues by the shortest path between the two selected members of the PSN. The frequencies of paths have been evaluated from the MD snapshots[1]. The conformational populations in different liganded states of the protein have been beautifully captured in terms of network parameters such as hubs, cliques and communities[2]. These parameters have been associated with the rigidity and plasticity of the protein conformations and can be associated with free energy landscape. A comparison of allosteric communication in MetRS and TrpRS [3] elucidated in this study highlights diverse means adopted by different enzymes to perform a similar function. The computational method described for these two enzymes can be applied to the investigation of allostery in other systems.

Random vibration of a second order non-linear elastic system

A method is presented for obtaining, approximately, the response covariance and probability distribution of a non-linear oscillator under a Gaussian excitation. The method has similarities with the hierarchy closure and the equivalent linearization approaches, but is different. A Gaussianization technique is used to arrive at the output autocorrelation and the input-output cross-correlation. This along with an energy equivalence criterion is used to estimate the response distribution function. The method is applicable in both the transient and steady state response analysis under either stationary or non-stationary excitations. Good comparison has been observed between the predicted and the exact steady state probability distribution of a Duffing oscillator under a white noise input.

Simulation of wavelength/time multiple-pulses-per-row fiber-optic CDMA network

Passive wavelength/time fiber-optic code division multiple access (WIT FO-CDMA) network is a viable option for highspeed access networks. Constructions of 2-D codes, suitable for incoherent WIT FO-CDMA, have been proposed to reduce the time spread of the 1-D sequences. The 2-D constructions can be broadly classified as 1) hybrid codes and 2) matrix codes. In our earlier work [141, we had proposed a new family of wavelength/time multiple-pulses-per-row (W/T MPR) matrix codes which have good cardinality, spectral efficiency and at the same time have the lowest off-peak autocorrelation and cross-correlation values equal to unity. In this paper we propose an architecture for a WIT MPR FO-CDAM network designed using the presently available devices and technology. A complete FO-CDMA network of ten users is simulated, for various number of simultaneous users and shown that 0 --> 1 errors can occur only when the number of interfering users is at least equal to the threshold value.

Stability of systems with power-law non-linearities

It is shown that a sufficient condition for the asymptotic stability-in-the-large of an autonomous system containing a linear part with transfer function G(jω) and a non-linearity belonging to a class of power-law non-linearities with slope restriction [0, K] in cascade in a negative feedback loop is ReZ(jω)[G(jω) + 1 K] ≥ 0 for all ω where the multiplier is given by, Z(jω) = 1 + αjω + Y(jω) - Y(-jω) with a real, y(t) = 0 for t < 0 and ∫ 0 ∞ |y(t)|dt < 1 2c2, c2 being a constant associated with the class of non-linearity. Any allowable multiplier can be converted to the above form and this form leads to lesser restrictions on the parameters in many cases. Criteria for the case of odd monotonic non-linearities and of linear gains are obtained as limiting cases of the criterion developed. A striking feature of the present result is that in the linear case it reduces to the necessary and sufficient conditions corresponding to the Nyquist criterion. An inequality of the type |R(T) - R(- T)| ≤ 2c2R(0) where R(T) is the input-output cross-correlation function of the non-linearity, is used in deriving the results.

A note on the measurement of travel times using bender and extender elements

By using the bender and extender elements tests, the travel times of the shear (S) and the primary (P) waves were measured for dry sand samples at different relative densities and effective confining pressures. Three methods of interpretations, namely, (i) the first time of arrival, (ii) the first peak to peak, and (iii) the cross-correlation method, were employed. All the methods provide almost a unique answer associated with the P-wave measurements. On contrary, a difference was noted in the arrival times obtained from the different methods for the S-wave due to the near field effect. The resonant column tests in the torsional mode were also performed to check indirectly the travel time of the shear wave. The study reveals that as compared to the S-wave, it is more reliable to depend on the arrival times' measurement for the P-wave. (C) 2010 Elsevier Ltd. All rights reserved.

A note on the measurement of travel times using bender and extender elements

By using the bender and extender elements tests, the travel times of the shear (S) and the primary (P) waves were measured for dry sand samples at different relative densities and effective confining pressures. Three methods of interpretations, namely, (i) the first time of arrival, (ii) the first peak to peak, and (iii) the cross-correlation method, were employed. All the methods provide almost a unique answer associated with the P-wave measurements. On contrary, a difference was noted in the arrival times obtained from the different methods for the S-wave due to the near field effect. The resonant column tests in the torsional mode were also performed to check indirectly the travel time of the shear wave. The study reveals that as compared to the S-wave, it is more reliable to depend on the arrival times’ measurement for the P-wave.

Processing of Ultrasonic Signal for Transducer Characterization and for Improving Signal-To-Noise Ratio

This paper describes the work related to characterisation of an ultrasonic transducer fabricated in the laboratory. The response of the medium to the ultrasonic wave was obtained by converting the time domain signal to frequency domain, using the FFT algorithm. Cross-correlation technique was adopted to increase the S/N ratio in the raw time domain signal and subsequently, to determine the ultrasonic velocity in the medium.

Dynamic coupling between the LID and NMP domain motions in the catalytic conversion of ATP and AMP to ADP by adenylate kinase

The catalytic conversion of adenosine triphosphate (ATP) and adenosine monophosphate (AMP) to adenosine diphosphate (ADP) by adenylate kinase (ADK) involves large amplitude, ligand induced domain motions, involving the opening and the closing of ATP binding domain (LID) and AMP binding domain (NMP) domains, during the repeated catalytic cycle. We discover and analyze an interesting dynamical coupling between the motion of the two domains during the opening, using large scale atomistic molecular dynamics trajectory analysis, covariance analysis, and multidimensional free energy calculations with explicit water. Initially, the LID domain must open by a certain amount before the NMP domain can begin to open. Dynamical correlation map shows interesting cross-peak between LID and NMP domain which suggests the presence of correlated motion between them. This is also reflected in our calculated two-dimensional free energy surface contour diagram which has an interesting elliptic shape, revealing a strong correlation between the opening of the LID domain and that of the NMP domain. Our free energy surface of the LID domain motion is rugged due to interaction with water and the signature of ruggedness is evident in the observed root mean square deviation variation and its fluctuation time correlation functions. We develop a correlated dynamical disorder-type theoretical model to explain the observed dynamic coupling between the motion of the two domains in ADK. Our model correctly reproduces several features of the cross-correlation observed in simulations. (C) 2011 American Institute of Physics. doi:10.1063/1.3516588]

Decorrelation of broad band signals by toeplitz-block-toeplitz structuring

We propose F-norm of the cross-correlation part of the array covariance matrix as a measure of correlation between the impinging signals and study the performance of different decorrelation methods in the broadband case using this measure. We first show that dimensionality of the composite signal subspace, defined as the number of significant eigenvectors of the source sample covariance matrix, collapses in the presence of multipath and the spatial smoothing recovers this dimensionality. Using an upper bound on the proposed measure, we then study the decorrelation of the broadband signals with spatial smoothing and the effect of spacing and directions of the sources on the rate of decorrelation with progressive smoothing. Next, we introduce a weighted smoothing method based on Toeplitz-block-Toeplitz (TBT) structuring of the data covariance matrix which decorrelates the signals much faster than the spatial smoothing. Computer simulations are included to demonstrate the performance of the two methods.

Believe it or Not! Multicore CPUs can Match GPUs for FLOP-intensive Applications

In this work, we evaluate performance of a real-world image processing application that uses a cross-correlation algorithm to compare a given image with a reference one. The algorithm processes individual images represented as 2-dimensional matrices of single-precision floating-point values using O(n4) operations involving dot-products and additions. We implement this algorithm on a nVidia GTX 285 GPU using CUDA, and also parallelize it for the Intel Xeon (Nehalem) and IBM Power7 processors, using both manual and automatic techniques. Pthreads and OpenMP with SSE and VSX vector intrinsics are used for the manually parallelized version, while a state-of-the-art optimization framework based on the polyhedral model is used for automatic compiler parallelization and optimization. The performance of this algorithm on the nVidia GPU suffers from: (1) a smaller shared memory, (2) unaligned device memory access patterns, (3) expensive atomic operations, and (4) weaker single-thread performance. On commodity multi-core processors, the application dataset is small enough to fit in caches, and when parallelized using a combination of task and short-vector data parallelism (via SSE/VSX) or through fully automatic optimization from the compiler, the application matches or beats the performance of the GPU version. The primary reasons for better multi-core performance include larger and faster caches, higher clock frequency, higher on-chip memory bandwidth, and better compiler optimization and support for parallelization. The best performing versions on the Power7, Nehalem, and GTX 285 run in 1.02s, 1.82s, and 1.75s, respectively. These results conclusively demonstrate that, under certain conditions, it is possible for a FLOP-intensive structured application running on a multi-core processor to match or even beat the performance of an equivalent GPU version.