True Bandwidth Research Articles

Functional data analysis by matrix completion

Functional data analyses typically proceed by smoothing, followed by functional PCA. This paradigm implicitly assumes that rough variation is due to nuisance noise. Nevertheless, relevant functional features such as time-localised or short scale fluctuations may indeed be rough relative to the global scale, but still smooth at shorter scales. These may be confounded with the global smooth components of variation by the smoothing and PCA, potentially distorting the parsimony and interpretability of the analysis. The goal of this paper is to investigate how both smooth and rough variations can be recovered on the basis of discretely observed functional data. Assuming that a functional datum arises as the sum of two uncorrelated components, one smooth and one rough, we develop identifiability conditions for the recovery of the two corresponding covariance operators. The key insight is that they should possess complementary forms of parsimony: one smooth and finite rank (large scale), and the other banded and potentially infinite rank (small scale). Our conditions elucidate the precise interplay between rank, bandwidth and grid resolution. Under these conditions, we show that the recovery problem is equivalent to rank-constrained matrix completion, and exploit this to construct estimators of the two covariances, without assuming knowledge of the true bandwidth or rank; we study their asymptotic behaviour, and then use them to recover the smooth and rough components of each functional datum by best linear prediction. As a result, we effectively produce separate functional PCAs for smooth and rough variation.

Sampling of Planar Curves: Theory and Fast Algorithms

We introduce a continuous domain framework for the recovery of a planar curve from a few samples. We model the curve as the zero level set of a trigonometric polynomial. We show that the exponential feature maps of the points on the curve lie on a low-dimensional subspace. We show that the null-space vector of the feature matrix can be used to uniquely identify the curve, given a sufficient number of samples. The worst-case theoretical guarantees show that the number of samples required for unique recovery depends on the bandwidth of the underlying trigonometric polynomial, which is a measure of the complexity of the curve. We introduce an iterative algorithm that relies on the low-rank property of the feature maps to recover the curves when the samples are noisy or when the true bandwidth of the curve is unknown. We also demonstrate the preliminary utility of the proposed curve representation in the context of image segmentation.

Improved Dynamic Bandwidth Allocation Algorithm for XGPON

Passive optical networks (PONs) require a dynamic bandwidth allocation (DBA) algorithm at the optical line terminal for efficient utilization of upstream bandwidth among the optical network units (ONUs) as per the quality of service requirements for each traffic class defined by PON standardizing bodies. The GigaPON access network (GIANT) was the first International Telecommunication Union compliant DBA algorithm, which is further improved by Immediate Allocation with Colorless Grant (IACG) and Efficient Bandwidth Utilization (EBU) algorithms. However, the polling mechanism of IACG and EBU may not report the true bandwidth demand of ONUs during a service interval. Furthermore, ONU scheduling mechanisms give preference to best effort traffic over the assured traffic during recursive allocation cycles in a service interval, which results in an increase in upstream delays for the assured traffic class. This paper presents an improved bandwidth utilization (IBU) algorithm, which rectifies these deficiencies with a novel polling and scheduling mechanism. Experimental results show that IBU improves the mean of upstream delays of type 2 traffic up to 98%, 93%, and 76% and up to 99%, 92%, and 73% for type 3 traffic compared to the GIANT, IACG, and EBU algorithms, respectively. IBU also shows the least frame loss compared to these state-of-the-art algorithms.

Study on the out-of-plane deformation of the Portevin–Le Chatelier band by using digital shearography

The out-of-plane deformation of the Portevin–Le Chatelier (PLC) band is investigated during tensile tests in an Al alloy using digital shearography for the first time. The fringe patterns, which reflect the out-of-plane displacement gradient, indicate that the PLC bands also appear in the out-of-plane deformation field corresponding to the serrations in the stress–strain curve. Unlike the results obtained from other methods, the true bandwidth is determined by subtracting the shearing amount from the observed bandwidth. The continuous propagation of type-A PLC bands is traced at three different shearing amounts. The out-of-plane displacement of a PLC band is obtained based on the gray-level distribution in a frame of fringe pattern. The maximum displacement is approximately 250nm in an interval of 1/15s during a continuous propagation. The displacement gradient is greater in the front of the PLC band than in the back. Moreover, the position change process of the PLC band is presented, i.e., a band disappearing and a new band forming concurrently in another place. The inclination transition process, such that the inclination direction of the PLC band turns from the “/” direction to the “⧹” direction, is also shown in detail. The results prove that the vibrations-proof and high sensitivity digital shearography is a valuable and important method in the investigation of the out-of-plane deformation of the PLC band.

JINSIL: A middleware for presentation of composite multimedia objects in a distributed environment

In a distributed environment, the presentation of structured, composite multimedia information poses new challenges in dealing with variable bandwidth (BW) requirements and synchronization of media data objects. The detailed knowledge of BW requirements obtained by analyzing document structure can be used for efficient utilization of system resources. A distributed multimedia environment consists of various system components that are either dedicated to a client (e.g., client buffer space and BW) or shared across multiple clients (e.g., server buffer space and BW). A shared server could benefit from fine granularity advanced reservation of resources based on true BW requirements. Prefetching by utilizing advance knowledge of BW requirements can further improve resource utilization. The prefetch schedule needs also to be aware of the BW fragmentation in a partitioned server. In this paper, we describe the JINSIL middleware for retrieval of a composite document that takes into account the available BW and buffer resources and the nature of sharing in each component on delivery paths. It reshapes BW requirements, creates prefetch schedules for efficient resource utilization, and reserves necessary BW and buffer space. We also consider good choices for placement of prefetch buffers across client and server nodes.

Performance of time-frequency representation techniques to measure blood flow turbulence with pulsed-wave Doppler ultrasound

The current processing performed by commercial instruments to obtain the time-frequency representation (TFR) of pulsed-wave Doppler signals may not be adequate to characterize turbulent flow motions. The assessment of the intensity of turbulence is of high clinical importance and measuring high-frequency (small-scale) flow motions, using Doppler ultrasound (US), is a difficult problem that has been studied very little. The objective was to optimize the performance of the spectrogram (SPEC), autoregressive modeling (AR), Choi–Williams distribution (CWD), Choi–Williams reduced interference distribution (CW-RID), Bessel distribution (BD), and matching pursuit method (MP) for mean velocity waveform estimation and turbulence detection. The intensity of turbulence was measured from the fluctuations of the Doppler mean velocity obtained from a simulation model under pulsatile flow. The Kolmogorov spectrum, which is used to determine the frequency of the fluctuations and, thus, the scale of the turbulent motions, was also computed for each method. The best set of parameters for each TFR method was determined by minimizing the error of the absolute frequency fluctuations and Kolmogorov spectral bandwidth measured from the simulated and computed Doppler spectra. The results showed that different parameters must be used for each method to minimize the velocity variance of the estimator, to optimize the detection of the turbulent frequency fluctuations, and to estimate the Kolmogorov spectrum. To minimize the variance and to measure the absolute turbulent frequency fluctuations, four methods provided similar results: SPEC (10-ms sine-cosine windows), AR (10-ms rectangular windows, model order = 8), CWD (wN and wM = 10-ms rectangular windows, σ = 0.01), and BD (wN = 10-ms rectangular windows, α = 16). The velocity variance in the absence of turbulence was on the order of 0.04 m/s (coefficient of variation ranging from 8.0% to 14.5%, depending on the method). With these spectral techniques, the peak of the turbulence intensity was adequately estimated (velocity bias < 0.01 m/s). To track the frequency of turbulence, the best method was BD (wN = 2-ms rectangular windows, α = 2). The bias in the estimate of the −10 dB bandwidth of the Kolmogorov spectrum was 354 ± 51 Hz in the absence of turbulence (the true bandwidth should be 0 Hz), and −193 ± 371 Hz with turbulence (the simulated −10-dB bandwidth was estimated at 1256 Hz instead of 1449 Hz). In conclusion, several TFR methods can be used to measure the magnitude of the turbulent fluctuations. To track eddies ranging from large vortex to small turbulent fluctuations (wide Kolmogorov spectrum), the Bessel distribution with appropriate set of parameters is recommended. (E-mail: cloutig@ircm.qc.ca)

Charge-Ordering in Manganates

Ordering of Mn3+ and Mn4+ ions occurs in the rare earth manganates of the general composition Ln1-xAxMnO3 (Ln = rare earth, A = Ca, Sr). Such charge-ordering is associated with antiferromagnetic and insulating properties. This phenomenon is to be contrasted with the ferromagnetic metallic behavior that occurs when double-exchange between the Mn3+ and Mn4+ ions predominates. Two distinct types of charge-ordering can be delineated. In one, a ferromagnetic metallic (FMM) state transforms to the charge-ordered (CO) state on cooling. In the other scenario, the CO state is found in the paramagnetic ground state and there is no ferromagnetism down to the lowest temperatures. Magnetic fields transform the CO state to the FMM state, when the average radius of the A-site cations is sufficiently large (〈rA〉 > 1.17 Å). Chemical melting of the CO state by Cr3+ substitution in the Mn site is also found only when 〈rA〉 ≳ 1.17 Å. The effect of the size of the A-cations on the Mn−O−Mn angle is not enough to explain the observed variations of the charge-ordering temperature as well as the ferromagnetic Curie temperature Tc. An explanation based on a competition between the Mn and A-cation orbitals for σ-bonding with the oxygen ρσ orbitals is considered to account for the large changes in Tc and hence the true bandwidth, with 〈rA〉. Effects of radiation, electric field, and other factors on the CO state are discussed along with charge-ordering in other manganate systems. Complex phase transitions, accompanied by changes in electronic and magnetic properties, occur in manganates with critical values of 〈rA〉 or bandwidth. Charge-ordering is found in layered manganates, BixCa1-xMnO3 and CaMnO3-δ.

The effect of apodisation and finite resolution on Fourier transform infrared and Raman spectra

The interferograms measured on Fourier transform infrared (FTIR) and Raman (FT-Raman) spectrometers are routinely apodised before the Fourier transform is carried out. The effects of finite resolution and different apodisation functions on synthetic bands of known Lorentz-Gauss character have been investigated. (The apodisation functions chosen were those commonly available on commercial FTIR and FT-Raman spectrometers). The effects are dramatic, the ratio of resolution/(true bandwidth) required to obtain less than 10% distortion (as judged by the peak height and width) in the band varied from 1 for boxcar to less than 0.2 for Norton-Beer (strong). Increasing Gaussian character of the band results in initially (i.e. at high resolution) the band being less altered by resolution and apodisation than a pure Lorentzian band. As the resolution is degraded, the band is more strongly affected. These results are explained in terms of the effect of truncation and distortion of the Fourier transform of the bandshape. A comparison of calculated and experimental results gave good agreement for the 1216 cm −1 band of chloroform in deuterochloroform. The experimental results also showed an increasing degree of Gaussian character as the resolution became comparable with the full width at half height of the band.

Efficient retrieval of composite multimedia objects in the JINSIL distributed system

In a distributed environment, presentation of structured, composite multimedia information poses new challenges in dealing with variable bandwidth (BW) requirement and synchronization of media data objects. The detailed knowledge of BW requirement obtained by analyzing the document structure can be used to create a prefetch schedule that results in efficient utilization of system resources. A distributed environment consists of various system components that are either dedicated to a client or shared across multiple clients. Shared system components could benefit from Fine Granularity Advanced Reservation (FGAR) of resources based on true BW requirement. Prefetching by utilizing advance knowledge of BW requirement can further improve resource utilization. In this paper, we describe the JINSIL retrieval system that takes into account the available bandwidth and buffer resources and the nature of sharing in each component on the delivery path. It reshapes BW requirement, creates prefetch schedule for efficient resource utilization in each component, and reserves necessary BW and buffer. We also consider good choices for placement of prefetch buffers across various system components.

Spectral recovery by analytic continuation in crossing-based spectrum analysis

By the use of analytic continuation, the correct spectrum of an undersampled analog input signal f(a) (t) of a true bandwidth B is recovered from an aliased Fourier spectrum that is computed directly from a data set consisting of sinusoid-crossing locations {t(i)}, where the signal f(a) (t) intersects with a reference sinusoid r(t) with a frequency of W <B/2 and an amplitude of A. If A ≥ ‖f(a) (t)‖ within the sampling period T, then a crossing exists within each time interval Δ = 1/2W, and a total of 2WT = 2M sinusoid crossings are detected, where M is a positive integer. The cut-off frequency for sampling is W = ±M/T. In a crossing detector, a trade-off exists between the size of Δ and the accuracy with which a crossing can be located within it because the detector has infinite response time. Low-accuracy detection of the crossing positions degrades the detection limit of the detector and results in a computed Fourier spectrum that contains spurious wideband frequencies. We show however that, if f(a)(t) has a known compact support within T, then sampling at a frequency of W < B/2 may still be possible because the correct f(a)(t) spectrum can be recovered from the aliased spectrum by means of analytic continuation. The technique is demonstrated for an interferogram test signal in both the absence and presence of additive Gaussian noise.

Big effects of small interventions: The informational role of intervention in exchange rate policy

In this paper we demonstrate how an infintesimal unsterilized foreign exchange intervention may cause a very large discrete change in the exchange rate. We analyze an example in which there is a target-zone policy in place but the actual width of the target zone is not known by participants in the foreign exchange market. In this case, intervention both affects fundamentals and conveys information about policy. The exchange rate jumps in response to intervention with the size of the jump related to the uncertainty about the true band width. Also in this model the relationship between the exchange rate and the fundamental depends upon both the history of the path of the exchange rate and whether or not intervention has occured.

Width of Zonal Centrifugation Bands

Abstract A method is presented to obtain a true band width in zonal centrifuga-tion runs from an experimental measurement either by a photographic method or by a light-scanning method.

Reduction of Bandwidth Required for High Resolution Hologram Transmission

A true bandwidth reduction in the transmission requirements of holograms is achieved by recording the diffraction pattern of a scene in the horizontal direction and the actual image in the vertical direction. The image reconstructed from such a unidirectional hologram will lack vertical parallax but will exhibit all other properties of a hologram, providing a virtual reconstruction with depth information. The basic characteristics and limitations of the technique, as well as recording and reconstruction configurations, are described. In addition, experimental results illustrating the main features of the method are given.