A statistical method for the identification and aggregation of regional linguistic variation

This paper introduces a method for the analysis of regional linguistic variation. The method identifies individual and common patterns of spatial clustering in a set of linguistic variables measured over a set of locations based on a combination of three statistical techniques: spatial autocorrelation, factor analysis, and cluster analysis. To demonstrate how to apply this method, it is used to analyze regional variation in the values of 40 continuously measured, high-frequency lexical alternation variables in a 26-million-word corpus of letters to the editor representing 206 cities from across the United States.

A regional analysis of contraction rate in written Standard American English

The goal of this study is to determine if various measures of contraction rate are regionally patterned in written Standard American English. In order to answer this question, this study employs a corpus-based approach to data collection and a statistical approach to data analysis. Based on a spatial autocorrelation analysis of the values of eleven measures of contraction across a 25 million word corpus of letters to the editor representing the language of 200 cities from across the contiguous United States, two primary regional patterns were identified: easterners tend to produce relatively few standard contractions (not contraction, verb contraction) compared to westerners, and northeasterners tend to produce relatively few non-standard contractions (to contraction, non-standard not contraction) compared to southeasterners. These findings demonstrate that regional linguistic variation exists in written Standard American English and that regional linguistic variation is more common than is generally assumed.

The Riesz transform and simultaneous representations of phase, energy and orientation in spatial vision

To represent the local orientation and energy of a 1-D image signal, many models of early visual processing employ bandpass quadrature filters, formed by combining the original signal with its Hilbert transform. However, representations capable of estimating an image signal's 2-D phase have been largely ignored. Here, we consider 2-D phase representations using a method based upon the Riesz transform. For spatial images there exist two Riesz transformed signals and one original signal from which orientation, phase and energy may be represented as a vector in 3-D signal space. We show that these image properties may be represented by a Singular Value Decomposition (SVD) of the higher-order derivatives of the original and the Riesz transformed signals. We further show that the expected responses of even and odd symmetric filters from the Riesz transform may be represented by a single signal autocorrelation function, which is beneficial in simplifying Bayesian computations for spatial orientation. Importantly, the Riesz transform allows one to weight linearly across orientation using both symmetric and asymmetric filters to account for some perceptual phase distortions observed in image signals - notably one's perception of edge structure within plaid patterns whose component gratings are either equal or unequal in contrast. Finally, exploiting the benefits that arise from the Riesz definition of local energy as a scalar quantity, we demonstrate the utility of Riesz signal representations in estimating the spatial orientation of second-order image signals. We conclude that the Riesz transform may be employed as a general tool for 2-D visual pattern recognition by its virtue of representing phase, orientation and energy as orthogonal signal quantities.

FemtoNewton force sensing with optically trapped nanotubes

We extract the distribution of both center-of-mass and angular fluctuations from three-dimensional tracking of optically trapped nanotubes. We measure the optical force and torque constants from autocorrelation and cross-correlation of the tracking signals. This allows us to isolate the angular Brownian motion. We demonstrate that nanotubes enable nanometer spatial and femtonewton force resolution in photonic force microscopy, the smallest to date. This has wide implications in nanotechnology, biotechnology, nanofluidics, and material science.

Optical autocorrelator that uses a surface-emitting second-harmonic generator on (211)B GaAs

An optical autocorrelator grown on a (211)B GaAs substrate that uses visible surface-emitted second-harmonic generation is demonstrated. The (211)B orientation needs TE mode excitation only, thus eliminating the problem of the beating between the TE and TM modes that is required for (100)-grown devices; it also has the advantage of giving higher upconversion efficiency than (111) growth. Values of waveguide loss and the difference in the effective refractive index between the TE(0) and TE(1) modes were also obtained from the autocorrelation experiment.

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)1751-811310.1088/1751-8113/46/3/035501; Nath, Phys. Rev. E 88, 013010 (2013)PLEEE81539-375510.1103/PhysRevE.88.013010] 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 3000 K is 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.

Serial correlation in the returns of UK capitalization based portfolios

This article examines whether UK portfolio returns are time varying so that expected returns follow an AR(1) process as proposed by Conrad and Kaul for the USA. It explores this hypothesis for four portfolios that have been formed on the basis of market capitalization. The portfolio returns are modelled using a kalman filter signal extraction model in which the unobservable expected return is the state variable and is allowed to evolve as a stationary first order autoregressive process. It finds that this model is a good representation of returns and can account for most of the autocorrelation present in observed portfolio returns. This study concludes that UK portfolio returns are time varying and the nature of the time variation appears to introduce a substantial amount of autocorrelation to portfolio returns. Like Conrad and Kaul if finds a link between the extent to which portfolio returns are time varying and the size of firms within a portfolio but not the monotonic one found for the USA. © 2004 Taylor and Francis Ltd.

Numerical implementation of the coarse step method with a varying differential group delay

The effect of having a fixed differential-group delay term in the coarse-step method results in a periodic pattern in the autocorrelation function. We solve this problem by inserting a varying DGD term at each integration step, according to a Gaussian distribution. Simulation results are given to illustrate the phenomenon and provide some evidence, about its statistical nature.

Bridging large and small scales of water models using hybrid Molecular Dynamics/Fluctuating Hydrodynamics framework

This thesis presents a two-dimensional water model investigation and development of a multiscale method for the modelling of large systems, such as virus in water or peptide immersed in the solvent. We have implemented a two-dimensional ‘Mercedes Benz’ (MB) or BN2D water model using Molecular Dynamics. We have studied its dynamical and structural properties dependence on the model’s parameters. For the first time we derived formulas to calculate thermodynamic properties of the MB model in the microcanonical (NVE) ensemble. We also derived equations of motion in the isothermal–isobaric (NPT) ensemble. We have analysed the rotational degree of freedom of the model in both ensembles. We have developed and implemented a self-consistent multiscale method, which is able to communicate micro- and macro- scales. This multiscale method assumes, that matter consists of the two phases. One phase is related to micro- and the other to macroscale. We simulate the macro scale using Landau Lifshitz-Fluctuating Hydrodynamics, while we describe the microscale using Molecular Dynamics. We have demonstrated that the communication between the disparate scales is possible without introduction of fictitious interface or approximations which reduce the accuracy of the information exchange between the scales. We have investigated control parameters, which were introduced to control the contribution of each phases to the matter behaviour. We have shown, that microscales inherit dynamical properties of the macroscales and vice versa, depending on the concentration of each phase. We have shown, that Radial Distribution Function is not altered and velocity autocorrelation functions are gradually transformed, from Molecular Dynamics to Fluctuating Hydrodynamics description, when phase balance is changed. In this work we test our multiscale method for the liquid argon, BN2D and SPC/E water models. For the SPC/E water model we investigate microscale fluctuations which are computed using advanced mapping technique of the small scales to the large scales, which was developed by Voulgarakisand et. al.

A statistical analysis of regional variation in adverb position in a corpus of written Standard American English

This paper investigates whether the position of adverb phrases in sentences is regionally patterned in written Standard American English, based on an analysis of a 25 million word corpus of letters to the editor representing the language of 200 cities from across the United States. Seven measures of adverb position were tested for regional patterns using the global spatial autocorrelation statistic Moran’s I and the local spatial autocorrelation statistic Getis-Ord Gi*. Three of these seven measures were indentified as exhibiting significant levels of spatial autocorrelation, contrasting the language of the Northeast with language of the Southeast and the South Central states. These results demonstrate that continuous regional grammatical variation exists in American English and that regional linguistic variation exists in written Standard English.

Stochasticity, periodicity and localized light structures in partially mode-locked fibre lasers

Physical systems with co-existence and interplay of processes featuring distinct spatio-temporal scales are found in various research areas ranging from studies of brain activity to astrophysics. The complexity of such systems makes their theoretical and experimental analysis technically and conceptually challenging. Here, we discovered that while radiation of partially mode-locked fibre lasers is stochastic and intermittent on a short time scale, it exhibits non-trivial periodicity and long-scale correlations over slow evolution from one round-trip to another. A new technique for evolution mapping of intensity autocorrelation function has enabled us to reveal a variety of localized spatio-temporal structures and to experimentally study their symbiotic co-existence with stochastic radiation. Real-time characterization of dynamical spatio-temporal regimes of laser operation is set to bring new insights into rich underlying nonlinear physics of practical active- and passive-cavity photonic systems.

Multiscale molecular dynamics/hydrodynamics implementation of two dimensional “Mercedes Benz” water model

A multiscale Molecular Dynamics/Hydrodynamics implementation of the 2D Mercedes Benz (MB or BN2D) [1] water model is developed and investigated. The concept and the governing equations of multiscale coupling together with the results of the two-way coupling implementation are reported. The sensitivity of the multiscale model for obtaining macroscopic and microscopic parameters of the system, such as macroscopic density and velocity fluctuations, radial distribution and velocity autocorrelation functions of MB particles, is evaluated. Critical issues for extending the current model to large systems are discussed.

Application of ensemble averaging to the analysis of electromyography recordings under whole body vibratory stimulation

The aim of this study is to evaluate the application of ensemble averaging to the analysis of electromyography recordings under whole body vibratory stimulation. Recordings from Rectus Femoris, collected during vibratory stimulation at different frequencies, are used. Each signal is subdivided in intervals, which time duration is related to the vibration frequency. Finally the average of the segmented intervals is performed. By using this method for the majority of the recordings the periodic components emerge. The autocorrelation of few seconds of signals confirms the presence of a pseudosinusoidal components strictly related to the soft tissues oscillations caused by the mechanical waves. © 2014 IEEE.

Channel model and lower capacity bound for the transmission based on nonlinear Fourier transform

The integrability of the nonlinear Schräodinger equation (NLSE) by the inverse scattering transform shown in a seminal work [1] gave an interesting opportunity to treat the corresponding nonlinear channel similar to a linear one by using the nonlinear Fourier transform. Integrability of the NLSE is in the background of the old idea of eigenvalue communications [2] that was resurrected in recent works [3{7]. In [6, 7] the new method for the coherent optical transmission employing the continuous nonlinear spectral data | nonlinear inverse synthesis was introduced. It assumes the modulation and detection of data using directly the continuous part of nonlinear spectrum associated with an integrable transmission channel (the NLSE in the case considered). Although such a transmission method is inherently free from nonlinear impairments, the noisy signal corruptions, arising due to the ampli¯er spontaneous emission, inevitably degrade the optical system performance. We study properties of the noise-corrupted channel model in the nonlinear spectral domain attributed to NLSE. We derive the general stochastic equations governing the signal evolution inside the nonlinear spectral domain and elucidate the properties of the emerging nonlinear spectral noise using well-established methods of perturbation theory based on inverse scattering transform [8]. It is shown that in the presence of small noise the communication channel in the nonlinear domain is the additive Gaussian channel with memory and signal-dependent correlation matrix. We demonstrate that the effective spectral noise acquires colouring", its autocorrelation function becomes slow decaying and non-diagonal as a function of \frequencies", and the noise loses its circular symmetry, becoming elliptically polarized. Then we derive a low bound for the spectral effiency for such a channel. Our main result is that by using the nonlinear spectral techniques one can significantly increase the achievable spectral effiency compared to the currently available methods [9]. REFERENCES 1. Zakharov, V. E. and A. B. Shabat, Sov. Phys. JETP, Vol. 34, 62{69, 1972. 2. Hasegawa, A. and T. Nyu, J. Lightwave Technol., Vol. 11, 395{399, 1993. 3. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4312{4328, 2014. 4. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4329{4345 2014. 5. Yousefi, M. I. and F. R. Kschischang, IEEE Trans. Inf. Theory, Vol. 60, 4346{4369, 2014. 6. Prilepsky, J. E., S. A. Derevyanko, K. J. Blow, I. Gabitov, and S. K. Turitsyn, Phys. Rev. Lett., Vol. 113, 013901, 2014. 7. Le, S. T., J. E. Prilepsky, and S. K. Turitsyn, Opt. Express, Vol. 22, 26720{26741, 2014. 8. Kaup, D. J. and A. C. Newell, Proc. R. Soc. Lond. A, Vol. 361, 413{446, 1978. 9. Essiambre, R.-J., G. Kramer, P. J. Winzer, G. J. Foschini, and B. Goebel, J. Lightwave Technol., Vol. 28, 662{701, 2010.

Early warnings of heart rate deterioration

Hospitals can experience difficulty in detecting and responding to early signs of patient deterioration leading to late intensive care referrals, excess mortality and morbidity, and increased hospital costs. Our study aims to explore potential indicators of physiological deterioration by the analysis of vital-signs. The dataset used comprises heart rate (HR) measurements from MIMIC II waveform database, taken from six patients admitted to the Intensive Care Unit (ICU) and diagnosed with severe sepsis. Different indicators were considered: 1) generic early warning indicators used in ecosystems analysis (autocorrelation at-1-lag (ACF1), standard deviation (SD), skewness, kurtosis and heteroskedasticity) and 2) entropy analysis (kernel entropy and multi scale entropy). Our preliminary findings suggest that when a critical transition is approaching, the equilibrium state changes what is visible in the ACF1 and SD values, but also by the analysis of the entropy. Entropy allows to characterize the complexity of the time series during the hospital stay and can be used as an indicator of regime shifts in a patient’s condition. One of the main problems is its dependency of the scale used. Our results demonstrate that different entropy scales should be used depending of the level of entropy verified.